Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [927,2,Mod(926,927)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(927, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("927.926");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 927 = 3^{2} \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 927.c (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: | \(7.40213226737\) |
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: | \( x^{16} - 34x^{14} + 564x^{12} - 5204x^{10} + 29740x^{8} - 99088x^{6} + 214644x^{4} - 222312x^{2} + 84100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 926.2 | ||
Root | \(1.54287 + 0.912316i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 927.926 |
Dual form | 927.2.c.a.926.16 |
$q$-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 \(\left(\mathbb{Z}/927\mathbb{Z}\right)^\times\).
\(n\) | \(722\) | \(829\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.10850i | − | 1.49094i | −0.666541 | − | 0.745469i | \(-0.732226\pi\) | ||
0.666541 | − | 0.745469i | \(-0.267774\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.44579 | −1.22289 | ||||||||
\(5\) | 3.56582 | 1.59468 | 0.797341 | − | 0.603529i | \(-0.206239\pi\) | ||||
0.797341 | + | 0.603529i | \(0.206239\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.463913 | 0.175343 | 0.0876713 | − | 0.996149i | \(-0.472057\pi\) | ||||
0.0876713 | + | 0.996149i | \(0.472057\pi\) | |||||||
\(8\) | 0.939944i | 0.332320i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − | 7.51854i | − | 2.37757i | ||||||
\(11\) | 3.08574 | 0.930387 | 0.465193 | − | 0.885209i | \(-0.345985\pi\) | ||||
0.465193 | + | 0.885209i | \(0.345985\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.329281 | −0.0913261 | −0.0456630 | − | 0.998957i | \(-0.514540\pi\) | ||||
−0.0456630 | + | 0.998957i | \(0.514540\pi\) | |||||||
\(14\) | − | 0.978162i | − | 0.261425i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.90970 | −0.727425 | ||||||||
\(17\) | 3.45887i | 0.838898i | 0.907779 | + | 0.419449i | \(0.137777\pi\) | ||||
−0.907779 | + | 0.419449i | \(0.862223\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.56229 | 1.27608 | 0.638039 | − | 0.770004i | \(-0.279746\pi\) | ||||
0.638039 | + | 0.770004i | \(0.279746\pi\) | |||||||
\(20\) | −8.72123 | −1.95013 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 6.50630i | − | 1.38715i | ||||||
\(23\) | 2.57418i | 0.536753i | 0.963314 | + | 0.268377i | \(0.0864871\pi\) | ||||
−0.963314 | + | 0.268377i | \(0.913513\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.71505 | 1.54301 | ||||||||
\(26\) | 0.694290i | 0.136161i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.13463 | −0.214425 | ||||||||
\(29\) | − | 0.157325i | − | 0.0292146i | −0.999893 | − | 0.0146073i | \(-0.995350\pi\) | ||
0.999893 | − | 0.0146073i | \(-0.00464981\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 3.35167i | − | 0.601977i | −0.953628 | − | 0.300989i | \(-0.902683\pi\) | ||
0.953628 | − | 0.300989i | \(-0.0973166\pi\) | |||||||
\(32\) | 8.01500i | 1.41687i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 7.29303 | 1.25074 | ||||||||
\(35\) | 1.65423 | 0.279616 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 5.82738i | − | 0.958015i | −0.877811 | − | 0.479007i | \(-0.840997\pi\) | ||
0.877811 | − | 0.479007i | \(-0.159003\pi\) | |||||||
\(38\) | − | 11.7281i | − | 1.90255i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.35167i | 0.529945i | ||||||||
\(41\) | − | 2.20543i | − | 0.344430i | −0.985059 | − | 0.172215i | \(-0.944908\pi\) | ||
0.985059 | − | 0.172215i | \(-0.0550924\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 4.81514i | − | 0.734302i | −0.930161 | − | 0.367151i | \(-0.880333\pi\) | ||
0.930161 | − | 0.367151i | \(-0.119667\pi\) | |||||||
\(44\) | −7.54707 | −1.13776 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.42766 | 0.800265 | ||||||||
\(47\) | −3.08574 | −0.450102 | −0.225051 | − | 0.974347i | \(-0.572255\pi\) | ||||
−0.225051 | + | 0.974347i | \(0.572255\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.78478 | −0.969255 | ||||||||
\(50\) | − | 16.2672i | − | 2.30053i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.805351 | 0.111682 | ||||||||
\(53\) | −7.54707 | −1.03667 | −0.518335 | − | 0.855178i | \(-0.673448\pi\) | ||||
−0.518335 | + | 0.855178i | \(0.673448\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 11.0032 | 1.48367 | ||||||||
\(56\) | 0.436052i | 0.0582699i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.331721 | −0.0435571 | ||||||||
\(59\) | 4.85205i | 0.631684i | 0.948812 | + | 0.315842i | \(0.102287\pi\) | ||||
−0.948812 | + | 0.315842i | \(0.897713\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.391738 | −0.0501570 | −0.0250785 | − | 0.999685i | \(-0.507984\pi\) | ||||
−0.0250785 | + | 0.999685i | \(0.507984\pi\) | |||||||
\(62\) | −7.06700 | −0.897510 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 11.0803 | 1.38503 | ||||||||
\(65\) | −1.17416 | −0.145636 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.98201i | 1.09733i | 0.836043 | + | 0.548664i | \(0.184863\pi\) | ||||
−0.836043 | + | 0.548664i | \(0.815137\pi\) | |||||||
\(68\) | − | 8.45965i | − | 1.02588i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | − | 3.48795i | − | 0.416889i | ||||||
\(71\) | −2.39166 | −0.283838 | −0.141919 | − | 0.989878i | \(-0.545327\pi\) | ||||
−0.141919 | + | 0.989878i | \(0.545327\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 4.84580i | − | 0.567158i | −0.958949 | − | 0.283579i | \(-0.908478\pi\) | ||
0.958949 | − | 0.283579i | \(-0.0915217\pi\) | |||||||
\(74\) | −12.2870 | −1.42834 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −13.6042 | −1.56051 | ||||||||
\(77\) | 1.43152 | 0.163136 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.7207 | −1.54370 | −0.771849 | − | 0.635806i | \(-0.780668\pi\) | ||||
−0.771849 | + | 0.635806i | \(0.780668\pi\) | |||||||
\(80\) | −10.3755 | −1.16001 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.65015 | −0.513523 | ||||||||
\(83\) | 9.77694i | 1.07316i | 0.843850 | + | 0.536579i | \(0.180284\pi\) | ||||
−0.843850 | + | 0.536579i | \(0.819716\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.3337i | 1.33778i | ||||||||
\(86\) | −10.1527 | −1.09480 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.90043i | 0.309186i | ||||||||
\(89\) | 15.7882 | 1.67355 | 0.836775 | − | 0.547548i | \(-0.184439\pi\) | ||||
0.836775 | + | 0.547548i | \(0.184439\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.152758 | −0.0160133 | ||||||||
\(92\) | − | 6.29589i | − | 0.656392i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.50630i | 0.671074i | ||||||||
\(95\) | 19.8341 | 2.03494 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.2084 | −1.64571 | −0.822855 | − | 0.568251i | \(-0.807620\pi\) | ||||
−0.822855 | + | 0.568251i | \(0.807620\pi\) | |||||||
\(98\) | 14.3057i | 1.44510i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −18.8694 | −1.88694 | ||||||||
