Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6014,2,Mod(1,6014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6014, 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("6014.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6014 = 2 \cdot 31 \cdot 97 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6014.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: | \(48.0220317756\) |
Analytic rank: | \(0\) |
Dimension: | \(37\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 6014.1 |
$q$-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 | ||||||||
\(3\) | −2.26430 | −1.30729 | −0.653646 | − | 0.756800i | \(-0.726762\pi\) | ||||
−0.653646 | + | 0.756800i | \(0.726762\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.734715 | −0.328574 | −0.164287 | − | 0.986413i | \(-0.552532\pi\) | ||||
−0.164287 | + | 0.986413i | \(0.552532\pi\) | |||||||
\(6\) | −2.26430 | −0.924396 | ||||||||
\(7\) | 2.48512 | 0.939286 | 0.469643 | − | 0.882856i | \(-0.344383\pi\) | ||||
0.469643 | + | 0.882856i | \(0.344383\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 2.12704 | 0.709015 | ||||||||
\(10\) | −0.734715 | −0.232337 | ||||||||
\(11\) | −1.69143 | −0.509985 | −0.254993 | − | 0.966943i | \(-0.582073\pi\) | ||||
−0.254993 | + | 0.966943i | \(0.582073\pi\) | |||||||
\(12\) | −2.26430 | −0.653646 | ||||||||
\(13\) | −0.551010 | −0.152823 | −0.0764114 | − | 0.997076i | \(-0.524346\pi\) | ||||
−0.0764114 | + | 0.997076i | \(0.524346\pi\) | |||||||
\(14\) | 2.48512 | 0.664176 | ||||||||
\(15\) | 1.66361 | 0.429543 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.06462 | 0.500744 | 0.250372 | − | 0.968150i | \(-0.419447\pi\) | ||||
0.250372 | + | 0.968150i | \(0.419447\pi\) | |||||||
\(18\) | 2.12704 | 0.501349 | ||||||||
\(19\) | −3.61939 | −0.830344 | −0.415172 | − | 0.909743i | \(-0.636279\pi\) | ||||
−0.415172 | + | 0.909743i | \(0.636279\pi\) | |||||||
\(20\) | −0.734715 | −0.164287 | ||||||||
\(21\) | −5.62705 | −1.22792 | ||||||||
\(22\) | −1.69143 | −0.360614 | ||||||||
\(23\) | −2.35182 | −0.490387 | −0.245194 | − | 0.969474i | \(-0.578852\pi\) | ||||
−0.245194 | + | 0.969474i | \(0.578852\pi\) | |||||||
\(24\) | −2.26430 | −0.462198 | ||||||||
\(25\) | −4.46019 | −0.892039 | ||||||||
\(26\) | −0.551010 | −0.108062 | ||||||||
\(27\) | 1.97663 | 0.380403 | ||||||||
\(28\) | 2.48512 | 0.469643 | ||||||||
\(29\) | 1.50891 | 0.280197 | 0.140099 | − | 0.990138i | \(-0.455258\pi\) | ||||
0.140099 | + | 0.990138i | \(0.455258\pi\) | |||||||
\(30\) | 1.66361 | 0.303733 | ||||||||
\(31\) | 1.00000 | 0.179605 | ||||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 3.82990 | 0.666700 | ||||||||
\(34\) | 2.06462 | 0.354080 | ||||||||
\(35\) | −1.82585 | −0.308625 | ||||||||
\(36\) | 2.12704 | 0.354507 | ||||||||
\(37\) | 3.67685 | 0.604470 | 0.302235 | − | 0.953233i | \(-0.402267\pi\) | ||||
0.302235 | + | 0.953233i | \(0.402267\pi\) | |||||||
\(38\) | −3.61939 | −0.587142 | ||||||||
\(39\) | 1.24765 | 0.199784 | ||||||||
\(40\) | −0.734715 | −0.116169 | ||||||||
\(41\) | 8.01876 | 1.25232 | 0.626160 | − | 0.779695i | \(-0.284626\pi\) | ||||
0.626160 | + | 0.779695i | \(0.284626\pi\) | |||||||
\(42\) | −5.62705 | −0.868272 | ||||||||
\(43\) | 9.97495 | 1.52117 | 0.760583 | − | 0.649241i | \(-0.224913\pi\) | ||||
0.760583 | + | 0.649241i | \(0.224913\pi\) | |||||||
\(44\) | −1.69143 | −0.254993 | ||||||||
\(45\) | −1.56277 | −0.232964 | ||||||||
\(46\) | −2.35182 | −0.346756 | ||||||||
\(47\) | −5.71342 | −0.833388 | −0.416694 | − | 0.909047i | \(-0.636811\pi\) | ||||
−0.416694 | + | 0.909047i | \(0.636811\pi\) | |||||||
\(48\) | −2.26430 | −0.326823 | ||||||||
\(49\) | −0.824189 | −0.117741 | ||||||||
\(50\) | −4.46019 | −0.630767 | ||||||||
\(51\) | −4.67492 | −0.654620 | ||||||||
\(52\) | −0.551010 | −0.0764114 | ||||||||
\(53\) | −6.88641 | −0.945921 | −0.472961 | − | 0.881084i | \(-0.656815\pi\) | ||||
−0.472961 | + | 0.881084i | \(0.656815\pi\) | |||||||
\(54\) | 1.97663 | 0.268986 | ||||||||
\(55\) | 1.24272 | 0.167568 | ||||||||
\(56\) | 2.48512 | 0.332088 | ||||||||
\(57\) | 8.19537 | 1.08550 | ||||||||
\(58\) | 1.50891 | 0.198129 | ||||||||
\(59\) | 12.3451 | 1.60720 | 0.803598 | − | 0.595173i | \(-0.202916\pi\) | ||||
0.803598 | + | 0.595173i | \(0.202916\pi\) | |||||||
\(60\) | 1.66361 | 0.214771 | ||||||||
\(61\) | −2.17917 | −0.279015 | −0.139507 | − | 0.990221i | \(-0.544552\pi\) | ||||
−0.139507 | + | 0.990221i | \(0.544552\pi\) | |||||||
\(62\) | 1.00000 | 0.127000 | ||||||||
\(63\) | 5.28596 | 0.665968 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.404835 | 0.0502136 | ||||||||
\(66\) | 3.82990 | 0.471428 | ||||||||
\(67\) | 11.2992 | 1.38042 | 0.690208 | − | 0.723611i | \(-0.257519\pi\) | ||||
0.690208 | + | 0.723611i | \(0.257519\pi\) | |||||||
\(68\) | 2.06462 | 0.250372 | ||||||||
\(69\) | 5.32521 | 0.641080 | ||||||||
\(70\) | −1.82585 | −0.218231 | ||||||||
\(71\) | −10.1686 | −1.20679 | −0.603397 | − | 0.797441i | \(-0.706186\pi\) | ||||
−0.603397 | + | 0.797441i | \(0.706186\pi\) | |||||||
\(72\) | 2.12704 | 0.250675 | ||||||||
\(73\) | 7.22772 | 0.845941 | 0.422970 | − | 0.906143i | \(-0.360987\pi\) | ||||
0.422970 | + | 0.906143i | \(0.360987\pi\) | |||||||
\(74\) | 3.67685 | 0.427425 | ||||||||
\(75\) | 10.0992 | 1.16616 | ||||||||
\(76\) | −3.61939 | −0.415172 | ||||||||
\(77\) | −4.20340 | −0.479022 | ||||||||
\(78\) | 1.24765 | 0.141269 | ||||||||
\(79\) | −1.00514 | −0.113088 | −0.0565438 | − | 0.998400i | \(-0.518008\pi\) | ||||
−0.0565438 | + | 0.998400i | \(0.518008\pi\) | |||||||
\(80\) | −0.734715 | −0.0821436 | ||||||||
\(81\) | −10.8568 | −1.20631 | ||||||||
\(82\) | 8.01876 | 0.885523 | ||||||||
\(83\) | −7.93622 | −0.871113 | −0.435557 | − | 0.900161i | \(-0.643448\pi\) | ||||
−0.435557 | + | 0.900161i | \(0.643448\pi\) | |||||||
\(84\) | −5.62705 | −0.613961 | ||||||||
\(85\) | −1.51691 | −0.164532 | ||||||||
\(86\) | 9.97495 | 1.07563 | ||||||||
\(87\) | −3.41662 | −0.366300 | ||||||||
\(88\) | −1.69143 | −0.180307 | ||||||||
\(89\) | −15.9659 | −1.69238 | −0.846191 | − | 0.532879i | \(-0.821110\pi\) | ||||
−0.846191 | + | 0.532879i | \(0.821110\pi\) | |||||||
\(90\) | −1.56277 | −0.164730 | ||||||||
\(91\) | −1.36933 | −0.143544 | ||||||||
\(92\) | −2.35182 | −0.245194 | ||||||||
\(93\) | −2.26430 | −0.234797 | ||||||||
\(94\) | −5.71342 | −0.589294 | ||||||||
\(95\) | 2.65922 | 0.272830 | ||||||||
\(96\) | −2.26430 | −0.231099 | ||||||||
\(97\) | 1.00000 | 0.101535 | ||||||||
\(98\) | −0.824189 | −0.0832557 | ||||||||
\(99\) | −3.59775 | −0.361587 | ||||||||
\(100\) | −4.46019 | −0.446019 | ||||||||
\(101\) | −4.25993 | −0.423879 | −0.211940 | − | 0.977283i | \(-0.567978\pi\) | ||||
−0.211940 | + | 0.977283i | \(0.567978\pi\) | |||||||
\(102\) | −4.67492 | −0.462886 | ||||||||
\(103\) | 16.2402 | 1.60019 | 0.800095 | − | 0.599873i | \(-0.204782\pi\) | ||||
0.800095 | + | 0.599873i | \(0.204782\pi\) | |||||||
\(104\) | −0.551010 | −0.0540310 | ||||||||
\(105\) | 4.13427 | 0.403464 | ||||||||
\(106\) | −6.88641 | −0.668867 | ||||||||
\(107\) | −5.63670 | −0.544921 | −0.272460 | − | 0.962167i | \(-0.587837\pi\) | ||||
−0.272460 | + | 0.962167i | \(0.587837\pi\) | |||||||
