Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1380,2,Mod(1241,1380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1380, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1380.1241");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1380.i (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: | \(11.0193554789\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{14} - 4 x^{13} - 2 x^{12} + 12 x^{11} + 17 x^{10} + 16 x^{9} - 110 x^{8} + 48 x^{7} + 153 x^{6} + 324 x^{5} - 162 x^{4} - 972 x^{3} - 729 x^{2} + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1241.1 | ||
Root | \(1.68259 - 0.410981i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1380.1241 |
Dual form | 1380.2.i.a.1241.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1380\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(691\) | \(1201\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.68259 | − | 0.410981i | −0.971441 | − | 0.237280i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 4.25920i | − | 1.60983i | −0.593393 | − | 0.804913i | \(-0.702212\pi\) | ||
0.593393 | − | 0.804913i | \(-0.297788\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.66219 | + | 1.38302i | 0.887396 | + | 0.461008i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.77042 | −0.533801 | −0.266900 | − | 0.963724i | \(-0.585999\pi\) | ||||
−0.266900 | + | 0.963724i | \(0.585999\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.14699 | 1.15017 | 0.575085 | − | 0.818094i | \(-0.304969\pi\) | ||||
0.575085 | + | 0.818094i | \(0.304969\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.68259 | + | 0.410981i | 0.434442 | + | 0.106115i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.86944 | 1.66609 | 0.833043 | − | 0.553209i | \(-0.186597\pi\) | ||||
0.833043 | + | 0.553209i | \(0.186597\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1.46552i | − | 0.336213i | −0.985769 | − | 0.168106i | \(-0.946235\pi\) | ||
0.985769 | − | 0.168106i | \(-0.0537652\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.75045 | + | 7.16646i | −0.381980 | + | 1.56385i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.73005 | + | 4.47291i | −0.360741 | + | 0.932666i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.91096 | − | 3.42116i | −0.752665 | − | 0.658403i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 4.10332i | − | 0.761968i | −0.924582 | − | 0.380984i | \(-0.875585\pi\) | ||
0.924582 | − | 0.380984i | \(-0.124415\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.05868 | −0.908566 | −0.454283 | − | 0.890857i | \(-0.650105\pi\) | ||||
−0.454283 | + | 0.890857i | \(0.650105\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.97888 | + | 0.727608i | 0.518556 | + | 0.126660i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.25920i | 0.719936i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 2.88245i | − | 0.473873i | −0.971525 | − | 0.236936i | \(-0.923857\pi\) | ||
0.971525 | − | 0.236936i | \(-0.0761433\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.97767 | − | 1.70434i | −1.11732 | − | 0.272912i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 4.56378i | − | 0.712742i | −0.934345 | − | 0.356371i | \(-0.884014\pi\) | ||
0.934345 | − | 0.356371i | \(-0.115986\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 3.27999i | − | 0.500193i | −0.968221 | − | 0.250097i | \(-0.919538\pi\) | ||
0.968221 | − | 0.250097i | \(-0.0804624\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.66219 | − | 1.38302i | −0.396856 | − | 0.206169i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.80230i | 0.846353i | 0.906047 | + | 0.423177i | \(0.139085\pi\) | ||||
−0.906047 | + | 0.423177i | \(0.860915\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −11.1408 | −1.59154 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −11.5584 | − | 2.82321i | −1.61850 | − | 0.395329i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.831510 | 0.114217 | 0.0571083 | − | 0.998368i | \(-0.481812\pi\) | ||||
0.0571083 | + | 0.998368i | \(0.481812\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.77042 | 0.238723 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.602301 | + | 2.46586i | −0.0797767 | + | 0.326611i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 11.8329i | − | 1.54052i | −0.637732 | − | 0.770258i | \(-0.720127\pi\) | ||
0.637732 | − | 0.770258i | \(-0.279873\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 12.0164i | − | 1.53855i | −0.638919 | − | 0.769274i | \(-0.720618\pi\) | ||
0.638919 | − | 0.769274i | \(-0.279382\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.89057 | − | 11.3388i | 0.742142 | − | 1.42855i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.14699 | −0.514371 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 10.3996i | − | 1.27051i | −0.772303 | − | 0.635254i | \(-0.780895\pi\) | ||
0.772303 | − | 0.635254i | \(-0.219105\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.74925 | − | 6.81503i | 0.571742 | − | 0.820433i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16.3046i | 1.93501i | 0.252861 | + | 0.967503i | \(0.418629\pi\) | ||||
−0.252861 | + | 0.967503i | \(0.581371\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.69014 | −0.197816 | −0.0989080 | − | 0.995097i | \(-0.531535\pi\) | ||||
−0.0989080 | + | 0.995097i | \(0.531535\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.68259 | − | 0.410981i | −0.194288 | − | 0.0474560i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.54056i | 0.859326i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 2.62553i | − | 0.295395i | −0.989033 | − | 0.147698i | \(-0.952814\pi\) | ||
0.989033 | − | 0.147698i | \(-0.0471863\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.17450 | + | 7.36373i | 0.574944 | + | 0.818193i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.22163 | −0.573149 | −0.286574 | − | 0.958058i | \(-0.592517\pi\) | ||||
−0.286574 | + | 0.958058i | \(0.592517\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.86944 | −0.745096 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.68639 | + | 6.90419i | −0.180800 | + | 0.740207i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.78113 | −1.03680 | −0.518399 | − | 0.855139i | \(-0.673472\pi\) | ||||
−0.518399 | + | 0.855139i | \(0.673472\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 17.6629i | − | 1.85157i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.51167 | + | 2.07902i | 0.882619 | + | 0.215585i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.46552i | 0.150359i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.26880i | 0.941104i | 0.882372 | + | 0.470552i | \(0.155945\pi\) | ||||
−0.882372 | + | 0.470552i | \(0.844055\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.71318 | − | 2.44853i | −0.473693 | − | 0.246086i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 10.1637i | − | 1.01133i | −0.862731 | − | 0.505663i | \(-0.831248\pi\) | ||
0.862731 | − | 0.505663i | \(-0.168752\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 9.36818i | − | 0.923074i | −0.887121 | − | 0.461537i | \(-0.847298\pi\) | ||
0.887121 | − | 0.461537i | \(-0.152702\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.75045 | − | 7.16646i | 0.170827 | − | 0.699375i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.58889 | 0.153604 | 0.0768019 | − | 0.997046i | \(-0.475529\pi\) | ||||
