Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2013,4,Mod(1,2013)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2013, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2013.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2013 = 3 \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2013.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: | \(118.770844842\) |
Analytic rank: | \(1\) |
Dimension: | \(37\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 2013.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.94279 | −1.74754 | −0.873770 | − | 0.486339i | \(-0.838332\pi\) | ||||
−0.873770 | + | 0.486339i | \(0.838332\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 16.4312 | 2.05390 | ||||||||
\(5\) | 0.994625 | 0.0889620 | 0.0444810 | − | 0.999010i | \(-0.485837\pi\) | ||||
0.0444810 | + | 0.999010i | \(0.485837\pi\) | |||||||
\(6\) | 14.8284 | 1.00894 | ||||||||
\(7\) | 23.9386 | 1.29256 | 0.646280 | − | 0.763100i | \(-0.276324\pi\) | ||||
0.646280 | + | 0.763100i | \(0.276324\pi\) | |||||||
\(8\) | −41.6735 | −1.84173 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −4.91622 | −0.155465 | ||||||||
\(11\) | 11.0000 | 0.301511 | ||||||||
\(12\) | −49.2935 | −1.18582 | ||||||||
\(13\) | −47.9281 | −1.02253 | −0.511264 | − | 0.859424i | \(-0.670823\pi\) | ||||
−0.511264 | + | 0.859424i | \(0.670823\pi\) | |||||||
\(14\) | −118.323 | −2.25880 | ||||||||
\(15\) | −2.98388 | −0.0513622 | ||||||||
\(16\) | 74.5342 | 1.16460 | ||||||||
\(17\) | 89.5307 | 1.27732 | 0.638658 | − | 0.769490i | \(-0.279490\pi\) | ||||
0.638658 | + | 0.769490i | \(0.279490\pi\) | |||||||
\(18\) | −44.4851 | −0.582513 | ||||||||
\(19\) | 94.1328 | 1.13661 | 0.568304 | − | 0.822819i | \(-0.307600\pi\) | ||||
0.568304 | + | 0.822819i | \(0.307600\pi\) | |||||||
\(20\) | 16.3429 | 0.182719 | ||||||||
\(21\) | −71.8157 | −0.746260 | ||||||||
\(22\) | −54.3707 | −0.526903 | ||||||||
\(23\) | −65.6083 | −0.594795 | −0.297397 | − | 0.954754i | \(-0.596119\pi\) | ||||
−0.297397 | + | 0.954754i | \(0.596119\pi\) | |||||||
\(24\) | 125.021 | 1.06332 | ||||||||
\(25\) | −124.011 | −0.992086 | ||||||||
\(26\) | 236.899 | 1.78691 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 393.339 | 2.65479 | ||||||||
\(29\) | 230.134 | 1.47361 | 0.736807 | − | 0.676104i | \(-0.236333\pi\) | ||||
0.736807 | + | 0.676104i | \(0.236333\pi\) | |||||||
\(30\) | 14.7487 | 0.0897575 | ||||||||
\(31\) | −116.788 | −0.676636 | −0.338318 | − | 0.941032i | \(-0.609858\pi\) | ||||
−0.338318 | + | 0.941032i | \(0.609858\pi\) | |||||||
\(32\) | −35.0184 | −0.193451 | ||||||||
\(33\) | −33.0000 | −0.174078 | ||||||||
\(34\) | −442.532 | −2.23216 | ||||||||
\(35\) | 23.8099 | 0.114989 | ||||||||
\(36\) | 147.881 | 0.684632 | ||||||||
\(37\) | 63.6647 | 0.282876 | 0.141438 | − | 0.989947i | \(-0.454827\pi\) | ||||
0.141438 | + | 0.989947i | \(0.454827\pi\) | |||||||
\(38\) | −465.279 | −1.98627 | ||||||||
\(39\) | 143.784 | 0.590357 | ||||||||
\(40\) | −41.4495 | −0.163844 | ||||||||
\(41\) | 211.619 | 0.806081 | 0.403040 | − | 0.915182i | \(-0.367953\pi\) | ||||
0.403040 | + | 0.915182i | \(0.367953\pi\) | |||||||
\(42\) | 354.970 | 1.30412 | ||||||||
\(43\) | −340.632 | −1.20804 | −0.604021 | − | 0.796968i | \(-0.706436\pi\) | ||||
−0.604021 | + | 0.796968i | \(0.706436\pi\) | |||||||
\(44\) | 180.743 | 0.619273 | ||||||||
\(45\) | 8.95163 | 0.0296540 | ||||||||
\(46\) | 324.288 | 1.03943 | ||||||||
\(47\) | −379.587 | −1.17805 | −0.589026 | − | 0.808114i | \(-0.700489\pi\) | ||||
−0.589026 | + | 0.808114i | \(0.700489\pi\) | |||||||
\(48\) | −223.602 | −0.672380 | ||||||||
\(49\) | 230.055 | 0.670713 | ||||||||
\(50\) | 612.959 | 1.73371 | ||||||||
\(51\) | −268.592 | −0.737459 | ||||||||
\(52\) | −787.515 | −2.10017 | ||||||||
\(53\) | 169.264 | 0.438682 | 0.219341 | − | 0.975648i | \(-0.429609\pi\) | ||||
0.219341 | + | 0.975648i | \(0.429609\pi\) | |||||||
\(54\) | 133.455 | 0.336314 | ||||||||
\(55\) | 10.9409 | 0.0268230 | ||||||||
\(56\) | −997.604 | −2.38054 | ||||||||
\(57\) | −282.398 | −0.656220 | ||||||||
\(58\) | −1137.50 | −2.57520 | ||||||||
\(59\) | −198.872 | −0.438829 | −0.219415 | − | 0.975632i | \(-0.570415\pi\) | ||||
−0.219415 | + | 0.975632i | \(0.570415\pi\) | |||||||
\(60\) | −49.0286 | −0.105493 | ||||||||
\(61\) | −61.0000 | −0.128037 | ||||||||
\(62\) | 577.258 | 1.18245 | ||||||||
\(63\) | 215.447 | 0.430854 | ||||||||
\(64\) | −423.185 | −0.826533 | ||||||||
\(65\) | −47.6705 | −0.0909661 | ||||||||
\(66\) | 163.112 | 0.304208 | ||||||||
\(67\) | −847.117 | −1.54465 | −0.772327 | − | 0.635226i | \(-0.780907\pi\) | ||||
−0.772327 | + | 0.635226i | \(0.780907\pi\) | |||||||
\(68\) | 1471.10 | 2.62348 | ||||||||
\(69\) | 196.825 | 0.343405 | ||||||||
\(70\) | −117.687 | −0.200947 | ||||||||
\(71\) | −1070.85 | −1.78995 | −0.894973 | − | 0.446121i | \(-0.852805\pi\) | ||||
−0.894973 | + | 0.446121i | \(0.852805\pi\) | |||||||
\(72\) | −375.062 | −0.613909 | ||||||||
\(73\) | −1053.15 | −1.68852 | −0.844258 | − | 0.535937i | \(-0.819958\pi\) | ||||
−0.844258 | + | 0.535937i | \(0.819958\pi\) | |||||||
\(74\) | −314.681 | −0.494337 | ||||||||
\(75\) | 372.032 | 0.572781 | ||||||||
\(76\) | 1546.71 | 2.33447 | ||||||||
\(77\) | 263.324 | 0.389722 | ||||||||
\(78\) | −710.696 | −1.03167 | ||||||||
\(79\) | −197.798 | −0.281696 | −0.140848 | − | 0.990031i | \(-0.544983\pi\) | ||||
−0.140848 | + | 0.990031i | \(0.544983\pi\) | |||||||
\(80\) | 74.1335 | 0.103605 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −1045.99 | −1.40866 | ||||||||
\(83\) | 20.8936 | 0.0276310 | 0.0138155 | − | 0.999905i | \(-0.495602\pi\) | ||||
0.0138155 | + | 0.999905i | \(0.495602\pi\) | |||||||
\(84\) | −1180.02 | −1.53274 | ||||||||
\(85\) | 89.0495 | 0.113633 | ||||||||
\(86\) | 1683.67 | 2.11110 | ||||||||
\(87\) | −690.402 | −0.850791 | ||||||||
\(88\) | −458.409 | −0.555302 | ||||||||
\(89\) | 317.430 | 0.378061 | 0.189031 | − | 0.981971i | \(-0.439465\pi\) | ||||
0.189031 | + | 0.981971i | \(0.439465\pi\) | |||||||
\(90\) | −44.2460 | −0.0518215 | ||||||||
\(91\) | −1147.33 | −1.32168 | ||||||||
\(92\) | −1078.02 | −1.22165 | ||||||||
\(93\) | 350.363 | 0.390656 | ||||||||
\(94\) | 1876.22 | 2.05869 | ||||||||
\(95\) | 93.6268 | 0.101115 | ||||||||
\(96\) | 105.055 | 0.111689 | ||||||||
\(97\) | 76.5033 | 0.0800798 | 0.0400399 | − | 0.999198i | \(-0.487252\pi\) | ||||
0.0400399 | + | 0.999198i | \(0.487252\pi\) | |||||||
\(98\) | −1137.11 | −1.17210 | ||||||||
\(99\) | 99.0000 | 0.100504 | ||||||||
\(100\) | −2037.64 | −2.03764 | ||||||||
\(101\) | 492.052 | 0.484763 | 0.242381 | − | 0.970181i | \(-0.422071\pi\) | ||||
0.242381 | + | 0.970181i | \(0.422071\pi\) | |||||||
\(102\) | 1327.59 | 1.28874 | ||||||||
\(103\) | 948.726 | 0.907580 | 0.453790 | − | 0.891109i | \(-0.350072\pi\) | ||||
0.453790 | + | 0.891109i | \(0.350072\pi\) | |||||||
\(104\) | 1997.33 | 1.88322 | ||||||||
\(105\) | −71.4297 | −0.0663888 | ||||||||
\(106\) | −836.635 | −0.766615 | ||||||||
\(107\) | −521.992 | −0.471616 | −0.235808 | − | 0.971800i | \(-0.575774\pi\) | ||||
−0.235808 | + | 0.971800i | \(0.575774\pi\) | |||||||
\(108\) | −443.642 | −0.395273 | ||||||||