\(108\) | 1.97663 | 0.190202 | ||||||||
\(109\) | 16.1521 | 1.54710 | 0.773548 | − | 0.633738i | \(-0.218480\pi\) | ||||
0.773548 | + | 0.633738i | \(0.218480\pi\) | |||||||
\(110\) | 1.24272 | 0.118489 | ||||||||
\(111\) | −8.32548 | −0.790219 | ||||||||
\(112\) | 2.48512 | 0.234822 | ||||||||
\(113\) | 13.5424 | 1.27396 | 0.636979 | − | 0.770881i | \(-0.280184\pi\) | ||||
0.636979 | + | 0.770881i | \(0.280184\pi\) | |||||||
\(114\) | 8.19537 | 0.767567 | ||||||||
\(115\) | 1.72791 | 0.161129 | ||||||||
\(116\) | 1.50891 | 0.140099 | ||||||||
\(117\) | −1.17202 | −0.108354 | ||||||||
\(118\) | 12.3451 | 1.13646 | ||||||||
\(119\) | 5.13083 | 0.470342 | ||||||||
\(120\) | 1.66361 | 0.151866 | ||||||||
\(121\) | −8.13907 | −0.739915 | ||||||||
\(122\) | −2.17917 | −0.197293 | ||||||||
\(123\) | −18.1569 | −1.63715 | ||||||||
\(124\) | 1.00000 | 0.0898027 | ||||||||
\(125\) | 6.95054 | 0.621675 | ||||||||
\(126\) | 5.28596 | 0.470910 | ||||||||
\(127\) | −8.01759 | −0.711446 | −0.355723 | − | 0.934591i | \(-0.615765\pi\) | ||||
−0.355723 | + | 0.934591i | \(0.615765\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −22.5863 | −1.98861 | ||||||||
\(130\) | 0.404835 | 0.0355064 | ||||||||
\(131\) | 12.8938 | 1.12654 | 0.563270 | − | 0.826273i | \(-0.309543\pi\) | ||||
0.563270 | + | 0.826273i | \(0.309543\pi\) | |||||||
\(132\) | 3.82990 | 0.333350 | ||||||||
\(133\) | −8.99460 | −0.779931 | ||||||||
\(134\) | 11.2992 | 0.976102 | ||||||||
\(135\) | −1.45226 | −0.124991 | ||||||||
\(136\) | 2.06462 | 0.177040 | ||||||||
\(137\) | 5.41363 | 0.462518 | 0.231259 | − | 0.972892i | \(-0.425716\pi\) | ||||
0.231259 | + | 0.972892i | \(0.425716\pi\) | |||||||
\(138\) | 5.32521 | 0.453312 | ||||||||
\(139\) | −8.79368 | −0.745870 | −0.372935 | − | 0.927857i | \(-0.621649\pi\) | ||||
−0.372935 | + | 0.927857i | \(0.621649\pi\) | |||||||
\(140\) | −1.82585 | −0.154313 | ||||||||
\(141\) | 12.9369 | 1.08948 | ||||||||
\(142\) | −10.1686 | −0.853332 | ||||||||
\(143\) | 0.931995 | 0.0779374 | ||||||||
\(144\) | 2.12704 | 0.177254 | ||||||||
\(145\) | −1.10862 | −0.0920657 | ||||||||
\(146\) | 7.22772 | 0.598171 | ||||||||
\(147\) | 1.86621 | 0.153922 | ||||||||
\(148\) | 3.67685 | 0.302235 | ||||||||
\(149\) | 12.9405 | 1.06013 | 0.530063 | − | 0.847959i | \(-0.322168\pi\) | ||||
0.530063 | + | 0.847959i | \(0.322168\pi\) | |||||||
\(150\) | 10.0992 | 0.824597 | ||||||||
\(151\) | 5.39464 | 0.439010 | 0.219505 | − | 0.975611i | \(-0.429556\pi\) | ||||
0.219505 | + | 0.975611i | \(0.429556\pi\) | |||||||
\(152\) | −3.61939 | −0.293571 | ||||||||
\(153\) | 4.39154 | 0.355035 | ||||||||
\(154\) | −4.20340 | −0.338720 | ||||||||
\(155\) | −0.734715 | −0.0590137 | ||||||||
\(156\) | 1.24765 | 0.0998921 | ||||||||
\(157\) | −13.0968 | −1.04524 | −0.522620 | − | 0.852566i | \(-0.675045\pi\) | ||||
−0.522620 | + | 0.852566i | \(0.675045\pi\) | |||||||
\(158\) | −1.00514 | −0.0799650 | ||||||||
\(159\) | 15.5929 | 1.23660 | ||||||||
\(160\) | −0.734715 | −0.0580843 | ||||||||
\(161\) | −5.84454 | −0.460614 | ||||||||
\(162\) | −10.8568 | −0.852992 | ||||||||
\(163\) | 17.8728 | 1.39991 | 0.699954 | − | 0.714188i | \(-0.253204\pi\) | ||||
0.699954 | + | 0.714188i | \(0.253204\pi\) | |||||||
\(164\) | 8.01876 | 0.626160 | ||||||||
\(165\) | −2.81388 | −0.219061 | ||||||||
\(166\) | −7.93622 | −0.615970 | ||||||||
\(167\) | 4.33885 | 0.335750 | 0.167875 | − | 0.985808i | \(-0.446309\pi\) | ||||
0.167875 | + | 0.985808i | \(0.446309\pi\) | |||||||
\(168\) | −5.62705 | −0.434136 | ||||||||
\(169\) | −12.6964 | −0.976645 | ||||||||
\(170\) | −1.51691 | −0.116342 | ||||||||
\(171\) | −7.69859 | −0.588726 | ||||||||
\(172\) | 9.97495 | 0.760583 | ||||||||
\(173\) | 8.05772 | 0.612617 | 0.306309 | − | 0.951932i | \(-0.400906\pi\) | ||||
0.306309 | + | 0.951932i | \(0.400906\pi\) | |||||||
\(174\) | −3.41662 | −0.259013 | ||||||||
\(175\) | −11.0841 | −0.837880 | ||||||||
\(176\) | −1.69143 | −0.127496 | ||||||||
\(177\) | −27.9530 | −2.10108 | ||||||||
\(178\) | −15.9659 | −1.19670 | ||||||||
\(179\) | −13.7709 | −1.02929 | −0.514643 | − | 0.857405i | \(-0.672075\pi\) | ||||
−0.514643 | + | 0.857405i | \(0.672075\pi\) | |||||||
\(180\) | −1.56277 | −0.116482 | ||||||||
\(181\) | 14.8883 | 1.10664 | 0.553321 | − | 0.832968i | \(-0.313360\pi\) | ||||
0.553321 | + | 0.832968i | \(0.313360\pi\) | |||||||
\(182\) | −1.36933 | −0.101501 | ||||||||
\(183\) | 4.93430 | 0.364754 | ||||||||
\(184\) | −2.35182 | −0.173378 | ||||||||
\(185\) | −2.70143 | −0.198613 | ||||||||
\(186\) | −2.26430 | −0.166026 | ||||||||
\(187\) | −3.49216 | −0.255372 | ||||||||
\(188\) | −5.71342 | −0.416694 | ||||||||
\(189\) | 4.91216 | 0.357307 | ||||||||
\(190\) | 2.65922 | 0.192920 | ||||||||
\(191\) | 18.0903 | 1.30897 | 0.654483 | − | 0.756077i | \(-0.272886\pi\) | ||||
0.654483 | + | 0.756077i | \(0.272886\pi\) | |||||||
\(192\) | −2.26430 | −0.163412 | ||||||||
\(193\) | −3.00761 | −0.216493 | −0.108246 | − | 0.994124i | \(-0.534524\pi\) | ||||
−0.108246 | + | 0.994124i | \(0.534524\pi\) | |||||||
\(194\) | 1.00000 | 0.0717958 | ||||||||
\(195\) | −0.916668 | −0.0656439 | ||||||||
\(196\) | −0.824189 | −0.0588707 | ||||||||
\(197\) | 14.9505 | 1.06518 | 0.532589 | − | 0.846374i | \(-0.321219\pi\) | ||||
0.532589 | + | 0.846374i | \(0.321219\pi\) | |||||||
\(198\) | −3.59775 | −0.255681 | ||||||||
\(199\) | 14.2779 | 1.01213 | 0.506066 | − | 0.862495i | \(-0.331099\pi\) | ||||
0.506066 | + | 0.862495i | \(0.331099\pi\) | |||||||
\(200\) | −4.46019 | −0.315383 | ||||||||
\(201\) | −25.5847 | −1.80461 | ||||||||
\(202\) | −4.25993 | −0.299728 | ||||||||
\(203\) | 3.74982 | 0.263186 | ||||||||
\(204\) | −4.67492 | −0.327310 | ||||||||
\(205\) | −5.89150 | −0.411480 | ||||||||
\(206\) | 16.2402 | 1.13151 | ||||||||
\(207\) | −5.00241 | −0.347692 | ||||||||
\(208\) | −0.551010 | −0.0382057 | ||||||||
\(209\) | 6.12194 | 0.423463 | ||||||||
\(210\) | 4.13427 | 0.285292 | ||||||||
\(211\) | 14.1715 | 0.975607 | 0.487803 | − | 0.872954i | \(-0.337798\pi\) | ||||
0.487803 | + | 0.872954i | \(0.337798\pi\) | |||||||
\(212\) | −6.88641 | −0.472961 | ||||||||
\(213\) | 23.0248 | 1.57763 | ||||||||
\(214\) | −5.63670 | −0.385317 | ||||||||
\(215\) | −7.32874 | −0.499816 | ||||||||
\(216\) | 1.97663 | 0.134493 | ||||||||
\(217\) | 2.48512 | 0.168701 | ||||||||
\(218\) | 16.1521 | 1.09396 | ||||||||
\(219\) | −16.3657 | −1.10589 | ||||||||
\(220\) | 1.24272 | 0.0837840 | ||||||||
\(221\) | −1.13763 | −0.0765252 | ||||||||
\(222\) | −8.32548 | −0.558769 | ||||||||
\(223\) | 13.0320 | 0.872688 | 0.436344 | − | 0.899780i | \(-0.356273\pi\) | ||||
0.436344 | + | 0.899780i | \(0.356273\pi\) | |||||||
\(224\) | 2.48512 | 0.166044 | ||||||||
\(225\) | −9.48703 | −0.632469 | ||||||||
\(226\) | 13.5424 | 0.900824 | ||||||||
\(227\) | 11.7044 | 0.776847 | 0.388423 | − | 0.921481i | \(-0.373020\pi\) | ||||
0.388423 | + | 0.921481i | \(0.373020\pi\) | |||||||
\(228\) | 8.19537 | 0.542752 | ||||||||
\(229\) | −0.805815 | −0.0532497 | −0.0266249 | − | 0.999645i | \(-0.508476\pi\) | ||||
−0.0266249 | + | 0.999645i | \(0.508476\pi\) | |||||||
\(230\) | 1.72791 | 0.113935 | ||||||||
\(231\) | 9.51775 | 0.626222 | ||||||||