0.0768019 | + | 0.997046i | \(0.475529\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 9.94643i | − | 0.952695i | −0.879257 | − | 0.476347i | \(-0.841960\pi\) | ||
0.879257 | − | 0.476347i | \(-0.158040\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.18464 | + | 4.84998i | −0.112441 | + | 0.460339i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.69423 | −0.441596 | −0.220798 | − | 0.975320i | \(-0.570866\pi\) | ||||
−0.220798 | + | 0.975320i | \(0.570866\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.73005 | − | 4.47291i | 0.161328 | − | 0.417101i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 11.0401 | + | 5.73539i | 1.02066 | + | 0.530237i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 29.2583i | − | 2.68211i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.86562 | −0.715057 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.87563 | + | 7.67894i | −0.169120 | + | 0.692387i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.49918 | 0.221767 | 0.110883 | − | 0.993833i | \(-0.464632\pi\) | ||||
0.110883 | + | 0.993833i | \(0.464632\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.34801 | + | 5.51886i | −0.118686 | + | 0.485908i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.14095i | 0.536537i | 0.963344 | + | 0.268269i | \(0.0864515\pi\) | ||||
−0.963344 | + | 0.268269i | \(0.913548\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.24193 | −0.541244 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.91096 | + | 3.42116i | 0.336602 | + | 0.294447i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.5065 | 0.983071 | 0.491535 | − | 0.870858i | \(-0.336436\pi\) | ||||
0.491535 | + | 0.870858i | \(0.336436\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.8249 | −1.17262 | −0.586308 | − | 0.810088i | \(-0.699419\pi\) | ||||
−0.586308 | + | 0.810088i | \(0.699419\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.38464 | − | 9.76287i | 0.200823 | − | 0.822182i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −7.34191 | −0.613961 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.10332i | 0.340762i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 18.7453 | + | 4.57865i | 1.54609 | + | 0.377640i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −16.3047 | −1.33573 | −0.667867 | − | 0.744281i | \(-0.732792\pi\) | ||||
−0.667867 | + | 0.744281i | \(0.732792\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.81062 | 0.391483 | 0.195741 | − | 0.980656i | \(-0.437289\pi\) | ||||
0.195741 | + | 0.980656i | \(0.437289\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 18.2878 | + | 9.50060i | 1.47848 | + | 0.768078i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.05868 | 0.406323 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 12.9122i | − | 1.03050i | −0.857039 | − | 0.515252i | \(-0.827698\pi\) | ||
0.857039 | − | 0.515252i | \(-0.172302\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.39909 | − | 0.341735i | −0.110955 | − | 0.0271014i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 19.0510 | + | 7.36864i | 1.50143 | + | 0.580730i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.1862 | −0.876174 | −0.438087 | − | 0.898933i | \(-0.644344\pi\) | ||||
−0.438087 | + | 0.898933i | \(0.644344\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.97888 | − | 0.727608i | −0.231905 | − | 0.0566442i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 0.273329i | − | 0.0211508i | −0.999944 | − | 0.0105754i | \(-0.996634\pi\) | ||
0.999944 | − | 0.0105754i | \(-0.00336632\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.19756 | 0.322889 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.02684 | − | 3.90149i | 0.154997 | − | 0.298354i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.8456i | 0.976631i | 0.872667 | + | 0.488315i | \(0.162388\pi\) | ||||
−0.872667 | + | 0.488315i | \(0.837612\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 4.25920i | − | 0.321965i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.86311 | + | 19.9099i | −0.365534 | + | 1.49652i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 5.54592i | − | 0.414522i | −0.978286 | − | 0.207261i | \(-0.933545\pi\) | ||
0.978286 | − | 0.207261i | \(-0.0664549\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.79986i | 0.728418i | 0.931317 | + | 0.364209i | \(0.118661\pi\) | ||||
−0.931317 | + | 0.364209i | \(0.881339\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.93853 | + | 20.2187i | −0.365067 | + | 1.49461i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.88245i | 0.211922i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.1618 | −0.889358 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −14.5714 | + | 16.6576i | −1.05991 | + | 1.21166i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.3769 | 1.32971 | 0.664854 | − | 0.746973i | \(-0.268494\pi\) | ||||
0.664854 | + | 0.746973i | \(0.268494\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.0944 | −1.08652 | −0.543260 | − | 0.839564i | \(-0.682810\pi\) | ||||
−0.543260 | + | 0.839564i | \(0.682810\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.97767 | + | 1.70434i | 0.499682 | + | 0.122050i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 21.1615i | 1.50769i | 0.657050 | + | 0.753847i | \(0.271804\pi\) | ||||
−0.657050 | + | 0.753847i | \(0.728196\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 3.16726i | − | 0.224521i | −0.993679 | − | 0.112261i | \(-0.964191\pi\) | ||
0.993679 | − | 0.112261i | \(-0.0358092\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.27402 | + | 17.4981i | −0.301466 | + | 1.23422i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −17.4769 | −1.22663 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.56378i | 0.318748i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −10.7919 | + | 9.51502i | −0.750086 | + | 0.661340i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.59458i | 0.179471i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.16177 | 0.355351 | 0.177676 | − | 0.984089i | \(-0.443142\pi\) | ||||
0.177676 | + | 0.984089i | \(0.443142\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.70091 | − | 27.4340i | 0.459138 | − | 1.87974i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.27999i | 0.223693i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 21.5459i | 1.46263i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.84381 | + | 0.694616i | 0.192167 | + | 0.0469378i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 28.4875 | 1.91628 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 29.1017 | 1.94879 | 0.974395 | − | 0.224842i | \(-0.0721864\pi\) | ||||
0.974395 | + | 0.224842i | \(0.0721864\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.66219 | + | 1.38302i | 0.177479 | + | 0.0922015i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.42076 | −0.359789 | −0.179894 | − | 0.983686i | \(-0.557576\pi\) | ||||
−0.179894 | + | 0.983686i | \(0.557576\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.5263i | 1.02601i | 0.858386 | + | 0.513004i | \(0.171467\pi\) | ||||
−0.858386 | + | 0.513004i | \(0.828533\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.09903 | − | 12.6876i | 0.203901 | − | 0.834785i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 29.1310i | − | 1.90844i | −0.299113 | − | 0.954218i | \(-0.596691\pi\) | ||