\(101\) | −13.4612 | −1.33944 | −0.669720 | − | 0.742614i | \(-0.733586\pi\) | ||||
−0.669720 | + | 0.742614i | \(0.733586\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.72477 | − | 8.98201i | −0.465545 | − | 0.885024i | ||||
\(104\) | − | 0.309505i | − | 0.0303495i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 15.9130i | 1.54561i | ||||||||
\(107\) | 3.47989i | 0.336414i | 0.985752 | + | 0.168207i | \(0.0537977\pi\) | ||||
−0.985752 | + | 0.168207i | \(0.946202\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 15.9130i | − | 1.52419i | −0.647464 | − | 0.762096i | \(-0.724170\pi\) | ||
0.647464 | − | 0.762096i | \(-0.275830\pi\) | |||||||
\(110\) | − | 23.2003i | − | 2.21206i | ||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.34985 | −0.127549 | ||||||||
\(113\) | 17.2844 | 1.62598 | 0.812989 | − | 0.582279i | \(-0.197839\pi\) | ||||
0.812989 | + | 0.582279i | \(0.197839\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.17904i | 0.855950i | ||||||||
\(116\) | 0.384784i | 0.0357263i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 10.2306 | 0.941800 | ||||||||
\(119\) | 1.60461i | 0.147095i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.47818 | −0.134380 | ||||||||
\(122\) | 0.825982i | 0.0747809i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 8.19746i | 0.736154i | ||||||||
\(125\) | 9.68137 | 0.865928 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.9253i | 1.50187i | 0.660374 | + | 0.750937i | \(0.270398\pi\) | ||||
−0.660374 | + | 0.750937i | \(0.729602\pi\) | |||||||
\(128\) | − | 7.33276i | − | 0.648130i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.47571i | 0.217134i | ||||||||
\(131\) | − | 0.973553i | − | 0.0850597i | −0.999095 | − | 0.0425299i | \(-0.986458\pi\) | ||
0.999095 | − | 0.0425299i | \(-0.0135418\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.58042 | 0.223751 | ||||||||
\(134\) | 18.9386 | 1.63605 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.25114 | −0.278783 | ||||||||
\(137\) | − | 4.79664i | − | 0.409805i | −0.978782 | − | 0.204902i | \(-0.934312\pi\) | ||
0.978782 | − | 0.204902i | \(-0.0656877\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.4619 | 1.48110 | 0.740552 | − | 0.672000i | \(-0.234564\pi\) | ||||
0.740552 | + | 0.672000i | \(0.234564\pi\) | |||||||
\(140\) | −4.04589 | −0.341940 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 5.04283i | 0.423185i | ||||||||
\(143\) | −1.01608 | −0.0849686 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 0.560994i | − | 0.0465880i | ||||||
\(146\) | −10.2174 | −0.845596 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 14.2525i | 1.17155i | ||||||||
\(149\) | 2.13529i | 0.174930i | 0.996168 | + | 0.0874651i | \(0.0278766\pi\) | ||||
−0.996168 | + | 0.0874651i | \(0.972123\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 11.7462i | − | 0.955889i | −0.878390 | − | 0.477944i | \(-0.841382\pi\) | ||
0.878390 | − | 0.477944i | \(-0.158618\pi\) | |||||||
\(152\) | 5.22824i | 0.424066i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | − | 3.01836i | − | 0.243226i | ||||||
\(155\) | − | 11.9514i | − | 0.959962i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.8400i | 1.50359i | 0.659394 | + | 0.751797i | \(0.270813\pi\) | ||||
−0.659394 | + | 0.751797i | \(0.729187\pi\) | |||||||
\(158\) | 28.9301i | 2.30156i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 28.5800i | 2.25945i | ||||||||
\(161\) | 1.19419i | 0.0941156i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.40146 | −0.658053 | −0.329026 | − | 0.944321i | \(-0.606721\pi\) | ||||
−0.329026 | + | 0.944321i | \(0.606721\pi\) | |||||||
\(164\) | 5.39401i | 0.421201i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 20.6147 | 1.60001 | ||||||||
\(167\) | 5.23223i | 0.404882i | 0.979294 | + | 0.202441i | \(0.0648874\pi\) | ||||
−0.979294 | + | 0.202441i | \(0.935113\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.8916 | −0.991660 | ||||||||
\(170\) | 26.0056 | 1.99454 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 11.7768i | 0.897974i | ||||||||
\(173\) | −0.737433 | −0.0560660 | −0.0280330 | − | 0.999607i | \(-0.508924\pi\) | ||||
−0.0280330 | + | 0.999607i | \(0.508924\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.57911 | 0.270555 | ||||||||
\(176\) | −8.97859 | −0.676787 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 33.2895i | − | 2.49516i | ||||||
\(179\) | 26.3976i | 1.97305i | 0.163609 | + | 0.986525i | \(0.447686\pi\) | ||||
−0.163609 | + | 0.986525i | \(0.552314\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 17.4821i | − | 1.29944i | −0.760175 | − | 0.649718i | \(-0.774887\pi\) | ||
0.760175 | − | 0.649718i | \(-0.225113\pi\) | |||||||
\(182\) | 0.322090i | 0.0238749i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.41958 | −0.178374 | ||||||||
\(185\) | − | 20.7794i | − | 1.52773i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.6732i | 0.780500i | ||||||||
\(188\) | 7.54707 | 0.550427 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | − | 41.8203i | − | 3.03396i | ||||||
\(191\) | 8.65660 | 0.626369 | 0.313185 | − | 0.949692i | \(-0.398604\pi\) | ||||
0.313185 | + | 0.949692i | \(0.398604\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 1.43695i | − | 0.103434i | −0.998662 | − | 0.0517169i | \(-0.983531\pi\) | ||
0.998662 | − | 0.0517169i | \(-0.0164694\pi\) | |||||||
\(194\) | 34.1754i | 2.45365i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 16.5941 | 1.18530 | ||||||||
\(197\) | −9.68137 | −0.689769 | −0.344885 | − | 0.938645i | \(-0.612082\pi\) | ||||
−0.344885 | + | 0.938645i | \(0.612082\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.91472i | 0.135731i | 0.997694 | + | 0.0678654i | \(0.0216188\pi\) | ||||
−0.997694 | + | 0.0678654i | \(0.978381\pi\) | |||||||
\(200\) | 7.25171i | 0.512773i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 28.3830i | 1.99702i | ||||||||
\(203\) | − | 0.0729853i | − | 0.00512256i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 7.86415i | − | 0.549256i | ||||||
\(206\) | −18.9386 | + | 9.96219i | −1.31952 | + | 0.694099i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.958109 | 0.0664329 | ||||||||
\(209\) | 17.1638 | 1.18725 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.6430i | 1.28343i | 0.766942 | + | 0.641717i | \(0.221778\pi\) | ||||
−0.766942 | + | 0.641717i | \(0.778222\pi\) | |||||||
\(212\) | 18.4585 | 1.26774 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 7.33736 | 0.501572 | ||||||||
\(215\) | − | 17.1699i | − | 1.17098i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 1.55488i | − | 0.105552i | ||||||
\(218\) | −33.5527 | −2.27247 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −26.9115 | −1.81437 | ||||||||
\(221\) | − | 1.13894i | − | 0.0766133i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.3046 | 0.957909 | 0.478955 | − | 0.877840i | \(-0.341016\pi\) | ||||
0.478955 | + | 0.877840i | \(0.341016\pi\) | |||||||
\(224\) | 3.71826i | 0.248437i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − | 36.4442i | − | 2.42423i | ||||||
