Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5290,2,Mod(1,5290)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5290, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("5290.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5290 = 2 \cdot 5 \cdot 23^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5290.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: | \(42.2408626693\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{24})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 4x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(0.517638\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5290.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −0.414214 | −0.239146 | −0.119573 | − | 0.992825i | \(-0.538153\pi\) | ||||
−0.119573 | + | 0.992825i | \(0.538153\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0.414214 | 0.169102 | ||||||||
\(7\) | 0.282561 | 0.106798 | 0.0533990 | − | 0.998573i | \(-0.482994\pi\) | ||||
0.0533990 | + | 0.998573i | \(0.482994\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.82843 | −0.942809 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 5.27792 | 1.59135 | 0.795676 | − | 0.605723i | \(-0.207116\pi\) | ||||
0.795676 | + | 0.605723i | \(0.207116\pi\) | |||||||
\(12\) | −0.414214 | −0.119573 | ||||||||
\(13\) | 1.86370 | 0.516898 | 0.258449 | − | 0.966025i | \(-0.416789\pi\) | ||||
0.258449 | + | 0.966025i | \(0.416789\pi\) | |||||||
\(14\) | −0.282561 | −0.0755176 | ||||||||
\(15\) | 0.414214 | 0.106949 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.24969 | −1.27324 | −0.636618 | − | 0.771179i | \(-0.719667\pi\) | ||||
−0.636618 | + | 0.771179i | \(0.719667\pi\) | |||||||
\(18\) | 2.82843 | 0.666667 | ||||||||
\(19\) | −0.946464 | −0.217134 | −0.108567 | − | 0.994089i | \(-0.534626\pi\) | ||||
−0.108567 | + | 0.994089i | \(0.534626\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | −0.117041 | −0.0255404 | ||||||||
\(22\) | −5.27792 | −1.12526 | ||||||||
\(23\) | 0 | 0 | ||||||||
\(24\) | 0.414214 | 0.0845510 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −1.86370 | −0.365502 | ||||||||
\(27\) | 2.41421 | 0.464616 | ||||||||
\(28\) | 0.282561 | 0.0533990 | ||||||||
\(29\) | −1.64689 | −0.305819 | −0.152910 | − | 0.988240i | \(-0.548864\pi\) | ||||
−0.152910 | + | 0.988240i | \(0.548864\pi\) | |||||||
\(30\) | −0.414214 | −0.0756247 | ||||||||
\(31\) | 3.85374 | 0.692151 | 0.346076 | − | 0.938207i | \(-0.387514\pi\) | ||||
0.346076 | + | 0.938207i | \(0.387514\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −2.18618 | −0.380566 | ||||||||
\(34\) | 5.24969 | 0.900314 | ||||||||
\(35\) | −0.282561 | −0.0477615 | ||||||||
\(36\) | −2.82843 | −0.471405 | ||||||||
\(37\) | 0.828427 | 0.136193 | 0.0680963 | − | 0.997679i | \(-0.478307\pi\) | ||||
0.0680963 | + | 0.997679i | \(0.478307\pi\) | |||||||
\(38\) | 0.946464 | 0.153537 | ||||||||
\(39\) | −0.771971 | −0.123614 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −7.53465 | −1.17672 | −0.588358 | − | 0.808601i | \(-0.700225\pi\) | ||||
−0.588358 | + | 0.808601i | \(0.700225\pi\) | |||||||
\(42\) | 0.117041 | 0.0180598 | ||||||||
\(43\) | −0.663902 | −0.101244 | −0.0506221 | − | 0.998718i | \(-0.516120\pi\) | ||||
−0.0506221 | + | 0.998718i | \(0.516120\pi\) | |||||||
\(44\) | 5.27792 | 0.795676 | ||||||||
\(45\) | 2.82843 | 0.421637 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.353113 | 0.0515069 | 0.0257534 | − | 0.999668i | \(-0.491802\pi\) | ||||
0.0257534 | + | 0.999668i | \(0.491802\pi\) | |||||||
\(48\) | −0.414214 | −0.0597866 | ||||||||
\(49\) | −6.92016 | −0.988594 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 2.17449 | 0.304490 | ||||||||
\(52\) | 1.86370 | 0.258449 | ||||||||
\(53\) | −10.2168 | −1.40339 | −0.701694 | − | 0.712479i | \(-0.747573\pi\) | ||||
−0.701694 | + | 0.712479i | \(0.747573\pi\) | |||||||
\(54\) | −2.41421 | −0.328533 | ||||||||
\(55\) | −5.27792 | −0.711674 | ||||||||
\(56\) | −0.282561 | −0.0377588 | ||||||||
\(57\) | 0.392038 | 0.0519267 | ||||||||
\(58\) | 1.64689 | 0.216247 | ||||||||
\(59\) | 3.00000 | 0.390567 | 0.195283 | − | 0.980747i | \(-0.437437\pi\) | ||||
0.195283 | + | 0.980747i | \(0.437437\pi\) | |||||||
\(60\) | 0.414214 | 0.0534747 | ||||||||
\(61\) | 9.75663 | 1.24921 | 0.624604 | − | 0.780941i | \(-0.285260\pi\) | ||||
0.624604 | + | 0.780941i | \(0.285260\pi\) | |||||||
\(62\) | −3.85374 | −0.489425 | ||||||||
\(63\) | −0.799203 | −0.100690 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.86370 | −0.231164 | ||||||||
\(66\) | 2.18618 | 0.269101 | ||||||||
\(67\) | 15.0628 | 1.84021 | 0.920105 | − | 0.391671i | \(-0.128103\pi\) | ||||
0.920105 | + | 0.391671i | \(0.128103\pi\) | |||||||
\(68\) | −5.24969 | −0.636618 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.282561 | 0.0337725 | ||||||||
\(71\) | 13.4448 | 1.59561 | 0.797805 | − | 0.602916i | \(-0.205995\pi\) | ||||
0.797805 | + | 0.602916i | \(0.205995\pi\) | |||||||
\(72\) | 2.82843 | 0.333333 | ||||||||
\(73\) | −15.9089 | −1.86200 | −0.931001 | − | 0.365017i | \(-0.881063\pi\) | ||||
−0.931001 | + | 0.365017i | \(0.881063\pi\) | |||||||
\(74\) | −0.828427 | −0.0963027 | ||||||||
\(75\) | −0.414214 | −0.0478293 | ||||||||
\(76\) | −0.946464 | −0.108567 | ||||||||
\(77\) | 1.49133 | 0.169953 | ||||||||
\(78\) | 0.771971 | 0.0874085 | ||||||||
\(79\) | −4.81116 | −0.541298 | −0.270649 | − | 0.962678i | \(-0.587238\pi\) | ||||
−0.270649 | + | 0.962678i | \(0.587238\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 7.48528 | 0.831698 | ||||||||
\(82\) | 7.53465 | 0.832063 | ||||||||
\(83\) | 0.643238 | 0.0706046 | 0.0353023 | − | 0.999377i | \(-0.488761\pi\) | ||||
0.0353023 | + | 0.999377i | \(0.488761\pi\) | |||||||
\(84\) | −0.117041 | −0.0127702 | ||||||||
\(85\) | 5.24969 | 0.569409 | ||||||||
\(86\) | 0.663902 | 0.0715904 | ||||||||
\(87\) | 0.682163 | 0.0731355 | ||||||||
\(88\) | −5.27792 | −0.562628 | ||||||||
\(89\) | −2.29326 | −0.243085 | −0.121542 | − | 0.992586i | \(-0.538784\pi\) | ||||
−0.121542 | + | 0.992586i | \(0.538784\pi\) | |||||||
\(90\) | −2.82843 | −0.298142 | ||||||||
\(91\) | 0.526610 | 0.0552037 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.59627 | −0.165525 | ||||||||
\(94\) | −0.353113 | −0.0364209 | ||||||||
\(95\) | 0.946464 | 0.0971051 | ||||||||
\(96\) | 0.414214 | 0.0422755 | ||||||||
\(97\) | 11.6702 | 1.18493 | 0.592466 | − | 0.805596i | \(-0.298155\pi\) | ||||
0.592466 | + | 0.805596i | \(0.298155\pi\) | |||||||
\(98\) | 6.92016 | 0.699042 | ||||||||
\(99\) | −14.9282 | −1.50034 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −10.6357 | −1.05829 | −0.529145 | − | 0.848532i | \(-0.677487\pi\) | ||||
−0.529145 | + | 0.848532i | \(0.677487\pi\) | |||||||
\(102\) | −2.17449 | −0.215307 | ||||||||
\(103\) | −12.2973 | −1.21169 | −0.605846 | − | 0.795582i | \(-0.707165\pi\) | ||||
−0.605846 | + | 0.795582i | \(0.707165\pi\) | |||||||
\(104\) | −1.86370 | −0.182751 | ||||||||
\(105\) | 0.117041 | 0.0114220 | ||||||||
\(106\) | 10.2168 | 0.992345 | ||||||||
\(107\) | −9.07107 | −0.876933 | −0.438467 | − | 0.898747i | \(-0.644478\pi\) | ||||
−0.438467 | + | 0.898747i | \(0.644478\pi\) | |||||||