\(109\) | −1836.07 | −1.61343 | −0.806716 | − | 0.590940i | \(-0.798757\pi\) | ||||
−0.806716 | + | 0.590940i | \(0.798757\pi\) | |||||||
\(110\) | −54.0785 | −0.0468743 | ||||||||
\(111\) | −190.994 | −0.163319 | ||||||||
\(112\) | 1784.24 | 1.50531 | ||||||||
\(113\) | −1054.84 | −0.878150 | −0.439075 | − | 0.898450i | \(-0.644694\pi\) | ||||
−0.439075 | + | 0.898450i | \(0.644694\pi\) | |||||||
\(114\) | 1395.84 | 1.14677 | ||||||||
\(115\) | −65.2556 | −0.0529141 | ||||||||
\(116\) | 3781.37 | 3.02665 | ||||||||
\(117\) | −431.353 | −0.340843 | ||||||||
\(118\) | 982.982 | 0.766871 | ||||||||
\(119\) | 2143.24 | 1.65101 | ||||||||
\(120\) | 124.349 | 0.0945952 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 301.510 | 0.223750 | ||||||||
\(123\) | −634.857 | −0.465391 | ||||||||
\(124\) | −1918.96 | −1.38974 | ||||||||
\(125\) | −247.672 | −0.177220 | ||||||||
\(126\) | −1064.91 | −0.752934 | ||||||||
\(127\) | −598.999 | −0.418524 | −0.209262 | − | 0.977860i | \(-0.567106\pi\) | ||||
−0.209262 | + | 0.977860i | \(0.567106\pi\) | |||||||
\(128\) | 2371.86 | 1.63785 | ||||||||
\(129\) | 1021.90 | 0.697464 | ||||||||
\(130\) | 235.625 | 0.158967 | ||||||||
\(131\) | 1004.02 | 0.669630 | 0.334815 | − | 0.942284i | \(-0.391326\pi\) | ||||
0.334815 | + | 0.942284i | \(0.391326\pi\) | |||||||
\(132\) | −542.229 | −0.357538 | ||||||||
\(133\) | 2253.40 | 1.46913 | ||||||||
\(134\) | 4187.12 | 2.69934 | ||||||||
\(135\) | −26.8549 | −0.0171207 | ||||||||
\(136\) | −3731.06 | −2.35247 | ||||||||
\(137\) | 1872.65 | 1.16782 | 0.583909 | − | 0.811819i | \(-0.301522\pi\) | ||||
0.583909 | + | 0.811819i | \(0.301522\pi\) | |||||||
\(138\) | −972.864 | −0.600114 | ||||||||
\(139\) | −298.707 | −0.182273 | −0.0911367 | − | 0.995838i | \(-0.529050\pi\) | ||||
−0.0911367 | + | 0.995838i | \(0.529050\pi\) | |||||||
\(140\) | 391.224 | 0.236175 | ||||||||
\(141\) | 1138.76 | 0.680149 | ||||||||
\(142\) | 5292.97 | 3.12800 | ||||||||
\(143\) | −527.209 | −0.308304 | ||||||||
\(144\) | 670.807 | 0.388199 | ||||||||
\(145\) | 228.897 | 0.131096 | ||||||||
\(146\) | 5205.49 | 2.95075 | ||||||||
\(147\) | −690.164 | −0.387236 | ||||||||
\(148\) | 1046.09 | 0.580998 | ||||||||
\(149\) | −2009.97 | −1.10512 | −0.552561 | − | 0.833473i | \(-0.686349\pi\) | ||||
−0.552561 | + | 0.833473i | \(0.686349\pi\) | |||||||
\(150\) | −1838.88 | −1.00096 | ||||||||
\(151\) | 218.136 | 0.117561 | 0.0587803 | − | 0.998271i | \(-0.481279\pi\) | ||||
0.0587803 | + | 0.998271i | \(0.481279\pi\) | |||||||
\(152\) | −3922.85 | −2.09332 | ||||||||
\(153\) | 805.776 | 0.425772 | ||||||||
\(154\) | −1301.56 | −0.681054 | ||||||||
\(155\) | −116.160 | −0.0601949 | ||||||||
\(156\) | 2362.55 | 1.21253 | ||||||||
\(157\) | 26.0045 | 0.0132190 | 0.00660951 | − | 0.999978i | \(-0.497896\pi\) | ||||
0.00660951 | + | 0.999978i | \(0.497896\pi\) | |||||||
\(158\) | 977.672 | 0.492275 | ||||||||
\(159\) | −507.791 | −0.253273 | ||||||||
\(160\) | −34.8302 | −0.0172098 | ||||||||
\(161\) | −1570.57 | −0.768808 | ||||||||
\(162\) | −400.366 | −0.194171 | ||||||||
\(163\) | −1566.24 | −0.752624 | −0.376312 | − | 0.926493i | \(-0.622808\pi\) | ||||
−0.376312 | + | 0.926493i | \(0.622808\pi\) | |||||||
\(164\) | 3477.15 | 1.65561 | ||||||||
\(165\) | −32.8226 | −0.0154863 | ||||||||
\(166\) | −103.273 | −0.0482863 | ||||||||
\(167\) | 1390.28 | 0.644210 | 0.322105 | − | 0.946704i | \(-0.395610\pi\) | ||||
0.322105 | + | 0.946704i | \(0.395610\pi\) | |||||||
\(168\) | 2992.81 | 1.37441 | ||||||||
\(169\) | 100.104 | 0.0455642 | ||||||||
\(170\) | −440.153 | −0.198578 | ||||||||
\(171\) | 847.195 | 0.378869 | ||||||||
\(172\) | −5596.98 | −2.48120 | ||||||||
\(173\) | 276.137 | 0.121355 | 0.0606773 | − | 0.998157i | \(-0.480674\pi\) | ||||
0.0606773 | + | 0.998157i | \(0.480674\pi\) | |||||||
\(174\) | 3412.51 | 1.48679 | ||||||||
\(175\) | −2968.64 | −1.28233 | ||||||||
\(176\) | 819.876 | 0.351139 | ||||||||
\(177\) | 596.616 | 0.253358 | ||||||||
\(178\) | −1568.99 | −0.660678 | ||||||||
\(179\) | −2853.94 | −1.19170 | −0.595849 | − | 0.803097i | \(-0.703184\pi\) | ||||
−0.595849 | + | 0.803097i | \(0.703184\pi\) | |||||||
\(180\) | 147.086 | 0.0609062 | ||||||||
\(181\) | −493.314 | −0.202584 | −0.101292 | − | 0.994857i | \(-0.532298\pi\) | ||||
−0.101292 | + | 0.994857i | \(0.532298\pi\) | |||||||
\(182\) | 5671.01 | 2.30969 | ||||||||
\(183\) | 183.000 | 0.0739221 | ||||||||
\(184\) | 2734.13 | 1.09545 | ||||||||
\(185\) | 63.3225 | 0.0251652 | ||||||||
\(186\) | −1731.77 | −0.682687 | ||||||||
\(187\) | 984.838 | 0.385126 | ||||||||
\(188\) | −6237.06 | −2.41960 | ||||||||
\(189\) | −646.341 | −0.248753 | ||||||||
\(190\) | −462.778 | −0.176702 | ||||||||
\(191\) | 2816.11 | 1.06684 | 0.533419 | − | 0.845851i | \(-0.320907\pi\) | ||||
0.533419 | + | 0.845851i | \(0.320907\pi\) | |||||||
\(192\) | 1269.55 | 0.477199 | ||||||||
\(193\) | 4246.41 | 1.58375 | 0.791875 | − | 0.610684i | \(-0.209105\pi\) | ||||
0.791875 | + | 0.610684i | \(0.209105\pi\) | |||||||
\(194\) | −378.140 | −0.139943 | ||||||||
\(195\) | 143.012 | 0.0525193 | ||||||||
\(196\) | 3780.07 | 1.37758 | ||||||||
\(197\) | −4707.06 | −1.70236 | −0.851178 | − | 0.524877i | \(-0.824111\pi\) | ||||
−0.851178 | + | 0.524877i | \(0.824111\pi\) | |||||||
\(198\) | −489.336 | −0.175634 | ||||||||
\(199\) | 2628.86 | 0.936457 | 0.468228 | − | 0.883608i | \(-0.344892\pi\) | ||||
0.468228 | + | 0.883608i | \(0.344892\pi\) | |||||||
\(200\) | 5167.97 | 1.82715 | ||||||||
\(201\) | 2541.35 | 0.891806 | ||||||||
\(202\) | −2432.11 | −0.847142 | ||||||||
\(203\) | 5509.07 | 1.90473 | ||||||||
\(204\) | −4413.29 | −1.51467 | ||||||||
\(205\) | 210.481 | 0.0717105 | ||||||||
\(206\) | −4689.35 | −1.58603 | ||||||||
\(207\) | −590.475 | −0.198265 | ||||||||
\(208\) | −3572.28 | −1.19083 | ||||||||
\(209\) | 1035.46 | 0.342700 | ||||||||
\(210\) | 353.062 | 0.116017 | ||||||||
\(211\) | 4801.43 | 1.56656 | 0.783279 | − | 0.621670i | \(-0.213546\pi\) | ||||
0.783279 | + | 0.621670i | \(0.213546\pi\) | |||||||
\(212\) | 2781.20 | 0.901008 | ||||||||
\(213\) | 3212.54 | 1.03343 | ||||||||
\(214\) | 2580.10 | 0.824167 | ||||||||
\(215\) | −338.801 | −0.107470 | ||||||||
\(216\) | 1125.19 | 0.354441 | ||||||||
\(217\) | −2795.73 | −0.874593 | ||||||||
\(218\) | 9075.33 | 2.81954 | ||||||||
\(219\) | 3159.44 | 0.974865 | ||||||||
\(220\) | 179.771 | 0.0550918 | ||||||||
\(221\) | −4291.04 | −1.30609 | ||||||||
\(222\) | 944.044 | 0.285406 | ||||||||
\(223\) | 842.574 | 0.253018 | 0.126509 | − | 0.991965i | \(-0.459623\pi\) | ||||
0.126509 | + | 0.991965i | \(0.459623\pi\) | |||||||
\(224\) | −838.289 | −0.250047 | ||||||||
\(225\) | −1116.10 | −0.330695 | ||||||||
\(226\) | 5213.85 | 1.53460 | ||||||||
\(227\) | 2288.30 | 0.669073 | 0.334536 | − | 0.942383i | \(-0.391420\pi\) | ||||
0.334536 | + | 0.942383i | \(0.391420\pi\) | |||||||
\(228\) | −4640.14 | −1.34781 | ||||||||
\(229\) | 2626.72 | 0.757984 | 0.378992 | − | 0.925400i | \(-0.376271\pi\) | ||||
0.378992 | + | 0.925400i | \(0.376271\pi\) | |||||||
\(230\) | 322.545 | 0.0924695 | ||||||||
\(231\) | −789.972 | −0.225006 | ||||||||
\(232\) | −9590.49 | −2.71399 | ||||||||
