Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [483,2,Mod(1,483)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(483, 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("483.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 483 = 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 483.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: | \(3.85677441763\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 483.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.61803 | −1.85123 | −0.925615 | − | 0.378467i | \(-0.876451\pi\) | ||||
−0.925615 | + | 0.378467i | \(0.876451\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 4.85410 | 2.42705 | ||||||||
\(5\) | −3.61803 | −1.61803 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(6\) | −2.61803 | −1.06881 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −7.47214 | −2.64180 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 9.47214 | 2.99535 | ||||||||
\(11\) | 3.47214 | 1.04689 | 0.523444 | − | 0.852060i | \(-0.324647\pi\) | ||||
0.523444 | + | 0.852060i | \(0.324647\pi\) | |||||||
\(12\) | 4.85410 | 1.40126 | ||||||||
\(13\) | −4.61803 | −1.28081 | −0.640406 | − | 0.768036i | \(-0.721234\pi\) | ||||
−0.640406 | + | 0.768036i | \(0.721234\pi\) | |||||||
\(14\) | −2.61803 | −0.699699 | ||||||||
\(15\) | −3.61803 | −0.934172 | ||||||||
\(16\) | 9.85410 | 2.46353 | ||||||||
\(17\) | −1.00000 | −0.242536 | −0.121268 | − | 0.992620i | \(-0.538696\pi\) | ||||
−0.121268 | + | 0.992620i | \(0.538696\pi\) | |||||||
\(18\) | −2.61803 | −0.617077 | ||||||||
\(19\) | −3.00000 | −0.688247 | −0.344124 | − | 0.938924i | \(-0.611824\pi\) | ||||
−0.344124 | + | 0.938924i | \(0.611824\pi\) | |||||||
\(20\) | −17.5623 | −3.92705 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | −9.09017 | −1.93803 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | −7.47214 | −1.52524 | ||||||||
\(25\) | 8.09017 | 1.61803 | ||||||||
\(26\) | 12.0902 | 2.37108 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 4.85410 | 0.917339 | ||||||||
\(29\) | 1.47214 | 0.273369 | 0.136684 | − | 0.990615i | \(-0.456355\pi\) | ||||
0.136684 | + | 0.990615i | \(0.456355\pi\) | |||||||
\(30\) | 9.47214 | 1.72937 | ||||||||
\(31\) | −8.23607 | −1.47924 | −0.739621 | − | 0.673024i | \(-0.764995\pi\) | ||||
−0.739621 | + | 0.673024i | \(0.764995\pi\) | |||||||
\(32\) | −10.8541 | −1.91875 | ||||||||
\(33\) | 3.47214 | 0.604421 | ||||||||
\(34\) | 2.61803 | 0.448989 | ||||||||
\(35\) | −3.61803 | −0.611559 | ||||||||
\(36\) | 4.85410 | 0.809017 | ||||||||
\(37\) | −7.47214 | −1.22841 | −0.614206 | − | 0.789146i | \(-0.710524\pi\) | ||||
−0.614206 | + | 0.789146i | \(0.710524\pi\) | |||||||
\(38\) | 7.85410 | 1.27410 | ||||||||
\(39\) | −4.61803 | −0.739477 | ||||||||
\(40\) | 27.0344 | 4.27452 | ||||||||
\(41\) | 8.70820 | 1.35999 | 0.679996 | − | 0.733215i | \(-0.261981\pi\) | ||||
0.679996 | + | 0.733215i | \(0.261981\pi\) | |||||||
\(42\) | −2.61803 | −0.403971 | ||||||||
\(43\) | −3.09017 | −0.471246 | −0.235623 | − | 0.971844i | \(-0.575713\pi\) | ||||
−0.235623 | + | 0.971844i | \(0.575713\pi\) | |||||||
\(44\) | 16.8541 | 2.54085 | ||||||||
\(45\) | −3.61803 | −0.539345 | ||||||||
\(46\) | 2.61803 | 0.386008 | ||||||||
\(47\) | −11.7082 | −1.70782 | −0.853909 | − | 0.520423i | \(-0.825774\pi\) | ||||
−0.853909 | + | 0.520423i | \(0.825774\pi\) | |||||||
\(48\) | 9.85410 | 1.42232 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −21.1803 | −2.99535 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | −22.4164 | −3.10860 | ||||||||
\(53\) | −5.61803 | −0.771696 | −0.385848 | − | 0.922562i | \(-0.626091\pi\) | ||||
−0.385848 | + | 0.922562i | \(0.626091\pi\) | |||||||
\(54\) | −2.61803 | −0.356269 | ||||||||
\(55\) | −12.5623 | −1.69390 | ||||||||
\(56\) | −7.47214 | −0.998506 | ||||||||
\(57\) | −3.00000 | −0.397360 | ||||||||
\(58\) | −3.85410 | −0.506068 | ||||||||
\(59\) | −12.8541 | −1.67346 | −0.836731 | − | 0.547614i | \(-0.815536\pi\) | ||||
−0.836731 | + | 0.547614i | \(0.815536\pi\) | |||||||
\(60\) | −17.5623 | −2.26728 | ||||||||
\(61\) | −10.7984 | −1.38259 | −0.691295 | − | 0.722573i | \(-0.742960\pi\) | ||||
−0.691295 | + | 0.722573i | \(0.742960\pi\) | |||||||
\(62\) | 21.5623 | 2.73842 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 8.70820 | 1.08853 | ||||||||
\(65\) | 16.7082 | 2.07240 | ||||||||
\(66\) | −9.09017 | −1.11892 | ||||||||
\(67\) | 10.8541 | 1.32604 | 0.663020 | − | 0.748602i | \(-0.269275\pi\) | ||||
0.663020 | + | 0.748602i | \(0.269275\pi\) | |||||||
\(68\) | −4.85410 | −0.588646 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 9.47214 | 1.13214 | ||||||||
\(71\) | −15.0902 | −1.79087 | −0.895437 | − | 0.445189i | \(-0.853137\pi\) | ||||
−0.895437 | + | 0.445189i | \(0.853137\pi\) | |||||||
\(72\) | −7.47214 | −0.880600 | ||||||||
\(73\) | −10.7082 | −1.25330 | −0.626650 | − | 0.779301i | \(-0.715575\pi\) | ||||
−0.626650 | + | 0.779301i | \(0.715575\pi\) | |||||||
\(74\) | 19.5623 | 2.27407 | ||||||||
\(75\) | 8.09017 | 0.934172 | ||||||||
\(76\) | −14.5623 | −1.67041 | ||||||||
\(77\) | 3.47214 | 0.395687 | ||||||||
\(78\) | 12.0902 | 1.36894 | ||||||||
\(79\) | 9.47214 | 1.06570 | 0.532849 | − | 0.846210i | \(-0.321121\pi\) | ||||
0.532849 | + | 0.846210i | \(0.321121\pi\) | |||||||
\(80\) | −35.6525 | −3.98607 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −22.7984 | −2.51766 | ||||||||
\(83\) | −3.00000 | −0.329293 | −0.164646 | − | 0.986353i | \(-0.552648\pi\) | ||||
−0.164646 | + | 0.986353i | \(0.552648\pi\) | |||||||
\(84\) | 4.85410 | 0.529626 | ||||||||
\(85\) | 3.61803 | 0.392431 | ||||||||
\(86\) | 8.09017 | 0.872385 | ||||||||
\(87\) | 1.47214 | 0.157830 | ||||||||
\(88\) | −25.9443 | −2.76567 | ||||||||
\(89\) | 9.85410 | 1.04453 | 0.522266 | − | 0.852782i | \(-0.325087\pi\) | ||||
0.522266 | + | 0.852782i | \(0.325087\pi\) | |||||||
\(90\) | 9.47214 | 0.998451 | ||||||||
\(91\) | −4.61803 | −0.484102 | ||||||||
\(92\) | −4.85410 | −0.506075 | ||||||||
\(93\) | −8.23607 | −0.854040 | ||||||||
\(94\) | 30.6525 | 3.16156 | ||||||||
\(95\) | 10.8541 | 1.11361 | ||||||||
\(96\) | −10.8541 | −1.10779 | ||||||||
\(97\) | 5.00000 | 0.507673 | 0.253837 | − | 0.967247i | \(-0.418307\pi\) | ||||
0.253837 | + | 0.967247i | \(0.418307\pi\) | |||||||
\(98\) | −2.61803 | −0.264461 | ||||||||
\(99\) | 3.47214 | 0.348963 | ||||||||
\(100\) | 39.2705 | 3.92705 | ||||||||
\(101\) | 4.85410 | 0.483001 | 0.241501 | − | 0.970401i | \(-0.422360\pi\) | ||||
0.241501 | + | 0.970401i | \(0.422360\pi\) | |||||||
\(102\) | 2.61803 | 0.259224 | ||||||||
\(103\) | 12.9443 | 1.27544 | 0.637719 | − | 0.770270i | \(-0.279878\pi\) | ||||
0.637719 | + | 0.770270i | \(0.279878\pi\) | |||||||
\(104\) | 34.5066 | 3.38365 | ||||||||
\(105\) | −3.61803 | −0.353084 | ||||||||
\(106\) | 14.7082 | 1.42859 | ||||||||
\(107\) | −12.7984 | −1.23727 | −0.618633 | − | 0.785680i | \(-0.712313\pi\) | ||||
−0.618633 | + | 0.785680i | \(0.712313\pi\) | |||||||
\(108\) | 4.85410 | 0.467086 | ||||||||
\(109\) | 9.32624 | 0.893292 | 0.446646 | − | 0.894711i | \(-0.352618\pi\) | ||||
0.446646 | + | 0.894711i | \(0.352618\pi\) | |||||||
