Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8021,2,Mod(1,8021)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8021, 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("8021.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8021 = 13 \cdot 617 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8021.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: | \(64.0480074613\) |
Analytic rank: | \(1\) |
Dimension: | \(140\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 8021.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.72092 | −1.92398 | −0.961989 | − | 0.273088i | \(-0.911955\pi\) | ||||
−0.961989 | + | 0.273088i | \(0.911955\pi\) | |||||||
\(3\) | 2.93492 | 1.69448 | 0.847239 | − | 0.531212i | \(-0.178263\pi\) | ||||
0.847239 | + | 0.531212i | \(0.178263\pi\) | |||||||
\(4\) | 5.40338 | 2.70169 | ||||||||
\(5\) | −0.339682 | −0.151910 | −0.0759551 | − | 0.997111i | \(-0.524201\pi\) | ||||
−0.0759551 | + | 0.997111i | \(0.524201\pi\) | |||||||
\(6\) | −7.98568 | −3.26014 | ||||||||
\(7\) | −0.916249 | −0.346310 | −0.173155 | − | 0.984895i | \(-0.555396\pi\) | ||||
−0.173155 | + | 0.984895i | \(0.555396\pi\) | |||||||
\(8\) | −9.26032 | −3.27402 | ||||||||
\(9\) | 5.61377 | 1.87126 | ||||||||
\(10\) | 0.924245 | 0.292272 | ||||||||
\(11\) | −0.141261 | −0.0425919 | −0.0212960 | − | 0.999773i | \(-0.506779\pi\) | ||||
−0.0212960 | + | 0.999773i | \(0.506779\pi\) | |||||||
\(12\) | 15.8585 | 4.57796 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 2.49304 | 0.666292 | ||||||||
\(15\) | −0.996939 | −0.257409 | ||||||||
\(16\) | 14.3898 | 3.59745 | ||||||||
\(17\) | −1.87864 | −0.455637 | −0.227819 | − | 0.973704i | \(-0.573159\pi\) | ||||
−0.227819 | + | 0.973704i | \(0.573159\pi\) | |||||||
\(18\) | −15.2746 | −3.60026 | ||||||||
\(19\) | 0.543254 | 0.124631 | 0.0623155 | − | 0.998057i | \(-0.480152\pi\) | ||||
0.0623155 | + | 0.998057i | \(0.480152\pi\) | |||||||
\(20\) | −1.83543 | −0.410415 | ||||||||
\(21\) | −2.68912 | −0.586814 | ||||||||
\(22\) | 0.384361 | 0.0819460 | ||||||||
\(23\) | 4.12163 | 0.859419 | 0.429710 | − | 0.902967i | \(-0.358616\pi\) | ||||
0.429710 | + | 0.902967i | \(0.358616\pi\) | |||||||
\(24\) | −27.1783 | −5.54775 | ||||||||
\(25\) | −4.88462 | −0.976923 | ||||||||
\(26\) | 2.72092 | 0.533616 | ||||||||
\(27\) | 7.67121 | 1.47633 | ||||||||
\(28\) | −4.95085 | −0.935622 | ||||||||
\(29\) | 3.91353 | 0.726724 | 0.363362 | − | 0.931648i | \(-0.381629\pi\) | ||||
0.363362 | + | 0.931648i | \(0.381629\pi\) | |||||||
\(30\) | 2.71259 | 0.495249 | ||||||||
\(31\) | −6.91321 | −1.24165 | −0.620824 | − | 0.783950i | \(-0.713202\pi\) | ||||
−0.620824 | + | 0.783950i | \(0.713202\pi\) | |||||||
\(32\) | −20.6328 | −3.64739 | ||||||||
\(33\) | −0.414592 | −0.0721711 | ||||||||
\(34\) | 5.11162 | 0.876636 | ||||||||
\(35\) | 0.311233 | 0.0526080 | ||||||||
\(36\) | 30.3334 | 5.05556 | ||||||||
\(37\) | −5.24871 | −0.862882 | −0.431441 | − | 0.902141i | \(-0.641995\pi\) | ||||
−0.431441 | + | 0.902141i | \(0.641995\pi\) | |||||||
\(38\) | −1.47815 | −0.239787 | ||||||||
\(39\) | −2.93492 | −0.469964 | ||||||||
\(40\) | 3.14556 | 0.497357 | ||||||||
\(41\) | 7.80986 | 1.21970 | 0.609848 | − | 0.792519i | \(-0.291231\pi\) | ||||
0.609848 | + | 0.792519i | \(0.291231\pi\) | |||||||
\(42\) | 7.31687 | 1.12902 | ||||||||
\(43\) | 1.62979 | 0.248540 | 0.124270 | − | 0.992248i | \(-0.460341\pi\) | ||||
0.124270 | + | 0.992248i | \(0.460341\pi\) | |||||||
\(44\) | −0.763290 | −0.115070 | ||||||||
\(45\) | −1.90689 | −0.284263 | ||||||||
\(46\) | −11.2146 | −1.65350 | ||||||||
\(47\) | 0.413613 | 0.0603316 | 0.0301658 | − | 0.999545i | \(-0.490396\pi\) | ||||
0.0301658 | + | 0.999545i | \(0.490396\pi\) | |||||||
\(48\) | 42.2329 | 6.09580 | ||||||||
\(49\) | −6.16049 | −0.880070 | ||||||||
\(50\) | 13.2906 | 1.87958 | ||||||||
\(51\) | −5.51367 | −0.772068 | ||||||||
\(52\) | −5.40338 | −0.749315 | ||||||||
\(53\) | −6.17696 | −0.848470 | −0.424235 | − | 0.905552i | \(-0.639457\pi\) | ||||
−0.424235 | + | 0.905552i | \(0.639457\pi\) | |||||||
\(54\) | −20.8727 | −2.84042 | ||||||||
\(55\) | 0.0479839 | 0.00647015 | ||||||||
\(56\) | 8.48476 | 1.13382 | ||||||||
\(57\) | 1.59441 | 0.211184 | ||||||||
\(58\) | −10.6484 | −1.39820 | ||||||||
\(59\) | −11.2268 | −1.46160 | −0.730802 | − | 0.682589i | \(-0.760854\pi\) | ||||
−0.730802 | + | 0.682589i | \(0.760854\pi\) | |||||||
\(60\) | −5.38685 | −0.695439 | ||||||||
\(61\) | 4.33420 | 0.554937 | 0.277469 | − | 0.960735i | \(-0.410505\pi\) | ||||
0.277469 | + | 0.960735i | \(0.410505\pi\) | |||||||
\(62\) | 18.8103 | 2.38890 | ||||||||
\(63\) | −5.14361 | −0.648034 | ||||||||
\(64\) | 27.3605 | 3.42006 | ||||||||
\(65\) | 0.339682 | 0.0421323 | ||||||||
\(66\) | 1.12807 | 0.138856 | ||||||||
\(67\) | −4.97675 | −0.608007 | −0.304003 | − | 0.952671i | \(-0.598323\pi\) | ||||
−0.304003 | + | 0.952671i | \(0.598323\pi\) | |||||||
\(68\) | −10.1510 | −1.23099 | ||||||||
\(69\) | 12.0967 | 1.45627 | ||||||||
\(70\) | −0.846839 | −0.101217 | ||||||||
\(71\) | −11.4122 | −1.35438 | −0.677188 | − | 0.735810i | \(-0.736802\pi\) | ||||
−0.677188 | + | 0.735810i | \(0.736802\pi\) | |||||||
\(72\) | −51.9853 | −6.12653 | ||||||||
\(73\) | 2.14580 | 0.251147 | 0.125573 | − | 0.992084i | \(-0.459923\pi\) | ||||
0.125573 | + | 0.992084i | \(0.459923\pi\) | |||||||
\(74\) | 14.2813 | 1.66017 | ||||||||
\(75\) | −14.3360 | −1.65538 | ||||||||
\(76\) | 2.93541 | 0.336714 | ||||||||
\(77\) | 0.129431 | 0.0147500 | ||||||||
\(78\) | 7.98568 | 0.904200 | ||||||||
\(79\) | −8.27677 | −0.931210 | −0.465605 | − | 0.884993i | \(-0.654163\pi\) | ||||
−0.465605 | + | 0.884993i | \(0.654163\pi\) | |||||||
\(80\) | −4.88795 | −0.546489 | ||||||||
\(81\) | 5.67311 | 0.630345 | ||||||||
\(82\) | −21.2500 | −2.34667 | ||||||||
\(83\) | −8.73569 | −0.958867 | −0.479433 | − | 0.877578i | \(-0.659158\pi\) | ||||
−0.479433 | + | 0.877578i | \(0.659158\pi\) | |||||||
\(84\) | −14.5304 | −1.58539 | ||||||||
\(85\) | 0.638140 | 0.0692160 | ||||||||
\(86\) | −4.43451 | −0.478185 | ||||||||
\(87\) | 11.4859 | 1.23142 | ||||||||
\(88\) | 1.30813 | 0.139447 | ||||||||
\(89\) | −0.171967 | −0.0182285 | −0.00911425 | − | 0.999958i | \(-0.502901\pi\) | ||||
−0.00911425 | + | 0.999958i | \(0.502901\pi\) | |||||||
\(90\) | 5.18850 | 0.546916 | ||||||||
\(91\) | 0.916249 | 0.0960490 | ||||||||
\(92\) | 22.2707 | 2.32189 | ||||||||
\(93\) | −20.2897 | −2.10395 | ||||||||
\(94\) | −1.12541 | −0.116077 | ||||||||
\(95\) | −0.184533 | −0.0189327 | ||||||||
\(96\) | −60.5556 | −6.18043 | ||||||||
\(97\) | −0.278775 | −0.0283053 | −0.0141526 | − | 0.999900i | \(-0.504505\pi\) | ||||
−0.0141526 | + | 0.999900i | \(0.504505\pi\) | |||||||
\(98\) | 16.7622 | 1.69323 | ||||||||
\(99\) | −0.793010 | −0.0797005 | ||||||||
\(100\) | −26.3935 | −2.63935 | ||||||||
\(101\) | −4.05663 | −0.403649 | −0.201825 | − | 0.979422i | \(-0.564687\pi\) | ||||
−0.201825 | + | 0.979422i | \(0.564687\pi\) | |||||||
\(102\) | 15.0022 | 1.48544 | ||||||||
\(103\) | −17.3849 | −1.71298 | −0.856491 | − | 0.516162i | \(-0.827360\pi\) | ||||
−0.856491 | + | 0.516162i | \(0.827360\pi\) | |||||||
\(104\) | 9.26032 | 0.908049 | ||||||||
