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: | \(0\) |
Dimension: | \(39\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.19520 | −1.83678 | −0.918390 | − | 0.395675i | \(-0.870511\pi\) | ||||
−0.918390 | + | 0.395675i | \(0.870511\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 18.9901 | 2.37376 | ||||||||
\(5\) | 20.2319 | 1.80960 | 0.904798 | − | 0.425841i | \(-0.140022\pi\) | ||||
0.904798 | + | 0.425841i | \(0.140022\pi\) | |||||||
\(6\) | −15.5856 | −1.06047 | ||||||||
\(7\) | −14.1923 | −0.766314 | −0.383157 | − | 0.923683i | \(-0.625163\pi\) | ||||
−0.383157 | + | 0.923683i | \(0.625163\pi\) | |||||||
\(8\) | −57.0959 | −2.52330 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −105.109 | −3.32383 | ||||||||
\(11\) | −11.0000 | −0.301511 | ||||||||
\(12\) | 56.9703 | 1.37049 | ||||||||
\(13\) | 3.52655 | 0.0752375 | 0.0376188 | − | 0.999292i | \(-0.488023\pi\) | ||||
0.0376188 | + | 0.999292i | \(0.488023\pi\) | |||||||
\(14\) | 73.7320 | 1.40755 | ||||||||
\(15\) | 60.6957 | 1.04477 | ||||||||
\(16\) | 144.704 | 2.26099 | ||||||||
\(17\) | −78.5007 | −1.11995 | −0.559977 | − | 0.828508i | \(-0.689190\pi\) | ||||
−0.559977 | + | 0.828508i | \(0.689190\pi\) | |||||||
\(18\) | −46.7568 | −0.612260 | ||||||||
\(19\) | −11.9618 | −0.144433 | −0.0722166 | − | 0.997389i | \(-0.523007\pi\) | ||||
−0.0722166 | + | 0.997389i | \(0.523007\pi\) | |||||||
\(20\) | 384.206 | 4.29555 | ||||||||
\(21\) | −42.5770 | −0.442432 | ||||||||
\(22\) | 57.1472 | 0.553810 | ||||||||
\(23\) | 96.6536 | 0.876246 | 0.438123 | − | 0.898915i | \(-0.355643\pi\) | ||||
0.438123 | + | 0.898915i | \(0.355643\pi\) | |||||||
\(24\) | −171.288 | −1.45683 | ||||||||
\(25\) | 284.330 | 2.27464 | ||||||||
\(26\) | −18.3211 | −0.138195 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | −269.514 | −1.81905 | ||||||||
\(29\) | −57.3192 | −0.367031 | −0.183516 | − | 0.983017i | \(-0.558748\pi\) | ||||
−0.183516 | + | 0.983017i | \(0.558748\pi\) | |||||||
\(30\) | −315.326 | −1.91902 | ||||||||
\(31\) | −41.0071 | −0.237583 | −0.118792 | − | 0.992919i | \(-0.537902\pi\) | ||||
−0.118792 | + | 0.992919i | \(0.537902\pi\) | |||||||
\(32\) | −294.997 | −1.62964 | ||||||||
\(33\) | −33.0000 | −0.174078 | ||||||||
\(34\) | 407.827 | 2.05711 | ||||||||
\(35\) | −287.138 | −1.38672 | ||||||||
\(36\) | 170.911 | 0.791255 | ||||||||
\(37\) | 171.676 | 0.762793 | 0.381396 | − | 0.924412i | \(-0.375443\pi\) | ||||
0.381396 | + | 0.924412i | \(0.375443\pi\) | |||||||
\(38\) | 62.1441 | 0.265292 | ||||||||
\(39\) | 10.5796 | 0.0434384 | ||||||||
\(40\) | −1155.16 | −4.56616 | ||||||||
\(41\) | 25.8180 | 0.0983439 | 0.0491720 | − | 0.998790i | \(-0.484342\pi\) | ||||
0.0491720 | + | 0.998790i | \(0.484342\pi\) | |||||||
\(42\) | 221.196 | 0.812650 | ||||||||
\(43\) | 16.8900 | 0.0598998 | 0.0299499 | − | 0.999551i | \(-0.490465\pi\) | ||||