\(232\) | 1.50891 | 0.0990647 | ||||||||
\(233\) | 0.944506 | 0.0618766 | 0.0309383 | − | 0.999521i | \(-0.490150\pi\) | ||||
0.0309383 | + | 0.999521i | \(0.490150\pi\) | |||||||
\(234\) | −1.17202 | −0.0766176 | ||||||||
\(235\) | 4.19773 | 0.273830 | ||||||||
\(236\) | 12.3451 | 0.803598 | ||||||||
\(237\) | 2.27595 | 0.147839 | ||||||||
\(238\) | 5.13083 | 0.332582 | ||||||||
\(239\) | 8.91165 | 0.576447 | 0.288223 | − | 0.957563i | \(-0.406935\pi\) | ||||
0.288223 | + | 0.957563i | \(0.406935\pi\) | |||||||
\(240\) | 1.66361 | 0.107386 | ||||||||
\(241\) | −14.8210 | −0.954703 | −0.477351 | − | 0.878712i | \(-0.658403\pi\) | ||||
−0.477351 | + | 0.878712i | \(0.658403\pi\) | |||||||
\(242\) | −8.13907 | −0.523199 | ||||||||
\(243\) | 18.6532 | 1.19660 | ||||||||
\(244\) | −2.17917 | −0.139507 | ||||||||
\(245\) | 0.605544 | 0.0386868 | ||||||||
\(246\) | −18.1569 | −1.15764 | ||||||||
\(247\) | 1.99432 | 0.126896 | ||||||||
\(248\) | 1.00000 | 0.0635001 | ||||||||
\(249\) | 17.9700 | 1.13880 | ||||||||
\(250\) | 6.95054 | 0.439591 | ||||||||
\(251\) | −14.0381 | −0.886078 | −0.443039 | − | 0.896502i | \(-0.646100\pi\) | ||||
−0.443039 | + | 0.896502i | \(0.646100\pi\) | |||||||
\(252\) | 5.28596 | 0.332984 | ||||||||
\(253\) | 3.97793 | 0.250090 | ||||||||
\(254\) | −8.01759 | −0.503069 | ||||||||
\(255\) | 3.43473 | 0.215091 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 25.9997 | 1.62182 | 0.810909 | − | 0.585173i | \(-0.198973\pi\) | ||||
0.810909 | + | 0.585173i | \(0.198973\pi\) | |||||||
\(258\) | −22.5863 | −1.40616 | ||||||||
\(259\) | 9.13740 | 0.567770 | ||||||||
\(260\) | 0.404835 | 0.0251068 | ||||||||
\(261\) | 3.20952 | 0.198664 | ||||||||
\(262\) | 12.8938 | 0.796584 | ||||||||
\(263\) | 4.08567 | 0.251933 | 0.125967 | − | 0.992034i | \(-0.459797\pi\) | ||||
0.125967 | + | 0.992034i | \(0.459797\pi\) | |||||||
\(264\) | 3.82990 | 0.235714 | ||||||||
\(265\) | 5.05955 | 0.310805 | ||||||||
\(266\) | −8.99460 | −0.551494 | ||||||||
\(267\) | 36.1516 | 2.21244 | ||||||||
\(268\) | 11.2992 | 0.690208 | ||||||||
\(269\) | 23.1887 | 1.41384 | 0.706921 | − | 0.707292i | \(-0.250083\pi\) | ||||
0.706921 | + | 0.707292i | \(0.250083\pi\) | |||||||
\(270\) | −1.45226 | −0.0883818 | ||||||||
\(271\) | 16.9915 | 1.03216 | 0.516079 | − | 0.856541i | \(-0.327391\pi\) | ||||
0.516079 | + | 0.856541i | \(0.327391\pi\) | |||||||
\(272\) | 2.06462 | 0.125186 | ||||||||
\(273\) | 3.10056 | 0.187655 | ||||||||
\(274\) | 5.41363 | 0.327049 | ||||||||
\(275\) | 7.54411 | 0.454927 | ||||||||
\(276\) | 5.32521 | 0.320540 | ||||||||
\(277\) | 31.3698 | 1.88483 | 0.942414 | − | 0.334448i | \(-0.108550\pi\) | ||||
0.942414 | + | 0.334448i | \(0.108550\pi\) | |||||||
\(278\) | −8.79368 | −0.527410 | ||||||||
\(279\) | 2.12704 | 0.127343 | ||||||||
\(280\) | −1.82585 | −0.109116 | ||||||||
\(281\) | −0.0450013 | −0.00268455 | −0.00134228 | − | 0.999999i | \(-0.500427\pi\) | ||||
−0.00134228 | + | 0.999999i | \(0.500427\pi\) | |||||||
\(282\) | 12.9369 | 0.770380 | ||||||||
\(283\) | −8.52415 | −0.506708 | −0.253354 | − | 0.967374i | \(-0.581534\pi\) | ||||
−0.253354 | + | 0.967374i | \(0.581534\pi\) | |||||||
\(284\) | −10.1686 | −0.603397 | ||||||||
\(285\) | −6.02126 | −0.356668 | ||||||||
\(286\) | 0.931995 | 0.0551100 | ||||||||
\(287\) | 19.9276 | 1.17629 | ||||||||
\(288\) | 2.12704 | 0.125337 | ||||||||
\(289\) | −12.7373 | −0.749255 | ||||||||
\(290\) | −1.10862 | −0.0651003 | ||||||||
\(291\) | −2.26430 | −0.132735 | ||||||||
\(292\) | 7.22772 | 0.422970 | ||||||||
\(293\) | 25.6664 | 1.49945 | 0.749723 | − | 0.661751i | \(-0.230187\pi\) | ||||
0.749723 | + | 0.661751i | \(0.230187\pi\) | |||||||
\(294\) | 1.86621 | 0.108840 | ||||||||
\(295\) | −9.07013 | −0.528083 | ||||||||
\(296\) | 3.67685 | 0.213712 | ||||||||
\(297\) | −3.34333 | −0.194000 | ||||||||
\(298\) | 12.9405 | 0.749622 | ||||||||
\(299\) | 1.29587 | 0.0749424 | ||||||||
\(300\) | 10.0992 | 0.583078 | ||||||||
\(301\) | 24.7889 | 1.42881 | ||||||||
\(302\) | 5.39464 | 0.310427 | ||||||||
\(303\) | 9.64576 | 0.554134 | ||||||||
\(304\) | −3.61939 | −0.207586 | ||||||||
\(305\) | 1.60107 | 0.0916770 | ||||||||
\(306\) | 4.39154 | 0.251048 | ||||||||
\(307\) | 30.2135 | 1.72438 | 0.862188 | − | 0.506589i | \(-0.169094\pi\) | ||||
0.862188 | + | 0.506589i | \(0.169094\pi\) | |||||||
\(308\) | −4.20340 | −0.239511 | ||||||||
\(309\) | −36.7726 | −2.09192 | ||||||||
\(310\) | −0.734715 | −0.0417290 | ||||||||
\(311\) | 4.18663 | 0.237402 | 0.118701 | − | 0.992930i | \(-0.462127\pi\) | ||||
0.118701 | + | 0.992930i | \(0.462127\pi\) | |||||||
\(312\) | 1.24765 | 0.0706344 | ||||||||
\(313\) | 16.5081 | 0.933092 | 0.466546 | − | 0.884497i | \(-0.345498\pi\) | ||||
0.466546 | + | 0.884497i | \(0.345498\pi\) | |||||||
\(314\) | −13.0968 | −0.739096 | ||||||||
\(315\) | −3.88367 | −0.218820 | ||||||||
\(316\) | −1.00514 | −0.0565438 | ||||||||
\(317\) | −34.2036 | −1.92107 | −0.960533 | − | 0.278166i | \(-0.910274\pi\) | ||||
−0.960533 | + | 0.278166i | \(0.910274\pi\) | |||||||
\(318\) | 15.5929 | 0.874406 | ||||||||
\(319\) | −2.55221 | −0.142897 | ||||||||
\(320\) | −0.734715 | −0.0410718 | ||||||||
\(321\) | 12.7632 | 0.712371 | ||||||||
\(322\) | −5.84454 | −0.325703 | ||||||||
\(323\) | −7.47267 | −0.415790 | ||||||||
\(324\) | −10.8568 | −0.603156 | ||||||||
\(325\) | 2.45761 | 0.136324 | ||||||||
\(326\) | 17.8728 | 0.989885 | ||||||||
\(327\) | −36.5733 | −2.02251 | ||||||||
\(328\) | 8.01876 | 0.442762 | ||||||||
\(329\) | −14.1985 | −0.782790 | ||||||||
\(330\) | −2.81388 | −0.154899 | ||||||||
\(331\) | 2.68074 | 0.147347 | 0.0736733 | − | 0.997282i | \(-0.476528\pi\) | ||||
0.0736733 | + | 0.997282i | \(0.476528\pi\) | |||||||
\(332\) | −7.93622 | −0.435557 | ||||||||
\(333\) | 7.82081 | 0.428578 | ||||||||
\(334\) | 4.33885 | 0.237411 | ||||||||
\(335\) | −8.30168 | −0.453569 | ||||||||
\(336\) | −5.62705 | −0.306981 | ||||||||
\(337\) | −8.21743 | −0.447632 | −0.223816 | − | 0.974631i | \(-0.571851\pi\) | ||||
−0.223816 | + | 0.974631i | \(0.571851\pi\) | |||||||
\(338\) | −12.6964 | −0.690592 | ||||||||
\(339\) | −30.6639 | −1.66544 | ||||||||
\(340\) | −1.51691 | −0.0822659 | ||||||||
\(341\) | −1.69143 | −0.0915960 | ||||||||
\(342\) | −7.69859 | −0.416292 | ||||||||
\(343\) | −19.4440 | −1.04988 | ||||||||
\(344\) | 9.97495 | 0.537813 | ||||||||
\(345\) | −3.91251 | −0.210642 | ||||||||
\(346\) | 8.05772 | 0.433186 | ||||||||
\(347\) | −15.2480 | −0.818553 | −0.409277 | − | 0.912410i | \(-0.634219\pi\) | ||||
−0.409277 | + | 0.912410i | \(0.634219\pi\) | |||||||
\(348\) | −3.41662 | −0.183150 | ||||||||
\(349\) | 24.0297 | 1.28628 | 0.643141 | − | 0.765748i | \(-0.277631\pi\) | ||||
0.643141 | + | 0.765748i | \(0.277631\pi\) | |||||||
\(350\) | −11.0841 | −0.592471 | ||||||||
\(351\) | −1.08914 | −0.0581343 | ||||||||
\(352\) | −1.69143 | −0.0901535 | ||||||||
\(353\) | −15.7063 | −0.835961 | −0.417980 | − | 0.908456i | \(-0.637262\pi\) | ||||
−0.417980 | + | 0.908456i | \(0.637262\pi\) | |||||||
\(354\) | −27.9530 | −1.48568 | ||||||||
\(355\) | 7.47104 | 0.396521 | ||||||||
\(356\) | −15.9659 | −0.846191 | ||||||||
\(357\) | −11.6177 | −0.614875 | ||||||||