\(108\) | 2.41421 | 0.232308 | ||||||||
\(109\) | −6.21201 | −0.595003 | −0.297501 | − | 0.954721i | \(-0.596153\pi\) | ||||
−0.297501 | + | 0.954721i | \(0.596153\pi\) | |||||||
\(110\) | 5.27792 | 0.503230 | ||||||||
\(111\) | −0.343146 | −0.0325700 | ||||||||
\(112\) | 0.282561 | 0.0266995 | ||||||||
\(113\) | −5.12925 | −0.482519 | −0.241260 | − | 0.970461i | \(-0.577561\pi\) | ||||
−0.241260 | + | 0.970461i | \(0.577561\pi\) | |||||||
\(114\) | −0.392038 | −0.0367177 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.64689 | −0.152910 | ||||||||
\(117\) | −5.27135 | −0.487336 | ||||||||
\(118\) | −3.00000 | −0.276172 | ||||||||
\(119\) | −1.48336 | −0.135979 | ||||||||
\(120\) | −0.414214 | −0.0378124 | ||||||||
\(121\) | 16.8564 | 1.53240 | ||||||||
\(122\) | −9.75663 | −0.883324 | ||||||||
\(123\) | 3.12096 | 0.281407 | ||||||||
\(124\) | 3.85374 | 0.346076 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0.799203 | 0.0711987 | ||||||||
\(127\) | 7.58114 | 0.672718 | 0.336359 | − | 0.941734i | \(-0.390805\pi\) | ||||
0.336359 | + | 0.941734i | \(0.390805\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0.274997 | 0.0242122 | ||||||||
\(130\) | 1.86370 | 0.163458 | ||||||||
\(131\) | 19.8776 | 1.73671 | 0.868356 | − | 0.495941i | \(-0.165177\pi\) | ||||
0.868356 | + | 0.495941i | \(0.165177\pi\) | |||||||
\(132\) | −2.18618 | −0.190283 | ||||||||
\(133\) | −0.267434 | −0.0231894 | ||||||||
\(134\) | −15.0628 | −1.30123 | ||||||||
\(135\) | −2.41421 | −0.207782 | ||||||||
\(136\) | 5.24969 | 0.450157 | ||||||||
\(137\) | −16.6067 | −1.41881 | −0.709404 | − | 0.704802i | \(-0.751036\pi\) | ||||
−0.709404 | + | 0.704802i | \(0.751036\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.1623 | 1.37087 | 0.685434 | − | 0.728135i | \(-0.259613\pi\) | ||||
0.685434 | + | 0.728135i | \(0.259613\pi\) | |||||||
\(140\) | −0.282561 | −0.0238808 | ||||||||
\(141\) | −0.146264 | −0.0123177 | ||||||||
\(142\) | −13.4448 | −1.12827 | ||||||||
\(143\) | 9.83647 | 0.822567 | ||||||||
\(144\) | −2.82843 | −0.235702 | ||||||||
\(145\) | 1.64689 | 0.136766 | ||||||||
\(146\) | 15.9089 | 1.31663 | ||||||||
\(147\) | 2.86642 | 0.236419 | ||||||||
\(148\) | 0.828427 | 0.0680963 | ||||||||
\(149\) | 4.83839 | 0.396377 | 0.198188 | − | 0.980164i | \(-0.436494\pi\) | ||||
0.198188 | + | 0.980164i | \(0.436494\pi\) | |||||||
\(150\) | 0.414214 | 0.0338204 | ||||||||
\(151\) | −3.19151 | −0.259721 | −0.129861 | − | 0.991532i | \(-0.541453\pi\) | ||||
−0.129861 | + | 0.991532i | \(0.541453\pi\) | |||||||
\(152\) | 0.946464 | 0.0767683 | ||||||||
\(153\) | 14.8484 | 1.20042 | ||||||||
\(154\) | −1.49133 | −0.120175 | ||||||||
\(155\) | −3.85374 | −0.309539 | ||||||||
\(156\) | −0.771971 | −0.0618072 | ||||||||
\(157\) | −10.4288 | −0.832311 | −0.416155 | − | 0.909293i | \(-0.636623\pi\) | ||||
−0.416155 | + | 0.909293i | \(0.636623\pi\) | |||||||
\(158\) | 4.81116 | 0.382756 | ||||||||
\(159\) | 4.23194 | 0.335615 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −7.48528 | −0.588099 | ||||||||
\(163\) | −3.87780 | −0.303733 | −0.151866 | − | 0.988401i | \(-0.548528\pi\) | ||||
−0.151866 | + | 0.988401i | \(0.548528\pi\) | |||||||
\(164\) | −7.53465 | −0.588358 | ||||||||
\(165\) | 2.18618 | 0.170194 | ||||||||
\(166\) | −0.643238 | −0.0499250 | ||||||||
\(167\) | 2.76681 | 0.214102 | 0.107051 | − | 0.994254i | \(-0.465859\pi\) | ||||
0.107051 | + | 0.994254i | \(0.465859\pi\) | |||||||
\(168\) | 0.117041 | 0.00902988 | ||||||||
\(169\) | −9.52661 | −0.732816 | ||||||||
\(170\) | −5.24969 | −0.402633 | ||||||||
\(171\) | 2.67700 | 0.204716 | ||||||||
\(172\) | −0.663902 | −0.0506221 | ||||||||
\(173\) | 19.2015 | 1.45986 | 0.729931 | − | 0.683521i | \(-0.239552\pi\) | ||||
0.729931 | + | 0.683521i | \(0.239552\pi\) | |||||||
\(174\) | −0.682163 | −0.0517146 | ||||||||
\(175\) | 0.282561 | 0.0213596 | ||||||||
\(176\) | 5.27792 | 0.397838 | ||||||||
\(177\) | −1.24264 | −0.0934026 | ||||||||
\(178\) | 2.29326 | 0.171887 | ||||||||
\(179\) | 21.6401 | 1.61746 | 0.808729 | − | 0.588182i | \(-0.200156\pi\) | ||||
0.808729 | + | 0.588182i | \(0.200156\pi\) | |||||||
\(180\) | 2.82843 | 0.210819 | ||||||||
\(181\) | −16.4288 | −1.22114 | −0.610572 | − | 0.791960i | \(-0.709061\pi\) | ||||
−0.610572 | + | 0.791960i | \(0.709061\pi\) | |||||||
\(182\) | −0.526610 | −0.0390349 | ||||||||
\(183\) | −4.04133 | −0.298744 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.828427 | −0.0609072 | ||||||||
\(186\) | 1.59627 | 0.117044 | ||||||||
\(187\) | −27.7074 | −2.02617 | ||||||||
\(188\) | 0.353113 | 0.0257534 | ||||||||
\(189\) | 0.682163 | 0.0496200 | ||||||||
\(190\) | −0.946464 | −0.0686637 | ||||||||
\(191\) | −24.6797 | −1.78576 | −0.892879 | − | 0.450296i | \(-0.851318\pi\) | ||||
−0.892879 | + | 0.450296i | \(0.851318\pi\) | |||||||
\(192\) | −0.414214 | −0.0298933 | ||||||||
\(193\) | −11.1429 | −0.802081 | −0.401040 | − | 0.916060i | \(-0.631351\pi\) | ||||
−0.401040 | + | 0.916060i | \(0.631351\pi\) | |||||||
\(194\) | −11.6702 | −0.837873 | ||||||||
\(195\) | 0.771971 | 0.0552820 | ||||||||
\(196\) | −6.92016 | −0.494297 | ||||||||
\(197\) | −10.9262 | −0.778460 | −0.389230 | − | 0.921141i | \(-0.627259\pi\) | ||||
−0.389230 | + | 0.921141i | \(0.627259\pi\) | |||||||
\(198\) | 14.9282 | 1.06090 | ||||||||
\(199\) | −21.4600 | −1.52126 | −0.760629 | − | 0.649187i | \(-0.775109\pi\) | ||||
−0.760629 | + | 0.649187i | \(0.775109\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | −6.23921 | −0.440080 | ||||||||
\(202\) | 10.6357 | 0.748323 | ||||||||
\(203\) | −0.465346 | −0.0326609 | ||||||||
\(204\) | 2.17449 | 0.152245 | ||||||||
\(205\) | 7.53465 | 0.526243 | ||||||||
\(206\) | 12.2973 | 0.856796 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.86370 | 0.129225 | ||||||||
\(209\) | −4.99536 | −0.345536 | ||||||||
\(210\) | −0.117041 | −0.00807657 | ||||||||
\(211\) | 2.88812 | 0.198826 | 0.0994132 | − | 0.995046i | \(-0.468303\pi\) | ||||
0.0994132 | + | 0.995046i | \(0.468303\pi\) | |||||||
\(212\) | −10.2168 | −0.701694 | ||||||||
\(213\) | −5.56904 | −0.381584 | ||||||||
\(214\) | 9.07107 | 0.620085 | ||||||||
\(215\) | 0.663902 | 0.0452778 | ||||||||
\(216\) | −2.41421 | −0.164266 | ||||||||
\(217\) | 1.08892 | 0.0739204 | ||||||||
\(218\) | 6.21201 | 0.420730 | ||||||||
\(219\) | 6.58970 | 0.445291 | ||||||||
\(220\) | −5.27792 | −0.355837 | ||||||||
\(221\) | −9.78386 | −0.658134 | ||||||||
\(222\) | 0.343146 | 0.0230304 | ||||||||
\(223\) | −13.5347 | −0.906347 | −0.453174 | − | 0.891422i | \(-0.649708\pi\) | ||||
−0.453174 | + | 0.891422i | \(0.649708\pi\) | |||||||
\(224\) | −0.282561 | −0.0188794 | ||||||||
\(225\) | −2.82843 | −0.188562 | ||||||||
\(226\) | 5.12925 | 0.341193 | ||||||||
\(227\) | −7.15648 | −0.474992 | −0.237496 | − | 0.971388i | \(-0.576327\pi\) | ||||
−0.237496 | + | 0.971388i | \(0.576327\pi\) | |||||||
\(228\) | 0.392038 | 0.0259634 | ||||||||
\(229\) | 0.818459 | 0.0540853 | 0.0270427 | − | 0.999634i | \(-0.491391\pi\) | ||||
0.0270427 | + | 0.999634i | \(0.491391\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.617731 | −0.0406437 | ||||||||
\(232\) | 1.64689 | 0.108123 | ||||||||