\(105\) | 0.913445 | 0.0891431 | ||||||||
\(106\) | 16.8070 | 1.63244 | ||||||||
\(107\) | 14.1339 | 1.36637 | 0.683187 | − | 0.730244i | \(-0.260594\pi\) | ||||
0.683187 | + | 0.730244i | \(0.260594\pi\) | |||||||
\(108\) | 41.4505 | 3.98858 | ||||||||
\(109\) | 4.07202 | 0.390029 | 0.195015 | − | 0.980800i | \(-0.437525\pi\) | ||||
0.195015 | + | 0.980800i | \(0.437525\pi\) | |||||||
\(110\) | −0.130560 | −0.0124484 | ||||||||
\(111\) | −15.4046 | −1.46214 | ||||||||
\(112\) | −13.1846 | −1.24583 | ||||||||
\(113\) | 2.37104 | 0.223049 | 0.111524 | − | 0.993762i | \(-0.464427\pi\) | ||||
0.111524 | + | 0.993762i | \(0.464427\pi\) | |||||||
\(114\) | −4.33825 | −0.406314 | ||||||||
\(115\) | −1.40004 | −0.130555 | ||||||||
\(116\) | 21.1463 | 1.96338 | ||||||||
\(117\) | −5.61377 | −0.518993 | ||||||||
\(118\) | 30.5472 | 2.81210 | ||||||||
\(119\) | 1.72130 | 0.157792 | ||||||||
\(120\) | 9.23198 | 0.842761 | ||||||||
\(121\) | −10.9800 | −0.998186 | ||||||||
\(122\) | −11.7930 | −1.06769 | ||||||||
\(123\) | 22.9213 | 2.06675 | ||||||||
\(124\) | −37.3547 | −3.35455 | ||||||||
\(125\) | 3.35762 | 0.300315 | ||||||||
\(126\) | 13.9953 | 1.24680 | ||||||||
\(127\) | 21.9292 | 1.94590 | 0.972949 | − | 0.231020i | \(-0.0742062\pi\) | ||||
0.972949 | + | 0.231020i | \(0.0742062\pi\) | |||||||
\(128\) | −33.1800 | −2.93272 | ||||||||
\(129\) | 4.78329 | 0.421145 | ||||||||
\(130\) | −0.924245 | −0.0810617 | ||||||||
\(131\) | −4.03182 | −0.352262 | −0.176131 | − | 0.984367i | \(-0.556358\pi\) | ||||
−0.176131 | + | 0.984367i | \(0.556358\pi\) | |||||||
\(132\) | −2.24020 | −0.194984 | ||||||||
\(133\) | −0.497756 | −0.0431609 | ||||||||
\(134\) | 13.5413 | 1.16979 | ||||||||
\(135\) | −2.60577 | −0.224269 | ||||||||
\(136\) | 17.3968 | 1.49177 | ||||||||
\(137\) | 5.94862 | 0.508225 | 0.254113 | − | 0.967175i | \(-0.418217\pi\) | ||||
0.254113 | + | 0.967175i | \(0.418217\pi\) | |||||||
\(138\) | −32.9140 | −2.80183 | ||||||||
\(139\) | −20.3388 | −1.72512 | −0.862558 | − | 0.505959i | \(-0.831139\pi\) | ||||
−0.862558 | + | 0.505959i | \(0.831139\pi\) | |||||||
\(140\) | 1.68171 | 0.142131 | ||||||||
\(141\) | 1.21392 | 0.102231 | ||||||||
\(142\) | 31.0516 | 2.60579 | ||||||||
\(143\) | 0.141261 | 0.0118129 | ||||||||
\(144\) | 80.7810 | 6.73175 | ||||||||
\(145\) | −1.32935 | −0.110397 | ||||||||
\(146\) | −5.83854 | −0.483201 | ||||||||
\(147\) | −18.0806 | −1.49126 | ||||||||
\(148\) | −28.3608 | −2.33124 | ||||||||
\(149\) | 16.6320 | 1.36255 | 0.681273 | − | 0.732030i | \(-0.261427\pi\) | ||||
0.681273 | + | 0.732030i | \(0.261427\pi\) | |||||||
\(150\) | 39.0070 | 3.18491 | ||||||||
\(151\) | −10.8420 | −0.882311 | −0.441156 | − | 0.897431i | \(-0.645431\pi\) | ||||
−0.441156 | + | 0.897431i | \(0.645431\pi\) | |||||||
\(152\) | −5.03070 | −0.408044 | ||||||||
\(153\) | −10.5463 | −0.852615 | ||||||||
\(154\) | −0.352170 | −0.0283787 | ||||||||
\(155\) | 2.34829 | 0.188619 | ||||||||
\(156\) | −15.8585 | −1.26970 | ||||||||
\(157\) | 21.9287 | 1.75010 | 0.875051 | − | 0.484030i | \(-0.160827\pi\) | ||||
0.875051 | + | 0.484030i | \(0.160827\pi\) | |||||||
\(158\) | 22.5204 | 1.79163 | ||||||||
\(159\) | −18.1289 | −1.43771 | ||||||||
\(160\) | 7.00857 | 0.554076 | ||||||||
\(161\) | −3.77644 | −0.297625 | ||||||||
\(162\) | −15.4361 | −1.21277 | ||||||||
\(163\) | 0.0564064 | 0.00441809 | 0.00220904 | − | 0.999998i | \(-0.499297\pi\) | ||||
0.00220904 | + | 0.999998i | \(0.499297\pi\) | |||||||
\(164\) | 42.1997 | 3.29524 | ||||||||
\(165\) | 0.140829 | 0.0109635 | ||||||||
\(166\) | 23.7691 | 1.84484 | ||||||||
\(167\) | 14.9477 | 1.15669 | 0.578344 | − | 0.815793i | \(-0.303699\pi\) | ||||
0.578344 | + | 0.815793i | \(0.303699\pi\) | |||||||
\(168\) | 24.9021 | 1.92124 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −1.73633 | −0.133170 | ||||||||
\(171\) | 3.04970 | 0.233216 | ||||||||
\(172\) | 8.80636 | 0.671478 | ||||||||
\(173\) | 9.91576 | 0.753881 | 0.376941 | − | 0.926237i | \(-0.376976\pi\) | ||||
0.376941 | + | 0.926237i | \(0.376976\pi\) | |||||||
\(174\) | −31.2522 | −2.36922 | ||||||||
\(175\) | 4.47553 | 0.338318 | ||||||||
\(176\) | −2.03272 | −0.153222 | ||||||||
\(177\) | −32.9498 | −2.47666 | ||||||||
\(178\) | 0.467909 | 0.0350712 | ||||||||
\(179\) | 6.47838 | 0.484217 | 0.242108 | − | 0.970249i | \(-0.422161\pi\) | ||||
0.242108 | + | 0.970249i | \(0.422161\pi\) | |||||||
\(180\) | −10.3037 | −0.767991 | ||||||||
\(181\) | −12.9390 | −0.961750 | −0.480875 | − | 0.876789i | \(-0.659681\pi\) | ||||
−0.480875 | + | 0.876789i | \(0.659681\pi\) | |||||||
\(182\) | −2.49304 | −0.184796 | ||||||||
\(183\) | 12.7205 | 0.940329 | ||||||||
\(184\) | −38.1676 | −2.81375 | ||||||||
\(185\) | 1.78289 | 0.131081 | ||||||||
\(186\) | 55.2066 | 4.04795 | ||||||||
\(187\) | 0.265380 | 0.0194065 | ||||||||
\(188\) | 2.23491 | 0.162997 | ||||||||
\(189\) | −7.02874 | −0.511266 | ||||||||
\(190\) | 0.502100 | 0.0364261 | ||||||||
\(191\) | −4.96058 | −0.358935 | −0.179468 | − | 0.983764i | \(-0.557438\pi\) | ||||
−0.179468 | + | 0.983764i | \(0.557438\pi\) | |||||||
\(192\) | 80.3008 | 5.79521 | ||||||||
\(193\) | 2.68022 | 0.192926 | 0.0964632 | − | 0.995337i | \(-0.469247\pi\) | ||||
0.0964632 | + | 0.995337i | \(0.469247\pi\) | |||||||
\(194\) | 0.758523 | 0.0544588 | ||||||||
\(195\) | 0.996939 | 0.0713923 | ||||||||
\(196\) | −33.2875 | −2.37768 | ||||||||
\(197\) | −2.25526 | −0.160681 | −0.0803403 | − | 0.996767i | \(-0.525601\pi\) | ||||
−0.0803403 | + | 0.996767i | \(0.525601\pi\) | |||||||
\(198\) | 2.15771 | 0.153342 | ||||||||
\(199\) | −16.7644 | −1.18840 | −0.594200 | − | 0.804317i | \(-0.702531\pi\) | ||||
−0.594200 | + | 0.804317i | \(0.702531\pi\) | |||||||
\(200\) | 45.2331 | 3.19846 | ||||||||
\(201\) | −14.6064 | −1.03025 | ||||||||
\(202\) | 11.0377 | 0.776613 | ||||||||
\(203\) | −3.58577 | −0.251671 | ||||||||
\(204\) | −29.7925 | −2.08589 | ||||||||
\(205\) | −2.65287 | −0.185284 | ||||||||
\(206\) | 47.3028 | 3.29574 | ||||||||
\(207\) | 23.1379 | 1.60819 | ||||||||
\(208\) | −14.3898 | −0.997753 | ||||||||
\(209\) | −0.0767408 | −0.00530827 | ||||||||
\(210\) | −2.48541 | −0.171509 | ||||||||
\(211\) | −12.4928 | −0.860040 | −0.430020 | − | 0.902819i | \(-0.641494\pi\) | ||||
−0.430020 | + | 0.902819i | \(0.641494\pi\) | |||||||
\(212\) | −33.3765 | −2.29231 | ||||||||
\(213\) | −33.4939 | −2.29496 | ||||||||
\(214\) | −38.4571 | −2.62887 | ||||||||
\(215\) | −0.553608 | −0.0377558 | ||||||||
\(216\) | −71.0379 | −4.83352 | ||||||||
\(217\) | 6.33422 | 0.429995 | ||||||||
\(218\) | −11.0796 | −0.750407 | ||||||||
\(219\) | 6.29775 | 0.425563 | ||||||||
\(220\) | 0.259276 | 0.0174804 | ||||||||
\(221\) | 1.87864 | 0.126371 | ||||||||
\(222\) | 41.9145 | 2.81312 | ||||||||
\(223\) | 10.3767 | 0.694875 | 0.347437 | − | 0.937703i | \(-0.387052\pi\) | ||||
0.347437 | + | 0.937703i | \(0.387052\pi\) | |||||||
\(224\) | 18.9048 | 1.26313 | ||||||||
\(225\) | −27.4211 | −1.82807 | ||||||||
\(226\) | −6.45140 | −0.429141 | ||||||||
\(227\) | −16.4239 | −1.09010 | −0.545048 | − | 0.838405i | \(-0.683488\pi\) | ||||
−0.545048 | + | 0.838405i | \(0.683488\pi\) | |||||||
\(228\) | 8.61519 | 0.570555 | ||||||||