\(110\) | 32.8885 | 3.13580 | ||||||||
\(111\) | −7.47214 | −0.709224 | ||||||||
\(112\) | 9.85410 | 0.931125 | ||||||||
\(113\) | −9.32624 | −0.877339 | −0.438669 | − | 0.898649i | \(-0.644550\pi\) | ||||
−0.438669 | + | 0.898649i | \(0.644550\pi\) | |||||||
\(114\) | 7.85410 | 0.735604 | ||||||||
\(115\) | 3.61803 | 0.337383 | ||||||||
\(116\) | 7.14590 | 0.663480 | ||||||||
\(117\) | −4.61803 | −0.426937 | ||||||||
\(118\) | 33.6525 | 3.09796 | ||||||||
\(119\) | −1.00000 | −0.0916698 | ||||||||
\(120\) | 27.0344 | 2.46790 | ||||||||
\(121\) | 1.05573 | 0.0959753 | ||||||||
\(122\) | 28.2705 | 2.55949 | ||||||||
\(123\) | 8.70820 | 0.785192 | ||||||||
\(124\) | −39.9787 | −3.59019 | ||||||||
\(125\) | −11.1803 | −1.00000 | ||||||||
\(126\) | −2.61803 | −0.233233 | ||||||||
\(127\) | 12.1459 | 1.07777 | 0.538887 | − | 0.842378i | \(-0.318845\pi\) | ||||
0.538887 | + | 0.842378i | \(0.318845\pi\) | |||||||
\(128\) | −1.09017 | −0.0963583 | ||||||||
\(129\) | −3.09017 | −0.272074 | ||||||||
\(130\) | −43.7426 | −3.83648 | ||||||||
\(131\) | −0.0557281 | −0.00486899 | −0.00243449 | − | 0.999997i | \(-0.500775\pi\) | ||||
−0.00243449 | + | 0.999997i | \(0.500775\pi\) | |||||||
\(132\) | 16.8541 | 1.46696 | ||||||||
\(133\) | −3.00000 | −0.260133 | ||||||||
\(134\) | −28.4164 | −2.45480 | ||||||||
\(135\) | −3.61803 | −0.311391 | ||||||||
\(136\) | 7.47214 | 0.640730 | ||||||||
\(137\) | −13.1803 | −1.12607 | −0.563036 | − | 0.826432i | \(-0.690367\pi\) | ||||
−0.563036 | + | 0.826432i | \(0.690367\pi\) | |||||||
\(138\) | 2.61803 | 0.222862 | ||||||||
\(139\) | −0.673762 | −0.0571478 | −0.0285739 | − | 0.999592i | \(-0.509097\pi\) | ||||
−0.0285739 | + | 0.999592i | \(0.509097\pi\) | |||||||
\(140\) | −17.5623 | −1.48429 | ||||||||
\(141\) | −11.7082 | −0.986009 | ||||||||
\(142\) | 39.5066 | 3.31532 | ||||||||
\(143\) | −16.0344 | −1.34087 | ||||||||
\(144\) | 9.85410 | 0.821175 | ||||||||
\(145\) | −5.32624 | −0.442320 | ||||||||
\(146\) | 28.0344 | 2.32015 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | −36.2705 | −2.98142 | ||||||||
\(149\) | 6.18034 | 0.506313 | 0.253157 | − | 0.967425i | \(-0.418531\pi\) | ||||
0.253157 | + | 0.967425i | \(0.418531\pi\) | |||||||
\(150\) | −21.1803 | −1.72937 | ||||||||
\(151\) | 5.23607 | 0.426105 | 0.213053 | − | 0.977041i | \(-0.431659\pi\) | ||||
0.213053 | + | 0.977041i | \(0.431659\pi\) | |||||||
\(152\) | 22.4164 | 1.81821 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | −9.09017 | −0.732507 | ||||||||
\(155\) | 29.7984 | 2.39346 | ||||||||
\(156\) | −22.4164 | −1.79475 | ||||||||
\(157\) | 10.6525 | 0.850160 | 0.425080 | − | 0.905156i | \(-0.360246\pi\) | ||||
0.425080 | + | 0.905156i | \(0.360246\pi\) | |||||||
\(158\) | −24.7984 | −1.97285 | ||||||||
\(159\) | −5.61803 | −0.445539 | ||||||||
\(160\) | 39.2705 | 3.10461 | ||||||||
\(161\) | −1.00000 | −0.0788110 | ||||||||
\(162\) | −2.61803 | −0.205692 | ||||||||
\(163\) | −21.7984 | −1.70738 | −0.853690 | − | 0.520781i | \(-0.825641\pi\) | ||||
−0.853690 | + | 0.520781i | \(0.825641\pi\) | |||||||
\(164\) | 42.2705 | 3.30077 | ||||||||
\(165\) | −12.5623 | −0.977974 | ||||||||
\(166\) | 7.85410 | 0.609597 | ||||||||
\(167\) | 23.4721 | 1.81633 | 0.908164 | − | 0.418614i | \(-0.137484\pi\) | ||||
0.908164 | + | 0.418614i | \(0.137484\pi\) | |||||||
\(168\) | −7.47214 | −0.576488 | ||||||||
\(169\) | 8.32624 | 0.640480 | ||||||||
\(170\) | −9.47214 | −0.726480 | ||||||||
\(171\) | −3.00000 | −0.229416 | ||||||||
\(172\) | −15.0000 | −1.14374 | ||||||||
\(173\) | 13.1803 | 1.00208 | 0.501041 | − | 0.865423i | \(-0.332950\pi\) | ||||
0.501041 | + | 0.865423i | \(0.332950\pi\) | |||||||
\(174\) | −3.85410 | −0.292179 | ||||||||
\(175\) | 8.09017 | 0.611559 | ||||||||
\(176\) | 34.2148 | 2.57904 | ||||||||
\(177\) | −12.8541 | −0.966173 | ||||||||
\(178\) | −25.7984 | −1.93367 | ||||||||
\(179\) | 1.14590 | 0.0856484 | 0.0428242 | − | 0.999083i | \(-0.486364\pi\) | ||||
0.0428242 | + | 0.999083i | \(0.486364\pi\) | |||||||
\(180\) | −17.5623 | −1.30902 | ||||||||
\(181\) | −1.47214 | −0.109423 | −0.0547115 | − | 0.998502i | \(-0.517424\pi\) | ||||
−0.0547115 | + | 0.998502i | \(0.517424\pi\) | |||||||
\(182\) | 12.0902 | 0.896183 | ||||||||
\(183\) | −10.7984 | −0.798239 | ||||||||
\(184\) | 7.47214 | 0.550853 | ||||||||
\(185\) | 27.0344 | 1.98761 | ||||||||
\(186\) | 21.5623 | 1.58102 | ||||||||
\(187\) | −3.47214 | −0.253908 | ||||||||
\(188\) | −56.8328 | −4.14496 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | −28.4164 | −2.06154 | ||||||||
\(191\) | 19.7082 | 1.42604 | 0.713018 | − | 0.701146i | \(-0.247328\pi\) | ||||
0.713018 | + | 0.701146i | \(0.247328\pi\) | |||||||
\(192\) | 8.70820 | 0.628460 | ||||||||
\(193\) | 8.18034 | 0.588834 | 0.294417 | − | 0.955677i | \(-0.404875\pi\) | ||||
0.294417 | + | 0.955677i | \(0.404875\pi\) | |||||||
\(194\) | −13.0902 | −0.939819 | ||||||||
\(195\) | 16.7082 | 1.19650 | ||||||||
\(196\) | 4.85410 | 0.346722 | ||||||||
\(197\) | −6.14590 | −0.437877 | −0.218939 | − | 0.975739i | \(-0.570259\pi\) | ||||
−0.218939 | + | 0.975739i | \(0.570259\pi\) | |||||||
\(198\) | −9.09017 | −0.646010 | ||||||||
\(199\) | 11.0344 | 0.782211 | 0.391105 | − | 0.920346i | \(-0.372093\pi\) | ||||
0.391105 | + | 0.920346i | \(0.372093\pi\) | |||||||
\(200\) | −60.4508 | −4.27452 | ||||||||
\(201\) | 10.8541 | 0.765589 | ||||||||
\(202\) | −12.7082 | −0.894146 | ||||||||
\(203\) | 1.47214 | 0.103324 | ||||||||
\(204\) | −4.85410 | −0.339855 | ||||||||
\(205\) | −31.5066 | −2.20051 | ||||||||
\(206\) | −33.8885 | −2.36113 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | −45.5066 | −3.15531 | ||||||||
\(209\) | −10.4164 | −0.720518 | ||||||||
\(210\) | 9.47214 | 0.653639 | ||||||||
\(211\) | −0.416408 | −0.0286667 | −0.0143333 | − | 0.999897i | \(-0.504563\pi\) | ||||
−0.0143333 | + | 0.999897i | \(0.504563\pi\) | |||||||
\(212\) | −27.2705 | −1.87295 | ||||||||
\(213\) | −15.0902 | −1.03396 | ||||||||
\(214\) | 33.5066 | 2.29046 | ||||||||
\(215\) | 11.1803 | 0.762493 | ||||||||
\(216\) | −7.47214 | −0.508414 | ||||||||
\(217\) | −8.23607 | −0.559101 | ||||||||
\(218\) | −24.4164 | −1.65369 | ||||||||
\(219\) | −10.7082 | −0.723593 | ||||||||
\(220\) | −60.9787 | −4.11118 | ||||||||
\(221\) | 4.61803 | 0.310643 | ||||||||
\(222\) | 19.5623 | 1.31294 | ||||||||
\(223\) | −4.67376 | −0.312978 | −0.156489 | − | 0.987680i | \(-0.550018\pi\) | ||||
−0.156489 | + | 0.987680i | \(0.550018\pi\) | |||||||
\(224\) | −10.8541 | −0.725220 | ||||||||
\(225\) | 8.09017 | 0.539345 | ||||||||
\(226\) | 24.4164 | 1.62416 | ||||||||
\(227\) | 15.7984 | 1.04857 | 0.524287 | − | 0.851541i | \(-0.324332\pi\) | ||||
0.524287 | + | 0.851541i | \(0.324332\pi\) | |||||||
\(228\) | −14.5623 | −0.964412 | ||||||||
\(229\) | −1.43769 | −0.0950055 | −0.0475028 | − | 0.998871i | \(-0.515126\pi\) | ||||
−0.0475028 | + | 0.998871i | \(0.515126\pi\) | |||||||
\(230\) | −9.47214 | −0.624574 | ||||||||
\(231\) | 3.47214 | 0.228450 | ||||||||
\(232\) | −11.0000 | −0.722185 | ||||||||
\(233\) | −14.2705 | −0.934892 | −0.467446 | − | 0.884022i | \(-0.654826\pi\) | ||||
−0.467446 | + | 0.884022i | \(0.654826\pi\) | |||||||
