Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4016,2,Mod(1,4016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4016, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("4016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4016 = 2^{4} \cdot 251 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4016.a (trivial) |
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: | yes |
Analytic conductor: | \(32.0679214517\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 3x^{6} - 6x^{5} + 18x^{4} + 8x^{3} - 17x^{2} - 9x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1004) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.358013\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4016.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | −0.358013 | −0.206699 | −0.103349 | − | 0.994645i | \(-0.532956\pi\) | ||||
−0.103349 | + | 0.994645i | \(0.532956\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.25358 | 1.00783 | 0.503916 | − | 0.863753i | \(-0.331892\pi\) | ||||
0.503916 | + | 0.863753i | \(0.331892\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.66949 | 1.76490 | 0.882451 | − | 0.470404i | \(-0.155892\pi\) | ||||
0.882451 | + | 0.470404i | \(0.155892\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.87183 | −0.957276 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.681867 | 0.205591 | 0.102795 | − | 0.994703i | \(-0.467221\pi\) | ||||
0.102795 | + | 0.994703i | \(0.467221\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.464791 | 0.128910 | 0.0644550 | − | 0.997921i | \(-0.479469\pi\) | ||||
0.0644550 | + | 0.997921i | \(0.479469\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.806810 | −0.208318 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.986388 | −0.239234 | −0.119617 | − | 0.992820i | \(-0.538167\pi\) | ||||
−0.119617 | + | 0.992820i | \(0.538167\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.32972 | 0.534474 | 0.267237 | − | 0.963631i | \(-0.413889\pi\) | ||||
0.267237 | + | 0.963631i | \(0.413889\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.67174 | −0.364803 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.37412 | 1.12058 | 0.560290 | − | 0.828296i | \(-0.310690\pi\) | ||||
0.560290 | + | 0.828296i | \(0.310690\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.0786287 | 0.0157257 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.10219 | 0.404566 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.75253 | −0.882523 | −0.441261 | − | 0.897379i | \(-0.645469\pi\) | ||||
−0.441261 | + | 0.897379i | \(0.645469\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.57250 | 0.282430 | 0.141215 | − | 0.989979i | \(-0.454899\pi\) | ||||
0.141215 | + | 0.989979i | \(0.454899\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.244117 | −0.0424953 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 10.5231 | 1.77873 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.55119 | 0.583812 | 0.291906 | − | 0.956447i | \(-0.405711\pi\) | ||||
0.291906 | + | 0.956447i | \(0.405711\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.166401 | −0.0266455 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.278393 | 0.0434777 | 0.0217389 | − | 0.999764i | \(-0.493080\pi\) | ||||
0.0217389 | + | 0.999764i | \(0.493080\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.78076 | 0.271563 | 0.135782 | − | 0.990739i | \(-0.456645\pi\) | ||||
0.135782 | + | 0.990739i | \(0.456645\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.47190 | −0.964773 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.22141 | −0.324026 | −0.162013 | − | 0.986789i | \(-0.551799\pi\) | ||||
−0.162013 | + | 0.986789i | \(0.551799\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 14.8042 | 2.11488 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.353139 | 0.0494494 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.88544 | 0.396346 | 0.198173 | − | 0.980167i | \(-0.436499\pi\) | ||||
0.198173 | + | 0.980167i | \(0.436499\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.53664 | 0.207201 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.834068 | −0.110475 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.32720 | 0.823731 | 0.411866 | − | 0.911245i | \(-0.364877\pi\) | ||||
0.411866 | + | 0.911245i | \(0.364877\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.0560602 | 0.00717778 | 0.00358889 | − | 0.999994i | \(-0.498858\pi\) | ||||
0.00358889 | + | 0.999994i | \(0.498858\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −13.4100 | −1.68950 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.04744 | 0.129920 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.83951 | 0.713410 | 0.356705 | − | 0.934217i | \(-0.383900\pi\) | ||||
0.356705 | + | 0.934217i | \(0.383900\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.92400 | −0.231623 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.74305 | 0.325540 | 0.162770 | − | 0.986664i | \(-0.447957\pi\) | ||||
0.162770 | + | 0.986664i | \(0.447957\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.63680 | 1.12790 | 0.563951 | − | 0.825808i | \(-0.309281\pi\) | ||||
0.563951 | + | 0.825808i | \(0.309281\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.0281501 | −0.00325049 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.18397 | 0.362847 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.00611 | −0.338214 | −0.169107 | − | 0.985598i | \(-0.554088\pi\) | ||||
−0.169107 | + | 0.985598i | \(0.554088\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.86287 | 0.873652 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.32667 | 0.255385 | 0.127693 | − | 0.991814i | \(-0.459243\pi\) | ||||
0.127693 | + | 0.991814i | \(0.459243\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.22291 | −0.241108 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.70147 | 0.182416 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.3727 | −1.09950 | −0.549750 | − | 0.835329i | \(-0.685277\pi\) | ||||
−0.549750 | + | 0.835329i | \(0.685277\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.17034 | 0.227513 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.562976 | −0.0583778 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.25021 | 0.538660 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.01956 | −0.408124 | −0.204062 | − | 0.978958i | \(-0.565414\pi\) | ||||
−0.204062 | + | 0.978958i | \(0.565414\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.95820 | −0.196807 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.3006 | −1.12445 | −0.562226 | − | 0.826983i | \(-0.690055\pi\) | ||||