\(227\) | 16.2037 | 1.07548 | 0.537738 | − | 0.843112i | \(-0.319279\pi\) | ||||
0.537738 | + | 0.843112i | \(0.319279\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 24.6601 | 1.62959 | 0.814793 | − | 0.579751i | \(-0.196850\pi\) | ||||
0.814793 | + | 0.579751i | \(0.196850\pi\) | |||||||
\(230\) | 19.3540 | 1.27617 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.147877 | 0.00970860 | ||||||||
\(233\) | 5.47741 | 0.358837 | 0.179418 | − | 0.983773i | \(-0.442578\pi\) | ||||
0.179418 | + | 0.983773i | \(0.442578\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.0032 | −0.717770 | ||||||||
\(236\) | − | 11.8671i | − | 0.772482i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.38333 | 0.219309 | ||||||||
\(239\) | 18.7320i | 1.21167i | 0.795589 | + | 0.605837i | \(0.207162\pi\) | ||||
−0.795589 | + | 0.605837i | \(0.792838\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 29.2896i | − | 1.88671i | −0.331787 | − | 0.943354i | \(-0.607651\pi\) | ||
0.331787 | − | 0.943354i | \(-0.392349\pi\) | |||||||
\(242\) | 3.11675i | 0.200352i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.958109 | 0.0613366 | ||||||||
\(245\) | −24.1933 | −1.54565 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.83156 | −0.116539 | ||||||||
\(248\) | 3.15038 | 0.200049 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − | 20.4132i | − | 1.29104i | ||||||
\(251\) | 11.2710 | 0.711417 | 0.355709 | − | 0.934597i | \(-0.384240\pi\) | ||||
0.355709 | + | 0.934597i | \(0.384240\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.94325i | 0.499388i | ||||||||
\(254\) | 35.6870 | 2.23920 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 6.69937 | 0.418710 | ||||||||
\(257\) | 10.4188 | 0.649907 | 0.324954 | − | 0.945730i | \(-0.394651\pi\) | ||||
0.324954 | + | 0.945730i | \(0.394651\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 2.70339i | − | 0.167981i | ||||||
\(260\) | 2.87173 | 0.178097 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.05274 | −0.126819 | ||||||||
\(263\) | 9.93874 | 0.612849 | 0.306424 | − | 0.951895i | \(-0.400867\pi\) | ||||
0.306424 | + | 0.951895i | \(0.400867\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −26.9115 | −1.65316 | ||||||||
\(266\) | − | 5.44082i | − | 0.333598i | ||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 21.9681i | − | 1.34191i | ||||||
\(269\) | − | 17.5532i | − | 1.07024i | −0.844777 | − | 0.535118i | \(-0.820267\pi\) | ||
0.844777 | − | 0.535118i | \(-0.179733\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.16069i | 0.374235i | 0.982338 | + | 0.187118i | \(0.0599145\pi\) | ||||
−0.982338 | + | 0.187118i | \(0.940085\pi\) | |||||||
\(272\) | − | 10.0643i | − | 0.610235i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10.1137 | −0.610993 | ||||||||
\(275\) | 23.8067 | 1.43560 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 13.7058i | − | 0.823499i | −0.911297 | − | 0.411749i | \(-0.864918\pi\) | ||
0.911297 | − | 0.411749i | \(-0.135082\pi\) | |||||||
\(278\) | − | 36.8186i | − | 2.20823i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.55488i | 0.0929219i | ||||||||
\(281\) | −15.0295 | −0.896586 | −0.448293 | − | 0.893887i | \(-0.647968\pi\) | ||||
−0.448293 | + | 0.893887i | \(0.647968\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.1672i | 0.961043i | 0.876983 | + | 0.480521i | \(0.159553\pi\) | ||||
−0.876983 | + | 0.480521i | \(0.840447\pi\) | |||||||
\(284\) | 5.84949 | 0.347104 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.14240i | 0.126683i | ||||||||
\(287\) | − | 1.02313i | − | 0.0603932i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.03625 | 0.296250 | ||||||||
\(290\) | −1.18286 | −0.0694598 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 11.8518i | 0.693573i | ||||||||
\(293\) | −1.31095 | −0.0765866 | −0.0382933 | − | 0.999267i | \(-0.512192\pi\) | ||||
−0.0382933 | + | 0.999267i | \(0.512192\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 17.3015i | 1.00733i | ||||||||
\(296\) | 5.47741 | 0.318368 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4.50228 | 0.260810 | ||||||||
\(299\) | − | 0.847627i | − | 0.0490196i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 2.23381i | − | 0.128754i | ||||||
\(302\) | −24.7668 | −1.42517 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −16.1846 | −0.928251 | ||||||||
\(305\) | −1.39687 | −0.0799844 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 24.4131i | 1.39333i | 0.717396 | + | 0.696666i | \(0.245334\pi\) | ||||
−0.717396 | + | 0.696666i | \(0.754666\pi\) | |||||||
\(308\) | −3.50118 | −0.199498 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −25.1996 | −1.43124 | ||||||||
\(311\) | − | 11.8206i | − | 0.670284i | −0.942168 | − | 0.335142i | \(-0.891216\pi\) | ||
0.942168 | − | 0.335142i | \(-0.108784\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.64477 | −0.262538 | −0.131269 | − | 0.991347i | \(-0.541905\pi\) | ||||
−0.131269 | + | 0.991347i | \(0.541905\pi\) | |||||||
\(314\) | 39.7242 | 2.24176 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 33.5579 | 1.88778 | ||||||||
\(317\) | 21.2873i | 1.19562i | 0.801640 | + | 0.597808i | \(0.203961\pi\) | ||||
−0.801640 | + | 0.597808i | \(0.796039\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 0.485466i | − | 0.0271809i | ||||||
\(320\) | 39.5102 | 2.20869 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.51796 | 0.140321 | ||||||||
\(323\) | 19.2392i | 1.07050i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.54042 | −0.140917 | ||||||||
\(326\) | 17.7145i | 0.981115i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.07298 | 0.114461 | ||||||||
\(329\) | −1.43152 | −0.0789220 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 11.7768i | − | 0.647312i | −0.946175 | − | 0.323656i | \(-0.895088\pi\) | ||
0.946175 | − | 0.323656i | \(-0.104912\pi\) | |||||||
\(332\) | − | 23.9123i | − | 1.31236i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 11.0322 | 0.603654 | ||||||||
\(335\) | 32.0282i | 1.74989i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.10890 | 0.114879 | 0.0574396 | − | 0.998349i | \(-0.481706\pi\) | ||||
0.0574396 | + | 0.998349i | \(0.481706\pi\) | |||||||
\(338\) | 27.1819i | 1.47850i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | − | 30.1656i | − | 1.63596i | ||||||
\(341\) | − | 10.3424i | − | 0.560072i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.39494 | −0.345294 | ||||||||
\(344\) | 4.52596 | 0.244024 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.55488i | 0.0835909i | ||||||||
\(347\) | 22.1641i | 1.18983i | 0.803788 | + | 0.594916i | \(0.202815\pi\) | ||||
−0.803788 | + | 0.594916i | \(0.797185\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 26.5597i | 1.42171i | 0.703340 | + | 0.710853i | \(0.251691\pi\) | ||||
−0.703340 | + | 0.710853i | \(0.748309\pi\) | |||||||
\(350\) | − | 7.54657i | − | 0.403381i | ||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 24.7322i | 1.31823i | ||||||||