0.299113 | − | 0.954218i | \(-0.403309\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 5.80230i | − | 0.378501i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.07904 | + | 4.41768i | −0.0700915 | + | 0.286959i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 25.1530i | − | 1.62701i | −0.581555 | − | 0.813507i | \(-0.697556\pi\) | ||
0.581555 | − | 0.813507i | \(-0.302444\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 23.5388i | 1.51627i | 0.652097 | + | 0.758135i | \(0.273889\pi\) | ||||
−0.652097 | + | 0.758135i | \(0.726111\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.68018 | − | 14.5167i | −0.364383 | − | 0.931249i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 11.1408 | 0.711757 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 6.07750i | − | 0.386702i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.78584 | + | 2.14599i | 0.556780 | + | 0.135997i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.64673 | 0.419538 | 0.209769 | − | 0.977751i | \(-0.432729\pi\) | ||||
0.209769 | + | 0.977751i | \(0.432729\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.06292 | − | 7.91891i | 0.192564 | − | 0.497858i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 11.5584 | + | 2.82321i | 0.723817 | + | 0.176797i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.11601i | 0.381506i | 0.981638 | + | 0.190753i | \(0.0610930\pi\) | ||||
−0.981638 | + | 0.190753i | \(0.938907\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12.2769 | −0.762852 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.67499 | − | 10.9238i | 0.351273 | − | 0.676167i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.17715 | −0.504225 | −0.252112 | − | 0.967698i | \(-0.581125\pi\) | ||||
−0.252112 | + | 0.967698i | \(0.581125\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.831510 | −0.0510792 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 16.4576 | + | 4.01986i | 1.00719 | + | 0.246012i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.00864764i | 0.000527256i | 1.00000 | 0.000263628i | \(8.39153e-5\pi\) | |||||
−1.00000 | 0.000263628i | \(0.999916\pi\) | ||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.9068 | 1.45223 | 0.726117 | − | 0.687571i | \(-0.241323\pi\) | ||||
0.726117 | + | 0.687571i | \(0.241323\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −7.25911 | + | 29.7193i | −0.439341 | + | 1.79869i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.77042 | −0.106760 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.6195 | 1.35907 | 0.679537 | − | 0.733641i | \(-0.262181\pi\) | ||||
0.679537 | + | 0.733641i | \(0.262181\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −13.4672 | − | 6.99627i | −0.806258 | − | 0.418856i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −32.6193 | −1.94590 | −0.972951 | − | 0.231013i | \(-0.925796\pi\) | ||||
−0.972951 | + | 0.231013i | \(0.925796\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.2989i | 0.731095i | 0.930793 | + | 0.365548i | \(0.119118\pi\) | ||||
−0.930793 | + | 0.365548i | \(0.880882\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.602301 | − | 2.46586i | 0.0356772 | − | 0.146065i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −19.4380 | −1.14739 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 30.1893 | 1.77584 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.80930 | − | 15.5955i | 0.223305 | − | 0.914227i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 22.1635 | 1.29481 | 0.647403 | − | 0.762148i | \(-0.275855\pi\) | ||||
0.647403 | + | 0.762148i | \(0.275855\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.8329i | 0.688940i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.92404 | + | 6.05689i | 0.401773 | + | 0.351456i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7.17452 | + | 18.5491i | −0.414913 | + | 1.07272i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13.9701 | −0.805223 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.17709 | + | 17.1013i | −0.239967 | + | 0.982443i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12.0164i | 0.688059i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 27.1627 | 1.55026 | 0.775129 | − | 0.631803i | \(-0.217685\pi\) | ||||
0.775129 | + | 0.631803i | \(0.217685\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.85015 | + | 15.7628i | −0.219027 | + | 0.896712i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 13.8045i | − | 0.782781i | −0.920225 | − | 0.391391i | \(-0.871994\pi\) | ||
0.920225 | − | 0.391391i | \(-0.128006\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 32.9723i | − | 1.86371i | −0.362834 | − | 0.931854i | \(-0.618191\pi\) | ||
0.362834 | − | 0.931854i | \(-0.381809\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5.89057 | + | 11.3388i | −0.331896 | + | 0.638868i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 10.9658i | − | 0.615900i | −0.951402 | − | 0.307950i | \(-0.900357\pi\) | ||
0.951402 | − | 0.307950i | \(-0.0996430\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.26459i | 0.406739i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.67344 | − | 0.653004i | −0.149217 | − | 0.0364471i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 10.0673i | − | 0.560159i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.14699 | 0.230034 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.08780 | + | 16.7357i | −0.226056 | + | 0.925487i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 24.7132 | 1.36248 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.0444 | −0.991811 | −0.495905 | − | 0.868377i | \(-0.665164\pi\) | ||||
−0.495905 | + | 0.868377i | \(0.665164\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.98650 | − | 7.67364i | 0.218459 | − | 0.420513i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10.3996i | 0.568188i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 0.830721i | − | 0.0452523i | −0.999744 | − | 0.0226261i | \(-0.992797\pi\) | ||
0.999744 | − | 0.0226261i | \(-0.00720274\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.89845 | + | 1.92924i | 0.428985 | + | 0.104782i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.95598 | 0.484993 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.6363i | 0.952272i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.74925 | + | 6.81503i | −0.255691 | + | 0.366909i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.54648i | 0.351434i | 0.984441 | + | 0.175717i | \(0.0562243\pi\) | ||||
−0.984441 | + | 0.175717i | \(0.943776\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.4584 | 0.934529 | 0.467264 | − | 0.884118i | \(-0.345240\pi\) | ||||
0.467264 | + | 0.884118i | \(0.345240\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −16.2187 | − | 14.1875i | −0.865693 | − | 0.757275i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 11.3823i | − | 0.605819i | −0.953019 | − | 0.302909i | \(-0.902042\pi\) | ||
0.953019 | − | 0.302909i | \(-0.0979579\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 16.3046i | − | 0.865361i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −12.0246 | + | 49.2296i | −0.636411 | + | 2.60551i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 30.3119 | 1.59980 | 0.799900 | − | 0.600134i | \(-0.204886\pi\) | ||||