−0.562226 | + | 0.826983i | \(0.690055\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.11246 | −0.109614 | −0.0548071 | − | 0.998497i | \(-0.517454\pi\) | ||||
−0.0548071 | + | 0.998497i | \(0.517454\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.76740 | −0.367660 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.37893 | 0.906696 | 0.453348 | − | 0.891334i | \(-0.350230\pi\) | ||||
0.453348 | + | 0.891334i | \(0.350230\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.44018 | −0.329510 | −0.164755 | − | 0.986335i | \(-0.552683\pi\) | ||||
−0.164755 | + | 0.986335i | \(0.552683\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.27137 | −0.120673 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.3670 | 1.35153 | 0.675767 | − | 0.737115i | \(-0.263813\pi\) | ||||
0.675767 | + | 0.737115i | \(0.263813\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.1110 | 1.12936 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.33480 | −0.123402 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.60593 | −0.422225 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.5351 | −0.957732 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.0996683 | −0.00898679 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.0907 | −0.991983 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.360627 | −0.0320005 | −0.0160002 | − | 0.999872i | \(-0.505093\pi\) | ||||
−0.0160002 | + | 0.999872i | \(0.505093\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.637534 | −0.0561318 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.6353 | −1.54080 | −0.770402 | − | 0.637558i | \(-0.779945\pi\) | ||||
−0.770402 | + | 0.637558i | \(0.779945\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.8786 | 0.943295 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.73745 | 0.407735 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.948673 | −0.0810506 | −0.0405253 | − | 0.999179i | \(-0.512903\pi\) | ||||
−0.0405253 | + | 0.999179i | \(0.512903\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.1604 | 1.11625 | 0.558126 | − | 0.829756i | \(-0.311520\pi\) | ||||
0.558126 | + | 0.829756i | \(0.311520\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.795293 | 0.0669758 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.316926 | 0.0265027 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.7102 | −0.889435 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.30008 | −0.437143 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.21002 | 0.754515 | 0.377257 | − | 0.926108i | \(-0.376867\pi\) | ||||
0.377257 | + | 0.926108i | \(0.376867\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.1103 | −1.22966 | −0.614828 | − | 0.788661i | \(-0.710774\pi\) | ||||
−0.614828 | + | 0.788661i | \(0.710774\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.83274 | 0.229013 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.54376 | 0.284642 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.02040 | 0.241054 | 0.120527 | − | 0.992710i | \(-0.461542\pi\) | ||||
0.120527 | + | 0.992710i | \(0.461542\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.03302 | −0.0819241 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 25.0944 | 1.97772 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.10519 | −0.478195 | −0.239098 | − | 0.970996i | \(-0.576852\pi\) | ||||
−0.239098 | + | 0.970996i | \(0.576852\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.550137 | −0.0428281 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.604730 | −0.0467954 | −0.0233977 | − | 0.999726i | \(-0.507448\pi\) | ||||
−0.0233977 | + | 0.999726i | \(0.507448\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.7840 | −0.983382 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.69055 | −0.511639 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.88294 | 0.219186 | 0.109593 | − | 0.993977i | \(-0.465045\pi\) | ||||
0.109593 | + | 0.993977i | \(0.465045\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.367156 | 0.0277544 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.26522 | −0.170264 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.12375 | −0.681941 | −0.340971 | − | 0.940074i | \(-0.610756\pi\) | ||||
−0.340971 | + | 0.940074i | \(0.610756\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.1054 | 0.899788 | 0.449894 | − | 0.893082i | \(-0.351462\pi\) | ||||
0.449894 | + | 0.893082i | \(0.351462\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.0200703 | −0.00148364 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.00289 | 0.588385 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.672585 | −0.0491843 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 9.81615 | 0.714020 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −21.7332 | −1.57256 | −0.786279 | − | 0.617872i | \(-0.787995\pi\) | ||||
−0.786279 | + | 0.617872i | \(0.787995\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.9952 | 1.00739 | 0.503697 | − | 0.863880i | \(-0.331973\pi\) | ||||
0.503697 | + | 0.863880i | \(0.331973\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.374998 | −0.0268542 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.06139 | −0.574350 | −0.287175 | − | 0.957878i | \(-0.592716\pi\) | ||||
−0.287175 | + | 0.957878i | \(0.592716\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.9548 | 1.41456 | 0.707281 | − | 0.706933i | \(-0.249922\pi\) | ||||
0.707281 | + | 0.706933i | \(0.249922\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.09062 | −0.147461 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −22.1919 | −1.55757 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.627382 | 0.0438183 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −15.4335 | −1.07270 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.58856 | 0.109883 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.5982 | 1.48688 | 0.743439 | − | 0.668803i | \(-0.233193\pi\) | ||||
0.743439 | + | 0.668803i | \(0.233193\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.982045 | −0.0672886 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.01309 | 0.273690 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.34279 | 0.498461 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.45009 | −0.233136 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.458465 | −0.0308397 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −23.1367 | −1.54935 | −0.774674 | − | 0.632361i | \(-0.782086\pi\) | ||||
−0.774674 | + | 0.632361i | \(0.782086\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.225808 | −0.0150539 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.98118 | 0.396985 | 0.198492 | − | 0.980102i | \(-0.436396\pi\) | ||||
