Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1512,2,Mod(757,1512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1512, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1512.757");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1512.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: | \(12.0733807856\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\Q(\zeta_{40})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{12} + x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 757.11 | ||
Root | \(0.987688 - 0.156434i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1512.757 |
Dual form | 1512.2.c.d.757.10 |
$q$-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 \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1081\) | \(1135\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.437016 | + | 1.34500i | 0.309017 | + | 0.951057i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.61803 | + | 1.17557i | −0.809017 | + | 0.587785i | ||||
\(5\) | 0.0549306i | 0.0245657i | 0.999925 | + | 0.0122828i | \(0.00390985\pi\) | ||||
−0.999925 | + | 0.0122828i | \(0.996090\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −2.28825 | − | 1.66251i | −0.809017 | − | 0.587785i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.0738814 | + | 0.0240055i | −0.0233634 | + | 0.00759122i | ||||
\(11\) | − | 2.63506i | − | 0.794502i | −0.917710 | − | 0.397251i | \(-0.869964\pi\) | ||
0.917710 | − | 0.397251i | \(-0.130036\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 3.67853i | − | 1.02024i | −0.860103 | − | 0.510121i | \(-0.829601\pi\) | ||
0.860103 | − | 0.510121i | \(-0.170399\pi\) | |||||||
\(14\) | −0.437016 | − | 1.34500i | −0.116797 | − | 0.359466i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.23607 | − | 3.80423i | 0.309017 | − | 0.951057i | ||||
\(17\) | 3.16228 | 0.766965 | 0.383482 | − | 0.923548i | \(-0.374725\pi\) | ||||
0.383482 | + | 0.923548i | \(0.374725\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.07768i | 0.706069i | 0.935610 | + | 0.353035i | \(0.114850\pi\) | ||||
−0.935610 | + | 0.353035i | \(0.885150\pi\) | |||||||
\(20\) | −0.0645747 | − | 0.0888795i | −0.0144394 | − | 0.0198741i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.54415 | − | 1.15156i | 0.755616 | − | 0.245514i | ||||
\(23\) | 2.86834 | 0.598090 | 0.299045 | − | 0.954239i | \(-0.403332\pi\) | ||||
0.299045 | + | 0.954239i | \(0.403332\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.99698 | 0.999397 | ||||||||
\(26\) | 4.94761 | − | 1.60758i | 0.970307 | − | 0.315272i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.61803 | − | 1.17557i | 0.305780 | − | 0.222162i | ||||
\(29\) | 10.1898i | 1.89219i | 0.323890 | + | 0.946095i | \(0.395009\pi\) | ||||
−0.323890 | + | 0.946095i | \(0.604991\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.32437 | 1.67471 | 0.837353 | − | 0.546662i | \(-0.184102\pi\) | ||||
0.837353 | + | 0.546662i | \(0.184102\pi\) | |||||||
\(32\) | 5.65685 | 1.00000 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.38197 | + | 4.25325i | 0.237005 | + | 0.729427i | ||||
\(35\) | − | 0.0549306i | − | 0.00928496i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.774554i | 0.127336i | 0.997971 | + | 0.0636679i | \(0.0202798\pi\) | ||||
−0.997971 | + | 0.0636679i | \(0.979720\pi\) | |||||||
\(38\) | −4.13948 | + | 1.34500i | −0.671512 | + | 0.218187i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.0913225 | − | 0.125695i | 0.0144394 | − | 0.0198741i | ||||
\(41\) | 6.36183 | 0.993551 | 0.496775 | − | 0.867879i | \(-0.334517\pi\) | ||||
0.496775 | + | 0.867879i | \(0.334517\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 9.98927i | − | 1.52335i | −0.647960 | − | 0.761674i | \(-0.724378\pi\) | ||
0.647960 | − | 0.761674i | \(-0.275622\pi\) | |||||||
\(44\) | 3.09770 | + | 4.26362i | 0.466996 | + | 0.642765i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.25351 | + | 3.85790i | 0.184820 | + | 0.568817i | ||||
\(47\) | −12.3126 | −1.79598 | −0.897990 | − | 0.440015i | \(-0.854973\pi\) | ||||
−0.897990 | + | 0.440015i | \(0.854973\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 2.18376 | + | 6.72093i | 0.308831 | + | 0.950483i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.32437 | + | 5.95199i | 0.599683 | + | 0.825392i | ||||
\(53\) | − | 3.39291i | − | 0.466052i | −0.972470 | − | 0.233026i | \(-0.925137\pi\) | ||
0.972470 | − | 0.233026i | \(-0.0748628\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.144746 | 0.0195175 | ||||||||
\(56\) | 2.28825 | + | 1.66251i | 0.305780 | + | 0.222162i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −13.7052 | + | 4.45309i | −1.79958 | + | 0.584719i | ||||
\(59\) | 6.93263i | 0.902552i | 0.892384 | + | 0.451276i | \(0.149031\pi\) | ||||
−0.892384 | + | 0.451276i | \(0.850969\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 8.35114i | − | 1.06925i | −0.845088 | − | 0.534627i | \(-0.820452\pi\) | ||
0.845088 | − | 0.534627i | \(-0.179548\pi\) | |||||||
\(62\) | 4.07490 | + | 12.5413i | 0.517513 | + | 1.59274i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.47214 | + | 7.60845i | 0.309017 | + | 0.951057i | ||||
\(65\) | 0.202064 | 0.0250629 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 8.93584i | − | 1.09169i | −0.837887 | − | 0.545843i | \(-0.816209\pi\) | ||
0.837887 | − | 0.545843i | \(-0.183791\pi\) | |||||||
\(68\) | −5.11667 | + | 3.71748i | −0.620488 | + | 0.450811i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.0738814 | − | 0.0240055i | 0.00883052 | − | 0.00286921i | ||||
\(71\) | 4.28255 | 0.508245 | 0.254123 | − | 0.967172i | \(-0.418213\pi\) | ||||
0.254123 | + | 0.967172i | \(0.418213\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.38081 | 0.980900 | 0.490450 | − | 0.871469i | \(-0.336832\pi\) | ||||
0.490450 | + | 0.871469i | \(0.336832\pi\) | |||||||
\(74\) | −1.04177 | + | 0.338492i | −0.121104 | + | 0.0393489i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.61803 | − | 4.97980i | −0.415017 | − | 0.571222i | ||||
\(77\) | 2.63506i | 0.300293i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.03186 | −0.341111 | −0.170556 | − | 0.985348i | \(-0.554556\pi\) | ||||
−0.170556 | + | 0.985348i | \(0.554556\pi\) | |||||||
\(80\) | 0.208968 | + | 0.0678979i | 0.0233634 | + | 0.00759122i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.78022 | + | 8.55664i | 0.307024 | + | 0.944923i | ||||
\(83\) | 10.3255i | 1.13338i | 0.823932 | + | 0.566688i | \(0.191776\pi\) | ||||
−0.823932 | + | 0.566688i | \(0.808224\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.173706i | 0.0188410i | ||||||||
\(86\) | 13.4355 | − | 4.36547i | 1.44879 | − | 0.470741i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.38081 | + | 6.02967i | −0.466996 | + | 0.642765i | ||||
\(89\) | 12.8155 | 1.35844 | 0.679222 | − | 0.733933i | \(-0.262317\pi\) | ||||
0.679222 | + | 0.733933i | \(0.262317\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.67853i | 0.385615i | ||||||||
\(92\) | −4.64107 | + | 3.37193i | −0.483865 | + | 0.351548i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.38081 | − | 16.5604i | −0.554989 | − | 1.70808i | ||||
\(95\) | −0.169059 | −0.0173451 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.1803 | −1.03366 | −0.516828 | − | 0.856089i | \(-0.672887\pi\) | ||||
−0.516828 | + | 0.856089i | \(0.672887\pi\) | |||||||
\(98\) | 0.437016 | + | 1.34500i | 0.0441453 | + | 0.135865i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −8.08529 | + | 5.87431i | −0.808529 | + | 0.587431i | ||||
\(101\) | 1.02749i | 0.102239i | 0.998693 | + | 0.0511194i | \(0.0162789\pi\) | ||||
−0.998693 | + | 0.0511194i | \(0.983721\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.72905 | 0.170368 | 0.0851842 | − | 0.996365i | \(-0.472852\pi\) | ||||
0.0851842 | + | 0.996365i | \(0.472852\pi\) | |||||||
\(104\) | −6.11559 | + | 8.41738i | −0.599683 | + | 0.825392i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.56346 | − | 1.48276i | 0.443242 | − | 0.144018i | ||||
\(107\) | 6.11985i | 0.591629i | 0.955245 | + | 0.295814i | \(0.0955910\pi\) | ||||