0.799900 | + | 0.600134i | \(0.204886\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.8523 | 0.886961 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 13.2346 | + | 3.23262i | 0.694636 | + | 0.169669i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.69014 | 0.0884660 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.1215i | 0.580540i | 0.956945 | + | 0.290270i | \(0.0937451\pi\) | ||||
−0.956945 | + | 0.290270i | \(0.906255\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.31180 | − | 12.1496i | 0.328579 | − | 0.632485i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 3.54156i | − | 0.183869i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.32753i | 0.379405i | 0.981842 | + | 0.189703i | \(0.0607524\pi\) | ||||
−0.981842 | + | 0.189703i | \(0.939248\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.68259 | + | 0.410981i | 0.0868883 | + | 0.0212230i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 17.0164i | − | 0.876392i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.54185i | 0.0791997i | 0.999216 | + | 0.0395998i | \(0.0126083\pi\) | ||||
−0.999216 | + | 0.0395998i | \(0.987392\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.20509 | − | 1.02712i | −0.215433 | − | 0.0526208i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 33.1055 | 1.69161 | 0.845805 | − | 0.533492i | \(-0.179121\pi\) | ||||
0.845805 | + | 0.533492i | \(0.179121\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 7.54056i | − | 0.384302i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.53629 | − | 8.73194i | 0.230593 | − | 0.443869i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −27.5503 | −1.39686 | −0.698428 | − | 0.715680i | \(-0.746117\pi\) | ||||
−0.698428 | + | 0.715680i | \(0.746117\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.8845 | + | 30.7264i | −0.601025 | + | 1.55390i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.52382 | − | 10.3327i | 0.127310 | − | 0.521215i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.62553i | 0.132105i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.4334 | 0.674205 | 0.337102 | − | 0.941468i | \(-0.390553\pi\) | ||||
0.337102 | + | 0.941468i | \(0.390553\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 10.5026 | + | 2.56532i | 0.525787 | + | 0.128427i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −17.8416 | −0.890965 | −0.445483 | − | 0.895291i | \(-0.646968\pi\) | ||||
−0.445483 | + | 0.895291i | \(0.646968\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −20.9783 | −1.04501 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −5.17450 | − | 7.36373i | −0.257123 | − | 0.365907i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.10315i | 0.252954i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.54963 | −0.373305 | −0.186653 | − | 0.982426i | \(-0.559764\pi\) | ||||
−0.186653 | + | 0.982426i | \(0.559764\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −19.3607 | − | 4.72898i | −0.954995 | − | 0.233263i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −50.3988 | −2.47996 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.22163 | 0.256320 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 23.2616 | + | 5.68179i | 1.13913 | + | 0.278238i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.14328 | −0.300119 | −0.150059 | − | 0.988677i | \(-0.547946\pi\) | ||||
−0.150059 | + | 0.988677i | \(0.547946\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 38.8307i | − | 1.89249i | −0.323449 | − | 0.946246i | \(-0.604842\pi\) | ||
0.323449 | − | 0.946246i | \(-0.395158\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8.02472 | + | 15.4468i | −0.390175 | + | 0.751051i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.86944 | 0.333217 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −51.1804 | −2.47679 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 12.3534 | + | 3.01739i | 0.596427 | + | 0.145681i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −25.7768 | −1.24163 | −0.620813 | − | 0.783959i | \(-0.713197\pi\) | ||||
−0.620813 | + | 0.783959i | \(0.713197\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 32.6236i | 1.56779i | 0.620894 | + | 0.783894i | \(0.286770\pi\) | ||||
−0.620894 | + | 0.783894i | \(0.713230\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.68639 | − | 6.90419i | 0.0808561 | − | 0.331031i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.55513 | + | 2.53543i | 0.313574 | + | 0.121286i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.8107 | −0.945513 | −0.472757 | − | 0.881193i | \(-0.656741\pi\) | ||||
−0.472757 | + | 0.881193i | \(0.656741\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −29.6588 | − | 15.4079i | −1.41232 | − | 0.733711i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.51886i | 0.0721631i | 0.999349 | + | 0.0360816i | \(0.0114876\pi\) | ||||
−0.999349 | + | 0.0360816i | \(0.988512\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.78113 | 0.463670 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 27.4341 | + | 6.70093i | 1.29759 | + | 0.316943i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 12.0706i | − | 0.569646i | −0.958580 | − | 0.284823i | \(-0.908065\pi\) | ||
0.958580 | − | 0.284823i | \(-0.0919348\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.07979i | 0.380462i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8.09428 | − | 1.97707i | −0.380302 | − | 0.0928911i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 17.6629i | 0.828048i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 36.0870i | − | 1.68808i | −0.536281 | − | 0.844039i | \(-0.680171\pi\) | ||
0.536281 | − | 0.844039i | \(-0.319829\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −26.8661 | − | 23.5015i | −1.25400 | − | 1.09696i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 39.9476i | 1.86054i | 0.366872 | + | 0.930271i | \(0.380429\pi\) | ||||
−0.366872 | + | 0.930271i | \(0.619571\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.60520 | 0.214022 | 0.107011 | − | 0.994258i | \(-0.465872\pi\) | ||||
0.107011 | + | 0.994258i | \(0.465872\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −8.51167 | − | 2.07902i | −0.394719 | − | 0.0964125i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 30.4087 | 1.40715 | 0.703573 | − | 0.710623i | \(-0.251587\pi\) | ||||
0.703573 | + | 0.710623i | \(0.251587\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −44.2938 | −2.04530 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.30666 | + | 21.7258i | −0.244518 | + | 1.00107i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.80694i | 0.267003i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 1.46552i | − | 0.0672426i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.21364 | + | 1.15000i | 0.101355 | + | 0.0526547i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −31.0474 | −1.41859 | −0.709297 | − | 0.704910i | \(-0.750987\pi\) | ||||
−0.709297 | + | 0.704910i | \(0.750987\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 11.9535i | − | 0.545034i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −29.0266 | − | 20.2280i | −1.32075 | − | 0.920405i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 9.26880i | − | 0.420875i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.7747 | −0.533563 | −0.266782 | − | 0.963757i | \(-0.585960\pi\) | ||||