\(229\) | 4.78607 | 0.316273 | 0.158136 | − | 0.987417i | \(-0.449451\pi\) | ||||
0.158136 | + | 0.987417i | \(0.449451\pi\) | |||||||
\(230\) | 3.80940 | 0.251184 | ||||||||
\(231\) | 0.379869 | 0.0249936 | ||||||||
\(232\) | −36.2405 | −2.37931 | ||||||||
\(233\) | −4.48572 | −0.293870 | −0.146935 | − | 0.989146i | \(-0.546941\pi\) | ||||
−0.146935 | + | 0.989146i | \(0.546941\pi\) | |||||||
\(234\) | 15.2746 | 0.998532 | ||||||||
\(235\) | −0.140497 | −0.00916499 | ||||||||
\(236\) | −60.6627 | −3.94881 | ||||||||
\(237\) | −24.2917 | −1.57791 | ||||||||
\(238\) | −4.68352 | −0.303588 | ||||||||
\(239\) | −13.3209 | −0.861658 | −0.430829 | − | 0.902434i | \(-0.641779\pi\) | ||||
−0.430829 | + | 0.902434i | \(0.641779\pi\) | |||||||
\(240\) | −14.3457 | −0.926014 | ||||||||
\(241\) | −6.13820 | −0.395396 | −0.197698 | − | 0.980263i | \(-0.563347\pi\) | ||||
−0.197698 | + | 0.980263i | \(0.563347\pi\) | |||||||
\(242\) | 29.8758 | 1.92049 | ||||||||
\(243\) | −6.36351 | −0.408219 | ||||||||
\(244\) | 23.4193 | 1.49927 | ||||||||
\(245\) | 2.09260 | 0.133692 | ||||||||
\(246\) | −62.3670 | −3.97638 | ||||||||
\(247\) | −0.543254 | −0.0345664 | ||||||||
\(248\) | 64.0185 | 4.06518 | ||||||||
\(249\) | −25.6386 | −1.62478 | ||||||||
\(250\) | −9.13581 | −0.577799 | ||||||||
\(251\) | 5.20804 | 0.328729 | 0.164364 | − | 0.986400i | \(-0.447443\pi\) | ||||
0.164364 | + | 0.986400i | \(0.447443\pi\) | |||||||
\(252\) | −27.7929 | −1.75079 | ||||||||
\(253\) | −0.582227 | −0.0366043 | ||||||||
\(254\) | −59.6674 | −3.74387 | ||||||||
\(255\) | 1.87289 | 0.117285 | ||||||||
\(256\) | 35.5590 | 2.22244 | ||||||||
\(257\) | 19.2781 | 1.20254 | 0.601268 | − | 0.799047i | \(-0.294662\pi\) | ||||
0.601268 | + | 0.799047i | \(0.294662\pi\) | |||||||
\(258\) | −13.0149 | −0.810275 | ||||||||
\(259\) | 4.80912 | 0.298824 | ||||||||
\(260\) | 1.83543 | 0.113829 | ||||||||
\(261\) | 21.9696 | 1.35989 | ||||||||
\(262\) | 10.9702 | 0.677744 | ||||||||
\(263\) | 13.5061 | 0.832822 | 0.416411 | − | 0.909176i | \(-0.363288\pi\) | ||||
0.416411 | + | 0.909176i | \(0.363288\pi\) | |||||||
\(264\) | 3.83925 | 0.236290 | ||||||||
\(265\) | 2.09820 | 0.128891 | ||||||||
\(266\) | 1.35435 | 0.0830406 | ||||||||
\(267\) | −0.504711 | −0.0308878 | ||||||||
\(268\) | −26.8913 | −1.64265 | ||||||||
\(269\) | 18.3837 | 1.12088 | 0.560438 | − | 0.828197i | \(-0.310633\pi\) | ||||
0.560438 | + | 0.828197i | \(0.310633\pi\) | |||||||
\(270\) | 7.09008 | 0.431489 | ||||||||
\(271\) | −1.88480 | −0.114493 | −0.0572467 | − | 0.998360i | \(-0.518232\pi\) | ||||
−0.0572467 | + | 0.998360i | \(0.518232\pi\) | |||||||
\(272\) | −27.0333 | −1.63913 | ||||||||
\(273\) | 2.68912 | 0.162753 | ||||||||
\(274\) | −16.1857 | −0.977814 | ||||||||
\(275\) | 0.690008 | 0.0416091 | ||||||||
\(276\) | 65.3629 | 3.93439 | ||||||||
\(277\) | −10.7232 | −0.644297 | −0.322148 | − | 0.946689i | \(-0.604405\pi\) | ||||
−0.322148 | + | 0.946689i | \(0.604405\pi\) | |||||||
\(278\) | 55.3402 | 3.31908 | ||||||||
\(279\) | −38.8091 | −2.32344 | ||||||||
\(280\) | −2.88212 | −0.172240 | ||||||||
\(281\) | −7.76933 | −0.463479 | −0.231740 | − | 0.972778i | \(-0.574442\pi\) | ||||
−0.231740 | + | 0.972778i | \(0.574442\pi\) | |||||||
\(282\) | −3.30298 | −0.196690 | ||||||||
\(283\) | −16.3991 | −0.974823 | −0.487411 | − | 0.873173i | \(-0.662059\pi\) | ||||
−0.487411 | + | 0.873173i | \(0.662059\pi\) | |||||||
\(284\) | −61.6644 | −3.65911 | ||||||||
\(285\) | −0.541591 | −0.0320811 | ||||||||
\(286\) | −0.384361 | −0.0227277 | ||||||||
\(287\) | −7.15578 | −0.422392 | ||||||||
\(288\) | −115.828 | −6.82521 | ||||||||
\(289\) | −13.4707 | −0.792395 | ||||||||
\(290\) | 3.61706 | 0.212401 | ||||||||
\(291\) | −0.818182 | −0.0479627 | ||||||||
\(292\) | 11.5946 | 0.678521 | ||||||||
\(293\) | −21.2182 | −1.23958 | −0.619792 | − | 0.784766i | \(-0.712783\pi\) | ||||
−0.619792 | + | 0.784766i | \(0.712783\pi\) | |||||||
\(294\) | 49.1957 | 2.86915 | ||||||||
\(295\) | 3.81354 | 0.222033 | ||||||||
\(296\) | 48.6047 | 2.82509 | ||||||||
\(297\) | −1.08365 | −0.0628796 | ||||||||
\(298\) | −45.2542 | −2.62151 | ||||||||
\(299\) | −4.12163 | −0.238360 | ||||||||
\(300\) | −77.4628 | −4.47231 | ||||||||
\(301\) | −1.49329 | −0.0860718 | ||||||||
\(302\) | 29.5002 | 1.69755 | ||||||||
\(303\) | −11.9059 | −0.683975 | ||||||||
\(304\) | 7.81731 | 0.448353 | ||||||||
\(305\) | −1.47225 | −0.0843006 | ||||||||
\(306\) | 28.6955 | 1.64041 | ||||||||
\(307\) | −2.52879 | −0.144325 | −0.0721627 | − | 0.997393i | \(-0.522990\pi\) | ||||
−0.0721627 | + | 0.997393i | \(0.522990\pi\) | |||||||
\(308\) | 0.699364 | 0.0398500 | ||||||||
\(309\) | −51.0232 | −2.90261 | ||||||||
\(310\) | −6.38950 | −0.362899 | ||||||||
\(311\) | 8.00889 | 0.454143 | 0.227071 | − | 0.973878i | \(-0.427085\pi\) | ||||
0.227071 | + | 0.973878i | \(0.427085\pi\) | |||||||
\(312\) | 27.1783 | 1.53867 | ||||||||
\(313\) | −18.7701 | −1.06095 | −0.530475 | − | 0.847700i | \(-0.677987\pi\) | ||||
−0.530475 | + | 0.847700i | \(0.677987\pi\) | |||||||
\(314\) | −59.6662 | −3.36716 | ||||||||
\(315\) | 1.74719 | 0.0984431 | ||||||||
\(316\) | −44.7226 | −2.51584 | ||||||||
\(317\) | −2.58701 | −0.145301 | −0.0726505 | − | 0.997357i | \(-0.523146\pi\) | ||||
−0.0726505 | + | 0.997357i | \(0.523146\pi\) | |||||||
\(318\) | 49.3272 | 2.76613 | ||||||||
\(319\) | −0.552831 | −0.0309526 | ||||||||
\(320\) | −9.29384 | −0.519542 | ||||||||
\(321\) | 41.4818 | 2.31529 | ||||||||
\(322\) | 10.2754 | 0.572624 | ||||||||
\(323\) | −1.02058 | −0.0567865 | ||||||||
\(324\) | 30.6540 | 1.70300 | ||||||||
\(325\) | 4.88462 | 0.270950 | ||||||||
\(326\) | −0.153477 | −0.00850031 | ||||||||
\(327\) | 11.9511 | 0.660896 | ||||||||
\(328\) | −72.3218 | −3.99330 | ||||||||
\(329\) | −0.378972 | −0.0208934 | ||||||||
\(330\) | −0.383184 | −0.0210936 | ||||||||
\(331\) | −8.90017 | −0.489198 | −0.244599 | − | 0.969624i | \(-0.578656\pi\) | ||||
−0.244599 | + | 0.969624i | \(0.578656\pi\) | |||||||
\(332\) | −47.2023 | −2.59056 | ||||||||
\(333\) | −29.4650 | −1.61467 | ||||||||
\(334\) | −40.6714 | −2.22544 | ||||||||
\(335\) | 1.69051 | 0.0923624 | ||||||||
\(336\) | −38.6959 | −2.11103 | ||||||||
\(337\) | −30.3247 | −1.65189 | −0.825945 | − | 0.563751i | \(-0.809358\pi\) | ||||
−0.825945 | + | 0.563751i | \(0.809358\pi\) | |||||||
\(338\) | −2.72092 | −0.147998 | ||||||||
\(339\) | 6.95882 | 0.377951 | ||||||||
\(340\) | 3.44811 | 0.187000 | ||||||||
\(341\) | 0.976570 | 0.0528842 | ||||||||
\(342\) | −8.29798 | −0.448703 | ||||||||
\(343\) | 12.0583 | 0.651086 | ||||||||
\(344\) | −15.0923 | −0.813724 | ||||||||
\(345\) | −4.10901 | −0.221222 | ||||||||
\(346\) | −26.9799 | −1.45045 | ||||||||
\(347\) | 23.4907 | 1.26105 | 0.630523 | − | 0.776171i | \(-0.282841\pi\) | ||||
0.630523 | + | 0.776171i | \(0.282841\pi\) | |||||||
\(348\) | 62.0627 | 3.32691 | ||||||||
\(349\) | 12.5047 | 0.669363 | 0.334681 | − | 0.942331i | \(-0.391371\pi\) | ||||
0.334681 | + | 0.942331i | \(0.391371\pi\) | |||||||
\(350\) | −12.1775 | −0.650916 | ||||||||
\(351\) | −7.67121 | −0.409459 | ||||||||
\(352\) | 2.91462 | 0.155350 | ||||||||
\(353\) | −29.4684 | −1.56845 | −0.784223 | − | 0.620479i | \(-0.786938\pi\) | ||||