\(353\) | −32.6012 | −1.73519 | −0.867594 | − | 0.497272i | \(-0.834335\pi\) | ||||
−0.867594 | + | 0.497272i | \(0.834335\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.52823 | −0.452631 | ||||||||
\(356\) | −38.6146 | −2.04657 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 55.6595 | 2.94169 | ||||||||
\(359\) | 24.3300i | 1.28409i | 0.766667 | + | 0.642045i | \(0.221914\pi\) | ||||
−0.766667 | + | 0.642045i | \(0.778086\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.9391 | 0.628374 | ||||||||
\(362\) | −36.8611 | −1.93738 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.373613 | 0.0195826 | ||||||||
\(365\) | − | 17.2792i | − | 0.904436i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −23.8705 | −1.24603 | −0.623014 | − | 0.782211i | \(-0.714092\pi\) | ||||
−0.623014 | + | 0.782211i | \(0.714092\pi\) | |||||||
\(368\) | − | 7.49008i | − | 0.390448i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −43.8134 | −2.27775 | ||||||||
\(371\) | −3.50118 | −0.181772 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −25.4114 | −1.31575 | −0.657877 | − | 0.753125i | \(-0.728545\pi\) | ||||
−0.657877 | + | 0.753125i | \(0.728545\pi\) | |||||||
\(374\) | 22.5044 | 1.16368 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 2.90043i | − | 0.149578i | ||||||
\(377\) | 0.0518043i | 0.00266806i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 9.96359i | − | 0.511795i | −0.966704 | − | 0.255898i | \(-0.917629\pi\) | ||
0.966704 | − | 0.255898i | \(-0.0823710\pi\) | |||||||
\(380\) | −48.5100 | −2.48851 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 18.2525i | − | 0.933877i | ||||||
\(383\) | −29.8288 | −1.52418 | −0.762090 | − | 0.647471i | \(-0.775827\pi\) | ||||
−0.762090 | + | 0.647471i | \(0.775827\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.10452 | 0.260151 | ||||||||
\(386\) | −3.02981 | −0.154213 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 39.6422 | 2.01253 | ||||||||
\(389\) | −6.15891 | −0.312269 | −0.156135 | − | 0.987736i | \(-0.549903\pi\) | ||||
−0.156135 | + | 0.987736i | \(0.549903\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.90373 | −0.450281 | ||||||||
\(392\) | − | 6.37731i | − | 0.322103i | ||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 20.4132i | 1.02840i | ||||||||
\(395\) | −48.9255 | −2.46171 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 27.9175i | 1.40114i | 0.713583 | + | 0.700570i | \(0.247071\pi\) | ||||
−0.713583 | + | 0.700570i | \(0.752929\pi\) | |||||||
\(398\) | 4.03719 | 0.202366 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −22.4485 | −1.12242 | ||||||||
\(401\) | − | 3.23784i | − | 0.161690i | −0.996727 | − | 0.0808451i | \(-0.974238\pi\) | ||
0.996727 | − | 0.0808451i | \(-0.0257619\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.10364i | 0.0549762i | ||||||||
\(404\) | 32.9232 | 1.63799 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.153890 | −0.00763742 | ||||||||
\(407\) | − | 17.9818i | − | 0.891325i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.5906 | −0.770906 | −0.385453 | − | 0.922727i | \(-0.625955\pi\) | ||||
−0.385453 | + | 0.922727i | \(0.625955\pi\) | |||||||
\(410\) | −16.5816 | −0.818907 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 11.5558 | + | 21.9681i | 0.569312 | + | 1.08229i | ||||
\(413\) | 2.25093i | 0.110761i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 34.8628i | 1.71135i | ||||||||
\(416\) | − | 2.63919i | − | 0.129397i | ||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 36.1900i | − | 1.77011i | ||||||
\(419\) | − | 38.5792i | − | 1.88472i | −0.334604 | − | 0.942359i | \(-0.608603\pi\) | ||
0.334604 | − | 0.942359i | \(-0.391397\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.4628 | 0.948556 | 0.474278 | − | 0.880375i | \(-0.342709\pi\) | ||||
0.474278 | + | 0.880375i | \(0.342709\pi\) | |||||||
\(422\) | 39.3087 | 1.91352 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 7.09382i | − | 0.344507i | ||||||
\(425\) | 26.6853i | 1.29443i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.181732 | −0.00879465 | ||||||||
\(428\) | − | 8.51107i | − | 0.411398i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −36.2028 | −1.74586 | ||||||||
\(431\) | − | 29.0104i | − | 1.39738i | −0.715424 | − | 0.698691i | \(-0.753766\pi\) | ||
0.715424 | − | 0.698691i | \(-0.246234\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.7078i | 0.899041i | 0.893270 | + | 0.449520i | \(0.148405\pi\) | ||||
−0.893270 | + | 0.449520i | \(0.851595\pi\) | |||||||
\(434\) | −3.27847 | −0.157372 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 38.9199i | 1.86392i | ||||||||
\(437\) | 14.3183i | 0.684938i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 4.06125i | − | 0.193833i | −0.995293 | − | 0.0969163i | \(-0.969102\pi\) | ||
0.995293 | − | 0.0969163i | \(-0.0308979\pi\) | |||||||
\(440\) | 10.3424i | 0.493054i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.40146 | −0.114226 | ||||||||
\(443\) | 35.5289 | 1.68803 | 0.844015 | − | 0.536320i | \(-0.180186\pi\) | ||||
0.844015 | + | 0.536320i | \(0.180186\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 56.2979 | 2.66878 | ||||||||
\(446\) | − | 30.1614i | − | 1.42818i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 5.14027 | 0.242855 | ||||||||
\(449\) | −22.0677 | −1.04144 | −0.520720 | − | 0.853728i | \(-0.674336\pi\) | ||||
−0.520720 | + | 0.853728i | \(0.674336\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 6.80539i | − | 0.320453i | ||||||
\(452\) | −42.2739 | −1.98840 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 34.1655i | − | 1.60347i | ||||||
\(455\) | −0.544706 | −0.0255362 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.11581i | 0.286086i | 0.989716 | + | 0.143043i | \(0.0456887\pi\) | ||||
−0.989716 | + | 0.143043i | \(0.954311\pi\) | |||||||
\(458\) | − | 51.9960i | − | 2.42961i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − | 22.4500i | − | 1.04674i | ||||||
\(461\) | 9.57694i | 0.446043i | 0.974814 | + | 0.223021i | \(0.0715919\pi\) | ||||
−0.974814 | + | 0.223021i | \(0.928408\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.6914i | 0.868663i | 0.900753 | + | 0.434331i | \(0.143015\pi\) | ||||
−0.900753 | + | 0.434331i | \(0.856985\pi\) | |||||||
\(464\) | 0.457770i | 0.0212514i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | − | 11.5491i | − | 0.535003i | ||||||
\(467\) | − | 30.8613i | − | 1.42809i | −0.700100 | − | 0.714045i | \(-0.746861\pi\) | ||
0.700100 | − | 0.714045i | \(-0.253139\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.16687i | 0.192408i | ||||||||
\(470\) | 23.2003i | 1.07015i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −4.56066 | −0.209921 | ||||||||
\(473\) | − | 14.8583i | − | 0.683185i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 42.9134 | 1.96900 | ||||||||
\(476\) | − | 3.92454i | − | 0.179881i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 39.4966 | 1.80653 | ||||||||
\(479\) | 11.6922 | 0.534232 | 0.267116 | − | 0.963664i | \(-0.413929\pi\) | ||||
