Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1232,2,Mod(177,1232)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1232, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1232.177");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1232 = 2^{4} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1232.q (of order \(3\), degree \(2\), 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: | \(9.83756952902\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.309123.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 308) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 177.3 | ||
Root | \(0.500000 - 1.41036i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1232.177 |
Dual form | 1232.2.q.l.529.3 |
$q$-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 \(\left(\mathbb{Z}/1232\mathbb{Z}\right)^\times\).
\(n\) | \(309\) | \(353\) | \(463\) | \(673\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.59097 | + | 2.75564i | 0.918548 | + | 1.59097i | 0.801622 | + | 0.597831i | \(0.203971\pi\) |
0.116926 | + | 0.993141i | \(0.462696\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.71053 | − | 2.96273i | 0.764974 | − | 1.32497i | −0.175287 | − | 0.984517i | \(-0.556085\pi\) |
0.940260 | − | 0.340456i | \(-0.110581\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.710533 | + | 2.54856i | 0.268556 | + | 0.963264i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.56238 | + | 6.17023i | −1.18746 | + | 2.05674i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.500000 | − | 0.866025i | −0.150756 | − | 0.261116i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.66019 | 1.01515 | 0.507577 | − | 0.861606i | \(-0.330541\pi\) | ||||
0.507577 | + | 0.861606i | \(0.330541\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 10.8856 | 2.81066 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.880438 | + | 1.52496i | 0.213538 | + | 0.369858i | 0.952819 | − | 0.303538i | \(-0.0981681\pi\) |
−0.739282 | + | 0.673396i | \(0.764835\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.88044 | − | 3.25701i | 0.431402 | − | 0.747210i | −0.565592 | − | 0.824685i | \(-0.691352\pi\) |
0.996994 | + | 0.0774746i | \(0.0246857\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.89248 | + | 6.01266i | −1.28584 | + | 1.31207i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.619562 | + | 1.07311i | −0.129188 | + | 0.223759i | −0.923362 | − | 0.383930i | \(-0.874570\pi\) |
0.794175 | + | 0.607690i | \(0.207904\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.35185 | − | 5.80557i | −0.670370 | − | 1.16111i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −13.1248 | −2.52586 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.89931 | −0.538389 | −0.269194 | − | 0.963086i | \(-0.586757\pi\) | ||||
−0.269194 | + | 0.963086i | \(0.586757\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.73229 | + | 8.19656i | 0.849944 | + | 1.47215i | 0.881258 | + | 0.472636i | \(0.156698\pi\) |
−0.0313138 | + | 0.999510i | \(0.509969\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.59097 | − | 2.75564i | 0.276953 | − | 0.479696i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 8.76608 | + | 2.25427i | 1.48174 | + | 0.381042i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.42107 | + | 2.46136i | −0.233622 | + | 0.404645i | −0.958871 | − | 0.283841i | \(-0.908391\pi\) |
0.725249 | + | 0.688486i | \(0.241724\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.82326 | + | 10.0862i | 0.932468 | + | 1.61508i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.70370 | 1.35929 | 0.679645 | − | 0.733542i | \(-0.262134\pi\) | ||||
0.679645 | + | 0.733542i | \(0.262134\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −12.0676 | −1.84029 | −0.920145 | − | 0.391579i | \(-0.871929\pi\) | ||||
−0.920145 | + | 0.391579i | \(0.871929\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 12.1871 | + | 21.1088i | 1.81675 | + | 3.14671i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.11956 | − | 3.67119i | 0.309170 | − | 0.535498i | −0.669011 | − | 0.743252i | \(-0.733282\pi\) |
0.978181 | + | 0.207754i | \(0.0666155\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.99028 | + | 3.62167i | −0.855755 | + | 0.517381i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.80150 | + | 4.85235i | −0.392289 | + | 0.679465i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.112725 | + | 0.195246i | 0.0154840 | + | 0.0268190i | 0.873664 | − | 0.486531i | \(-0.161738\pi\) |
−0.858180 | + | 0.513350i | \(0.828404\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.42107 | −0.461297 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 11.9669 | 1.58505 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.27292 | − | 5.66886i | −0.426097 | − | 0.738022i | 0.570425 | − | 0.821350i | \(-0.306779\pi\) |
−0.996522 | + | 0.0833277i | \(0.973445\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.12476 | − | 8.87635i | 0.656159 | − | 1.13650i | −0.325443 | − | 0.945562i | \(-0.605514\pi\) |
0.981602 | − | 0.190939i | \(-0.0611532\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −18.2564 | − | 4.69478i | −2.30009 | − | 0.591487i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.26088 | − | 10.8442i | 0.776566 | − | 1.34505i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.70370 | − | 2.95089i | −0.208140 | − | 0.360509i | 0.742989 | − | 0.669304i | \(-0.233408\pi\) |
−0.951129 | + | 0.308795i | \(0.900074\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.94282 | −0.474660 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.23912 | 0.503091 | 0.251546 | − | 0.967845i | \(-0.419061\pi\) | ||||
0.251546 | + | 0.967845i | \(0.419061\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.09097 | − | 8.81782i | −0.595853 | − | 1.03205i | −0.993426 | − | 0.114477i | \(-0.963481\pi\) |
0.397573 | − | 0.917571i | \(-0.369853\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 10.6654 | − | 18.4730i | 1.23153 | − | 2.13308i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.85185 | − | 1.88962i | 0.211038 | − | 0.215342i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.67511 | + | 6.36547i | −0.413482 | + | 0.716172i | −0.995268 | − | 0.0971704i | \(-0.969021\pi\) |
0.581786 | + | 0.813342i | \(0.302354\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.1940 | − | 17.6565i | −1.13266 | − | 1.96183i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.4887 | 1.15128 | 0.575639 | − | 0.817704i | \(-0.304753\pi\) | ||||
0.575639 | + | 0.817704i | \(0.304753\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.02408 | 0.653403 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.61273 | − | 7.98947i | −0.494536 | − | 0.856562i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.63160 | + | 6.29012i | −0.384949 | + | 0.666751i | −0.991762 | − | 0.128094i | \(-0.959114\pi\) |
0.606813 | + | 0.794844i | \(0.292448\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.60069 | + | 9.32820i | 0.272626 | + | 0.977861i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −15.0579 | + | 26.0810i | −1.56143 | + | 2.70447i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.43310 | − | 11.1425i | −0.660023 | − | 1.14319i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.7472 | 1.19275 | 0.596374 | − | 0.802707i | \(-0.296608\pi\) | ||||
0.596374 | + | 0.802707i | \(0.296608\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.12476 | 0.716066 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.02696 | − | 10.4390i | −0.599704 | − | 1.03872i | −0.992864 | − | 0.119249i | \(-0.961951\pi\) |
0.393160 | − | 0.919470i | \(-0.371382\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.44802 | + | 14.6324i | −0.832408 | + | 1.44177i | 0.0637149 | + | 0.997968i | \(0.479705\pi\) |
−0.896123 | + | 0.443805i | \(0.853628\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 7.73461 | + | 27.7427i | 0.754821 | + | 2.70741i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.572097 | − | 0.990901i | 0.0553067 | − | 0.0957940i | −0.837047 | − | 0.547132i | \(-0.815720\pi\) |