−0.955245 | + | 0.295814i | \(0.904409\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 8.85597i | − | 0.848248i | −0.905604 | − | 0.424124i | \(-0.860582\pi\) | ||
0.905604 | − | 0.424124i | \(-0.139418\pi\) | |||||||
\(110\) | 0.0632561 | + | 0.194682i | 0.00603123 | + | 0.0185622i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.23607 | + | 3.80423i | −0.116797 | + | 0.359466i | ||||
\(113\) | 9.02383 | 0.848891 | 0.424445 | − | 0.905454i | \(-0.360469\pi\) | ||||
0.424445 | + | 0.905454i | \(0.360469\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.157559i | 0.0146925i | ||||||||
\(116\) | −11.9788 | − | 16.4874i | −1.11220 | − | 1.53081i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −9.32437 | + | 3.02967i | −0.858378 | + | 0.278904i | ||||
\(119\) | −3.16228 | −0.289886 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.05644 | 0.368767 | ||||||||
\(122\) | 11.2323 | − | 3.64958i | 1.01692 | − | 0.330418i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −15.0872 | + | 10.9615i | −1.35487 | + | 0.984368i | ||||
\(125\) | 0.549140i | 0.0491166i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.2656 | 1.62081 | 0.810406 | − | 0.585868i | \(-0.199246\pi\) | ||||
0.810406 | + | 0.585868i | \(0.199246\pi\) | |||||||
\(128\) | −9.15298 | + | 6.65003i | −0.809017 | + | 0.587785i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.0883051 | + | 0.271775i | 0.00774487 | + | 0.0238363i | ||||
\(131\) | − | 17.4470i | − | 1.52435i | −0.647373 | − | 0.762174i | \(-0.724132\pi\) | ||
0.647373 | − | 0.762174i | \(-0.275868\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 3.07768i | − | 0.266869i | ||||||
\(134\) | 12.0187 | − | 3.90511i | 1.03826 | − | 0.337350i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.23607 | − | 5.25731i | −0.620488 | − | 0.450811i | ||||
\(137\) | 7.73613 | 0.660942 | 0.330471 | − | 0.943816i | \(-0.392792\pi\) | ||||
0.330471 | + | 0.943816i | \(0.392792\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.802034i | 0.0680276i | 0.999421 | + | 0.0340138i | \(0.0108290\pi\) | ||||
−0.999421 | + | 0.0340138i | \(0.989171\pi\) | |||||||
\(140\) | 0.0645747 | + | 0.0888795i | 0.00545756 | + | 0.00751169i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.87154 | + | 5.76002i | 0.157056 | + | 0.483370i | ||||
\(143\) | −9.69316 | −0.810583 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.559729 | −0.0464829 | ||||||||
\(146\) | 3.66255 | + | 11.2722i | 0.303115 | + | 0.932891i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.910542 | − | 1.25325i | −0.0748461 | − | 0.103017i | ||||
\(149\) | 15.7165i | 1.28755i | 0.765215 | + | 0.643775i | \(0.222633\pi\) | ||||
−0.765215 | + | 0.643775i | \(0.777367\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.58129 | 0.210062 | 0.105031 | − | 0.994469i | \(-0.466506\pi\) | ||||
0.105031 | + | 0.994469i | \(0.466506\pi\) | |||||||
\(152\) | 5.11667 | − | 7.04250i | 0.415017 | − | 0.571222i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.54415 | + | 1.15156i | −0.285596 | + | 0.0927957i | ||||
\(155\) | 0.512193i | 0.0411403i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 0.680724i | − | 0.0543277i | −0.999631 | − | 0.0271638i | \(-0.991352\pi\) | ||
0.999631 | − | 0.0271638i | \(-0.00864758\pi\) | |||||||
\(158\) | −1.32497 | − | 4.07785i | −0.105409 | − | 0.324416i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.310734i | 0.0245657i | ||||||||
\(161\) | −2.86834 | −0.226057 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 21.8339i | − | 1.71016i | −0.518494 | − | 0.855081i | \(-0.673507\pi\) | ||
0.518494 | − | 0.855081i | \(-0.326493\pi\) | |||||||
\(164\) | −10.2937 | + | 7.47878i | −0.803799 | + | 0.583994i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −13.8878 | + | 4.51243i | −1.07790 | + | 0.350232i | ||||
\(167\) | −17.2203 | −1.33255 | −0.666274 | − | 0.745707i | \(-0.732112\pi\) | ||||
−0.666274 | + | 0.745707i | \(0.732112\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.531594 | −0.0408918 | ||||||||
\(170\) | −0.233634 | + | 0.0759122i | −0.0179189 | + | 0.00582220i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 11.7431 | + | 16.1630i | 0.895402 | + | 1.23242i | ||||
\(173\) | 2.57218i | 0.195559i | 0.995208 | + | 0.0977797i | \(0.0311741\pi\) | ||||
−0.995208 | + | 0.0977797i | \(0.968826\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.99698 | −0.377736 | ||||||||
\(176\) | −10.0244 | − | 3.25712i | −0.755616 | − | 0.245514i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 5.60059 | + | 17.2369i | 0.419782 | + | 1.29196i | ||||
\(179\) | − | 5.26703i | − | 0.393676i | −0.980436 | − | 0.196838i | \(-0.936933\pi\) | ||
0.980436 | − | 0.196838i | \(-0.0630673\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.0189i | 1.19068i | 0.803475 | + | 0.595339i | \(0.202982\pi\) | ||||
−0.803475 | + | 0.595339i | \(0.797018\pi\) | |||||||
\(182\) | −4.94761 | + | 1.60758i | −0.366742 | + | 0.119162i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −6.56346 | − | 4.76863i | −0.483865 | − | 0.351548i | ||||
\(185\) | −0.0425467 | −0.00312809 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 8.33280i | − | 0.609355i | ||||||
\(188\) | 19.9222 | − | 14.4744i | 1.45298 | − | 1.05565i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.0738814 | − | 0.227384i | −0.00535992 | − | 0.0164961i | ||||
\(191\) | −1.83730 | −0.132943 | −0.0664713 | − | 0.997788i | \(-0.521174\pi\) | ||||
−0.0664713 | + | 0.997788i | \(0.521174\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.3429 | 1.10441 | 0.552204 | − | 0.833709i | \(-0.313787\pi\) | ||||
0.552204 | + | 0.833709i | \(0.313787\pi\) | |||||||
\(194\) | −4.44897 | − | 13.6925i | −0.319418 | − | 0.983066i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.61803 | + | 1.17557i | −0.115574 | + | 0.0839693i | ||||
\(197\) | − | 5.02447i | − | 0.357979i | −0.983851 | − | 0.178989i | \(-0.942717\pi\) | ||
0.983851 | − | 0.178989i | \(-0.0572828\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −22.0333 | −1.56190 | −0.780949 | − | 0.624595i | \(-0.785264\pi\) | ||||
−0.780949 | + | 0.624595i | \(0.785264\pi\) | |||||||
\(200\) | −11.4343 | − | 8.30752i | −0.808529 | − | 0.587431i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.38197 | + | 0.449028i | −0.0972348 | + | 0.0315935i | ||||
\(203\) | − | 10.1898i | − | 0.715180i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.349459i | 0.0244073i | ||||||||
\(206\) | 0.755623 | + | 2.32557i | 0.0526467 | + | 0.162030i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −13.9940 | − | 4.54691i | −0.970307 | − | 0.315272i | ||||
\(209\) | 8.10989 | 0.560973 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.50651i | 0.585612i | 0.956172 | + | 0.292806i | \(0.0945890\pi\) | ||||
−0.956172 | + | 0.292806i | \(0.905411\pi\) | |||||||
\(212\) | 3.98861 | + | 5.48985i | 0.273939 | + | 0.377044i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −8.23119 | + | 2.67447i | −0.562672 | + | 0.182823i | ||||
\(215\) | 0.548716 | 0.0374221 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.32437 | −0.632980 | ||||||||
\(218\) | 11.9112 | − | 3.87020i | 0.806732 | − | 0.262123i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.234203 | + | 0.170159i | −0.0157900 | + | 0.0114721i | ||||
\(221\) | − | 11.6325i | − | 0.782489i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.5574 | −0.907872 | −0.453936 | − | 0.891034i | \(-0.649981\pi\) | ||||
−0.453936 | + | 0.891034i | \(0.649981\pi\) | |||||||
\(224\) | −5.65685 | −0.377964 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.94356 | + | 12.1370i | 0.262322 | + | 0.807343i | ||||
\(227\) | − | 16.0721i | − | 1.06674i | −0.845882 | − | 0.533370i | \(-0.820925\pi\) | ||
0.845882 | − | 0.533370i | \(-0.179075\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 5.50870i | − | 0.364025i | −0.983296 | − | 0.182013i | \(-0.941739\pi\) | ||
0.983296 | − | 0.182013i | \(-0.0582612\pi\) | |||||||
\(230\) | −0.211917 | + | 0.0688559i | −0.0139734 | + | 0.00454023i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 16.9405 | − | 23.3167i | 1.11220 | − | 1.53081i | ||||