−0.266782 | + | 0.963757i | \(0.585960\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 18.8218 | + | 4.59733i | 0.851151 | + | 0.207899i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 23.6929i | 1.06924i | 0.845091 | + | 0.534622i | \(0.179546\pi\) | ||||
−0.845091 | + | 0.534622i | \(0.820454\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 28.1875i | − | 1.26950i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.71318 | + | 2.44853i | 0.211842 | + | 0.110053i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 69.4447 | 3.11502 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 36.7997 | 1.64738 | 0.823689 | − | 0.567041i | \(-0.191912\pi\) | ||||
0.823689 | + | 0.567041i | \(0.191912\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.112333 | + | 0.459899i | −0.00501867 | + | 0.0205468i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 39.7986 | 1.77453 | 0.887266 | − | 0.461259i | \(-0.152602\pi\) | ||||
0.887266 | + | 0.461259i | \(0.152602\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.1637i | 0.452278i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.06276 | − | 1.72512i | −0.313668 | − | 0.0766153i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10.3012i | 0.456593i | 0.973592 | + | 0.228297i | \(0.0733156\pi\) | ||||
−0.973592 | + | 0.228297i | \(0.926684\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.19864i | 0.318449i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.01378 | + | 5.73159i | −0.221364 | + | 0.253056i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9.36818i | 0.412811i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 10.2725i | − | 0.451784i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.27929 | − | 21.6138i | 0.231735 | − | 0.948739i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −24.8553 | −1.08893 | −0.544465 | − | 0.838784i | \(-0.683267\pi\) | ||||
−0.544465 | + | 0.838784i | \(0.683267\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 12.6351i | − | 0.552496i | −0.961086 | − | 0.276248i | \(-0.910909\pi\) | ||
0.961086 | − | 0.276248i | \(-0.0890912\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.75045 | + | 7.16646i | −0.0763959 | + | 0.312770i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −34.7503 | −1.51375 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.0138 | − | 15.4767i | −0.739732 | − | 0.672902i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 16.3652 | − | 31.5015i | 0.710190 | − | 1.36705i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 18.9260i | − | 0.819774i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.58889 | −0.0686937 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.27927 | + | 9.33149i | −0.0983578 | + | 0.402683i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 19.7238 | 0.849564 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.7627 | −0.935653 | −0.467826 | − | 0.883820i | \(-0.654963\pi\) | ||||
−0.467826 | + | 0.883820i | \(0.654963\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.02756 | − | 16.4891i | 0.172839 | − | 0.707615i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.94643i | 0.426058i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.652614 | 0.0279038 | 0.0139519 | − | 0.999903i | \(-0.495559\pi\) | ||||
0.0139519 | + | 0.999903i | \(0.495559\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 16.6190 | − | 31.9900i | 0.709282 | − | 1.36530i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.01349 | −0.256183 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.1827 | −0.475535 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.18464 | − | 4.84998i | 0.0502850 | − | 0.205870i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −43.7961 | −1.85570 | −0.927850 | − | 0.372953i | \(-0.878345\pi\) | ||||
−0.927850 | + | 0.372953i | \(0.878345\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 13.6021i | − | 0.575307i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 20.4632 | + | 4.99827i | 0.863959 | + | 0.211027i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.04662 | 0.170545 | 0.0852723 | − | 0.996358i | \(-0.472824\pi\) | ||||
0.0852723 | + | 0.996358i | \(0.472824\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.69423 | 0.197488 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 31.3636 | − | 22.0392i | 1.31715 | − | 0.925560i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −17.6778 | −0.741092 | −0.370546 | − | 0.928814i | \(-0.620829\pi\) | ||||
−0.370546 | + | 0.928814i | \(0.620829\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 9.47431i | − | 0.396488i | −0.980153 | − | 0.198244i | \(-0.936476\pi\) | ||
0.980153 | − | 0.198244i | \(-0.0635238\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −30.9208 | − | 7.55257i | −1.29173 | − | 0.315513i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.73005 | + | 4.47291i | −0.0721482 | + | 0.186533i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 27.6920 | 1.15284 | 0.576418 | − | 0.817155i | \(-0.304450\pi\) | ||||
0.576418 | + | 0.817155i | \(0.304450\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 25.3977 | + | 6.20353i | 1.05549 | + | 0.257810i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 22.2400i | 0.922669i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.47212 | −0.0609689 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −11.0401 | − | 5.73539i | −0.456451 | − | 0.237129i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 33.9922i | − | 1.40301i | −0.712665 | − | 0.701504i | \(-0.752512\pi\) | ||
0.712665 | − | 0.701504i | \(-0.247488\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.41359i | 0.305472i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.69698 | − | 35.6060i | 0.357746 | − | 1.46464i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 45.4678i | − | 1.86714i | −0.358398 | − | 0.933569i | \(-0.616677\pi\) | ||
0.358398 | − | 0.933569i | \(-0.383323\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 29.2583i | 1.19947i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.30169 | + | 5.32919i | −0.0532745 | + | 0.218109i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 23.7247i | − | 0.969364i | −0.874691 | − | 0.484682i | \(-0.838935\pi\) | ||
0.874691 | − | 0.484682i | \(-0.161065\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 34.9900 | 1.42727 | 0.713636 | − | 0.700517i | \(-0.247047\pi\) | ||||
0.713636 | + | 0.700517i | \(0.247047\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.3828 | − | 27.6856i | 0.585714 | − | 1.12744i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.86562 | 0.319783 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 26.2120 | 1.06391 | 0.531955 | − | 0.846773i | \(-0.321457\pi\) | ||||
0.531955 | + | 0.846773i | \(0.321457\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 29.4063 | + | 7.18266i | 1.19160 | + | 0.291056i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 24.0621i | 0.973449i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 27.1765i | 1.09765i | 0.835938 | + | 0.548824i | \(0.184924\pi\) | ||||