0.198492 | + | 0.980102i | \(0.436396\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 24.9844 | 1.65101 | 0.825506 | − | 0.564393i | \(-0.190890\pi\) | ||||
0.825506 | + | 0.564393i | \(0.190890\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.13990 | −0.0750001 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.09995 | 0.530646 | 0.265323 | − | 0.964160i | \(-0.414521\pi\) | ||||
0.265323 | + | 0.964160i | \(0.414521\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.00613 | −0.326564 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.07623 | 0.0699084 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.5792 | 0.943052 | 0.471526 | − | 0.881852i | \(-0.343703\pi\) | ||||
0.471526 | + | 0.881852i | \(0.343703\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −30.4446 | −1.96111 | −0.980553 | − | 0.196254i | \(-0.937122\pi\) | ||||
−0.980553 | + | 0.196254i | \(0.937122\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −9.12157 | −0.585149 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 33.3624 | 2.13145 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.08283 | 0.0688990 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.832978 | −0.0527878 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.00000 | −0.0631194 | ||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.66443 | 0.230381 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.795828 | 0.0498367 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.48685 | 0.467017 | 0.233508 | − | 0.972355i | \(-0.424979\pi\) | ||||
0.233508 | + | 0.972355i | \(0.424979\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 16.5823 | 1.03037 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 13.6484 | 0.844818 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.11608 | −0.0688202 | −0.0344101 | − | 0.999408i | \(-0.510955\pi\) | ||||
−0.0344101 | + | 0.999408i | \(0.510955\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.50257 | 0.399450 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.71354 | 0.227265 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.28310 | −0.505029 | −0.252515 | − | 0.967593i | \(-0.581258\pi\) | ||||
−0.252515 | + | 0.967593i | \(0.581258\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22.2358 | 1.35073 | 0.675364 | − | 0.737484i | \(-0.263986\pi\) | ||||
0.675364 | + | 0.737484i | \(0.263986\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.777009 | −0.0470267 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.0536143 | 0.00323306 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.6054 | −0.637219 | −0.318609 | − | 0.947886i | \(-0.603216\pi\) | ||||
−0.318609 | + | 0.947886i | \(0.603216\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.51596 | −0.270363 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.18734 | 0.488416 | 0.244208 | − | 0.969723i | \(-0.421472\pi\) | ||||
0.244208 | + | 0.969723i | \(0.421472\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 27.4202 | 1.62996 | 0.814980 | − | 0.579490i | \(-0.196748\pi\) | ||||
0.814980 | + | 0.579490i | \(0.196748\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.87964 | −0.111340 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.29996 | 0.0767340 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.0270 | −0.942767 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.43905 | 0.0843587 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.15462 | −0.184295 | −0.0921475 | − | 0.995745i | \(-0.529373\pi\) | ||||
−0.0921475 | + | 0.995745i | \(0.529373\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.2589 | 0.830183 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.43341 | 0.0831750 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.49784 | 0.144454 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.31525 | 0.479283 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.04576 | 0.232423 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.126336 | 0.00723400 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.4553 | 1.05330 | 0.526650 | − | 0.850082i | \(-0.323448\pi\) | ||||
0.526650 | + | 0.850082i | \(0.323448\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.398275 | 0.0226571 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −25.0171 | −1.41859 | −0.709296 | − | 0.704911i | \(-0.750987\pi\) | ||||
−0.709296 | + | 0.704911i | \(0.750987\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.0867 | 0.570132 | 0.285066 | − | 0.958508i | \(-0.407984\pi\) | ||||
0.285066 | + | 0.958508i | \(0.407984\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −30.2205 | −1.70273 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 22.3677 | 1.25629 | 0.628147 | − | 0.778095i | \(-0.283814\pi\) | ||||
0.628147 | + | 0.778095i | \(0.283814\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.24059 | −0.181438 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.35777 | −0.187413 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.29801 | −0.127864 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.0365459 | 0.00202720 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.23163 | 0.0681092 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −10.3729 | −0.571875 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.0247 | 1.04569 | 0.522846 | − | 0.852427i | \(-0.324870\pi\) | ||||
0.522846 | + | 0.852427i | \(0.324870\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −10.1984 | −0.558869 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 13.1598 | 0.718998 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.3647 | 0.891445 | 0.445722 | − | 0.895171i | \(-0.352947\pi\) | ||||
0.445722 | + | 0.895171i | \(0.352947\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.14357 | −0.279360 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.07224 | 0.0580649 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 36.4415 | 1.96766 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.33589 | −0.233437 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.559753 | −0.0300491 | −0.0150246 | − | 0.999887i | \(-0.504783\pi\) | ||||
−0.0150246 | + | 0.999887i | \(0.504783\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.4850 | −0.614777 | −0.307389 | − | 0.951584i | \(-0.599455\pi\) | ||||
−0.307389 | + | 0.951584i | \(0.599455\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.977079 | 0.0521526 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.0283464 | −0.00150872 | −0.000754362 | − | 1.00000i | \(-0.500240\pi\) | ||||