−0.784223 | + | 0.620479i | \(0.786938\pi\) | |||||||
\(354\) | 89.6536 | 4.76503 | ||||||||
\(355\) | 3.87651 | 0.205744 | ||||||||
\(356\) | −0.929206 | −0.0492478 | ||||||||
\(357\) | 5.05189 | 0.267375 | ||||||||
\(358\) | −17.6271 | −0.931623 | ||||||||
\(359\) | −27.6530 | −1.45947 | −0.729734 | − | 0.683731i | \(-0.760356\pi\) | ||||
−0.729734 | + | 0.683731i | \(0.760356\pi\) | |||||||
\(360\) | 17.6585 | 0.930683 | ||||||||
\(361\) | −18.7049 | −0.984467 | ||||||||
\(362\) | 35.2060 | 1.85039 | ||||||||
\(363\) | −32.2256 | −1.69140 | ||||||||
\(364\) | 4.95085 | 0.259495 | ||||||||
\(365\) | −0.728889 | −0.0381518 | ||||||||
\(366\) | −34.6115 | −1.80917 | ||||||||
\(367\) | 1.64682 | 0.0859631 | 0.0429816 | − | 0.999076i | \(-0.486314\pi\) | ||||
0.0429816 | + | 0.999076i | \(0.486314\pi\) | |||||||
\(368\) | 59.3094 | 3.09172 | ||||||||
\(369\) | 43.8428 | 2.28236 | ||||||||
\(370\) | −4.85109 | −0.252196 | ||||||||
\(371\) | 5.65963 | 0.293833 | ||||||||
\(372\) | −109.633 | −5.68421 | ||||||||
\(373\) | −5.79690 | −0.300152 | −0.150076 | − | 0.988674i | \(-0.547952\pi\) | ||||
−0.150076 | + | 0.988674i | \(0.547952\pi\) | |||||||
\(374\) | −0.722076 | −0.0373376 | ||||||||
\(375\) | 9.85436 | 0.508877 | ||||||||
\(376\) | −3.83019 | −0.197527 | ||||||||
\(377\) | −3.91353 | −0.201557 | ||||||||
\(378\) | 19.1246 | 0.983664 | ||||||||
\(379\) | −4.99393 | −0.256521 | −0.128261 | − | 0.991741i | \(-0.540939\pi\) | ||||
−0.128261 | + | 0.991741i | \(0.540939\pi\) | |||||||
\(380\) | −0.997104 | −0.0511504 | ||||||||
\(381\) | 64.3604 | 3.29728 | ||||||||
\(382\) | 13.4973 | 0.690584 | ||||||||
\(383\) | 19.7483 | 1.00909 | 0.504545 | − | 0.863386i | \(-0.331660\pi\) | ||||
0.504545 | + | 0.863386i | \(0.331660\pi\) | |||||||
\(384\) | −97.3806 | −4.96943 | ||||||||
\(385\) | −0.0439652 | −0.00224068 | ||||||||
\(386\) | −7.29265 | −0.371186 | ||||||||
\(387\) | 9.14924 | 0.465082 | ||||||||
\(388\) | −1.50633 | −0.0764722 | ||||||||
\(389\) | −37.7425 | −1.91362 | −0.956811 | − | 0.290709i | \(-0.906109\pi\) | ||||
−0.956811 | + | 0.290709i | \(0.906109\pi\) | |||||||
\(390\) | −2.71259 | −0.137357 | ||||||||
\(391\) | −7.74306 | −0.391583 | ||||||||
\(392\) | 57.0481 | 2.88136 | ||||||||
\(393\) | −11.8331 | −0.596900 | ||||||||
\(394\) | 6.13637 | 0.309146 | ||||||||
\(395\) | 2.81147 | 0.141460 | ||||||||
\(396\) | −4.28494 | −0.215326 | ||||||||
\(397\) | −12.7327 | −0.639034 | −0.319517 | − | 0.947581i | \(-0.603521\pi\) | ||||
−0.319517 | + | 0.947581i | \(0.603521\pi\) | |||||||
\(398\) | 45.6146 | 2.28646 | ||||||||
\(399\) | −1.46087 | −0.0731352 | ||||||||
\(400\) | −70.2886 | −3.51443 | ||||||||
\(401\) | 26.2938 | 1.31305 | 0.656525 | − | 0.754304i | \(-0.272026\pi\) | ||||
0.656525 | + | 0.754304i | \(0.272026\pi\) | |||||||
\(402\) | 39.7427 | 1.98219 | ||||||||
\(403\) | 6.91321 | 0.344371 | ||||||||
\(404\) | −21.9195 | −1.09054 | ||||||||
\(405\) | −1.92705 | −0.0957559 | ||||||||
\(406\) | 9.75657 | 0.484210 | ||||||||
\(407\) | 0.741440 | 0.0367518 | ||||||||
\(408\) | 51.0583 | 2.52776 | ||||||||
\(409\) | −12.4813 | −0.617159 | −0.308579 | − | 0.951199i | \(-0.599854\pi\) | ||||
−0.308579 | + | 0.951199i | \(0.599854\pi\) | |||||||
\(410\) | 7.21823 | 0.356483 | ||||||||
\(411\) | 17.4587 | 0.861177 | ||||||||
\(412\) | −93.9371 | −4.62795 | ||||||||
\(413\) | 10.2865 | 0.506168 | ||||||||
\(414\) | −62.9562 | −3.09413 | ||||||||
\(415\) | 2.96735 | 0.145662 | ||||||||
\(416\) | 20.6328 | 1.01160 | ||||||||
\(417\) | −59.6928 | −2.92317 | ||||||||
\(418\) | 0.208805 | 0.0102130 | ||||||||
\(419\) | 8.91406 | 0.435480 | 0.217740 | − | 0.976007i | \(-0.430131\pi\) | ||||
0.217740 | + | 0.976007i | \(0.430131\pi\) | |||||||
\(420\) | 4.93569 | 0.240837 | ||||||||
\(421\) | 36.5538 | 1.78152 | 0.890761 | − | 0.454471i | \(-0.150172\pi\) | ||||
0.890761 | + | 0.454471i | \(0.150172\pi\) | |||||||
\(422\) | 33.9919 | 1.65470 | ||||||||
\(423\) | 2.32193 | 0.112896 | ||||||||
\(424\) | 57.2006 | 2.77791 | ||||||||
\(425\) | 9.17644 | 0.445123 | ||||||||
\(426\) | 91.1340 | 4.41546 | ||||||||
\(427\) | −3.97121 | −0.192180 | ||||||||
\(428\) | 76.3707 | 3.69152 | ||||||||
\(429\) | 0.414592 | 0.0200167 | ||||||||
\(430\) | 1.50632 | 0.0726413 | ||||||||
\(431\) | −22.3038 | −1.07433 | −0.537167 | − | 0.843476i | \(-0.680505\pi\) | ||||
−0.537167 | + | 0.843476i | \(0.680505\pi\) | |||||||
\(432\) | 110.387 | 5.31101 | ||||||||
\(433\) | −9.22629 | −0.443387 | −0.221694 | − | 0.975116i | \(-0.571158\pi\) | ||||
−0.221694 | + | 0.975116i | \(0.571158\pi\) | |||||||
\(434\) | −17.2349 | −0.827301 | ||||||||
\(435\) | −3.90155 | −0.187065 | ||||||||
\(436\) | 22.0027 | 1.05374 | ||||||||
\(437\) | 2.23909 | 0.107110 | ||||||||
\(438\) | −17.1357 | −0.818774 | ||||||||
\(439\) | −22.3566 | −1.06702 | −0.533510 | − | 0.845794i | \(-0.679127\pi\) | ||||
−0.533510 | + | 0.845794i | \(0.679127\pi\) | |||||||
\(440\) | −0.444347 | −0.0211834 | ||||||||
\(441\) | −34.5836 | −1.64684 | ||||||||
\(442\) | −5.11162 | −0.243135 | ||||||||
\(443\) | −15.7742 | −0.749455 | −0.374728 | − | 0.927135i | \(-0.622264\pi\) | ||||
−0.374728 | + | 0.927135i | \(0.622264\pi\) | |||||||
\(444\) | −83.2367 | −3.95024 | ||||||||
\(445\) | 0.0584141 | 0.00276910 | ||||||||
\(446\) | −28.2341 | −1.33692 | ||||||||
\(447\) | 48.8136 | 2.30880 | ||||||||
\(448\) | −25.0690 | −1.18440 | ||||||||
\(449\) | −16.5762 | −0.782281 | −0.391140 | − | 0.920331i | \(-0.627919\pi\) | ||||
−0.391140 | + | 0.920331i | \(0.627919\pi\) | |||||||
\(450\) | 74.6106 | 3.51718 | ||||||||
\(451\) | −1.10323 | −0.0519492 | ||||||||
\(452\) | 12.8116 | 0.602609 | ||||||||
\(453\) | −31.8205 | −1.49506 | ||||||||
\(454\) | 44.6882 | 2.09732 | ||||||||
\(455\) | −0.311233 | −0.0145908 | ||||||||
\(456\) | −14.7647 | −0.691422 | ||||||||
\(457\) | 0.632841 | 0.0296031 | 0.0148015 | − | 0.999890i | \(-0.495288\pi\) | ||||
0.0148015 | + | 0.999890i | \(0.495288\pi\) | |||||||
\(458\) | −13.0225 | −0.608502 | ||||||||
\(459\) | −14.4115 | −0.672669 | ||||||||
\(460\) | −7.56496 | −0.352718 | ||||||||
\(461\) | 12.6252 | 0.588014 | 0.294007 | − | 0.955803i | \(-0.405011\pi\) | ||||
0.294007 | + | 0.955803i | \(0.405011\pi\) | |||||||
\(462\) | −1.03359 | −0.0480871 | ||||||||
\(463\) | 12.4025 | 0.576395 | 0.288198 | − | 0.957571i | \(-0.406944\pi\) | ||||
0.288198 | + | 0.957571i | \(0.406944\pi\) | |||||||
\(464\) | 56.3148 | 2.61435 | ||||||||
\(465\) | 6.89205 | 0.319611 | ||||||||
\(466\) | 12.2053 | 0.565399 | ||||||||
\(467\) | −14.9898 | −0.693646 | −0.346823 | − | 0.937931i | \(-0.612740\pi\) | ||||
−0.346823 | + | 0.937931i | \(0.612740\pi\) | |||||||
\(468\) | −30.3334 | −1.40216 | ||||||||
\(469\) | 4.55994 | 0.210559 | ||||||||
\(470\) | 0.382280 | 0.0176332 | ||||||||
\(471\) | 64.3591 | 2.96551 | ||||||||
\(472\) | 103.964 | 4.78532 | ||||||||
\(473\) | −0.230226 | −0.0105858 | ||||||||
\(474\) | 66.0956 | 3.03587 | ||||||||
\(475\) | −2.65359 | −0.121755 | ||||||||
\(476\) | 9.30086 | 0.426304 | ||||||||
\(477\) | −34.6760 | −1.58771 | ||||||||
\(478\) | 36.2451 | 1.65781 | ||||||||
\(479\) | 32.8969 | 1.50310 | 0.751548 | − | 0.659678i | \(-0.229307\pi\) | ||||