\(233\) | −22.0311 | −1.44331 | −0.721654 | − | 0.692254i | \(-0.756618\pi\) | ||||
−0.721654 | + | 0.692254i | \(0.756618\pi\) | |||||||
\(234\) | 5.27135 | 0.344599 | ||||||||
\(235\) | −0.353113 | −0.0230346 | ||||||||
\(236\) | 3.00000 | 0.195283 | ||||||||
\(237\) | 1.99285 | 0.129449 | ||||||||
\(238\) | 1.48336 | 0.0961518 | ||||||||
\(239\) | −27.0892 | −1.75226 | −0.876129 | − | 0.482077i | \(-0.839882\pi\) | ||||
−0.876129 | + | 0.482077i | \(0.839882\pi\) | |||||||
\(240\) | 0.414214 | 0.0267374 | ||||||||
\(241\) | 6.86078 | 0.441942 | 0.220971 | − | 0.975280i | \(-0.429077\pi\) | ||||
0.220971 | + | 0.975280i | \(0.429077\pi\) | |||||||
\(242\) | −16.8564 | −1.08357 | ||||||||
\(243\) | −10.3431 | −0.663513 | ||||||||
\(244\) | 9.75663 | 0.624604 | ||||||||
\(245\) | 6.92016 | 0.442113 | ||||||||
\(246\) | −3.12096 | −0.198985 | ||||||||
\(247\) | −1.76393 | −0.112236 | ||||||||
\(248\) | −3.85374 | −0.244712 | ||||||||
\(249\) | −0.266438 | −0.0168848 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −6.15456 | −0.388472 | −0.194236 | − | 0.980955i | \(-0.562223\pi\) | ||||
−0.194236 | + | 0.980955i | \(0.562223\pi\) | |||||||
\(252\) | −0.799203 | −0.0503451 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −7.58114 | −0.475683 | ||||||||
\(255\) | −2.17449 | −0.136172 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −7.41297 | −0.462408 | −0.231204 | − | 0.972905i | \(-0.574267\pi\) | ||||
−0.231204 | + | 0.972905i | \(0.574267\pi\) | |||||||
\(258\) | −0.274997 | −0.0171206 | ||||||||
\(259\) | 0.234081 | 0.0145451 | ||||||||
\(260\) | −1.86370 | −0.115582 | ||||||||
\(261\) | 4.65810 | 0.288329 | ||||||||
\(262\) | −19.8776 | −1.22804 | ||||||||
\(263\) | −22.4263 | −1.38287 | −0.691434 | − | 0.722440i | \(-0.743021\pi\) | ||||
−0.691434 | + | 0.722440i | \(0.743021\pi\) | |||||||
\(264\) | 2.18618 | 0.134550 | ||||||||
\(265\) | 10.2168 | 0.627614 | ||||||||
\(266\) | 0.267434 | 0.0163974 | ||||||||
\(267\) | 0.949898 | 0.0581328 | ||||||||
\(268\) | 15.0628 | 0.920105 | ||||||||
\(269\) | −4.25120 | −0.259200 | −0.129600 | − | 0.991566i | \(-0.541369\pi\) | ||||
−0.129600 | + | 0.991566i | \(0.541369\pi\) | |||||||
\(270\) | 2.41421 | 0.146924 | ||||||||
\(271\) | 13.9859 | 0.849583 | 0.424792 | − | 0.905291i | \(-0.360347\pi\) | ||||
0.424792 | + | 0.905291i | \(0.360347\pi\) | |||||||
\(272\) | −5.24969 | −0.318309 | ||||||||
\(273\) | −0.218129 | −0.0132018 | ||||||||
\(274\) | 16.6067 | 1.00325 | ||||||||
\(275\) | 5.27792 | 0.318270 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.4023 | 1.10569 | 0.552843 | − | 0.833286i | \(-0.313543\pi\) | ||||
0.552843 | + | 0.833286i | \(0.313543\pi\) | |||||||
\(278\) | −16.1623 | −0.969349 | ||||||||
\(279\) | −10.9000 | −0.652567 | ||||||||
\(280\) | 0.282561 | 0.0168863 | ||||||||
\(281\) | −5.00292 | −0.298449 | −0.149225 | − | 0.988803i | \(-0.547678\pi\) | ||||
−0.149225 | + | 0.988803i | \(0.547678\pi\) | |||||||
\(282\) | 0.146264 | 0.00870992 | ||||||||
\(283\) | 18.9114 | 1.12416 | 0.562082 | − | 0.827082i | \(-0.310001\pi\) | ||||
0.562082 | + | 0.827082i | \(0.310001\pi\) | |||||||
\(284\) | 13.4448 | 0.797805 | ||||||||
\(285\) | −0.392038 | −0.0232223 | ||||||||
\(286\) | −9.83647 | −0.581643 | ||||||||
\(287\) | −2.12900 | −0.125671 | ||||||||
\(288\) | 2.82843 | 0.166667 | ||||||||
\(289\) | 10.5592 | 0.621131 | ||||||||
\(290\) | −1.64689 | −0.0967085 | ||||||||
\(291\) | −4.83396 | −0.283372 | ||||||||
\(292\) | −15.9089 | −0.931001 | ||||||||
\(293\) | −32.9481 | −1.92485 | −0.962425 | − | 0.271546i | \(-0.912465\pi\) | ||||
−0.962425 | + | 0.271546i | \(0.912465\pi\) | |||||||
\(294\) | −2.86642 | −0.167173 | ||||||||
\(295\) | −3.00000 | −0.174667 | ||||||||
\(296\) | −0.828427 | −0.0481513 | ||||||||
\(297\) | 12.7420 | 0.739367 | ||||||||
\(298\) | −4.83839 | −0.280281 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −0.414214 | −0.0239146 | ||||||||
\(301\) | −0.187593 | −0.0108127 | ||||||||
\(302\) | 3.19151 | 0.183651 | ||||||||
\(303\) | 4.40544 | 0.253086 | ||||||||
\(304\) | −0.946464 | −0.0542834 | ||||||||
\(305\) | −9.75663 | −0.558663 | ||||||||
\(306\) | −14.8484 | −0.848824 | ||||||||
\(307\) | 8.01942 | 0.457692 | 0.228846 | − | 0.973463i | \(-0.426505\pi\) | ||||
0.228846 | + | 0.973463i | \(0.426505\pi\) | |||||||
\(308\) | 1.49133 | 0.0849766 | ||||||||
\(309\) | 5.09372 | 0.289772 | ||||||||
\(310\) | 3.85374 | 0.218877 | ||||||||
\(311\) | 24.6291 | 1.39659 | 0.698293 | − | 0.715812i | \(-0.253943\pi\) | ||||
0.698293 | + | 0.715812i | \(0.253943\pi\) | |||||||
\(312\) | 0.771971 | 0.0437043 | ||||||||
\(313\) | 15.0842 | 0.852608 | 0.426304 | − | 0.904580i | \(-0.359815\pi\) | ||||
0.426304 | + | 0.904580i | \(0.359815\pi\) | |||||||
\(314\) | 10.4288 | 0.588533 | ||||||||
\(315\) | 0.799203 | 0.0450300 | ||||||||
\(316\) | −4.81116 | −0.270649 | ||||||||
\(317\) | −23.2015 | −1.30312 | −0.651562 | − | 0.758595i | \(-0.725886\pi\) | ||||
−0.651562 | + | 0.758595i | \(0.725886\pi\) | |||||||
\(318\) | −4.23194 | −0.237316 | ||||||||
\(319\) | −8.69213 | −0.486666 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 3.75736 | 0.209715 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.96864 | 0.276462 | ||||||||
\(324\) | 7.48528 | 0.415849 | ||||||||
\(325\) | 1.86370 | 0.103380 | ||||||||
\(326\) | 3.87780 | 0.214771 | ||||||||
\(327\) | 2.57310 | 0.142293 | ||||||||
\(328\) | 7.53465 | 0.416032 | ||||||||
\(329\) | 0.0997761 | 0.00550083 | ||||||||
\(330\) | −2.18618 | −0.120346 | ||||||||
\(331\) | 3.25120 | 0.178702 | 0.0893511 | − | 0.996000i | \(-0.471521\pi\) | ||||
0.0893511 | + | 0.996000i | \(0.471521\pi\) | |||||||
\(332\) | 0.643238 | 0.0353023 | ||||||||
\(333\) | −2.34315 | −0.128404 | ||||||||
\(334\) | −2.76681 | −0.151393 | ||||||||
\(335\) | −15.0628 | −0.822967 | ||||||||
\(336\) | −0.117041 | −0.00638509 | ||||||||
\(337\) | −23.5714 | −1.28402 | −0.642009 | − | 0.766697i | \(-0.721899\pi\) | ||||
−0.642009 | + | 0.766697i | \(0.721899\pi\) | |||||||
\(338\) | 9.52661 | 0.518179 | ||||||||
\(339\) | 2.12460 | 0.115393 | ||||||||
\(340\) | 5.24969 | 0.284704 | ||||||||
\(341\) | 20.3397 | 1.10146 | ||||||||
\(342\) | −2.67700 | −0.144756 | ||||||||
\(343\) | −3.93330 | −0.212378 | ||||||||
\(344\) | 0.663902 | 0.0357952 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −19.2015 | −1.03228 | ||||||||
\(347\) | 13.0980 | 0.703138 | 0.351569 | − | 0.936162i | \(-0.385648\pi\) | ||||
0.351569 | + | 0.936162i | \(0.385648\pi\) | |||||||
\(348\) | 0.682163 | 0.0365678 | ||||||||
\(349\) | −2.69412 | −0.144213 | −0.0721065 | − | 0.997397i | \(-0.522972\pi\) | ||||
−0.0721065 | + | 0.997397i | \(0.522972\pi\) | |||||||
\(350\) | −0.282561 | −0.0151035 | ||||||||
\(351\) | 4.49938 | 0.240159 | ||||||||
\(352\) | −5.27792 | −0.281314 | ||||||||
\(353\) | 3.54727 | 0.188802 | 0.0944012 | − | 0.995534i | \(-0.469906\pi\) | ||||
0.0944012 | + | 0.995534i | \(0.469906\pi\) | |||||||
\(354\) | 1.24264 | 0.0660456 | ||||||||
\(355\) | −13.4448 | −0.713578 | ||||||||
\(356\) | −2.29326 | −0.121542 | ||||||||
\(357\) | 0.614427 | 0.0325189 | ||||||||
\(358\) | −21.6401 | −1.14372 | ||||||||