−0.000754362 | 1.00000i | \(0.500240\pi\) | ||||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.18168 | 0.328089 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.64898 | 0.0872734 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.12611 | 0.323324 | 0.161662 | − | 0.986846i | \(-0.448315\pi\) | ||||
0.161662 | + | 0.986846i | \(0.448315\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.5724 | −0.714338 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.77168 | 0.197962 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 21.7173 | 1.13674 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.29169 | 0.276224 | 0.138112 | − | 0.990417i | \(-0.455897\pi\) | ||||
0.138112 | + | 0.990417i | \(0.455897\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.799498 | −0.0416202 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 13.4735 | 0.699511 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 27.7468 | 1.43668 | 0.718338 | − | 0.695694i | \(-0.244903\pi\) | ||||
0.718338 | + | 0.695694i | \(0.244903\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.97061 | 0.205042 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.20893 | −0.113766 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.91895 | −0.252669 | −0.126335 | − | 0.991988i | \(-0.540321\pi\) | ||||
−0.126335 | + | 0.991988i | \(0.540321\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.129109 | 0.00661446 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.62298 | 0.287321 | 0.143661 | − | 0.989627i | \(-0.454113\pi\) | ||||
0.143661 | + | 0.989627i | \(0.454113\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.17534 | 0.365689 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.11403 | −0.259961 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 32.4279 | 1.64416 | 0.822080 | − | 0.569372i | \(-0.192813\pi\) | ||||
0.822080 | + | 0.569372i | \(0.192813\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.30096 | −0.268081 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.31366 | 0.318482 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.77452 | −0.340863 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.65060 | −0.233407 | −0.116704 | − | 0.993167i | \(-0.537233\pi\) | ||||
−0.116704 | + | 0.993167i | \(0.537233\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.89468 | −0.194978 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −19.4879 | −0.973180 | −0.486590 | − | 0.873630i | \(-0.661759\pi\) | ||||
−0.486590 | + | 0.873630i | \(0.661759\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.730885 | 0.0364080 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 17.7196 | 0.880495 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.42144 | 0.120026 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −20.7056 | −1.02383 | −0.511913 | − | 0.859037i | \(-0.671063\pi\) | ||||
−0.511913 | + | 0.859037i | \(0.671063\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.339637 | 0.0167531 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 29.5448 | 1.45381 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.24334 | 0.257386 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.71160 | −0.230728 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −30.0719 | −1.46911 | −0.734555 | − | 0.678549i | \(-0.762609\pi\) | ||||
−0.734555 | + | 0.678549i | \(0.762609\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −24.2237 | −1.18059 | −0.590295 | − | 0.807188i | \(-0.700988\pi\) | ||||
−0.590295 | + | 0.807188i | \(0.700988\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.37951 | 0.310182 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.0775584 | −0.00376214 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.261773 | 0.0126681 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.113463 | −0.00547807 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.0779 | −0.581774 | −0.290887 | − | 0.956757i | \(-0.593950\pi\) | ||||
−0.290887 | + | 0.956757i | \(0.593950\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.5412 | 0.939089 | 0.469544 | − | 0.882909i | \(-0.344418\pi\) | ||||
0.469544 | + | 0.882909i | \(0.344418\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.83439 | 0.183845 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 12.5202 | 0.598921 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.2606 | 0.585168 | 0.292584 | − | 0.956240i | \(-0.405485\pi\) | ||||
0.292584 | + | 0.956240i | \(0.405485\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −42.5150 | −2.02452 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −24.8669 | −1.18146 | −0.590731 | − | 0.806869i | \(-0.701160\pi\) | ||||
−0.590731 | + | 0.806869i | \(0.701160\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −23.3756 | −1.10811 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.29730 | −0.155957 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −20.3163 | −0.958785 | −0.479393 | − | 0.877601i | \(-0.659143\pi\) | ||||
−0.479393 | + | 0.877601i | \(0.659143\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.189827 | 0.00893862 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.40966 | 0.254168 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.89104 | 0.229295 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −26.0262 | −1.21746 | −0.608728 | − | 0.793379i | \(-0.708320\pi\) | ||||
−0.608728 | + | 0.793379i | \(0.708320\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.07357 | −0.0967861 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.3380 | −0.481490 | −0.240745 | − | 0.970588i | \(-0.577392\pi\) | ||||
−0.240745 | + | 0.970588i | \(0.577392\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.96910 | −0.0915117 | −0.0457559 | − | 0.998953i | \(-0.514570\pi\) | ||||
−0.0457559 | + | 0.998953i | \(0.514570\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.26871 | −0.0588351 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 34.7843 | 1.60963 | 0.804814 | − | 0.593528i | \(-0.202265\pi\) | ||||
0.804814 | + | 0.593528i | \(0.202265\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 27.2676 | 1.25910 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.08134 | −0.0498256 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.21424 | 0.0558309 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.183183 | 0.00840500 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.28648 | −0.379412 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.7833 | −0.492701 | −0.246351 | − | 0.969181i | \(-0.579232\pi\) | ||||