0.751548 | + | 0.659678i | \(0.229307\pi\) | |||||||
\(480\) | 20.5696 | 0.938870 | ||||||||
\(481\) | 5.24871 | 0.239320 | ||||||||
\(482\) | 16.7015 | 0.760734 | ||||||||
\(483\) | −11.0836 | −0.504319 | ||||||||
\(484\) | −59.3294 | −2.69679 | ||||||||
\(485\) | 0.0946947 | 0.00429986 | ||||||||
\(486\) | 17.3146 | 0.785405 | ||||||||
\(487\) | 16.0678 | 0.728100 | 0.364050 | − | 0.931379i | \(-0.381394\pi\) | ||||
0.364050 | + | 0.931379i | \(0.381394\pi\) | |||||||
\(488\) | −40.1361 | −1.81687 | ||||||||
\(489\) | 0.165548 | 0.00748636 | ||||||||
\(490\) | −5.69380 | −0.257220 | ||||||||
\(491\) | −4.82964 | −0.217959 | −0.108979 | − | 0.994044i | \(-0.534758\pi\) | ||||
−0.108979 | + | 0.994044i | \(0.534758\pi\) | |||||||
\(492\) | 123.853 | 5.58371 | ||||||||
\(493\) | −7.35211 | −0.331123 | ||||||||
\(494\) | 1.47815 | 0.0665050 | ||||||||
\(495\) | 0.269371 | 0.0121073 | ||||||||
\(496\) | −99.4796 | −4.46677 | ||||||||
\(497\) | 10.4564 | 0.469034 | ||||||||
\(498\) | 69.7604 | 3.12604 | ||||||||
\(499\) | 25.2221 | 1.12910 | 0.564549 | − | 0.825400i | \(-0.309050\pi\) | ||||
0.564549 | + | 0.825400i | \(0.309050\pi\) | |||||||
\(500\) | 18.1425 | 0.811358 | ||||||||
\(501\) | 43.8703 | 1.95998 | ||||||||
\(502\) | −14.1706 | −0.632467 | ||||||||
\(503\) | 37.3377 | 1.66480 | 0.832402 | − | 0.554172i | \(-0.186965\pi\) | ||||
0.832402 | + | 0.554172i | \(0.186965\pi\) | |||||||
\(504\) | 47.6315 | 2.12168 | ||||||||
\(505\) | 1.37796 | 0.0613185 | ||||||||
\(506\) | 1.58419 | 0.0704259 | ||||||||
\(507\) | 2.93492 | 0.130344 | ||||||||
\(508\) | 118.492 | 5.25722 | ||||||||
\(509\) | 2.30116 | 0.101997 | 0.0509986 | − | 0.998699i | \(-0.483760\pi\) | ||||
0.0509986 | + | 0.998699i | \(0.483760\pi\) | |||||||
\(510\) | −5.09598 | −0.225654 | ||||||||
\(511\) | −1.96609 | −0.0869746 | ||||||||
\(512\) | −30.3931 | −1.34320 | ||||||||
\(513\) | 4.16741 | 0.183996 | ||||||||
\(514\) | −52.4542 | −2.31365 | ||||||||
\(515\) | 5.90532 | 0.260220 | ||||||||
\(516\) | 25.8460 | 1.13781 | ||||||||
\(517\) | −0.0584276 | −0.00256964 | ||||||||
\(518\) | −13.0852 | −0.574932 | ||||||||
\(519\) | 29.1020 | 1.27744 | ||||||||
\(520\) | −3.14556 | −0.137942 | ||||||||
\(521\) | 18.4466 | 0.808162 | 0.404081 | − | 0.914723i | \(-0.367591\pi\) | ||||
0.404081 | + | 0.914723i | \(0.367591\pi\) | |||||||
\(522\) | −59.7776 | −2.61639 | ||||||||
\(523\) | 14.6846 | 0.642114 | 0.321057 | − | 0.947060i | \(-0.395962\pi\) | ||||
0.321057 | + | 0.947060i | \(0.395962\pi\) | |||||||
\(524\) | −21.7855 | −0.951703 | ||||||||
\(525\) | 13.1353 | 0.573272 | ||||||||
\(526\) | −36.7490 | −1.60233 | ||||||||
\(527\) | 12.9874 | 0.565741 | ||||||||
\(528\) | −5.96589 | −0.259632 | ||||||||
\(529\) | −6.01217 | −0.261399 | ||||||||
\(530\) | −5.70902 | −0.247984 | ||||||||
\(531\) | −63.0247 | −2.73504 | ||||||||
\(532\) | −2.68957 | −0.116607 | ||||||||
\(533\) | −7.80986 | −0.338283 | ||||||||
\(534\) | 1.37328 | 0.0594275 | ||||||||
\(535\) | −4.80102 | −0.207566 | ||||||||
\(536\) | 46.0863 | 1.99063 | ||||||||
\(537\) | 19.0135 | 0.820495 | ||||||||
\(538\) | −50.0206 | −2.15654 | ||||||||
\(539\) | 0.870240 | 0.0374839 | ||||||||
\(540\) | −14.0800 | −0.605906 | ||||||||
\(541\) | −31.3502 | −1.34785 | −0.673925 | − | 0.738800i | \(-0.735393\pi\) | ||||
−0.673925 | + | 0.738800i | \(0.735393\pi\) | |||||||
\(542\) | 5.12838 | 0.220283 | ||||||||
\(543\) | −37.9750 | −1.62967 | ||||||||
\(544\) | 38.7616 | 1.66189 | ||||||||
\(545\) | −1.38319 | −0.0592494 | ||||||||
\(546\) | −7.31687 | −0.313133 | ||||||||
\(547\) | 9.37126 | 0.400686 | 0.200343 | − | 0.979726i | \(-0.435794\pi\) | ||||
0.200343 | + | 0.979726i | \(0.435794\pi\) | |||||||
\(548\) | 32.1427 | 1.37307 | ||||||||
\(549\) | 24.3312 | 1.03843 | ||||||||
\(550\) | −1.87745 | −0.0800549 | ||||||||
\(551\) | 2.12604 | 0.0905723 | ||||||||
\(552\) | −112.019 | −4.76785 | ||||||||
\(553\) | 7.58359 | 0.322487 | ||||||||
\(554\) | 29.1770 | 1.23961 | ||||||||
\(555\) | 5.23264 | 0.222113 | ||||||||
\(556\) | −109.898 | −4.66073 | ||||||||
\(557\) | −10.4499 | −0.442774 | −0.221387 | − | 0.975186i | \(-0.571058\pi\) | ||||
−0.221387 | + | 0.975186i | \(0.571058\pi\) | |||||||
\(558\) | 105.596 | 4.47025 | ||||||||
\(559\) | −1.62979 | −0.0689326 | ||||||||
\(560\) | 4.47858 | 0.189255 | ||||||||
\(561\) | 0.778869 | 0.0328839 | ||||||||
\(562\) | 21.1397 | 0.891724 | ||||||||
\(563\) | −2.82873 | −0.119217 | −0.0596085 | − | 0.998222i | \(-0.518985\pi\) | ||||
−0.0596085 | + | 0.998222i | \(0.518985\pi\) | |||||||
\(564\) | 6.55928 | 0.276196 | ||||||||
\(565\) | −0.805399 | −0.0338834 | ||||||||
\(566\) | 44.6204 | 1.87554 | ||||||||
\(567\) | −5.19798 | −0.218295 | ||||||||
\(568\) | 105.680 | 4.43425 | ||||||||
\(569\) | −5.71832 | −0.239724 | −0.119862 | − | 0.992791i | \(-0.538245\pi\) | ||||
−0.119862 | + | 0.992791i | \(0.538245\pi\) | |||||||
\(570\) | 1.47362 | 0.0617233 | ||||||||
\(571\) | 3.46274 | 0.144911 | 0.0724555 | − | 0.997372i | \(-0.476916\pi\) | ||||
0.0724555 | + | 0.997372i | \(0.476916\pi\) | |||||||
\(572\) | 0.763290 | 0.0319148 | ||||||||
\(573\) | −14.5589 | −0.608208 | ||||||||
\(574\) | 19.4703 | 0.812673 | ||||||||
\(575\) | −20.1326 | −0.839587 | ||||||||
\(576\) | 153.595 | 6.39980 | ||||||||
\(577\) | 25.6526 | 1.06793 | 0.533966 | − | 0.845506i | \(-0.320701\pi\) | ||||
0.533966 | + | 0.845506i | \(0.320701\pi\) | |||||||
\(578\) | 36.6527 | 1.52455 | ||||||||
\(579\) | 7.86623 | 0.326909 | ||||||||
\(580\) | −7.18301 | −0.298258 | ||||||||
\(581\) | 8.00407 | 0.332065 | ||||||||
\(582\) | 2.22621 | 0.0922792 | ||||||||
\(583\) | 0.872566 | 0.0361380 | ||||||||
\(584\) | −19.8708 | −0.822259 | ||||||||
\(585\) | 1.90689 | 0.0788404 | ||||||||
\(586\) | 57.7331 | 2.38493 | ||||||||
\(587\) | −25.9961 | −1.07298 | −0.536488 | − | 0.843908i | \(-0.680249\pi\) | ||||
−0.536488 | + | 0.843908i | \(0.680249\pi\) | |||||||
\(588\) | −97.6962 | −4.02892 | ||||||||
\(589\) | −3.75562 | −0.154748 | ||||||||
\(590\) | −10.3763 | −0.427186 | ||||||||
\(591\) | −6.61901 | −0.272270 | ||||||||
\(592\) | −75.5278 | −3.10417 | ||||||||
\(593\) | −15.5139 | −0.637078 | −0.318539 | − | 0.947910i | \(-0.603192\pi\) | ||||
−0.318539 | + | 0.947910i | \(0.603192\pi\) | |||||||
\(594\) | 2.94851 | 0.120979 | ||||||||
\(595\) | −0.584695 | −0.0239702 | ||||||||
\(596\) | 89.8690 | 3.68118 | ||||||||
\(597\) | −49.2023 | −2.01372 | ||||||||
\(598\) | 11.2146 | 0.458599 | ||||||||
\(599\) | −35.8101 | −1.46316 | −0.731581 | − | 0.681755i | \(-0.761217\pi\) | ||||
−0.731581 | + | 0.681755i | \(0.761217\pi\) | |||||||
\(600\) | 132.756 | 5.41973 | ||||||||
\(601\) | 21.9562 | 0.895613 | 0.447807 | − | 0.894130i | \(-0.352205\pi\) | ||||
0.447807 | + | 0.894130i | \(0.352205\pi\) | |||||||
\(602\) | 4.06312 | 0.165600 | ||||||||
\(603\) | −27.9383 | −1.13774 | ||||||||
\(604\) | −58.5836 | −2.38373 | ||||||||
\(605\) | 3.72972 | 0.151635 | ||||||||
\(606\) | 32.3949 | 1.31595 | ||||||||
\(607\) | −23.8046 | −0.966199 | −0.483100 | − | 0.875565i | \(-0.660489\pi\) | ||||
−0.483100 | + | 0.875565i | \(0.660489\pi\) | |||||||
\(608\) | −11.2088 | −0.454578 | ||||||||
\(609\) | −10.5239 | −0.426452 | ||||||||