\(233\) | −969.360 | −0.272553 | −0.136277 | − | 0.990671i | \(-0.543514\pi\) | ||||
−0.136277 | + | 0.990671i | \(0.543514\pi\) | |||||||
\(234\) | 2132.09 | 0.595636 | ||||||||
\(235\) | −377.547 | −0.104802 | ||||||||
\(236\) | −3267.70 | −0.901310 | ||||||||
\(237\) | 593.393 | 0.162637 | ||||||||
\(238\) | −10593.6 | −2.88521 | ||||||||
\(239\) | −3010.38 | −0.814750 | −0.407375 | − | 0.913261i | \(-0.633556\pi\) | ||||
−0.407375 | + | 0.913261i | \(0.633556\pi\) | |||||||
\(240\) | −222.401 | −0.0598162 | ||||||||
\(241\) | −1925.35 | −0.514618 | −0.257309 | − | 0.966329i | \(-0.582836\pi\) | ||||
−0.257309 | + | 0.966329i | \(0.582836\pi\) | |||||||
\(242\) | −598.078 | −0.158867 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | −1002.30 | −0.262975 | ||||||||
\(245\) | 228.818 | 0.0596679 | ||||||||
\(246\) | 3137.96 | 0.813290 | ||||||||
\(247\) | −4511.61 | −1.16221 | ||||||||
\(248\) | 4866.96 | 1.24618 | ||||||||
\(249\) | −62.6808 | −0.0159528 | ||||||||
\(250\) | 1224.19 | 0.309699 | ||||||||
\(251\) | 5763.38 | 1.44933 | 0.724664 | − | 0.689102i | \(-0.241995\pi\) | ||||
0.724664 | + | 0.689102i | \(0.241995\pi\) | |||||||
\(252\) | 3540.05 | 0.884929 | ||||||||
\(253\) | −721.691 | −0.179337 | ||||||||
\(254\) | 2960.73 | 0.731388 | ||||||||
\(255\) | −267.148 | −0.0656058 | ||||||||
\(256\) | −8338.13 | −2.03568 | ||||||||
\(257\) | 2199.45 | 0.533843 | 0.266922 | − | 0.963718i | \(-0.413993\pi\) | ||||
0.266922 | + | 0.963718i | \(0.413993\pi\) | |||||||
\(258\) | −5051.01 | −1.21885 | ||||||||
\(259\) | 1524.04 | 0.365634 | ||||||||
\(260\) | −783.282 | −0.186835 | ||||||||
\(261\) | 2071.20 | 0.491204 | ||||||||
\(262\) | −4962.65 | −1.17021 | ||||||||
\(263\) | −5575.32 | −1.30718 | −0.653592 | − | 0.756847i | \(-0.726739\pi\) | ||||
−0.653592 | + | 0.756847i | \(0.726739\pi\) | |||||||
\(264\) | 1375.23 | 0.320604 | ||||||||
\(265\) | 168.354 | 0.0390260 | ||||||||
\(266\) | −11138.1 | −2.56737 | ||||||||
\(267\) | −952.289 | −0.218274 | ||||||||
\(268\) | −13919.1 | −3.17256 | ||||||||
\(269\) | −3312.34 | −0.750770 | −0.375385 | − | 0.926869i | \(-0.622490\pi\) | ||||
−0.375385 | + | 0.926869i | \(0.622490\pi\) | |||||||
\(270\) | 132.738 | 0.0299192 | ||||||||
\(271\) | 897.640 | 0.201209 | 0.100605 | − | 0.994926i | \(-0.467922\pi\) | ||||
0.100605 | + | 0.994926i | \(0.467922\pi\) | |||||||
\(272\) | 6673.10 | 1.48756 | ||||||||
\(273\) | 3441.99 | 0.763072 | ||||||||
\(274\) | −9256.10 | −2.04081 | ||||||||
\(275\) | −1364.12 | −0.299125 | ||||||||
\(276\) | 3234.06 | 0.705318 | ||||||||
\(277\) | −5615.99 | −1.21817 | −0.609083 | − | 0.793107i | \(-0.708462\pi\) | ||||
−0.609083 | + | 0.793107i | \(0.708462\pi\) | |||||||
\(278\) | 1476.45 | 0.318530 | ||||||||
\(279\) | −1051.09 | −0.225545 | ||||||||
\(280\) | −992.242 | −0.211778 | ||||||||
\(281\) | −3111.46 | −0.660548 | −0.330274 | − | 0.943885i | \(-0.607141\pi\) | ||||
−0.330274 | + | 0.943885i | \(0.607141\pi\) | |||||||
\(282\) | −5628.66 | −1.18859 | ||||||||
\(283\) | 3424.08 | 0.719225 | 0.359612 | − | 0.933102i | \(-0.382909\pi\) | ||||
0.359612 | + | 0.933102i | \(0.382909\pi\) | |||||||
\(284\) | −17595.3 | −3.67636 | ||||||||
\(285\) | −280.880 | −0.0583787 | ||||||||
\(286\) | 2605.89 | 0.538773 | ||||||||
\(287\) | 5065.85 | 1.04191 | ||||||||
\(288\) | −315.165 | −0.0644837 | ||||||||
\(289\) | 3102.75 | 0.631539 | ||||||||
\(290\) | −1131.39 | −0.229095 | ||||||||
\(291\) | −229.510 | −0.0462341 | ||||||||
\(292\) | −17304.5 | −3.46804 | ||||||||
\(293\) | 2733.03 | 0.544932 | 0.272466 | − | 0.962165i | \(-0.412161\pi\) | ||||
0.272466 | + | 0.962165i | \(0.412161\pi\) | |||||||
\(294\) | 3411.33 | 0.676711 | ||||||||
\(295\) | −197.803 | −0.0390391 | ||||||||
\(296\) | −2653.13 | −0.520981 | ||||||||
\(297\) | −297.000 | −0.0580259 | ||||||||
\(298\) | 9934.86 | 1.93124 | ||||||||
\(299\) | 3144.48 | 0.608194 | ||||||||
\(300\) | 6112.93 | 1.17643 | ||||||||
\(301\) | −8154.23 | −1.56147 | ||||||||
\(302\) | −1078.20 | −0.205442 | ||||||||
\(303\) | −1476.16 | −0.279878 | ||||||||
\(304\) | 7016.11 | 1.32369 | ||||||||
\(305\) | −60.6721 | −0.0113904 | ||||||||
\(306\) | −3982.78 | −0.744054 | ||||||||
\(307\) | 2391.95 | 0.444677 | 0.222338 | − | 0.974970i | \(-0.428631\pi\) | ||||
0.222338 | + | 0.974970i | \(0.428631\pi\) | |||||||
\(308\) | 4326.73 | 0.800448 | ||||||||
\(309\) | −2846.18 | −0.523991 | ||||||||
\(310\) | 574.155 | 0.105193 | ||||||||
\(311\) | 9993.31 | 1.82209 | 0.911043 | − | 0.412312i | \(-0.135279\pi\) | ||||
0.911043 | + | 0.412312i | \(0.135279\pi\) | |||||||
\(312\) | −5992.00 | −1.08728 | ||||||||
\(313\) | −1001.54 | −0.180864 | −0.0904320 | − | 0.995903i | \(-0.528825\pi\) | ||||
−0.0904320 | + | 0.995903i | \(0.528825\pi\) | |||||||
\(314\) | −128.535 | −0.0231008 | ||||||||
\(315\) | 214.289 | 0.0383296 | ||||||||
\(316\) | −3250.05 | −0.578574 | ||||||||
\(317\) | −1030.24 | −0.182537 | −0.0912684 | − | 0.995826i | \(-0.529092\pi\) | ||||
−0.0912684 | + | 0.995826i | \(0.529092\pi\) | |||||||
\(318\) | 2509.90 | 0.442605 | ||||||||
\(319\) | 2531.47 | 0.444311 | ||||||||
\(320\) | −420.910 | −0.0735300 | ||||||||
\(321\) | 1565.98 | 0.272287 | ||||||||
\(322\) | 7762.99 | 1.34352 | ||||||||
\(323\) | 8427.77 | 1.45181 | ||||||||
\(324\) | 1330.93 | 0.228211 | ||||||||
\(325\) | 5943.60 | 1.01444 | ||||||||
\(326\) | 7741.61 | 1.31524 | ||||||||
\(327\) | 5508.22 | 0.931515 | ||||||||
\(328\) | −8818.91 | −1.48458 | ||||||||
\(329\) | −9086.77 | −1.52270 | ||||||||
\(330\) | 162.235 | 0.0270629 | ||||||||
\(331\) | −7925.99 | −1.31617 | −0.658085 | − | 0.752944i | \(-0.728633\pi\) | ||||
−0.658085 | + | 0.752944i | \(0.728633\pi\) | |||||||
\(332\) | 343.307 | 0.0567512 | ||||||||
\(333\) | 572.982 | 0.0942920 | ||||||||
\(334\) | −6871.86 | −1.12578 | ||||||||
\(335\) | −842.563 | −0.137415 | ||||||||
\(336\) | −5352.72 | −0.869092 | ||||||||
\(337\) | 3732.81 | 0.603380 | 0.301690 | − | 0.953406i | \(-0.402449\pi\) | ||||
0.301690 | + | 0.953406i | \(0.402449\pi\) | |||||||
\(338\) | −494.795 | −0.0796252 | ||||||||
\(339\) | 3164.52 | 0.507000 | ||||||||
\(340\) | 1463.19 | 0.233390 | ||||||||
\(341\) | −1284.67 | −0.204013 | ||||||||
\(342\) | −4187.51 | −0.662089 | ||||||||
\(343\) | −2703.75 | −0.425623 | ||||||||
\(344\) | 14195.3 | 2.22489 | ||||||||
\(345\) | 195.767 | 0.0305500 | ||||||||
\(346\) | −1364.89 | −0.212072 | ||||||||
\(347\) | −1248.79 | −0.193195 | −0.0965973 | − | 0.995324i | \(-0.530796\pi\) | ||||
−0.0965973 | + | 0.995324i | \(0.530796\pi\) | |||||||
\(348\) | −11344.1 | −1.74744 | ||||||||
\(349\) | 834.492 | 0.127992 | 0.0639962 | − | 0.997950i | \(-0.479615\pi\) | ||||
0.0639962 | + | 0.997950i | \(0.479615\pi\) | |||||||
\(350\) | 14673.4 | 2.24093 | ||||||||
\(351\) | 1294.06 | 0.196786 | ||||||||
\(352\) | −385.202 | −0.0583277 | ||||||||
\(353\) | −5827.55 | −0.878667 | −0.439333 | − | 0.898324i | \(-0.644785\pi\) | ||||
−0.439333 | + | 0.898324i | \(0.644785\pi\) | |||||||
\(354\) | −2948.95 | −0.442753 | ||||||||
\(355\) | −1065.09 | −0.159237 | ||||||||
\(356\) | 5215.74 | 0.776499 | ||||||||
\(357\) | −6429.71 | −0.953211 | ||||||||