−0.246351 | + | 0.969181i | \(0.579232\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.65056 | 0.0752592 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −8.98411 | −0.408791 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9.05840 | −0.411321 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −21.7901 | −0.987402 | −0.493701 | − | 0.869632i | \(-0.664356\pi\) | ||||
−0.493701 | + | 0.869632i | \(0.664356\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.18573 | 0.0988423 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −23.6974 | −1.06945 | −0.534725 | − | 0.845026i | \(-0.679585\pi\) | ||||
−0.534725 | + | 0.845026i | \(0.679585\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.68784 | 0.211130 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.41297 | −0.198348 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.8086 | 0.574546 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.33650 | 0.238895 | 0.119447 | − | 0.992841i | \(-0.461888\pi\) | ||||
0.119447 | + | 0.992841i | \(0.461888\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.216501 | 0.00967255 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21.7718 | 0.970755 | 0.485378 | − | 0.874305i | \(-0.338682\pi\) | ||||
0.485378 | + | 0.874305i | \(0.338682\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −25.4668 | −1.13326 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.57682 | 0.203264 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.15914 | 0.184351 | 0.0921753 | − | 0.995743i | \(-0.470618\pi\) | ||||
0.0921753 | + | 0.995743i | \(0.470618\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 44.9990 | 1.99064 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.89750 | 0.216230 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.50702 | −0.110473 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.51471 | −0.0666167 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.03213 | −0.0453055 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −37.9596 | −1.66304 | −0.831520 | − | 0.555494i | \(-0.812529\pi\) | ||||
−0.831520 | + | 0.555494i | \(0.812529\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 27.9866 | 1.22377 | 0.611884 | − | 0.790947i | \(-0.290412\pi\) | ||||
0.611884 | + | 0.790947i | \(0.290412\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.131447 | −0.00573680 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.55110 | −0.0675669 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.88113 | 0.255701 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −18.1706 | −0.788538 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.129395 | 0.00560471 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 21.1362 | 0.913797 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.26642 | 0.140956 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10.0945 | 0.434800 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −25.0936 | −1.07886 | −0.539429 | − | 0.842031i | \(-0.681360\pi\) | ||||
−0.539429 | + | 0.842031i | \(0.681360\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.33389 | −0.185985 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.75273 | −0.332091 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.9856 | 0.555225 | 0.277613 | − | 0.960693i | \(-0.410457\pi\) | ||||
0.277613 | + | 0.960693i | \(0.410457\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.160995 | −0.00687111 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11.0721 | −0.471685 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −14.0370 | −0.596915 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.86514 | −0.121618 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −43.4396 | −1.84060 | −0.920298 | − | 0.391219i | \(-0.872054\pi\) | ||||
−0.920298 | + | 0.391219i | \(0.872054\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.827682 | 0.0350072 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.240794 | 0.0101663 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 31.9340 | 1.34586 | 0.672929 | − | 0.739707i | \(-0.265036\pi\) | ||||
0.672929 | + | 0.739707i | \(0.265036\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 32.3772 | 1.36212 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 36.7156 | 1.54191 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −22.4340 | −0.940480 | −0.470240 | − | 0.882539i | \(-0.655833\pi\) | ||||
−0.470240 | + | 0.882539i | \(0.655833\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.4435 | −0.646291 | −0.323146 | − | 0.946349i | \(-0.604740\pi\) | ||||
−0.323146 | + | 0.946349i | \(0.604740\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.78075 | 0.325045 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.422560 | 0.0176220 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −34.0505 | −1.41754 | −0.708771 | − | 0.705439i | \(-0.750750\pi\) | ||||
−0.708771 | + | 0.705439i | \(0.750750\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5.01044 | −0.208227 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.8644 | 0.450730 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.96749 | 0.0814849 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.00808 | −0.124369 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −21.8100 | −0.900195 | −0.450098 | − | 0.892979i | \(-0.648611\pi\) | ||||
−0.450098 | + | 0.892979i | \(0.648611\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.66349 | 0.150951 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.88608 | 0.118717 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −25.9000 | −1.06359 | −0.531794 | − | 0.846874i | \(-0.678482\pi\) | ||||
−0.531794 | + | 0.846874i | \(0.678482\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10.3798 | −0.425532 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7.14409 | −0.292388 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 48.0636 | 1.96383 | 0.981913 | − | 0.189331i | \(-0.0606319\pi\) | ||||
0.981913 | + | 0.189331i | \(0.0606319\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.37140 | 0.137522 | 0.0687611 | − | 0.997633i | \(-0.478095\pi\) | ||||
0.0687611 | + | 0.997633i | \(0.478095\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −16.7701 | −0.682930 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −23.7416 | −0.965234 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13.6598 | −0.554433 | −0.277216 | − | 0.960808i | \(-0.589412\pi\) | ||||
−0.277216 | + | 0.960808i | \(0.589412\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.94498 | 0.321947 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.03249 | −0.0417702 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.0736 | −0.406870 | −0.203435 | − | 0.979088i | \(-0.565211\pi\) | ||||