\(233\) | 28.6599 | 1.87757 | 0.938787 | − | 0.344498i | \(-0.111951\pi\) | ||||
0.938787 | + | 0.344498i | \(0.111951\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 0.676339i | − | 0.0441195i | ||||||
\(236\) | −8.14980 | − | 11.2172i | −0.530507 | − | 0.730180i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.38197 | − | 4.25325i | −0.0895796 | − | 0.275698i | ||||
\(239\) | 3.82998 | 0.247741 | 0.123870 | − | 0.992298i | \(-0.460469\pi\) | ||||
0.123870 | + | 0.992298i | \(0.460469\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.72834 | −0.111332 | −0.0556660 | − | 0.998449i | \(-0.517728\pi\) | ||||
−0.0556660 | + | 0.998449i | \(0.517728\pi\) | |||||||
\(242\) | 1.77273 | + | 5.45590i | 0.113955 | + | 0.350719i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 9.81736 | + | 13.5124i | 0.628492 | + | 0.865045i | ||||
\(245\) | 0.0549306i | 0.00350938i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.3214 | 0.720361 | ||||||||
\(248\) | −21.3365 | − | 15.5018i | −1.35487 | − | 0.984368i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.738591 | + | 0.239983i | −0.0467126 | + | 0.0151779i | ||||
\(251\) | 0.245657i | 0.0155057i | 0.999970 | + | 0.00775286i | \(0.00246784\pi\) | ||||
−0.999970 | + | 0.00775286i | \(0.997532\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 7.55825i | − | 0.475183i | ||||||
\(254\) | 7.98237 | + | 24.5672i | 0.500859 | + | 1.54148i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −12.9443 | − | 9.40456i | −0.809017 | − | 0.587785i | ||||
\(257\) | −16.2120 | −1.01128 | −0.505638 | − | 0.862746i | \(-0.668743\pi\) | ||||
−0.505638 | + | 0.862746i | \(0.668743\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 0.774554i | − | 0.0481284i | ||||||
\(260\) | −0.326946 | + | 0.237540i | −0.0202763 | + | 0.0147316i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 23.4661 | − | 7.62460i | 1.44974 | − | 0.471049i | ||||
\(263\) | −23.3265 | −1.43837 | −0.719187 | − | 0.694817i | \(-0.755485\pi\) | ||||
−0.719187 | + | 0.694817i | \(0.755485\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.186375 | 0.0114489 | ||||||||
\(266\) | 4.13948 | − | 1.34500i | 0.253808 | − | 0.0824671i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 10.5047 | + | 14.4585i | 0.641677 | + | 0.883193i | ||||
\(269\) | − | 23.6947i | − | 1.44469i | −0.691534 | − | 0.722344i | \(-0.743065\pi\) | ||
0.691534 | − | 0.722344i | \(-0.256935\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.52786 | 0.214302 | 0.107151 | − | 0.994243i | \(-0.465827\pi\) | ||||
0.107151 | + | 0.994243i | \(0.465827\pi\) | |||||||
\(272\) | 3.90879 | − | 12.0300i | 0.237005 | − | 0.729427i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.38081 | + | 10.4051i | 0.204242 | + | 0.628594i | ||||
\(275\) | − | 13.1674i | − | 0.794022i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 28.6014i | − | 1.71849i | −0.511561 | − | 0.859247i | \(-0.670932\pi\) | ||
0.511561 | − | 0.859247i | \(-0.329068\pi\) | |||||||
\(278\) | −1.07873 | + | 0.350502i | −0.0646981 | + | 0.0210217i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.0913225 | + | 0.125695i | −0.00545756 | + | 0.00751169i | ||||
\(281\) | −25.6546 | −1.53043 | −0.765214 | − | 0.643776i | \(-0.777367\pi\) | ||||
−0.765214 | + | 0.643776i | \(0.777367\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.8539i | 0.882974i | 0.897268 | + | 0.441487i | \(0.145549\pi\) | ||||
−0.897268 | + | 0.441487i | \(0.854451\pi\) | |||||||
\(284\) | −6.92931 | + | 5.03444i | −0.411179 | + | 0.298739i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.23607 | − | 13.0373i | −0.250484 | − | 0.770910i | ||||
\(287\) | −6.36183 | −0.375527 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.00000 | −0.411765 | ||||||||
\(290\) | −0.244610 | − | 0.752834i | −0.0143640 | − | 0.0442079i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −13.5604 | + | 9.85224i | −0.793565 | + | 0.576559i | ||||
\(293\) | 21.6946i | 1.26741i | 0.773574 | + | 0.633706i | \(0.218467\pi\) | ||||
−0.773574 | + | 0.633706i | \(0.781533\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.380813 | −0.0221718 | ||||||||
\(296\) | 1.28770 | − | 1.77237i | 0.0748461 | − | 0.103017i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −21.1387 | + | 6.86838i | −1.22453 | + | 0.397875i | ||||
\(299\) | − | 10.5513i | − | 0.610195i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.98927i | 0.575772i | ||||||||
\(302\) | 1.12806 | + | 3.47182i | 0.0649128 | + | 0.199781i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 11.7082 | + | 3.80423i | 0.671512 | + | 0.218187i | ||||
\(305\) | 0.458733 | 0.0262670 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 0.422903i | − | 0.0241363i | −0.999927 | − | 0.0120682i | \(-0.996158\pi\) | ||
0.999927 | − | 0.0120682i | \(-0.00384151\pi\) | |||||||
\(308\) | −3.09770 | − | 4.26362i | −0.176508 | − | 0.242942i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.688898 | + | 0.223837i | −0.0391268 | + | 0.0127131i | ||||
\(311\) | −13.6732 | −0.775338 | −0.387669 | − | 0.921799i | \(-0.626720\pi\) | ||||
−0.387669 | + | 0.921799i | \(0.626720\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.68665 | −0.434475 | −0.217237 | − | 0.976119i | \(-0.569705\pi\) | ||||
−0.217237 | + | 0.976119i | \(0.569705\pi\) | |||||||
\(314\) | 0.915571 | − | 0.297487i | 0.0516687 | − | 0.0167882i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.90566 | − | 3.56417i | 0.275965 | − | 0.200500i | ||||
\(317\) | 24.2068i | 1.35959i | 0.733401 | + | 0.679796i | \(0.237932\pi\) | ||||
−0.733401 | + | 0.679796i | \(0.762068\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 26.8506 | 1.50335 | ||||||||
\(320\) | −0.417937 | + | 0.135796i | −0.0233634 | + | 0.00759122i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.25351 | − | 3.85790i | −0.0698553 | − | 0.214993i | ||||
\(323\) | 9.73249i | 0.541530i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 18.3816i | − | 1.01963i | ||||||
\(326\) | 29.3665 | − | 9.54176i | 1.62646 | − | 0.528469i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −14.5574 | − | 10.5766i | −0.803799 | − | 0.583994i | ||||
\(329\) | 12.3126 | 0.678817 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.15756i | 0.503345i | 0.967812 | + | 0.251672i | \(0.0809806\pi\) | ||||
−0.967812 | + | 0.251672i | \(0.919019\pi\) | |||||||
\(332\) | −12.1384 | − | 16.7071i | −0.666182 | − | 0.916921i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −7.52556 | − | 23.1613i | −0.411780 | − | 1.26733i | ||||
\(335\) | 0.490851 | 0.0268180 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 33.2441 | 1.81092 | 0.905460 | − | 0.424432i | \(-0.139526\pi\) | ||||
0.905460 | + | 0.424432i | \(0.139526\pi\) | |||||||
\(338\) | −0.232315 | − | 0.714992i | −0.0126363 | − | 0.0388904i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.204203 | − | 0.281062i | −0.0110745 | − | 0.0152427i | ||||
\(341\) | − | 24.5703i | − | 1.33056i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −16.6072 | + | 22.8579i | −0.895402 | + | 1.23242i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.45958 | + | 1.12408i | −0.185988 | + | 0.0604312i | ||||
\(347\) | − | 8.03418i | − | 0.431297i | −0.976471 | − | 0.215649i | \(-0.930813\pi\) | ||
0.976471 | − | 0.215649i | \(-0.0691866\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.46493i | 0.292531i | 0.989245 | + | 0.146265i | \(0.0467254\pi\) | ||||
−0.989245 | + | 0.146265i | \(0.953275\pi\) | |||||||
\(350\) | −2.18376 | − | 6.72093i | −0.116727 | − | 0.359249i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 14.9062i | − | 0.794502i | ||||||
\(353\) | −7.85159 | −0.417898 | −0.208949 | − | 0.977927i | \(-0.567004\pi\) | ||||
−0.208949 | + | 0.977927i | \(0.567004\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.235243i | 0.0124854i | ||||||||
\(356\) | −20.7360 | + | 15.0656i | −1.09900 | + | 0.798473i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7.08414 | − | 2.30178i | 0.374408 | − | 0.121653i | ||||
\(359\) | −30.4616 | −1.60770 | −0.803851 | − | 0.594831i | \(-0.797219\pi\) | ||||
−0.803851 | + | 0.594831i | \(0.797219\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.52786 | 0.501467 | ||||||||