\(234\) | 12.0902 | 0.790359 | ||||||||
\(235\) | 42.3607 | 2.76331 | ||||||||
\(236\) | −62.3951 | −4.06158 | ||||||||
\(237\) | 9.47214 | 0.615281 | ||||||||
\(238\) | 2.61803 | 0.169702 | ||||||||
\(239\) | −11.1459 | −0.720968 | −0.360484 | − | 0.932765i | \(-0.617388\pi\) | ||||
−0.360484 | + | 0.932765i | \(0.617388\pi\) | |||||||
\(240\) | −35.6525 | −2.30136 | ||||||||
\(241\) | 6.41641 | 0.413317 | 0.206659 | − | 0.978413i | \(-0.433741\pi\) | ||||
0.206659 | + | 0.978413i | \(0.433741\pi\) | |||||||
\(242\) | −2.76393 | −0.177672 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −52.4164 | −3.35562 | ||||||||
\(245\) | −3.61803 | −0.231148 | ||||||||
\(246\) | −22.7984 | −1.45357 | ||||||||
\(247\) | 13.8541 | 0.881515 | ||||||||
\(248\) | 61.5410 | 3.90786 | ||||||||
\(249\) | −3.00000 | −0.190117 | ||||||||
\(250\) | 29.2705 | 1.85123 | ||||||||
\(251\) | −3.23607 | −0.204259 | −0.102129 | − | 0.994771i | \(-0.532566\pi\) | ||||
−0.102129 | + | 0.994771i | \(0.532566\pi\) | |||||||
\(252\) | 4.85410 | 0.305780 | ||||||||
\(253\) | −3.47214 | −0.218291 | ||||||||
\(254\) | −31.7984 | −1.99521 | ||||||||
\(255\) | 3.61803 | 0.226570 | ||||||||
\(256\) | −14.5623 | −0.910144 | ||||||||
\(257\) | 17.5967 | 1.09765 | 0.548827 | − | 0.835936i | \(-0.315074\pi\) | ||||
0.548827 | + | 0.835936i | \(0.315074\pi\) | |||||||
\(258\) | 8.09017 | 0.503672 | ||||||||
\(259\) | −7.47214 | −0.464296 | ||||||||
\(260\) | 81.1033 | 5.02981 | ||||||||
\(261\) | 1.47214 | 0.0911229 | ||||||||
\(262\) | 0.145898 | 0.00901361 | ||||||||
\(263\) | −7.65248 | −0.471872 | −0.235936 | − | 0.971769i | \(-0.575816\pi\) | ||||
−0.235936 | + | 0.971769i | \(0.575816\pi\) | |||||||
\(264\) | −25.9443 | −1.59676 | ||||||||
\(265\) | 20.3262 | 1.24863 | ||||||||
\(266\) | 7.85410 | 0.481566 | ||||||||
\(267\) | 9.85410 | 0.603061 | ||||||||
\(268\) | 52.6869 | 3.21837 | ||||||||
\(269\) | 19.2705 | 1.17494 | 0.587472 | − | 0.809245i | \(-0.300123\pi\) | ||||
0.587472 | + | 0.809245i | \(0.300123\pi\) | |||||||
\(270\) | 9.47214 | 0.576456 | ||||||||
\(271\) | −21.8328 | −1.32625 | −0.663125 | − | 0.748509i | \(-0.730770\pi\) | ||||
−0.663125 | + | 0.748509i | \(0.730770\pi\) | |||||||
\(272\) | −9.85410 | −0.597493 | ||||||||
\(273\) | −4.61803 | −0.279496 | ||||||||
\(274\) | 34.5066 | 2.08462 | ||||||||
\(275\) | 28.0902 | 1.69390 | ||||||||
\(276\) | −4.85410 | −0.292183 | ||||||||
\(277\) | −25.8541 | −1.55342 | −0.776711 | − | 0.629857i | \(-0.783114\pi\) | ||||
−0.776711 | + | 0.629857i | \(0.783114\pi\) | |||||||
\(278\) | 1.76393 | 0.105794 | ||||||||
\(279\) | −8.23607 | −0.493080 | ||||||||
\(280\) | 27.0344 | 1.61562 | ||||||||
\(281\) | 14.2918 | 0.852577 | 0.426289 | − | 0.904587i | \(-0.359821\pi\) | ||||
0.426289 | + | 0.904587i | \(0.359821\pi\) | |||||||
\(282\) | 30.6525 | 1.82533 | ||||||||
\(283\) | −15.9098 | −0.945741 | −0.472871 | − | 0.881132i | \(-0.656782\pi\) | ||||
−0.472871 | + | 0.881132i | \(0.656782\pi\) | |||||||
\(284\) | −73.2492 | −4.34654 | ||||||||
\(285\) | 10.8541 | 0.642942 | ||||||||
\(286\) | 41.9787 | 2.48225 | ||||||||
\(287\) | 8.70820 | 0.514029 | ||||||||
\(288\) | −10.8541 | −0.639584 | ||||||||
\(289\) | −16.0000 | −0.941176 | ||||||||
\(290\) | 13.9443 | 0.818836 | ||||||||
\(291\) | 5.00000 | 0.293105 | ||||||||
\(292\) | −51.9787 | −3.04182 | ||||||||
\(293\) | −23.4164 | −1.36800 | −0.684001 | − | 0.729481i | \(-0.739761\pi\) | ||||
−0.684001 | + | 0.729481i | \(0.739761\pi\) | |||||||
\(294\) | −2.61803 | −0.152687 | ||||||||
\(295\) | 46.5066 | 2.70772 | ||||||||
\(296\) | 55.8328 | 3.24522 | ||||||||
\(297\) | 3.47214 | 0.201474 | ||||||||
\(298\) | −16.1803 | −0.937302 | ||||||||
\(299\) | 4.61803 | 0.267068 | ||||||||
\(300\) | 39.2705 | 2.26728 | ||||||||
\(301\) | −3.09017 | −0.178114 | ||||||||
\(302\) | −13.7082 | −0.788818 | ||||||||
\(303\) | 4.85410 | 0.278861 | ||||||||
\(304\) | −29.5623 | −1.69551 | ||||||||
\(305\) | 39.0689 | 2.23708 | ||||||||
\(306\) | 2.61803 | 0.149663 | ||||||||
\(307\) | −9.29180 | −0.530311 | −0.265155 | − | 0.964206i | \(-0.585423\pi\) | ||||
−0.265155 | + | 0.964206i | \(0.585423\pi\) | |||||||
\(308\) | 16.8541 | 0.960352 | ||||||||
\(309\) | 12.9443 | 0.736374 | ||||||||
\(310\) | −78.0132 | −4.43085 | ||||||||
\(311\) | −16.5066 | −0.936002 | −0.468001 | − | 0.883728i | \(-0.655026\pi\) | ||||
−0.468001 | + | 0.883728i | \(0.655026\pi\) | |||||||
\(312\) | 34.5066 | 1.95355 | ||||||||
\(313\) | 6.47214 | 0.365827 | 0.182913 | − | 0.983129i | \(-0.441447\pi\) | ||||
0.182913 | + | 0.983129i | \(0.441447\pi\) | |||||||
\(314\) | −27.8885 | −1.57384 | ||||||||
\(315\) | −3.61803 | −0.203853 | ||||||||
\(316\) | 45.9787 | 2.58650 | ||||||||
\(317\) | −0.201626 | −0.0113245 | −0.00566223 | − | 0.999984i | \(-0.501802\pi\) | ||||
−0.00566223 | + | 0.999984i | \(0.501802\pi\) | |||||||
\(318\) | 14.7082 | 0.824795 | ||||||||
\(319\) | 5.11146 | 0.286187 | ||||||||
\(320\) | −31.5066 | −1.76127 | ||||||||
\(321\) | −12.7984 | −0.714336 | ||||||||
\(322\) | 2.61803 | 0.145897 | ||||||||
\(323\) | 3.00000 | 0.166924 | ||||||||
\(324\) | 4.85410 | 0.269672 | ||||||||
\(325\) | −37.3607 | −2.07240 | ||||||||
\(326\) | 57.0689 | 3.16075 | ||||||||
\(327\) | 9.32624 | 0.515742 | ||||||||
\(328\) | −65.0689 | −3.59283 | ||||||||
\(329\) | −11.7082 | −0.645494 | ||||||||
\(330\) | 32.8885 | 1.81045 | ||||||||
\(331\) | 1.05573 | 0.0580281 | 0.0290140 | − | 0.999579i | \(-0.490763\pi\) | ||||
0.0290140 | + | 0.999579i | \(0.490763\pi\) | |||||||
\(332\) | −14.5623 | −0.799210 | ||||||||
\(333\) | −7.47214 | −0.409471 | ||||||||
\(334\) | −61.4508 | −3.36244 | ||||||||
\(335\) | −39.2705 | −2.14558 | ||||||||
\(336\) | 9.85410 | 0.537585 | ||||||||
\(337\) | 28.3262 | 1.54303 | 0.771514 | − | 0.636212i | \(-0.219500\pi\) | ||||
0.771514 | + | 0.636212i | \(0.219500\pi\) | |||||||
\(338\) | −21.7984 | −1.18568 | ||||||||
\(339\) | −9.32624 | −0.506532 | ||||||||
\(340\) | 17.5623 | 0.952450 | ||||||||
\(341\) | −28.5967 | −1.54860 | ||||||||
\(342\) | 7.85410 | 0.424701 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 23.0902 | 1.24494 | ||||||||
\(345\) | 3.61803 | 0.194788 | ||||||||
\(346\) | −34.5066 | −1.85509 | ||||||||
\(347\) | 20.4164 | 1.09601 | 0.548005 | − | 0.836475i | \(-0.315387\pi\) | ||||
0.548005 | + | 0.836475i | \(0.315387\pi\) | |||||||
\(348\) | 7.14590 | 0.383060 | ||||||||
\(349\) | 15.2148 | 0.814429 | 0.407214 | − | 0.913333i | \(-0.366500\pi\) | ||||
0.407214 | + | 0.913333i | \(0.366500\pi\) | |||||||
\(350\) | −21.1803 | −1.13214 | ||||||||
\(351\) | −4.61803 | −0.246492 | ||||||||
\(352\) | −37.6869 | −2.00872 | ||||||||
\(353\) | −19.6525 | −1.04600 | −0.522998 | − | 0.852334i | \(-0.675186\pi\) | ||||
−0.522998 | + | 0.852334i | \(0.675186\pi\) | |||||||
\(354\) | 33.6525 | 1.78861 | ||||||||
\(355\) | 54.5967 | 2.89769 | ||||||||
\(356\) | 47.8328 | 2.53513 | ||||||||
\(357\) | −1.00000 | −0.0529256 | ||||||||
\(358\) | −3.00000 | −0.158555 | ||||||||
\(359\) | 21.5066 | 1.13507 | 0.567537 | − | 0.823348i | \(-0.307896\pi\) | ||||
0.567537 | + | 0.823348i | \(0.307896\pi\) | |||||||