−0.203435 | + | 0.979088i | \(0.565211\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.224611 | −0.00905717 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.2686 | 0.896500 | 0.448250 | − | 0.893908i | \(-0.352048\pi\) | ||||
0.448250 | + | 0.893908i | \(0.352048\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.92761 | −0.117671 | −0.0588354 | − | 0.998268i | \(-0.518739\pi\) | ||||
−0.0588354 | + | 0.998268i | \(0.518739\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 11.2974 | 0.453349 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −48.4351 | −1.94051 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.3870 | −1.01548 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.568724 | −0.0227126 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.50285 | −0.139668 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.95941 | 0.0780027 | 0.0390014 | − | 0.999239i | \(-0.487582\pi\) | ||||
0.0390014 | + | 0.999239i | \(0.487582\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7.73241 | −0.307336 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.812703 | −0.0322511 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.88085 | 0.272629 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.87756 | −0.311631 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −43.3664 | −1.71287 | −0.856435 | − | 0.516255i | \(-0.827326\pi\) | ||||
−0.856435 | + | 0.516255i | \(0.827326\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20.0953 | −0.792480 | −0.396240 | − | 0.918147i | \(-0.629685\pi\) | ||||
−0.396240 | + | 0.918147i | \(0.629685\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.43674 | −0.0565714 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.18944 | 0.361274 | 0.180637 | − | 0.983550i | \(-0.442184\pi\) | ||||
0.180637 | + | 0.983550i | \(0.442184\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.31431 | 0.169351 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.62881 | −0.103031 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.73955 | 0.302872 | 0.151436 | − | 0.988467i | \(-0.451610\pi\) | ||||
0.151436 | + | 0.988467i | \(0.451610\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −39.7426 | −1.55287 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −27.6752 | −1.07971 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.9678 | 0.427243 | 0.213622 | − | 0.976916i | \(-0.431474\pi\) | ||||
0.213622 | + | 0.976916i | \(0.431474\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.9753 | −0.893636 | −0.446818 | − | 0.894625i | \(-0.647443\pi\) | ||||
−0.446818 | + | 0.894625i | \(0.647443\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.164136 | 0.00637452 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 24.5158 | 0.950683 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −25.5407 | −0.988938 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8.28323 | 0.320248 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.0382256 | 0.00147568 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −40.6928 | −1.56859 | −0.784296 | − | 0.620387i | \(-0.786976\pi\) | ||||
−0.784296 | + | 0.620387i | \(0.786976\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.165292 | 0.00636210 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.47467 | −0.133543 | −0.0667713 | − | 0.997768i | \(-0.521270\pi\) | ||||
−0.0667713 | + | 0.997768i | \(0.521270\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −18.7693 | −0.720299 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.14134 | −0.0820562 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −13.6429 | −0.522033 | −0.261016 | − | 0.965334i | \(-0.584058\pi\) | ||||
−0.261016 | + | 0.965334i | \(0.584058\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.13791 | −0.0816854 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8.94471 | −0.341262 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.34113 | 0.0510929 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −51.5022 | −1.95924 | −0.979619 | − | 0.200867i | \(-0.935624\pi\) | ||||
−0.979619 | + | 0.200867i | \(0.935624\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −9.14382 | −0.347345 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 29.6581 | 1.12500 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.274604 | −0.0104014 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.89988 | −0.109684 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −29.0166 | −1.09594 | −0.547971 | − | 0.836497i | \(-0.684600\pi\) | ||||
−0.547971 | + | 0.836497i | \(0.684600\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.27327 | 0.312032 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.79226 | 0.0675003 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −52.7681 | −1.98455 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18.5227 | −0.695634 | −0.347817 | − | 0.937563i | \(-0.613077\pi\) | ||||
−0.347817 | + | 0.937563i | \(0.613077\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.63303 | 0.323764 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.45081 | 0.316485 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.714218 | 0.0267102 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5.21955 | −0.194927 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 16.7133 | 0.623300 | 0.311650 | − | 0.950197i | \(-0.399118\pi\) | ||||
0.311650 | + | 0.950197i | \(0.399118\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.19463 | −0.193458 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 10.8995 | 0.405358 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.373685 | −0.0138783 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.88214 | −0.218156 | −0.109078 | − | 0.994033i | \(-0.534790\pi\) | ||||
−0.109078 | + | 0.994033i | \(0.534790\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −20.3230 | −0.752703 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.75652 | −0.0649672 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.631585 | 0.0233281 | 0.0116641 | − | 0.999932i | \(-0.496287\pi\) | ||||
0.0116641 | + | 0.999932i | \(0.496287\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −11.9442 | −0.440567 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.98177 | 0.146670 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −24.4246 | −0.898473 | −0.449236 | − | 0.893413i | \(-0.648304\pi\) | ||||