\(362\) | −21.5454 | + | 7.00053i | −1.13240 | + | 0.367940i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4.32437 | − | 5.95199i | −0.226659 | − | 0.311969i | ||||
\(365\) | 0.460363i | 0.0240965i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.97241 | 0.468356 | 0.234178 | − | 0.972194i | \(-0.424760\pi\) | ||||
0.234178 | + | 0.972194i | \(0.424760\pi\) | |||||||
\(368\) | 3.54546 | − | 10.9118i | 0.184820 | − | 0.568817i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.0185936 | − | 0.0572251i | −0.000966634 | − | 0.00297499i | ||||
\(371\) | 3.39291i | 0.176151i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 19.6614i | 1.01803i | 0.860759 | + | 0.509013i | \(0.169990\pi\) | ||||
−0.860759 | + | 0.509013i | \(0.830010\pi\) | |||||||
\(374\) | 11.2076 | − | 3.64157i | 0.579531 | − | 0.188301i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 28.1743 | + | 20.4698i | 1.45298 | + | 1.05565i | ||||
\(377\) | 37.4833 | 1.93049 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.9871i | 1.28350i | 0.766914 | + | 0.641750i | \(0.221791\pi\) | ||||
−0.766914 | + | 0.641750i | \(0.778209\pi\) | |||||||
\(380\) | 0.273543 | − | 0.198741i | 0.0140325 | − | 0.0101952i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −0.802931 | − | 2.47117i | −0.0410815 | − | 0.126436i | ||||
\(383\) | −20.3323 | −1.03893 | −0.519465 | − | 0.854492i | \(-0.673869\pi\) | ||||
−0.519465 | + | 0.854492i | \(0.673869\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.144746 | −0.00737691 | ||||||||
\(386\) | 6.70510 | + | 20.6362i | 0.341281 | + | 1.05035i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 16.4721 | − | 11.9677i | 0.836246 | − | 0.607568i | ||||
\(389\) | 2.92753i | 0.148432i | 0.997242 | + | 0.0742159i | \(0.0236454\pi\) | ||||
−0.997242 | + | 0.0742159i | \(0.976355\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.07048 | 0.458714 | ||||||||
\(392\) | −2.28825 | − | 1.66251i | −0.115574 | − | 0.0839693i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6.75790 | − | 2.19577i | 0.340458 | − | 0.110621i | ||||
\(395\) | − | 0.166542i | − | 0.00837964i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.20287i | 0.411690i | 0.978585 | + | 0.205845i | \(0.0659943\pi\) | ||||
−0.978585 | + | 0.205845i | \(0.934006\pi\) | |||||||
\(398\) | −9.62890 | − | 29.6347i | −0.482653 | − | 1.48545i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 6.17661 | − | 19.0097i | 0.308831 | − | 0.950483i | ||||
\(401\) | 36.5590 | 1.82567 | 0.912834 | − | 0.408332i | \(-0.133889\pi\) | ||||
0.912834 | + | 0.408332i | \(0.133889\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 34.3000i | − | 1.70860i | ||||||
\(404\) | −1.20788 | − | 1.66251i | −0.0600944 | − | 0.0827129i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 13.7052 | − | 4.45309i | 0.680177 | − | 0.221003i | ||||
\(407\) | 2.04100 | 0.101169 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.01783 | −0.297562 | −0.148781 | − | 0.988870i | \(-0.547535\pi\) | ||||
−0.148781 | + | 0.988870i | \(0.547535\pi\) | |||||||
\(410\) | −0.470021 | + | 0.152719i | −0.0232127 | + | 0.00754226i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.79766 | + | 2.03262i | −0.137831 | + | 0.100140i | ||||
\(413\) | − | 6.93263i | − | 0.341133i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.567188 | −0.0278422 | ||||||||
\(416\) | − | 20.8089i | − | 1.02024i | ||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.54415 | + | 10.9078i | 0.173350 | + | 0.533517i | ||||
\(419\) | 2.25247i | 0.110040i | 0.998485 | + | 0.0550201i | \(0.0175223\pi\) | ||||
−0.998485 | + | 0.0550201i | \(0.982478\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 2.87431i | − | 0.140085i | −0.997544 | − | 0.0700425i | \(-0.977686\pi\) | ||
0.997544 | − | 0.0700425i | \(-0.0223135\pi\) | |||||||
\(422\) | −11.4412 | + | 3.71748i | −0.556950 | + | 0.180964i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −5.64074 | + | 7.76382i | −0.273939 | + | 0.377044i | ||||
\(425\) | 15.8018 | 0.766502 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.35114i | 0.404140i | ||||||||
\(428\) | −7.19432 | − | 9.90213i | −0.347751 | − | 0.478638i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.239798 | + | 0.738021i | 0.0115641 | + | 0.0355905i | ||||
\(431\) | −15.7211 | −0.757261 | −0.378630 | − | 0.925548i | \(-0.623605\pi\) | ||||
−0.378630 | + | 0.925548i | \(0.623605\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.44027 | −0.165329 | −0.0826644 | − | 0.996577i | \(-0.526343\pi\) | ||||
−0.0826644 | + | 0.996577i | \(0.526343\pi\) | |||||||
\(434\) | −4.07490 | − | 12.5413i | −0.195601 | − | 0.601999i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 10.4108 | + | 14.3293i | 0.498588 | + | 0.686247i | ||||
\(437\) | 8.82783i | 0.422292i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.2955 | −0.586833 | −0.293417 | − | 0.955985i | \(-0.594792\pi\) | ||||
−0.293417 | + | 0.955985i | \(0.594792\pi\) | |||||||
\(440\) | −0.331213 | − | 0.240641i | −0.0157900 | − | 0.0114721i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 15.6457 | − | 5.08361i | 0.744191 | − | 0.241802i | ||||
\(443\) | 15.8932i | 0.755107i | 0.925988 | + | 0.377553i | \(0.123235\pi\) | ||||
−0.925988 | + | 0.377553i | \(0.876765\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.703964i | 0.0333711i | ||||||||
\(446\) | −5.92481 | − | 18.2347i | −0.280548 | − | 0.863438i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.47214 | − | 7.60845i | −0.116797 | − | 0.359466i | ||||
\(449\) | 8.97450 | 0.423533 | 0.211766 | − | 0.977320i | \(-0.432078\pi\) | ||||
0.211766 | + | 0.977320i | \(0.432078\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 16.7638i | − | 0.789377i | ||||||
\(452\) | −14.6009 | + | 10.6082i | −0.686767 | + | 0.498965i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 21.6169 | − | 7.02375i | 1.01453 | − | 0.329641i | ||||
\(455\) | −0.202064 | −0.00947290 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.0037 | −0.701845 | −0.350922 | − | 0.936405i | \(-0.614132\pi\) | ||||
−0.350922 | + | 0.936405i | \(0.614132\pi\) | |||||||
\(458\) | 7.40919 | − | 2.40739i | 0.346209 | − | 0.112490i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.185222 | − | 0.254936i | −0.00863602 | − | 0.0118865i | ||||
\(461\) | − | 8.69884i | − | 0.405145i | −0.979267 | − | 0.202573i | \(-0.935070\pi\) | ||
0.979267 | − | 0.202573i | \(-0.0649303\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.34522 | −0.434309 | −0.217155 | − | 0.976137i | \(-0.569678\pi\) | ||||
−0.217155 | + | 0.976137i | \(0.569678\pi\) | |||||||
\(464\) | 38.7641 | + | 12.5952i | 1.79958 | + | 0.584719i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 12.5248 | + | 38.5475i | 0.580202 | + | 1.78568i | ||||
\(467\) | 9.23326i | 0.427265i | 0.976914 | + | 0.213632i | \(0.0685294\pi\) | ||||
−0.976914 | + | 0.213632i | \(0.931471\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.93584i | 0.412619i | ||||||||
\(470\) | 0.909674 | − | 0.295571i | 0.0419601 | − | 0.0136337i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 11.5256 | − | 15.8636i | 0.530507 | − | 0.730180i | ||||
\(473\) | −26.3223 | −1.21030 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 15.3791i | 0.705643i | ||||||||
\(476\) | 5.11667 | − | 3.71748i | 0.234522 | − | 0.170390i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.67376 | + | 5.15131i | 0.0765561 | + | 0.235615i | ||||
\(479\) | 8.66050 | 0.395708 | 0.197854 | − | 0.980231i | \(-0.436603\pi\) | ||||
0.197854 | + | 0.980231i | \(0.436603\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.84922 | 0.129913 | ||||||||
\(482\) | −0.755311 | − | 2.32461i | −0.0344035 | − | 0.105883i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.56346 | + | 4.76863i | −0.298339 | + | 0.216756i | ||||
\(485\) | − | 0.559212i | − | 0.0253925i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.1424 | 0.504912 | 0.252456 | − | 0.967608i | \(-0.418762\pi\) | ||||
0.252456 | + | 0.967608i | \(0.418762\pi\) | |||||||