\(610\) | 4.00586 | 0.162193 | ||||||||
\(611\) | −0.413613 | −0.0167330 | ||||||||
\(612\) | −56.9855 | −2.30350 | ||||||||
\(613\) | 33.7696 | 1.36394 | 0.681971 | − | 0.731379i | \(-0.261123\pi\) | ||||
0.681971 | + | 0.731379i | \(0.261123\pi\) | |||||||
\(614\) | 6.88062 | 0.277679 | ||||||||
\(615\) | −7.78596 | −0.313960 | ||||||||
\(616\) | −1.19857 | −0.0482918 | ||||||||
\(617\) | −1.00000 | −0.0402585 | ||||||||
\(618\) | 138.830 | 5.58456 | ||||||||
\(619\) | 18.0793 | 0.726668 | 0.363334 | − | 0.931659i | \(-0.381638\pi\) | ||||
0.363334 | + | 0.931659i | \(0.381638\pi\) | |||||||
\(620\) | 12.6887 | 0.509591 | ||||||||
\(621\) | 31.6179 | 1.26878 | ||||||||
\(622\) | −21.7915 | −0.873760 | ||||||||
\(623\) | 0.157565 | 0.00631271 | ||||||||
\(624\) | −42.2329 | −1.69067 | ||||||||
\(625\) | 23.2826 | 0.931302 | ||||||||
\(626\) | 51.0720 | 2.04125 | ||||||||
\(627\) | −0.225228 | −0.00899475 | ||||||||
\(628\) | 118.489 | 4.72824 | ||||||||
\(629\) | 9.86044 | 0.393161 | ||||||||
\(630\) | −4.75396 | −0.189402 | ||||||||
\(631\) | 3.45034 | 0.137356 | 0.0686780 | − | 0.997639i | \(-0.478122\pi\) | ||||
0.0686780 | + | 0.997639i | \(0.478122\pi\) | |||||||
\(632\) | 76.6456 | 3.04880 | ||||||||
\(633\) | −36.6654 | −1.45732 | ||||||||
\(634\) | 7.03904 | 0.279556 | ||||||||
\(635\) | −7.44893 | −0.295602 | ||||||||
\(636\) | −97.9573 | −3.88426 | ||||||||
\(637\) | 6.16049 | 0.244087 | ||||||||
\(638\) | 1.50421 | 0.0595521 | ||||||||
\(639\) | −64.0654 | −2.53439 | ||||||||
\(640\) | 11.2706 | 0.445510 | ||||||||
\(641\) | 10.0031 | 0.395100 | 0.197550 | − | 0.980293i | \(-0.436701\pi\) | ||||
0.197550 | + | 0.980293i | \(0.436701\pi\) | |||||||
\(642\) | −112.869 | −4.45457 | ||||||||
\(643\) | −14.6630 | −0.578252 | −0.289126 | − | 0.957291i | \(-0.593365\pi\) | ||||
−0.289126 | + | 0.957291i | \(0.593365\pi\) | |||||||
\(644\) | −20.4056 | −0.804092 | ||||||||
\(645\) | −1.62480 | −0.0639763 | ||||||||
\(646\) | 2.77691 | 0.109256 | ||||||||
\(647\) | −5.28800 | −0.207893 | −0.103946 | − | 0.994583i | \(-0.533147\pi\) | ||||
−0.103946 | + | 0.994583i | \(0.533147\pi\) | |||||||
\(648\) | −52.5348 | −2.06376 | ||||||||
\(649\) | 1.58591 | 0.0622526 | ||||||||
\(650\) | −13.2906 | −0.521301 | ||||||||
\(651\) | 18.5904 | 0.728617 | ||||||||
\(652\) | 0.304785 | 0.0119363 | ||||||||
\(653\) | 7.61096 | 0.297840 | 0.148920 | − | 0.988849i | \(-0.452420\pi\) | ||||
0.148920 | + | 0.988849i | \(0.452420\pi\) | |||||||
\(654\) | −32.5179 | −1.27155 | ||||||||
\(655\) | 1.36954 | 0.0535122 | ||||||||
\(656\) | 112.382 | 4.38779 | ||||||||
\(657\) | 12.0460 | 0.469960 | ||||||||
\(658\) | 1.03115 | 0.0401985 | ||||||||
\(659\) | −10.8727 | −0.423541 | −0.211771 | − | 0.977319i | \(-0.567923\pi\) | ||||
−0.211771 | + | 0.977319i | \(0.567923\pi\) | |||||||
\(660\) | 0.760954 | 0.0296201 | ||||||||
\(661\) | −32.9464 | −1.28146 | −0.640732 | − | 0.767764i | \(-0.721369\pi\) | ||||
−0.640732 | + | 0.767764i | \(0.721369\pi\) | |||||||
\(662\) | 24.2166 | 0.941206 | ||||||||
\(663\) | 5.51367 | 0.214133 | ||||||||
\(664\) | 80.8953 | 3.13935 | ||||||||
\(665\) | 0.169078 | 0.00655658 | ||||||||
\(666\) | 80.1719 | 3.10660 | ||||||||
\(667\) | 16.1301 | 0.624560 | ||||||||
\(668\) | 80.7681 | 3.12501 | ||||||||
\(669\) | 30.4548 | 1.17745 | ||||||||
\(670\) | −4.59974 | −0.177703 | ||||||||
\(671\) | −0.612255 | −0.0236358 | ||||||||
\(672\) | 55.4840 | 2.14034 | ||||||||
\(673\) | 23.1745 | 0.893312 | 0.446656 | − | 0.894706i | \(-0.352615\pi\) | ||||
0.446656 | + | 0.894706i | \(0.352615\pi\) | |||||||
\(674\) | 82.5109 | 3.17820 | ||||||||
\(675\) | −37.4709 | −1.44226 | ||||||||
\(676\) | 5.40338 | 0.207822 | ||||||||
\(677\) | 44.7560 | 1.72011 | 0.860057 | − | 0.510199i | \(-0.170428\pi\) | ||||
0.860057 | + | 0.510199i | \(0.170428\pi\) | |||||||
\(678\) | −18.9344 | −0.727170 | ||||||||
\(679\) | 0.255427 | 0.00980240 | ||||||||
\(680\) | −5.90938 | −0.226614 | ||||||||
\(681\) | −48.2030 | −1.84714 | ||||||||
\(682\) | −2.65716 | −0.101748 | ||||||||
\(683\) | −20.7697 | −0.794729 | −0.397364 | − | 0.917661i | \(-0.630075\pi\) | ||||
−0.397364 | + | 0.917661i | \(0.630075\pi\) | |||||||
\(684\) | 16.4787 | 0.630079 | ||||||||
\(685\) | −2.02064 | −0.0772046 | ||||||||
\(686\) | −32.8096 | −1.25268 | ||||||||
\(687\) | 14.0468 | 0.535917 | ||||||||
\(688\) | 23.4523 | 0.894109 | ||||||||
\(689\) | 6.17696 | 0.235323 | ||||||||
\(690\) | 11.1803 | 0.425626 | ||||||||
\(691\) | −13.7788 | −0.524171 | −0.262086 | − | 0.965045i | \(-0.584410\pi\) | ||||
−0.262086 | + | 0.965045i | \(0.584410\pi\) | |||||||
\(692\) | 53.5786 | 2.03675 | ||||||||
\(693\) | 0.726594 | 0.0276010 | ||||||||
\(694\) | −63.9161 | −2.42622 | ||||||||
\(695\) | 6.90872 | 0.262063 | ||||||||
\(696\) | −106.363 | −4.03168 | ||||||||
\(697\) | −14.6719 | −0.555739 | ||||||||
\(698\) | −34.0243 | −1.28784 | ||||||||
\(699\) | −13.1653 | −0.497956 | ||||||||
\(700\) | 24.1830 | 0.914031 | ||||||||
\(701\) | −7.94853 | −0.300212 | −0.150106 | − | 0.988670i | \(-0.547961\pi\) | ||||
−0.150106 | + | 0.988670i | \(0.547961\pi\) | |||||||
\(702\) | 20.8727 | 0.787790 | ||||||||
\(703\) | −2.85138 | −0.107542 | ||||||||
\(704\) | −3.86498 | −0.145667 | ||||||||
\(705\) | −0.412347 | −0.0155299 | ||||||||
\(706\) | 80.1811 | 3.01766 | ||||||||
\(707\) | 3.71688 | 0.139788 | ||||||||
\(708\) | −178.040 | −6.69116 | ||||||||
\(709\) | −28.1949 | −1.05888 | −0.529440 | − | 0.848347i | \(-0.677598\pi\) | ||||
−0.529440 | + | 0.848347i | \(0.677598\pi\) | |||||||
\(710\) | −10.5477 | −0.395846 | ||||||||
\(711\) | −46.4639 | −1.74253 | ||||||||
\(712\) | 1.59247 | 0.0596805 | ||||||||
\(713\) | −28.4937 | −1.06710 | ||||||||
\(714\) | −13.7458 | −0.514423 | ||||||||
\(715\) | −0.0479839 | −0.00179450 | ||||||||
\(716\) | 35.0052 | 1.30820 | ||||||||
\(717\) | −39.0958 | −1.46006 | ||||||||
\(718\) | 75.2414 | 2.80798 | ||||||||
\(719\) | −1.20833 | −0.0450633 | −0.0225316 | − | 0.999746i | \(-0.507173\pi\) | ||||
−0.0225316 | + | 0.999746i | \(0.507173\pi\) | |||||||
\(720\) | −27.4398 | −1.02262 | ||||||||
\(721\) | 15.9289 | 0.593222 | ||||||||
\(722\) | 50.8944 | 1.89409 | ||||||||
\(723\) | −18.0151 | −0.669990 | ||||||||
\(724\) | −69.9145 | −2.59835 | ||||||||
\(725\) | −19.1161 | −0.709953 | ||||||||
\(726\) | 87.6831 | 3.25423 | ||||||||
\(727\) | −38.9710 | −1.44535 | −0.722677 | − | 0.691186i | \(-0.757089\pi\) | ||||
−0.722677 | + | 0.691186i | \(0.757089\pi\) | |||||||
\(728\) | −8.48476 | −0.314466 | ||||||||
\(729\) | −35.6957 | −1.32206 | ||||||||
\(730\) | 1.98324 | 0.0734032 | ||||||||
\(731\) | −3.06178 | −0.113244 | ||||||||
\(732\) | 68.7339 | 2.54048 | ||||||||
\(733\) | 9.17060 | 0.338724 | 0.169362 | − | 0.985554i | \(-0.445829\pi\) | ||||
0.169362 | + | 0.985554i | \(0.445829\pi\) | |||||||
\(734\) | −4.48085 | −0.165391 | ||||||||
\(735\) | 6.14163 | 0.226538 | ||||||||
\(736\) | −85.0406 | −3.13464 | ||||||||
\(737\) | 0.703023 | 0.0258962 | ||||||||
\(738\) | −119.292 | −4.39122 | ||||||||
\(739\) | 9.34542 | 0.343777 | 0.171888 | − | 0.985116i | \(-0.445013\pi\) | ||||
0.171888 | + | 0.985116i | \(0.445013\pi\) | |||||||
\(740\) | 9.63364 | 0.354140 | ||||||||