\(358\) | 14106.5 | 2.08254 | ||||||||
\(359\) | −232.438 | −0.0341717 | −0.0170858 | − | 0.999854i | \(-0.505439\pi\) | ||||
−0.0170858 | + | 0.999854i | \(0.505439\pi\) | |||||||
\(360\) | −373.046 | −0.0546146 | ||||||||
\(361\) | 2001.98 | 0.291876 | ||||||||
\(362\) | 2438.35 | 0.354024 | ||||||||
\(363\) | −363.000 | −0.0524864 | ||||||||
\(364\) | −18852.0 | −2.71459 | ||||||||
\(365\) | −1047.49 | −0.150214 | ||||||||
\(366\) | −904.531 | −0.129182 | ||||||||
\(367\) | −10954.4 | −1.55808 | −0.779039 | − | 0.626975i | \(-0.784293\pi\) | ||||
−0.779039 | + | 0.626975i | \(0.784293\pi\) | |||||||
\(368\) | −4890.06 | −0.692695 | ||||||||
\(369\) | 1904.57 | 0.268694 | ||||||||
\(370\) | −312.990 | −0.0439772 | ||||||||
\(371\) | 4051.93 | 0.567023 | ||||||||
\(372\) | 5756.88 | 0.802367 | ||||||||
\(373\) | −5422.99 | −0.752793 | −0.376397 | − | 0.926459i | \(-0.622837\pi\) | ||||
−0.376397 | + | 0.926459i | \(0.622837\pi\) | |||||||
\(374\) | −4867.85 | −0.673022 | ||||||||
\(375\) | 743.017 | 0.102318 | ||||||||
\(376\) | 15818.7 | 2.16965 | ||||||||
\(377\) | −11029.9 | −1.50681 | ||||||||
\(378\) | 3194.73 | 0.434707 | ||||||||
\(379\) | −6148.13 | −0.833267 | −0.416634 | − | 0.909074i | \(-0.636790\pi\) | ||||
−0.416634 | + | 0.909074i | \(0.636790\pi\) | |||||||
\(380\) | 1538.40 | 0.207679 | ||||||||
\(381\) | 1797.00 | 0.241635 | ||||||||
\(382\) | −13919.4 | −1.86434 | ||||||||
\(383\) | 12509.4 | 1.66893 | 0.834467 | − | 0.551058i | \(-0.185776\pi\) | ||||
0.834467 | + | 0.551058i | \(0.185776\pi\) | |||||||
\(384\) | −7115.58 | −0.945613 | ||||||||
\(385\) | 261.909 | 0.0346704 | ||||||||
\(386\) | −20989.1 | −2.76767 | ||||||||
\(387\) | −3065.69 | −0.402681 | ||||||||
\(388\) | 1257.04 | 0.164476 | ||||||||
\(389\) | 4748.98 | 0.618979 | 0.309490 | − | 0.950903i | \(-0.399842\pi\) | ||||
0.309490 | + | 0.950903i | \(0.399842\pi\) | |||||||
\(390\) | −706.876 | −0.0917796 | ||||||||
\(391\) | −5873.96 | −0.759741 | ||||||||
\(392\) | −9587.19 | −1.23527 | ||||||||
\(393\) | −3012.06 | −0.386611 | ||||||||
\(394\) | 23266.0 | 2.97494 | ||||||||
\(395\) | −196.734 | −0.0250602 | ||||||||
\(396\) | 1626.69 | 0.206424 | ||||||||
\(397\) | −8079.84 | −1.02145 | −0.510725 | − | 0.859744i | \(-0.670623\pi\) | ||||
−0.510725 | + | 0.859744i | \(0.670623\pi\) | |||||||
\(398\) | −12993.9 | −1.63650 | ||||||||
\(399\) | −6760.21 | −0.848205 | ||||||||
\(400\) | −9243.03 | −1.15538 | ||||||||
\(401\) | 2771.81 | 0.345181 | 0.172590 | − | 0.984994i | \(-0.444786\pi\) | ||||
0.172590 | + | 0.984994i | \(0.444786\pi\) | |||||||
\(402\) | −12561.4 | −1.55847 | ||||||||
\(403\) | 5597.42 | 0.691879 | ||||||||
\(404\) | 8085.00 | 0.995653 | ||||||||
\(405\) | 80.5646 | 0.00988466 | ||||||||
\(406\) | −27230.2 | −3.32860 | ||||||||
\(407\) | 700.312 | 0.0852903 | ||||||||
\(408\) | 11193.2 | 1.35820 | ||||||||
\(409\) | −5765.16 | −0.696990 | −0.348495 | − | 0.937311i | \(-0.613307\pi\) | ||||
−0.348495 | + | 0.937311i | \(0.613307\pi\) | |||||||
\(410\) | −1040.37 | −0.125317 | ||||||||
\(411\) | −5617.94 | −0.674240 | ||||||||
\(412\) | 15588.7 | 1.86408 | ||||||||
\(413\) | −4760.71 | −0.567213 | ||||||||
\(414\) | 2918.59 | 0.346476 | ||||||||
\(415\) | 20.7813 | 0.00245811 | ||||||||
\(416\) | 1678.36 | 0.197809 | ||||||||
\(417\) | 896.121 | 0.105236 | ||||||||
\(418\) | −5118.06 | −0.598882 | ||||||||
\(419\) | −5313.26 | −0.619499 | −0.309749 | − | 0.950818i | \(-0.600245\pi\) | ||||
−0.309749 | + | 0.950818i | \(0.600245\pi\) | |||||||
\(420\) | −1173.67 | −0.136356 | ||||||||
\(421\) | 11151.1 | 1.29091 | 0.645453 | − | 0.763800i | \(-0.276668\pi\) | ||||
0.645453 | + | 0.763800i | \(0.276668\pi\) | |||||||
\(422\) | −23732.4 | −2.73762 | ||||||||
\(423\) | −3416.28 | −0.392684 | ||||||||
\(424\) | −7053.82 | −0.807933 | ||||||||
\(425\) | −11102.8 | −1.26721 | ||||||||
\(426\) | −15878.9 | −1.80595 | ||||||||
\(427\) | −1460.25 | −0.165495 | ||||||||
\(428\) | −8576.94 | −0.968650 | ||||||||
\(429\) | 1581.63 | 0.177999 | ||||||||
\(430\) | 1674.62 | 0.187808 | ||||||||
\(431\) | 1509.61 | 0.168713 | 0.0843567 | − | 0.996436i | \(-0.473116\pi\) | ||||
0.0843567 | + | 0.996436i | \(0.473116\pi\) | |||||||
\(432\) | −2012.42 | −0.224127 | ||||||||
\(433\) | −208.125 | −0.0230989 | −0.0115495 | − | 0.999933i | \(-0.503676\pi\) | ||||
−0.0115495 | + | 0.999933i | \(0.503676\pi\) | |||||||
\(434\) | 13818.7 | 1.52839 | ||||||||
\(435\) | −686.691 | −0.0756880 | ||||||||
\(436\) | −30168.9 | −3.31382 | ||||||||
\(437\) | −6175.89 | −0.676048 | ||||||||
\(438\) | −15616.5 | −1.70362 | ||||||||
\(439\) | −15002.1 | −1.63101 | −0.815503 | − | 0.578753i | \(-0.803540\pi\) | ||||
−0.815503 | + | 0.578753i | \(0.803540\pi\) | |||||||
\(440\) | −455.945 | −0.0494007 | ||||||||
\(441\) | 2070.49 | 0.223571 | ||||||||
\(442\) | 21209.7 | 2.28245 | ||||||||
\(443\) | −15932.9 | −1.70879 | −0.854397 | − | 0.519620i | \(-0.826073\pi\) | ||||
−0.854397 | + | 0.519620i | \(0.826073\pi\) | |||||||
\(444\) | −3138.26 | −0.335440 | ||||||||
\(445\) | 315.723 | 0.0336331 | ||||||||
\(446\) | −4164.67 | −0.442158 | ||||||||
\(447\) | 6029.91 | 0.638042 | ||||||||
\(448\) | −10130.4 | −1.06834 | ||||||||
\(449\) | −3370.19 | −0.354230 | −0.177115 | − | 0.984190i | \(-0.556676\pi\) | ||||
−0.177115 | + | 0.984190i | \(0.556676\pi\) | |||||||
\(450\) | 5516.63 | 0.577903 | ||||||||
\(451\) | 2327.81 | 0.243043 | ||||||||
\(452\) | −17332.3 | −1.80363 | ||||||||
\(453\) | −654.407 | −0.0678736 | ||||||||
\(454\) | −11310.6 | −1.16923 | ||||||||
\(455\) | −1141.16 | −0.117579 | ||||||||
\(456\) | 11768.5 | 1.20858 | ||||||||
\(457\) | −18661.6 | −1.91018 | −0.955089 | − | 0.296319i | \(-0.904241\pi\) | ||||
−0.955089 | + | 0.296319i | \(0.904241\pi\) | |||||||
\(458\) | −12983.3 | −1.32461 | ||||||||
\(459\) | −2417.33 | −0.245820 | ||||||||
\(460\) | −1072.23 | −0.108680 | ||||||||
\(461\) | 9582.81 | 0.968147 | 0.484074 | − | 0.875027i | \(-0.339157\pi\) | ||||
0.484074 | + | 0.875027i | \(0.339157\pi\) | |||||||
\(462\) | 3904.67 | 0.393207 | ||||||||
\(463\) | 4729.90 | 0.474767 | 0.237383 | − | 0.971416i | \(-0.423710\pi\) | ||||
0.237383 | + | 0.971416i | \(0.423710\pi\) | |||||||
\(464\) | 17152.8 | 1.71616 | ||||||||
\(465\) | 348.480 | 0.0347535 | ||||||||
\(466\) | 4791.34 | 0.476297 | ||||||||
\(467\) | −9491.13 | −0.940465 | −0.470233 | − | 0.882542i | \(-0.655830\pi\) | ||||
−0.470233 | + | 0.882542i | \(0.655830\pi\) | |||||||
\(468\) | −7087.64 | −0.700056 | ||||||||
\(469\) | −20278.7 | −1.99656 | ||||||||
\(470\) | 1866.13 | 0.183145 | ||||||||
\(471\) | −78.0136 | −0.00763201 | ||||||||
\(472\) | 8287.70 | 0.808204 | ||||||||
\(473\) | −3746.95 | −0.364239 | ||||||||
\(474\) | −2933.02 | −0.284215 | ||||||||
\(475\) | −11673.5 | −1.12761 | ||||||||
\(476\) | 35215.9 | 3.39100 | ||||||||
\(477\) | 1523.37 | 0.146227 | ||||||||
\(478\) | 14879.7 | 1.42381 | ||||||||
\(479\) | −11089.0 | −1.05776 | −0.528880 | − | 0.848696i | \(-0.677388\pi\) | ||||
−0.528880 | + | 0.848696i | \(0.677388\pi\) | |||||||
\(480\) | 104.490 | 0.00993607 | ||||||||
\(481\) | −3051.33 | −0.289249 | ||||||||
\(482\) | 9516.62 | 0.899316 | ||||||||