0.0299499 | + | 0.999551i | \(0.490465\pi\) | |||||||
\(44\) | −208.891 | −0.715717 | ||||||||
\(45\) | 182.087 | 0.603199 | ||||||||
\(46\) | −502.135 | −1.60947 | ||||||||
\(47\) | −230.926 | −0.716681 | −0.358340 | − | 0.933591i | \(-0.616657\pi\) | ||||
−0.358340 | + | 0.933591i | \(0.616657\pi\) | |||||||
\(48\) | 434.111 | 1.30538 | ||||||||
\(49\) | −141.578 | −0.412763 | ||||||||
\(50\) | −1477.15 | −4.17801 | ||||||||
\(51\) | −235.502 | −0.646606 | ||||||||
\(52\) | 66.9695 | 0.178596 | ||||||||
\(53\) | −264.082 | −0.684424 | −0.342212 | − | 0.939623i | \(-0.611176\pi\) | ||||
−0.342212 | + | 0.939623i | \(0.611176\pi\) | |||||||
\(54\) | −140.270 | −0.353489 | ||||||||
\(55\) | −222.551 | −0.545614 | ||||||||
\(56\) | 810.323 | 1.93364 | ||||||||
\(57\) | −35.8855 | −0.0833886 | ||||||||
\(58\) | 297.785 | 0.674156 | ||||||||
\(59\) | 90.9484 | 0.200686 | 0.100343 | − | 0.994953i | \(-0.468006\pi\) | ||||
0.100343 | + | 0.994953i | \(0.468006\pi\) | |||||||
\(60\) | 1152.62 | 2.48004 | ||||||||
\(61\) | 61.0000 | 0.128037 | ||||||||
\(62\) | 213.040 | 0.436389 | ||||||||
\(63\) | −127.731 | −0.255438 | ||||||||
\(64\) | 374.941 | 0.732307 | ||||||||
\(65\) | 71.3487 | 0.136150 | ||||||||
\(66\) | 171.442 | 0.319743 | ||||||||
\(67\) | −498.257 | −0.908534 | −0.454267 | − | 0.890866i | \(-0.650099\pi\) | ||||
−0.454267 | + | 0.890866i | \(0.650099\pi\) | |||||||
\(68\) | −1490.74 | −2.65851 | ||||||||
\(69\) | 289.961 | 0.505901 | ||||||||
\(70\) | 1491.74 | 2.54710 | ||||||||
\(71\) | 655.048 | 1.09493 | 0.547464 | − | 0.836829i | \(-0.315593\pi\) | ||||
0.547464 | + | 0.836829i | \(0.315593\pi\) | |||||||
\(72\) | −513.863 | −0.841101 | ||||||||
\(73\) | 698.166 | 1.11937 | 0.559686 | − | 0.828705i | \(-0.310922\pi\) | ||||
0.559686 | + | 0.828705i | \(0.310922\pi\) | |||||||
\(74\) | −891.890 | −1.40108 | ||||||||
\(75\) | 852.989 | 1.31326 | ||||||||
\(76\) | −227.157 | −0.342851 | ||||||||
\(77\) | 156.116 | 0.231052 | ||||||||
\(78\) | −54.9634 | −0.0797868 | ||||||||
\(79\) | 937.199 | 1.33472 | 0.667362 | − | 0.744734i | \(-0.267424\pi\) | ||||
0.667362 | + | 0.744734i | \(0.267424\pi\) | |||||||
\(80\) | 2927.63 | 4.09148 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −134.130 | −0.180636 | ||||||||
\(83\) | 1309.79 | 1.73215 | 0.866074 | − | 0.499916i | \(-0.166636\pi\) | ||||
0.866074 | + | 0.499916i | \(0.166636\pi\) | |||||||
\(84\) | −808.542 | −1.05023 | ||||||||
\(85\) | −1588.22 | −2.02667 | ||||||||
\(86\) | −87.7467 | −0.110023 | ||||||||
\(87\) | −171.958 | −0.211906 | ||||||||
\(88\) | 628.054 | 0.760805 | ||||||||
\(89\) | 447.699 | 0.533213 | 0.266607 | − | 0.963805i | \(-0.414098\pi\) | ||||
0.266607 | + | 0.963805i | \(0.414098\pi\) | |||||||
\(90\) | −945.979 | −1.10794 | ||||||||
\(91\) | −50.0499 | −0.0576556 | ||||||||