\(358\) | −13.7709 | −0.727815 | ||||||||
\(359\) | 24.8295 | 1.31045 | 0.655225 | − | 0.755434i | \(-0.272574\pi\) | ||||
0.655225 | + | 0.755434i | \(0.272574\pi\) | |||||||
\(360\) | −1.56277 | −0.0823652 | ||||||||
\(361\) | −5.90004 | −0.310529 | ||||||||
\(362\) | 14.8883 | 0.782513 | ||||||||
\(363\) | 18.4293 | 0.967286 | ||||||||
\(364\) | −1.36933 | −0.0717722 | ||||||||
\(365\) | −5.31031 | −0.277954 | ||||||||
\(366\) | 4.93430 | 0.257920 | ||||||||
\(367\) | −23.1779 | −1.20988 | −0.604939 | − | 0.796272i | \(-0.706802\pi\) | ||||
−0.604939 | + | 0.796272i | \(0.706802\pi\) | |||||||
\(368\) | −2.35182 | −0.122597 | ||||||||
\(369\) | 17.0562 | 0.887913 | ||||||||
\(370\) | −2.70143 | −0.140441 | ||||||||
\(371\) | −17.1135 | −0.888491 | ||||||||
\(372\) | −2.26430 | −0.117398 | ||||||||
\(373\) | −10.3221 | −0.534456 | −0.267228 | − | 0.963633i | \(-0.586108\pi\) | ||||
−0.267228 | + | 0.963633i | \(0.586108\pi\) | |||||||
\(374\) | −3.49216 | −0.180575 | ||||||||
\(375\) | −15.7381 | −0.812712 | ||||||||
\(376\) | −5.71342 | −0.294647 | ||||||||
\(377\) | −0.831425 | −0.0428205 | ||||||||
\(378\) | 4.91216 | 0.252654 | ||||||||
\(379\) | 23.0561 | 1.18431 | 0.592155 | − | 0.805824i | \(-0.298277\pi\) | ||||
0.592155 | + | 0.805824i | \(0.298277\pi\) | |||||||
\(380\) | 2.65922 | 0.136415 | ||||||||
\(381\) | 18.1542 | 0.930069 | ||||||||
\(382\) | 18.0903 | 0.925578 | ||||||||
\(383\) | −4.03493 | −0.206175 | −0.103088 | − | 0.994672i | \(-0.532872\pi\) | ||||
−0.103088 | + | 0.994672i | \(0.532872\pi\) | |||||||
\(384\) | −2.26430 | −0.115549 | ||||||||
\(385\) | 3.08830 | 0.157394 | ||||||||
\(386\) | −3.00761 | −0.153084 | ||||||||
\(387\) | 21.2172 | 1.07853 | ||||||||
\(388\) | 1.00000 | 0.0507673 | ||||||||
\(389\) | 3.15696 | 0.160064 | 0.0800321 | − | 0.996792i | \(-0.474498\pi\) | ||||
0.0800321 | + | 0.996792i | \(0.474498\pi\) | |||||||
\(390\) | −0.916668 | −0.0464173 | ||||||||
\(391\) | −4.85561 | −0.245559 | ||||||||
\(392\) | −0.824189 | −0.0416278 | ||||||||
\(393\) | −29.1955 | −1.47272 | ||||||||
\(394\) | 14.9505 | 0.753195 | ||||||||
\(395\) | 0.738495 | 0.0371577 | ||||||||
\(396\) | −3.59775 | −0.180794 | ||||||||
\(397\) | −12.5824 | −0.631491 | −0.315745 | − | 0.948844i | \(-0.602255\pi\) | ||||
−0.315745 | + | 0.948844i | \(0.602255\pi\) | |||||||
\(398\) | 14.2779 | 0.715685 | ||||||||
\(399\) | 20.3665 | 1.01960 | ||||||||
\(400\) | −4.46019 | −0.223010 | ||||||||
\(401\) | −7.57778 | −0.378416 | −0.189208 | − | 0.981937i | \(-0.560592\pi\) | ||||
−0.189208 | + | 0.981937i | \(0.560592\pi\) | |||||||
\(402\) | −25.5847 | −1.27605 | ||||||||
\(403\) | −0.551010 | −0.0274478 | ||||||||
\(404\) | −4.25993 | −0.211940 | ||||||||
\(405\) | 7.97666 | 0.396363 | ||||||||
\(406\) | 3.74982 | 0.186100 | ||||||||
\(407\) | −6.21913 | −0.308271 | ||||||||
\(408\) | −4.67492 | −0.231443 | ||||||||
\(409\) | −8.60124 | −0.425304 | −0.212652 | − | 0.977128i | \(-0.568210\pi\) | ||||
−0.212652 | + | 0.977128i | \(0.568210\pi\) | |||||||
\(410\) | −5.89150 | −0.290960 | ||||||||
\(411\) | −12.2581 | −0.604646 | ||||||||
\(412\) | 16.2402 | 0.800095 | ||||||||
\(413\) | 30.6790 | 1.50962 | ||||||||
\(414\) | −5.00241 | −0.245855 | ||||||||
\(415\) | 5.83086 | 0.286226 | ||||||||
\(416\) | −0.551010 | −0.0270155 | ||||||||
\(417\) | 19.9115 | 0.975071 | ||||||||
\(418\) | 6.12194 | 0.299434 | ||||||||
\(419\) | 33.9778 | 1.65992 | 0.829962 | − | 0.557820i | \(-0.188362\pi\) | ||||
0.829962 | + | 0.557820i | \(0.188362\pi\) | |||||||
\(420\) | 4.13427 | 0.201732 | ||||||||
\(421\) | −11.5606 | −0.563427 | −0.281714 | − | 0.959499i | \(-0.590903\pi\) | ||||
−0.281714 | + | 0.959499i | \(0.590903\pi\) | |||||||
\(422\) | 14.1715 | 0.689858 | ||||||||
\(423\) | −12.1527 | −0.590884 | ||||||||
\(424\) | −6.88641 | −0.334434 | ||||||||
\(425\) | −9.20862 | −0.446684 | ||||||||
\(426\) | 23.0248 | 1.11555 | ||||||||
\(427\) | −5.41550 | −0.262075 | ||||||||
\(428\) | −5.63670 | −0.272460 | ||||||||
\(429\) | −2.11031 | −0.101887 | ||||||||
\(430\) | −7.32874 | −0.353423 | ||||||||
\(431\) | 20.5775 | 0.991181 | 0.495591 | − | 0.868556i | \(-0.334952\pi\) | ||||
0.495591 | + | 0.868556i | \(0.334952\pi\) | |||||||
\(432\) | 1.97663 | 0.0951008 | ||||||||
\(433\) | 21.6847 | 1.04210 | 0.521049 | − | 0.853527i | \(-0.325541\pi\) | ||||
0.521049 | + | 0.853527i | \(0.325541\pi\) | |||||||
\(434\) | 2.48512 | 0.119289 | ||||||||
\(435\) | 2.51024 | 0.120357 | ||||||||
\(436\) | 16.1521 | 0.773548 | ||||||||
\(437\) | 8.51213 | 0.407190 | ||||||||
\(438\) | −16.3657 | −0.781984 | ||||||||
\(439\) | −0.185278 | −0.00884285 | −0.00442142 | − | 0.999990i | \(-0.501407\pi\) | ||||
−0.00442142 | + | 0.999990i | \(0.501407\pi\) | |||||||
\(440\) | 1.24272 | 0.0592443 | ||||||||
\(441\) | −1.75309 | −0.0834803 | ||||||||
\(442\) | −1.13763 | −0.0541115 | ||||||||
\(443\) | 0.880293 | 0.0418240 | 0.0209120 | − | 0.999781i | \(-0.493343\pi\) | ||||
0.0209120 | + | 0.999781i | \(0.493343\pi\) | |||||||
\(444\) | −8.32548 | −0.395110 | ||||||||
\(445\) | 11.7304 | 0.556074 | ||||||||
\(446\) | 13.0320 | 0.617084 | ||||||||
\(447\) | −29.3011 | −1.38589 | ||||||||
\(448\) | 2.48512 | 0.117411 | ||||||||
\(449\) | 29.5313 | 1.39367 | 0.696833 | − | 0.717233i | \(-0.254592\pi\) | ||||
0.696833 | + | 0.717233i | \(0.254592\pi\) | |||||||
\(450\) | −9.48703 | −0.447223 | ||||||||
\(451\) | −13.5632 | −0.638664 | ||||||||
\(452\) | 13.5424 | 0.636979 | ||||||||
\(453\) | −12.2151 | −0.573914 | ||||||||
\(454\) | 11.7044 | 0.549314 | ||||||||
\(455\) | 1.00606 | 0.0471650 | ||||||||
\(456\) | 8.19537 | 0.383783 | ||||||||
\(457\) | −28.1549 | −1.31703 | −0.658514 | − | 0.752568i | \(-0.728815\pi\) | ||||
−0.658514 | + | 0.752568i | \(0.728815\pi\) | |||||||
\(458\) | −0.805815 | −0.0376533 | ||||||||
\(459\) | 4.08100 | 0.190485 | ||||||||
\(460\) | 1.72791 | 0.0805644 | ||||||||
\(461\) | −15.2922 | −0.712230 | −0.356115 | − | 0.934442i | \(-0.615899\pi\) | ||||
−0.356115 | + | 0.934442i | \(0.615899\pi\) | |||||||
\(462\) | 9.51775 | 0.442806 | ||||||||
\(463\) | 8.84392 | 0.411012 | 0.205506 | − | 0.978656i | \(-0.434116\pi\) | ||||
0.205506 | + | 0.978656i | \(0.434116\pi\) | |||||||
\(464\) | 1.50891 | 0.0700493 | ||||||||
\(465\) | 1.66361 | 0.0771482 | ||||||||
\(466\) | 0.944506 | 0.0437534 | ||||||||
\(467\) | −5.75283 | −0.266209 | −0.133105 | − | 0.991102i | \(-0.542495\pi\) | ||||
−0.133105 | + | 0.991102i | \(0.542495\pi\) | |||||||
\(468\) | −1.17202 | −0.0541768 | ||||||||
\(469\) | 28.0798 | 1.29661 | ||||||||
\(470\) | 4.19773 | 0.193627 | ||||||||
\(471\) | 29.6551 | 1.36643 | ||||||||
\(472\) | 12.3451 | 0.568230 | ||||||||
\(473\) | −16.8719 | −0.775772 | ||||||||
\(474\) | 2.27595 | 0.104538 | ||||||||
\(475\) | 16.1432 | 0.740699 | ||||||||
\(476\) | 5.13083 | 0.235171 | ||||||||
\(477\) | −14.6477 | −0.670672 | ||||||||
\(478\) | 8.91165 | 0.407609 | ||||||||
\(479\) | −29.9180 | −1.36699 | −0.683495 | − | 0.729955i | \(-0.739541\pi\) | ||||
−0.683495 | + | 0.729955i | \(0.739541\pi\) | |||||||
\(480\) | 1.66361 | 0.0759332 | ||||||||
\(481\) | −2.02598 | −0.0923768 | ||||||||
\(482\) | −14.8210 | −0.675077 | ||||||||