\(488\) | −13.8838 | + | 19.1095i | −0.628492 | + | 0.865045i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.0738814 | + | 0.0240055i | −0.00333762 | + | 0.00108446i | ||||
\(491\) | − | 25.4479i | − | 1.14845i | −0.818698 | − | 0.574224i | \(-0.805304\pi\) | ||
0.818698 | − | 0.574224i | \(-0.194696\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 32.2228i | 1.45124i | ||||||||
\(494\) | 4.94761 | + | 15.2272i | 0.222604 | + | 0.685104i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 11.5256 | − | 35.4720i | 0.517513 | − | 1.59274i | ||||
\(497\) | −4.28255 | −0.192099 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 4.17422i | − | 0.186864i | −0.995626 | − | 0.0934318i | \(-0.970216\pi\) | ||
0.995626 | − | 0.0934318i | \(-0.0297837\pi\) | |||||||
\(500\) | −0.645553 | − | 0.888527i | −0.0288700 | − | 0.0397361i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −0.330408 | + | 0.107356i | −0.0147468 | + | 0.00479153i | ||||
\(503\) | −10.6106 | −0.473105 | −0.236552 | − | 0.971619i | \(-0.576017\pi\) | ||||
−0.236552 | + | 0.971619i | \(0.576017\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.0564404 | −0.00251156 | ||||||||
\(506\) | 10.1658 | − | 3.30308i | 0.451926 | − | 0.146840i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −29.5544 | + | 21.4725i | −1.31126 | + | 0.952690i | ||||
\(509\) | 24.1111i | 1.06871i | 0.845262 | + | 0.534353i | \(0.179445\pi\) | ||||
−0.845262 | + | 0.534353i | \(0.820555\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.38081 | −0.370745 | ||||||||
\(512\) | 6.99226 | − | 21.5200i | 0.309017 | − | 0.951057i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −7.08490 | − | 21.8051i | −0.312502 | − | 0.961781i | ||||
\(515\) | 0.0949777i | 0.00418522i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 32.4445i | 1.42691i | ||||||||
\(518\) | 1.04177 | − | 0.338492i | 0.0457728 | − | 0.0148725i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.462372 | − | 0.335933i | −0.0202763 | − | 0.0147316i | ||||
\(521\) | −32.5642 | −1.42666 | −0.713331 | − | 0.700827i | \(-0.752815\pi\) | ||||
−0.713331 | + | 0.700827i | \(0.752815\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 18.6166i | − | 0.814046i | −0.913418 | − | 0.407023i | \(-0.866567\pi\) | ||
0.913418 | − | 0.407023i | \(-0.133433\pi\) | |||||||
\(524\) | 20.5101 | + | 28.2298i | 0.895989 | + | 1.23322i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −10.1941 | − | 31.3741i | −0.444482 | − | 1.36797i | ||||
\(527\) | 29.4863 | 1.28444 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.7726 | −0.642289 | ||||||||
\(530\) | 0.0814487 | + | 0.250673i | 0.00353791 | + | 0.0108886i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.61803 | + | 4.97980i | 0.156862 | + | 0.215902i | ||||
\(533\) | − | 23.4022i | − | 1.01366i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.336167 | −0.0145338 | ||||||||
\(536\) | −14.8559 | + | 20.4474i | −0.641677 | + | 0.883193i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 31.8692 | − | 10.3549i | 1.37398 | − | 0.446433i | ||||
\(539\) | − | 2.63506i | − | 0.113500i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 41.3556i | − | 1.77802i | −0.457891 | − | 0.889008i | \(-0.651395\pi\) | ||
0.457891 | − | 0.889008i | \(-0.348605\pi\) | |||||||
\(542\) | 1.54173 | + | 4.74497i | 0.0662231 | + | 0.203814i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 17.8885 | 0.766965 | ||||||||
\(545\) | 0.486463 | 0.0208378 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 18.8135i | − | 0.804408i | −0.915550 | − | 0.402204i | \(-0.868244\pi\) | ||
0.915550 | − | 0.402204i | \(-0.131756\pi\) | |||||||
\(548\) | −12.5173 | + | 9.09437i | −0.534714 | + | 0.388492i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 17.7101 | − | 5.75435i | 0.755160 | − | 0.245366i | ||||
\(551\) | −31.3608 | −1.33602 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.03186 | 0.128928 | ||||||||
\(554\) | 38.4689 | − | 12.4993i | 1.63439 | − | 0.531044i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.942847 | − | 1.29772i | −0.0399856 | − | 0.0550355i | ||||
\(557\) | − | 4.05808i | − | 0.171946i | −0.996297 | − | 0.0859731i | \(-0.972600\pi\) | ||
0.996297 | − | 0.0859731i | \(-0.0273999\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −36.7458 | −1.55418 | ||||||||
\(560\) | −0.208968 | − | 0.0678979i | −0.00883052 | − | 0.00286921i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −11.2115 | − | 34.5054i | −0.472928 | − | 1.45552i | ||||
\(563\) | − | 45.2454i | − | 1.90687i | −0.301605 | − | 0.953433i | \(-0.597522\pi\) | ||
0.301605 | − | 0.953433i | \(-0.402478\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.495684i | 0.0208536i | ||||||||
\(566\) | −19.9785 | + | 6.49140i | −0.839758 | + | 0.272854i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9.79953 | − | 7.11977i | −0.411179 | − | 0.298739i | ||||
\(569\) | 13.6255 | 0.571212 | 0.285606 | − | 0.958347i | \(-0.407805\pi\) | ||||
0.285606 | + | 0.958347i | \(0.407805\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 30.9574i | 1.29553i | 0.761842 | + | 0.647763i | \(0.224295\pi\) | ||||
−0.761842 | + | 0.647763i | \(0.775705\pi\) | |||||||
\(572\) | 15.6839 | − | 11.3950i | 0.655775 | − | 0.476449i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.78022 | − | 8.55664i | −0.116044 | − | 0.357147i | ||||
\(575\) | 14.3330 | 0.597729 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −38.4675 | −1.60142 | −0.800712 | − | 0.599049i | \(-0.795545\pi\) | ||||
−0.800712 | + | 0.599049i | \(0.795545\pi\) | |||||||
\(578\) | −3.05911 | − | 9.41498i | −0.127242 | − | 0.391612i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.905660 | − | 0.658001i | 0.0376055 | − | 0.0273220i | ||||
\(581\) | − | 10.3255i | − | 0.428376i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.94054 | −0.370279 | ||||||||
\(584\) | −19.1774 | − | 13.9332i | −0.793565 | − | 0.576559i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −29.1792 | + | 9.48089i | −1.20538 | + | 0.391652i | ||||
\(587\) | − | 28.6131i | − | 1.18099i | −0.807041 | − | 0.590495i | \(-0.798932\pi\) | ||
0.807041 | − | 0.590495i | \(-0.201068\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 28.6975i | 1.18246i | ||||||||
\(590\) | −0.166422 | − | 0.512193i | −0.00685147 | − | 0.0210867i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.94658 | + | 0.957401i | 0.121104 | + | 0.0393489i | ||||
\(593\) | 22.5554 | 0.926239 | 0.463119 | − | 0.886296i | \(-0.346730\pi\) | ||||
0.463119 | + | 0.886296i | \(0.346730\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 0.173706i | − | 0.00712124i | ||||||
\(596\) | −18.4759 | − | 25.4299i | −0.756803 | − | 1.04165i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 14.1914 | − | 4.61107i | 0.580330 | − | 0.188561i | ||||
\(599\) | 42.1743 | 1.72319 | 0.861597 | − | 0.507593i | \(-0.169465\pi\) | ||||
0.861597 | + | 0.507593i | \(0.169465\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.0155 | −0.571705 | −0.285853 | − | 0.958274i | \(-0.592277\pi\) | ||||
−0.285853 | + | 0.958274i | \(0.592277\pi\) | |||||||
\(602\) | −13.4355 | + | 4.36547i | −0.547591 | + | 0.177923i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4.17661 | + | 3.03448i | −0.169944 | + | 0.123471i | ||||
\(605\) | 0.222823i | 0.00905902i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −21.5893 | −0.876282 | −0.438141 | − | 0.898906i | \(-0.644363\pi\) | ||||
−0.438141 | + | 0.898906i | \(0.644363\pi\) | |||||||
\(608\) | 17.4100i | 0.706069i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.200474 | + | 0.616994i | 0.00811694 | + | 0.0249814i | ||||
\(611\) | 45.2924i | 1.83233i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 0.788508i | − | 0.0318475i | −0.999873 | − | 0.0159238i | \(-0.994931\pi\) | ||
0.999873 | − | 0.0159238i | \(-0.00506891\pi\) | |||||||
\(614\) | 0.568803 | − | 0.184815i | 0.0229550 | − | 0.00745854i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.38081 | − | 6.02967i | 0.176508 | − | 0.242942i | ||||
\(617\) | −34.4936 | −1.38866 | −0.694331 | − | 0.719656i | \(-0.744299\pi\) | ||||