\(359\) | 21.8220 | 1.15172 | 0.575861 | − | 0.817548i | \(-0.304667\pi\) | ||||
0.575861 | + | 0.817548i | \(0.304667\pi\) | |||||||
\(360\) | −2.82843 | −0.149071 | ||||||||
\(361\) | −18.1042 | −0.952853 | ||||||||
\(362\) | 16.4288 | 0.863480 | ||||||||
\(363\) | −6.98215 | −0.366468 | ||||||||
\(364\) | 0.526610 | 0.0276019 | ||||||||
\(365\) | 15.9089 | 0.832712 | ||||||||
\(366\) | 4.04133 | 0.211244 | ||||||||
\(367\) | −9.98177 | −0.521044 | −0.260522 | − | 0.965468i | \(-0.583895\pi\) | ||||
−0.260522 | + | 0.965468i | \(0.583895\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 21.3112 | 1.10942 | ||||||||
\(370\) | 0.828427 | 0.0430679 | ||||||||
\(371\) | −2.88687 | −0.149879 | ||||||||
\(372\) | −1.59627 | −0.0827627 | ||||||||
\(373\) | 13.8537 | 0.717319 | 0.358660 | − | 0.933468i | \(-0.383234\pi\) | ||||
0.358660 | + | 0.933468i | \(0.383234\pi\) | |||||||
\(374\) | 27.7074 | 1.43272 | ||||||||
\(375\) | 0.414214 | 0.0213899 | ||||||||
\(376\) | −0.353113 | −0.0182104 | ||||||||
\(377\) | −3.06931 | −0.158077 | ||||||||
\(378\) | −0.682163 | −0.0350867 | ||||||||
\(379\) | −27.1798 | −1.39613 | −0.698067 | − | 0.716033i | \(-0.745956\pi\) | ||||
−0.698067 | + | 0.716033i | \(0.745956\pi\) | |||||||
\(380\) | 0.946464 | 0.0485526 | ||||||||
\(381\) | −3.14021 | −0.160878 | ||||||||
\(382\) | 24.6797 | 1.26272 | ||||||||
\(383\) | −9.17260 | −0.468698 | −0.234349 | − | 0.972153i | \(-0.575296\pi\) | ||||
−0.234349 | + | 0.972153i | \(0.575296\pi\) | |||||||
\(384\) | 0.414214 | 0.0211377 | ||||||||
\(385\) | −1.49133 | −0.0760054 | ||||||||
\(386\) | 11.1429 | 0.567157 | ||||||||
\(387\) | 1.87780 | 0.0954539 | ||||||||
\(388\) | 11.6702 | 0.592466 | ||||||||
\(389\) | −16.0048 | −0.811476 | −0.405738 | − | 0.913989i | \(-0.632985\pi\) | ||||
−0.405738 | + | 0.913989i | \(0.632985\pi\) | |||||||
\(390\) | −0.771971 | −0.0390903 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 6.92016 | 0.349521 | ||||||||
\(393\) | −8.23357 | −0.415328 | ||||||||
\(394\) | 10.9262 | 0.550455 | ||||||||
\(395\) | 4.81116 | 0.242076 | ||||||||
\(396\) | −14.9282 | −0.750170 | ||||||||
\(397\) | 28.4776 | 1.42925 | 0.714626 | − | 0.699507i | \(-0.246597\pi\) | ||||
0.714626 | + | 0.699507i | \(0.246597\pi\) | |||||||
\(398\) | 21.4600 | 1.07569 | ||||||||
\(399\) | 0.110775 | 0.00554567 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −13.9535 | −0.696807 | −0.348403 | − | 0.937345i | \(-0.613276\pi\) | ||||
−0.348403 | + | 0.937345i | \(0.613276\pi\) | |||||||
\(402\) | 6.23921 | 0.311183 | ||||||||
\(403\) | 7.18222 | 0.357772 | ||||||||
\(404\) | −10.6357 | −0.529145 | ||||||||
\(405\) | −7.48528 | −0.371947 | ||||||||
\(406\) | 0.465346 | 0.0230947 | ||||||||
\(407\) | 4.37237 | 0.216730 | ||||||||
\(408\) | −2.17449 | −0.107653 | ||||||||
\(409\) | −19.8732 | −0.982664 | −0.491332 | − | 0.870972i | \(-0.663490\pi\) | ||||
−0.491332 | + | 0.870972i | \(0.663490\pi\) | |||||||
\(410\) | −7.53465 | −0.372110 | ||||||||
\(411\) | 6.87873 | 0.339303 | ||||||||
\(412\) | −12.2973 | −0.605846 | ||||||||
\(413\) | 0.847683 | 0.0417118 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.643238 | −0.0315753 | ||||||||
\(416\) | −1.86370 | −0.0913756 | ||||||||
\(417\) | −6.69464 | −0.327838 | ||||||||
\(418\) | 4.99536 | 0.244331 | ||||||||
\(419\) | 22.7512 | 1.11147 | 0.555735 | − | 0.831360i | \(-0.312437\pi\) | ||||
0.555735 | + | 0.831360i | \(0.312437\pi\) | |||||||
\(420\) | 0.117041 | 0.00571100 | ||||||||
\(421\) | −40.7127 | −1.98422 | −0.992109 | − | 0.125379i | \(-0.959985\pi\) | ||||
−0.992109 | + | 0.125379i | \(0.959985\pi\) | |||||||
\(422\) | −2.88812 | −0.140591 | ||||||||
\(423\) | −0.998756 | −0.0485612 | ||||||||
\(424\) | 10.2168 | 0.496172 | ||||||||
\(425\) | −5.24969 | −0.254647 | ||||||||
\(426\) | 5.56904 | 0.269821 | ||||||||
\(427\) | 2.75684 | 0.133413 | ||||||||
\(428\) | −9.07107 | −0.438467 | ||||||||
\(429\) | −4.07440 | −0.196714 | ||||||||
\(430\) | −0.663902 | −0.0320162 | ||||||||
\(431\) | −24.2843 | −1.16973 | −0.584866 | − | 0.811130i | \(-0.698853\pi\) | ||||
−0.584866 | + | 0.811130i | \(0.698853\pi\) | |||||||
\(432\) | 2.41421 | 0.116154 | ||||||||
\(433\) | −17.2074 | −0.826933 | −0.413467 | − | 0.910519i | \(-0.635682\pi\) | ||||
−0.413467 | + | 0.910519i | \(0.635682\pi\) | |||||||
\(434\) | −1.08892 | −0.0522696 | ||||||||
\(435\) | −0.682163 | −0.0327072 | ||||||||
\(436\) | −6.21201 | −0.297501 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −6.58970 | −0.314868 | ||||||||
\(439\) | 36.9825 | 1.76508 | 0.882540 | − | 0.470238i | \(-0.155832\pi\) | ||||
0.882540 | + | 0.470238i | \(0.155832\pi\) | |||||||
\(440\) | 5.27792 | 0.251615 | ||||||||
\(441\) | 19.5732 | 0.932056 | ||||||||
\(442\) | 9.78386 | 0.465371 | ||||||||
\(443\) | −15.0698 | −0.715989 | −0.357994 | − | 0.933724i | \(-0.616539\pi\) | ||||
−0.357994 | + | 0.933724i | \(0.616539\pi\) | |||||||
\(444\) | −0.343146 | −0.0162850 | ||||||||
\(445\) | 2.29326 | 0.108711 | ||||||||
\(446\) | 13.5347 | 0.640884 | ||||||||
\(447\) | −2.00413 | −0.0947920 | ||||||||
\(448\) | 0.282561 | 0.0133498 | ||||||||
\(449\) | −18.4675 | −0.871535 | −0.435768 | − | 0.900059i | \(-0.643523\pi\) | ||||
−0.435768 | + | 0.900059i | \(0.643523\pi\) | |||||||
\(450\) | 2.82843 | 0.133333 | ||||||||
\(451\) | −39.7673 | −1.87257 | ||||||||
\(452\) | −5.12925 | −0.241260 | ||||||||
\(453\) | 1.32197 | 0.0621114 | ||||||||
\(454\) | 7.15648 | 0.335870 | ||||||||
\(455\) | −0.526610 | −0.0246879 | ||||||||
\(456\) | −0.392038 | −0.0183589 | ||||||||
\(457\) | −28.5891 | −1.33734 | −0.668672 | − | 0.743558i | \(-0.733137\pi\) | ||||
−0.668672 | + | 0.743558i | \(0.733137\pi\) | |||||||
\(458\) | −0.818459 | −0.0382441 | ||||||||
\(459\) | −12.6739 | −0.591566 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.13986 | −0.332536 | −0.166268 | − | 0.986081i | \(-0.553172\pi\) | ||||
−0.166268 | + | 0.986081i | \(0.553172\pi\) | |||||||
\(462\) | 0.617731 | 0.0287394 | ||||||||
\(463\) | 3.77073 | 0.175241 | 0.0876203 | − | 0.996154i | \(-0.472074\pi\) | ||||
0.0876203 | + | 0.996154i | \(0.472074\pi\) | |||||||
\(464\) | −1.64689 | −0.0764548 | ||||||||
\(465\) | 1.59627 | 0.0740252 | ||||||||
\(466\) | 22.0311 | 1.02057 | ||||||||
\(467\) | 26.5448 | 1.22835 | 0.614173 | − | 0.789171i | \(-0.289490\pi\) | ||||
0.614173 | + | 0.789171i | \(0.289490\pi\) | |||||||
\(468\) | −5.27135 | −0.243668 | ||||||||
\(469\) | 4.25615 | 0.196531 | ||||||||
\(470\) | 0.353113 | 0.0162879 | ||||||||
\(471\) | 4.31976 | 0.199044 | ||||||||
\(472\) | −3.00000 | −0.138086 | ||||||||
\(473\) | −3.50402 | −0.161115 | ||||||||
\(474\) | −1.99285 | −0.0915346 | ||||||||
\(475\) | −0.946464 | −0.0434267 | ||||||||
\(476\) | −1.48336 | −0.0679896 | ||||||||
\(477\) | 28.8975 | 1.32313 | ||||||||
\(478\) | 27.0892 | 1.23903 | ||||||||
\(479\) | −21.1723 | −0.967385 | −0.483692 | − | 0.875238i | \(-0.660705\pi\) | ||||
−0.483692 | + | 0.875238i | \(0.660705\pi\) | |||||||
\(480\) | −0.414214 | −0.0189062 | ||||||||
\(481\) | 1.54394 | 0.0703977 | ||||||||
\(482\) | −6.86078 | −0.312500 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 16.8564 | 0.766200 | ||||||||