\(360\) | 27.0344 | 1.42484 | ||||||||
\(361\) | −10.0000 | −0.526316 | ||||||||
\(362\) | 3.85410 | 0.202567 | ||||||||
\(363\) | 1.05573 | 0.0554114 | ||||||||
\(364\) | −22.4164 | −1.17494 | ||||||||
\(365\) | 38.7426 | 2.02788 | ||||||||
\(366\) | 28.2705 | 1.47772 | ||||||||
\(367\) | 4.43769 | 0.231646 | 0.115823 | − | 0.993270i | \(-0.463050\pi\) | ||||
0.115823 | + | 0.993270i | \(0.463050\pi\) | |||||||
\(368\) | −9.85410 | −0.513681 | ||||||||
\(369\) | 8.70820 | 0.453331 | ||||||||
\(370\) | −70.7771 | −3.67953 | ||||||||
\(371\) | −5.61803 | −0.291674 | ||||||||
\(372\) | −39.9787 | −2.07280 | ||||||||
\(373\) | −29.9443 | −1.55046 | −0.775228 | − | 0.631682i | \(-0.782365\pi\) | ||||
−0.775228 | + | 0.631682i | \(0.782365\pi\) | |||||||
\(374\) | 9.09017 | 0.470041 | ||||||||
\(375\) | −11.1803 | −0.577350 | ||||||||
\(376\) | 87.4853 | 4.51171 | ||||||||
\(377\) | −6.79837 | −0.350134 | ||||||||
\(378\) | −2.61803 | −0.134657 | ||||||||
\(379\) | −12.3607 | −0.634925 | −0.317463 | − | 0.948271i | \(-0.602831\pi\) | ||||
−0.317463 | + | 0.948271i | \(0.602831\pi\) | |||||||
\(380\) | 52.6869 | 2.70278 | ||||||||
\(381\) | 12.1459 | 0.622253 | ||||||||
\(382\) | −51.5967 | −2.63992 | ||||||||
\(383\) | −18.5279 | −0.946730 | −0.473365 | − | 0.880866i | \(-0.656961\pi\) | ||||
−0.473365 | + | 0.880866i | \(0.656961\pi\) | |||||||
\(384\) | −1.09017 | −0.0556325 | ||||||||
\(385\) | −12.5623 | −0.640234 | ||||||||
\(386\) | −21.4164 | −1.09007 | ||||||||
\(387\) | −3.09017 | −0.157082 | ||||||||
\(388\) | 24.2705 | 1.23215 | ||||||||
\(389\) | −18.4164 | −0.933749 | −0.466874 | − | 0.884324i | \(-0.654620\pi\) | ||||
−0.466874 | + | 0.884324i | \(0.654620\pi\) | |||||||
\(390\) | −43.7426 | −2.21499 | ||||||||
\(391\) | 1.00000 | 0.0505722 | ||||||||
\(392\) | −7.47214 | −0.377400 | ||||||||
\(393\) | −0.0557281 | −0.00281111 | ||||||||
\(394\) | 16.0902 | 0.810611 | ||||||||
\(395\) | −34.2705 | −1.72434 | ||||||||
\(396\) | 16.8541 | 0.846950 | ||||||||
\(397\) | −16.2918 | −0.817662 | −0.408831 | − | 0.912610i | \(-0.634063\pi\) | ||||
−0.408831 | + | 0.912610i | \(0.634063\pi\) | |||||||
\(398\) | −28.8885 | −1.44805 | ||||||||
\(399\) | −3.00000 | −0.150188 | ||||||||
\(400\) | 79.7214 | 3.98607 | ||||||||
\(401\) | −32.4164 | −1.61880 | −0.809399 | − | 0.587259i | \(-0.800207\pi\) | ||||
−0.809399 | + | 0.587259i | \(0.800207\pi\) | |||||||
\(402\) | −28.4164 | −1.41728 | ||||||||
\(403\) | 38.0344 | 1.89463 | ||||||||
\(404\) | 23.5623 | 1.17227 | ||||||||
\(405\) | −3.61803 | −0.179782 | ||||||||
\(406\) | −3.85410 | −0.191276 | ||||||||
\(407\) | −25.9443 | −1.28601 | ||||||||
\(408\) | 7.47214 | 0.369926 | ||||||||
\(409\) | −4.41641 | −0.218377 | −0.109189 | − | 0.994021i | \(-0.534825\pi\) | ||||
−0.109189 | + | 0.994021i | \(0.534825\pi\) | |||||||
\(410\) | 82.4853 | 4.07366 | ||||||||
\(411\) | −13.1803 | −0.650138 | ||||||||
\(412\) | 62.8328 | 3.09555 | ||||||||
\(413\) | −12.8541 | −0.632509 | ||||||||
\(414\) | 2.61803 | 0.128669 | ||||||||
\(415\) | 10.8541 | 0.532807 | ||||||||
\(416\) | 50.1246 | 2.45756 | ||||||||
\(417\) | −0.673762 | −0.0329943 | ||||||||
\(418\) | 27.2705 | 1.33384 | ||||||||
\(419\) | −18.2705 | −0.892573 | −0.446286 | − | 0.894890i | \(-0.647254\pi\) | ||||
−0.446286 | + | 0.894890i | \(0.647254\pi\) | |||||||
\(420\) | −17.5623 | −0.856953 | ||||||||
\(421\) | −13.3820 | −0.652197 | −0.326099 | − | 0.945336i | \(-0.605734\pi\) | ||||
−0.326099 | + | 0.945336i | \(0.605734\pi\) | |||||||
\(422\) | 1.09017 | 0.0530686 | ||||||||
\(423\) | −11.7082 | −0.569272 | ||||||||
\(424\) | 41.9787 | 2.03867 | ||||||||
\(425\) | −8.09017 | −0.392431 | ||||||||
\(426\) | 39.5066 | 1.91410 | ||||||||
\(427\) | −10.7984 | −0.522570 | ||||||||
\(428\) | −62.1246 | −3.00291 | ||||||||
\(429\) | −16.0344 | −0.774150 | ||||||||
\(430\) | −29.2705 | −1.41155 | ||||||||
\(431\) | 37.1591 | 1.78989 | 0.894944 | − | 0.446178i | \(-0.147215\pi\) | ||||
0.894944 | + | 0.446178i | \(0.147215\pi\) | |||||||
\(432\) | 9.85410 | 0.474106 | ||||||||
\(433\) | 8.18034 | 0.393122 | 0.196561 | − | 0.980492i | \(-0.437023\pi\) | ||||
0.196561 | + | 0.980492i | \(0.437023\pi\) | |||||||
\(434\) | 21.5623 | 1.03502 | ||||||||
\(435\) | −5.32624 | −0.255374 | ||||||||
\(436\) | 45.2705 | 2.16806 | ||||||||
\(437\) | 3.00000 | 0.143509 | ||||||||
\(438\) | 28.0344 | 1.33954 | ||||||||
\(439\) | 19.1803 | 0.915428 | 0.457714 | − | 0.889100i | \(-0.348668\pi\) | ||||
0.457714 | + | 0.889100i | \(0.348668\pi\) | |||||||
\(440\) | 93.8673 | 4.47495 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −12.0902 | −0.575071 | ||||||||
\(443\) | 31.4164 | 1.49264 | 0.746319 | − | 0.665588i | \(-0.231819\pi\) | ||||
0.746319 | + | 0.665588i | \(0.231819\pi\) | |||||||
\(444\) | −36.2705 | −1.72132 | ||||||||
\(445\) | −35.6525 | −1.69009 | ||||||||
\(446\) | 12.2361 | 0.579395 | ||||||||
\(447\) | 6.18034 | 0.292320 | ||||||||
\(448\) | 8.70820 | 0.411424 | ||||||||
\(449\) | −1.50658 | −0.0710998 | −0.0355499 | − | 0.999368i | \(-0.511318\pi\) | ||||
−0.0355499 | + | 0.999368i | \(0.511318\pi\) | |||||||
\(450\) | −21.1803 | −0.998451 | ||||||||
\(451\) | 30.2361 | 1.42376 | ||||||||
\(452\) | −45.2705 | −2.12935 | ||||||||
\(453\) | 5.23607 | 0.246012 | ||||||||
\(454\) | −41.3607 | −1.94115 | ||||||||
\(455\) | 16.7082 | 0.783293 | ||||||||
\(456\) | 22.4164 | 1.04974 | ||||||||
\(457\) | 30.0902 | 1.40756 | 0.703779 | − | 0.710419i | \(-0.251494\pi\) | ||||
0.703779 | + | 0.710419i | \(0.251494\pi\) | |||||||
\(458\) | 3.76393 | 0.175877 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | 17.5623 | 0.818847 | ||||||||
\(461\) | −1.61803 | −0.0753594 | −0.0376797 | − | 0.999290i | \(-0.511997\pi\) | ||||
−0.0376797 | + | 0.999290i | \(0.511997\pi\) | |||||||
\(462\) | −9.09017 | −0.422913 | ||||||||
\(463\) | 6.34752 | 0.294994 | 0.147497 | − | 0.989062i | \(-0.452878\pi\) | ||||
0.147497 | + | 0.989062i | \(0.452878\pi\) | |||||||
\(464\) | 14.5066 | 0.673451 | ||||||||
\(465\) | 29.7984 | 1.38187 | ||||||||
\(466\) | 37.3607 | 1.73070 | ||||||||
\(467\) | −32.7771 | −1.51674 | −0.758371 | − | 0.651823i | \(-0.774005\pi\) | ||||
−0.758371 | + | 0.651823i | \(0.774005\pi\) | |||||||
\(468\) | −22.4164 | −1.03620 | ||||||||
\(469\) | 10.8541 | 0.501196 | ||||||||
\(470\) | −110.902 | −5.11551 | ||||||||
\(471\) | 10.6525 | 0.490840 | ||||||||
\(472\) | 96.0476 | 4.42095 | ||||||||
\(473\) | −10.7295 | −0.493342 | ||||||||
\(474\) | −24.7984 | −1.13903 | ||||||||
\(475\) | −24.2705 | −1.11361 | ||||||||
\(476\) | −4.85410 | −0.222487 | ||||||||
\(477\) | −5.61803 | −0.257232 | ||||||||
\(478\) | 29.1803 | 1.33468 | ||||||||
\(479\) | 13.7639 | 0.628890 | 0.314445 | − | 0.949276i | \(-0.398182\pi\) | ||||
0.314445 | + | 0.949276i | \(0.398182\pi\) | |||||||
\(480\) | 39.2705 | 1.79245 | ||||||||
\(481\) | 34.5066 | 1.57336 | ||||||||
\(482\) | −16.7984 | −0.765145 | ||||||||
\(483\) | −1.00000 | −0.0455016 | ||||||||
\(484\) | 5.12461 | 0.232937 | ||||||||
\(485\) | −18.0902 | −0.821432 | ||||||||
\(486\) | −2.61803 | −0.118756 | ||||||||
\(487\) | 0.708204 | 0.0320918 | 0.0160459 | − | 0.999871i | \(-0.494892\pi\) | ||||