0.892353 | + | 0.451338i | \(0.149053\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.65335 | + | 2.86369i | 0.158363 | + | 0.274292i | 0.934278 | − | 0.356545i | \(-0.116045\pi\) |
−0.775916 | + | 0.630836i | \(0.782712\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.04351 | −0.858372 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −17.5322 | −1.64929 | −0.824643 | − | 0.565653i | \(-0.808624\pi\) | ||||
−0.824643 | + | 0.565653i | \(0.808624\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.11956 | + | 3.67119i | 0.197650 | + | 0.342340i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −13.0390 | + | 22.5842i | −1.20546 | + | 2.08791i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.26088 | + | 3.32738i | −0.298924 | + | 0.305021i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.500000 | + | 0.866025i | −0.0454545 | + | 0.0787296i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 13.8473 | + | 23.9843i | 1.24857 | + | 2.16259i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.82846 | −0.521313 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.660190 | −0.0585824 | −0.0292912 | − | 0.999571i | \(-0.509325\pi\) | ||||
−0.0292912 | + | 0.999571i | \(0.509325\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −19.1992 | − | 33.2540i | −1.69039 | − | 2.92785i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.85705 | − | 17.0729i | 0.861214 | − | 1.49167i | −0.00954300 | − | 0.999954i | \(-0.503038\pi\) |
0.870757 | − | 0.491713i | \(-0.163629\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.63680 | + | 2.47819i | 0.835617 | + | 0.214886i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −22.4503 | + | 38.8851i | −1.93222 | + | 3.34670i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.38727 | − | 2.40283i | −0.118523 | − | 0.205288i | 0.800660 | − | 0.599119i | \(-0.204483\pi\) |
−0.919183 | + | 0.393832i | \(0.871149\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.0000 | −0.933008 | −0.466504 | − | 0.884519i | \(-0.654487\pi\) | ||||
−0.466504 | + | 0.884519i | \(0.654487\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 13.4887 | 1.13595 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.83009 | − | 3.16982i | −0.153040 | − | 0.265073i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.95937 | + | 8.58988i | −0.411853 | + | 0.713351i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −19.5104 | − | 10.7451i | −1.60919 | − | 0.886242i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.39931 | − | 7.61983i | 0.360406 | − | 0.624241i | −0.627622 | − | 0.778518i | \(-0.715972\pi\) |
0.988028 | + | 0.154277i | \(0.0493049\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.1940 | − | 17.6565i | −0.829574 | − | 1.43687i | −0.898372 | − | 0.439235i | \(-0.855250\pi\) |
0.0687980 | − | 0.997631i | \(-0.478084\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −12.5458 | −1.01427 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 32.3789 | 2.60074 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.79630 | + | 6.57539i | 0.302978 | + | 0.524773i | 0.976809 | − | 0.214112i | \(-0.0686858\pi\) |
−0.673831 | + | 0.738885i | \(0.735352\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.358685 | + | 0.621261i | −0.0284456 | + | 0.0492692i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.17511 | − | 0.816506i | −0.250233 | − | 0.0643497i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.02175 | + | 6.96588i | −0.315008 | + | 0.545610i | −0.979439 | − | 0.201740i | \(-0.935341\pi\) |
0.664431 | + | 0.747349i | \(0.268674\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.44282 | − | 9.42724i | −0.423723 | − | 0.733910i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −15.7414 | −1.21811 | −0.609055 | − | 0.793128i | \(-0.708451\pi\) | ||||
−0.609055 | + | 0.793128i | \(0.708451\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.396990 | 0.0305377 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 13.3977 | + | 23.2055i | 1.02455 | + | 1.77457i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.87360 | − | 3.24517i | 0.142447 | − | 0.246726i | −0.785970 | − | 0.618264i | \(-0.787836\pi\) |
0.928418 | + | 0.371538i | \(0.121170\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12.4142 | − | 12.6674i | 0.938428 | − | 0.957568i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.4142 | − | 18.0380i | 0.782781 | − | 1.35582i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.75116 | − | 9.96130i | −0.429862 | − | 0.744543i | 0.566999 | − | 0.823719i | \(-0.308104\pi\) |
−0.996861 | + | 0.0791759i | \(0.974771\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.79071 | −0.430420 | −0.215210 | − | 0.976568i | \(-0.569044\pi\) | ||||
−0.215210 | + | 0.976568i | \(0.569044\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 32.6134 | 2.41085 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.86156 | + | 8.42048i | 0.357429 | + | 0.619086i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.880438 | − | 1.52496i | 0.0643840 | − | 0.111516i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −9.32558 | − | 33.4492i | −0.678336 | − | 2.43307i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.26088 | − | 16.0403i | 0.670094 | − | 1.16064i | −0.307784 | − | 0.951456i | \(-0.599587\pi\) |
0.977877 | − | 0.209180i | \(-0.0670794\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.88727 | + | 3.26886i | 0.135849 | + | 0.235297i | 0.925921 | − | 0.377716i | \(-0.123290\pi\) |
−0.790072 | + | 0.613013i | \(0.789957\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 39.8435 | 2.85325 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.1683 | 0.724459 | 0.362230 | − | 0.932089i | \(-0.382016\pi\) | ||||
0.362230 | + | 0.932089i | \(0.382016\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.03899 | − | 8.72779i | −0.357205 | − | 0.618697i | 0.630288 | − | 0.776361i | \(-0.282937\pi\) |
−0.987493 | + | 0.157665i | \(0.949604\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.42107 | − | 9.38956i | 0.382373 | − | 0.662289i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.06006 | − | 7.38906i | −0.144588 | − | 0.518611i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 14.8880 | − | 25.7867i | 1.03982 | − | 1.80102i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.41423 | − | 7.64567i | −0.306810 | − | 0.531411i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.76088 | −0.260145 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.72313 | 0.118625 | 0.0593125 | − | 0.998239i | \(-0.481109\pi\) | ||||
0.0593125 | + | 0.998239i | \(0.481109\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.74433 | + | 11.6815i | 0.462114 | + | 0.800404i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −20.6420 | + | 35.7530i | −1.40777 | + | 2.43833i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −17.5270 | + | 17.8844i | −1.18981 | + | 1.21407i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 16.1992 | − | 28.0578i | 1.09464 | − | 1.89597i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.22257 | + | 5.58166i | 0.216774 | + | 0.375463i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.47825 | 0.634710 | 0.317355 | − | 0.948307i | \(-0.397205\pi\) | ||||
0.317355 | + | 0.948307i | \(0.397205\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 47.7623 | 3.18415 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.72094 | − | 16.8372i | −0.645201 | − | 1.11752i | −0.984255 | − | 0.176754i | \(-0.943440\pi\) |
0.339054 | − | 0.940767i | \(-0.389893\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.16019 | − | 8.93771i | 0.340995 | − | 0.590621i | −0.643623 | − | 0.765343i | \(-0.722569\pi\) |
0.984618 | + | 0.174722i | \(0.0559028\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.15335 | + | 2.09671i | 0.536451 | + | 0.137953i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.557180 | + | 0.965064i | −0.0365021 | + | 0.0632234i | −0.883699 | − | 0.468055i | \(-0.844955\pi\) |