\(485\) | −11.6702 | −0.529917 | ||||||||
\(486\) | 10.3431 | 0.469175 | ||||||||
\(487\) | −30.3727 | −1.37632 | −0.688159 | − | 0.725560i | \(-0.741581\pi\) | ||||
−0.688159 | + | 0.725560i | \(0.741581\pi\) | |||||||
\(488\) | −9.75663 | −0.441662 | ||||||||
\(489\) | 1.60624 | 0.0726366 | ||||||||
\(490\) | −6.92016 | −0.312621 | ||||||||
\(491\) | 28.0706 | 1.26681 | 0.633403 | − | 0.773822i | \(-0.281658\pi\) | ||||
0.633403 | + | 0.773822i | \(0.281658\pi\) | |||||||
\(492\) | 3.12096 | 0.140704 | ||||||||
\(493\) | 8.64564 | 0.389380 | ||||||||
\(494\) | 1.76393 | 0.0793628 | ||||||||
\(495\) | 14.9282 | 0.670973 | ||||||||
\(496\) | 3.85374 | 0.173038 | ||||||||
\(497\) | 3.79899 | 0.170408 | ||||||||
\(498\) | 0.266438 | 0.0119394 | ||||||||
\(499\) | 1.52719 | 0.0683666 | 0.0341833 | − | 0.999416i | \(-0.489117\pi\) | ||||
0.0341833 | + | 0.999416i | \(0.489117\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | −1.14605 | −0.0512018 | ||||||||
\(502\) | 6.15456 | 0.274691 | ||||||||
\(503\) | −30.1177 | −1.34288 | −0.671441 | − | 0.741058i | \(-0.734324\pi\) | ||||
−0.671441 | + | 0.741058i | \(0.734324\pi\) | |||||||
\(504\) | 0.799203 | 0.0355993 | ||||||||
\(505\) | 10.6357 | 0.473281 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.94605 | 0.175250 | ||||||||
\(508\) | 7.58114 | 0.336359 | ||||||||
\(509\) | 27.4988 | 1.21886 | 0.609432 | − | 0.792839i | \(-0.291398\pi\) | ||||
0.609432 | + | 0.792839i | \(0.291398\pi\) | |||||||
\(510\) | 2.17449 | 0.0962881 | ||||||||
\(511\) | −4.49525 | −0.198858 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −2.28497 | −0.100884 | ||||||||
\(514\) | 7.41297 | 0.326972 | ||||||||
\(515\) | 12.2973 | 0.541885 | ||||||||
\(516\) | 0.274997 | 0.0121061 | ||||||||
\(517\) | 1.86370 | 0.0819656 | ||||||||
\(518\) | −0.234081 | −0.0102849 | ||||||||
\(519\) | −7.95351 | −0.349120 | ||||||||
\(520\) | 1.86370 | 0.0817288 | ||||||||
\(521\) | −41.2097 | −1.80543 | −0.902715 | − | 0.430240i | \(-0.858429\pi\) | ||||
−0.902715 | + | 0.430240i | \(0.858429\pi\) | |||||||
\(522\) | −4.65810 | −0.203879 | ||||||||
\(523\) | 2.30390 | 0.100743 | 0.0503714 | − | 0.998731i | \(-0.483960\pi\) | ||||
0.0503714 | + | 0.998731i | \(0.483960\pi\) | |||||||
\(524\) | 19.8776 | 0.868356 | ||||||||
\(525\) | −0.117041 | −0.00510807 | ||||||||
\(526\) | 22.4263 | 0.977835 | ||||||||
\(527\) | −20.2309 | −0.881272 | ||||||||
\(528\) | −2.18618 | −0.0951415 | ||||||||
\(529\) | 0 | 0 | ||||||||
\(530\) | −10.2168 | −0.443790 | ||||||||
\(531\) | −8.48528 | −0.368230 | ||||||||
\(532\) | −0.267434 | −0.0115947 | ||||||||
\(533\) | −14.0424 | −0.608242 | ||||||||
\(534\) | −0.949898 | −0.0411061 | ||||||||
\(535\) | 9.07107 | 0.392176 | ||||||||
\(536\) | −15.0628 | −0.650613 | ||||||||
\(537\) | −8.96363 | −0.386809 | ||||||||
\(538\) | 4.25120 | 0.183282 | ||||||||
\(539\) | −36.5240 | −1.57320 | ||||||||
\(540\) | −2.41421 | −0.103891 | ||||||||
\(541\) | 25.1430 | 1.08098 | 0.540492 | − | 0.841349i | \(-0.318238\pi\) | ||||
0.540492 | + | 0.841349i | \(0.318238\pi\) | |||||||
\(542\) | −13.9859 | −0.600746 | ||||||||
\(543\) | 6.80504 | 0.292032 | ||||||||
\(544\) | 5.24969 | 0.225079 | ||||||||
\(545\) | 6.21201 | 0.266093 | ||||||||
\(546\) | 0.218129 | 0.00933506 | ||||||||
\(547\) | −43.1127 | −1.84337 | −0.921683 | − | 0.387944i | \(-0.873185\pi\) | ||||
−0.921683 | + | 0.387944i | \(0.873185\pi\) | |||||||
\(548\) | −16.6067 | −0.709404 | ||||||||
\(549\) | −27.5959 | −1.17777 | ||||||||
\(550\) | −5.27792 | −0.225051 | ||||||||
\(551\) | 1.55872 | 0.0664036 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.35945 | −0.0578096 | ||||||||
\(554\) | −18.4023 | −0.781838 | ||||||||
\(555\) | 0.343146 | 0.0145657 | ||||||||
\(556\) | 16.1623 | 0.685434 | ||||||||
\(557\) | −24.3814 | −1.03307 | −0.516536 | − | 0.856265i | \(-0.672779\pi\) | ||||
−0.516536 | + | 0.856265i | \(0.672779\pi\) | |||||||
\(558\) | 10.9000 | 0.461434 | ||||||||
\(559\) | −1.23732 | −0.0523329 | ||||||||
\(560\) | −0.282561 | −0.0119404 | ||||||||
\(561\) | 11.4768 | 0.484550 | ||||||||
\(562\) | 5.00292 | 0.211035 | ||||||||
\(563\) | −42.5108 | −1.79162 | −0.895808 | − | 0.444441i | \(-0.853402\pi\) | ||||
−0.895808 | + | 0.444441i | \(0.853402\pi\) | |||||||
\(564\) | −0.146264 | −0.00615884 | ||||||||
\(565\) | 5.12925 | 0.215789 | ||||||||
\(566\) | −18.9114 | −0.794903 | ||||||||
\(567\) | 2.11505 | 0.0888237 | ||||||||
\(568\) | −13.4448 | −0.564133 | ||||||||
\(569\) | 29.2954 | 1.22813 | 0.614065 | − | 0.789256i | \(-0.289533\pi\) | ||||
0.614065 | + | 0.789256i | \(0.289533\pi\) | |||||||
\(570\) | 0.392038 | 0.0164207 | ||||||||
\(571\) | 35.8550 | 1.50049 | 0.750243 | − | 0.661162i | \(-0.229936\pi\) | ||||
0.750243 | + | 0.661162i | \(0.229936\pi\) | |||||||
\(572\) | 9.83647 | 0.411284 | ||||||||
\(573\) | 10.2227 | 0.427058 | ||||||||
\(574\) | 2.12900 | 0.0888627 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.82843 | −0.117851 | ||||||||
\(577\) | 14.7477 | 0.613955 | 0.306977 | − | 0.951717i | \(-0.400682\pi\) | ||||
0.306977 | + | 0.951717i | \(0.400682\pi\) | |||||||
\(578\) | −10.5592 | −0.439206 | ||||||||
\(579\) | 4.61553 | 0.191815 | ||||||||
\(580\) | 1.64689 | 0.0683832 | ||||||||
\(581\) | 0.181754 | 0.00754043 | ||||||||
\(582\) | 4.83396 | 0.200374 | ||||||||
\(583\) | −53.9235 | −2.23328 | ||||||||
\(584\) | 15.9089 | 0.658317 | ||||||||
\(585\) | 5.27135 | 0.217943 | ||||||||
\(586\) | 32.9481 | 1.36108 | ||||||||
\(587\) | −44.8649 | −1.85177 | −0.925887 | − | 0.377801i | \(-0.876680\pi\) | ||||
−0.925887 | + | 0.377801i | \(0.876680\pi\) | |||||||
\(588\) | 2.86642 | 0.118209 | ||||||||
\(589\) | −3.64742 | −0.150289 | ||||||||
\(590\) | 3.00000 | 0.123508 | ||||||||
\(591\) | 4.52579 | 0.186166 | ||||||||
\(592\) | 0.828427 | 0.0340481 | ||||||||
\(593\) | −8.71603 | −0.357924 | −0.178962 | − | 0.983856i | \(-0.557274\pi\) | ||||
−0.178962 | + | 0.983856i | \(0.557274\pi\) | |||||||
\(594\) | −12.7420 | −0.522811 | ||||||||
\(595\) | 1.48336 | 0.0608117 | ||||||||
\(596\) | 4.83839 | 0.198188 | ||||||||
\(597\) | 8.88901 | 0.363803 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −22.1390 | −0.904574 | −0.452287 | − | 0.891873i | \(-0.649392\pi\) | ||||
−0.452287 | + | 0.891873i | \(0.649392\pi\) | |||||||
\(600\) | 0.414214 | 0.0169102 | ||||||||
\(601\) | 40.3898 | 1.64753 | 0.823767 | − | 0.566928i | \(-0.191868\pi\) | ||||
0.823767 | + | 0.566928i | \(0.191868\pi\) | |||||||
\(602\) | 0.187593 | 0.00764572 | ||||||||
\(603\) | −42.6040 | −1.73497 | ||||||||
\(604\) | −3.19151 | −0.129861 | ||||||||
\(605\) | −16.8564 | −0.685310 | ||||||||
\(606\) | −4.40544 | −0.178959 | ||||||||
\(607\) | −17.8158 | −0.723119 | −0.361560 | − | 0.932349i | \(-0.617756\pi\) | ||||
−0.361560 | + | 0.932349i | \(0.617756\pi\) | |||||||
\(608\) | 0.946464 | 0.0383842 | ||||||||
\(609\) | 0.192753 | 0.00781073 | ||||||||
\(610\) | 9.75663 | 0.395034 | ||||||||
\(611\) | 0.658099 | 0.0266238 | ||||||||
\(612\) | 14.8484 | 0.600209 | ||||||||
\(613\) | 15.3499 | 0.619976 | 0.309988 | − | 0.950741i | \(-0.399675\pi\) | ||||
0.309988 | + | 0.950741i | \(0.399675\pi\) | |||||||