−0.449236 | + | 0.893413i | \(0.648304\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.387668 | −0.0142413 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −42.5291 | −1.56024 | −0.780120 | − | 0.625629i | \(-0.784842\pi\) | ||||
−0.780120 | + | 0.625629i | \(0.784842\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 20.7555 | 0.760424 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.68180 | −0.244474 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 43.7949 | 1.60023 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −28.3865 | −1.03584 | −0.517919 | − | 0.855429i | \(-0.673293\pi\) | ||||
−0.517919 | + | 0.855429i | \(0.673293\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.358013 | 0.0130467 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −34.0522 | −1.23929 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23.1842 | 0.842645 | 0.421323 | − | 0.906911i | \(-0.361566\pi\) | ||||
0.421323 | + | 0.906911i | \(0.361566\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.31191 | −0.0476194 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −29.7476 | −1.07835 | −0.539174 | − | 0.842194i | \(-0.681264\pi\) | ||||
−0.539174 | + | 0.842194i | \(0.681264\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −16.0639 | −0.581553 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.38380 | 0.230807 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.94083 | 0.106187 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30.6145 | 1.10399 | 0.551993 | − | 0.833849i | \(-0.313867\pi\) | ||||
0.551993 | + | 0.833849i | \(0.313867\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.68038 | −0.0965317 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 24.8766 | 0.894748 | 0.447374 | − | 0.894347i | \(-0.352359\pi\) | ||||
0.447374 | + | 0.894347i | \(0.352359\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.123644 | 0.00444142 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.93666 | −0.212976 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.648578 | 0.0232377 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.87039 | 0.0669279 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −9.99071 | −0.357039 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.80672 | 0.242942 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −32.1374 | −1.14557 | −0.572787 | − | 0.819704i | \(-0.694138\pi\) | ||||
−0.572787 | + | 0.819704i | \(0.694138\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.399569 | 0.0142250 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 67.0866 | 2.38533 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.0260563 | 0.000925287 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.32800 | −0.0825657 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.16154 | 0.0411440 | 0.0205720 | − | 0.999788i | \(-0.493451\pi\) | ||||
0.0205720 | + | 0.999788i | \(0.493451\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.19117 | 0.0775182 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 29.7885 | 1.05252 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.57101 | 0.231886 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 56.5523 | 1.99321 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.96545 | 0.104389 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 27.8304 | 0.978465 | 0.489232 | − | 0.872153i | \(-0.337277\pi\) | ||||
0.489232 | + | 0.872153i | \(0.337277\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28.3598 | 0.995847 | 0.497924 | − | 0.867221i | \(-0.334096\pi\) | ||||
0.497924 | + | 0.867221i | \(0.334096\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7.96069 | −0.279194 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −13.7585 | −0.481941 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.14867 | 0.145144 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.23284 | −0.217793 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.07414 | 0.246889 | 0.123445 | − | 0.992351i | \(-0.460606\pi\) | ||||
0.123445 | + | 0.992351i | \(0.460606\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 32.8771 | 1.14602 | 0.573011 | − | 0.819548i | \(-0.305775\pi\) | ||||
0.573011 | + | 0.819548i | \(0.305775\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.0191946 | −0.000668270 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 35.8898 | 1.24801 | 0.624006 | − | 0.781420i | \(-0.285504\pi\) | ||||
0.624006 | + | 0.781420i | \(0.285504\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 32.7648 | 1.13797 | 0.568984 | − | 0.822349i | \(-0.307337\pi\) | ||||
0.568984 | + | 0.822349i | \(0.307337\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.79688 | 0.131712 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −14.6027 | −0.505952 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.36281 | −0.0471619 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.30570 | 0.114262 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8.55189 | 0.295244 | 0.147622 | − | 0.989044i | \(-0.452838\pi\) | ||||
0.147622 | + | 0.989044i | \(0.452838\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.41345 | −0.221154 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.93117 | −0.100955 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −28.8097 | −0.991084 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −49.1934 | −1.69030 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9.81676 | −0.336910 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 19.0845 | 0.654208 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −40.7800 | −1.39628 | −0.698140 | − | 0.715961i | \(-0.745989\pi\) | ||||
−0.698140 | + | 0.715961i | \(0.745989\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −15.0777 | −0.515646 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −22.2800 | −0.761069 | −0.380535 | − | 0.924767i | \(-0.624260\pi\) | ||||
−0.380535 | + | 0.924767i | \(0.624260\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 44.1604 | 1.50673 | 0.753367 | − | 0.657600i | \(-0.228428\pi\) | ||||
0.753367 | + | 0.657600i | \(0.228428\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.465401 | −0.0158608 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −54.9486 | −1.87047 | −0.935236 | − | 0.354024i | \(-0.884813\pi\) | ||||
−0.935236 | + | 0.354024i | \(0.884813\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.49695 | 0.220903 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.73788 | 0.194869 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.04977 | −0.0695336 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.71415 | 0.0919656 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 11.5435 | 0.390687 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −51.7880 | −1.75075 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 52.8730 | 1.78540 | 0.892698 | − | 0.450656i | \(-0.148810\pi\) | ||||