\(483\) | 4711.70 | 0.443872 | ||||||||
\(484\) | 1988.17 | 0.186718 | ||||||||
\(485\) | 76.0921 | 0.00712405 | ||||||||
\(486\) | 1201.10 | 0.112105 | ||||||||
\(487\) | −12873.4 | −1.19784 | −0.598920 | − | 0.800809i | \(-0.704403\pi\) | ||||
−0.598920 | + | 0.800809i | \(0.704403\pi\) | |||||||
\(488\) | 2542.09 | 0.235809 | ||||||||
\(489\) | 4698.73 | 0.434527 | ||||||||
\(490\) | −1131.00 | −0.104272 | ||||||||
\(491\) | −5566.31 | −0.511617 | −0.255808 | − | 0.966728i | \(-0.582342\pi\) | ||||
−0.255808 | + | 0.966728i | \(0.582342\pi\) | |||||||
\(492\) | −10431.4 | −0.955865 | ||||||||
\(493\) | 20604.1 | 1.88227 | ||||||||
\(494\) | 22299.9 | 2.03101 | ||||||||
\(495\) | 98.4679 | 0.00894101 | ||||||||
\(496\) | −8704.68 | −0.788007 | ||||||||
\(497\) | −25634.5 | −2.31361 | ||||||||
\(498\) | 309.818 | 0.0278781 | ||||||||
\(499\) | 4195.12 | 0.376352 | 0.188176 | − | 0.982135i | \(-0.439743\pi\) | ||||
0.188176 | + | 0.982135i | \(0.439743\pi\) | |||||||
\(500\) | −4069.55 | −0.363991 | ||||||||
\(501\) | −4170.84 | −0.371935 | ||||||||
\(502\) | −28487.2 | −2.53276 | ||||||||
\(503\) | −5672.18 | −0.502803 | −0.251401 | − | 0.967883i | \(-0.580891\pi\) | ||||
−0.251401 | + | 0.967883i | \(0.580891\pi\) | |||||||
\(504\) | −8978.44 | −0.793515 | ||||||||
\(505\) | 489.408 | 0.0431254 | ||||||||
\(506\) | 3567.17 | 0.313399 | ||||||||
\(507\) | −300.313 | −0.0263065 | ||||||||
\(508\) | −9842.25 | −0.859605 | ||||||||
\(509\) | −3458.25 | −0.301147 | −0.150574 | − | 0.988599i | \(-0.548112\pi\) | ||||
−0.150574 | + | 0.988599i | \(0.548112\pi\) | |||||||
\(510\) | 1320.46 | 0.114649 | ||||||||
\(511\) | −25210.8 | −2.18251 | ||||||||
\(512\) | 22238.7 | 1.91958 | ||||||||
\(513\) | −2541.58 | −0.218740 | ||||||||
\(514\) | −10871.4 | −0.932913 | ||||||||
\(515\) | 943.626 | 0.0807401 | ||||||||
\(516\) | 16790.9 | 1.43252 | ||||||||
\(517\) | −4175.46 | −0.355196 | ||||||||
\(518\) | −7533.02 | −0.638961 | ||||||||
\(519\) | −828.412 | −0.0700641 | ||||||||
\(520\) | 1986.60 | 0.167535 | ||||||||
\(521\) | −1565.88 | −0.131674 | −0.0658372 | − | 0.997830i | \(-0.520972\pi\) | ||||
−0.0658372 | + | 0.997830i | \(0.520972\pi\) | |||||||
\(522\) | −10237.5 | −0.858400 | ||||||||
\(523\) | 16391.4 | 1.37045 | 0.685225 | − | 0.728331i | \(-0.259704\pi\) | ||||
0.685225 | + | 0.728331i | \(0.259704\pi\) | |||||||
\(524\) | 16497.2 | 1.37535 | ||||||||
\(525\) | 8905.91 | 0.740354 | ||||||||
\(526\) | 27557.7 | 2.28436 | ||||||||
\(527\) | −10456.1 | −0.864278 | ||||||||
\(528\) | −2459.63 | −0.202730 | ||||||||
\(529\) | −7862.55 | −0.646219 | ||||||||
\(530\) | −832.138 | −0.0681996 | ||||||||
\(531\) | −1789.85 | −0.146276 | ||||||||
\(532\) | 37026.1 | 3.01745 | ||||||||
\(533\) | −10142.5 | −0.824241 | ||||||||
\(534\) | 4706.96 | 0.381442 | ||||||||
\(535\) | −519.186 | −0.0419558 | ||||||||
\(536\) | 35302.3 | 2.84483 | ||||||||
\(537\) | 8561.83 | 0.688027 | ||||||||
\(538\) | 16372.2 | 1.31200 | ||||||||
\(539\) | 2530.60 | 0.202228 | ||||||||
\(540\) | −441.257 | −0.0351642 | ||||||||
\(541\) | 13779.7 | 1.09507 | 0.547537 | − | 0.836781i | \(-0.315565\pi\) | ||||
0.547537 | + | 0.836781i | \(0.315565\pi\) | |||||||
\(542\) | −4436.85 | −0.351622 | ||||||||
\(543\) | 1479.94 | 0.116962 | ||||||||
\(544\) | −3135.22 | −0.247098 | ||||||||
\(545\) | −1826.21 | −0.143534 | ||||||||
\(546\) | −17013.0 | −1.33350 | ||||||||
\(547\) | 17157.8 | 1.34116 | 0.670580 | − | 0.741837i | \(-0.266045\pi\) | ||||
0.670580 | + | 0.741837i | \(0.266045\pi\) | |||||||
\(548\) | 30769.8 | 2.39858 | ||||||||
\(549\) | −549.000 | −0.0426790 | ||||||||
\(550\) | 6742.55 | 0.522733 | ||||||||
\(551\) | 21663.1 | 1.67492 | ||||||||
\(552\) | −8202.39 | −0.632458 | ||||||||
\(553\) | −4734.99 | −0.364109 | ||||||||
\(554\) | 27758.6 | 2.12879 | ||||||||
\(555\) | −189.968 | −0.0145291 | ||||||||
\(556\) | −4908.11 | −0.374371 | ||||||||
\(557\) | 11266.1 | 0.857018 | 0.428509 | − | 0.903538i | \(-0.359039\pi\) | ||||
0.428509 | + | 0.903538i | \(0.359039\pi\) | |||||||
\(558\) | 5195.32 | 0.394149 | ||||||||
\(559\) | 16325.8 | 1.23526 | ||||||||
\(560\) | 1774.65 | 0.133915 | ||||||||
\(561\) | −2954.51 | −0.222352 | ||||||||
\(562\) | 15379.3 | 1.15433 | ||||||||
\(563\) | −11396.4 | −0.853112 | −0.426556 | − | 0.904461i | \(-0.640273\pi\) | ||||
−0.426556 | + | 0.904461i | \(0.640273\pi\) | |||||||
\(564\) | 18711.2 | 1.39696 | ||||||||
\(565\) | −1049.17 | −0.0781220 | ||||||||
\(566\) | −16924.5 | −1.25687 | ||||||||
\(567\) | 1939.02 | 0.143618 | ||||||||
\(568\) | 44626.0 | 3.29659 | ||||||||
\(569\) | 3493.84 | 0.257415 | 0.128708 | − | 0.991683i | \(-0.458917\pi\) | ||||
0.128708 | + | 0.991683i | \(0.458917\pi\) | |||||||
\(570\) | 1388.33 | 0.102019 | ||||||||
\(571\) | 19828.2 | 1.45321 | 0.726606 | − | 0.687054i | \(-0.241096\pi\) | ||||
0.726606 | + | 0.687054i | \(0.241096\pi\) | |||||||
\(572\) | −8662.67 | −0.633224 | ||||||||
\(573\) | −8448.32 | −0.615940 | ||||||||
\(574\) | −25039.4 | −1.82078 | ||||||||
\(575\) | 8136.13 | 0.590087 | ||||||||
\(576\) | −3808.66 | −0.275511 | ||||||||
\(577\) | −892.360 | −0.0643838 | −0.0321919 | − | 0.999482i | \(-0.510249\pi\) | ||||
−0.0321919 | + | 0.999482i | \(0.510249\pi\) | |||||||
\(578\) | −15336.2 | −1.10364 | ||||||||
\(579\) | −12739.2 | −0.914378 | ||||||||
\(580\) | 3761.05 | 0.269257 | ||||||||
\(581\) | 500.163 | 0.0357147 | ||||||||
\(582\) | 1134.42 | 0.0807959 | ||||||||
\(583\) | 1861.90 | 0.132268 | ||||||||
\(584\) | 43888.4 | 3.10979 | ||||||||
\(585\) | −429.035 | −0.0303220 | ||||||||
\(586\) | −13508.8 | −0.952291 | ||||||||
\(587\) | −22118.1 | −1.55522 | −0.777608 | − | 0.628750i | \(-0.783567\pi\) | ||||
−0.777608 | + | 0.628750i | \(0.783567\pi\) | |||||||
\(588\) | −11340.2 | −0.795344 | ||||||||
\(589\) | −10993.6 | −0.769069 | ||||||||
\(590\) | 977.699 | 0.0682224 | ||||||||
\(591\) | 14121.2 | 0.982856 | ||||||||
\(592\) | 4745.19 | 0.329436 | ||||||||
\(593\) | −9554.16 | −0.661623 | −0.330811 | − | 0.943697i | \(-0.607322\pi\) | ||||
−0.330811 | + | 0.943697i | \(0.607322\pi\) | |||||||
\(594\) | 1468.01 | 0.101403 | ||||||||
\(595\) | 2131.72 | 0.146877 | ||||||||
\(596\) | −33026.2 | −2.26981 | ||||||||
\(597\) | −7886.58 | −0.540663 | ||||||||
\(598\) | −15542.5 | −1.06284 | ||||||||
\(599\) | 3768.21 | 0.257037 | 0.128518 | − | 0.991707i | \(-0.458978\pi\) | ||||
0.128518 | + | 0.991707i | \(0.458978\pi\) | |||||||
\(600\) | −15503.9 | −1.05491 | ||||||||
\(601\) | 8296.73 | 0.563112 | 0.281556 | − | 0.959545i | \(-0.409149\pi\) | ||||
0.281556 | + | 0.959545i | \(0.409149\pi\) | |||||||
\(602\) | 40304.7 | 2.72873 | ||||||||
\(603\) | −7624.05 | −0.514884 | ||||||||
\(604\) | 3584.23 | 0.241457 | ||||||||
\(605\) | 120.350 | 0.00808745 | ||||||||
\(606\) | 7296.33 | 0.489098 | ||||||||
\(607\) | 5812.47 | 0.388667 | 0.194333 | − | 0.980936i | \(-0.437746\pi\) | ||||
0.194333 | + | 0.980936i | \(0.437746\pi\) | |||||||
\(608\) | −3296.38 | −0.219878 | ||||||||
\(609\) | −16527.2 | −1.09970 | ||||||||
\(610\) | 299.890 | 0.0199052 | ||||||||
\(611\) | 18192.9 | 1.20459 | ||||||||
\(612\) | 13239.9 | 0.874493 | ||||||||