\(614\) | −8.01942 | −0.323637 | ||||||||
\(615\) | −3.12096 | −0.125849 | ||||||||
\(616\) | −1.49133 | −0.0600876 | ||||||||
\(617\) | −20.2454 | −0.815049 | −0.407524 | − | 0.913194i | \(-0.633608\pi\) | ||||
−0.407524 | + | 0.913194i | \(0.633608\pi\) | |||||||
\(618\) | −5.09372 | −0.204900 | ||||||||
\(619\) | −10.0426 | −0.403646 | −0.201823 | − | 0.979422i | \(-0.564687\pi\) | ||||
−0.201823 | + | 0.979422i | \(0.564687\pi\) | |||||||
\(620\) | −3.85374 | −0.154770 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −24.6291 | −0.987535 | ||||||||
\(623\) | −0.647985 | −0.0259610 | ||||||||
\(624\) | −0.771971 | −0.0309036 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −15.0842 | −0.602885 | ||||||||
\(627\) | 2.06914 | 0.0826337 | ||||||||
\(628\) | −10.4288 | −0.416155 | ||||||||
\(629\) | −4.34898 | −0.173405 | ||||||||
\(630\) | −0.799203 | −0.0318410 | ||||||||
\(631\) | 24.4305 | 0.972561 | 0.486281 | − | 0.873803i | \(-0.338353\pi\) | ||||
0.486281 | + | 0.873803i | \(0.338353\pi\) | |||||||
\(632\) | 4.81116 | 0.191378 | ||||||||
\(633\) | −1.19630 | −0.0475486 | ||||||||
\(634\) | 23.2015 | 0.921448 | ||||||||
\(635\) | −7.58114 | −0.300848 | ||||||||
\(636\) | 4.23194 | 0.167807 | ||||||||
\(637\) | −12.8971 | −0.511003 | ||||||||
\(638\) | 8.69213 | 0.344125 | ||||||||
\(639\) | −38.0278 | −1.50436 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −19.3395 | −0.763864 | −0.381932 | − | 0.924190i | \(-0.624741\pi\) | ||||
−0.381932 | + | 0.924190i | \(0.624741\pi\) | |||||||
\(642\) | −3.75736 | −0.148291 | ||||||||
\(643\) | 35.7466 | 1.40971 | 0.704854 | − | 0.709352i | \(-0.251012\pi\) | ||||
0.704854 | + | 0.709352i | \(0.251012\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.274997 | −0.0108280 | ||||||||
\(646\) | −4.96864 | −0.195488 | ||||||||
\(647\) | −31.8753 | −1.25315 | −0.626574 | − | 0.779362i | \(-0.715543\pi\) | ||||
−0.626574 | + | 0.779362i | \(0.715543\pi\) | |||||||
\(648\) | −7.48528 | −0.294050 | ||||||||
\(649\) | 15.8338 | 0.621529 | ||||||||
\(650\) | −1.86370 | −0.0731005 | ||||||||
\(651\) | −0.451044 | −0.0176778 | ||||||||
\(652\) | −3.87780 | −0.151866 | ||||||||
\(653\) | −31.3226 | −1.22575 | −0.612875 | − | 0.790180i | \(-0.709987\pi\) | ||||
−0.612875 | + | 0.790180i | \(0.709987\pi\) | |||||||
\(654\) | −2.57310 | −0.100616 | ||||||||
\(655\) | −19.8776 | −0.776682 | ||||||||
\(656\) | −7.53465 | −0.294179 | ||||||||
\(657\) | 44.9973 | 1.75551 | ||||||||
\(658\) | −0.0997761 | −0.00388968 | ||||||||
\(659\) | −14.1631 | −0.551717 | −0.275858 | − | 0.961198i | \(-0.588962\pi\) | ||||
−0.275858 | + | 0.961198i | \(0.588962\pi\) | |||||||
\(660\) | 2.18618 | 0.0850971 | ||||||||
\(661\) | −34.3365 | −1.33554 | −0.667768 | − | 0.744369i | \(-0.732750\pi\) | ||||
−0.667768 | + | 0.744369i | \(0.732750\pi\) | |||||||
\(662\) | −3.25120 | −0.126361 | ||||||||
\(663\) | 4.05261 | 0.157390 | ||||||||
\(664\) | −0.643238 | −0.0249625 | ||||||||
\(665\) | 0.267434 | 0.0103706 | ||||||||
\(666\) | 2.34315 | 0.0907951 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 2.76681 | 0.107051 | ||||||||
\(669\) | 5.60624 | 0.216750 | ||||||||
\(670\) | 15.0628 | 0.581926 | ||||||||
\(671\) | 51.4947 | 1.98793 | ||||||||
\(672\) | 0.117041 | 0.00451494 | ||||||||
\(673\) | −22.5656 | −0.869841 | −0.434921 | − | 0.900469i | \(-0.643224\pi\) | ||||
−0.434921 | + | 0.900469i | \(0.643224\pi\) | |||||||
\(674\) | 23.5714 | 0.907938 | ||||||||
\(675\) | 2.41421 | 0.0929231 | ||||||||
\(676\) | −9.52661 | −0.366408 | ||||||||
\(677\) | −2.61539 | −0.100518 | −0.0502588 | − | 0.998736i | \(-0.516005\pi\) | ||||
−0.0502588 | + | 0.998736i | \(0.516005\pi\) | |||||||
\(678\) | −2.12460 | −0.0815949 | ||||||||
\(679\) | 3.29755 | 0.126548 | ||||||||
\(680\) | −5.24969 | −0.201316 | ||||||||
\(681\) | 2.96431 | 0.113593 | ||||||||
\(682\) | −20.3397 | −0.778847 | ||||||||
\(683\) | 3.99911 | 0.153022 | 0.0765108 | − | 0.997069i | \(-0.475622\pi\) | ||||
0.0765108 | + | 0.997069i | \(0.475622\pi\) | |||||||
\(684\) | 2.67700 | 0.102358 | ||||||||
\(685\) | 16.6067 | 0.634510 | ||||||||
\(686\) | 3.93330 | 0.150174 | ||||||||
\(687\) | −0.339017 | −0.0129343 | ||||||||
\(688\) | −0.663902 | −0.0253110 | ||||||||
\(689\) | −19.0411 | −0.725409 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −30.3616 | −1.15501 | −0.577505 | − | 0.816387i | \(-0.695974\pi\) | ||||
−0.577505 | + | 0.816387i | \(0.695974\pi\) | |||||||
\(692\) | 19.2015 | 0.729931 | ||||||||
\(693\) | −4.21813 | −0.160233 | ||||||||
\(694\) | −13.0980 | −0.497194 | ||||||||
\(695\) | −16.1623 | −0.613070 | ||||||||
\(696\) | −0.682163 | −0.0258573 | ||||||||
\(697\) | 39.5546 | 1.49824 | ||||||||
\(698\) | 2.69412 | 0.101974 | ||||||||
\(699\) | 9.12560 | 0.345162 | ||||||||
\(700\) | 0.282561 | 0.0106798 | ||||||||
\(701\) | 31.0073 | 1.17113 | 0.585564 | − | 0.810626i | \(-0.300873\pi\) | ||||
0.585564 | + | 0.810626i | \(0.300873\pi\) | |||||||
\(702\) | −4.49938 | −0.169818 | ||||||||
\(703\) | −0.784076 | −0.0295720 | ||||||||
\(704\) | 5.27792 | 0.198919 | ||||||||
\(705\) | 0.146264 | 0.00550863 | ||||||||
\(706\) | −3.54727 | −0.133503 | ||||||||
\(707\) | −3.00523 | −0.113023 | ||||||||
\(708\) | −1.24264 | −0.0467013 | ||||||||
\(709\) | 28.9157 | 1.08595 | 0.542977 | − | 0.839748i | \(-0.317297\pi\) | ||||
0.542977 | + | 0.839748i | \(0.317297\pi\) | |||||||
\(710\) | 13.4448 | 0.504576 | ||||||||
\(711\) | 13.6080 | 0.510341 | ||||||||
\(712\) | 2.29326 | 0.0859435 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | −0.614427 | −0.0229943 | ||||||||
\(715\) | −9.83647 | −0.367863 | ||||||||
\(716\) | 21.6401 | 0.808729 | ||||||||
\(717\) | 11.2207 | 0.419046 | ||||||||
\(718\) | −21.8220 | −0.814391 | ||||||||
\(719\) | −2.06340 | −0.0769519 | −0.0384759 | − | 0.999260i | \(-0.512250\pi\) | ||||
−0.0384759 | + | 0.999260i | \(0.512250\pi\) | |||||||
\(720\) | 2.82843 | 0.105409 | ||||||||
\(721\) | −3.47475 | −0.129406 | ||||||||
\(722\) | 18.1042 | 0.673769 | ||||||||
\(723\) | −2.84183 | −0.105689 | ||||||||
\(724\) | −16.4288 | −0.610572 | ||||||||
\(725\) | −1.64689 | −0.0611638 | ||||||||
\(726\) | 6.98215 | 0.259132 | ||||||||
\(727\) | −7.61304 | −0.282352 | −0.141176 | − | 0.989985i | \(-0.545088\pi\) | ||||
−0.141176 | + | 0.989985i | \(0.545088\pi\) | |||||||
\(728\) | −0.526610 | −0.0195175 | ||||||||
\(729\) | −18.1716 | −0.673021 | ||||||||
\(730\) | −15.9089 | −0.588817 | ||||||||
\(731\) | 3.48528 | 0.128908 | ||||||||
\(732\) | −4.04133 | −0.149372 | ||||||||
\(733\) | 0.545866 | 0.0201620 | 0.0100810 | − | 0.999949i | \(-0.496791\pi\) | ||||
0.0100810 | + | 0.999949i | \(0.496791\pi\) | |||||||
\(734\) | 9.98177 | 0.368434 | ||||||||
\(735\) | −2.86642 | −0.105730 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 79.5001 | 2.92842 | ||||||||
\(738\) | −21.3112 | −0.784477 | ||||||||
\(739\) | −1.49333 | −0.0549329 | −0.0274664 | − | 0.999623i | \(-0.508744\pi\) | ||||
−0.0274664 | + | 0.999623i | \(0.508744\pi\) | |||||||
\(740\) | −0.828427 | −0.0304536 | ||||||||
\(741\) | 0.730643 | 0.0268408 | ||||||||
\(742\) | 2.88687 | 0.105981 | ||||||||