0.847197 | + | 0.531279i | \(0.178288\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.25116 | − | 12.5594i | −0.473014 | − | 0.819284i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −23.3880 | −1.51921 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 26.1053 | 1.68861 | 0.844307 | − | 0.535860i | \(-0.180013\pi\) | ||||
0.844307 | + | 0.535860i | \(0.180013\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.39768 | − | 12.8132i | −0.476526 | − | 0.825368i | 0.523112 | − | 0.852264i | \(-0.324771\pi\) |
−0.999638 | + | 0.0268962i | \(0.991438\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 12.7495 | − | 22.0828i | 0.817883 | − | 1.41661i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.483448 | + | 23.9426i | 0.0308864 | + | 1.52964i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.88276 | − | 11.9213i | 0.437940 | − | 0.758534i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 16.6871 | + | 28.9030i | 1.05750 | + | 1.83165i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.96225 | 0.123856 | 0.0619281 | − | 0.998081i | \(-0.480275\pi\) | ||||
0.0619281 | + | 0.998081i | \(0.480275\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.23912 | 0.0779030 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 9.58414 | + | 16.6002i | 0.600182 | + | 1.03955i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.25404 | + | 2.17206i | −0.0782249 | + | 0.135489i | −0.902484 | − | 0.430723i | \(-0.858259\pi\) |
0.824259 | + | 0.566213i | \(0.191592\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.28263 | − | 1.87279i | −0.452521 | − | 0.116370i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.3285 | − | 17.8894i | 0.639316 | − | 1.10733i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.08414 | − | 3.60983i | −0.128513 | − | 0.222592i | 0.794587 | − | 0.607150i | \(-0.207687\pi\) |
−0.923101 | + | 0.384558i | \(0.874354\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.771280 | 0.0473794 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −23.1111 | −1.41438 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.5744 | + | 18.3154i | 0.644734 | + | 1.11671i | 0.984363 | + | 0.176152i | \(0.0563651\pi\) |
−0.339629 | + | 0.940559i | \(0.610302\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.63844 | − | 11.4981i | 0.403256 | − | 0.698460i | −0.590861 | − | 0.806774i | \(-0.701212\pi\) |
0.994117 | + | 0.108313i | \(0.0345450\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −21.5676 | + | 22.0075i | −1.30533 | + | 1.33195i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.35185 | + | 5.80557i | −0.202124 | + | 0.350089i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.75116 | + | 8.22925i | 0.285470 | + | 0.494448i | 0.972723 | − | 0.231970i | \(-0.0745171\pi\) |
−0.687253 | + | 0.726418i | \(0.741184\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −67.4328 | −4.03710 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.8766 | 1.60332 | 0.801662 | − | 0.597777i | \(-0.203949\pi\) | ||||
0.801662 | + | 0.597777i | \(0.203949\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.154988 | + | 0.268447i | 0.00921309 | + | 0.0159575i | 0.870595 | − | 0.492000i | \(-0.163734\pi\) |
−0.861382 | + | 0.507958i | \(0.830401\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 20.4698 | − | 35.4547i | 1.21252 | − | 2.10015i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.18427 | + | 22.1819i | 0.365046 | + | 1.30935i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.94966 | − | 12.0372i | 0.408803 | − | 0.708068i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 18.6895 | + | 32.3711i | 1.09560 | + | 1.89763i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 31.2222 | 1.82402 | 0.912010 | − | 0.410169i | \(-0.134530\pi\) | ||||
0.912010 | + | 0.410169i | \(0.134530\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −22.3937 | −1.30381 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.56238 | + | 11.3664i | 0.380788 | + | 0.659544i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.26771 | + | 3.92779i | −0.131145 | + | 0.227150i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.57442 | − | 30.7549i | −0.494221 | − | 1.77268i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 19.1774 | − | 33.2163i | 1.10171 | − | 1.90823i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −17.5322 | − | 30.3666i | −1.00389 | − | 1.73879i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.50808 | −0.428509 | −0.214254 | − | 0.976778i | \(-0.568732\pi\) | ||||
−0.214254 | + | 0.976778i | \(0.568732\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −53.7623 | −3.05843 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.767713 | − | 1.32972i | −0.0435330 | − | 0.0754014i | 0.843438 | − | 0.537227i | \(-0.180528\pi\) |
−0.886971 | + | 0.461825i | \(0.847195\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.42627 | − | 11.1306i | 0.363234 | − | 0.629140i | −0.625257 | − | 0.780419i | \(-0.715006\pi\) |
0.988491 | + | 0.151279i | \(0.0483392\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −45.1375 | + | 46.0581i | −2.54321 | + | 2.59508i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.21574 | + | 2.10571i | −0.0682825 | + | 0.118269i | −0.898145 | − | 0.439699i | \(-0.855085\pi\) |
0.829863 | + | 0.557967i | \(0.188419\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.44966 | + | 2.51088i | 0.0811652 | + | 0.140582i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.64076 | 0.203207 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.62244 | 0.368482 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −12.2684 | − | 21.2495i | −0.680528 | − | 1.17871i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.26088 | + | 9.11211i | −0.290927 | + | 0.503901i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10.8623 | + | 2.79332i | 0.598855 | + | 0.154001i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.20370 | − | 9.01307i | 0.286021 | − | 0.495403i | −0.686835 | − | 0.726813i | \(-0.741001\pi\) |
0.972856 | + | 0.231410i | \(0.0743339\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −10.1248 | − | 17.5366i | −0.554834 | − | 0.961000i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.6569 | −0.636886 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.2164 | −0.610998 | −0.305499 | − | 0.952192i | \(-0.598823\pi\) | ||||
−0.305499 | + | 0.952192i | \(0.598823\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −27.8932 | − | 48.3124i | −1.51495 | − | 2.62397i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.73229 | − | 8.19656i | 0.256268 | − | 0.443869i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.4863 | − | 12.6933i | −0.728193 | − | 0.685372i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6.74433 | + | 11.6815i | −0.363102 | + | 0.628912i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −13.3788 | − | 23.1728i | −0.718212 | − | 1.24398i | −0.961708 | − | 0.274077i | \(-0.911628\pi\) |
0.243496 | − | 0.969902i | \(-0.421706\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.11436 | −0.273765 | −0.136883 | − | 0.990587i | \(-0.543708\pi\) | ||||
−0.136883 | + | 0.990587i | \(0.543708\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −48.0391 | −2.56414 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.1505 | + | 17.5811i | 0.540255 | + | 0.935750i | 0.998889 | + | 0.0471242i | \(0.0150057\pi\) |
−0.458634 | + | 0.888625i | \(0.651661\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.25116 | − | 12.5594i | 0.384852 | − | 0.666583i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −14.3571 | − | 3.69204i | −0.759856 | − | 0.195403i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.73392 | − | 8.19939i | 0.249847 | − | 0.432747i | −0.713636 | − | 0.700516i | \(-0.752953\pi\) |