0.0160459 | + | 0.999871i | \(0.494892\pi\) | |||||||
\(488\) | 80.6869 | 3.65253 | ||||||||
\(489\) | −21.7984 | −0.985757 | ||||||||
\(490\) | 9.47214 | 0.427907 | ||||||||
\(491\) | −30.9787 | −1.39805 | −0.699025 | − | 0.715097i | \(-0.746382\pi\) | ||||
−0.699025 | + | 0.715097i | \(0.746382\pi\) | |||||||
\(492\) | 42.2705 | 1.90570 | ||||||||
\(493\) | −1.47214 | −0.0663017 | ||||||||
\(494\) | −36.2705 | −1.63189 | ||||||||
\(495\) | −12.5623 | −0.564634 | ||||||||
\(496\) | −81.1591 | −3.64415 | ||||||||
\(497\) | −15.0902 | −0.676887 | ||||||||
\(498\) | 7.85410 | 0.351951 | ||||||||
\(499\) | 19.0344 | 0.852099 | 0.426049 | − | 0.904700i | \(-0.359905\pi\) | ||||
0.426049 | + | 0.904700i | \(0.359905\pi\) | |||||||
\(500\) | −54.2705 | −2.42705 | ||||||||
\(501\) | 23.4721 | 1.04866 | ||||||||
\(502\) | 8.47214 | 0.378130 | ||||||||
\(503\) | 4.74265 | 0.211464 | 0.105732 | − | 0.994395i | \(-0.466281\pi\) | ||||
0.105732 | + | 0.994395i | \(0.466281\pi\) | |||||||
\(504\) | −7.47214 | −0.332835 | ||||||||
\(505\) | −17.5623 | −0.781512 | ||||||||
\(506\) | 9.09017 | 0.404107 | ||||||||
\(507\) | 8.32624 | 0.369781 | ||||||||
\(508\) | 58.9574 | 2.61581 | ||||||||
\(509\) | −14.1803 | −0.628533 | −0.314266 | − | 0.949335i | \(-0.601758\pi\) | ||||
−0.314266 | + | 0.949335i | \(0.601758\pi\) | |||||||
\(510\) | −9.47214 | −0.419433 | ||||||||
\(511\) | −10.7082 | −0.473703 | ||||||||
\(512\) | 40.3050 | 1.78124 | ||||||||
\(513\) | −3.00000 | −0.132453 | ||||||||
\(514\) | −46.0689 | −2.03201 | ||||||||
\(515\) | −46.8328 | −2.06370 | ||||||||
\(516\) | −15.0000 | −0.660338 | ||||||||
\(517\) | −40.6525 | −1.78789 | ||||||||
\(518\) | 19.5623 | 0.859518 | ||||||||
\(519\) | 13.1803 | 0.578553 | ||||||||
\(520\) | −124.846 | −5.47486 | ||||||||
\(521\) | 6.58359 | 0.288432 | 0.144216 | − | 0.989546i | \(-0.453934\pi\) | ||||
0.144216 | + | 0.989546i | \(0.453934\pi\) | |||||||
\(522\) | −3.85410 | −0.168689 | ||||||||
\(523\) | 30.3607 | 1.32758 | 0.663790 | − | 0.747919i | \(-0.268947\pi\) | ||||
0.663790 | + | 0.747919i | \(0.268947\pi\) | |||||||
\(524\) | −0.270510 | −0.0118173 | ||||||||
\(525\) | 8.09017 | 0.353084 | ||||||||
\(526\) | 20.0344 | 0.873543 | ||||||||
\(527\) | 8.23607 | 0.358769 | ||||||||
\(528\) | 34.2148 | 1.48901 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −53.2148 | −2.31150 | ||||||||
\(531\) | −12.8541 | −0.557821 | ||||||||
\(532\) | −14.5623 | −0.631356 | ||||||||
\(533\) | −40.2148 | −1.74190 | ||||||||
\(534\) | −25.7984 | −1.11640 | ||||||||
\(535\) | 46.3050 | 2.00194 | ||||||||
\(536\) | −81.1033 | −3.50313 | ||||||||
\(537\) | 1.14590 | 0.0494492 | ||||||||
\(538\) | −50.4508 | −2.17509 | ||||||||
\(539\) | 3.47214 | 0.149555 | ||||||||
\(540\) | −17.5623 | −0.755761 | ||||||||
\(541\) | −7.34752 | −0.315895 | −0.157947 | − | 0.987448i | \(-0.550488\pi\) | ||||
−0.157947 | + | 0.987448i | \(0.550488\pi\) | |||||||
\(542\) | 57.1591 | 2.45519 | ||||||||
\(543\) | −1.47214 | −0.0631754 | ||||||||
\(544\) | 10.8541 | 0.465366 | ||||||||
\(545\) | −33.7426 | −1.44538 | ||||||||
\(546\) | 12.0902 | 0.517412 | ||||||||
\(547\) | −26.2705 | −1.12325 | −0.561623 | − | 0.827393i | \(-0.689823\pi\) | ||||
−0.561623 | + | 0.827393i | \(0.689823\pi\) | |||||||
\(548\) | −63.9787 | −2.73304 | ||||||||
\(549\) | −10.7984 | −0.460863 | ||||||||
\(550\) | −73.5410 | −3.13580 | ||||||||
\(551\) | −4.41641 | −0.188145 | ||||||||
\(552\) | 7.47214 | 0.318035 | ||||||||
\(553\) | 9.47214 | 0.402796 | ||||||||
\(554\) | 67.6869 | 2.87574 | ||||||||
\(555\) | 27.0344 | 1.14755 | ||||||||
\(556\) | −3.27051 | −0.138701 | ||||||||
\(557\) | 14.2918 | 0.605563 | 0.302781 | − | 0.953060i | \(-0.402085\pi\) | ||||
0.302781 | + | 0.953060i | \(0.402085\pi\) | |||||||
\(558\) | 21.5623 | 0.912805 | ||||||||
\(559\) | 14.2705 | 0.603578 | ||||||||
\(560\) | −35.6525 | −1.50659 | ||||||||
\(561\) | −3.47214 | −0.146594 | ||||||||
\(562\) | −37.4164 | −1.57832 | ||||||||
\(563\) | −9.74265 | −0.410604 | −0.205302 | − | 0.978699i | \(-0.565818\pi\) | ||||
−0.205302 | + | 0.978699i | \(0.565818\pi\) | |||||||
\(564\) | −56.8328 | −2.39309 | ||||||||
\(565\) | 33.7426 | 1.41956 | ||||||||
\(566\) | 41.6525 | 1.75078 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 112.756 | 4.73113 | ||||||||
\(569\) | 34.8328 | 1.46027 | 0.730134 | − | 0.683304i | \(-0.239458\pi\) | ||||
0.730134 | + | 0.683304i | \(0.239458\pi\) | |||||||
\(570\) | −28.4164 | −1.19023 | ||||||||
\(571\) | 3.11146 | 0.130210 | 0.0651052 | − | 0.997878i | \(-0.479262\pi\) | ||||
0.0651052 | + | 0.997878i | \(0.479262\pi\) | |||||||
\(572\) | −77.8328 | −3.25435 | ||||||||
\(573\) | 19.7082 | 0.823322 | ||||||||
\(574\) | −22.7984 | −0.951586 | ||||||||
\(575\) | −8.09017 | −0.337383 | ||||||||
\(576\) | 8.70820 | 0.362842 | ||||||||
\(577\) | −7.52786 | −0.313389 | −0.156695 | − | 0.987647i | \(-0.550084\pi\) | ||||
−0.156695 | + | 0.987647i | \(0.550084\pi\) | |||||||
\(578\) | 41.8885 | 1.74233 | ||||||||
\(579\) | 8.18034 | 0.339963 | ||||||||
\(580\) | −25.8541 | −1.07353 | ||||||||
\(581\) | −3.00000 | −0.124461 | ||||||||
\(582\) | −13.0902 | −0.542605 | ||||||||
\(583\) | −19.5066 | −0.807880 | ||||||||
\(584\) | 80.0132 | 3.31097 | ||||||||
\(585\) | 16.7082 | 0.690799 | ||||||||
\(586\) | 61.3050 | 2.53248 | ||||||||
\(587\) | 37.2705 | 1.53832 | 0.769159 | − | 0.639057i | \(-0.220675\pi\) | ||||
0.769159 | + | 0.639057i | \(0.220675\pi\) | |||||||
\(588\) | 4.85410 | 0.200180 | ||||||||
\(589\) | 24.7082 | 1.01808 | ||||||||
\(590\) | −121.756 | −5.01261 | ||||||||
\(591\) | −6.14590 | −0.252808 | ||||||||
\(592\) | −73.6312 | −3.02622 | ||||||||
\(593\) | −21.1246 | −0.867484 | −0.433742 | − | 0.901037i | \(-0.642807\pi\) | ||||
−0.433742 | + | 0.901037i | \(0.642807\pi\) | |||||||
\(594\) | −9.09017 | −0.372974 | ||||||||
\(595\) | 3.61803 | 0.148325 | ||||||||
\(596\) | 30.0000 | 1.22885 | ||||||||
\(597\) | 11.0344 | 0.451610 | ||||||||
\(598\) | −12.0902 | −0.494404 | ||||||||
\(599\) | 2.90983 | 0.118892 | 0.0594462 | − | 0.998232i | \(-0.481067\pi\) | ||||
0.0594462 | + | 0.998232i | \(0.481067\pi\) | |||||||
\(600\) | −60.4508 | −2.46790 | ||||||||
\(601\) | −31.3262 | −1.27782 | −0.638912 | − | 0.769280i | \(-0.720615\pi\) | ||||
−0.638912 | + | 0.769280i | \(0.720615\pi\) | |||||||
\(602\) | 8.09017 | 0.329731 | ||||||||
\(603\) | 10.8541 | 0.442013 | ||||||||
\(604\) | 25.4164 | 1.03418 | ||||||||
\(605\) | −3.81966 | −0.155291 | ||||||||
\(606\) | −12.7082 | −0.516235 | ||||||||
\(607\) | 8.90983 | 0.361639 | 0.180819 | − | 0.983516i | \(-0.442125\pi\) | ||||
0.180819 | + | 0.983516i | \(0.442125\pi\) | |||||||
\(608\) | 32.5623 | 1.32058 | ||||||||
\(609\) | 1.47214 | 0.0596540 | ||||||||
\(610\) | −102.284 | −4.14134 | ||||||||
\(611\) | 54.0689 | 2.18739 | ||||||||
\(612\) | −4.85410 | −0.196215 | ||||||||
\(613\) | 29.6525 | 1.19765 | 0.598826 | − | 0.800879i | \(-0.295634\pi\) | ||||
0.598826 | + | 0.800879i | \(0.295634\pi\) | |||||||
\(614\) | 24.3262 | 0.981727 | ||||||||
\(615\) | −31.5066 | −1.27047 | ||||||||
\(616\) | −25.9443 | −1.04532 | ||||||||