\(92\) | 1835.46 | 2.08000 | ||||||||
\(93\) | −123.021 | −0.137169 | ||||||||
\(94\) | 1199.71 | 1.31639 | ||||||||
\(95\) | −242.011 | −0.261366 | ||||||||
\(96\) | −884.991 | −0.940876 | ||||||||
\(97\) | 883.212 | 0.924501 | 0.462250 | − | 0.886749i | \(-0.347042\pi\) | ||||
0.462250 | + | 0.886749i | \(0.347042\pi\) | |||||||
\(98\) | 735.525 | 0.758155 | ||||||||
\(99\) | −99.0000 | −0.100504 | ||||||||
\(100\) | 5399.45 | 5.39945 | ||||||||
\(101\) | −278.939 | −0.274806 | −0.137403 | − | 0.990515i | \(-0.543876\pi\) | ||||
−0.137403 | + | 0.990515i | \(0.543876\pi\) | |||||||
\(102\) | 1223.48 | 1.18767 | ||||||||
\(103\) | −416.553 | −0.398488 | −0.199244 | − | 0.979950i | \(-0.563849\pi\) | ||||
−0.199244 | + | 0.979950i | \(0.563849\pi\) | |||||||
\(104\) | −201.351 | −0.189847 | ||||||||
\(105\) | −861.413 | −0.800622 | ||||||||
\(106\) | 1371.96 | 1.25714 | ||||||||
\(107\) | 1693.07 | 1.52967 | 0.764836 | − | 0.644225i | \(-0.222820\pi\) | ||||
0.764836 | + | 0.644225i | \(0.222820\pi\) | |||||||
\(108\) | 512.733 | 0.456831 | ||||||||
\(109\) | −1172.28 | −1.03013 | −0.515063 | − | 0.857152i | \(-0.672232\pi\) | ||||
−0.515063 | + | 0.857152i | \(0.672232\pi\) | |||||||
\(110\) | 1156.20 | 1.00217 | ||||||||
\(111\) | 515.027 | 0.440399 | ||||||||
\(112\) | −2053.68 | −1.73263 | ||||||||
\(113\) | 1950.16 | 1.62350 | 0.811750 | − | 0.584005i | \(-0.198515\pi\) | ||||
0.811750 | + | 0.584005i | \(0.198515\pi\) | |||||||
\(114\) | 186.432 | 0.153167 | ||||||||
\(115\) | 1955.49 | 1.58565 | ||||||||
\(116\) | −1088.50 | −0.871246 | ||||||||
\(117\) | 31.7389 | 0.0250792 | ||||||||
\(118\) | −472.495 | −0.368616 | ||||||||
\(119\) | 1114.11 | 0.858237 | ||||||||
\(120\) | −3465.47 | −2.63627 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | −316.907 | −0.235176 | ||||||||
\(123\) | 77.4541 | 0.0567789 | ||||||||
\(124\) | −778.729 | −0.563967 | ||||||||
\(125\) | 3223.54 | 2.30658 | ||||||||
\(126\) | 663.588 | 0.469184 | ||||||||
\(127\) | 793.341 | 0.554312 | 0.277156 | − | 0.960825i | \(-0.410608\pi\) | ||||
0.277156 | + | 0.960825i | \(0.410608\pi\) | |||||||
\(128\) | 412.083 | 0.284557 | ||||||||
\(129\) | 50.6699 | 0.0345832 | ||||||||
\(130\) | −370.671 | −0.250077 | ||||||||
\(131\) | 824.555 | 0.549937 | 0.274968 | − | 0.961453i | \(-0.411333\pi\) | ||||
0.274968 | + | 0.961453i | \(0.411333\pi\) | |||||||
\(132\) | −626.674 | −0.413219 | ||||||||
\(133\) | 169.766 | 0.110681 | ||||||||
\(134\) | 2588.54 | 1.66878 | ||||||||
\(135\) | 546.261 | 0.348257 | ||||||||
\(136\) | 4482.07 | 2.82599 | ||||||||
\(137\) | 1877.41 | 1.17079 | 0.585393 | − | 0.810750i | \(-0.300940\pi\) | ||||
0.585393 | + | 0.810750i | \(0.300940\pi\) | |||||||
\(138\) | −1506.40 | −0.929229 | ||||||||
\(139\) | 1417.53 | 0.864986 | 0.432493 | − | 0.901637i | \(-0.357634\pi\) | ||||