0.963483 | + | 0.267769i | \(0.0862864\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.42790 | + | 4.20525i | 0.127784 | + | 0.221329i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.18194 | −0.167009 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −34.8331 | −1.82325 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.7323 | + | 18.5889i | 0.560221 | + | 0.970331i | 0.997477 | + | 0.0709938i | \(0.0226171\pi\) |
−0.437256 | + | 0.899337i | \(0.644050\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −31.0059 | + | 53.7038i | −1.61410 | + | 2.79571i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.417500 | + | 0.426015i | −0.0216755 | + | 0.0221176i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.66827 | + | 11.5498i | −0.345270 | + | 0.598025i | −0.985403 | − | 0.170239i | \(-0.945546\pi\) |
0.640133 | + | 0.768264i | \(0.278879\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −9.27292 | − | 16.0612i | −0.478851 | − | 0.829395i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −10.6120 | −0.546548 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.76088 | 0.295916 | 0.147958 | − | 0.988994i | \(-0.452730\pi\) | ||||
0.147958 | + | 0.988994i | \(0.452730\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.05034 | − | 1.81925i | −0.0538107 | − | 0.0932029i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14.6150 | + | 25.3140i | −0.746794 | + | 1.29349i | 0.202558 | + | 0.979270i | \(0.435075\pi\) |
−0.949352 | + | 0.314215i | \(0.898259\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.43078 | − | 8.71878i | −0.123884 | − | 0.444350i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 42.9893 | − | 74.4597i | 2.18527 | − | 3.78500i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.2540 | + | 17.7605i | 0.519900 | + | 0.900494i | 0.999732 | + | 0.0231336i | \(0.00736431\pi\) |
−0.479832 | + | 0.877360i | \(0.659302\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.18194 | −0.110346 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 62.7292 | 3.16427 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 12.5728 | + | 21.7767i | 0.632605 | + | 1.09570i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.78495 | + | 10.0198i | −0.290338 | + | 0.502881i | −0.973890 | − | 0.227022i | \(-0.927101\pi\) |
0.683551 | + | 0.729903i | \(0.260435\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8.50288 | + | 30.4983i | 0.425676 | + | 1.52683i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.5933 | + | 21.8122i | −0.628879 | + | 1.08925i | 0.358898 | + | 0.933377i | \(0.383153\pi\) |
−0.987777 | + | 0.155874i | \(0.950181\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 17.3211 | + | 30.0010i | 0.862824 | + | 1.49445i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −69.7486 | −3.46583 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.84213 | 0.140879 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.90383 | − | 3.29752i | −0.0941382 | − | 0.163052i | 0.815110 | − | 0.579306i | \(-0.196676\pi\) |
−0.909249 | + | 0.416254i | \(0.863343\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.41423 | − | 7.64567i | 0.217738 | − | 0.377133i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 12.1219 | − | 12.3691i | 0.596479 | − | 0.608645i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 17.9412 | − | 31.0750i | 0.880698 | − | 1.52541i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −17.5007 | − | 30.3121i | −0.857012 | − | 1.48439i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.08701 | 0.248517 | 0.124258 | − | 0.992250i | \(-0.460345\pi\) | ||||
0.124258 | + | 0.992250i | \(0.460345\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.9442 | −0.825810 | −0.412905 | − | 0.910774i | \(-0.635486\pi\) | ||||
−0.412905 | + | 0.910774i | \(0.635486\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 15.1014 | + | 26.1563i | 0.734254 | + | 1.27177i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.90219 | − | 10.2229i | 0.286298 | − | 0.495883i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 26.2632 | + | 6.75381i | 1.27097 | + | 0.326840i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.82326 | − | 10.0862i | 0.281150 | − | 0.486965i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.22777 | + | 2.12657i | 0.0591398 | + | 0.102433i | 0.894079 | − | 0.447908i | \(-0.147831\pi\) |
−0.834940 | + | 0.550341i | \(0.814498\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −32.8629 | −1.57929 | −0.789646 | − | 0.613563i | \(-0.789736\pi\) | ||||
−0.789646 | + | 0.613563i | \(0.789736\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −31.5609 | −1.51323 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.33009 | + | 4.03584i | 0.111464 | + | 0.193061i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.0406283 | + | 0.0703702i | −0.00193908 | + | 0.00335859i | −0.866993 | − | 0.498320i | \(-0.833951\pi\) |
0.865054 | + | 0.501678i | \(0.167284\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.00684 | − | 49.8632i | −0.0479446 | − | 2.37444i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.86840 | + | 6.70027i | −0.183793 | + | 0.318339i | −0.943169 | − | 0.332313i | \(-0.892171\pi\) |
0.759376 | + | 0.650652i | \(0.225504\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.4239 | + | 21.5189i | 0.588951 | + | 1.02009i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 27.9967 | 1.32420 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −21.1078 | −0.996140 | −0.498070 | − | 0.867137i | \(-0.665958\pi\) | ||||
−0.498070 | + | 0.867137i | \(0.665958\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.35185 | − | 7.53762i | −0.204921 | − | 0.354933i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 32.4367 | − | 56.1820i | 1.52401 | − | 2.63966i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 32.0855 | + | 8.25107i | 1.50419 | + | 0.386816i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.35868 | − | 14.4777i | 0.391003 | − | 0.677237i | −0.601579 | − | 0.798813i | \(-0.705462\pi\) |
0.992582 | + | 0.121576i | \(0.0387949\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −11.5555 | − | 20.0148i | −0.539367 | − | 0.934210i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.62571 | −0.262015 | −0.131008 | − | 0.991381i | \(-0.541821\pi\) | ||||
−0.131008 | + | 0.991381i | \(0.541821\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.3341 | −1.13090 | −0.565450 | − | 0.824783i | \(-0.691297\pi\) | ||||
−0.565450 | + | 0.824783i | \(0.691297\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 51.5140 | + | 89.2248i | 2.38890 | + | 4.13770i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9.42395 | + | 16.3228i | −0.436088 | + | 0.755327i | −0.997384 | − | 0.0722885i | \(-0.976970\pi\) |
0.561296 | + | 0.827615i | \(0.310303\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.30998 | − | 6.43867i | 0.291368 | − | 0.297310i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −12.0796 | + | 20.9225i | −0.556600 | + | 0.964059i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.03379 | + | 10.4508i | 0.277434 | + | 0.480530i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −25.2118 | −1.15680 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.60628 | −0.0735465 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.9383 | + | 25.8739i | 0.682549 | + | 1.18221i | 0.974200 | + | 0.225684i | \(0.0724618\pi\) |
−0.291652 | + | 0.956525i | \(0.594205\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.20137 | + | 9.00904i | −0.237162 | + | 0.410777i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.80150 | − | 10.0485i | −0.127473 | − | 0.457223i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 20.0940 | − | 34.8038i | 0.912421 | − | 1.58036i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.21574 | − | 10.7660i | −0.281662 | − | 0.487853i | 0.690132 | − | 0.723683i | \(-0.257552\pi\) |
−0.971794 | + | 0.235831i | \(0.924219\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −25.5940 | −1.15740 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.0917 | −0.455430 | −0.227715 | − | 0.973728i | \(-0.573125\pi\) | ||||