\(741\) | −1.59441 | −0.0585720 | ||||||||
\(742\) | −15.3994 | −0.565329 | ||||||||
\(743\) | 30.4263 | 1.11623 | 0.558116 | − | 0.829763i | \(-0.311524\pi\) | ||||
0.558116 | + | 0.829763i | \(0.311524\pi\) | |||||||
\(744\) | 187.889 | 6.88836 | ||||||||
\(745\) | −5.64958 | −0.206985 | ||||||||
\(746\) | 15.7729 | 0.577486 | ||||||||
\(747\) | −49.0402 | −1.79429 | ||||||||
\(748\) | 1.43395 | 0.0524303 | ||||||||
\(749\) | −12.9502 | −0.473188 | ||||||||
\(750\) | −26.8129 | −0.979068 | ||||||||
\(751\) | 15.3942 | 0.561741 | 0.280870 | − | 0.959746i | \(-0.409377\pi\) | ||||
0.280870 | + | 0.959746i | \(0.409377\pi\) | |||||||
\(752\) | 5.95180 | 0.217040 | ||||||||
\(753\) | 15.2852 | 0.557024 | ||||||||
\(754\) | 10.6484 | 0.387791 | ||||||||
\(755\) | 3.68284 | 0.134032 | ||||||||
\(756\) | −37.9790 | −1.38128 | ||||||||
\(757\) | −0.0813838 | −0.00295794 | −0.00147897 | − | 0.999999i | \(-0.500471\pi\) | ||||
−0.00147897 | + | 0.999999i | \(0.500471\pi\) | |||||||
\(758\) | 13.5881 | 0.493541 | ||||||||
\(759\) | −1.70879 | −0.0620252 | ||||||||
\(760\) | 1.70884 | 0.0619861 | ||||||||
\(761\) | −23.0825 | −0.836739 | −0.418369 | − | 0.908277i | \(-0.637398\pi\) | ||||
−0.418369 | + | 0.908277i | \(0.637398\pi\) | |||||||
\(762\) | −175.119 | −6.34390 | ||||||||
\(763\) | −3.73099 | −0.135071 | ||||||||
\(764\) | −26.8039 | −0.969733 | ||||||||
\(765\) | 3.58237 | 0.129521 | ||||||||
\(766\) | −53.7334 | −1.94147 | ||||||||
\(767\) | 11.2268 | 0.405376 | ||||||||
\(768\) | 104.363 | 3.76587 | ||||||||
\(769\) | 22.6610 | 0.817178 | 0.408589 | − | 0.912718i | \(-0.366021\pi\) | ||||
0.408589 | + | 0.912718i | \(0.366021\pi\) | |||||||
\(770\) | 0.119626 | 0.00431101 | ||||||||
\(771\) | 56.5798 | 2.03767 | ||||||||
\(772\) | 14.4822 | 0.521228 | ||||||||
\(773\) | 13.6021 | 0.489235 | 0.244617 | − | 0.969620i | \(-0.421338\pi\) | ||||
0.244617 | + | 0.969620i | \(0.421338\pi\) | |||||||
\(774\) | −24.8943 | −0.894808 | ||||||||
\(775\) | 33.7684 | 1.21300 | ||||||||
\(776\) | 2.58154 | 0.0926720 | ||||||||
\(777\) | 14.1144 | 0.506352 | ||||||||
\(778\) | 102.694 | 3.68177 | ||||||||
\(779\) | 4.24273 | 0.152012 | ||||||||
\(780\) | 5.38685 | 0.192880 | ||||||||
\(781\) | 1.61210 | 0.0576855 | ||||||||
\(782\) | 21.0682 | 0.753398 | ||||||||
\(783\) | 30.0215 | 1.07288 | ||||||||
\(784\) | −88.6481 | −3.16600 | ||||||||
\(785\) | −7.44878 | −0.265859 | ||||||||
\(786\) | 32.1968 | 1.14842 | ||||||||
\(787\) | −43.2051 | −1.54010 | −0.770048 | − | 0.637986i | \(-0.779768\pi\) | ||||
−0.770048 | + | 0.637986i | \(0.779768\pi\) | |||||||
\(788\) | −12.1860 | −0.434109 | ||||||||
\(789\) | 39.6394 | 1.41120 | ||||||||
\(790\) | −7.64977 | −0.272167 | ||||||||
\(791\) | −2.17246 | −0.0772439 | ||||||||
\(792\) | 7.34352 | 0.260941 | ||||||||
\(793\) | −4.33420 | −0.153912 | ||||||||
\(794\) | 34.6445 | 1.22949 | ||||||||
\(795\) | 6.15805 | 0.218404 | ||||||||
\(796\) | −90.5847 | −3.21069 | ||||||||
\(797\) | −12.8182 | −0.454045 | −0.227023 | − | 0.973890i | \(-0.572899\pi\) | ||||
−0.227023 | + | 0.973890i | \(0.572899\pi\) | |||||||
\(798\) | 3.97492 | 0.140711 | ||||||||
\(799\) | −0.777030 | −0.0274893 | ||||||||
\(800\) | 100.783 | 3.56322 | ||||||||
\(801\) | −0.965385 | −0.0341102 | ||||||||
\(802\) | −71.5432 | −2.52628 | ||||||||
\(803\) | −0.303119 | −0.0106968 | ||||||||
\(804\) | −78.9238 | −2.78343 | ||||||||
\(805\) | 1.28279 | 0.0452123 | ||||||||
\(806\) | −18.8103 | −0.662563 | ||||||||
\(807\) | 53.9548 | 1.89930 | ||||||||
\(808\) | 37.5657 | 1.32156 | ||||||||
\(809\) | −41.5073 | −1.45932 | −0.729660 | − | 0.683810i | \(-0.760322\pi\) | ||||
−0.729660 | + | 0.683810i | \(0.760322\pi\) | |||||||
\(810\) | 5.24334 | 0.184232 | ||||||||
\(811\) | −24.6821 | −0.866705 | −0.433352 | − | 0.901225i | \(-0.642669\pi\) | ||||
−0.433352 | + | 0.901225i | \(0.642669\pi\) | |||||||
\(812\) | −19.3753 | −0.679939 | ||||||||
\(813\) | −5.53174 | −0.194007 | ||||||||
\(814\) | −2.01740 | −0.0707097 | ||||||||
\(815\) | −0.0191602 | −0.000671153 0 | ||||||||
\(816\) | −79.3405 | −2.77747 | ||||||||
\(817\) | 0.885387 | 0.0309758 | ||||||||
\(818\) | 33.9605 | 1.18740 | ||||||||
\(819\) | 5.14361 | 0.179732 | ||||||||
\(820\) | −14.3345 | −0.500581 | ||||||||
\(821\) | 39.0831 | 1.36401 | 0.682005 | − | 0.731348i | \(-0.261108\pi\) | ||||
0.682005 | + | 0.731348i | \(0.261108\pi\) | |||||||
\(822\) | −47.5038 | −1.65688 | ||||||||
\(823\) | 31.0180 | 1.08122 | 0.540609 | − | 0.841274i | \(-0.318194\pi\) | ||||
0.540609 | + | 0.841274i | \(0.318194\pi\) | |||||||
\(824\) | 160.989 | 5.60833 | ||||||||
\(825\) | 2.02512 | 0.0705056 | ||||||||
\(826\) | −27.9888 | −0.973856 | ||||||||
\(827\) | 24.2810 | 0.844333 | 0.422167 | − | 0.906518i | \(-0.361270\pi\) | ||||
0.422167 | + | 0.906518i | \(0.361270\pi\) | |||||||
\(828\) | 125.023 | 4.34484 | ||||||||
\(829\) | −17.7059 | −0.614951 | −0.307475 | − | 0.951556i | \(-0.599484\pi\) | ||||
−0.307475 | + | 0.951556i | \(0.599484\pi\) | |||||||
\(830\) | −8.07392 | −0.280250 | ||||||||
\(831\) | −31.4719 | −1.09175 | ||||||||
\(832\) | −27.3605 | −0.948553 | ||||||||
\(833\) | 11.5733 | 0.400993 | ||||||||
\(834\) | 162.419 | 5.62412 | ||||||||
\(835\) | −5.07746 | −0.175713 | ||||||||
\(836\) | −0.414660 | −0.0143413 | ||||||||
\(837\) | −53.0327 | −1.83308 | ||||||||
\(838\) | −24.2544 | −0.837855 | ||||||||
\(839\) | −27.7243 | −0.957148 | −0.478574 | − | 0.878047i | \(-0.658846\pi\) | ||||
−0.478574 | + | 0.878047i | \(0.658846\pi\) | |||||||
\(840\) | −8.45879 | −0.291856 | ||||||||
\(841\) | −13.6843 | −0.471873 | ||||||||
\(842\) | −99.4598 | −3.42761 | ||||||||
\(843\) | −22.8024 | −0.785356 | ||||||||
\(844\) | −67.5034 | −2.32356 | ||||||||
\(845\) | −0.339682 | −0.0116854 | ||||||||
\(846\) | −6.31777 | −0.217209 | ||||||||
\(847\) | 10.0605 | 0.345681 | ||||||||
\(848\) | −88.8851 | −3.05233 | ||||||||
\(849\) | −48.1300 | −1.65182 | ||||||||
\(850\) | −24.9683 | −0.856407 | ||||||||
\(851\) | −21.6332 | −0.741578 | ||||||||
\(852\) | −180.980 | −6.20028 | ||||||||
\(853\) | 31.2073 | 1.06852 | 0.534259 | − | 0.845321i | \(-0.320591\pi\) | ||||
0.534259 | + | 0.845321i | \(0.320591\pi\) | |||||||
\(854\) | 10.8053 | 0.369750 | ||||||||
\(855\) | −1.03593 | −0.0354280 | ||||||||
\(856\) | −130.884 | −4.47353 | ||||||||
\(857\) | −5.53797 | −0.189173 | −0.0945867 | − | 0.995517i | \(-0.530153\pi\) | ||||
−0.0945867 | + | 0.995517i | \(0.530153\pi\) | |||||||
\(858\) | −1.12807 | −0.0385116 | ||||||||
\(859\) | 22.4391 | 0.765612 | 0.382806 | − | 0.923829i | \(-0.374958\pi\) | ||||
0.382806 | + | 0.923829i | \(0.374958\pi\) | |||||||
\(860\) | −2.99136 | −0.102004 | ||||||||
\(861\) | −21.0017 | −0.715735 | ||||||||
\(862\) | 60.6866 | 2.06699 | ||||||||
\(863\) | 22.3406 | 0.760484 | 0.380242 | − | 0.924887i | \(-0.375841\pi\) | ||||
0.380242 | + | 0.924887i | \(0.375841\pi\) | |||||||
\(864\) | −158.278 | −5.38474 | ||||||||
\(865\) | −3.36820 | −0.114522 | ||||||||
\(866\) | 25.1040 | 0.853067 | ||||||||
\(867\) | −39.5355 | −1.34270 | ||||||||
\(868\) | 34.2262 | 1.16171 | ||||||||
\(869\) | 1.16919 | 0.0396620 | ||||||||
\(870\) | 10.6158 | 0.359909 | ||||||||
\(871\) | 4.97675 | 0.168631 | ||||||||