0.432493 | + | 0.901637i | \(0.357634\pi\) | |||||||
\(140\) | −5452.78 | −3.29174 | ||||||||
\(141\) | −692.778 | −0.413776 | ||||||||
\(142\) | −3403.10 | −2.01114 | ||||||||
\(143\) | −38.7920 | −0.0226850 | ||||||||
\(144\) | 1302.33 | 0.753664 | ||||||||
\(145\) | −1159.68 | −0.664178 | ||||||||
\(146\) | −3627.11 | −2.05604 | ||||||||
\(147\) | −424.733 | −0.238309 | ||||||||
\(148\) | 3260.14 | 1.81069 | ||||||||
\(149\) | −2221.54 | −1.22145 | −0.610723 | − | 0.791844i | \(-0.709121\pi\) | ||||
−0.610723 | + | 0.791844i | \(0.709121\pi\) | |||||||
\(150\) | −4431.45 | −2.41218 | ||||||||
\(151\) | −1774.71 | −0.956452 | −0.478226 | − | 0.878237i | \(-0.658720\pi\) | ||||
−0.478226 | + | 0.878237i | \(0.658720\pi\) | |||||||
\(152\) | 682.971 | 0.364449 | ||||||||
\(153\) | −706.507 | −0.373318 | ||||||||
\(154\) | −811.052 | −0.424393 | ||||||||
\(155\) | −829.651 | −0.429930 | ||||||||
\(156\) | 200.909 | 0.103113 | ||||||||
\(157\) | −1212.79 | −0.616503 | −0.308252 | − | 0.951305i | \(-0.599744\pi\) | ||||
−0.308252 | + | 0.951305i | \(0.599744\pi\) | |||||||
\(158\) | −4868.94 | −2.45159 | ||||||||
\(159\) | −792.247 | −0.395153 | ||||||||
\(160\) | −5968.35 | −2.94900 | ||||||||
\(161\) | −1371.74 | −0.671480 | ||||||||
\(162\) | −420.811 | −0.204087 | ||||||||
\(163\) | −201.341 | −0.0967500 | −0.0483750 | − | 0.998829i | \(-0.515404\pi\) | ||||
−0.0483750 | + | 0.998829i | \(0.515404\pi\) | |||||||
\(164\) | 490.288 | 0.233445 | ||||||||
\(165\) | −667.653 | −0.315010 | ||||||||
\(166\) | −6804.63 | −3.18158 | ||||||||
\(167\) | 1879.88 | 0.871077 | 0.435538 | − | 0.900170i | \(-0.356558\pi\) | ||||
0.435538 | + | 0.900170i | \(0.356558\pi\) | |||||||
\(168\) | 2430.97 | 1.11639 | ||||||||
\(169\) | −2184.56 | −0.994339 | ||||||||
\(170\) | 8251.12 | 3.72254 | ||||||||
\(171\) | −107.656 | −0.0481444 | ||||||||
\(172\) | 320.742 | 0.142188 | ||||||||
\(173\) | −755.825 | −0.332164 | −0.166082 | − | 0.986112i | \(-0.553112\pi\) | ||||
−0.166082 | + | 0.986112i | \(0.553112\pi\) | |||||||
\(174\) | 893.354 | 0.389224 | ||||||||
\(175\) | −4035.30 | −1.74309 | ||||||||
\(176\) | −1591.74 | −0.681715 | ||||||||
\(177\) | 272.845 | 0.115866 | ||||||||
\(178\) | −2325.88 | −0.979396 | ||||||||
\(179\) | 2500.82 | 1.04424 | 0.522122 | − | 0.852871i | \(-0.325140\pi\) | ||||
0.522122 | + | 0.852871i | \(0.325140\pi\) | |||||||
\(180\) | 3457.85 | 1.43185 | ||||||||
\(181\) | 283.622 | 0.116472 | 0.0582362 | − | 0.998303i | \(-0.481452\pi\) | ||||
0.0582362 | + | 0.998303i | \(0.481452\pi\) | |||||||
\(182\) | 260.019 | 0.105901 | ||||||||
\(183\) | 183.000 | 0.0739221 | ||||||||
\(184\) | −5518.52 | −2.21104 | ||||||||
\(185\) | 3473.33 | 1.38035 | ||||||||
\(186\) | 639.120 | 0.251949 | ||||||||
\(187\) | 863.508 | 0.337679 | ||||||||
\(188\) | −4385.31 | −1.70123 | ||||||||