0.267116 | + | 0.963664i | \(0.413929\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.91884i | 0.0874918i | ||||||||
\(482\) | −61.7572 | −2.81296 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.61532 | 0.164333 | ||||||||
\(485\) | −57.7961 | −2.62438 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 19.8563i | − | 0.899777i | −0.893085 | − | 0.449888i | \(-0.851464\pi\) | ||
0.893085 | − | 0.449888i | \(-0.148536\pi\) | |||||||
\(488\) | − | 0.368212i | − | 0.0166682i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 51.0117i | 2.30447i | ||||||||
\(491\) | 32.8239i | 1.48132i | 0.671879 | + | 0.740661i | \(0.265487\pi\) | ||||
−0.671879 | + | 0.740661i | \(0.734513\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.544167 | 0.0245081 | ||||||||
\(494\) | 3.86184i | 0.173753i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9.75234i | 0.437893i | ||||||||
\(497\) | −1.10952 | −0.0497689 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 28.4479i | − | 1.27350i | −0.771070 | − | 0.636751i | \(-0.780278\pi\) | ||
0.771070 | − | 0.636751i | \(-0.219722\pi\) | |||||||
\(500\) | −23.6786 | −1.05894 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 23.7649i | − | 1.06068i | ||||||
\(503\) | − | 17.3702i | − | 0.774501i | −0.921975 | − | 0.387251i | \(-0.873425\pi\) | ||
0.921975 | − | 0.387251i | \(-0.126575\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −48.0002 | −2.13598 | ||||||||
\(506\) | 16.7484 | 0.744556 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 41.3956i | − | 1.83663i | ||||||
\(509\) | − | 9.34372i | − | 0.414153i | −0.978325 | − | 0.207076i | \(-0.933605\pi\) | ||
0.978325 | − | 0.207076i | \(-0.0663949\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 2.24803i | − | 0.0994469i | ||||||
\(512\) | − | 28.7911i | − | 1.27240i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 21.9681i | − | 0.968971i | ||||||
\(515\) | −16.8477 | − | 32.0282i | −0.742396 | − | 1.41133i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.52182 | −0.418769 | ||||||||
\(518\) | −5.70012 | −0.250449 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | − | 1.10364i | − | 0.0483978i | ||||||
\(521\) | −21.5172 | −0.942684 | −0.471342 | − | 0.881951i | \(-0.656230\pi\) | ||||
−0.471342 | + | 0.881951i | \(0.656230\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.12003 | −0.0927026 | −0.0463513 | − | 0.998925i | \(-0.514759\pi\) | ||||
−0.0463513 | + | 0.998925i | \(0.514759\pi\) | |||||||
\(524\) | 2.38110i | 0.104019i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 20.9559i | − | 0.913719i | ||||||
\(527\) | 11.5930 | 0.504997 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16.3736 | 0.711896 | ||||||||
\(530\) | 56.7430i | 2.46476i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −6.31116 | −0.273623 | ||||||||
\(533\) | 0.726205i | 0.0314554i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.4087i | 0.536473i | ||||||||
\(536\) | −8.44259 | −0.364664 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −37.0110 | −1.59566 | ||||||||
\(539\) | −20.9361 | −0.901782 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.2008 | 0.696528 | 0.348264 | − | 0.937396i | \(-0.386771\pi\) | ||||
0.348264 | + | 0.937396i | \(0.386771\pi\) | |||||||
\(542\) | 12.9898 | 0.557961 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −27.7228 | −1.18861 | ||||||||
\(545\) | − | 56.7430i | − | 2.43060i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.1635 | −0.477316 | −0.238658 | − | 0.971104i | \(-0.576708\pi\) | ||||
−0.238658 | + | 0.971104i | \(0.576708\pi\) | |||||||
\(548\) | 11.7316i | 0.501148i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | − | 50.1965i | − | 2.14038i | ||||||
\(551\) | − | 0.875090i | − | 0.0372801i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.36520 | −0.270676 | ||||||||
\(554\) | −28.8986 | −1.22778 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −42.7082 | −1.81123 | ||||||||
\(557\) | −15.5742 | −0.659901 | −0.329950 | − | 0.943998i | \(-0.607032\pi\) | ||||
−0.329950 | + | 0.943998i | \(0.607032\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.58553i | 0.0670610i | ||||||||
\(560\) | −4.81331 | −0.203399 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 31.6898i | 1.33675i | ||||||||
\(563\) | −2.16311 | −0.0911644 | −0.0455822 | − | 0.998961i | \(-0.514514\pi\) | ||||
−0.0455822 | + | 0.998961i | \(0.514514\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 61.6329 | 2.59292 | ||||||||
\(566\) | 34.0887 | 1.43285 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 2.24803i | − | 0.0943251i | ||||||
\(569\) | 29.3054 | 1.22854 | 0.614272 | − | 0.789094i | \(-0.289450\pi\) | ||||
0.614272 | + | 0.789094i | \(0.289450\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.5600 | −0.902258 | −0.451129 | − | 0.892459i | \(-0.648979\pi\) | ||||
−0.451129 | + | 0.892459i | \(0.648979\pi\) | |||||||
\(572\) | 2.48511 | 0.103908 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.15727 | −0.0900425 | ||||||||
\(575\) | 19.8599i | 0.828215i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 6.08572i | − | 0.253352i | −0.991944 | − | 0.126676i | \(-0.959569\pi\) | ||
0.991944 | − | 0.126676i | \(-0.0404308\pi\) | |||||||
\(578\) | − | 10.6190i | − | 0.441690i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.37207i | 0.0569721i | ||||||||
\(581\) | 4.53565i | 0.188170i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −23.2883 | −0.964504 | ||||||||
\(584\) | 4.55477 | 0.188478 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.76415i | 0.114186i | ||||||||
\(587\) | − | 19.7929i | − | 0.816941i | −0.912772 | − | 0.408471i | \(-0.866062\pi\) | ||
0.912772 | − | 0.408471i | \(-0.133938\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 18.6430i | − | 0.768169i | ||||||
\(590\) | 36.4803 | 1.50187 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 16.9559i | 0.696884i | ||||||||
\(593\) | −40.2129 | −1.65135 | −0.825674 | − | 0.564148i | \(-0.809205\pi\) | ||||
−0.825674 | + | 0.564148i | \(0.809205\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.72175i | 0.234569i | ||||||||
\(596\) | − | 5.22248i | − | 0.213921i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.78723 | −0.0730851 | ||||||||
\(599\) | 42.3385 | 1.72991 | 0.864953 | − | 0.501853i | \(-0.167348\pi\) | ||||
0.864953 | + | 0.501853i | \(0.167348\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 41.7289i | − | 1.70216i | −0.525038 | − | 0.851079i | \(-0.675949\pi\) | ||
0.525038 | − | 0.851079i | \(-0.324051\pi\) | |||||||
\(602\) | −4.70999 | −0.191965 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 28.7286i | 1.16895i | ||||||||
\(605\) | −5.27093 | −0.214294 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23.0083 | −0.933878 | −0.466939 | − | 0.884289i | \(-0.654643\pi\) | ||||
−0.466939 | + | 0.884289i | \(0.654643\pi\) | |||||||
\(608\) | 44.5818i | 1.80803i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.94530i | 0.119252i | ||||||||