\(872\) | −37.7082 | −1.27696 | ||||||||
\(873\) | −1.56498 | −0.0529665 | ||||||||
\(874\) | −6.09238 | −0.206078 | ||||||||
\(875\) | −3.07642 | −0.104002 | ||||||||
\(876\) | 34.0292 | 1.14974 | ||||||||
\(877\) | 2.94357 | 0.0993972 | 0.0496986 | − | 0.998764i | \(-0.484174\pi\) | ||||
0.0496986 | + | 0.998764i | \(0.484174\pi\) | |||||||
\(878\) | 60.8303 | 2.05292 | ||||||||
\(879\) | −62.2739 | −2.10045 | ||||||||
\(880\) | 0.690479 | 0.0232760 | ||||||||
\(881\) | −38.8817 | −1.30996 | −0.654979 | − | 0.755647i | \(-0.727322\pi\) | ||||
−0.654979 | + | 0.755647i | \(0.727322\pi\) | |||||||
\(882\) | 94.0990 | 3.16848 | ||||||||
\(883\) | −34.5946 | −1.16420 | −0.582100 | − | 0.813117i | \(-0.697769\pi\) | ||||
−0.582100 | + | 0.813117i | \(0.697769\pi\) | |||||||
\(884\) | 10.1510 | 0.341416 | ||||||||
\(885\) | 11.1924 | 0.376230 | ||||||||
\(886\) | 42.9203 | 1.44194 | ||||||||
\(887\) | 37.2524 | 1.25081 | 0.625406 | − | 0.780300i | \(-0.284933\pi\) | ||||
0.625406 | + | 0.780300i | \(0.284933\pi\) | |||||||
\(888\) | 142.651 | 4.78706 | ||||||||
\(889\) | −20.0926 | −0.673883 | ||||||||
\(890\) | −0.158940 | −0.00532768 | ||||||||
\(891\) | −0.801392 | −0.0268476 | ||||||||
\(892\) | 56.0692 | 1.87734 | ||||||||
\(893\) | 0.224697 | 0.00751919 | ||||||||
\(894\) | −132.818 | −4.44209 | ||||||||
\(895\) | −2.20059 | −0.0735575 | ||||||||
\(896\) | 30.4011 | 1.01563 | ||||||||
\(897\) | −12.0967 | −0.403896 | ||||||||
\(898\) | 45.1025 | 1.50509 | ||||||||
\(899\) | −27.0550 | −0.902335 | ||||||||
\(900\) | −148.167 | −4.93889 | ||||||||
\(901\) | 11.6043 | 0.386595 | ||||||||
\(902\) | 3.00180 | 0.0999491 | ||||||||
\(903\) | −4.38269 | −0.145847 | ||||||||
\(904\) | −21.9566 | −0.730265 | ||||||||
\(905\) | 4.39515 | 0.146100 | ||||||||
\(906\) | 86.5809 | 2.87646 | ||||||||
\(907\) | 36.8032 | 1.22203 | 0.611015 | − | 0.791619i | \(-0.290762\pi\) | ||||
0.611015 | + | 0.791619i | \(0.290762\pi\) | |||||||
\(908\) | −88.7449 | −2.94510 | ||||||||
\(909\) | −22.7730 | −0.755332 | ||||||||
\(910\) | 0.846839 | 0.0280724 | ||||||||
\(911\) | −44.8063 | −1.48450 | −0.742250 | − | 0.670123i | \(-0.766241\pi\) | ||||
−0.742250 | + | 0.670123i | \(0.766241\pi\) | |||||||
\(912\) | 22.9432 | 0.759725 | ||||||||
\(913\) | 1.23402 | 0.0408400 | ||||||||
\(914\) | −1.72191 | −0.0569556 | ||||||||
\(915\) | −4.32093 | −0.142846 | ||||||||
\(916\) | 25.8610 | 0.854471 | ||||||||
\(917\) | 3.69415 | 0.121992 | ||||||||
\(918\) | 39.2124 | 1.29420 | ||||||||
\(919\) | −42.3690 | −1.39762 | −0.698812 | − | 0.715305i | \(-0.746288\pi\) | ||||
−0.698812 | + | 0.715305i | \(0.746288\pi\) | |||||||
\(920\) | 12.9648 | 0.427438 | ||||||||
\(921\) | −7.42179 | −0.244556 | ||||||||
\(922\) | −34.3521 | −1.13133 | ||||||||
\(923\) | 11.4122 | 0.375637 | ||||||||
\(924\) | 2.05258 | 0.0675249 | ||||||||
\(925\) | 25.6379 | 0.842970 | ||||||||
\(926\) | −33.7463 | −1.10897 | ||||||||
\(927\) | −97.5947 | −3.20543 | ||||||||
\(928\) | −80.7469 | −2.65065 | ||||||||
\(929\) | 9.83207 | 0.322580 | 0.161290 | − | 0.986907i | \(-0.448435\pi\) | ||||
0.161290 | + | 0.986907i | \(0.448435\pi\) | |||||||
\(930\) | −18.7527 | −0.614925 | ||||||||
\(931\) | −3.34671 | −0.109684 | ||||||||
\(932\) | −24.2381 | −0.793945 | ||||||||
\(933\) | 23.5055 | 0.769535 | ||||||||
\(934\) | 40.7860 | 1.33456 | ||||||||
\(935\) | −0.0901446 | −0.00294804 | ||||||||
\(936\) | 51.9853 | 1.69919 | ||||||||
\(937\) | −5.42285 | −0.177157 | −0.0885784 | − | 0.996069i | \(-0.528232\pi\) | ||||
−0.0885784 | + | 0.996069i | \(0.528232\pi\) | |||||||
\(938\) | −12.4072 | −0.405110 | ||||||||
\(939\) | −55.0889 | −1.79776 | ||||||||
\(940\) | −0.759157 | −0.0247610 | ||||||||
\(941\) | −49.1300 | −1.60159 | −0.800796 | − | 0.598937i | \(-0.795590\pi\) | ||||
−0.800796 | + | 0.598937i | \(0.795590\pi\) | |||||||
\(942\) | −175.116 | −5.70558 | ||||||||
\(943\) | 32.1893 | 1.04823 | ||||||||
\(944\) | −161.551 | −5.25805 | ||||||||
\(945\) | 2.38754 | 0.0776665 | ||||||||
\(946\) | 0.626425 | 0.0203668 | ||||||||
\(947\) | −31.3713 | −1.01943 | −0.509716 | − | 0.860343i | \(-0.670249\pi\) | ||||
−0.509716 | + | 0.860343i | \(0.670249\pi\) | |||||||
\(948\) | −131.257 | −4.26304 | ||||||||
\(949\) | −2.14580 | −0.0696556 | ||||||||
\(950\) | 7.22018 | 0.234254 | ||||||||
\(951\) | −7.59268 | −0.246209 | ||||||||
\(952\) | −15.9398 | −0.516613 | ||||||||
\(953\) | 41.1524 | 1.33306 | 0.666529 | − | 0.745479i | \(-0.267779\pi\) | ||||
0.666529 | + | 0.745479i | \(0.267779\pi\) | |||||||
\(954\) | 94.3505 | 3.05471 | ||||||||
\(955\) | 1.68502 | 0.0545260 | ||||||||
\(956\) | −71.9780 | −2.32794 | ||||||||
\(957\) | −1.62252 | −0.0524485 | ||||||||
\(958\) | −89.5096 | −2.89193 | ||||||||
\(959\) | −5.45042 | −0.176003 | ||||||||
\(960\) | −27.2767 | −0.880352 | ||||||||
\(961\) | 16.7924 | 0.541691 | ||||||||
\(962\) | −14.2813 | −0.460447 | ||||||||
\(963\) | 79.3443 | 2.55683 | ||||||||
\(964\) | −33.1670 | −1.06824 | ||||||||
\(965\) | −0.910421 | −0.0293075 | ||||||||
\(966\) | 30.1574 | 0.970300 | ||||||||
\(967\) | −24.3093 | −0.781735 | −0.390868 | − | 0.920447i | \(-0.627825\pi\) | ||||
−0.390868 | + | 0.920447i | \(0.627825\pi\) | |||||||
\(968\) | 101.679 | 3.26808 | ||||||||
\(969\) | −2.99532 | −0.0962235 | ||||||||
\(970\) | −0.257656 | −0.00827284 | ||||||||
\(971\) | 13.8394 | 0.444127 | 0.222064 | − | 0.975032i | \(-0.428721\pi\) | ||||
0.222064 | + | 0.975032i | \(0.428721\pi\) | |||||||
\(972\) | −34.3845 | −1.10288 | ||||||||
\(973\) | 18.6354 | 0.597424 | ||||||||
\(974\) | −43.7191 | −1.40085 | ||||||||
\(975\) | 14.3360 | 0.459119 | ||||||||
\(976\) | 62.3682 | 1.99636 | ||||||||
\(977\) | −16.7100 | −0.534599 | −0.267299 | − | 0.963614i | \(-0.586131\pi\) | ||||
−0.267299 | + | 0.963614i | \(0.586131\pi\) | |||||||
\(978\) | −0.450443 | −0.0144036 | ||||||||
\(979\) | 0.0242924 | 0.000776387 0 | ||||||||
\(980\) | 11.3071 | 0.361194 | ||||||||
\(981\) | 22.8594 | 0.729844 | ||||||||
\(982\) | 13.1411 | 0.419348 | ||||||||
\(983\) | −10.9191 | −0.348267 | −0.174133 | − | 0.984722i | \(-0.555712\pi\) | ||||
−0.174133 | + | 0.984722i | \(0.555712\pi\) | |||||||
\(984\) | −212.259 | −6.76657 | ||||||||
\(985\) | 0.766070 | 0.0244090 | ||||||||
\(986\) | 20.0045 | 0.637073 | ||||||||
\(987\) | −1.11225 | −0.0354035 | ||||||||
\(988\) | −2.93541 | −0.0933878 | ||||||||
\(989\) | 6.71737 | 0.213600 | ||||||||
\(990\) | −0.732935 | −0.0232942 | ||||||||
\(991\) | 25.4467 | 0.808341 | 0.404171 | − | 0.914684i | \(-0.367560\pi\) | ||||
0.404171 | + | 0.914684i | \(0.367560\pi\) | |||||||
\(992\) | 142.639 | 4.52878 | ||||||||
\(993\) | −26.1213 | −0.828935 | ||||||||
\(994\) | −28.4510 | −0.902411 | ||||||||
\(995\) | 5.69457 | 0.180530 | ||||||||
\(996\) | −138.535 | −4.38965 | ||||||||
\(997\) | 24.6748 | 0.781458 | 0.390729 | − | 0.920506i | \(-0.372223\pi\) | ||||
0.390729 | + | 0.920506i | \(0.372223\pi\) | |||||||
\(998\) | −68.6273 | −2.17236 | ||||||||
\(999\) | −40.2640 | −1.27390 |
(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 | 8021.2.a.b.1.2 | ✓ | 140 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8021.2.a.b.1.2 | ✓ | 140 | 1.1 | even | 1 | trivial |