\(483\) | 13.2338 | 0.602158 | ||||||||
\(484\) | −8.13907 | −0.369958 | ||||||||
\(485\) | −0.734715 | −0.0333617 | ||||||||
\(486\) | 18.6532 | 0.846125 | ||||||||
\(487\) | 9.40494 | 0.426178 | 0.213089 | − | 0.977033i | \(-0.431647\pi\) | ||||
0.213089 | + | 0.977033i | \(0.431647\pi\) | |||||||
\(488\) | −2.17917 | −0.0986465 | ||||||||
\(489\) | −40.4694 | −1.83009 | ||||||||
\(490\) | 0.605544 | 0.0273557 | ||||||||
\(491\) | −38.5146 | −1.73814 | −0.869069 | − | 0.494691i | \(-0.835281\pi\) | ||||
−0.869069 | + | 0.494691i | \(0.835281\pi\) | |||||||
\(492\) | −18.1569 | −0.818574 | ||||||||
\(493\) | 3.11533 | 0.140307 | ||||||||
\(494\) | 1.99432 | 0.0897287 | ||||||||
\(495\) | 2.64332 | 0.118808 | ||||||||
\(496\) | 1.00000 | 0.0449013 | ||||||||
\(497\) | −25.2702 | −1.13352 | ||||||||
\(498\) | 17.9700 | 0.805253 | ||||||||
\(499\) | 29.8674 | 1.33705 | 0.668525 | − | 0.743690i | \(-0.266926\pi\) | ||||
0.668525 | + | 0.743690i | \(0.266926\pi\) | |||||||
\(500\) | 6.95054 | 0.310838 | ||||||||
\(501\) | −9.82445 | −0.438924 | ||||||||
\(502\) | −14.0381 | −0.626552 | ||||||||
\(503\) | −14.5502 | −0.648763 | −0.324382 | − | 0.945926i | \(-0.605156\pi\) | ||||
−0.324382 | + | 0.945926i | \(0.605156\pi\) | |||||||
\(504\) | 5.28596 | 0.235455 | ||||||||
\(505\) | 3.12984 | 0.139276 | ||||||||
\(506\) | 3.97793 | 0.176841 | ||||||||
\(507\) | 28.7484 | 1.27676 | ||||||||
\(508\) | −8.01759 | −0.355723 | ||||||||
\(509\) | 0.623508 | 0.0276365 | 0.0138183 | − | 0.999905i | \(-0.495601\pi\) | ||||
0.0138183 | + | 0.999905i | \(0.495601\pi\) | |||||||
\(510\) | 3.43473 | 0.152092 | ||||||||
\(511\) | 17.9617 | 0.794581 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −7.15420 | −0.315865 | ||||||||
\(514\) | 25.9997 | 1.14680 | ||||||||
\(515\) | −11.9319 | −0.525781 | ||||||||
\(516\) | −22.5863 | −0.994305 | ||||||||
\(517\) | 9.66385 | 0.425016 | ||||||||
\(518\) | 9.13740 | 0.401474 | ||||||||
\(519\) | −18.2451 | −0.800870 | ||||||||
\(520\) | 0.404835 | 0.0177532 | ||||||||
\(521\) | 27.8599 | 1.22056 | 0.610282 | − | 0.792184i | \(-0.291056\pi\) | ||||
0.610282 | + | 0.792184i | \(0.291056\pi\) | |||||||
\(522\) | 3.20952 | 0.140477 | ||||||||
\(523\) | 26.4855 | 1.15813 | 0.579065 | − | 0.815281i | \(-0.303418\pi\) | ||||
0.579065 | + | 0.815281i | \(0.303418\pi\) | |||||||
\(524\) | 12.8938 | 0.563270 | ||||||||
\(525\) | 25.0977 | 1.09535 | ||||||||
\(526\) | 4.08567 | 0.178144 | ||||||||
\(527\) | 2.06462 | 0.0899364 | ||||||||
\(528\) | 3.82990 | 0.166675 | ||||||||
\(529\) | −17.4690 | −0.759520 | ||||||||
\(530\) | 5.05955 | 0.219773 | ||||||||
\(531\) | 26.2586 | 1.13953 | ||||||||
\(532\) | −8.99460 | −0.389965 | ||||||||
\(533\) | −4.41842 | −0.191383 | ||||||||
\(534\) | 36.1516 | 1.56443 | ||||||||
\(535\) | 4.14137 | 0.179047 | ||||||||
\(536\) | 11.2992 | 0.488051 | ||||||||
\(537\) | 31.1814 | 1.34558 | ||||||||
\(538\) | 23.1887 | 0.999738 | ||||||||
\(539\) | 1.39406 | 0.0600463 | ||||||||
\(540\) | −1.45226 | −0.0624953 | ||||||||
\(541\) | −33.9847 | −1.46112 | −0.730558 | − | 0.682851i | \(-0.760740\pi\) | ||||
−0.730558 | + | 0.682851i | \(0.760740\pi\) | |||||||
\(542\) | 16.9915 | 0.729846 | ||||||||
\(543\) | −33.7116 | −1.44670 | ||||||||
\(544\) | 2.06462 | 0.0885199 | ||||||||
\(545\) | −11.8672 | −0.508336 | ||||||||
\(546\) | 3.10056 | 0.132692 | ||||||||
\(547\) | −24.0639 | −1.02890 | −0.514449 | − | 0.857521i | \(-0.672004\pi\) | ||||
−0.514449 | + | 0.857521i | \(0.672004\pi\) | |||||||
\(548\) | 5.41363 | 0.231259 | ||||||||
\(549\) | −4.63520 | −0.197825 | ||||||||
\(550\) | 7.54411 | 0.321682 | ||||||||
\(551\) | −5.46132 | −0.232660 | ||||||||
\(552\) | 5.32521 | 0.226656 | ||||||||
\(553\) | −2.49790 | −0.106222 | ||||||||
\(554\) | 31.3698 | 1.33277 | ||||||||
\(555\) | 6.11685 | 0.259646 | ||||||||
\(556\) | −8.79368 | −0.372935 | ||||||||
\(557\) | −33.3480 | −1.41300 | −0.706501 | − | 0.707712i | \(-0.749727\pi\) | ||||
−0.706501 | + | 0.707712i | \(0.749727\pi\) | |||||||
\(558\) | 2.12704 | 0.0900450 | ||||||||
\(559\) | −5.49630 | −0.232469 | ||||||||
\(560\) | −1.82585 | −0.0771563 | ||||||||
\(561\) | 7.90730 | 0.333846 | ||||||||
\(562\) | −0.0450013 | −0.00189827 | ||||||||
\(563\) | 18.6596 | 0.786408 | 0.393204 | − | 0.919451i | \(-0.371367\pi\) | ||||
0.393204 | + | 0.919451i | \(0.371367\pi\) | |||||||
\(564\) | 12.9369 | 0.544741 | ||||||||
\(565\) | −9.94976 | −0.418590 | ||||||||
\(566\) | −8.52415 | −0.358297 | ||||||||
\(567\) | −26.9805 | −1.13307 | ||||||||
\(568\) | −10.1686 | −0.426666 | ||||||||
\(569\) | 5.48240 | 0.229834 | 0.114917 | − | 0.993375i | \(-0.463340\pi\) | ||||
0.114917 | + | 0.993375i | \(0.463340\pi\) | |||||||
\(570\) | −6.02126 | −0.252203 | ||||||||
\(571\) | 20.4642 | 0.856399 | 0.428200 | − | 0.903684i | \(-0.359148\pi\) | ||||
0.428200 | + | 0.903684i | \(0.359148\pi\) | |||||||
\(572\) | 0.931995 | 0.0389687 | ||||||||
\(573\) | −40.9617 | −1.71120 | ||||||||
\(574\) | 19.9276 | 0.831760 | ||||||||
\(575\) | 10.4896 | 0.437445 | ||||||||
\(576\) | 2.12704 | 0.0886268 | ||||||||
\(577\) | 16.0086 | 0.666445 | 0.333222 | − | 0.942848i | \(-0.391864\pi\) | ||||
0.333222 | + | 0.942848i | \(0.391864\pi\) | |||||||
\(578\) | −12.7373 | −0.529803 | ||||||||
\(579\) | 6.81014 | 0.283020 | ||||||||
\(580\) | −1.10862 | −0.0460328 | ||||||||
\(581\) | −19.7224 | −0.818225 | ||||||||
\(582\) | −2.26430 | −0.0938582 | ||||||||
\(583\) | 11.6479 | 0.482406 | ||||||||
\(584\) | 7.22772 | 0.299085 | ||||||||
\(585\) | 0.861103 | 0.0356022 | ||||||||
\(586\) | 25.6664 | 1.06027 | ||||||||
\(587\) | 9.45334 | 0.390181 | 0.195091 | − | 0.980785i | \(-0.437500\pi\) | ||||
0.195091 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(588\) | 1.86621 | 0.0769612 | ||||||||
\(589\) | −3.61939 | −0.149134 | ||||||||
\(590\) | −9.07013 | −0.373411 | ||||||||
\(591\) | −33.8523 | −1.39250 | ||||||||
\(592\) | 3.67685 | 0.151117 | ||||||||
\(593\) | 22.7369 | 0.933694 | 0.466847 | − | 0.884338i | \(-0.345390\pi\) | ||||
0.466847 | + | 0.884338i | \(0.345390\pi\) | |||||||
\(594\) | −3.34333 | −0.137179 | ||||||||
\(595\) | −3.76970 | −0.154542 | ||||||||
\(596\) | 12.9405 | 0.530063 | ||||||||
\(597\) | −32.3294 | −1.32315 | ||||||||
\(598\) | 1.29587 | 0.0529923 | ||||||||
\(599\) | 7.73999 | 0.316247 | 0.158124 | − | 0.987419i | \(-0.449456\pi\) | ||||
0.158124 | + | 0.987419i | \(0.449456\pi\) | |||||||
\(600\) | 10.0992 | 0.412298 | ||||||||
\(601\) | −24.1112 | −0.983515 | −0.491758 | − | 0.870732i | \(-0.663645\pi\) | ||||
−0.491758 | + | 0.870732i | \(0.663645\pi\) | |||||||
\(602\) | 24.7889 | 1.01032 | ||||||||
\(603\) | 24.0339 | 0.978735 | ||||||||
\(604\) | 5.39464 | 0.219505 | ||||||||
\(605\) | 5.97989 | 0.243117 | ||||||||
\(606\) | 9.64576 | 0.391832 | ||||||||
\(607\) | 38.8537 | 1.57702 | 0.788512 | − | 0.615019i | \(-0.210852\pi\) | ||||
0.788512 | + | 0.615019i | \(0.210852\pi\) | |||||||
\(608\) | −3.61939 | −0.146785 | ||||||||
\(609\) | −8.49070 | −0.344061 | ||||||||
\(610\) | 1.60107 | 0.0648254 | ||||||||
\(611\) | 3.14815 | 0.127361 | ||||||||
\(612\) | 4.39154 | 0.177518 | ||||||||
\(613\) | 0.713440 | 0.0288156 | 0.0144078 | − | 0.999896i | \(-0.495414\pi\) | ||||