−0.227715 | + | 0.973728i | \(0.573125\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.55267 | − | 4.42135i | −0.114966 | − | 0.199128i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 12.1871 | − | 21.1088i | 0.547771 | − | 0.948768i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.01204 | + | 10.8036i | 0.135108 | + | 0.484610i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.74269 | + | 13.4107i | −0.346610 | + | 0.600347i | −0.985645 | − | 0.168831i | \(-0.946001\pi\) |
0.639035 | + | 0.769178i | \(0.279334\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −25.0442 | − | 43.3778i | −1.11889 | − | 1.93798i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.99673 | 0.178205 | 0.0891027 | − | 0.996022i | \(-0.471600\pi\) | ||||
0.0891027 | + | 0.996022i | \(0.471600\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −41.2372 | −1.83503 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.631600 | + | 1.09396i | 0.0280503 | + | 0.0485846i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.891788 | − | 1.54462i | 0.0395278 | − | 0.0684642i | −0.845585 | − | 0.533841i | \(-0.820748\pi\) |
0.885112 | + | 0.465377i | \(0.154081\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 18.8554 | − | 19.2400i | 0.834114 | − | 0.851127i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −24.6803 | + | 42.7475i | −1.08966 | + | 1.88735i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 28.9012 | + | 50.0584i | 1.27354 | + | 2.20584i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.23912 | −0.186436 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11.9234 | 0.523379 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −16.5865 | − | 28.7286i | −0.726666 | − | 1.25862i | −0.958285 | − | 0.285816i | \(-0.907735\pi\) |
0.231619 | − | 0.972807i | \(-0.425598\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.6219 | + | 21.8617i | −0.551916 | + | 0.955947i | 0.446220 | + | 0.894923i | \(0.352770\pi\) |
−0.998136 | + | 0.0610240i | \(0.980563\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 54.6576 | + | 14.0557i | 2.38545 | + | 0.613440i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.33297 | + | 14.4331i | −0.362990 | + | 0.628717i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.7323 | + | 18.5889i | 0.466621 | + | 0.808212i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 46.6375 | 2.02389 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 31.8572 | 1.37989 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.95718 | − | 3.38994i | −0.0846163 | − | 0.146560i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 18.2999 | − | 31.6963i | 0.789698 | − | 1.36780i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.13160 | + | 3.37690i | 0.264107 | + | 0.145454i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.97141 | − | 6.87868i | 0.170744 | − | 0.295738i | −0.767936 | − | 0.640527i | \(-0.778716\pi\) |
0.938680 | + | 0.344789i | \(0.112049\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −9.21286 | − | 15.9571i | −0.395362 | − | 0.684786i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 11.3125 | 0.484573 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.2495 | −0.737537 | −0.368768 | − | 0.929521i | \(-0.620220\pi\) | ||||
−0.368768 | + | 0.929521i | \(0.620220\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 36.5127 | + | 63.2419i | 1.55833 | + | 2.69910i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.45198 | + | 9.44311i | −0.232262 | + | 0.402290i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −18.8341 | − | 4.84334i | −0.800905 | − | 0.205960i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −15.4692 | + | 26.7935i | −0.656632 | + | 1.13732i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.62928 | − | 9.75019i | −0.238520 | − | 0.413129i | 0.721770 | − | 0.692133i | \(-0.243329\pi\) |
−0.960290 | + | 0.279004i | \(0.909996\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −44.1696 | −1.86818 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.60301 | 0.236559 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.16143 | − | 8.93987i | −0.217528 | − | 0.376770i | 0.736523 | − | 0.676412i | \(-0.236466\pi\) |
−0.954052 | + | 0.299642i | \(0.903133\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −29.9893 | + | 51.9431i | −1.26166 | + | 2.18526i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 37.7554 | − | 38.5255i | 1.58558 | − | 1.61792i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.57605 | + | 9.65801i | −0.233760 | + | 0.404885i | −0.958912 | − | 0.283705i | \(-0.908436\pi\) |
0.725151 | + | 0.688590i | \(0.241770\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.28783 | + | 7.42674i | 0.179440 | + | 0.310800i | 0.941689 | − | 0.336485i | \(-0.109238\pi\) |
−0.762249 | + | 0.647284i | \(0.775905\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 58.9352 | 2.46205 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.30671 | 0.346414 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −21.7902 | − | 37.7417i | −0.907136 | − | 1.57121i | −0.818024 | − | 0.575184i | \(-0.804930\pi\) |
−0.0891120 | − | 0.996022i | \(-0.528403\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6.00520 | + | 10.4013i | −0.249568 | + | 0.432264i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.45254 | + | 26.7309i | 0.309183 | + | 1.10899i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.112725 | − | 0.195246i | 0.00466860 | − | 0.00808625i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 44.6073 | + | 77.2620i | 1.84428 | + | 3.19439i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 44.4315 | 1.83388 | 0.916942 | − | 0.399022i | \(-0.130650\pi\) | ||||
0.916942 | + | 0.399022i | \(0.130650\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 35.5951 | 1.46667 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 16.1774 | + | 28.0201i | 0.665451 | + | 1.15259i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.51724 | − | 4.35999i | 0.103371 | − | 0.179043i | −0.809701 | − | 0.586843i | \(-0.800371\pi\) |
0.913071 | + | 0.407800i | \(0.133704\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.28031 | + | 15.3527i | 0.175475 | + | 0.629399i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 16.0338 | − | 27.7713i | 0.656219 | − | 1.13661i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.36784 | − | 5.83328i | −0.137606 | − | 0.238341i | 0.788984 | − | 0.614414i | \(-0.210608\pi\) |
−0.926590 | + | 0.376073i | \(0.877274\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −30.4854 | −1.24352 | −0.621762 | − | 0.783206i | \(-0.713583\pi\) | ||||
−0.621762 | + | 0.783206i | \(0.713583\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 24.2769 | 0.988631 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.71053 | + | 2.96273i | 0.0695431 | + | 0.120452i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.6586 | − | 23.6573i | 0.554384 | − | 0.960221i | −0.443568 | − | 0.896241i | \(-0.646287\pi\) |
0.997951 | − | 0.0639797i | \(-0.0203793\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 17.0841 | − | 17.4326i | 0.692284 | − | 0.706404i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.75800 | − | 13.4372i | 0.313855 | − | 0.543613i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17.1248 | + | 29.6610i | 0.691663 | + | 1.19799i | 0.971293 | + | 0.237887i | \(0.0764548\pi\) |
−0.279630 | + | 0.960108i | \(0.590212\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 94.7453 | 3.82050 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.13052 | 0.367581 | 0.183790 | − | 0.982965i | \(-0.441163\pi\) | ||||
0.183790 | + | 0.982965i | \(0.441163\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.66019 | − | 6.33963i | −0.147115 | − | 0.254811i | 0.783045 | − | 0.621965i | \(-0.213666\pi\) |