\(613\) | 4868.11 | 0.320752 | 0.160376 | − | 0.987056i | \(-0.448729\pi\) | ||||
0.160376 | + | 0.987056i | \(0.448729\pi\) | |||||||
\(614\) | −11822.9 | −0.777090 | ||||||||
\(615\) | −631.444 | −0.0414021 | ||||||||
\(616\) | −10973.6 | −0.717761 | ||||||||
\(617\) | 631.980 | 0.0412359 | 0.0206180 | − | 0.999787i | \(-0.493437\pi\) | ||||
0.0206180 | + | 0.999787i | \(0.493437\pi\) | |||||||
\(618\) | 14068.1 | 0.915696 | ||||||||
\(619\) | −20297.7 | −1.31798 | −0.658992 | − | 0.752150i | \(-0.729017\pi\) | ||||
−0.658992 | + | 0.752150i | \(0.729017\pi\) | |||||||
\(620\) | −1908.65 | −0.123634 | ||||||||
\(621\) | 1771.42 | 0.114468 | ||||||||
\(622\) | −49394.8 | −3.18417 | ||||||||
\(623\) | 7598.81 | 0.488667 | ||||||||
\(624\) | 10716.8 | 0.687527 | ||||||||
\(625\) | 15255.0 | 0.976320 | ||||||||
\(626\) | 4950.41 | 0.316067 | ||||||||
\(627\) | −3106.38 | −0.197858 | ||||||||
\(628\) | 427.285 | 0.0271505 | ||||||||
\(629\) | 5699.95 | 0.361322 | ||||||||
\(630\) | −1059.19 | −0.0669825 | ||||||||
\(631\) | 13604.1 | 0.858276 | 0.429138 | − | 0.903239i | \(-0.358817\pi\) | ||||
0.429138 | + | 0.903239i | \(0.358817\pi\) | |||||||
\(632\) | 8242.93 | 0.518807 | ||||||||
\(633\) | −14404.3 | −0.904453 | ||||||||
\(634\) | 5092.27 | 0.318990 | ||||||||
\(635\) | −595.779 | −0.0372327 | ||||||||
\(636\) | −8343.61 | −0.520197 | ||||||||
\(637\) | −11026.1 | −0.685823 | ||||||||
\(638\) | −12512.5 | −0.776452 | ||||||||
\(639\) | −9637.62 | −0.596648 | ||||||||
\(640\) | 2359.11 | 0.145706 | ||||||||
\(641\) | 30896.0 | 1.90378 | 0.951888 | − | 0.306446i | \(-0.0991399\pi\) | ||||
0.951888 | + | 0.306446i | \(0.0991399\pi\) | |||||||
\(642\) | −7740.29 | −0.475833 | ||||||||
\(643\) | −24107.8 | −1.47857 | −0.739284 | − | 0.673394i | \(-0.764836\pi\) | ||||
−0.739284 | + | 0.673394i | \(0.764836\pi\) | |||||||
\(644\) | −25806.3 | −1.57905 | ||||||||
\(645\) | 1016.40 | 0.0620478 | ||||||||
\(646\) | −41656.7 | −2.53709 | ||||||||
\(647\) | 7172.65 | 0.435836 | 0.217918 | − | 0.975967i | \(-0.430073\pi\) | ||||
0.217918 | + | 0.975967i | \(0.430073\pi\) | |||||||
\(648\) | −3375.56 | −0.204636 | ||||||||
\(649\) | −2187.59 | −0.132312 | ||||||||
\(650\) | −29378.0 | −1.77277 | ||||||||
\(651\) | 8387.20 | 0.504946 | ||||||||
\(652\) | −25735.2 | −1.54581 | ||||||||
\(653\) | 1741.09 | 0.104340 | 0.0521701 | − | 0.998638i | \(-0.483386\pi\) | ||||
0.0521701 | + | 0.998638i | \(0.483386\pi\) | |||||||
\(654\) | −27226.0 | −1.62786 | ||||||||
\(655\) | 998.622 | 0.0595716 | ||||||||
\(656\) | 15772.8 | 0.938759 | ||||||||
\(657\) | −9478.33 | −0.562839 | ||||||||
\(658\) | 44914.0 | 2.66099 | ||||||||
\(659\) | 18651.6 | 1.10252 | 0.551261 | − | 0.834333i | \(-0.314147\pi\) | ||||
0.551261 | + | 0.834333i | \(0.314147\pi\) | |||||||
\(660\) | −539.314 | −0.0318072 | ||||||||
\(661\) | 18880.3 | 1.11098 | 0.555491 | − | 0.831522i | \(-0.312530\pi\) | ||||
0.555491 | + | 0.831522i | \(0.312530\pi\) | |||||||
\(662\) | 39176.5 | 2.30006 | ||||||||
\(663\) | 12873.1 | 0.754073 | ||||||||
\(664\) | −870.711 | −0.0508887 | ||||||||
\(665\) | 2241.29 | 0.130697 | ||||||||
\(666\) | −2832.13 | −0.164779 | ||||||||
\(667\) | −15098.7 | −0.876497 | ||||||||
\(668\) | 22843.9 | 1.32314 | ||||||||
\(669\) | −2527.72 | −0.146080 | ||||||||
\(670\) | 4164.61 | 0.240139 | ||||||||
\(671\) | −671.000 | −0.0386046 | ||||||||
\(672\) | 2514.87 | 0.144365 | ||||||||
\(673\) | −2703.36 | −0.154839 | −0.0774197 | − | 0.996999i | \(-0.524668\pi\) | ||||
−0.0774197 | + | 0.996999i | \(0.524668\pi\) | |||||||
\(674\) | −18450.5 | −1.05443 | ||||||||
\(675\) | 3348.29 | 0.190927 | ||||||||
\(676\) | 1644.83 | 0.0935841 | ||||||||
\(677\) | −8428.11 | −0.478462 | −0.239231 | − | 0.970963i | \(-0.576895\pi\) | ||||
−0.239231 | + | 0.970963i | \(0.576895\pi\) | |||||||
\(678\) | −15641.6 | −0.886003 | ||||||||
\(679\) | 1831.38 | 0.103508 | ||||||||
\(680\) | −3711.01 | −0.209280 | ||||||||
\(681\) | −6864.89 | −0.386289 | ||||||||
\(682\) | 6349.83 | 0.356522 | ||||||||
\(683\) | 27381.4 | 1.53400 | 0.766999 | − | 0.641648i | \(-0.221749\pi\) | ||||
0.766999 | + | 0.641648i | \(0.221749\pi\) | |||||||
\(684\) | 13920.4 | 0.778158 | ||||||||
\(685\) | 1862.58 | 0.103891 | ||||||||
\(686\) | 13364.1 | 0.743794 | ||||||||
\(687\) | −7880.15 | −0.437622 | ||||||||
\(688\) | −25388.7 | −1.40688 | ||||||||
\(689\) | −8112.49 | −0.448565 | ||||||||
\(690\) | −967.635 | −0.0533873 | ||||||||
\(691\) | 15987.3 | 0.880152 | 0.440076 | − | 0.897961i | \(-0.354952\pi\) | ||||
0.440076 | + | 0.897961i | \(0.354952\pi\) | |||||||
\(692\) | 4537.26 | 0.249250 | ||||||||
\(693\) | 2369.92 | 0.129907 | ||||||||
\(694\) | 6172.50 | 0.337615 | ||||||||
\(695\) | −297.101 | −0.0162154 | ||||||||
\(696\) | 28771.5 | 1.56693 | ||||||||
\(697\) | 18946.4 | 1.02962 | ||||||||
\(698\) | −4124.72 | −0.223672 | ||||||||
\(699\) | 2908.08 | 0.157359 | ||||||||
\(700\) | −48778.2 | −2.63378 | ||||||||
\(701\) | 7109.81 | 0.383073 | 0.191536 | − | 0.981486i | \(-0.438653\pi\) | ||||
0.191536 | + | 0.981486i | \(0.438653\pi\) | |||||||
\(702\) | −6396.26 | −0.343891 | ||||||||
\(703\) | 5992.93 | 0.321519 | ||||||||
\(704\) | −4655.03 | −0.249209 | ||||||||
\(705\) | 1132.64 | 0.0605074 | ||||||||
\(706\) | 28804.4 | 1.53551 | ||||||||
\(707\) | 11779.0 | 0.626585 | ||||||||
\(708\) | 9803.10 | 0.520371 | ||||||||
\(709\) | 12182.2 | 0.645291 | 0.322645 | − | 0.946520i | \(-0.395428\pi\) | ||||
0.322645 | + | 0.946520i | \(0.395428\pi\) | |||||||
\(710\) | 5264.52 | 0.278273 | ||||||||
\(711\) | −1780.18 | −0.0938986 | ||||||||
\(712\) | −13228.4 | −0.696286 | ||||||||
\(713\) | 7662.25 | 0.402459 | ||||||||
\(714\) | 31780.7 | 1.66577 | ||||||||
\(715\) | −524.376 | −0.0274273 | ||||||||
\(716\) | −46893.7 | −2.44762 | ||||||||
\(717\) | 9031.13 | 0.470396 | ||||||||
\(718\) | 1148.89 | 0.0597164 | ||||||||
\(719\) | −26753.0 | −1.38765 | −0.693824 | − | 0.720144i | \(-0.744075\pi\) | ||||
−0.693824 | + | 0.720144i | \(0.744075\pi\) | |||||||
\(720\) | 667.202 | 0.0345349 | ||||||||
\(721\) | 22711.1 | 1.17310 | ||||||||
\(722\) | −9895.35 | −0.510065 | ||||||||
\(723\) | 5776.06 | 0.297115 | ||||||||
\(724\) | −8105.74 | −0.416087 | ||||||||
\(725\) | −28539.1 | −1.46195 | ||||||||
\(726\) | 1794.23 | 0.0917221 | ||||||||
\(727\) | −11951.9 | −0.609725 | −0.304863 | − | 0.952396i | \(-0.598611\pi\) | ||||
−0.304863 | + | 0.952396i | \(0.598611\pi\) | |||||||
\(728\) | 47813.3 | 2.43417 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 5177.51 | 0.262505 | ||||||||
\(731\) | −30497.0 | −1.54305 | ||||||||
\(732\) | 3006.91 | 0.151828 | ||||||||
\(733\) | 20469.5 | 1.03146 | 0.515729 | − | 0.856751i | \(-0.327521\pi\) | ||||
0.515729 | + | 0.856751i | \(0.327521\pi\) | |||||||
\(734\) | 54145.3 | 2.72280 | ||||||||
\(735\) | −686.454 | −0.0344493 | ||||||||
\(736\) | 2297.50 | 0.115064 | ||||||||
\(737\) | −9318.28 | −0.465730 | ||||||||
\(738\) | −9413.89 | −0.469553 | ||||||||
\(739\) | −17968.0 | −0.894402 | −0.447201 | − | 0.894433i | \(-0.647579\pi\) | ||||
−0.447201 | + | 0.894433i | \(0.647579\pi\) | |||||||
\(740\) | 1040.46 | 0.0516867 | ||||||||
\(741\) | 13534.8 | 0.671004 | ||||||||