0.0144078 | + | 0.999896i | \(0.495414\pi\) | |||||||
\(614\) | 30.2135 | 1.21932 | ||||||||
\(615\) | 13.3401 | 0.537925 | ||||||||
\(616\) | −4.20340 | −0.169360 | ||||||||
\(617\) | −48.1952 | −1.94027 | −0.970133 | − | 0.242572i | \(-0.922009\pi\) | ||||
−0.970133 | + | 0.242572i | \(0.922009\pi\) | |||||||
\(618\) | −36.7726 | −1.47921 | ||||||||
\(619\) | −15.6590 | −0.629388 | −0.314694 | − | 0.949193i | \(-0.601902\pi\) | ||||
−0.314694 | + | 0.949193i | \(0.601902\pi\) | |||||||
\(620\) | −0.734715 | −0.0295068 | ||||||||
\(621\) | −4.64867 | −0.186545 | ||||||||
\(622\) | 4.18663 | 0.167868 | ||||||||
\(623\) | −39.6772 | −1.58963 | ||||||||
\(624\) | 1.24765 | 0.0499460 | ||||||||
\(625\) | 17.1943 | 0.687772 | ||||||||
\(626\) | 16.5081 | 0.659796 | ||||||||
\(627\) | −13.8619 | −0.553590 | ||||||||
\(628\) | −13.0968 | −0.522620 | ||||||||
\(629\) | 7.59130 | 0.302685 | ||||||||
\(630\) | −3.88367 | −0.154729 | ||||||||
\(631\) | −39.7457 | −1.58225 | −0.791125 | − | 0.611654i | \(-0.790505\pi\) | ||||
−0.791125 | + | 0.611654i | \(0.790505\pi\) | |||||||
\(632\) | −1.00514 | −0.0399825 | ||||||||
\(633\) | −32.0885 | −1.27540 | ||||||||
\(634\) | −34.2036 | −1.35840 | ||||||||
\(635\) | 5.89064 | 0.233763 | ||||||||
\(636\) | 15.5929 | 0.618298 | ||||||||
\(637\) | 0.454137 | 0.0179936 | ||||||||
\(638\) | −2.55221 | −0.101043 | ||||||||
\(639\) | −21.6291 | −0.855634 | ||||||||
\(640\) | −0.734715 | −0.0290421 | ||||||||
\(641\) | −10.5816 | −0.417949 | −0.208975 | − | 0.977921i | \(-0.567013\pi\) | ||||
−0.208975 | + | 0.977921i | \(0.567013\pi\) | |||||||
\(642\) | 12.7632 | 0.503722 | ||||||||
\(643\) | 34.9093 | 1.37669 | 0.688344 | − | 0.725384i | \(-0.258338\pi\) | ||||
0.688344 | + | 0.725384i | \(0.258338\pi\) | |||||||
\(644\) | −5.84454 | −0.230307 | ||||||||
\(645\) | 16.5945 | 0.653406 | ||||||||
\(646\) | −7.47267 | −0.294008 | ||||||||
\(647\) | −38.5462 | −1.51541 | −0.757704 | − | 0.652599i | \(-0.773679\pi\) | ||||
−0.757704 | + | 0.652599i | \(0.773679\pi\) | |||||||
\(648\) | −10.8568 | −0.426496 | ||||||||
\(649\) | −20.8809 | −0.819646 | ||||||||
\(650\) | 2.45761 | 0.0963955 | ||||||||
\(651\) | −5.62705 | −0.220541 | ||||||||
\(652\) | 17.8728 | 0.699954 | ||||||||
\(653\) | −39.9980 | −1.56524 | −0.782621 | − | 0.622499i | \(-0.786118\pi\) | ||||
−0.782621 | + | 0.622499i | \(0.786118\pi\) | |||||||
\(654\) | −36.5733 | −1.43013 | ||||||||
\(655\) | −9.47329 | −0.370152 | ||||||||
\(656\) | 8.01876 | 0.313080 | ||||||||
\(657\) | 15.3737 | 0.599785 | ||||||||
\(658\) | −14.1985 | −0.553516 | ||||||||
\(659\) | 47.8018 | 1.86210 | 0.931048 | − | 0.364897i | \(-0.118896\pi\) | ||||
0.931048 | + | 0.364897i | \(0.118896\pi\) | |||||||
\(660\) | −2.81388 | −0.109530 | ||||||||
\(661\) | 18.0889 | 0.703576 | 0.351788 | − | 0.936080i | \(-0.385574\pi\) | ||||
0.351788 | + | 0.936080i | \(0.385574\pi\) | |||||||
\(662\) | 2.68074 | 0.104190 | ||||||||
\(663\) | 2.57593 | 0.100041 | ||||||||
\(664\) | −7.93622 | −0.307985 | ||||||||
\(665\) | 6.60846 | 0.256265 | ||||||||
\(666\) | 7.82081 | 0.303050 | ||||||||
\(667\) | −3.54868 | −0.137405 | ||||||||
\(668\) | 4.33885 | 0.167875 | ||||||||
\(669\) | −29.5084 | −1.14086 | ||||||||
\(670\) | −8.30168 | −0.320722 | ||||||||
\(671\) | 3.68592 | 0.142293 | ||||||||
\(672\) | −5.62705 | −0.217068 | ||||||||
\(673\) | 28.9438 | 1.11570 | 0.557850 | − | 0.829942i | \(-0.311626\pi\) | ||||
0.557850 | + | 0.829942i | \(0.311626\pi\) | |||||||
\(674\) | −8.21743 | −0.316524 | ||||||||
\(675\) | −8.81616 | −0.339334 | ||||||||
\(676\) | −12.6964 | −0.488323 | ||||||||
\(677\) | 13.5748 | 0.521723 | 0.260861 | − | 0.965376i | \(-0.415993\pi\) | ||||
0.260861 | + | 0.965376i | \(0.415993\pi\) | |||||||
\(678\) | −30.6639 | −1.17764 | ||||||||
\(679\) | 2.48512 | 0.0953701 | ||||||||
\(680\) | −1.51691 | −0.0581708 | ||||||||
\(681\) | −26.5022 | −1.01557 | ||||||||
\(682\) | −1.69143 | −0.0647682 | ||||||||
\(683\) | 47.3732 | 1.81269 | 0.906343 | − | 0.422543i | \(-0.138862\pi\) | ||||
0.906343 | + | 0.422543i | \(0.138862\pi\) | |||||||
\(684\) | −7.69859 | −0.294363 | ||||||||
\(685\) | −3.97747 | −0.151971 | ||||||||
\(686\) | −19.4440 | −0.742377 | ||||||||
\(687\) | 1.82460 | 0.0696130 | ||||||||
\(688\) | 9.97495 | 0.380291 | ||||||||
\(689\) | 3.79448 | 0.144558 | ||||||||
\(690\) | −3.91251 | −0.148947 | ||||||||
\(691\) | 39.3747 | 1.49789 | 0.748943 | − | 0.662635i | \(-0.230562\pi\) | ||||
0.748943 | + | 0.662635i | \(0.230562\pi\) | |||||||
\(692\) | 8.05772 | 0.306309 | ||||||||
\(693\) | −8.94082 | −0.339634 | ||||||||
\(694\) | −15.2480 | −0.578805 | ||||||||
\(695\) | 6.46085 | 0.245074 | ||||||||
\(696\) | −3.41662 | −0.129507 | ||||||||
\(697\) | 16.5557 | 0.627092 | ||||||||
\(698\) | 24.0297 | 0.909538 | ||||||||
\(699\) | −2.13864 | −0.0808909 | ||||||||
\(700\) | −11.0841 | −0.418940 | ||||||||
\(701\) | −1.84441 | −0.0696624 | −0.0348312 | − | 0.999393i | \(-0.511089\pi\) | ||||
−0.0348312 | + | 0.999393i | \(0.511089\pi\) | |||||||
\(702\) | −1.08914 | −0.0411071 | ||||||||
\(703\) | −13.3079 | −0.501918 | ||||||||
\(704\) | −1.69143 | −0.0637482 | ||||||||
\(705\) | −9.50492 | −0.357976 | ||||||||
\(706\) | −15.7063 | −0.591114 | ||||||||
\(707\) | −10.5864 | −0.398144 | ||||||||
\(708\) | −27.9530 | −1.05054 | ||||||||
\(709\) | −30.0606 | −1.12895 | −0.564474 | − | 0.825451i | \(-0.690921\pi\) | ||||
−0.564474 | + | 0.825451i | \(0.690921\pi\) | |||||||
\(710\) | 7.47104 | 0.280383 | ||||||||
\(711\) | −2.13799 | −0.0801808 | ||||||||
\(712\) | −15.9659 | −0.598348 | ||||||||
\(713\) | −2.35182 | −0.0880762 | ||||||||
\(714\) | −11.6177 | −0.434782 | ||||||||
\(715\) | −0.684751 | −0.0256082 | ||||||||
\(716\) | −13.7709 | −0.514643 | ||||||||
\(717\) | −20.1786 | −0.753585 | ||||||||
\(718\) | 24.8295 | 0.926628 | ||||||||
\(719\) | −38.5415 | −1.43735 | −0.718677 | − | 0.695344i | \(-0.755252\pi\) | ||||
−0.718677 | + | 0.695344i | \(0.755252\pi\) | |||||||
\(720\) | −1.56277 | −0.0582410 | ||||||||
\(721\) | 40.3587 | 1.50304 | ||||||||
\(722\) | −5.90004 | −0.219577 | ||||||||
\(723\) | 33.5591 | 1.24808 | ||||||||
\(724\) | 14.8883 | 0.553321 | ||||||||
\(725\) | −6.73003 | −0.249947 | ||||||||
\(726\) | 18.4293 | 0.683974 | ||||||||
\(727\) | 48.4299 | 1.79617 | 0.898083 | − | 0.439826i | \(-0.144960\pi\) | ||||
0.898083 | + | 0.439826i | \(0.144960\pi\) | |||||||
\(728\) | −1.36933 | −0.0507506 | ||||||||
\(729\) | −9.66587 | −0.357995 | ||||||||
\(730\) | −5.31031 | −0.196544 | ||||||||
\(731\) | 20.5945 | 0.761715 | ||||||||
\(732\) | 4.93430 | 0.182377 | ||||||||
\(733\) | 25.9372 | 0.958011 | 0.479005 | − | 0.877812i | \(-0.340997\pi\) | ||||
0.479005 | + | 0.877812i | \(0.340997\pi\) | |||||||
\(734\) | −23.1779 | −0.855513 | ||||||||
\(735\) | −1.37113 | −0.0505750 | ||||||||
\(736\) | −2.35182 | −0.0866891 | ||||||||
\(737\) | −19.1118 | −0.703992 | ||||||||
\(738\) | 17.0562 | 0.627849 | ||||||||
\(739\) | −36.6210 | −1.34712 | −0.673562 | − | 0.739131i | \(-0.735236\pi\) | ||||
−0.673562 | + | 0.739131i | \(0.735236\pi\) | |||||||
\(740\) | −2.70143 | −0.0993066 | ||||||||
\(741\) | −4.51573 | −0.165890 | ||||||||