0.892698 | + | 0.450656i | \(0.148810\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.12939 | 0.0380935 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −36.9873 | −1.24613 | −0.623067 | − | 0.782168i | \(-0.714114\pi\) | ||||
−0.623067 | + | 0.782168i | \(0.714114\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 55.4842 | 1.86719 | 0.933597 | − | 0.358326i | \(-0.116652\pi\) | ||||
0.933597 | + | 0.358326i | \(0.116652\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5.10485 | −0.171598 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −27.5877 | −0.926306 | −0.463153 | − | 0.886278i | \(-0.653282\pi\) | ||||
−0.463153 | + | 0.886278i | \(0.653282\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.68395 | −0.0564777 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.36143 | 0.179615 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.17526 | −0.173184 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −20.5611 | −0.687282 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.894259 | −0.0298584 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.47337 | −0.249251 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.84616 | −0.0948194 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.97696 | −0.0990671 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 27.2805 | 0.906836 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 31.2818 | 1.03870 | 0.519348 | − | 0.854563i | \(-0.326175\pi\) | ||||
0.519348 | + | 0.854563i | \(0.326175\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 32.4534 | 1.07641 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −41.7288 | −1.38254 | −0.691268 | − | 0.722598i | \(-0.742948\pi\) | ||||
−0.691268 | + | 0.722598i | \(0.742948\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.58648 | 0.0525048 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.0452300 | −0.00149526 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −82.3480 | −2.71937 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 34.8630 | 1.15002 | 0.575012 | − | 0.818145i | \(-0.304997\pi\) | ||||
0.575012 | + | 0.818145i | \(0.304997\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.60723 | −0.217716 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.27494 | 0.0419653 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.279225 | 0.00918088 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.19480 | 0.104931 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 38.2158 | 1.25382 | 0.626910 | − | 0.779092i | \(-0.284320\pi\) | ||||
0.626910 | + | 0.779092i | \(0.284320\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 34.4895 | 1.13035 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.95645 | 0.293221 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.51573 | −0.0495695 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −23.1614 | −0.756651 | −0.378326 | − | 0.925673i | \(-0.623500\pi\) | ||||
−0.378326 | + | 0.925673i | \(0.623500\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.61115 | −0.117846 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −53.5932 | −1.74709 | −0.873544 | − | 0.486744i | \(-0.838184\pi\) | ||||
−0.873544 | + | 0.486744i | \(0.838184\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.49612 | 0.0487203 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 22.1215 | 0.719612 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 52.7975 | 1.71569 | 0.857844 | − | 0.513911i | \(-0.171804\pi\) | ||||
0.857844 | + | 0.513911i | \(0.171804\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.47910 | 0.145398 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.00791 | −0.259674 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.49662 | −0.178053 | −0.0890264 | − | 0.996029i | \(-0.528376\pi\) | ||||
−0.0890264 | + | 0.996029i | \(0.528376\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −48.9775 | −1.58487 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.16017 | 0.0375031 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.42982 | −0.143046 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.5272 | −0.920233 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −26.9347 | −0.867958 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 31.5392 | 1.01528 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −18.1431 | −0.583442 | −0.291721 | − | 0.956503i | \(-0.594228\pi\) | ||||
−0.291721 | + | 0.956503i | \(0.594228\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.822715 | 0.0264294 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15.9803 | 0.512832 | 0.256416 | − | 0.966567i | \(-0.417458\pi\) | ||||
0.256416 | + | 0.966567i | \(0.417458\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 61.4525 | 1.97008 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.0130839 | −0.000419020 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 34.0089 | 1.08804 | 0.544020 | − | 0.839072i | \(-0.316901\pi\) | ||||
0.544020 | + | 0.839072i | \(0.316901\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.07278 | −0.226047 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.87961 | 0.315432 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.66699 | −0.0850637 | −0.0425318 | − | 0.999095i | \(-0.513542\pi\) | ||||
−0.0425318 | + | 0.999095i | \(0.513542\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −18.1670 | −0.578849 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.71362 | 0.118206 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.57001 | 0.304309 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.2217 | 0.737660 | 0.368830 | − | 0.929497i | \(-0.379758\pi\) | ||||
0.368830 | + | 0.929497i | \(0.379758\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6.81107 | −0.216143 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 44.9699 | 1.42564 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 25.3804 | 0.803805 | 0.401903 | − | 0.915682i | \(-0.368349\pi\) | ||||
0.401903 | + | 0.915682i | \(0.368349\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.46527 | 0.236191 |
(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 | 4016.2.a.g.1.3 | 7 | ||
4.3 | odd | 2 | 1004.2.a.a.1.5 | ✓ | 7 | ||
12.11 | even | 2 | 9036.2.a.i.1.2 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1004.2.a.a.1.5 | ✓ | 7 | 4.3 | odd | 2 | ||
4016.2.a.g.1.3 | 7 | 1.1 | even | 1 | trivial | ||
9036.2.a.i.1.2 | 7 | 12.11 | even | 2 |