\(743\) | 42.4290 | 1.55657 | 0.778285 | − | 0.627912i | \(-0.216090\pi\) | ||||
0.778285 | + | 0.627912i | \(0.216090\pi\) | |||||||
\(744\) | 1.59627 | 0.0585221 | ||||||||
\(745\) | −4.83839 | −0.177265 | ||||||||
\(746\) | −13.8537 | −0.507221 | ||||||||
\(747\) | −1.81935 | −0.0665666 | ||||||||
\(748\) | −27.7074 | −1.01308 | ||||||||
\(749\) | −2.56313 | −0.0936548 | ||||||||
\(750\) | −0.414214 | −0.0151249 | ||||||||
\(751\) | 32.0575 | 1.16979 | 0.584897 | − | 0.811107i | \(-0.301135\pi\) | ||||
0.584897 | + | 0.811107i | \(0.301135\pi\) | |||||||
\(752\) | 0.353113 | 0.0128767 | ||||||||
\(753\) | 2.54930 | 0.0929017 | ||||||||
\(754\) | 3.06931 | 0.111778 | ||||||||
\(755\) | 3.19151 | 0.116151 | ||||||||
\(756\) | 0.682163 | 0.0248100 | ||||||||
\(757\) | 24.4763 | 0.889608 | 0.444804 | − | 0.895628i | \(-0.353273\pi\) | ||||
0.444804 | + | 0.895628i | \(0.353273\pi\) | |||||||
\(758\) | 27.1798 | 0.987215 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.946464 | −0.0343318 | ||||||||
\(761\) | −19.3184 | −0.700290 | −0.350145 | − | 0.936696i | \(-0.613868\pi\) | ||||
−0.350145 | + | 0.936696i | \(0.613868\pi\) | |||||||
\(762\) | 3.14021 | 0.113758 | ||||||||
\(763\) | −1.75527 | −0.0635451 | ||||||||
\(764\) | −24.6797 | −0.892879 | ||||||||
\(765\) | −14.8484 | −0.536844 | ||||||||
\(766\) | 9.17260 | 0.331420 | ||||||||
\(767\) | 5.59111 | 0.201883 | ||||||||
\(768\) | −0.414214 | −0.0149466 | ||||||||
\(769\) | 30.5045 | 1.10002 | 0.550010 | − | 0.835158i | \(-0.314624\pi\) | ||||
0.550010 | + | 0.835158i | \(0.314624\pi\) | |||||||
\(770\) | 1.49133 | 0.0537439 | ||||||||
\(771\) | 3.07055 | 0.110583 | ||||||||
\(772\) | −11.1429 | −0.401040 | ||||||||
\(773\) | −18.7589 | −0.674711 | −0.337355 | − | 0.941377i | \(-0.609532\pi\) | ||||
−0.337355 | + | 0.941377i | \(0.609532\pi\) | |||||||
\(774\) | −1.87780 | −0.0674961 | ||||||||
\(775\) | 3.85374 | 0.138430 | ||||||||
\(776\) | −11.6702 | −0.418937 | ||||||||
\(777\) | −0.0969596 | −0.00347841 | ||||||||
\(778\) | 16.0048 | 0.573800 | ||||||||
\(779\) | 7.13128 | 0.255504 | ||||||||
\(780\) | 0.771971 | 0.0276410 | ||||||||
\(781\) | 70.9608 | 2.53918 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.97594 | −0.142088 | ||||||||
\(784\) | −6.92016 | −0.247149 | ||||||||
\(785\) | 10.4288 | 0.372221 | ||||||||
\(786\) | 8.23357 | 0.293682 | ||||||||
\(787\) | −25.0638 | −0.893428 | −0.446714 | − | 0.894677i | \(-0.647406\pi\) | ||||
−0.446714 | + | 0.894677i | \(0.647406\pi\) | |||||||
\(788\) | −10.9262 | −0.389230 | ||||||||
\(789\) | 9.28929 | 0.330708 | ||||||||
\(790\) | −4.81116 | −0.171173 | ||||||||
\(791\) | −1.44933 | −0.0515321 | ||||||||
\(792\) | 14.9282 | 0.530451 | ||||||||
\(793\) | 18.1835 | 0.645714 | ||||||||
\(794\) | −28.4776 | −1.01063 | ||||||||
\(795\) | −4.23194 | −0.150092 | ||||||||
\(796\) | −21.4600 | −0.760629 | ||||||||
\(797\) | −30.1700 | −1.06868 | −0.534338 | − | 0.845271i | \(-0.679439\pi\) | ||||
−0.534338 | + | 0.845271i | \(0.679439\pi\) | |||||||
\(798\) | −0.110775 | −0.00392138 | ||||||||
\(799\) | −1.85374 | −0.0655805 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 6.48631 | 0.229183 | ||||||||
\(802\) | 13.9535 | 0.492717 | ||||||||
\(803\) | −83.9661 | −2.96310 | ||||||||
\(804\) | −6.23921 | −0.220040 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −7.18222 | −0.252983 | ||||||||
\(807\) | 1.76090 | 0.0619868 | ||||||||
\(808\) | 10.6357 | 0.374162 | ||||||||
\(809\) | −23.4794 | −0.825491 | −0.412746 | − | 0.910846i | \(-0.635430\pi\) | ||||
−0.412746 | + | 0.910846i | \(0.635430\pi\) | |||||||
\(810\) | 7.48528 | 0.263006 | ||||||||
\(811\) | −0.772718 | −0.0271338 | −0.0135669 | − | 0.999908i | \(-0.504319\pi\) | ||||
−0.0135669 | + | 0.999908i | \(0.504319\pi\) | |||||||
\(812\) | −0.465346 | −0.0163304 | ||||||||
\(813\) | −5.79315 | −0.203175 | ||||||||
\(814\) | −4.37237 | −0.153251 | ||||||||
\(815\) | 3.87780 | 0.135833 | ||||||||
\(816\) | 2.17449 | 0.0761225 | ||||||||
\(817\) | 0.628359 | 0.0219835 | ||||||||
\(818\) | 19.8732 | 0.694849 | ||||||||
\(819\) | −1.48948 | −0.0520466 | ||||||||
\(820\) | 7.53465 | 0.263122 | ||||||||
\(821\) | 22.8683 | 0.798109 | 0.399055 | − | 0.916927i | \(-0.369338\pi\) | ||||
0.399055 | + | 0.916927i | \(0.369338\pi\) | |||||||
\(822\) | −6.87873 | −0.239923 | ||||||||
\(823\) | 29.3381 | 1.02266 | 0.511331 | − | 0.859384i | \(-0.329153\pi\) | ||||
0.511331 | + | 0.859384i | \(0.329153\pi\) | |||||||
\(824\) | 12.2973 | 0.428398 | ||||||||
\(825\) | −2.18618 | −0.0761132 | ||||||||
\(826\) | −0.847683 | −0.0294947 | ||||||||
\(827\) | −42.1809 | −1.46678 | −0.733388 | − | 0.679811i | \(-0.762062\pi\) | ||||
−0.733388 | + | 0.679811i | \(0.762062\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.69089 | −0.128190 | −0.0640949 | − | 0.997944i | \(-0.520416\pi\) | ||||
−0.0640949 | + | 0.997944i | \(0.520416\pi\) | |||||||
\(830\) | 0.643238 | 0.0223271 | ||||||||
\(831\) | −7.62247 | −0.264421 | ||||||||
\(832\) | 1.86370 | 0.0646123 | ||||||||
\(833\) | 36.3287 | 1.25871 | ||||||||
\(834\) | 6.69464 | 0.231816 | ||||||||
\(835\) | −2.76681 | −0.0957495 | ||||||||
\(836\) | −4.99536 | −0.172768 | ||||||||
\(837\) | 9.30374 | 0.321584 | ||||||||
\(838\) | −22.7512 | −0.785928 | ||||||||
\(839\) | 38.1981 | 1.31874 | 0.659372 | − | 0.751817i | \(-0.270822\pi\) | ||||
0.659372 | + | 0.751817i | \(0.270822\pi\) | |||||||
\(840\) | −0.117041 | −0.00403829 | ||||||||
\(841\) | −26.2878 | −0.906475 | ||||||||
\(842\) | 40.7127 | 1.40305 | ||||||||
\(843\) | 2.07228 | 0.0713730 | ||||||||
\(844\) | 2.88812 | 0.0994132 | ||||||||
\(845\) | 9.52661 | 0.327725 | ||||||||
\(846\) | 0.998756 | 0.0343379 | ||||||||
\(847\) | 4.76296 | 0.163657 | ||||||||
\(848\) | −10.2168 | −0.350847 | ||||||||
\(849\) | −7.83334 | −0.268839 | ||||||||
\(850\) | 5.24969 | 0.180063 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −5.56904 | −0.190792 | ||||||||
\(853\) | −15.5099 | −0.531049 | −0.265525 | − | 0.964104i | \(-0.585545\pi\) | ||||
−0.265525 | + | 0.964104i | \(0.585545\pi\) | |||||||
\(854\) | −2.75684 | −0.0943373 | ||||||||
\(855\) | −2.67700 | −0.0915516 | ||||||||
\(856\) | 9.07107 | 0.310043 | ||||||||
\(857\) | −31.5049 | −1.07619 | −0.538093 | − | 0.842886i | \(-0.680855\pi\) | ||||
−0.538093 | + | 0.842886i | \(0.680855\pi\) | |||||||
\(858\) | 4.07440 | 0.139098 | ||||||||
\(859\) | −41.9647 | −1.43182 | −0.715908 | − | 0.698195i | \(-0.753987\pi\) | ||||
−0.715908 | + | 0.698195i | \(0.753987\pi\) | |||||||
\(860\) | 0.663902 | 0.0226389 | ||||||||
\(861\) | 0.881861 | 0.0300537 | ||||||||
\(862\) | 24.2843 | 0.827126 | ||||||||
\(863\) | −12.3497 | −0.420387 | −0.210194 | − | 0.977660i | \(-0.567409\pi\) | ||||
−0.210194 | + | 0.977660i | \(0.567409\pi\) | |||||||
\(864\) | −2.41421 | −0.0821332 | ||||||||
\(865\) | −19.2015 | −0.652870 | ||||||||
\(866\) | 17.2074 | 0.584730 | ||||||||
\(867\) | −4.37378 | −0.148541 | ||||||||
\(868\) | 1.08892 | 0.0369602 | ||||||||
\(869\) | −25.3929 | −0.861396 | ||||||||
\(870\) | 0.682163 | 0.0231275 | ||||||||
\(871\) | 28.0725 | 0.951202 | ||||||||
\(872\) | 6.21201 | 0.210365 | ||||||||