−0.930160 | + | 0.367154i | \(0.880332\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.13160 | − | 14.0843i | 0.326310 | − | 0.565185i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −18.6111 | − | 4.78600i | −0.745638 | − | 0.191747i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.78947 | − | 11.7597i | 0.271579 | − | 0.470388i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.98345 | − | 10.3636i | −0.238956 | − | 0.413884i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.00465 | −0.199548 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.7199 | −0.506370 | −0.253185 | − | 0.967418i | \(-0.581478\pi\) | ||||
−0.253185 | + | 0.967418i | \(0.581478\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.74145 | + | 4.74832i | 0.108963 | + | 0.188729i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.12928 | + | 1.95596i | −0.0448140 | + | 0.0776201i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −21.9256 | + | 13.2560i | −0.868723 | + | 0.525222i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −15.1014 | + | 26.1563i | −0.597401 | + | 1.03473i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.08250 | + | 7.07110i | 0.161249 | + | 0.279292i | 0.935317 | − | 0.353811i | \(-0.115114\pi\) |
−0.774068 | + | 0.633103i | \(0.781781\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.39123 | −0.330918 | −0.165459 | − | 0.986217i | \(-0.552911\pi\) | ||||
−0.165459 | + | 0.986217i | \(0.552911\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −131.363 | −5.17243 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 20.2599 | + | 35.0912i | 0.796500 | + | 1.37958i | 0.921882 | + | 0.387470i | \(0.126651\pi\) |
−0.125382 | + | 0.992109i | \(0.540016\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.27292 | + | 5.66886i | −0.128473 | + | 0.222522i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −77.1680 | − | 19.8444i | −3.02445 | − | 0.777764i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7.35185 | + | 12.7338i | −0.287700 | + | 0.498311i | −0.973260 | − | 0.229705i | \(-0.926224\pi\) |
0.685560 | + | 0.728016i | \(0.259557\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −33.7216 | − | 58.4076i | −1.31761 | − | 2.28217i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 72.5439 | 2.83021 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.2873 | −0.751326 | −0.375663 | − | 0.926756i | \(-0.622585\pi\) | ||||
−0.375663 | + | 0.926756i | \(0.622585\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.90615 | + | 17.1580i | 0.385305 | + | 0.667367i | 0.991811 | − | 0.127711i | \(-0.0407631\pi\) |
−0.606507 | + | 0.795078i | \(0.707430\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −10.2540 | + | 17.7605i | −0.398234 | + | 0.689761i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 23.8263 | − | 24.3122i | 0.923943 | − | 0.942788i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.79630 | − | 3.11129i | 0.0695531 | − | 0.120470i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 15.0796 | + | 26.1187i | 0.583012 | + | 1.00981i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10.2495 | −0.395679 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.11901 | −0.0431345 | −0.0215673 | − | 0.999767i | \(-0.506866\pi\) | ||||
−0.0215673 | + | 0.999767i | \(0.506866\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 43.9922 | + | 76.1968i | 1.69326 | + | 2.93281i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −21.7571 | + | 37.6843i | −0.836191 | + | 1.44833i | 0.0568653 | + | 0.998382i | \(0.481889\pi\) |
−0.893057 | + | 0.449944i | \(0.851444\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.34678 | + | 29.9384i | 0.320320 | + | 1.14893i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 30.9315 | − | 53.5749i | 1.18530 | − | 2.05299i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.54746 | − | 13.0726i | −0.288796 | − | 0.500209i | 0.684727 | − | 0.728800i | \(-0.259922\pi\) |
−0.973523 | + | 0.228591i | \(0.926588\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.49192 | −0.362668 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 32.8389 | 1.25288 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.412595 | + | 0.714636i | 0.0157186 | + | 0.0272255i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.07085 | − | 1.85477i | 0.0407372 | − | 0.0705588i | −0.844938 | − | 0.534864i | \(-0.820363\pi\) |
0.885675 | + | 0.464306i | \(0.153696\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.06238 | + | 18.1579i | 0.192304 | + | 0.689760i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −18.8159 | + | 32.5900i | −0.713726 | + | 1.23621i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.66307 | + | 13.2728i | 0.290259 | + | 0.502744i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.54583 | −0.134116 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10.1910 | −0.384908 | −0.192454 | − | 0.981306i | \(-0.561645\pi\) | ||||
−0.192454 | + | 0.981306i | \(0.561645\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.34446 | + | 9.25687i | 0.201570 | + | 0.349129i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 23.0728 | − | 39.9632i | 0.868971 | − | 1.50510i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 22.3220 | − | 22.7773i | 0.839506 | − | 0.856628i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.172784 | + | 0.299270i | −0.00648903 | + | 0.0112393i | −0.869252 | − | 0.494370i | \(-0.835399\pi\) |
0.862763 | + | 0.505609i | \(0.168732\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −26.1843 | − | 45.3525i | −0.981987 | − | 1.70085i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −11.7278 | −0.439209 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.5218 | −0.468287 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 41.5328 | + | 71.9370i | 1.55107 | + | 2.68654i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −13.4383 | + | 23.2758i | −0.501164 | + | 0.868042i | 0.498835 | + | 0.866697i | \(0.333761\pi\) |
−0.999999 | + | 0.00134491i | \(0.999572\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −43.2941 | − | 11.1335i | −1.61236 | − | 0.414632i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 23.5390 | − | 40.7707i | 0.875425 | − | 1.51628i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.71806 | + | 16.8322i | 0.360920 | + | 0.625131i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 46.1261 | 1.71072 | 0.855362 | − | 0.518031i | \(-0.173335\pi\) | ||||
0.855362 | + | 0.518031i | \(0.173335\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 19.9727 | 0.739728 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10.6248 | − | 18.4026i | −0.392971 | − | 0.680646i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15.4698 | + | 26.7944i | −0.571389 | + | 0.989675i | 0.425034 | + | 0.905177i | \(0.360262\pi\) |
−0.996424 | + | 0.0844979i | \(0.973071\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −65.2081 | + | 39.4242i | −2.40524 | + | 1.45418i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.70370 | + | 2.95089i | −0.0627565 | + | 0.108697i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.1150 | + | 34.8403i | 0.739944 | + | 1.28162i | 0.952520 | + | 0.304476i | \(0.0984814\pi\) |
−0.212576 | + | 0.977145i | \(0.568185\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 43.8011 | 1.60907 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −37.3710 | −1.37101 | −0.685505 | − | 0.728068i | \(-0.740418\pi\) | ||||
−0.685505 | + | 0.728068i | \(0.740418\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.0503 | − | 26.0680i | −0.551402 | − | 0.955056i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −37.3646 | + | 64.7173i | −1.36710 | + | 2.36788i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.93186 | + | 0.753953i | 0.107128 | + | 0.0275489i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19.8698 | − | 34.4155i | 0.725058 | − | 1.25584i | −0.233891 | − | 0.972263i | \(-0.575146\pi\) |