−0.694331 | + | 0.719656i | \(0.744299\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 47.8005i | 1.92127i | 0.277822 | + | 0.960633i | \(0.410388\pi\) | ||||
−0.277822 | + | 0.960633i | \(0.589612\pi\) | |||||||
\(620\) | −0.602119 | − | 0.828746i | −0.0241817 | − | 0.0332832i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −5.97542 | − | 18.3905i | −0.239593 | − | 0.737390i | ||||
\(623\) | −12.8155 | −0.513443 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.9547 | 0.998190 | ||||||||
\(626\) | −3.35919 | − | 10.3385i | −0.134260 | − | 0.413210i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.800239 | + | 1.10143i | 0.0319330 | + | 0.0439520i | ||||
\(629\) | 2.44935i | 0.0976621i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21.7200 | −0.864659 | −0.432330 | − | 0.901716i | \(-0.642308\pi\) | ||||
−0.432330 | + | 0.901716i | \(0.642308\pi\) | |||||||
\(632\) | 6.93765 | + | 5.04050i | 0.275965 | + | 0.200500i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −32.5581 | + | 10.5788i | −1.29305 | + | 0.420137i | ||||
\(635\) | 1.00334i | 0.0398164i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 3.67853i | − | 0.145749i | ||||||
\(638\) | 11.7342 | + | 36.1140i | 0.464560 | + | 1.42977i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.365290 | − | 0.502778i | −0.0144394 | − | 0.0198741i | ||||
\(641\) | 17.0166 | 0.672117 | 0.336058 | − | 0.941841i | \(-0.390906\pi\) | ||||
0.336058 | + | 0.941841i | \(0.390906\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 38.4170i | 1.51502i | 0.652824 | + | 0.757509i | \(0.273584\pi\) | ||||
−0.652824 | + | 0.757509i | \(0.726416\pi\) | |||||||
\(644\) | 4.64107 | − | 3.37193i | 0.182884 | − | 0.132873i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −13.0902 | + | 4.25325i | −0.515026 | + | 0.167342i | ||||
\(647\) | 22.7497 | 0.894382 | 0.447191 | − | 0.894439i | \(-0.352425\pi\) | ||||
0.447191 | + | 0.894439i | \(0.352425\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 18.2679 | 0.717079 | ||||||||
\(650\) | 24.7231 | − | 8.03304i | 0.969721 | − | 0.315082i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 25.6673 | + | 35.3280i | 1.00521 | + | 1.38355i | ||||
\(653\) | 12.9198i | 0.505591i | 0.967520 | + | 0.252795i | \(0.0813499\pi\) | ||||
−0.967520 | + | 0.252795i | \(0.918650\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.958371 | 0.0374466 | ||||||||
\(656\) | 7.86365 | − | 24.2018i | 0.307024 | − | 0.944923i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 5.38081 | + | 16.5604i | 0.209766 | + | 0.645593i | ||||
\(659\) | 47.1905i | 1.83828i | 0.393932 | + | 0.919140i | \(0.371115\pi\) | ||||
−0.393932 | + | 0.919140i | \(0.628885\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 31.5648i | 1.22773i | 0.789412 | + | 0.613864i | \(0.210386\pi\) | ||||
−0.789412 | + | 0.613864i | \(0.789614\pi\) | |||||||
\(662\) | −12.3169 | + | 4.00200i | −0.478710 | + | 0.155542i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 17.1663 | − | 23.6274i | 0.666182 | − | 0.916921i | ||||
\(665\) | 0.169059 | 0.00655582 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 29.2276i | 1.13170i | ||||||||
\(668\) | 27.8631 | − | 20.2437i | 1.07805 | − | 0.783253i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0.214510 | + | 0.660193i | 0.00828723 | + | 0.0255055i | ||||
\(671\) | −22.0058 | −0.849524 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −37.1186 | −1.43082 | −0.715408 | − | 0.698707i | \(-0.753759\pi\) | ||||
−0.715408 | + | 0.698707i | \(0.753759\pi\) | |||||||
\(674\) | 14.5282 | + | 44.7132i | 0.559605 | + | 1.72229i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.860137 | − | 0.624926i | 0.0330822 | − | 0.0240356i | ||||
\(677\) | 15.8912i | 0.610750i | 0.952232 | + | 0.305375i | \(0.0987818\pi\) | ||||
−0.952232 | + | 0.305375i | \(0.901218\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.1803 | 0.390686 | ||||||||
\(680\) | 0.288787 | − | 0.397481i | 0.0110745 | − | 0.0152427i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 33.0470 | − | 10.7376i | 1.26544 | − | 0.411165i | ||||
\(683\) | 27.4319i | 1.04965i | 0.851210 | + | 0.524826i | \(0.175869\pi\) | ||||
−0.851210 | + | 0.524826i | \(0.824131\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.424950i | 0.0162365i | ||||||||
\(686\) | −0.437016 | − | 1.34500i | −0.0166853 | − | 0.0513522i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −38.0014 | − | 12.3474i | −1.44879 | − | 0.470741i | ||||
\(689\) | −12.4809 | −0.475486 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.57770i | 0.250227i | 0.992142 | + | 0.125114i | \(0.0399296\pi\) | ||||
−0.992142 | + | 0.125114i | \(0.960070\pi\) | |||||||
\(692\) | −3.02378 | − | 4.16188i | −0.114947 | − | 0.158211i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 10.8059 | − | 3.51107i | 0.410188 | − | 0.133278i | ||||
\(695\) | −0.0440562 | −0.00167115 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 20.1179 | 0.762018 | ||||||||
\(698\) | −7.35031 | + | 2.38826i | −0.278213 | + | 0.0903970i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 8.08529 | − | 5.87431i | 0.305595 | − | 0.222028i | ||||
\(701\) | − | 9.07153i | − | 0.342627i | −0.985217 | − | 0.171314i | \(-0.945199\pi\) | ||
0.985217 | − | 0.171314i | \(-0.0548011\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.38383 | −0.0899079 | ||||||||
\(704\) | 20.0488 | − | 6.51424i | 0.755616 | − | 0.245514i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.43127 | − | 10.5604i | −0.129138 | − | 0.397445i | ||||
\(707\) | − | 1.02749i | − | 0.0386426i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.16889i | 0.231678i | 0.993268 | + | 0.115839i | \(0.0369556\pi\) | ||||
−0.993268 | + | 0.115839i | \(0.963044\pi\) | |||||||
\(710\) | −0.316401 | + | 0.102805i | −0.0118743 | + | 0.00385820i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −29.3251 | − | 21.3059i | −1.09900 | − | 0.798473i | ||||
\(713\) | 26.7454 | 1.00162 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 0.532451i | − | 0.0199125i | ||||||
\(716\) | 6.19176 | + | 8.52223i | 0.231397 | + | 0.318491i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −13.3122 | − | 40.9707i | −0.496807 | − | 1.52901i | ||||
\(719\) | −30.5440 | −1.13910 | −0.569550 | − | 0.821956i | \(-0.692883\pi\) | ||||
−0.569550 | + | 0.821956i | \(0.692883\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.72905 | −0.0643932 | ||||||||
\(722\) | 4.16383 | + | 12.8149i | 0.154962 | + | 0.476923i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −18.8314 | − | 25.9192i | −0.699863 | − | 0.963279i | ||||
\(725\) | 50.9180i | 1.89105i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −21.3429 | −0.791565 | −0.395782 | − | 0.918344i | \(-0.629527\pi\) | ||||
−0.395782 | + | 0.918344i | \(0.629527\pi\) | |||||||
\(728\) | 6.11559 | − | 8.41738i | 0.226659 | − | 0.311969i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.619187 | + | 0.201186i | −0.0229171 | + | 0.00744622i | ||||
\(731\) | − | 31.5888i | − | 1.16836i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 15.1235i | − | 0.558599i | −0.960204 | − | 0.279300i | \(-0.909898\pi\) | ||
0.960204 | − | 0.279300i | \(-0.0901023\pi\) | |||||||
\(734\) | 3.92109 | + | 12.0679i | 0.144730 | + | 0.445433i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 16.2258 | 0.598090 | ||||||||
\(737\) | −23.5465 | −0.867347 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 38.7212i | − | 1.42438i | −0.701985 | − | 0.712192i | \(-0.747703\pi\) | ||
0.701985 | − | 0.712192i | \(-0.252297\pi\) | |||||||
\(740\) | 0.0688419 | − | 0.0500166i | 0.00253068 | − | 0.00183865i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4.56346 | + | 1.48276i | −0.167530 | + | 0.0544337i | ||||
\(743\) | 39.7258 | 1.45740 | 0.728698 | − | 0.684835i | \(-0.240126\pi\) | ||||
0.728698 | + | 0.684835i | \(0.240126\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.863319 | −0.0316296 | ||||||||
\(746\) | −26.4445 | + | 8.59233i | −0.968201 | + | 0.314588i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 9.79580 | + | 13.4828i | 0.358170 | + | 0.492978i | ||||