−0.835938 | + | 0.548824i | \(0.815076\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.87563 | − | 7.67894i | 0.0756326 | − | 0.309645i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.364713 | 0.0146828 | 0.00734140 | − | 0.999973i | \(-0.497663\pi\) | ||||
0.00734140 | + | 0.999973i | \(0.497663\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 0.854713i | − | 0.0343538i | −0.999852 | − | 0.0171769i | \(-0.994532\pi\) | ||
0.999852 | − | 0.0171769i | \(-0.00546785\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 22.0687 | − | 11.5746i | 0.885588 | − | 0.464472i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 41.6598i | 1.66906i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.06632 | − | 4.36560i | 0.0425848 | − | 0.174345i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 19.8009i | − | 0.789512i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 43.6340i | 1.73704i | 0.495654 | + | 0.868520i | \(0.334928\pi\) | ||||
−0.495654 | + | 0.868520i | \(0.665072\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.68512 | − | 2.12139i | −0.345203 | − | 0.0843178i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.49918 | −0.0991770 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −46.2007 | −1.83054 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −22.5497 | + | 43.4060i | −0.892052 | + | 1.71712i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.9445 | −0.432282 | −0.216141 | − | 0.976362i | \(-0.569347\pi\) | ||||
−0.216141 | + | 0.976362i | \(0.569347\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 27.3836i | 1.07990i | 0.841696 | + | 0.539952i | \(0.181558\pi\) | ||||
−0.841696 | + | 0.539952i | \(0.818442\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.34801 | − | 5.51886i | 0.0530780 | − | 0.217305i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11.8734i | 0.466791i | 0.972382 | + | 0.233395i | \(0.0749836\pi\) | ||||
−0.972382 | + | 0.233395i | \(0.925016\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 20.9492i | 0.822329i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.85498 | − | 36.2529i | 0.347054 | − | 1.42086i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 15.0075i | − | 0.587289i | −0.955915 | − | 0.293644i | \(-0.905132\pi\) | ||
0.955915 | − | 0.293644i | \(-0.0948681\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 6.14095i | − | 0.239947i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.49947 | − | 2.33750i | −0.175541 | − | 0.0911946i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 25.1920 | 0.981342 | 0.490671 | − | 0.871345i | \(-0.336752\pi\) | ||||
0.490671 | + | 0.871345i | \(0.336752\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.3817i | 0.442698i | 0.975195 | + | 0.221349i | \(0.0710459\pi\) | ||||
−0.975195 | + | 0.221349i | \(0.928954\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −47.9327 | − | 11.7079i | −1.86155 | − | 0.454695i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.24193 | 0.242052 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18.3538 | + | 7.09897i | 0.710661 | + | 0.274873i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −48.9660 | − | 11.9602i | −1.89314 | − | 0.462409i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 21.2741i | 0.821278i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.04251 | 0.271469 | 0.135734 | − | 0.990745i | \(-0.456661\pi\) | ||||
0.135734 | + | 0.990745i | \(0.456661\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.91096 | − | 3.42116i | −0.150533 | − | 0.131681i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.06545 | 0.156248 | 0.0781239 | − | 0.996944i | \(-0.475107\pi\) | ||||
0.0781239 | + | 0.996944i | \(0.475107\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 39.4776 | 1.51501 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.12090 | + | 2.22783i | 0.349514 | + | 0.0853707i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 45.4211i | − | 1.73799i | −0.494819 | − | 0.868996i | \(-0.664766\pi\) | ||
0.494819 | − | 0.868996i | \(-0.335234\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11.5065 | −0.439643 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.38102 | − | 26.1243i | 0.243451 | − | 0.996706i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.44827 | 0.131369 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15.9715 | −0.607586 | −0.303793 | − | 0.952738i | \(-0.598253\pi\) | ||||
−0.303793 | + | 0.952738i | \(0.598253\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −10.4288 | + | 20.0744i | −0.396156 | + | 0.762563i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 13.8249 | 0.524410 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 31.3506i | − | 1.18749i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −11.9723 | + | 49.0154i | −0.452834 | + | 1.85393i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19.3116 | 0.729391 | 0.364695 | − | 0.931127i | \(-0.381173\pi\) | ||||
0.364695 | + | 0.931127i | \(0.381173\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.22429 | −0.159322 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.38464 | + | 9.76287i | −0.0898107 | + | 0.367691i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −43.2892 | −1.62806 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 35.6708i | − | 1.33964i | −0.742521 | − | 0.669822i | \(-0.766370\pi\) | ||
0.742521 | − | 0.669822i | \(-0.233630\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.63117 | − | 6.98966i | 0.136180 | − | 0.262133i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.75179 | − | 22.6270i | 0.327757 | − | 0.847389i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.34191 | 0.274572 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −10.3374 | + | 42.3221i | −0.386058 | + | 1.58055i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.77126i | 0.327113i | 0.986534 | + | 0.163556i | \(0.0522966\pi\) | ||||
−0.986534 | + | 0.163556i | \(0.947703\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −39.9009 | −1.48599 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.67403 | − | 39.6061i | 0.359781 | − | 1.47297i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 4.10332i | − | 0.152394i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26.4591i | 0.981315i | 0.871353 | + | 0.490657i | \(0.163243\pi\) | ||||
−0.871353 | + | 0.490657i | \(0.836757\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.59127 | + | 26.7601i | 0.133010 | + | 0.991115i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 22.5317i | − | 0.833364i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 40.6758i | 1.50240i | 0.660077 | + | 0.751198i | \(0.270523\pi\) | ||||
−0.660077 | + | 0.751198i | \(0.729477\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −18.7453 | − | 4.57865i | −0.691430 | − | 0.168886i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 18.4115i | 0.678198i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.06596 | −0.149569 | −0.0747844 | − | 0.997200i | \(-0.523827\pi\) | ||||
−0.0747844 | + | 0.997200i | \(0.523827\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.49774 | + | 10.2259i | −0.0917567 | + | 0.375658i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 37.8267 | 1.38773 | 0.693863 | − | 0.720107i | \(-0.255907\pi\) | ||||