\(611\) | 1.01608 | 0.0411061 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.8502 | 0.438237 | 0.219118 | − | 0.975698i | \(-0.429682\pi\) | ||||
0.219118 | + | 0.975698i | \(0.429682\pi\) | |||||||
\(614\) | 51.4752 | 2.07737 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.34554i | 0.0542135i | ||||||||
\(617\) | 9.30929 | 0.374778 | 0.187389 | − | 0.982286i | \(-0.439998\pi\) | ||||
0.187389 | + | 0.982286i | \(0.439998\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.29194 | −0.252894 | −0.126447 | − | 0.991973i | \(-0.540357\pi\) | ||||
−0.126447 | + | 0.991973i | \(0.540357\pi\) | |||||||
\(620\) | 29.2307i | 1.17393i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −24.9237 | −0.999351 | ||||||||
\(623\) | 7.32436 | 0.293444 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.05325 | −0.162130 | ||||||||
\(626\) | 9.79351i | 0.391427i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 46.0786i | − | 1.83874i | ||||||
\(629\) | 20.1561 | 0.803677 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.5182 | −0.577961 | −0.288981 | − | 0.957335i | \(-0.593316\pi\) | ||||
−0.288981 | + | 0.957335i | \(0.593316\pi\) | |||||||
\(632\) | − | 12.8967i | − | 0.513002i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 44.8844 | 1.78259 | ||||||||
\(635\) | 60.3524i | 2.39501i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.23410 | 0.0885183 | ||||||||
\(638\) | −1.02361 | −0.0405250 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − | 26.1473i | − | 1.03356i | ||||||
\(641\) | − | 45.4231i | − | 1.79411i | −0.441924 | − | 0.897053i | \(-0.645704\pi\) | ||
0.441924 | − | 0.897053i | \(-0.354296\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.58883 | −0.102093 | −0.0510467 | − | 0.998696i | \(-0.516256\pi\) | ||||
−0.0510467 | + | 0.998696i | \(0.516256\pi\) | |||||||
\(644\) | − | 2.92074i | − | 0.115093i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 40.5660 | 1.59605 | ||||||||
\(647\) | − | 21.4687i | − | 0.844020i | −0.906591 | − | 0.422010i | \(-0.861325\pi\) | ||
0.906591 | − | 0.422010i | \(-0.138675\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14.9722i | 0.587710i | ||||||||
\(650\) | 5.35648i | 0.210099i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 20.5482 | 0.804728 | ||||||||
\(653\) | −28.4261 | −1.11240 | −0.556199 | − | 0.831049i | \(-0.687741\pi\) | ||||
−0.556199 | + | 0.831049i | \(0.687741\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 3.47151i | − | 0.135643i | ||||||
\(656\) | 6.41713i | 0.250547i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3.01836i | 0.117668i | ||||||||
\(659\) | 5.66246i | 0.220578i | 0.993900 | + | 0.110289i | \(0.0351777\pi\) | ||||
−0.993900 | + | 0.110289i | \(0.964822\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.30110i | 0.361771i | 0.983504 | + | 0.180885i | \(0.0578963\pi\) | ||||
−0.983504 | + | 0.180885i | \(0.942104\pi\) | |||||||
\(662\) | −24.8315 | −0.965102 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −9.18977 | −0.356632 | ||||||||
\(665\) | 9.20130 | 0.356811 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.404983 | 0.0156810 | ||||||||
\(668\) | − | 12.7969i | − | 0.495128i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 67.5316 | 2.60897 | ||||||||
\(671\) | −1.20880 | −0.0466654 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 43.1135 | 1.66190 | 0.830951 | − | 0.556346i | \(-0.187797\pi\) | ||||
0.830951 | + | 0.556346i | \(0.187797\pi\) | |||||||
\(674\) | − | 4.44662i | − | 0.171278i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 31.5300 | 1.21269 | ||||||||
\(677\) | 21.4645i | 0.824948i | 0.910969 | + | 0.412474i | \(0.135335\pi\) | ||||
−0.910969 | + | 0.412474i | \(0.864665\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.51927 | −0.288563 | ||||||||
\(680\) | −11.5930 | −0.444570 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −21.8070 | −0.835032 | ||||||||
\(683\) | 24.5182 | 0.938161 | 0.469081 | − | 0.883155i | \(-0.344585\pi\) | ||||
0.469081 | + | 0.883155i | \(0.344585\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 17.1039i | − | 0.653508i | ||||||
\(686\) | 13.4837i | 0.514812i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 14.0106i | 0.534150i | ||||||||
\(689\) | 2.48511 | 0.0946750 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 42.1966i | − | 1.60523i | −0.596495 | − | 0.802617i | \(-0.703440\pi\) | ||
0.596495 | − | 0.802617i | \(-0.296560\pi\) | |||||||
\(692\) | 1.80361 | 0.0685628 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 46.7331 | 1.77396 | ||||||||
\(695\) | 62.2661 | 2.36189 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.62828 | 0.288942 | ||||||||
\(698\) | 56.0012 | 2.11968 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −8.75374 | −0.330860 | ||||||||
\(701\) | 33.5523i | 1.26725i | 0.773639 | + | 0.633627i | \(0.218435\pi\) | ||||
−0.773639 | + | 0.633627i | \(0.781565\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 32.4136i | − | 1.22250i | ||||||
\(704\) | 34.1908 | 1.28862 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 68.7398i | 2.58706i | ||||||||
\(707\) | −6.24482 | −0.234861 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.79748 | −0.367952 | −0.183976 | − | 0.982931i | \(-0.558897\pi\) | ||||
−0.183976 | + | 0.982931i | \(0.558897\pi\) | |||||||
\(710\) | 17.9818i | 0.674845i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 14.8400i | 0.556154i | ||||||||
\(713\) | 8.62778 | 0.323113 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.62314 | −0.135498 | ||||||||
\(716\) | − | 64.5629i | − | 2.41283i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 51.2999 | 1.91450 | ||||||||
\(719\) | 47.9220 | 1.78719 | 0.893594 | − | 0.448876i | \(-0.148176\pi\) | ||||
0.893594 | + | 0.448876i | \(0.148176\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.19188 | − | 4.16687i | −0.0816299 | − | 0.155182i | ||||
\(722\) | − | 25.1736i | − | 0.936866i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 42.7576i | 1.58907i | ||||||||
\(725\) | − | 1.21377i | − | 0.0450784i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.99012i | 0.370513i | 0.982690 | + | 0.185257i | \(0.0593116\pi\) | ||||
−0.982690 | + | 0.185257i | \(0.940688\pi\) | |||||||
\(728\) | − | 0.143584i | − | 0.00532156i | ||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −36.4333 | −1.34846 | ||||||||
\(731\) | 16.6549 | 0.616005 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 35.1471i | − | 1.29819i | −0.760709 | − | 0.649093i | \(-0.775148\pi\) | ||
0.760709 | − | 0.649093i | \(-0.224852\pi\) | |||||||
\(734\) | 50.3309i | 1.85775i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −20.6320 | −0.760507 | ||||||||
\(737\) | 27.7162i | 1.02094i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −46.4078 | −1.70714 | −0.853569 | − | 0.520980i | \(-0.825567\pi\) | ||||
−0.853569 | + | 0.520980i | \(0.825567\pi\) | |||||||
\(740\) | 50.8219i | 1.86825i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 7.38226i | 0.271011i | ||||||||