\(873\) | −33.0084 | −1.11716 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.282561 | −0.00955231 | ||||||||
\(876\) | 6.58970 | 0.222645 | ||||||||
\(877\) | 29.9235 | 1.01045 | 0.505223 | − | 0.862989i | \(-0.331410\pi\) | ||||
0.505223 | + | 0.862989i | \(0.331410\pi\) | |||||||
\(878\) | −36.9825 | −1.24810 | ||||||||
\(879\) | 13.6476 | 0.460321 | ||||||||
\(880\) | −5.27792 | −0.177919 | ||||||||
\(881\) | −8.56618 | −0.288602 | −0.144301 | − | 0.989534i | \(-0.546093\pi\) | ||||
−0.144301 | + | 0.989534i | \(0.546093\pi\) | |||||||
\(882\) | −19.5732 | −0.659063 | ||||||||
\(883\) | 19.9994 | 0.673035 | 0.336517 | − | 0.941677i | \(-0.390751\pi\) | ||||
0.336517 | + | 0.941677i | \(0.390751\pi\) | |||||||
\(884\) | −9.78386 | −0.329067 | ||||||||
\(885\) | 1.24264 | 0.0417709 | ||||||||
\(886\) | 15.0698 | 0.506281 | ||||||||
\(887\) | 53.1363 | 1.78414 | 0.892071 | − | 0.451896i | \(-0.149252\pi\) | ||||
0.892071 | + | 0.451896i | \(0.149252\pi\) | |||||||
\(888\) | 0.343146 | 0.0115152 | ||||||||
\(889\) | 2.14214 | 0.0718449 | ||||||||
\(890\) | −2.29326 | −0.0768702 | ||||||||
\(891\) | 39.5067 | 1.32352 | ||||||||
\(892\) | −13.5347 | −0.453174 | ||||||||
\(893\) | −0.334209 | −0.0111839 | ||||||||
\(894\) | 2.00413 | 0.0670281 | ||||||||
\(895\) | −21.6401 | −0.723349 | ||||||||
\(896\) | −0.282561 | −0.00943970 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 18.4675 | 0.616269 | ||||||||
\(899\) | −6.34667 | −0.211673 | ||||||||
\(900\) | −2.82843 | −0.0942809 | ||||||||
\(901\) | 53.6351 | 1.78684 | ||||||||
\(902\) | 39.7673 | 1.32411 | ||||||||
\(903\) | 0.0777036 | 0.00258581 | ||||||||
\(904\) | 5.12925 | 0.170596 | ||||||||
\(905\) | 16.4288 | 0.546113 | ||||||||
\(906\) | −1.32197 | −0.0439194 | ||||||||
\(907\) | 21.8713 | 0.726223 | 0.363112 | − | 0.931746i | \(-0.381714\pi\) | ||||
0.363112 | + | 0.931746i | \(0.381714\pi\) | |||||||
\(908\) | −7.15648 | −0.237496 | ||||||||
\(909\) | 30.0822 | 0.997765 | ||||||||
\(910\) | 0.526610 | 0.0174570 | ||||||||
\(911\) | −55.8763 | −1.85127 | −0.925633 | − | 0.378423i | \(-0.876467\pi\) | ||||
−0.925633 | + | 0.378423i | \(0.876467\pi\) | |||||||
\(912\) | 0.392038 | 0.0129817 | ||||||||
\(913\) | 3.39496 | 0.112357 | ||||||||
\(914\) | 28.5891 | 0.945645 | ||||||||
\(915\) | 4.04133 | 0.133602 | ||||||||
\(916\) | 0.818459 | 0.0270427 | ||||||||
\(917\) | 5.61663 | 0.185478 | ||||||||
\(918\) | 12.6739 | 0.418300 | ||||||||
\(919\) | −19.4789 | −0.642549 | −0.321274 | − | 0.946986i | \(-0.604111\pi\) | ||||
−0.321274 | + | 0.946986i | \(0.604111\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.32175 | −0.109455 | ||||||||
\(922\) | 7.13986 | 0.235139 | ||||||||
\(923\) | 25.0572 | 0.824768 | ||||||||
\(924\) | −0.617731 | −0.0203218 | ||||||||
\(925\) | 0.828427 | 0.0272385 | ||||||||
\(926\) | −3.77073 | −0.123914 | ||||||||
\(927\) | 34.7821 | 1.14239 | ||||||||
\(928\) | 1.64689 | 0.0540617 | ||||||||
\(929\) | 49.9789 | 1.63976 | 0.819878 | − | 0.572539i | \(-0.194041\pi\) | ||||
0.819878 | + | 0.572539i | \(0.194041\pi\) | |||||||
\(930\) | −1.59627 | −0.0523437 | ||||||||
\(931\) | 6.54968 | 0.214657 | ||||||||
\(932\) | −22.0311 | −0.721654 | ||||||||
\(933\) | −10.2017 | −0.333988 | ||||||||
\(934\) | −26.5448 | −0.868572 | ||||||||
\(935\) | 27.7074 | 0.906130 | ||||||||
\(936\) | 5.27135 | 0.172299 | ||||||||
\(937\) | 26.2127 | 0.856330 | 0.428165 | − | 0.903701i | \(-0.359160\pi\) | ||||
0.428165 | + | 0.903701i | \(0.359160\pi\) | |||||||
\(938\) | −4.25615 | −0.138968 | ||||||||
\(939\) | −6.24807 | −0.203898 | ||||||||
\(940\) | −0.353113 | −0.0115173 | ||||||||
\(941\) | −23.1300 | −0.754015 | −0.377008 | − | 0.926210i | \(-0.623047\pi\) | ||||
−0.377008 | + | 0.926210i | \(0.623047\pi\) | |||||||
\(942\) | −4.31976 | −0.140745 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 3.00000 | 0.0976417 | ||||||||
\(945\) | −0.682163 | −0.0221908 | ||||||||
\(946\) | 3.50402 | 0.113926 | ||||||||
\(947\) | −31.2797 | −1.01645 | −0.508227 | − | 0.861223i | \(-0.669699\pi\) | ||||
−0.508227 | + | 0.861223i | \(0.669699\pi\) | |||||||
\(948\) | 1.99285 | 0.0647247 | ||||||||
\(949\) | −29.6496 | −0.962465 | ||||||||
\(950\) | 0.946464 | 0.0307073 | ||||||||
\(951\) | 9.61037 | 0.311637 | ||||||||
\(952\) | 1.48336 | 0.0480759 | ||||||||
\(953\) | 46.1117 | 1.49370 | 0.746852 | − | 0.664990i | \(-0.231564\pi\) | ||||
0.746852 | + | 0.664990i | \(0.231564\pi\) | |||||||
\(954\) | −28.8975 | −0.935592 | ||||||||
\(955\) | 24.6797 | 0.798615 | ||||||||
\(956\) | −27.0892 | −0.876129 | ||||||||
\(957\) | 3.60040 | 0.116384 | ||||||||
\(958\) | 21.1723 | 0.684044 | ||||||||
\(959\) | −4.69241 | −0.151526 | ||||||||
\(960\) | 0.414214 | 0.0133687 | ||||||||
\(961\) | −16.1487 | −0.520927 | ||||||||
\(962\) | −1.54394 | −0.0497787 | ||||||||
\(963\) | 25.6569 | 0.826781 | ||||||||
\(964\) | 6.86078 | 0.220971 | ||||||||
\(965\) | 11.1429 | 0.358702 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17.5750 | −0.565175 | −0.282587 | − | 0.959242i | \(-0.591193\pi\) | ||||
−0.282587 | + | 0.959242i | \(0.591193\pi\) | |||||||
\(968\) | −16.8564 | −0.541785 | ||||||||
\(969\) | −2.05808 | −0.0661150 | ||||||||
\(970\) | 11.6702 | 0.374708 | ||||||||
\(971\) | 21.9107 | 0.703148 | 0.351574 | − | 0.936160i | \(-0.385647\pi\) | ||||
0.351574 | + | 0.936160i | \(0.385647\pi\) | |||||||
\(972\) | −10.3431 | −0.331757 | ||||||||
\(973\) | 4.56683 | 0.146406 | ||||||||
\(974\) | 30.3727 | 0.973204 | ||||||||
\(975\) | −0.771971 | −0.0247229 | ||||||||
\(976\) | 9.75663 | 0.312302 | ||||||||
\(977\) | −24.4929 | −0.783597 | −0.391798 | − | 0.920051i | \(-0.628147\pi\) | ||||
−0.391798 | + | 0.920051i | \(0.628147\pi\) | |||||||
\(978\) | −1.60624 | −0.0513618 | ||||||||
\(979\) | −12.1036 | −0.386833 | ||||||||
\(980\) | 6.92016 | 0.221056 | ||||||||
\(981\) | 17.5702 | 0.560974 | ||||||||
\(982\) | −28.0706 | −0.895767 | ||||||||
\(983\) | −11.9177 | −0.380115 | −0.190057 | − | 0.981773i | \(-0.560867\pi\) | ||||
−0.190057 | + | 0.981773i | \(0.560867\pi\) | |||||||
\(984\) | −3.12096 | −0.0994924 | ||||||||
\(985\) | 10.9262 | 0.348138 | ||||||||
\(986\) | −8.64564 | −0.275333 | ||||||||
\(987\) | −0.0413286 | −0.00131550 | ||||||||
\(988\) | −1.76393 | −0.0561180 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −14.9282 | −0.474449 | ||||||||
\(991\) | 53.9572 | 1.71401 | 0.857004 | − | 0.515310i | \(-0.172323\pi\) | ||||
0.857004 | + | 0.515310i | \(0.172323\pi\) | |||||||
\(992\) | −3.85374 | −0.122356 | ||||||||
\(993\) | −1.34669 | −0.0427360 | ||||||||
\(994\) | −3.79899 | −0.120497 | ||||||||
\(995\) | 21.4600 | 0.680327 | ||||||||
\(996\) | −0.266438 | −0.00844241 | ||||||||
\(997\) | −9.63795 | −0.305237 | −0.152618 | − | 0.988285i | \(-0.548771\pi\) | ||||
−0.152618 | + | 0.988285i | \(0.548771\pi\) | |||||||
\(998\) | −1.52719 | −0.0483425 | ||||||||
\(999\) | 2.00000 | 0.0632772 |
(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 | 5290.2.a.u.1.1 | ✓ | 4 | |
23.22 | odd | 2 | 5290.2.a.v.1.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5290.2.a.u.1.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
5290.2.a.v.1.2 | yes | 4 | 23.22 | odd | 2 |