\(742\) | −20027.8 | −0.990896 | ||||||||
\(743\) | 29478.7 | 1.45554 | 0.727771 | − | 0.685820i | \(-0.240556\pi\) | ||||
0.727771 | + | 0.685820i | \(0.240556\pi\) | |||||||
\(744\) | −14600.9 | −0.719482 | ||||||||
\(745\) | −1999.17 | −0.0983138 | ||||||||
\(746\) | 26804.7 | 1.31554 | ||||||||
\(747\) | 188.042 | 0.00921033 | ||||||||
\(748\) | 16182.0 | 0.791008 | ||||||||
\(749\) | −12495.7 | −0.609592 | ||||||||
\(750\) | −3672.58 | −0.178805 | ||||||||
\(751\) | −38472.7 | −1.86936 | −0.934680 | − | 0.355491i | \(-0.884314\pi\) | ||||
−0.934680 | + | 0.355491i | \(0.884314\pi\) | |||||||
\(752\) | −28292.2 | −1.37196 | ||||||||
\(753\) | −17290.1 | −0.836770 | ||||||||
\(754\) | 54518.4 | 2.63321 | ||||||||
\(755\) | 216.963 | 0.0104584 | ||||||||
\(756\) | −10620.1 | −0.510914 | ||||||||
\(757\) | −27092.8 | −1.30080 | −0.650399 | − | 0.759592i | \(-0.725398\pi\) | ||||
−0.650399 | + | 0.759592i | \(0.725398\pi\) | |||||||
\(758\) | 30388.9 | 1.45617 | ||||||||
\(759\) | 2165.07 | 0.103540 | ||||||||
\(760\) | −3901.76 | −0.186226 | ||||||||
\(761\) | 9383.97 | 0.447002 | 0.223501 | − | 0.974704i | \(-0.428251\pi\) | ||||
0.223501 | + | 0.974704i | \(0.428251\pi\) | |||||||
\(762\) | −8882.18 | −0.422267 | ||||||||
\(763\) | −43953.0 | −2.08546 | ||||||||
\(764\) | 46271.9 | 2.19118 | ||||||||
\(765\) | 801.445 | 0.0378775 | ||||||||
\(766\) | −61831.5 | −2.91653 | ||||||||
\(767\) | 9531.55 | 0.448715 | ||||||||
\(768\) | 25014.4 | 1.17530 | ||||||||
\(769\) | 28687.2 | 1.34524 | 0.672619 | − | 0.739989i | \(-0.265169\pi\) | ||||
0.672619 | + | 0.739989i | \(0.265169\pi\) | |||||||
\(770\) | −1294.56 | −0.0605879 | ||||||||
\(771\) | −6598.34 | −0.308215 | ||||||||
\(772\) | 69773.6 | 3.25286 | ||||||||
\(773\) | 27568.6 | 1.28276 | 0.641381 | − | 0.767223i | \(-0.278362\pi\) | ||||
0.641381 | + | 0.767223i | \(0.278362\pi\) | |||||||
\(774\) | 15153.0 | 0.703701 | ||||||||
\(775\) | 14482.9 | 0.671281 | ||||||||
\(776\) | −3188.16 | −0.147485 | ||||||||
\(777\) | −4572.12 | −0.211099 | ||||||||
\(778\) | −23473.2 | −1.08169 | ||||||||
\(779\) | 19920.3 | 0.916197 | ||||||||
\(780\) | 2349.85 | 0.107869 | ||||||||
\(781\) | −11779.3 | −0.539689 | ||||||||
\(782\) | 29033.7 | 1.32768 | ||||||||
\(783\) | −6213.61 | −0.283597 | ||||||||
\(784\) | 17146.9 | 0.781110 | ||||||||
\(785\) | 25.8647 | 0.00117599 | ||||||||
\(786\) | 14888.0 | 0.675618 | ||||||||
\(787\) | −35460.2 | −1.60612 | −0.803062 | − | 0.595896i | \(-0.796797\pi\) | ||||
−0.803062 | + | 0.595896i | \(0.796797\pi\) | |||||||
\(788\) | −77342.6 | −3.49646 | ||||||||
\(789\) | 16726.0 | 0.754703 | ||||||||
\(790\) | 972.417 | 0.0437937 | ||||||||
\(791\) | −25251.3 | −1.13506 | ||||||||
\(792\) | −4125.68 | −0.185101 | ||||||||
\(793\) | 2923.62 | 0.130921 | ||||||||
\(794\) | 39937.0 | 1.78502 | ||||||||
\(795\) | −505.062 | −0.0225317 | ||||||||
\(796\) | 43195.2 | 1.92339 | ||||||||
\(797\) | −21603.2 | −0.960131 | −0.480066 | − | 0.877233i | \(-0.659387\pi\) | ||||
−0.480066 | + | 0.877233i | \(0.659387\pi\) | |||||||
\(798\) | 33414.3 | 1.48227 | ||||||||
\(799\) | −33984.7 | −1.50475 | ||||||||
\(800\) | 4342.65 | 0.191920 | ||||||||
\(801\) | 2856.87 | 0.126020 | ||||||||
\(802\) | −13700.5 | −0.603218 | ||||||||
\(803\) | −11584.6 | −0.509107 | ||||||||
\(804\) | 41757.4 | 1.83168 | ||||||||
\(805\) | −1562.13 | −0.0683947 | ||||||||
\(806\) | −27666.9 | −1.20909 | ||||||||
\(807\) | 9937.03 | 0.433457 | ||||||||
\(808\) | −20505.6 | −0.892801 | ||||||||
\(809\) | 26195.0 | 1.13840 | 0.569200 | − | 0.822199i | \(-0.307253\pi\) | ||||
0.569200 | + | 0.822199i | \(0.307253\pi\) | |||||||
\(810\) | −398.214 | −0.0172738 | ||||||||
\(811\) | −34492.8 | −1.49347 | −0.746735 | − | 0.665121i | \(-0.768380\pi\) | ||||
−0.746735 | + | 0.665121i | \(0.768380\pi\) | |||||||
\(812\) | 90520.5 | 3.91213 | ||||||||
\(813\) | −2692.92 | −0.116168 | ||||||||
\(814\) | −3461.49 | −0.149048 | ||||||||
\(815\) | −1557.82 | −0.0669549 | ||||||||
\(816\) | −20019.3 | −0.858842 | ||||||||
\(817\) | −32064.6 | −1.37307 | ||||||||
\(818\) | 28496.0 | 1.21802 | ||||||||
\(819\) | −10326.0 | −0.440560 | ||||||||
\(820\) | 3458.46 | 0.147286 | ||||||||
\(821\) | −34296.1 | −1.45791 | −0.728954 | − | 0.684563i | \(-0.759993\pi\) | ||||
−0.728954 | + | 0.684563i | \(0.759993\pi\) | |||||||
\(822\) | 27768.3 | 1.17826 | ||||||||
\(823\) | −27005.1 | −1.14379 | −0.571894 | − | 0.820328i | \(-0.693791\pi\) | ||||
−0.571894 | + | 0.820328i | \(0.693791\pi\) | |||||||
\(824\) | −39536.8 | −1.67151 | ||||||||
\(825\) | 4092.35 | 0.172700 | ||||||||
\(826\) | 23531.2 | 0.991228 | ||||||||
\(827\) | −18435.1 | −0.775153 | −0.387576 | − | 0.921838i | \(-0.626688\pi\) | ||||
−0.387576 | + | 0.921838i | \(0.626688\pi\) | |||||||
\(828\) | −9702.19 | −0.407216 | ||||||||
\(829\) | 27.5036 | 0.00115228 | 0.000576139 | − | 1.00000i | \(-0.499817\pi\) | ||||
0.000576139 | 1.00000i | \(0.499817\pi\) | ||||||||
\(830\) | −102.718 | −0.00429564 | ||||||||
\(831\) | 16848.0 | 0.703308 | ||||||||
\(832\) | 20282.4 | 0.845153 | ||||||||
\(833\) | 20597.0 | 0.856713 | ||||||||
\(834\) | −4429.34 | −0.183903 | ||||||||
\(835\) | 1382.81 | 0.0573102 | ||||||||
\(836\) | 17013.8 | 0.703870 | ||||||||
\(837\) | 3153.27 | 0.130219 | ||||||||
\(838\) | 26262.3 | 1.08260 | ||||||||
\(839\) | 41533.5 | 1.70905 | 0.854526 | − | 0.519409i | \(-0.173848\pi\) | ||||
0.854526 | + | 0.519409i | \(0.173848\pi\) | |||||||
\(840\) | 2976.73 | 0.122270 | ||||||||
\(841\) | 28572.6 | 1.17154 | ||||||||
\(842\) | −55117.6 | −2.25591 | ||||||||
\(843\) | 9334.37 | 0.381368 | ||||||||
\(844\) | 78893.1 | 3.21755 | ||||||||
\(845\) | 99.5664 | 0.00405348 | ||||||||
\(846\) | 16886.0 | 0.686231 | ||||||||
\(847\) | 2896.57 | 0.117506 | ||||||||
\(848\) | 12615.9 | 0.510888 | ||||||||
\(849\) | −10272.2 | −0.415245 | ||||||||
\(850\) | 54878.7 | 2.21450 | ||||||||
\(851\) | −4176.93 | −0.168253 | ||||||||
\(852\) | 52785.8 | 2.12255 | ||||||||
\(853\) | −1143.31 | −0.0458922 | −0.0229461 | − | 0.999737i | \(-0.507305\pi\) | ||||
−0.0229461 | + | 0.999737i | \(0.507305\pi\) | |||||||
\(854\) | 7217.72 | 0.289210 | ||||||||
\(855\) | 842.641 | 0.0337049 | ||||||||
\(856\) | 21753.2 | 0.868587 | ||||||||
\(857\) | 9107.41 | 0.363014 | 0.181507 | − | 0.983390i | \(-0.441902\pi\) | ||||
0.181507 | + | 0.983390i | \(0.441902\pi\) | |||||||
\(858\) | −7817.66 | −0.311061 | ||||||||
\(859\) | −28420.4 | −1.12886 | −0.564430 | − | 0.825481i | \(-0.690904\pi\) | ||||
−0.564430 | + | 0.825481i | \(0.690904\pi\) | |||||||
\(860\) | −5566.90 | −0.220732 | ||||||||
\(861\) | −15197.6 | −0.601546 | ||||||||
\(862\) | −7461.70 | −0.294833 | ||||||||
\(863\) | −31.5674 | −0.00124515 | −0.000622577 | − | 1.00000i | \(-0.500198\pi\) | ||||
−0.000622577 | 1.00000i | \(0.500198\pi\) | ||||||||
\(864\) | 945.496 | 0.0372297 | ||||||||
\(865\) | 274.653 | 0.0107959 | ||||||||
\(866\) | 1028.72 | 0.0403663 | ||||||||
\(867\) | −9308.25 | −0.364619 | ||||||||
\(868\) | −45937.2 | −1.79632 | ||||||||
\(869\) | −2175.77 | −0.0849345 | ||||||||
\(870\) | 3394.17 | 0.132268 | ||||||||
\(871\) | 40600.7 | 1.57945 | ||||||||