\(617\) | 40.3951 | 1.62625 | 0.813123 | − | 0.582092i | \(-0.197766\pi\) | ||||
0.813123 | + | 0.582092i | \(0.197766\pi\) | |||||||
\(618\) | −33.8885 | −1.36320 | ||||||||
\(619\) | 41.3820 | 1.66328 | 0.831641 | − | 0.555314i | \(-0.187402\pi\) | ||||
0.831641 | + | 0.555314i | \(0.187402\pi\) | |||||||
\(620\) | 144.644 | 5.80906 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 43.2148 | 1.73275 | ||||||||
\(623\) | 9.85410 | 0.394796 | ||||||||
\(624\) | −45.5066 | −1.82172 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −16.9443 | −0.677229 | ||||||||
\(627\) | −10.4164 | −0.415991 | ||||||||
\(628\) | 51.7082 | 2.06338 | ||||||||
\(629\) | 7.47214 | 0.297934 | ||||||||
\(630\) | 9.47214 | 0.377379 | ||||||||
\(631\) | −7.29180 | −0.290282 | −0.145141 | − | 0.989411i | \(-0.546364\pi\) | ||||
−0.145141 | + | 0.989411i | \(0.546364\pi\) | |||||||
\(632\) | −70.7771 | −2.81536 | ||||||||
\(633\) | −0.416408 | −0.0165507 | ||||||||
\(634\) | 0.527864 | 0.0209642 | ||||||||
\(635\) | −43.9443 | −1.74388 | ||||||||
\(636\) | −27.2705 | −1.08135 | ||||||||
\(637\) | −4.61803 | −0.182973 | ||||||||
\(638\) | −13.3820 | −0.529797 | ||||||||
\(639\) | −15.0902 | −0.596958 | ||||||||
\(640\) | 3.94427 | 0.155911 | ||||||||
\(641\) | −24.2148 | −0.956426 | −0.478213 | − | 0.878244i | \(-0.658715\pi\) | ||||
−0.478213 | + | 0.878244i | \(0.658715\pi\) | |||||||
\(642\) | 33.5066 | 1.32240 | ||||||||
\(643\) | 11.8541 | 0.467480 | 0.233740 | − | 0.972299i | \(-0.424904\pi\) | ||||
0.233740 | + | 0.972299i | \(0.424904\pi\) | |||||||
\(644\) | −4.85410 | −0.191278 | ||||||||
\(645\) | 11.1803 | 0.440225 | ||||||||
\(646\) | −7.85410 | −0.309016 | ||||||||
\(647\) | 2.67376 | 0.105116 | 0.0525582 | − | 0.998618i | \(-0.483262\pi\) | ||||
0.0525582 | + | 0.998618i | \(0.483262\pi\) | |||||||
\(648\) | −7.47214 | −0.293533 | ||||||||
\(649\) | −44.6312 | −1.75193 | ||||||||
\(650\) | 97.8115 | 3.83648 | ||||||||
\(651\) | −8.23607 | −0.322797 | ||||||||
\(652\) | −105.812 | −4.14390 | ||||||||
\(653\) | −19.4377 | −0.760656 | −0.380328 | − | 0.924852i | \(-0.624189\pi\) | ||||
−0.380328 | + | 0.924852i | \(0.624189\pi\) | |||||||
\(654\) | −24.4164 | −0.954757 | ||||||||
\(655\) | 0.201626 | 0.00787818 | ||||||||
\(656\) | 85.8115 | 3.35038 | ||||||||
\(657\) | −10.7082 | −0.417767 | ||||||||
\(658\) | 30.6525 | 1.19496 | ||||||||
\(659\) | −20.5279 | −0.799652 | −0.399826 | − | 0.916591i | \(-0.630929\pi\) | ||||
−0.399826 | + | 0.916591i | \(0.630929\pi\) | |||||||
\(660\) | −60.9787 | −2.37359 | ||||||||
\(661\) | −38.7771 | −1.50825 | −0.754127 | − | 0.656729i | \(-0.771940\pi\) | ||||
−0.754127 | + | 0.656729i | \(0.771940\pi\) | |||||||
\(662\) | −2.76393 | −0.107423 | ||||||||
\(663\) | 4.61803 | 0.179350 | ||||||||
\(664\) | 22.4164 | 0.869925 | ||||||||
\(665\) | 10.8541 | 0.420904 | ||||||||
\(666\) | 19.5623 | 0.758024 | ||||||||
\(667\) | −1.47214 | −0.0570013 | ||||||||
\(668\) | 113.936 | 4.40832 | ||||||||
\(669\) | −4.67376 | −0.180698 | ||||||||
\(670\) | 102.812 | 3.97196 | ||||||||
\(671\) | −37.4934 | −1.44742 | ||||||||
\(672\) | −10.8541 | −0.418706 | ||||||||
\(673\) | 2.88854 | 0.111345 | 0.0556726 | − | 0.998449i | \(-0.482270\pi\) | ||||
0.0556726 | + | 0.998449i | \(0.482270\pi\) | |||||||
\(674\) | −74.1591 | −2.85650 | ||||||||
\(675\) | 8.09017 | 0.311391 | ||||||||
\(676\) | 40.4164 | 1.55448 | ||||||||
\(677\) | −1.38197 | −0.0531133 | −0.0265566 | − | 0.999647i | \(-0.508454\pi\) | ||||
−0.0265566 | + | 0.999647i | \(0.508454\pi\) | |||||||
\(678\) | 24.4164 | 0.937706 | ||||||||
\(679\) | 5.00000 | 0.191882 | ||||||||
\(680\) | −27.0344 | −1.03672 | ||||||||
\(681\) | 15.7984 | 0.605395 | ||||||||
\(682\) | 74.8673 | 2.86682 | ||||||||
\(683\) | 0.888544 | 0.0339992 | 0.0169996 | − | 0.999855i | \(-0.494589\pi\) | ||||
0.0169996 | + | 0.999855i | \(0.494589\pi\) | |||||||
\(684\) | −14.5623 | −0.556804 | ||||||||
\(685\) | 47.6869 | 1.82202 | ||||||||
\(686\) | −2.61803 | −0.0999570 | ||||||||
\(687\) | −1.43769 | −0.0548515 | ||||||||
\(688\) | −30.4508 | −1.16093 | ||||||||
\(689\) | 25.9443 | 0.988398 | ||||||||
\(690\) | −9.47214 | −0.360598 | ||||||||
\(691\) | 28.0344 | 1.06648 | 0.533240 | − | 0.845964i | \(-0.320974\pi\) | ||||
0.533240 | + | 0.845964i | \(0.320974\pi\) | |||||||
\(692\) | 63.9787 | 2.43211 | ||||||||
\(693\) | 3.47214 | 0.131896 | ||||||||
\(694\) | −53.4508 | −2.02897 | ||||||||
\(695\) | 2.43769 | 0.0924670 | ||||||||
\(696\) | −11.0000 | −0.416954 | ||||||||
\(697\) | −8.70820 | −0.329847 | ||||||||
\(698\) | −39.8328 | −1.50769 | ||||||||
\(699\) | −14.2705 | −0.539760 | ||||||||
\(700\) | 39.2705 | 1.48429 | ||||||||
\(701\) | 9.03444 | 0.341226 | 0.170613 | − | 0.985338i | \(-0.445425\pi\) | ||||
0.170613 | + | 0.985338i | \(0.445425\pi\) | |||||||
\(702\) | 12.0902 | 0.456314 | ||||||||
\(703\) | 22.4164 | 0.845451 | ||||||||
\(704\) | 30.2361 | 1.13956 | ||||||||
\(705\) | 42.3607 | 1.59540 | ||||||||
\(706\) | 51.4508 | 1.93638 | ||||||||
\(707\) | 4.85410 | 0.182557 | ||||||||
\(708\) | −62.3951 | −2.34495 | ||||||||
\(709\) | −33.9230 | −1.27400 | −0.637002 | − | 0.770862i | \(-0.719826\pi\) | ||||
−0.637002 | + | 0.770862i | \(0.719826\pi\) | |||||||
\(710\) | −142.936 | −5.36430 | ||||||||
\(711\) | 9.47214 | 0.355233 | ||||||||
\(712\) | −73.6312 | −2.75945 | ||||||||
\(713\) | 8.23607 | 0.308443 | ||||||||
\(714\) | 2.61803 | 0.0979775 | ||||||||
\(715\) | 58.0132 | 2.16957 | ||||||||
\(716\) | 5.56231 | 0.207873 | ||||||||
\(717\) | −11.1459 | −0.416251 | ||||||||
\(718\) | −56.3050 | −2.10128 | ||||||||
\(719\) | −15.2918 | −0.570288 | −0.285144 | − | 0.958485i | \(-0.592041\pi\) | ||||
−0.285144 | + | 0.958485i | \(0.592041\pi\) | |||||||
\(720\) | −35.6525 | −1.32869 | ||||||||
\(721\) | 12.9443 | 0.482070 | ||||||||
\(722\) | 26.1803 | 0.974331 | ||||||||
\(723\) | 6.41641 | 0.238629 | ||||||||
\(724\) | −7.14590 | −0.265575 | ||||||||
\(725\) | 11.9098 | 0.442320 | ||||||||
\(726\) | −2.76393 | −0.102579 | ||||||||
\(727\) | −41.3607 | −1.53398 | −0.766991 | − | 0.641657i | \(-0.778247\pi\) | ||||
−0.766991 | + | 0.641657i | \(0.778247\pi\) | |||||||
\(728\) | 34.5066 | 1.27890 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −101.430 | −3.75408 | ||||||||
\(731\) | 3.09017 | 0.114294 | ||||||||
\(732\) | −52.4164 | −1.93737 | ||||||||
\(733\) | −20.1803 | −0.745378 | −0.372689 | − | 0.927956i | \(-0.621564\pi\) | ||||
−0.372689 | + | 0.927956i | \(0.621564\pi\) | |||||||
\(734\) | −11.6180 | −0.428829 | ||||||||
\(735\) | −3.61803 | −0.133453 | ||||||||
\(736\) | 10.8541 | 0.400088 | ||||||||
\(737\) | 37.6869 | 1.38822 | ||||||||
\(738\) | −22.7984 | −0.839220 | ||||||||
\(739\) | −30.8885 | −1.13625 | −0.568127 | − | 0.822941i | \(-0.692332\pi\) | ||||
−0.568127 | + | 0.822941i | \(0.692332\pi\) | |||||||
\(740\) | 131.228 | 4.82403 | ||||||||
\(741\) | 13.8541 | 0.508943 | ||||||||
\(742\) | 14.7082 | 0.539955 | ||||||||
\(743\) | 7.03444 | 0.258069 | 0.129034 | − | 0.991640i | \(-0.458812\pi\) | ||||
0.129034 | + | 0.991640i | \(0.458812\pi\) | |||||||
\(744\) | 61.5410 | 2.25620 | ||||||||