\(749\) | − | 6.11985i | − | 0.223615i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.96814 | −0.108309 | −0.0541544 | − | 0.998533i | \(-0.517246\pi\) | ||||
−0.0541544 | + | 0.998533i | \(0.517246\pi\) | |||||||
\(752\) | −15.2192 | + | 46.8400i | −0.554989 | + | 1.70808i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 16.3808 | + | 50.4150i | 0.596554 | + | 1.83600i | ||||
\(755\) | 0.141792i | 0.00516032i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 47.1588i | 1.71401i | 0.515305 | + | 0.857007i | \(0.327679\pi\) | ||||
−0.515305 | + | 0.857007i | \(0.672321\pi\) | |||||||
\(758\) | −33.6075 | + | 10.9198i | −1.22068 | + | 0.396623i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.386848 | + | 0.281062i | 0.0140325 | + | 0.0101952i | ||||
\(761\) | 40.8000 | 1.47900 | 0.739499 | − | 0.673158i | \(-0.235063\pi\) | ||||
0.739499 | + | 0.673158i | \(0.235063\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.85597i | 0.320608i | ||||||||
\(764\) | 2.97282 | − | 2.15988i | 0.107553 | − | 0.0781417i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −8.88553 | − | 27.3468i | −0.321047 | − | 0.988081i | ||||
\(767\) | 25.5019 | 0.920821 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −52.9121 | −1.90806 | −0.954029 | − | 0.299714i | \(-0.903109\pi\) | ||||
−0.954029 | + | 0.299714i | \(0.903109\pi\) | |||||||
\(770\) | −0.0632561 | − | 0.194682i | −0.00227959 | − | 0.00701586i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −24.8254 | + | 18.0367i | −0.893484 | + | 0.649154i | ||||
\(773\) | − | 39.0168i | − | 1.40334i | −0.712503 | − | 0.701669i | \(-0.752439\pi\) | ||
0.712503 | − | 0.701669i | \(-0.247561\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 46.5937 | 1.67370 | ||||||||
\(776\) | 23.2951 | + | 16.9249i | 0.836246 | + | 0.607568i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −3.93752 | + | 1.27938i | −0.141167 | + | 0.0458680i | ||||
\(779\) | 19.5797i | 0.701515i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 11.2848i | − | 0.403802i | ||||||
\(782\) | 3.96394 | + | 12.1998i | 0.141750 | + | 0.436263i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.23607 | − | 3.80423i | 0.0441453 | − | 0.135865i | ||||
\(785\) | 0.0373925 | 0.00133460 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.01675i | 0.0362431i | 0.999836 | + | 0.0181215i | \(0.00576858\pi\) | ||||
−0.999836 | + | 0.0181215i | \(0.994231\pi\) | |||||||
\(788\) | 5.90662 | + | 8.12976i | 0.210415 | + | 0.289611i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0.223999 | − | 0.0727815i | 0.00796951 | − | 0.00258945i | ||||
\(791\) | −9.02383 | −0.320851 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −30.7199 | −1.09090 | ||||||||
\(794\) | −11.0328 | + | 3.58478i | −0.391541 | + | 0.127219i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 35.6506 | − | 25.9017i | 1.26360 | − | 0.918061i | ||||
\(797\) | 50.9667i | 1.80533i | 0.430339 | + | 0.902667i | \(0.358394\pi\) | ||||
−0.430339 | + | 0.902667i | \(0.641606\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −38.9359 | −1.37745 | ||||||||
\(800\) | 28.2672 | 0.999397 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 15.9768 | + | 49.1717i | 0.564162 | + | 1.73631i | ||||
\(803\) | − | 22.0840i | − | 0.779327i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 0.157559i | − | 0.00555324i | ||||||
\(806\) | 46.1334 | − | 14.9896i | 1.62498 | − | 0.527988i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.70820 | − | 2.35114i | 0.0600944 | − | 0.0827129i | ||||
\(809\) | −20.3800 | −0.716522 | −0.358261 | − | 0.933622i | \(-0.616630\pi\) | ||||
−0.358261 | + | 0.933622i | \(0.616630\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 40.7638i | 1.43141i | 0.698402 | + | 0.715706i | \(0.253895\pi\) | ||||
−0.698402 | + | 0.715706i | \(0.746105\pi\) | |||||||
\(812\) | 11.9788 | + | 16.4874i | 0.420372 | + | 0.578593i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.891949 | + | 2.74514i | 0.0312628 | + | 0.0962170i | ||||
\(815\) | 1.19935 | 0.0420113 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 30.7438 | 1.07559 | ||||||||
\(818\) | −2.62989 | − | 8.09396i | −0.0919519 | − | 0.282999i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.410813 | − | 0.565436i | −0.0143462 | − | 0.0197459i | ||||
\(821\) | 35.8394i | 1.25080i | 0.780303 | + | 0.625402i | \(0.215065\pi\) | ||||
−0.780303 | + | 0.625402i | \(0.784935\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 34.8745 | 1.21565 | 0.607824 | − | 0.794071i | \(-0.292042\pi\) | ||||
0.607824 | + | 0.794071i | \(0.292042\pi\) | |||||||
\(824\) | −3.95649 | − | 2.87456i | −0.137831 | − | 0.100140i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 9.32437 | − | 3.02967i | 0.324436 | − | 0.105416i | ||||
\(827\) | 42.4727i | 1.47692i | 0.674296 | + | 0.738461i | \(0.264447\pi\) | ||||
−0.674296 | + | 0.738461i | \(0.735553\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 33.1210i | 1.15034i | 0.818034 | + | 0.575169i | \(0.195064\pi\) | ||||
−0.818034 | + | 0.575169i | \(0.804936\pi\) | |||||||
\(830\) | −0.247870 | − | 0.762866i | −0.00860370 | − | 0.0264795i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 27.9879 | − | 9.09383i | 0.970307 | − | 0.315272i | ||||
\(833\) | 3.16228 | 0.109566 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 0.945922i | − | 0.0327350i | ||||||
\(836\) | −13.1221 | + | 9.53375i | −0.453837 | + | 0.329732i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −3.02956 | + | 0.984364i | −0.104654 | + | 0.0340043i | ||||
\(839\) | 43.5817 | 1.50461 | 0.752304 | − | 0.658817i | \(-0.228943\pi\) | ||||
0.752304 | + | 0.658817i | \(0.228943\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −74.8311 | −2.58038 | ||||||||
\(842\) | 3.86593 | − | 1.25612i | 0.133229 | − | 0.0432887i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −10.0000 | − | 13.7638i | −0.344214 | − | 0.473770i | ||||
\(845\) | − | 0.0292007i | − | 0.00100454i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.05644 | −0.139381 | ||||||||
\(848\) | −12.9074 | − | 4.19387i | −0.443242 | − | 0.144018i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 6.90566 | + | 21.2534i | 0.236862 | + | 0.728987i | ||||
\(851\) | 2.22168i | 0.0761582i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 36.8928i | − | 1.26319i | −0.775300 | − | 0.631593i | \(-0.782401\pi\) | ||
0.775300 | − | 0.631593i | \(-0.217599\pi\) | |||||||
\(854\) | −11.2323 | + | 3.64958i | −0.384360 | + | 0.124886i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 10.1743 | − | 14.0037i | 0.347751 | − | 0.478638i | ||||
\(857\) | −19.2607 | −0.657933 | −0.328967 | − | 0.944342i | \(-0.606700\pi\) | ||||
−0.328967 | + | 0.944342i | \(0.606700\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 19.4667i | − | 0.664195i | −0.943245 | − | 0.332098i | \(-0.892244\pi\) | ||
0.943245 | − | 0.332098i | \(-0.107756\pi\) | |||||||
\(860\) | −0.887841 | + | 0.645054i | −0.0302751 | + | 0.0219962i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −6.87039 | − | 21.1449i | −0.234006 | − | 0.720198i | ||||
\(863\) | 21.4715 | 0.730898 | 0.365449 | − | 0.930831i | \(-0.380915\pi\) | ||||
0.365449 | + | 0.930831i | \(0.380915\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.141291 | −0.00480405 | ||||||||
\(866\) | −1.50345 | − | 4.62715i | −0.0510894 | − | 0.157237i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 15.0872 | − | 10.9615i | 0.512091 | − | 0.372056i | ||||
\(869\) | 7.98916i | 0.271014i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −32.8708 | −1.11378 | ||||||||
\(872\) | −14.7231 | + | 20.2646i | −0.498588 | + | 0.686247i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −11.8734 | + | 3.85790i | −0.401624 | + | 0.130496i | ||||
\(875\) | − | 0.549140i | − | 0.0185643i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 23.8421i | − | 0.805091i | −0.915400 | − | 0.402545i | \(-0.868126\pi\) | ||
0.915400 | − | 0.402545i | \(-0.131874\pi\) | |||||||
\(878\) | −5.37334 | − | 16.5374i | −0.181342 | − | 0.558112i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.178915 | − | 0.550645i | 0.00603123 | − | 0.0185622i | ||||