0.693863 | + | 0.720107i | \(0.255907\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 16.3047 | 0.597358 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −13.9010 | − | 7.22164i | −0.508610 | − | 0.264226i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 6.76739i | − | 0.247275i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 37.9249i | − | 1.38390i | −0.721946 | − | 0.691950i | \(-0.756752\pi\) | ||
0.721946 | − | 0.691950i | \(-0.243248\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −11.1837 | − | 2.73168i | −0.407556 | − | 0.0995480i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.81062 | −0.175076 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14.6543i | 0.532618i | 0.963888 | + | 0.266309i | \(0.0858041\pi\) | ||||
−0.963888 | + | 0.266309i | \(0.914196\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −8.40815 | + | 12.0654i | −0.305196 | + | 0.437948i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.11993i | 0.258097i | 0.991638 | + | 0.129049i | \(0.0411923\pi\) | ||||
−0.991638 | + | 0.129049i | \(0.958808\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −42.3638 | −1.53367 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −18.2878 | − | 9.50060i | −0.661195 | − | 0.343495i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 49.0711i | − | 1.77185i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 32.0781i | − | 1.15676i | −0.815766 | − | 0.578382i | \(-0.803684\pi\) | ||
0.815766 | − | 0.578382i | \(-0.196316\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.51356 | − | 10.2907i | 0.0905238 | − | 0.370611i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8.51413 | 0.306232 | 0.153116 | − | 0.988208i | \(-0.451069\pi\) | ||||
0.153116 | + | 0.988208i | \(0.451069\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.05868 | −0.181713 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 20.6570 | + | 5.04559i | 0.741066 | + | 0.181010i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.68830 | −0.239633 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 28.8660i | − | 1.03291i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −14.0381 | + | 16.0479i | −0.501682 | + | 0.573507i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.9122i | 0.460855i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.9810i | 0.427078i | 0.976935 | + | 0.213539i | \(0.0684990\pi\) | ||||
−0.976935 | + | 0.213539i | \(0.931501\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 13.7588 | + | 3.36066i | 0.489825 | + | 0.119643i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 19.9937i | 0.710893i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 49.8321i | − | 1.76959i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.39909 | + | 0.341735i | 0.0496205 | + | 0.0121201i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −15.5987 | −0.552533 | −0.276266 | − | 0.961081i | \(-0.589097\pi\) | ||||
−0.276266 | + | 0.961081i | \(0.589097\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 39.8586i | 1.41010i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −26.0392 | − | 13.5275i | −0.920051 | − | 0.477972i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.99225 | 0.105594 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −19.0510 | − | 7.36864i | −0.671460 | − | 0.259710i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.00355402 | − | 0.0145504i | 0.000125107 | − | 0.000512198i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 12.8819i | 0.452904i | 0.974022 | + | 0.226452i | \(0.0727127\pi\) | ||||
−0.974022 | + | 0.226452i | \(0.927287\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18.9804 | 0.666491 | 0.333245 | − | 0.942840i | \(-0.391856\pi\) | ||||
0.333245 | + | 0.942840i | \(0.391856\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −40.2252 | − | 9.82525i | −1.41076 | − | 0.344587i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 11.1862 | 0.391837 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.80688 | −0.168171 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 24.4281 | − | 47.0219i | 0.853589 | − | 1.64308i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 10.5143i | − | 0.366952i | −0.983024 | − | 0.183476i | \(-0.941265\pi\) | ||
0.983024 | − | 0.183476i | \(-0.0587350\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.7205 | 0.722270 | 0.361135 | − | 0.932514i | \(-0.382389\pi\) | ||||
0.361135 | + | 0.932514i | \(0.382389\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.97888 | + | 0.727608i | 0.103711 | + | 0.0253321i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −45.9796 | −1.59887 | −0.799434 | − | 0.600754i | \(-0.794867\pi\) | ||||
−0.799434 | + | 0.600754i | \(0.794867\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 46.1501 | 1.60286 | 0.801429 | − | 0.598089i | \(-0.204073\pi\) | ||||
0.801429 | + | 0.598089i | \(0.204073\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −38.0593 | − | 9.29619i | −1.32026 | − | 0.322481i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −76.5309 | −2.65164 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.273329i | 0.00945894i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 19.7843 | + | 17.3066i | 0.683846 | + | 0.598203i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −53.3483 | −1.84179 | −0.920894 | − | 0.389812i | \(-0.872540\pi\) | ||||
−0.920894 | + | 0.389812i | \(0.872540\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.1628 | 0.419405 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 54.8847 | + | 13.4059i | 1.89033 | + | 0.461724i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.19756 | −0.144401 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 33.5012i | 1.15112i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.05463 | − | 20.6940i | 0.173474 | − | 0.710216i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.8930 | + | 4.98680i | 0.441965 | + | 0.170945i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −20.9563 | −0.717530 | −0.358765 | − | 0.933428i | \(-0.616802\pi\) | ||||
−0.358765 | + | 0.933428i | \(0.616802\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.02684 | + | 3.90149i | −0.0693166 | + | 0.133428i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 44.3899i | 1.51633i | 0.652063 | + | 0.758165i | \(0.273904\pi\) | ||||
−0.652063 | + | 0.758165i | \(0.726096\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13.2571 | −0.452326 | −0.226163 | − | 0.974089i | \(-0.572618\pi\) | ||||
−0.226163 | + | 0.974089i | \(0.572618\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 32.7061 | + | 7.98866i | 1.11462 | + | 0.272253i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 34.1455i | − | 1.16233i | −0.813787 | − | 0.581164i | \(-0.802598\pi\) | ||
0.813787 | − | 0.581164i | \(-0.197402\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 12.8456i | − | 0.436762i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −50.7960 | − | 12.4072i | −1.72512 | − | 0.421372i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.64829i | 0.157682i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 43.1269i | − | 1.46130i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −12.8190 | + | 24.6753i | −0.433856 | + | 0.835132i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.25920i | 0.143987i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.23583 | −0.210569 | −0.105284 | − | 0.994442i | \(-0.533575\pi\) | ||||