\(745\) | −22.3607 | −0.819232 | ||||||||
\(746\) | 78.3951 | 2.87025 | ||||||||
\(747\) | −3.00000 | −0.109764 | ||||||||
\(748\) | −16.8541 | −0.616247 | ||||||||
\(749\) | −12.7984 | −0.467642 | ||||||||
\(750\) | 29.2705 | 1.06881 | ||||||||
\(751\) | 29.3951 | 1.07264 | 0.536322 | − | 0.844014i | \(-0.319813\pi\) | ||||
0.536322 | + | 0.844014i | \(0.319813\pi\) | |||||||
\(752\) | −115.374 | −4.20725 | ||||||||
\(753\) | −3.23607 | −0.117929 | ||||||||
\(754\) | 17.7984 | 0.648179 | ||||||||
\(755\) | −18.9443 | −0.689453 | ||||||||
\(756\) | 4.85410 | 0.176542 | ||||||||
\(757\) | 38.8885 | 1.41343 | 0.706714 | − | 0.707499i | \(-0.250177\pi\) | ||||
0.706714 | + | 0.707499i | \(0.250177\pi\) | |||||||
\(758\) | 32.3607 | 1.17539 | ||||||||
\(759\) | −3.47214 | −0.126031 | ||||||||
\(760\) | −81.1033 | −2.94193 | ||||||||
\(761\) | −49.3050 | −1.78730 | −0.893652 | − | 0.448762i | \(-0.851865\pi\) | ||||
−0.893652 | + | 0.448762i | \(0.851865\pi\) | |||||||
\(762\) | −31.7984 | −1.15193 | ||||||||
\(763\) | 9.32624 | 0.337632 | ||||||||
\(764\) | 95.6656 | 3.46106 | ||||||||
\(765\) | 3.61803 | 0.130810 | ||||||||
\(766\) | 48.5066 | 1.75261 | ||||||||
\(767\) | 59.3607 | 2.14339 | ||||||||
\(768\) | −14.5623 | −0.525472 | ||||||||
\(769\) | 31.5967 | 1.13941 | 0.569704 | − | 0.821850i | \(-0.307058\pi\) | ||||
0.569704 | + | 0.821850i | \(0.307058\pi\) | |||||||
\(770\) | 32.8885 | 1.18522 | ||||||||
\(771\) | 17.5967 | 0.633731 | ||||||||
\(772\) | 39.7082 | 1.42913 | ||||||||
\(773\) | 36.0132 | 1.29530 | 0.647652 | − | 0.761937i | \(-0.275751\pi\) | ||||
0.647652 | + | 0.761937i | \(0.275751\pi\) | |||||||
\(774\) | 8.09017 | 0.290795 | ||||||||
\(775\) | −66.6312 | −2.39346 | ||||||||
\(776\) | −37.3607 | −1.34117 | ||||||||
\(777\) | −7.47214 | −0.268061 | ||||||||
\(778\) | 48.2148 | 1.72858 | ||||||||
\(779\) | −26.1246 | −0.936011 | ||||||||
\(780\) | 81.1033 | 2.90396 | ||||||||
\(781\) | −52.3951 | −1.87484 | ||||||||
\(782\) | −2.61803 | −0.0936207 | ||||||||
\(783\) | 1.47214 | 0.0526098 | ||||||||
\(784\) | 9.85410 | 0.351932 | ||||||||
\(785\) | −38.5410 | −1.37559 | ||||||||
\(786\) | 0.145898 | 0.00520401 | ||||||||
\(787\) | −0.965558 | −0.0344184 | −0.0172092 | − | 0.999852i | \(-0.505478\pi\) | ||||
−0.0172092 | + | 0.999852i | \(0.505478\pi\) | |||||||
\(788\) | −29.8328 | −1.06275 | ||||||||
\(789\) | −7.65248 | −0.272435 | ||||||||
\(790\) | 89.7214 | 3.19214 | ||||||||
\(791\) | −9.32624 | −0.331603 | ||||||||
\(792\) | −25.9443 | −0.921890 | ||||||||
\(793\) | 49.8673 | 1.77084 | ||||||||
\(794\) | 42.6525 | 1.51368 | ||||||||
\(795\) | 20.3262 | 0.720897 | ||||||||
\(796\) | 53.5623 | 1.89847 | ||||||||
\(797\) | 13.5967 | 0.481622 | 0.240811 | − | 0.970572i | \(-0.422587\pi\) | ||||
0.240811 | + | 0.970572i | \(0.422587\pi\) | |||||||
\(798\) | 7.85410 | 0.278032 | ||||||||
\(799\) | 11.7082 | 0.414206 | ||||||||
\(800\) | −87.8115 | −3.10461 | ||||||||
\(801\) | 9.85410 | 0.348178 | ||||||||
\(802\) | 84.8673 | 2.99677 | ||||||||
\(803\) | −37.1803 | −1.31207 | ||||||||
\(804\) | 52.6869 | 1.85812 | ||||||||
\(805\) | 3.61803 | 0.127519 | ||||||||
\(806\) | −99.5755 | −3.50740 | ||||||||
\(807\) | 19.2705 | 0.678354 | ||||||||
\(808\) | −36.2705 | −1.27599 | ||||||||
\(809\) | 30.0344 | 1.05595 | 0.527977 | − | 0.849258i | \(-0.322951\pi\) | ||||
0.527977 | + | 0.849258i | \(0.322951\pi\) | |||||||
\(810\) | 9.47214 | 0.332817 | ||||||||
\(811\) | −19.4721 | −0.683759 | −0.341880 | − | 0.939744i | \(-0.611064\pi\) | ||||
−0.341880 | + | 0.939744i | \(0.611064\pi\) | |||||||
\(812\) | 7.14590 | 0.250772 | ||||||||
\(813\) | −21.8328 | −0.765710 | ||||||||
\(814\) | 67.9230 | 2.38070 | ||||||||
\(815\) | 78.8673 | 2.76260 | ||||||||
\(816\) | −9.85410 | −0.344963 | ||||||||
\(817\) | 9.27051 | 0.324334 | ||||||||
\(818\) | 11.5623 | 0.404267 | ||||||||
\(819\) | −4.61803 | −0.161367 | ||||||||
\(820\) | −152.936 | −5.34076 | ||||||||
\(821\) | −2.18034 | −0.0760944 | −0.0380472 | − | 0.999276i | \(-0.512114\pi\) | ||||
−0.0380472 | + | 0.999276i | \(0.512114\pi\) | |||||||
\(822\) | 34.5066 | 1.20356 | ||||||||
\(823\) | −40.5623 | −1.41391 | −0.706957 | − | 0.707257i | \(-0.749932\pi\) | ||||
−0.706957 | + | 0.707257i | \(0.749932\pi\) | |||||||
\(824\) | −96.7214 | −3.36945 | ||||||||
\(825\) | 28.0902 | 0.977974 | ||||||||
\(826\) | 33.6525 | 1.17092 | ||||||||
\(827\) | −13.4377 | −0.467274 | −0.233637 | − | 0.972324i | \(-0.575063\pi\) | ||||
−0.233637 | + | 0.972324i | \(0.575063\pi\) | |||||||
\(828\) | −4.85410 | −0.168692 | ||||||||
\(829\) | −47.9443 | −1.66517 | −0.832587 | − | 0.553895i | \(-0.813141\pi\) | ||||
−0.832587 | + | 0.553895i | \(0.813141\pi\) | |||||||
\(830\) | −28.4164 | −0.986348 | ||||||||
\(831\) | −25.8541 | −0.896869 | ||||||||
\(832\) | −40.2148 | −1.39420 | ||||||||
\(833\) | −1.00000 | −0.0346479 | ||||||||
\(834\) | 1.76393 | 0.0610800 | ||||||||
\(835\) | −84.9230 | −2.93888 | ||||||||
\(836\) | −50.5623 | −1.74873 | ||||||||
\(837\) | −8.23607 | −0.284680 | ||||||||
\(838\) | 47.8328 | 1.65236 | ||||||||
\(839\) | −21.8541 | −0.754487 | −0.377244 | − | 0.926114i | \(-0.623128\pi\) | ||||
−0.377244 | + | 0.926114i | \(0.623128\pi\) | |||||||
\(840\) | 27.0344 | 0.932777 | ||||||||
\(841\) | −26.8328 | −0.925270 | ||||||||
\(842\) | 35.0344 | 1.20737 | ||||||||
\(843\) | 14.2918 | 0.492236 | ||||||||
\(844\) | −2.02129 | −0.0695755 | ||||||||
\(845\) | −30.1246 | −1.03632 | ||||||||
\(846\) | 30.6525 | 1.05385 | ||||||||
\(847\) | 1.05573 | 0.0362752 | ||||||||
\(848\) | −55.3607 | −1.90109 | ||||||||
\(849\) | −15.9098 | −0.546024 | ||||||||
\(850\) | 21.1803 | 0.726480 | ||||||||
\(851\) | 7.47214 | 0.256142 | ||||||||
\(852\) | −73.2492 | −2.50948 | ||||||||
\(853\) | 42.6525 | 1.46039 | 0.730196 | − | 0.683237i | \(-0.239429\pi\) | ||||
0.730196 | + | 0.683237i | \(0.239429\pi\) | |||||||
\(854\) | 28.2705 | 0.967397 | ||||||||
\(855\) | 10.8541 | 0.371202 | ||||||||
\(856\) | 95.6312 | 3.26861 | ||||||||
\(857\) | −13.1246 | −0.448328 | −0.224164 | − | 0.974551i | \(-0.571965\pi\) | ||||
−0.224164 | + | 0.974551i | \(0.571965\pi\) | |||||||
\(858\) | 41.9787 | 1.43313 | ||||||||
\(859\) | −36.8328 | −1.25672 | −0.628360 | − | 0.777923i | \(-0.716273\pi\) | ||||
−0.628360 | + | 0.777923i | \(0.716273\pi\) | |||||||
\(860\) | 54.2705 | 1.85061 | ||||||||
\(861\) | 8.70820 | 0.296775 | ||||||||
\(862\) | −97.2837 | −3.31349 | ||||||||
\(863\) | −8.18034 | −0.278462 | −0.139231 | − | 0.990260i | \(-0.544463\pi\) | ||||
−0.139231 | + | 0.990260i | \(0.544463\pi\) | |||||||
\(864\) | −10.8541 | −0.369264 | ||||||||
\(865\) | −47.6869 | −1.62140 | ||||||||
\(866\) | −21.4164 | −0.727759 | ||||||||
\(867\) | −16.0000 | −0.543388 | ||||||||
\(868\) | −39.9787 | −1.35697 | ||||||||
\(869\) | 32.8885 | 1.11567 | ||||||||
\(870\) | 13.9443 | 0.472755 | ||||||||
\(871\) | −50.1246 | −1.69841 | ||||||||
\(872\) | −69.6869 | −2.35990 | ||||||||
\(873\) | 5.00000 | 0.169224 | ||||||||
\(874\) | −7.85410 | −0.265669 | ||||||||
\(875\) | −11.1803 | −0.377964 | ||||||||
\(876\) | −51.9787 | −1.75620 | ||||||||
\(877\) | 11.4164 | 0.385505 | 0.192752 | − | 0.981247i | \(-0.438259\pi\) | ||||