0.958950 | − | 0.283575i | \(-0.0915206\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.12188 | + | 5.40726i | 0.113768 | + | 0.197052i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −69.7486 | −2.53841 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.60628 | 0.240109 | 0.120055 | − | 0.992767i | \(-0.461693\pi\) | ||||
0.120055 | + | 0.992767i | \(0.461693\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.97141 | + | 3.41458i | 0.0715577 | + | 0.123941i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −0.518875 | + | 0.898718i | −0.0188092 | + | 0.0325785i | −0.875277 | − | 0.483622i | \(-0.839321\pi\) |
0.856468 | + | 0.516201i | \(0.172654\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.12352 | + | 6.24841i | −0.221686 | + | 0.226208i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −21.4601 | + | 37.1699i | −0.775890 | + | 1.34388i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −11.9795 | − | 20.7491i | −0.432554 | − | 0.749206i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.03199 | 0.217519 | 0.108760 | − | 0.994068i | \(-0.465312\pi\) | ||||
0.108760 | + | 0.994068i | \(0.465312\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.98057 | −0.287413 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7.45034 | − | 12.9044i | −0.267970 | − | 0.464138i | 0.700367 | − | 0.713783i | \(-0.253020\pi\) |
−0.968338 | + | 0.249645i | \(0.919686\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 31.7238 | − | 54.9473i | 1.13955 | − | 1.97376i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6.42571 | − | 23.0479i | −0.230521 | − | 0.826839i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 16.3668 | − | 28.3481i | 0.586400 | − | 1.01567i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.11956 | − | 3.67119i | −0.0758439 | − | 0.131365i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 38.0528 | 1.35990 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 25.9748 | 0.927081 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.490285 | + | 0.849198i | 0.0174768 | + | 0.0302706i | 0.874632 | − | 0.484788i | \(-0.161103\pi\) |
−0.857155 | + | 0.515059i | \(0.827770\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.63160 | − | 11.4863i | 0.236091 | − | 0.408922i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.4572 | − | 44.6817i | −0.442926 | − | 1.58870i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18.7576 | − | 32.4891i | 0.666102 | − | 1.15372i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.22708 | + | 2.12537i | 0.0435202 | + | 0.0753792i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −37.2873 | −1.32078 | −0.660392 | − | 0.750921i | \(-0.729610\pi\) | ||||
−0.660392 | + | 0.750921i | \(0.729610\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.46457 | 0.264078 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −25.8743 | − | 44.8156i | −0.914223 | − | 1.58348i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.09097 | + | 8.81782i | −0.179656 | + | 0.311174i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.85021 | + | 8.01033i | −0.276684 | + | 0.282327i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −33.6472 | + | 58.2787i | −1.18444 | + | 2.05151i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −13.4234 | − | 23.2500i | −0.471941 | − | 0.817426i | 0.527543 | − | 0.849528i | \(-0.323113\pi\) |
−0.999485 | + | 0.0321019i | \(0.989780\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −31.0572 | −1.09057 | −0.545283 | − | 0.838252i | \(-0.683578\pi\) | ||||
−0.545283 | + | 0.838252i | \(0.683578\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 42.2463 | 1.48164 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 13.7587 | + | 23.8307i | 0.481946 | + | 0.834755i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −22.6923 | + | 39.3043i | −0.793905 | + | 1.37508i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −66.8218 | − | 17.1838i | −2.33494 | − | 0.600450i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.92231 | − | 17.1859i | 0.346291 | − | 0.599794i | −0.639296 | − | 0.768960i | \(-0.720774\pi\) |
0.985587 | + | 0.169167i | \(0.0541076\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.29179 | + | 16.0939i | 0.323891 | + | 0.560996i | 0.981287 | − | 0.192549i | \(-0.0616754\pi\) |
−0.657396 | + | 0.753545i | \(0.728342\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −21.3308 | −0.742643 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7.25744 | −0.252366 | −0.126183 | − | 0.992007i | \(-0.540273\pi\) | ||||
−0.126183 | + | 0.992007i | \(0.540273\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 21.4893 | + | 37.2206i | 0.746356 | + | 1.29273i | 0.949559 | + | 0.313589i | \(0.101531\pi\) |
−0.203203 | + | 0.979137i | \(0.565135\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15.1179 | + | 26.1850i | −0.524435 | + | 0.908348i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −10.7970 | − | 5.94631i | −0.374094 | − | 0.206028i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −26.9263 | + | 46.6377i | −0.931822 | + | 1.61396i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −62.1101 | − | 107.578i | −2.14684 | − | 3.71844i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −35.1650 | −1.21403 | −0.607015 | − | 0.794690i | \(-0.707633\pi\) | ||||
−0.607015 | + | 0.794690i | \(0.707633\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.5940 | −0.710137 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 42.7599 | + | 74.0624i | 1.47273 | + | 2.55084i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.679065 | − | 1.17617i | 0.0233605 | − | 0.0404616i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.56238 | − | 0.658939i | −0.0880445 | − | 0.0226414i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.493163 | + | 0.854184i | −0.0169253 | + | 0.0293155i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.76088 | − | 3.04993i | −0.0603621 | − | 0.104550i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −40.5587 | −1.38870 | −0.694352 | − | 0.719635i | \(-0.744309\pi\) | ||||
−0.694352 | + | 0.719635i | \(0.744309\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 91.6687 | 3.13500 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 21.0978 | + | 36.5425i | 0.720687 | + | 1.24827i | 0.960725 | + | 0.277504i | \(0.0895070\pi\) |
−0.240037 | + | 0.970764i | \(0.577160\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26.5715 | − | 46.0233i | 0.906609 | − | 1.57029i | 0.0878670 | − | 0.996132i | \(-0.471995\pi\) |
0.818742 | − | 0.574161i | \(-0.194672\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −51.2863 | + | 52.3324i | −1.74783 | + | 1.78348i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 15.9932 | − | 27.7010i | 0.544414 | − | 0.942952i | −0.454230 | − | 0.890884i | \(-0.650086\pi\) |
0.998644 | − | 0.0520676i | \(-0.0165811\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.40972 | − | 11.1020i | −0.217937 | − | 0.377478i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 44.2268 | 1.50202 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.35021 | 0.249339 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.23585 | − | 10.8008i | −0.211294 | − | 0.365972i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −41.8480 | + | 72.4829i | −1.41634 | + | 2.45317i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.14132 | − | 14.8542i | −0.140002 | − | 0.502162i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.84609 | + | 17.0539i | −0.332479 | + | 0.575870i | −0.982997 | − | 0.183620i | \(-0.941218\pi\) |
0.650518 | + | 0.759491i | \(0.274552\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 49.6736 | + | 86.0372i | 1.67545 | + | 2.90196i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −42.3333 | −1.42624 | −0.713122 | − | 0.701040i | \(-0.752719\pi\) | ||||
−0.713122 | + | 0.701040i | \(0.752719\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −22.5023 | −0.757263 | −0.378632 | − | 0.925547i | \(-0.623605\pi\) | ||||