\(872\) | 76515.7 | 2.97150 | ||||||||
\(873\) | 688.530 | 0.0266933 | ||||||||
\(874\) | 30526.1 | 1.18142 | ||||||||
\(875\) | −5928.92 | −0.229067 | ||||||||
\(876\) | 51913.4 | 2.00227 | ||||||||
\(877\) | −23337.9 | −0.898592 | −0.449296 | − | 0.893383i | \(-0.648325\pi\) | ||||
−0.449296 | + | 0.893383i | \(0.648325\pi\) | |||||||
\(878\) | 74152.3 | 2.85025 | ||||||||
\(879\) | −8199.08 | −0.314617 | ||||||||
\(880\) | 815.469 | 0.0312380 | ||||||||
\(881\) | −8155.91 | −0.311895 | −0.155948 | − | 0.987765i | \(-0.549843\pi\) | ||||
−0.155948 | + | 0.987765i | \(0.549843\pi\) | |||||||
\(882\) | −10234.0 | −0.390699 | ||||||||
\(883\) | −19097.3 | −0.727831 | −0.363916 | − | 0.931432i | \(-0.618560\pi\) | ||||
−0.363916 | + | 0.931432i | \(0.618560\pi\) | |||||||
\(884\) | −70506.8 | −2.68258 | ||||||||
\(885\) | 593.409 | 0.0225392 | ||||||||
\(886\) | 78753.1 | 2.98619 | ||||||||
\(887\) | −40907.0 | −1.54850 | −0.774252 | − | 0.632877i | \(-0.781874\pi\) | ||||
−0.774252 | + | 0.632877i | \(0.781874\pi\) | |||||||
\(888\) | 7959.40 | 0.300788 | ||||||||
\(889\) | −14339.2 | −0.540968 | ||||||||
\(890\) | −1560.55 | −0.0587752 | ||||||||
\(891\) | 891.000 | 0.0335013 | ||||||||
\(892\) | 13844.5 | 0.519672 | ||||||||
\(893\) | −35731.6 | −1.33898 | ||||||||
\(894\) | −29804.6 | −1.11500 | ||||||||
\(895\) | −2838.60 | −0.106016 | ||||||||
\(896\) | 56778.9 | 2.11702 | ||||||||
\(897\) | −9433.45 | −0.351141 | ||||||||
\(898\) | 16658.2 | 0.619031 | ||||||||
\(899\) | −26876.8 | −0.997100 | ||||||||
\(900\) | −18338.8 | −0.679214 | ||||||||
\(901\) | 15154.3 | 0.560336 | ||||||||
\(902\) | −11505.9 | −0.424727 | ||||||||
\(903\) | 24462.7 | 0.901514 | ||||||||
\(904\) | 43958.9 | 1.61731 | ||||||||
\(905\) | −490.663 | −0.0180223 | ||||||||
\(906\) | 3234.60 | 0.118612 | ||||||||
\(907\) | −7.84024 | −0.000287024 0 | −0.000143512 | − | 1.00000i | \(-0.500046\pi\) | ||||
−0.000143512 | 1.00000i | \(0.500046\pi\) | ||||||||
\(908\) | 37599.4 | 1.37421 | ||||||||
\(909\) | 4428.47 | 0.161588 | ||||||||
\(910\) | 5640.53 | 0.205474 | ||||||||
\(911\) | 24894.6 | 0.905373 | 0.452687 | − | 0.891670i | \(-0.350466\pi\) | ||||
0.452687 | + | 0.891670i | \(0.350466\pi\) | |||||||
\(912\) | −21048.3 | −0.764232 | ||||||||
\(913\) | 229.830 | 0.00833105 | ||||||||
\(914\) | 92240.2 | 3.33811 | ||||||||
\(915\) | 182.016 | 0.00657626 | ||||||||
\(916\) | 43160.0 | 1.55682 | ||||||||
\(917\) | 24034.8 | 0.865537 | ||||||||
\(918\) | 11948.4 | 0.429580 | ||||||||
\(919\) | −27657.3 | −0.992742 | −0.496371 | − | 0.868110i | \(-0.665334\pi\) | ||||
−0.496371 | + | 0.868110i | \(0.665334\pi\) | |||||||
\(920\) | 2719.43 | 0.0974533 | ||||||||
\(921\) | −7175.85 | −0.256734 | ||||||||
\(922\) | −47365.8 | −1.69188 | ||||||||
\(923\) | 51323.7 | 1.83027 | ||||||||
\(924\) | −12980.2 | −0.462139 | ||||||||
\(925\) | −7895.11 | −0.280637 | ||||||||
\(926\) | −23378.9 | −0.829674 | ||||||||
\(927\) | 8538.53 | 0.302527 | ||||||||
\(928\) | −8058.91 | −0.285072 | ||||||||
\(929\) | −27859.9 | −0.983910 | −0.491955 | − | 0.870621i | \(-0.663717\pi\) | ||||
−0.491955 | + | 0.870621i | \(0.663717\pi\) | |||||||
\(930\) | −1722.46 | −0.0607332 | ||||||||
\(931\) | 21655.7 | 0.762337 | ||||||||
\(932\) | −15927.7 | −0.559796 | ||||||||
\(933\) | −29979.9 | −1.05198 | ||||||||
\(934\) | 46912.7 | 1.64350 | ||||||||
\(935\) | 979.544 | 0.0342615 | ||||||||
\(936\) | 17976.0 | 0.627740 | ||||||||
\(937\) | −19777.0 | −0.689528 | −0.344764 | − | 0.938689i | \(-0.612041\pi\) | ||||
−0.344764 | + | 0.938689i | \(0.612041\pi\) | |||||||
\(938\) | 100234. | 3.48907 | ||||||||
\(939\) | 3004.62 | 0.104422 | ||||||||
\(940\) | −6203.54 | −0.215252 | ||||||||
\(941\) | −23726.0 | −0.821938 | −0.410969 | − | 0.911649i | \(-0.634810\pi\) | ||||
−0.410969 | + | 0.911649i | \(0.634810\pi\) | |||||||
\(942\) | 385.605 | 0.0133372 | ||||||||
\(943\) | −13884.0 | −0.479452 | ||||||||
\(944\) | −14822.7 | −0.511059 | ||||||||
\(945\) | −642.867 | −0.0221296 | ||||||||
\(946\) | 18520.4 | 0.636522 | ||||||||
\(947\) | −19624.9 | −0.673414 | −0.336707 | − | 0.941609i | \(-0.609313\pi\) | ||||
−0.336707 | + | 0.941609i | \(0.609313\pi\) | |||||||
\(948\) | 9750.14 | 0.334040 | ||||||||
\(949\) | 50475.4 | 1.72656 | ||||||||
\(950\) | 57699.5 | 1.97055 | ||||||||
\(951\) | 3090.73 | 0.105388 | ||||||||
\(952\) | −89316.2 | −3.04071 | ||||||||
\(953\) | −1209.15 | −0.0410999 | −0.0205500 | − | 0.999789i | \(-0.506542\pi\) | ||||
−0.0205500 | + | 0.999789i | \(0.506542\pi\) | |||||||
\(954\) | −7529.71 | −0.255538 | ||||||||
\(955\) | 2800.97 | 0.0949081 | ||||||||
\(956\) | −49464.0 | −1.67341 | ||||||||
\(957\) | −7594.42 | −0.256523 | ||||||||
\(958\) | 54810.4 | 1.84848 | ||||||||
\(959\) | 44828.5 | 1.50948 | ||||||||
\(960\) | 1262.73 | 0.0424525 | ||||||||
\(961\) | −16151.6 | −0.542164 | ||||||||
\(962\) | 15082.1 | 0.505474 | ||||||||
\(963\) | −4697.93 | −0.157205 | ||||||||
\(964\) | −31635.8 | −1.05697 | ||||||||
\(965\) | 4223.59 | 0.140893 | ||||||||
\(966\) | −23289.0 | −0.775683 | ||||||||
\(967\) | −56991.1 | −1.89525 | −0.947627 | − | 0.319378i | \(-0.896526\pi\) | ||||
−0.947627 | + | 0.319378i | \(0.896526\pi\) | |||||||
\(968\) | −5042.50 | −0.167430 | ||||||||
\(969\) | −25283.3 | −0.838202 | ||||||||
\(970\) | −376.107 | −0.0124496 | ||||||||
\(971\) | −33215.1 | −1.09776 | −0.548879 | − | 0.835902i | \(-0.684945\pi\) | ||||
−0.548879 | + | 0.835902i | \(0.684945\pi\) | |||||||
\(972\) | −3992.78 | −0.131758 | ||||||||
\(973\) | −7150.61 | −0.235599 | ||||||||
\(974\) | 63630.3 | 2.09327 | ||||||||
\(975\) | −17830.8 | −0.585685 | ||||||||
\(976\) | −4546.58 | −0.149111 | ||||||||
\(977\) | −16932.1 | −0.554459 | −0.277229 | − | 0.960804i | \(-0.589416\pi\) | ||||
−0.277229 | + | 0.960804i | \(0.589416\pi\) | |||||||
\(978\) | −23224.8 | −0.759354 | ||||||||
\(979\) | 3491.73 | 0.113990 | ||||||||
\(980\) | 3759.75 | 0.122552 | ||||||||
\(981\) | −16524.7 | −0.537810 | ||||||||
\(982\) | 27513.1 | 0.894071 | ||||||||
\(983\) | 25288.2 | 0.820518 | 0.410259 | − | 0.911969i | \(-0.365438\pi\) | ||||
0.410259 | + | 0.911969i | \(0.365438\pi\) | |||||||
\(984\) | 26456.7 | 0.857123 | ||||||||
\(985\) | −4681.76 | −0.151445 | ||||||||
\(986\) | −101842. | −3.28934 | ||||||||
\(987\) | 27260.3 | 0.879134 | ||||||||
\(988\) | −74131.0 | −2.38707 | ||||||||
\(989\) | 22348.3 | 0.718537 | ||||||||
\(990\) | −486.706 | −0.0156248 | ||||||||
\(991\) | −22868.3 | −0.733033 | −0.366517 | − | 0.930411i | \(-0.619450\pi\) | ||||
−0.366517 | + | 0.930411i | \(0.619450\pi\) | |||||||
\(992\) | 4089.72 | 0.130896 | ||||||||
\(993\) | 23778.0 | 0.759891 | ||||||||
\(994\) | 126706. | 4.04313 | ||||||||
\(995\) | 2614.73 | 0.0833090 | ||||||||
\(996\) | −1029.92 | −0.0327653 | ||||||||
\(997\) | 41127.5 | 1.30644 | 0.653219 | − | 0.757169i | \(-0.273418\pi\) | ||||
0.653219 | + | 0.757169i | \(0.273418\pi\) | |||||||
\(998\) | −20735.6 | −0.657690 | ||||||||
\(999\) | −1718.95 | −0.0544395 |
(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 | 2013.4.a.d.1.4 | ✓ | 37 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2013.4.a.d.1.4 | ✓ | 37 | 1.1 | even | 1 | trivial |