0.192752 | + | 0.981247i | \(0.438259\pi\) | |||||||
\(878\) | −50.2148 | −1.69467 | ||||||||
\(879\) | −23.4164 | −0.789816 | ||||||||
\(880\) | −123.790 | −4.17297 | ||||||||
\(881\) | 37.4853 | 1.26291 | 0.631456 | − | 0.775412i | \(-0.282458\pi\) | ||||
0.631456 | + | 0.775412i | \(0.282458\pi\) | |||||||
\(882\) | −2.61803 | −0.0881538 | ||||||||
\(883\) | −30.5066 | −1.02663 | −0.513314 | − | 0.858201i | \(-0.671582\pi\) | ||||
−0.513314 | + | 0.858201i | \(0.671582\pi\) | |||||||
\(884\) | 22.4164 | 0.753945 | ||||||||
\(885\) | 46.5066 | 1.56330 | ||||||||
\(886\) | −82.2492 | −2.76322 | ||||||||
\(887\) | 43.8541 | 1.47248 | 0.736238 | − | 0.676722i | \(-0.236600\pi\) | ||||
0.736238 | + | 0.676722i | \(0.236600\pi\) | |||||||
\(888\) | 55.8328 | 1.87363 | ||||||||
\(889\) | 12.1459 | 0.407360 | ||||||||
\(890\) | 93.3394 | 3.12874 | ||||||||
\(891\) | 3.47214 | 0.116321 | ||||||||
\(892\) | −22.6869 | −0.759614 | ||||||||
\(893\) | 35.1246 | 1.17540 | ||||||||
\(894\) | −16.1803 | −0.541152 | ||||||||
\(895\) | −4.14590 | −0.138582 | ||||||||
\(896\) | −1.09017 | −0.0364200 | ||||||||
\(897\) | 4.61803 | 0.154192 | ||||||||
\(898\) | 3.94427 | 0.131622 | ||||||||
\(899\) | −12.1246 | −0.404378 | ||||||||
\(900\) | 39.2705 | 1.30902 | ||||||||
\(901\) | 5.61803 | 0.187164 | ||||||||
\(902\) | −79.1591 | −2.63571 | ||||||||
\(903\) | −3.09017 | −0.102834 | ||||||||
\(904\) | 69.6869 | 2.31775 | ||||||||
\(905\) | 5.32624 | 0.177050 | ||||||||
\(906\) | −13.7082 | −0.455425 | ||||||||
\(907\) | 53.0344 | 1.76098 | 0.880490 | − | 0.474065i | \(-0.157214\pi\) | ||||
0.880490 | + | 0.474065i | \(0.157214\pi\) | |||||||
\(908\) | 76.6869 | 2.54494 | ||||||||
\(909\) | 4.85410 | 0.161000 | ||||||||
\(910\) | −43.7426 | −1.45005 | ||||||||
\(911\) | −13.8197 | −0.457866 | −0.228933 | − | 0.973442i | \(-0.573524\pi\) | ||||
−0.228933 | + | 0.973442i | \(0.573524\pi\) | |||||||
\(912\) | −29.5623 | −0.978906 | ||||||||
\(913\) | −10.4164 | −0.344733 | ||||||||
\(914\) | −78.7771 | −2.60571 | ||||||||
\(915\) | 39.0689 | 1.29158 | ||||||||
\(916\) | −6.97871 | −0.230583 | ||||||||
\(917\) | −0.0557281 | −0.00184030 | ||||||||
\(918\) | 2.61803 | 0.0864080 | ||||||||
\(919\) | −43.0689 | −1.42071 | −0.710356 | − | 0.703843i | \(-0.751466\pi\) | ||||
−0.710356 | + | 0.703843i | \(0.751466\pi\) | |||||||
\(920\) | −27.0344 | −0.891299 | ||||||||
\(921\) | −9.29180 | −0.306175 | ||||||||
\(922\) | 4.23607 | 0.139507 | ||||||||
\(923\) | 69.6869 | 2.29377 | ||||||||
\(924\) | 16.8541 | 0.554459 | ||||||||
\(925\) | −60.4508 | −1.98761 | ||||||||
\(926\) | −16.6180 | −0.546102 | ||||||||
\(927\) | 12.9443 | 0.425146 | ||||||||
\(928\) | −15.9787 | −0.524527 | ||||||||
\(929\) | −52.3820 | −1.71860 | −0.859298 | − | 0.511475i | \(-0.829099\pi\) | ||||
−0.859298 | + | 0.511475i | \(0.829099\pi\) | |||||||
\(930\) | −78.0132 | −2.55815 | ||||||||
\(931\) | −3.00000 | −0.0983210 | ||||||||
\(932\) | −69.2705 | −2.26903 | ||||||||
\(933\) | −16.5066 | −0.540401 | ||||||||
\(934\) | 85.8115 | 2.80784 | ||||||||
\(935\) | 12.5623 | 0.410831 | ||||||||
\(936\) | 34.5066 | 1.12788 | ||||||||
\(937\) | 3.87539 | 0.126603 | 0.0633017 | − | 0.997994i | \(-0.479837\pi\) | ||||
0.0633017 | + | 0.997994i | \(0.479837\pi\) | |||||||
\(938\) | −28.4164 | −0.927829 | ||||||||
\(939\) | 6.47214 | 0.211210 | ||||||||
\(940\) | 205.623 | 6.70668 | ||||||||
\(941\) | −26.8328 | −0.874725 | −0.437362 | − | 0.899285i | \(-0.644087\pi\) | ||||
−0.437362 | + | 0.899285i | \(0.644087\pi\) | |||||||
\(942\) | −27.8885 | −0.908658 | ||||||||
\(943\) | −8.70820 | −0.283578 | ||||||||
\(944\) | −126.666 | −4.12262 | ||||||||
\(945\) | −3.61803 | −0.117695 | ||||||||
\(946\) | 28.0902 | 0.913290 | ||||||||
\(947\) | −18.5836 | −0.603886 | −0.301943 | − | 0.953326i | \(-0.597635\pi\) | ||||
−0.301943 | + | 0.953326i | \(0.597635\pi\) | |||||||
\(948\) | 45.9787 | 1.49332 | ||||||||
\(949\) | 49.4508 | 1.60524 | ||||||||
\(950\) | 63.5410 | 2.06154 | ||||||||
\(951\) | −0.201626 | −0.00653818 | ||||||||
\(952\) | 7.47214 | 0.242173 | ||||||||
\(953\) | −0.686918 | −0.0222514 | −0.0111257 | − | 0.999938i | \(-0.503542\pi\) | ||||
−0.0111257 | + | 0.999938i | \(0.503542\pi\) | |||||||
\(954\) | 14.7082 | 0.476196 | ||||||||
\(955\) | −71.3050 | −2.30737 | ||||||||
\(956\) | −54.1033 | −1.74983 | ||||||||
\(957\) | 5.11146 | 0.165230 | ||||||||
\(958\) | −36.0344 | −1.16422 | ||||||||
\(959\) | −13.1803 | −0.425615 | ||||||||
\(960\) | −31.5066 | −1.01687 | ||||||||
\(961\) | 36.8328 | 1.18816 | ||||||||
\(962\) | −90.3394 | −2.91266 | ||||||||
\(963\) | −12.7984 | −0.412422 | ||||||||
\(964\) | 31.1459 | 1.00314 | ||||||||
\(965\) | −29.5967 | −0.952753 | ||||||||
\(966\) | 2.61803 | 0.0842339 | ||||||||
\(967\) | 49.7771 | 1.60072 | 0.800362 | − | 0.599518i | \(-0.204641\pi\) | ||||
0.800362 | + | 0.599518i | \(0.204641\pi\) | |||||||
\(968\) | −7.88854 | −0.253547 | ||||||||
\(969\) | 3.00000 | 0.0963739 | ||||||||
\(970\) | 47.3607 | 1.52066 | ||||||||
\(971\) | −10.9787 | −0.352324 | −0.176162 | − | 0.984361i | \(-0.556368\pi\) | ||||
−0.176162 | + | 0.984361i | \(0.556368\pi\) | |||||||
\(972\) | 4.85410 | 0.155695 | ||||||||
\(973\) | −0.673762 | −0.0215998 | ||||||||
\(974\) | −1.85410 | −0.0594093 | ||||||||
\(975\) | −37.3607 | −1.19650 | ||||||||
\(976\) | −106.408 | −3.40605 | ||||||||
\(977\) | −48.7984 | −1.56120 | −0.780599 | − | 0.625032i | \(-0.785086\pi\) | ||||
−0.780599 | + | 0.625032i | \(0.785086\pi\) | |||||||
\(978\) | 57.0689 | 1.82486 | ||||||||
\(979\) | 34.2148 | 1.09351 | ||||||||
\(980\) | −17.5623 | −0.561007 | ||||||||
\(981\) | 9.32624 | 0.297764 | ||||||||
\(982\) | 81.1033 | 2.58811 | ||||||||
\(983\) | 11.3607 | 0.362349 | 0.181175 | − | 0.983451i | \(-0.442010\pi\) | ||||
0.181175 | + | 0.983451i | \(0.442010\pi\) | |||||||
\(984\) | −65.0689 | −2.07432 | ||||||||
\(985\) | 22.2361 | 0.708500 | ||||||||
\(986\) | 3.85410 | 0.122740 | ||||||||
\(987\) | −11.7082 | −0.372676 | ||||||||
\(988\) | 67.2492 | 2.13948 | ||||||||
\(989\) | 3.09017 | 0.0982617 | ||||||||
\(990\) | 32.8885 | 1.04527 | ||||||||
\(991\) | 2.90983 | 0.0924338 | 0.0462169 | − | 0.998931i | \(-0.485283\pi\) | ||||
0.0462169 | + | 0.998931i | \(0.485283\pi\) | |||||||
\(992\) | 89.3951 | 2.83830 | ||||||||
\(993\) | 1.05573 | 0.0335025 | ||||||||
\(994\) | 39.5066 | 1.25307 | ||||||||
\(995\) | −39.9230 | −1.26564 | ||||||||
\(996\) | −14.5623 | −0.461424 | ||||||||
\(997\) | −5.11146 | −0.161881 | −0.0809407 | − | 0.996719i | \(-0.525792\pi\) | ||||
−0.0809407 | + | 0.996719i | \(0.525792\pi\) | |||||||
\(998\) | −49.8328 | −1.57743 | ||||||||
\(999\) | −7.47214 | −0.236408 |
(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 | 483.2.a.c.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 1449.2.a.k.1.2 | 2 | |||
4.3 | odd | 2 | 7728.2.a.v.1.1 | 2 | |||
7.6 | odd | 2 | 3381.2.a.n.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
483.2.a.c.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
1449.2.a.k.1.2 | 2 | 3.2 | odd | 2 | |||
3381.2.a.n.1.1 | 2 | 7.6 | odd | 2 | |||
7728.2.a.v.1.1 | 2 | 4.3 | odd | 2 |