\(743\) | −2.38583 | −0.0875274 | −0.0437637 | − | 0.999042i | \(-0.513935\pi\) | ||||
−0.0437637 | + | 0.999042i | \(0.513935\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.61407i | 0.278958i | ||||||||
\(746\) | 53.5801i | 1.96171i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 26.1043i | − | 0.954468i | ||||||
\(749\) | 1.61437i | 0.0589876i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.39814 | −0.0510188 | −0.0255094 | − | 0.999675i | \(-0.508121\pi\) | ||||
−0.0255094 | + | 0.999675i | \(0.508121\pi\) | |||||||
\(752\) | 8.97859 | 0.327415 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.109229 | 0.00397790 | ||||||||
\(755\) | − | 41.8847i | − | 1.52434i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 48.7659 | 1.77243 | 0.886214 | − | 0.463276i | \(-0.153326\pi\) | ||||
0.886214 | + | 0.463276i | \(0.153326\pi\) | |||||||
\(758\) | −21.0083 | −0.763055 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 18.6430i | 0.676251i | ||||||||
\(761\) | −17.4136 | −0.631244 | −0.315622 | − | 0.948885i | \(-0.602213\pi\) | ||||
−0.315622 | + | 0.948885i | \(0.602213\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 7.38226i | − | 0.267256i | ||||||
\(764\) | −21.1722 | −0.765983 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 62.8941i | 2.27246i | ||||||||
\(767\) | − | 1.59769i | − | 0.0576892i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 19.7507i | − | 0.712229i | −0.934442 | − | 0.356115i | \(-0.884101\pi\) | ||
0.934442 | − | 0.356115i | \(-0.115899\pi\) | |||||||
\(770\) | − | 10.7629i | − | 0.387868i | ||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3.51447i | 0.126489i | ||||||||
\(773\) | − | 33.3915i | − | 1.20101i | −0.799622 | − | 0.600504i | \(-0.794967\pi\) | ||
0.799622 | − | 0.600504i | \(-0.205033\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 25.8583i | − | 0.928857i | ||||||
\(776\) | − | 15.2350i | − | 0.546903i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 12.9861i | 0.465573i | ||||||||
\(779\) | − | 12.2672i | − | 0.439519i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.38006 | −0.264079 | ||||||||
\(782\) | 18.7735i | 0.671341i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 19.7417 | 0.705060 | ||||||||
\(785\) | 67.1799i | 2.39775i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.38788 | −0.227703 | −0.113852 | − | 0.993498i | \(-0.536319\pi\) | ||||
−0.113852 | + | 0.993498i | \(0.536319\pi\) | |||||||
\(788\) | 23.6786 | 0.843514 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 103.160i | 3.67025i | ||||||||
\(791\) | 8.01844 | 0.285103 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.128992 | 0.00458064 | ||||||||
\(794\) | 58.8642 | 2.08901 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 4.68299i | − | 0.165984i | ||||||
\(797\) | 33.3121i | 1.17998i | 0.807412 | + | 0.589988i | \(0.200868\pi\) | ||||
−0.807412 | + | 0.589988i | \(0.799132\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 10.6732i | − | 0.377590i | ||||||
\(800\) | 61.8361i | 2.18624i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −6.82700 | −0.241070 | ||||||||
\(803\) | − | 14.9529i | − | 0.527676i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.25828i | 0.150085i | ||||||||
\(806\) | 2.32703 | 0.0819661 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 12.6528i | − | 0.445123i | ||||||
\(809\) | −10.3379 | −0.363463 | −0.181731 | − | 0.983348i | \(-0.558170\pi\) | ||||
−0.181731 | + | 0.983348i | \(0.558170\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 38.5866i | − | 1.35496i | −0.735542 | − | 0.677479i | \(-0.763072\pi\) | ||
0.735542 | − | 0.677479i | \(-0.236928\pi\) | |||||||
\(812\) | 0.178506i | 0.00626435i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −37.9147 | −1.32891 | ||||||||
\(815\) | −29.9581 | −1.04938 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 26.7832i | − | 0.937027i | ||||||
\(818\) | 32.8729i | 1.14937i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 19.2340i | 0.671682i | ||||||||
\(821\) | 18.4581i | 0.644193i | 0.946707 | + | 0.322096i | \(0.104388\pi\) | ||||
−0.946707 | + | 0.322096i | \(0.895612\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22.1002i | 0.770366i | 0.922840 | + | 0.385183i | \(0.125862\pi\) | ||||
−0.922840 | + | 0.385183i | \(0.874138\pi\) | |||||||
\(824\) | 8.44259 | − | 4.44101i | 0.294111 | − | 0.154710i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.74609 | 0.165138 | ||||||||
\(827\) | −38.8374 | −1.35051 | −0.675254 | − | 0.737586i | \(-0.735966\pi\) | ||||
−0.675254 | + | 0.737586i | \(0.735966\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 29.7102i | − | 1.03188i | −0.856625 | − | 0.515939i | \(-0.827443\pi\) | ||
0.856625 | − | 0.515939i | \(-0.172557\pi\) | |||||||
\(830\) | 73.5083 | 2.55151 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.64852 | −0.126490 | ||||||||
\(833\) | − | 23.4677i | − | 0.813106i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18.6572i | 0.645658i | ||||||||
\(836\) | −41.9790 | −1.45188 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −81.3444 | −2.81000 | ||||||||
\(839\) | 15.2721i | 0.527251i | 0.964625 | + | 0.263626i | \(0.0849184\pi\) | ||||
−0.964625 | + | 0.263626i | \(0.915082\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.9752 | 0.999147 | ||||||||
\(842\) | − | 41.0373i | − | 1.41424i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 45.5967i | − | 1.56950i | ||||||
\(845\) | −45.9690 | −1.58138 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.685747 | −0.0235626 | ||||||||
\(848\) | 21.9597 | 0.754100 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 56.2661 | 1.92991 | ||||||||
\(851\) | 15.0007 | 0.514217 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −18.2525 | −0.624953 | −0.312477 | − | 0.949925i | \(-0.601159\pi\) | ||||
−0.312477 | + | 0.949925i | \(0.601159\pi\) | |||||||
\(854\) | 0.383183i | 0.0131123i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.27090 | −0.111797 | ||||||||
\(857\) | − | 30.7422i | − | 1.05013i | −0.851061 | − | 0.525067i | \(-0.824040\pi\) | ||
0.851061 | − | 0.525067i | \(-0.175960\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.9171i | 0.440725i | 0.975418 | + | 0.220362i | \(0.0707240\pi\) | ||||
−0.975418 | + | 0.220362i | \(0.929276\pi\) | |||||||
\(860\) | 41.9940i | 1.43198i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −61.1685 | −2.08341 | ||||||||
\(863\) | −46.1058 | −1.56946 | −0.784730 | − | 0.619838i | \(-0.787198\pi\) | ||||
−0.784730 | + | 0.619838i | \(0.787198\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.62955 | −0.0894075 | ||||||||
\(866\) | 39.4455 | 1.34041 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3.80291i | 0.129079i | ||||||||
\(869\) | −42.3385 | −1.43624 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 2.95761i | − | 0.100215i | ||||||
\(872\) | 14.9574 | 0.506520 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 30.1902 | 1.02120 | ||||||||