−0.105284 | + | 0.994442i | \(0.533575\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −37.2920 | − | 9.10879i | −1.25783 | − | 0.307232i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 32.4198 | 1.09225 | 0.546125 | − | 0.837704i | \(-0.316102\pi\) | ||||
0.546125 | + | 0.837704i | \(0.316102\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 47.9132 | 1.61241 | 0.806204 | − | 0.591637i | \(-0.201518\pi\) | ||||
0.806204 | + | 0.591637i | \(0.201518\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.86311 | − | 19.9099i | 0.163472 | − | 0.669265i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.06146i | 0.203524i | 0.994809 | + | 0.101762i | \(0.0324480\pi\) | ||||
−0.994809 | + | 0.101762i | \(0.967552\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 10.6445i | − | 0.357005i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −9.16102 | − | 13.0369i | −0.306906 | − | 0.436752i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.50338 | 0.284555 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.54592i | 0.185380i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 19.6951 | − | 28.2619i | 0.657600 | − | 0.943637i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 20.7574i | 0.692298i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.71201 | 0.190295 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 23.5059 | + | 5.74145i | 0.782227 | + | 0.191064i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 9.79986i | − | 0.325758i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 26.5492i | − | 0.881552i | −0.897617 | − | 0.440776i | \(-0.854703\pi\) | ||
0.897617 | − | 0.440776i | \(-0.145297\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 14.0566 | − | 27.0577i | 0.466229 | − | 0.897446i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33.4165 | 1.10714 | 0.553569 | − | 0.832804i | \(-0.313266\pi\) | ||||
0.553569 | + | 0.832804i | \(0.313266\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.24447 | 0.305947 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.93853 | − | 20.2187i | 0.163263 | − | 0.668409i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 26.1555 | 0.863732 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 43.3201i | 1.42900i | 0.699637 | + | 0.714498i | \(0.253345\pi\) | ||||
−0.699637 | + | 0.714498i | \(0.746655\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −45.7036 | − | 11.1634i | −1.50599 | − | 0.367846i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 67.6153i | 2.22558i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 2.88245i | − | 0.0947745i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 12.9564 | − | 24.9399i | 0.425544 | − | 0.819132i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 18.3726i | 0.602785i | 0.953500 | + | 0.301393i | \(0.0974515\pi\) | ||||
−0.953500 | + | 0.301393i | \(0.902549\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 16.3270i | 0.535095i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.67339 | + | 23.2273i | −0.185739 | + | 0.760426i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 12.1618 | 0.397733 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 36.2126i | 1.18301i | 0.806300 | + | 0.591507i | \(0.201467\pi\) | ||||
−0.806300 | + | 0.591507i | \(0.798533\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −13.5510 | + | 55.4788i | −0.442221 | + | 1.81048i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16.1480 | 0.526409 | 0.263204 | − | 0.964740i | \(-0.415221\pi\) | ||||
0.263204 | + | 0.964740i | \(0.415221\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 20.4134 | + | 7.89558i | 0.664750 | + | 0.257115i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 14.5714 | − | 16.6576i | 0.474008 | − | 0.541871i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 32.7857i | − | 1.06539i | −0.846306 | − | 0.532697i | \(-0.821179\pi\) | ||
0.846306 | − | 0.532697i | \(-0.178821\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.00900 | −0.227522 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.50674 | + | 18.4509i | −0.146141 | + | 0.598311i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.84790 | 0.124646 | 0.0623228 | − | 0.998056i | \(-0.480149\pi\) | ||||
0.0623228 | + | 0.998056i | \(0.480149\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −18.3769 | −0.594663 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.98561 | − | 12.2233i | 0.0965111 | − | 0.395123i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 49.0087i | − | 1.58257i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.40973 | −0.174507 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.22992 | + | 2.19747i | 0.136307 | + | 0.0708125i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 15.0944 | 0.485907 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25.0017 | 0.804001 | 0.402001 | − | 0.915639i | \(-0.368315\pi\) | ||||
0.402001 | + | 0.915639i | \(0.368315\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.13747 | + | 16.9391i | −0.132915 | + | 0.544162i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −26.2788 | −0.843326 | −0.421663 | − | 0.906753i | \(-0.638553\pi\) | ||||
−0.421663 | + | 0.906753i | \(0.638553\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 58.8831i | 1.88771i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.97767 | − | 1.70434i | −0.223464 | − | 0.0545825i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −21.4585 | −0.686517 | −0.343258 | − | 0.939241i | \(-0.611531\pi\) | ||||
−0.343258 | + | 0.939241i | \(0.611531\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17.3167 | 0.553444 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 13.7561 | − | 26.4793i | 0.439199 | − | 0.845418i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −14.7143 | −0.469313 | −0.234656 | − | 0.972078i | \(-0.575397\pi\) | ||||
−0.234656 | + | 0.972078i | \(0.575397\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 21.1615i | − | 0.674262i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −41.5820 | − | 10.1566i | −1.32357 | − | 0.323290i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 14.6711 | + | 5.67455i | 0.466513 | + | 0.180440i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 38.7963 | 1.23240 | 0.616202 | − | 0.787588i | \(-0.288670\pi\) | ||||
0.616202 | + | 0.787588i | \(0.288670\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 30.3613 | + | 7.41592i | 0.963486 | + | 0.235337i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.16726i | 0.100409i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.4649 | 0.363097 | 0.181549 | − | 0.983382i | \(-0.441889\pi\) | ||||
0.181549 | + | 0.983382i | \(0.441889\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −9.86135 | + | 11.2732i | −0.311999 | + | 0.356667i |
(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 | 1380.2.i.a.1241.1 | ✓ | 16 | |
3.2 | odd | 2 | 1380.2.i.b.1241.2 | yes | 16 | ||
23.22 | odd | 2 | 1380.2.i.b.1241.1 | yes | 16 | ||
69.68 | even | 2 | inner | 1380.2.i.a.1241.2 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1380.2.i.a.1241.1 | ✓ | 16 | 1.1 | even | 1 | trivial | |
1380.2.i.a.1241.2 | yes | 16 | 69.68 | even | 2 | inner | |
1380.2.i.b.1241.1 | yes | 16 | 23.22 | odd | 2 | ||
1380.2.i.b.1241.2 | yes | 16 | 3.2 | odd | 2 |