\(881\) | −8.81134 | −0.296862 | −0.148431 | − | 0.988923i | \(-0.547422\pi\) | ||||
−0.148431 | + | 0.988923i | \(0.547422\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 30.0935i | 1.01273i | 0.862320 | + | 0.506363i | \(0.169011\pi\) | ||||
−0.862320 | + | 0.506363i | \(0.830989\pi\) | |||||||
\(884\) | 13.6749 | + | 18.8218i | 0.459936 | + | 0.633047i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −21.3763 | + | 6.94557i | −0.718149 | + | 0.233341i | ||||
\(887\) | 13.0549 | 0.438340 | 0.219170 | − | 0.975687i | \(-0.429665\pi\) | ||||
0.219170 | + | 0.975687i | \(0.429665\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18.2656 | −0.612609 | ||||||||
\(890\) | −0.946830 | + | 0.307644i | −0.0317378 | + | 0.0103122i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 21.9364 | − | 15.9377i | 0.734484 | − | 0.533634i | ||||
\(893\) | − | 37.8944i | − | 1.26809i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.289321 | 0.00967092 | ||||||||
\(896\) | 9.15298 | − | 6.65003i | 0.305780 | − | 0.222162i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3.92200 | + | 12.0707i | 0.130879 | + | 0.402804i | ||||
\(899\) | 95.0131i | 3.16886i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 10.7293i | − | 0.357446i | ||||||
\(902\) | 22.5473 | − | 7.32606i | 0.750743 | − | 0.243931i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −20.6487 | − | 15.0022i | −0.686767 | − | 0.498965i | ||||
\(905\) | −0.879929 | −0.0292498 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 35.8987i | − | 1.19200i | −0.802985 | − | 0.595999i | \(-0.796756\pi\) | ||
0.802985 | − | 0.595999i | \(-0.203244\pi\) | |||||||
\(908\) | 18.8938 | + | 26.0051i | 0.627014 | + | 0.863011i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.0883051 | − | 0.271775i | −0.00292729 | − | 0.00900926i | ||||
\(911\) | 46.3926 | 1.53705 | 0.768527 | − | 0.639817i | \(-0.220990\pi\) | ||||
0.768527 | + | 0.639817i | \(0.220990\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 27.2085 | 0.900469 | ||||||||
\(914\) | −6.55687 | − | 20.1800i | −0.216882 | − | 0.667494i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 6.47587 | + | 8.91326i | 0.213969 | + | 0.294503i | ||||
\(917\) | 17.4470i | 0.576149i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9.87878 | −0.325871 | −0.162935 | − | 0.986637i | \(-0.552096\pi\) | ||||
−0.162935 | + | 0.986637i | \(0.552096\pi\) | |||||||
\(920\) | 0.261944 | − | 0.360534i | 0.00863602 | − | 0.0118865i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 11.6999 | − | 3.80153i | 0.385316 | − | 0.125197i | ||||
\(923\) | − | 15.7535i | − | 0.518533i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.87043i | 0.127259i | ||||||||
\(926\) | −4.08401 | − | 12.5693i | −0.134209 | − | 0.413053i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 57.6419i | 1.89219i | ||||||||
\(929\) | −3.21688 | −0.105543 | −0.0527713 | − | 0.998607i | \(-0.516805\pi\) | ||||
−0.0527713 | + | 0.998607i | \(0.516805\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.07768i | 0.100867i | ||||||||
\(932\) | −46.3727 | + | 33.6918i | −1.51899 | + | 1.10361i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −12.4187 | + | 4.03508i | −0.406353 | + | 0.132032i | ||||
\(935\) | 0.457725 | 0.0149692 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 54.7874 | 1.78983 | 0.894913 | − | 0.446241i | \(-0.147237\pi\) | ||||
0.894913 | + | 0.446241i | \(0.147237\pi\) | |||||||
\(938\) | −12.0187 | + | 3.90511i | −0.392424 | + | 0.127506i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.795084 | + | 1.09434i | 0.0259328 | + | 0.0356934i | ||||
\(941\) | 8.31449i | 0.271045i | 0.990774 | + | 0.135522i | \(0.0432713\pi\) | ||||
−0.990774 | + | 0.135522i | \(0.956729\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 18.2479 | 0.594232 | ||||||||
\(944\) | 26.3733 | + | 8.56921i | 0.858378 | + | 0.278904i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −11.5033 | − | 35.4035i | −0.374004 | − | 1.15107i | ||||
\(947\) | − | 12.2157i | − | 0.396958i | −0.980105 | − | 0.198479i | \(-0.936400\pi\) | ||
0.980105 | − | 0.198479i | \(-0.0636001\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 30.8291i | − | 1.00075i | ||||||
\(950\) | −20.6849 | + | 6.72093i | −0.671106 | + | 0.218056i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 7.23607 | + | 5.25731i | 0.234522 | + | 0.170390i | ||||
\(953\) | −50.2955 | −1.62923 | −0.814615 | − | 0.580002i | \(-0.803052\pi\) | ||||
−0.814615 | + | 0.580002i | \(0.803052\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 0.100924i | − | 0.00326583i | ||||||
\(956\) | −6.19704 | + | 4.50241i | −0.200426 | + | 0.145618i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3.78478 | + | 11.6483i | 0.122281 | + | 0.376341i | ||||
\(959\) | −7.73613 | −0.249813 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 55.9439 | 1.80464 | ||||||||
\(962\) | 1.24515 | + | 3.83219i | 0.0401454 | + | 0.123555i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.79651 | − | 2.03178i | 0.0900695 | − | 0.0654393i | ||||
\(965\) | 0.842795i | 0.0271305i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.17661 | 0.198626 | 0.0993132 | − | 0.995056i | \(-0.468335\pi\) | ||||
0.0993132 | + | 0.995056i | \(0.468335\pi\) | |||||||
\(968\) | −9.28213 | − | 6.74386i | −0.298339 | − | 0.216756i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.752138 | − | 0.244384i | 0.0241497 | − | 0.00784671i | ||||
\(971\) | 3.74342i | 0.120132i | 0.998194 | + | 0.0600660i | \(0.0191311\pi\) | ||||
−0.998194 | + | 0.0600660i | \(0.980869\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 0.802034i | − | 0.0257120i | ||||||
\(974\) | 4.86943 | + | 14.9865i | 0.156026 | + | 0.480200i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −31.7696 | − | 10.3226i | −1.01692 | − | 0.330418i | ||||
\(977\) | −43.1012 | −1.37893 | −0.689464 | − | 0.724320i | \(-0.742154\pi\) | ||||
−0.689464 | + | 0.724320i | \(0.742154\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 33.7697i | − | 1.07929i | ||||||
\(980\) | −0.0645747 | − | 0.0888795i | −0.00206276 | − | 0.00283915i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 34.2273 | − | 11.1211i | 1.09224 | − | 0.354890i | ||||
\(983\) | 46.8079 | 1.49294 | 0.746470 | − | 0.665419i | \(-0.231747\pi\) | ||||
0.746470 | + | 0.665419i | \(0.231747\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.275997 | 0.00879399 | ||||||||
\(986\) | −43.3396 | + | 14.0819i | −1.38021 | + | 0.448459i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −18.3183 | + | 13.3091i | −0.582784 | + | 0.423417i | ||||
\(989\) | − | 28.6526i | − | 0.911099i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −44.6923 | −1.41970 | −0.709850 | − | 0.704353i | \(-0.751237\pi\) | ||||
−0.709850 | + | 0.704353i | \(0.751237\pi\) | |||||||
\(992\) | 52.7466 | 1.67471 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.87154 | − | 5.76002i | −0.0593617 | − | 0.182697i | ||||
\(995\) | − | 1.21030i | − | 0.0383691i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 41.1361i | 1.30279i | 0.758737 | + | 0.651397i | \(0.225817\pi\) | ||||
−0.758737 | + | 0.651397i | \(0.774183\pi\) | |||||||
\(998\) | 5.61431 | − | 1.82420i | 0.177718 | − | 0.0577440i | ||||
\(999\) | 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 | 1512.2.c.d.757.11 | yes | 16 | |
3.2 | odd | 2 | inner | 1512.2.c.d.757.6 | ✓ | 16 | |
4.3 | odd | 2 | 6048.2.c.d.3025.9 | 16 | |||
8.3 | odd | 2 | 6048.2.c.d.3025.8 | 16 | |||
8.5 | even | 2 | inner | 1512.2.c.d.757.10 | yes | 16 | |
12.11 | even | 2 | 6048.2.c.d.3025.7 | 16 | |||
24.5 | odd | 2 | inner | 1512.2.c.d.757.7 | yes | 16 | |
24.11 | even | 2 | 6048.2.c.d.3025.10 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.c.d.757.6 | ✓ | 16 | 3.2 | odd | 2 | inner | |
1512.2.c.d.757.7 | yes | 16 | 24.5 | odd | 2 | inner | |
1512.2.c.d.757.10 | yes | 16 | 8.5 | even | 2 | inner | |
1512.2.c.d.757.11 | yes | 16 | 1.1 | even | 1 | trivial | |
6048.2.c.d.3025.7 | 16 | 12.11 | even | 2 | |||
6048.2.c.d.3025.8 | 16 | 8.3 | odd | 2 | |||
6048.2.c.d.3025.9 | 16 | 4.3 | odd | 2 | |||
6048.2.c.d.3025.10 | 16 | 24.11 | even | 2 |