\(875\) | 4.49131 | 0.151834 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 56.2841i | − | 1.90058i | −0.311368 | − | 0.950289i | \(-0.600787\pi\) | ||
0.311368 | − | 0.950289i | \(-0.399213\pi\) | |||||||
\(878\) | −8.56315 | −0.288992 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −32.0160 | −1.07926 | ||||||||
\(881\) | 13.7832 | 0.464368 | 0.232184 | − | 0.972672i | \(-0.425413\pi\) | ||||
0.232184 | + | 0.972672i | \(0.425413\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −36.2843 | −1.22106 | −0.610531 | − | 0.791992i | \(-0.709044\pi\) | ||||
−0.610531 | + | 0.791992i | \(0.709044\pi\) | |||||||
\(884\) | 2.78560i | 0.0936899i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | − | 74.9128i | − | 2.51675i | ||||||
\(887\) | 9.07781i | 0.304803i | 0.988319 | + | 0.152402i | \(0.0487007\pi\) | ||||
−0.988319 | + | 0.152402i | \(0.951299\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.85185i | 0.263343i | ||||||||
\(890\) | − | 118.704i | − | 3.97898i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −34.9861 | −1.17142 | ||||||||
\(893\) | −17.1638 | −0.574365 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 94.1291i | 3.14639i | ||||||||
\(896\) | − | 3.40176i | − | 0.113645i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 46.5298i | 1.55272i | ||||||||
\(899\) | −0.527302 | −0.0175865 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 26.1043i | − | 0.869661i | ||||||
\(902\) | −14.3492 | −0.477776 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 16.2463i | 0.540345i | ||||||||
\(905\) | − | 62.3381i | − | 2.07219i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28.5157 | 0.946847 | 0.473424 | − | 0.880835i | \(-0.343018\pi\) | ||||
0.473424 | + | 0.880835i | \(0.343018\pi\) | |||||||
\(908\) | −39.6307 | −1.31519 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.14851i | 0.0380729i | ||||||||
\(911\) | 11.3327 | 0.375470 | 0.187735 | − | 0.982220i | \(-0.439885\pi\) | ||||
0.187735 | + | 0.982220i | \(0.439885\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 30.1691i | 0.998452i | ||||||||
\(914\) | 12.8952 | 0.426536 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −60.3134 | −1.99281 | ||||||||
\(917\) | − | 0.451644i | − | 0.0149146i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 9.63854i | − | 0.317946i | −0.987283 | − | 0.158973i | \(-0.949182\pi\) | ||
0.987283 | − | 0.158973i | \(-0.0508183\pi\) | |||||||
\(920\) | −8.62778 | −0.284450 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 20.1930 | 0.665021 | ||||||||
\(923\) | 0.787528 | 0.0259218 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 44.9585i | − | 1.47823i | ||||||
\(926\) | 39.4109 | 1.29512 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.26096 | 0.0413931 | ||||||||
\(929\) | 36.6056i | 1.20099i | 0.799628 | + | 0.600496i | \(0.205030\pi\) | ||||
−0.799628 | + | 0.600496i | \(0.794970\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −37.7390 | −1.23684 | ||||||||
\(932\) | −13.3966 | −0.438819 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −65.0711 | −2.12919 | ||||||||
\(935\) | 38.0586i | 1.24465i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 39.4461i | 1.28865i | 0.764753 | + | 0.644324i | \(0.222861\pi\) | ||||
−0.764753 | + | 0.644324i | \(0.777139\pi\) | |||||||
\(938\) | 8.78586 | 0.286869 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 26.9115 | 0.877756 | ||||||||
\(941\) | − | 34.7821i | − | 1.13387i | −0.823764 | − | 0.566933i | \(-0.808130\pi\) | ||
0.823764 | − | 0.566933i | \(-0.191870\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.67716 | 0.184874 | ||||||||
\(944\) | − | 14.1180i | − | 0.459502i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −31.3288 | −1.01859 | ||||||||
\(947\) | 53.6529 | 1.74348 | 0.871742 | − | 0.489965i | \(-0.162991\pi\) | ||||
0.871742 | + | 0.489965i | \(0.162991\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.59563i | 0.0517963i | ||||||||
\(950\) | − | 90.4830i | − | 2.93566i | ||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.50824 | −0.0488825 | ||||||||
\(953\) | 21.1602i | 0.685445i | 0.939437 | + | 0.342722i | \(0.111349\pi\) | ||||
−0.939437 | + | 0.342722i | \(0.888651\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 30.8678 | 0.998860 | ||||||||
\(956\) | − | 45.8146i | − | 1.48175i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 24.6531i | − | 0.796507i | ||||||
\(959\) | − | 2.22522i | − | 0.0718562i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.7663 | 0.637624 | ||||||||
\(962\) | 4.04589 | 0.130445 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 71.6361i | 2.30724i | ||||||||
\(965\) | − | 5.12390i | − | 0.164944i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 6.10811i | − | 0.196424i | −0.995166 | − | 0.0982119i | \(-0.968688\pi\) | ||
0.995166 | − | 0.0982119i | \(-0.0313123\pi\) | |||||||
\(968\) | − | 1.38941i | − | 0.0446572i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 121.863i | 3.91279i | ||||||||
\(971\) | 52.7428 | 1.69260 | 0.846299 | − | 0.532709i | \(-0.178826\pi\) | ||||
0.846299 | + | 0.532709i | \(0.178826\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.10082 | 0.259700 | ||||||||
\(974\) | −41.8672 | −1.34151 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.13984 | 0.0364854 | ||||||||
\(977\) | − | 41.3547i | − | 1.32305i | −0.749921 | − | 0.661527i | \(-0.769909\pi\) | ||
0.749921 | − | 0.661527i | \(-0.230091\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 48.7184 | 1.55705 | ||||||||
\(980\) | 59.1717 | 1.89017 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 69.2093 | 2.20856 | ||||||||
\(983\) | − | 35.9511i | − | 1.14666i | −0.819324 | − | 0.573331i | \(-0.805651\pi\) | ||
0.819324 | − | 0.573331i | \(-0.194349\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −34.5220 | −1.09996 | ||||||||
\(986\) | − | 1.14738i | − | 0.0365400i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.47960 | 0.142515 | ||||||||
\(989\) | 12.3950 | 0.394139 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28.9615 | 0.919993 | 0.459997 | − | 0.887921i | \(-0.347851\pi\) | ||||
0.459997 | + | 0.887921i | \(0.347851\pi\) | |||||||
\(992\) | 26.8636 | 0.852920 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.33943i | 0.0742023i | ||||||||
\(995\) | 6.82753i | 0.216447i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.36995i | 0.233409i | 0.993167 | + | 0.116704i | \(0.0372330\pi\) | ||||
−0.993167 | + | 0.116704i | \(0.962767\pi\) | |||||||
\(998\) | −59.9824 | −1.89871 | ||||||||
\(999\) | 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 | 927.2.c.a.926.2 | yes | 16 | |
3.2 | odd | 2 | inner | 927.2.c.a.926.15 | yes | 16 | |
103.102 | odd | 2 | inner | 927.2.c.a.926.1 | ✓ | 16 | |
309.308 | even | 2 | inner | 927.2.c.a.926.16 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
927.2.c.a.926.1 | ✓ | 16 | 103.102 | odd | 2 | inner | |
927.2.c.a.926.2 | yes | 16 | 1.1 | even | 1 | trivial | |
927.2.c.a.926.15 | yes | 16 | 3.2 | odd | 2 | inner | |
927.2.c.a.926.16 | yes | 16 | 309.308 | even | 2 | inner |