\(742\) | −17.1135 | −0.628258 | ||||||||
\(743\) | −13.2562 | −0.486323 | −0.243161 | − | 0.969986i | \(-0.578184\pi\) | ||||
−0.243161 | + | 0.969986i | \(0.578184\pi\) | |||||||
\(744\) | −2.26430 | −0.0830132 | ||||||||
\(745\) | −9.50756 | −0.348330 | ||||||||
\(746\) | −10.3221 | −0.377917 | ||||||||
\(747\) | −16.8807 | −0.617632 | ||||||||
\(748\) | −3.49216 | −0.127686 | ||||||||
\(749\) | −14.0079 | −0.511836 | ||||||||
\(750\) | −15.7381 | −0.574674 | ||||||||
\(751\) | 15.0905 | 0.550660 | 0.275330 | − | 0.961350i | \(-0.411213\pi\) | ||||
0.275330 | + | 0.961350i | \(0.411213\pi\) | |||||||
\(752\) | −5.71342 | −0.208347 | ||||||||
\(753\) | 31.7865 | 1.15836 | ||||||||
\(754\) | −0.831425 | −0.0302787 | ||||||||
\(755\) | −3.96352 | −0.144247 | ||||||||
\(756\) | 4.91216 | 0.178654 | ||||||||
\(757\) | 33.7874 | 1.22803 | 0.614013 | − | 0.789296i | \(-0.289554\pi\) | ||||
0.614013 | + | 0.789296i | \(0.289554\pi\) | |||||||
\(758\) | 23.0561 | 0.837434 | ||||||||
\(759\) | −9.00722 | −0.326941 | ||||||||
\(760\) | 2.65922 | 0.0964599 | ||||||||
\(761\) | 0.613416 | 0.0222363 | 0.0111182 | − | 0.999938i | \(-0.496461\pi\) | ||||
0.0111182 | + | 0.999938i | \(0.496461\pi\) | |||||||
\(762\) | 18.1542 | 0.657658 | ||||||||
\(763\) | 40.1400 | 1.45317 | ||||||||
\(764\) | 18.0903 | 0.654483 | ||||||||
\(765\) | −3.22653 | −0.116655 | ||||||||
\(766\) | −4.03493 | −0.145788 | ||||||||
\(767\) | −6.80228 | −0.245616 | ||||||||
\(768\) | −2.26430 | −0.0817058 | ||||||||
\(769\) | −31.8028 | −1.14684 | −0.573418 | − | 0.819263i | \(-0.694383\pi\) | ||||
−0.573418 | + | 0.819263i | \(0.694383\pi\) | |||||||
\(770\) | 3.08830 | 0.111295 | ||||||||
\(771\) | −58.8711 | −2.12019 | ||||||||
\(772\) | −3.00761 | −0.108246 | ||||||||
\(773\) | −47.5547 | −1.71042 | −0.855211 | − | 0.518280i | \(-0.826573\pi\) | ||||
−0.855211 | + | 0.518280i | \(0.826573\pi\) | |||||||
\(774\) | 21.2172 | 0.762635 | ||||||||
\(775\) | −4.46019 | −0.160215 | ||||||||
\(776\) | 1.00000 | 0.0358979 | ||||||||
\(777\) | −20.6898 | −0.742242 | ||||||||
\(778\) | 3.15696 | 0.113182 | ||||||||
\(779\) | −29.0230 | −1.03986 | ||||||||
\(780\) | −0.916668 | −0.0328220 | ||||||||
\(781\) | 17.1995 | 0.615447 | ||||||||
\(782\) | −4.85561 | −0.173636 | ||||||||
\(783\) | 2.98256 | 0.106588 | ||||||||
\(784\) | −0.824189 | −0.0294353 | ||||||||
\(785\) | 9.62242 | 0.343439 | ||||||||
\(786\) | −29.1955 | −1.04137 | ||||||||
\(787\) | −7.57394 | −0.269982 | −0.134991 | − | 0.990847i | \(-0.543101\pi\) | ||||
−0.134991 | + | 0.990847i | \(0.543101\pi\) | |||||||
\(788\) | 14.9505 | 0.532589 | ||||||||
\(789\) | −9.25117 | −0.329351 | ||||||||
\(790\) | 0.738495 | 0.0262745 | ||||||||
\(791\) | 33.6543 | 1.19661 | ||||||||
\(792\) | −3.59775 | −0.127840 | ||||||||
\(793\) | 1.20075 | 0.0426398 | ||||||||
\(794\) | −12.5824 | −0.446531 | ||||||||
\(795\) | −11.4563 | −0.406314 | ||||||||
\(796\) | 14.2779 | 0.506066 | ||||||||
\(797\) | −51.4090 | −1.82100 | −0.910500 | − | 0.413509i | \(-0.864303\pi\) | ||||
−0.910500 | + | 0.413509i | \(0.864303\pi\) | |||||||
\(798\) | 20.3665 | 0.720965 | ||||||||
\(799\) | −11.7961 | −0.417314 | ||||||||
\(800\) | −4.46019 | −0.157692 | ||||||||
\(801\) | −33.9602 | −1.19992 | ||||||||
\(802\) | −7.57778 | −0.267581 | ||||||||
\(803\) | −12.2252 | −0.431417 | ||||||||
\(804\) | −25.5847 | −0.902304 | ||||||||
\(805\) | 4.29407 | 0.151346 | ||||||||
\(806\) | −0.551010 | −0.0194085 | ||||||||
\(807\) | −52.5062 | −1.84831 | ||||||||
\(808\) | −4.25993 | −0.149864 | ||||||||
\(809\) | −36.7914 | −1.29352 | −0.646759 | − | 0.762694i | \(-0.723876\pi\) | ||||
−0.646759 | + | 0.762694i | \(0.723876\pi\) | |||||||
\(810\) | 7.97666 | 0.280271 | ||||||||
\(811\) | 4.55401 | 0.159913 | 0.0799564 | − | 0.996798i | \(-0.474522\pi\) | ||||
0.0799564 | + | 0.996798i | \(0.474522\pi\) | |||||||
\(812\) | 3.74982 | 0.131593 | ||||||||
\(813\) | −38.4738 | −1.34933 | ||||||||
\(814\) | −6.21913 | −0.217980 | ||||||||
\(815\) | −13.1314 | −0.459974 | ||||||||
\(816\) | −4.67492 | −0.163655 | ||||||||
\(817\) | −36.1032 | −1.26309 | ||||||||
\(818\) | −8.60124 | −0.300735 | ||||||||
\(819\) | −2.91262 | −0.101775 | ||||||||
\(820\) | −5.89150 | −0.205740 | ||||||||
\(821\) | 38.1829 | 1.33259 | 0.666297 | − | 0.745687i | \(-0.267878\pi\) | ||||
0.666297 | + | 0.745687i | \(0.267878\pi\) | |||||||
\(822\) | −12.2581 | −0.427549 | ||||||||
\(823\) | 21.1201 | 0.736201 | 0.368101 | − | 0.929786i | \(-0.380008\pi\) | ||||
0.368101 | + | 0.929786i | \(0.380008\pi\) | |||||||
\(824\) | 16.2402 | 0.565753 | ||||||||
\(825\) | −17.0821 | −0.594722 | ||||||||
\(826\) | 30.6790 | 1.06746 | ||||||||
\(827\) | −36.7906 | −1.27933 | −0.639667 | − | 0.768652i | \(-0.720928\pi\) | ||||
−0.639667 | + | 0.768652i | \(0.720928\pi\) | |||||||
\(828\) | −5.00241 | −0.173846 | ||||||||
\(829\) | −6.99177 | −0.242834 | −0.121417 | − | 0.992602i | \(-0.538744\pi\) | ||||
−0.121417 | + | 0.992602i | \(0.538744\pi\) | |||||||
\(830\) | 5.83086 | 0.202392 | ||||||||
\(831\) | −71.0306 | −2.46402 | ||||||||
\(832\) | −0.551010 | −0.0191028 | ||||||||
\(833\) | −1.70164 | −0.0589583 | ||||||||
\(834\) | 19.9115 | 0.689479 | ||||||||
\(835\) | −3.18782 | −0.110319 | ||||||||
\(836\) | 6.12194 | 0.211732 | ||||||||
\(837\) | 1.97663 | 0.0683224 | ||||||||
\(838\) | 33.9778 | 1.17374 | ||||||||
\(839\) | 6.26794 | 0.216393 | 0.108197 | − | 0.994130i | \(-0.465492\pi\) | ||||
0.108197 | + | 0.994130i | \(0.465492\pi\) | |||||||
\(840\) | 4.13427 | 0.142646 | ||||||||
\(841\) | −26.7232 | −0.921489 | ||||||||
\(842\) | −11.5606 | −0.398403 | ||||||||
\(843\) | 0.101896 | 0.00350950 | ||||||||
\(844\) | 14.1715 | 0.487803 | ||||||||
\(845\) | 9.32822 | 0.320901 | ||||||||
\(846\) | −12.1527 | −0.417818 | ||||||||
\(847\) | −20.2265 | −0.694992 | ||||||||
\(848\) | −6.88641 | −0.236480 | ||||||||
\(849\) | 19.3012 | 0.662416 | ||||||||
\(850\) | −9.20862 | −0.315853 | ||||||||
\(851\) | −8.64726 | −0.296424 | ||||||||
\(852\) | 23.0248 | 0.788816 | ||||||||
\(853\) | 27.4504 | 0.939885 | 0.469943 | − | 0.882697i | \(-0.344275\pi\) | ||||
0.469943 | + | 0.882697i | \(0.344275\pi\) | |||||||
\(854\) | −5.41550 | −0.185315 | ||||||||
\(855\) | 5.65627 | 0.193440 | ||||||||
\(856\) | −5.63670 | −0.192659 | ||||||||
\(857\) | −43.8912 | −1.49929 | −0.749647 | − | 0.661838i | \(-0.769777\pi\) | ||||
−0.749647 | + | 0.661838i | \(0.769777\pi\) | |||||||
\(858\) | −2.11031 | −0.0720450 | ||||||||
\(859\) | 32.0026 | 1.09192 | 0.545958 | − | 0.837813i | \(-0.316166\pi\) | ||||
0.545958 | + | 0.837813i | \(0.316166\pi\) | |||||||
\(860\) | −7.32874 | −0.249908 | ||||||||
\(861\) | −45.1219 | −1.53775 | ||||||||
\(862\) | 20.5775 | 0.700871 | ||||||||
\(863\) | −50.0273 | −1.70295 | −0.851474 | − | 0.524397i | \(-0.824291\pi\) | ||||
−0.851474 | + | 0.524397i | \(0.824291\pi\) | |||||||
\(864\) | 1.97663 | 0.0672464 | ||||||||
\(865\) | −5.92013 | −0.201290 | ||||||||
\(866\) | 21.6847 | 0.736875 | ||||||||
\(867\) | 28.8411 | 0.979496 | ||||||||
\(868\) | 2.48512 | 0.0843504 | ||||||||
\(869\) | 1.70013 | 0.0576730 | ||||||||
\(870\) | 2.51024 | 0.0851051 | ||||||||
\(871\) | −6.22597 | −0.210959 | ||||||||