−0.378632 | + | 0.925547i | \(0.623605\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −35.6278 | − | 61.7091i | −1.19761 | − | 2.07433i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12.9286 | + | 22.3930i | −0.434100 | + | 0.751883i | −0.997222 | − | 0.0744911i | \(-0.976267\pi\) |
0.563122 | + | 0.826374i | \(0.309600\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.469087 | − | 1.68253i | −0.0157327 | − | 0.0564303i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −10.1940 | + | 17.6565i | −0.341511 | + | 0.591515i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.97141 | − | 13.8069i | −0.266753 | − | 0.462030i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −39.3502 | −1.31533 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −14.4315 | −0.481853 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −13.7204 | − | 23.7644i | −0.457600 | − | 0.792587i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.198495 | + | 0.343803i | −0.00661283 | + | 0.0114538i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 71.1080 | − | 72.5583i | 2.36632 | − | 2.41459i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9.90520 | + | 17.1563i | −0.329260 | + | 0.570295i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.29071 | + | 12.6279i | 0.242084 | + | 0.419302i | 0.961308 | − | 0.275477i | \(-0.0888357\pi\) |
−0.719224 | + | 0.694779i | \(0.755502\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 85.8813 | 2.84850 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.63860 | 0.286210 | 0.143105 | − | 0.989708i | \(-0.454291\pi\) | ||||
0.143105 | + | 0.989708i | \(0.454291\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.24433 | − | 9.08344i | −0.173562 | − | 0.300618i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 55.7863 | − | 96.6248i | 1.84424 | − | 3.19432i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 50.5150 | + | 12.9904i | 1.66815 | + | 0.428980i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15.5241 | + | 26.8885i | −0.512092 | + | 0.886969i | 0.487810 | + | 0.872950i | \(0.337796\pi\) |
−0.999902 | + | 0.0140194i | \(0.995537\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11.9451 | − | 20.6896i | −0.393606 | − | 0.681745i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 15.5160 | 0.510715 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 19.0528 | 0.626452 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −60.1902 | − | 104.252i | −1.97690 | − | 3.42410i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.96333 | + | 6.86469i | −0.130033 | + | 0.225223i | −0.923689 | − | 0.383143i | \(-0.874842\pi\) |
0.793656 | + | 0.608366i | \(0.208175\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.531469 | + | 26.3208i | 0.0174182 | + | 0.862628i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.44282 | − | 4.23109i | 0.0799743 | − | 0.138520i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.01204 | − | 5.21700i | −0.0985042 | − | 0.170614i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9.42571 | −0.307925 | −0.153962 | − | 0.988077i | \(-0.549203\pi\) | ||||
−0.153962 | + | 0.988077i | \(0.549203\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 40.8960 | 1.33459 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 23.1826 | + | 40.1535i | 0.755732 | + | 1.30897i | 0.945009 | + | 0.327043i | \(0.106052\pi\) |
−0.189277 | + | 0.981924i | \(0.560615\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.39248 | + | 9.34004i | −0.175603 | + | 0.304154i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −115.053 | − | 29.5868i | −3.74266 | − | 0.962459i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.06075 | − | 3.56932i | 0.0669653 | − | 0.115987i | −0.830599 | − | 0.556871i | \(-0.812002\pi\) |
0.897564 | + | 0.440884i | \(0.145335\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −18.6339 | − | 32.2749i | −0.604883 | − | 1.04769i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.73680 | −0.250883 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 37.6446 | 1.21943 | 0.609714 | − | 0.792621i | \(-0.291284\pi\) | ||||
0.609714 | + | 0.792621i | \(0.291284\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −31.6821 | − | 54.8750i | −1.02521 | − | 1.77571i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.61273 | + | 7.98947i | −0.149108 | + | 0.258263i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.13805 | − | 5.24284i | 0.165916 | − | 0.169300i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.2891 | + | 50.7302i | −0.944809 | + | 1.63646i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.07605 | + | 7.05993i | 0.131349 | + | 0.227503i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 12.9130 | 0.415684 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.22545 | 0.0394078 | 0.0197039 | − | 0.999806i | \(-0.493728\pi\) | ||||
0.0197039 | + | 0.999806i | \(0.493728\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 10.5361 | + | 18.2491i | 0.338469 | + | 0.586245i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −16.6814 | + | 28.8930i | −0.535331 | + | 0.927221i | 0.463816 | + | 0.885932i | \(0.346480\pi\) |
−0.999147 | + | 0.0412893i | \(0.986853\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.81587 | − | 28.0341i | −0.250565 | − | 0.898733i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 39.0374 | − | 67.6147i | 1.25020 | − | 2.16540i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −18.1460 | − | 31.4297i | −0.580541 | − | 1.00553i | −0.995415 | − | 0.0956474i | \(-0.969508\pi\) |
0.414875 | − | 0.909879i | \(-0.363825\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.26320 | 0.232133 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −23.5595 | −0.752197 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −0.574975 | − | 0.995887i | −0.0183389 | − | 0.0317639i | 0.856710 | − | 0.515798i | \(-0.172504\pi\) |
−0.875049 | + | 0.484034i | \(0.839171\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 17.3932 | − | 30.1258i | 0.554192 | − | 0.959889i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9.58414 | + | 34.3766i | 0.305066 | + | 1.09422i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.47661 | − | 12.9499i | 0.237742 | − | 0.411782i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.7603 | + | 22.1015i | 0.405345 | + | 0.702078i | 0.994362 | − | 0.106043i | \(-0.0338181\pi\) |
−0.589017 | + | 0.808121i | \(0.700485\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 33.1157 | 1.05090 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −34.4775 | −1.09301 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.27059 | + | 7.39688i | 0.135251 | + | 0.234262i | 0.925693 | − | 0.378275i | \(-0.123483\pi\) |
−0.790442 | + | 0.612536i | \(0.790149\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 18.6512 | − | 32.3048i | 0.590097 | − | 1.02208i |
(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 | 1232.2.q.l.177.3 | 6 | ||
4.3 | odd | 2 | 308.2.i.a.177.1 | ✓ | 6 | ||
7.2 | even | 3 | 8624.2.a.ci.1.1 | 3 | |||
7.4 | even | 3 | inner | 1232.2.q.l.529.3 | 6 | ||
7.5 | odd | 6 | 8624.2.a.cn.1.3 | 3 | |||
12.11 | even | 2 | 2772.2.s.f.793.1 | 6 | |||
28.3 | even | 6 | 2156.2.i.l.1145.3 | 6 | |||
28.11 | odd | 6 | 308.2.i.a.221.1 | yes | 6 | ||
28.19 | even | 6 | 2156.2.a.h.1.1 | 3 | |||
28.23 | odd | 6 | 2156.2.a.i.1.3 | 3 | |||
28.27 | even | 2 | 2156.2.i.l.177.3 | 6 | |||
84.11 | even | 6 | 2772.2.s.f.2377.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
308.2.i.a.177.1 | ✓ | 6 | 4.3 | odd | 2 | ||
308.2.i.a.221.1 | yes | 6 | 28.11 | odd | 6 | ||
1232.2.q.l.177.3 | 6 | 1.1 | even | 1 | trivial | ||
1232.2.q.l.529.3 | 6 | 7.4 | even | 3 | inner | ||
2156.2.a.h.1.1 | 3 | 28.19 | even | 6 | |||
2156.2.a.i.1.3 | 3 | 28.23 | odd | 6 | |||
2156.2.i.l.177.3 | 6 | 28.27 | even | 2 | |||
2156.2.i.l.1145.3 | 6 | 28.3 | even | 6 | |||
2772.2.s.f.793.1 | 6 | 12.11 | even | 2 | |||
2772.2.s.f.2377.1 | 6 | 84.11 | even | 6 | |||
8624.2.a.ci.1.1 | 3 | 7.2 | even | 3 | |||
8624.2.a.cn.1.3 | 3 | 7.5 | odd | 6 |