\(872\) | 16.1521 | 0.546981 | ||||||||
\(873\) | 2.12704 | 0.0719895 | ||||||||
\(874\) | 8.51213 | 0.287927 | ||||||||
\(875\) | 17.2729 | 0.583931 | ||||||||
\(876\) | −16.3657 | −0.552946 | ||||||||
\(877\) | −8.12972 | −0.274521 | −0.137261 | − | 0.990535i | \(-0.543830\pi\) | ||||
−0.137261 | + | 0.990535i | \(0.543830\pi\) | |||||||
\(878\) | −0.185278 | −0.00625284 | ||||||||
\(879\) | −58.1164 | −1.96022 | ||||||||
\(880\) | 1.24272 | 0.0418920 | ||||||||
\(881\) | −9.12965 | −0.307586 | −0.153793 | − | 0.988103i | \(-0.549149\pi\) | ||||
−0.153793 | + | 0.988103i | \(0.549149\pi\) | |||||||
\(882\) | −1.75309 | −0.0590295 | ||||||||
\(883\) | 46.4164 | 1.56203 | 0.781017 | − | 0.624509i | \(-0.214701\pi\) | ||||
0.781017 | + | 0.624509i | \(0.214701\pi\) | |||||||
\(884\) | −1.13763 | −0.0382626 | ||||||||
\(885\) | 20.5375 | 0.690360 | ||||||||
\(886\) | 0.880293 | 0.0295740 | ||||||||
\(887\) | −35.8795 | −1.20472 | −0.602358 | − | 0.798226i | \(-0.705772\pi\) | ||||
−0.602358 | + | 0.798226i | \(0.705772\pi\) | |||||||
\(888\) | −8.32548 | −0.279385 | ||||||||
\(889\) | −19.9247 | −0.668252 | ||||||||
\(890\) | 11.7304 | 0.393203 | ||||||||
\(891\) | 18.3635 | 0.615202 | ||||||||
\(892\) | 13.0320 | 0.436344 | ||||||||
\(893\) | 20.6791 | 0.691999 | ||||||||
\(894\) | −29.3011 | −0.979975 | ||||||||
\(895\) | 10.1177 | 0.338197 | ||||||||
\(896\) | 2.48512 | 0.0830220 | ||||||||
\(897\) | −2.93425 | −0.0979716 | ||||||||
\(898\) | 29.5313 | 0.985471 | ||||||||
\(899\) | 1.50891 | 0.0503249 | ||||||||
\(900\) | −9.48703 | −0.316234 | ||||||||
\(901\) | −14.2178 | −0.473665 | ||||||||
\(902\) | −13.5632 | −0.451604 | ||||||||
\(903\) | −56.1295 | −1.86787 | ||||||||
\(904\) | 13.5424 | 0.450412 | ||||||||
\(905\) | −10.9387 | −0.363614 | ||||||||
\(906\) | −12.2151 | −0.405819 | ||||||||
\(907\) | −57.5367 | −1.91047 | −0.955237 | − | 0.295843i | \(-0.904400\pi\) | ||||
−0.955237 | + | 0.295843i | \(0.904400\pi\) | |||||||
\(908\) | 11.7044 | 0.388423 | ||||||||
\(909\) | −9.06107 | −0.300537 | ||||||||
\(910\) | 1.00606 | 0.0333507 | ||||||||
\(911\) | −55.7847 | −1.84823 | −0.924115 | − | 0.382115i | \(-0.875196\pi\) | ||||
−0.924115 | + | 0.382115i | \(0.875196\pi\) | |||||||
\(912\) | 8.19537 | 0.271376 | ||||||||
\(913\) | 13.4236 | 0.444255 | ||||||||
\(914\) | −28.1549 | −0.931280 | ||||||||
\(915\) | −3.62530 | −0.119849 | ||||||||
\(916\) | −0.805815 | −0.0266249 | ||||||||
\(917\) | 32.0427 | 1.05814 | ||||||||
\(918\) | 4.08100 | 0.134693 | ||||||||
\(919\) | 17.2992 | 0.570647 | 0.285324 | − | 0.958431i | \(-0.407899\pi\) | ||||
0.285324 | + | 0.958431i | \(0.407899\pi\) | |||||||
\(920\) | 1.72791 | 0.0569676 | ||||||||
\(921\) | −68.4124 | −2.25426 | ||||||||
\(922\) | −15.2922 | −0.503622 | ||||||||
\(923\) | 5.60302 | 0.184426 | ||||||||
\(924\) | 9.51775 | 0.313111 | ||||||||
\(925\) | −16.3995 | −0.539211 | ||||||||
\(926\) | 8.84392 | 0.290629 | ||||||||
\(927\) | 34.5435 | 1.13456 | ||||||||
\(928\) | 1.50891 | 0.0495324 | ||||||||
\(929\) | −37.7190 | −1.23752 | −0.618761 | − | 0.785580i | \(-0.712365\pi\) | ||||
−0.618761 | + | 0.785580i | \(0.712365\pi\) | |||||||
\(930\) | 1.66361 | 0.0545520 | ||||||||
\(931\) | 2.98306 | 0.0977658 | ||||||||
\(932\) | 0.944506 | 0.0309383 | ||||||||
\(933\) | −9.47977 | −0.310354 | ||||||||
\(934\) | −5.75283 | −0.188238 | ||||||||
\(935\) | 2.56574 | 0.0839088 | ||||||||
\(936\) | −1.17202 | −0.0383088 | ||||||||
\(937\) | 29.8648 | 0.975640 | 0.487820 | − | 0.872944i | \(-0.337792\pi\) | ||||
0.487820 | + | 0.872944i | \(0.337792\pi\) | |||||||
\(938\) | 28.0798 | 0.916839 | ||||||||
\(939\) | −37.3792 | −1.21982 | ||||||||
\(940\) | 4.19773 | 0.136915 | ||||||||
\(941\) | −13.0443 | −0.425231 | −0.212615 | − | 0.977136i | \(-0.568198\pi\) | ||||
−0.212615 | + | 0.977136i | \(0.568198\pi\) | |||||||
\(942\) | 29.6551 | 0.966214 | ||||||||
\(943\) | −18.8586 | −0.614122 | ||||||||
\(944\) | 12.3451 | 0.401799 | ||||||||
\(945\) | −3.60904 | −0.117402 | ||||||||
\(946\) | −16.8719 | −0.548554 | ||||||||
\(947\) | −43.6636 | −1.41888 | −0.709438 | − | 0.704768i | \(-0.751051\pi\) | ||||
−0.709438 | + | 0.704768i | \(0.751051\pi\) | |||||||
\(948\) | 2.27595 | 0.0739193 | ||||||||
\(949\) | −3.98255 | −0.129279 | ||||||||
\(950\) | 16.1432 | 0.523753 | ||||||||
\(951\) | 77.4472 | 2.51140 | ||||||||
\(952\) | 5.13083 | 0.166291 | ||||||||
\(953\) | 58.8771 | 1.90722 | 0.953608 | − | 0.301050i | \(-0.0973372\pi\) | ||||
0.953608 | + | 0.301050i | \(0.0973372\pi\) | |||||||
\(954\) | −14.6477 | −0.474237 | ||||||||
\(955\) | −13.2912 | −0.430092 | ||||||||
\(956\) | 8.91165 | 0.288223 | ||||||||
\(957\) | 5.77897 | 0.186808 | ||||||||
\(958\) | −29.9180 | −0.966608 | ||||||||
\(959\) | 13.4535 | 0.434436 | ||||||||
\(960\) | 1.66361 | 0.0536929 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | −2.02598 | −0.0653202 | ||||||||
\(963\) | −11.9895 | −0.386357 | ||||||||
\(964\) | −14.8210 | −0.477351 | ||||||||
\(965\) | 2.20974 | 0.0711340 | ||||||||
\(966\) | 13.2338 | 0.425790 | ||||||||
\(967\) | −4.60845 | −0.148198 | −0.0740988 | − | 0.997251i | \(-0.523608\pi\) | ||||
−0.0740988 | + | 0.997251i | \(0.523608\pi\) | |||||||
\(968\) | −8.13907 | −0.261599 | ||||||||
\(969\) | 16.9203 | 0.543560 | ||||||||
\(970\) | −0.734715 | −0.0235903 | ||||||||
\(971\) | 24.9391 | 0.800333 | 0.400167 | − | 0.916442i | \(-0.368952\pi\) | ||||
0.400167 | + | 0.916442i | \(0.368952\pi\) | |||||||
\(972\) | 18.6532 | 0.598301 | ||||||||
\(973\) | −21.8533 | −0.700586 | ||||||||
\(974\) | 9.40494 | 0.301354 | ||||||||
\(975\) | −5.56477 | −0.178215 | ||||||||
\(976\) | −2.17917 | −0.0697536 | ||||||||
\(977\) | 2.51429 | 0.0804393 | 0.0402197 | − | 0.999191i | \(-0.487194\pi\) | ||||
0.0402197 | + | 0.999191i | \(0.487194\pi\) | |||||||
\(978\) | −40.4694 | −1.29407 | ||||||||
\(979\) | 27.0052 | 0.863090 | ||||||||
\(980\) | 0.605544 | 0.0193434 | ||||||||
\(981\) | 34.3563 | 1.09691 | ||||||||
\(982\) | −38.5146 | −1.22905 | ||||||||
\(983\) | 6.30240 | 0.201015 | 0.100508 | − | 0.994936i | \(-0.467953\pi\) | ||||
0.100508 | + | 0.994936i | \(0.467953\pi\) | |||||||
\(984\) | −18.1569 | −0.578819 | ||||||||
\(985\) | −10.9843 | −0.349990 | ||||||||
\(986\) | 3.11533 | 0.0992122 | ||||||||
\(987\) | 32.1497 | 1.02334 | ||||||||
\(988\) | 1.99432 | 0.0634478 | ||||||||
\(989\) | −23.4592 | −0.745961 | ||||||||
\(990\) | 2.64332 | 0.0840101 | ||||||||
\(991\) | 50.9434 | 1.61827 | 0.809135 | − | 0.587623i | \(-0.199936\pi\) | ||||
0.809135 | + | 0.587623i | \(0.199936\pi\) | |||||||
\(992\) | 1.00000 | 0.0317500 | ||||||||
\(993\) | −6.06999 | −0.192625 | ||||||||
\(994\) | −25.2702 | −0.801523 | ||||||||
\(995\) | −10.4902 | −0.332561 | ||||||||
\(996\) | 17.9700 | 0.569400 | ||||||||
\(997\) | 27.2266 | 0.862277 | 0.431138 | − | 0.902286i | \(-0.358112\pi\) | ||||
0.431138 | + | 0.902286i | \(0.358112\pi\) | |||||||
\(998\) | 29.8674 | 0.945437 | ||||||||
\(999\) | 7.26777 | 0.229942 |
(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 | 6014.2.a.k.1.7 | ✓ | 37 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6014.2.a.k.1.7 | ✓ | 37 | 1.1 | even | 1 | trivial |