\(189\) | −383.193 | −0.147477 | ||||||||
\(190\) | 1257.29 | 0.480072 | ||||||||
\(191\) | 1071.87 | 0.406061 | 0.203030 | − | 0.979172i | \(-0.434921\pi\) | ||||
0.203030 | + | 0.979172i | \(0.434921\pi\) | |||||||
\(192\) | 1124.82 | 0.422798 | ||||||||
\(193\) | −3395.00 | −1.26620 | −0.633101 | − | 0.774069i | \(-0.718218\pi\) | ||||
−0.633101 | + | 0.774069i | \(0.718218\pi\) | |||||||
\(194\) | −4588.46 | −1.69811 | ||||||||
\(195\) | 214.046 | 0.0786060 | ||||||||
\(196\) | −2688.58 | −0.979802 | ||||||||
\(197\) | 3436.28 | 1.24277 | 0.621383 | − | 0.783507i | \(-0.286571\pi\) | ||||
0.621383 | + | 0.783507i | \(0.286571\pi\) | |||||||
\(198\) | 514.325 | 0.184603 | ||||||||
\(199\) | −3160.28 | −1.12576 | −0.562881 | − | 0.826538i | \(-0.690307\pi\) | ||||
−0.562881 | + | 0.826538i | \(0.690307\pi\) | |||||||
\(200\) | −16234.0 | −5.73960 | ||||||||
\(201\) | −1494.77 | −0.524542 | ||||||||
\(202\) | 1449.14 | 0.504759 | ||||||||
\(203\) | 813.493 | 0.281261 | ||||||||
\(204\) | −4472.21 | −1.53489 | ||||||||
\(205\) | 522.348 | 0.177963 | ||||||||
\(206\) | 2164.08 | 0.731935 | ||||||||
\(207\) | 869.882 | 0.292082 | ||||||||
\(208\) | 510.304 | 0.170112 | ||||||||
\(209\) | 131.580 | 0.0435483 | ||||||||
\(210\) | 4475.22 | 1.47057 | ||||||||
\(211\) | 5289.73 | 1.72588 | 0.862938 | − | 0.505309i | \(-0.168622\pi\) | ||||
0.862938 | + | 0.505309i | \(0.168622\pi\) | |||||||
\(212\) | −5014.95 | −1.62466 | ||||||||
\(213\) | 1965.14 | 0.632157 | ||||||||
\(214\) | −8795.82 | −2.80967 | ||||||||
\(215\) | 341.716 | 0.108395 | ||||||||
\(216\) | −1541.59 | −0.485610 | ||||||||
\(217\) | 581.986 | 0.182064 | ||||||||
\(218\) | 6090.21 | 1.89212 | ||||||||
\(219\) | 2094.50 | 0.646270 | ||||||||
\(220\) | −4226.27 | −1.29516 | ||||||||
\(221\) | −276.836 | −0.0842626 | ||||||||
\(222\) | −2675.67 | −0.808916 | ||||||||
\(223\) | 1423.29 | 0.427401 | 0.213700 | − | 0.976899i | \(-0.431448\pi\) | ||||
0.213700 | + | 0.976899i | \(0.431448\pi\) | |||||||
\(224\) | 4186.70 | 1.24882 | ||||||||
\(225\) | 2558.97 | 0.758213 | ||||||||
\(226\) | −10131.5 | −2.98202 | ||||||||
\(227\) | −4068.61 | −1.18962 | −0.594808 | − | 0.803868i | \(-0.702772\pi\) | ||||
−0.594808 | + | 0.803868i | \(0.702772\pi\) | |||||||
\(228\) | −681.470 | −0.197945 | ||||||||
\(229\) | 639.092 | 0.184421 | 0.0922104 | − | 0.995740i | \(-0.470607\pi\) | ||||
0.0922104 | + | 0.995740i | \(0.470607\pi\) | |||||||
\(230\) | −10159.1 | −2.91249 | ||||||||
\(231\) | 468.347 | 0.133398 | ||||||||
\(232\) | 3272.69 | 0.926131 | ||||||||
\(233\) | 3664.11 | 1.03023 | 0.515116 | − | 0.857120i | \(-0.327749\pi\) | ||||
0.515116 | + | 0.857120i | \(0.327749\pi\) | |||||||
\(234\) | −164.890 | −0.0460650 | ||||||||
\(235\) | −4672.07 | −1.29690 | ||||||||
\(236\) | 1727.12 | 0.476381 | ||||||||
\(237\) | 2811.60 | 0.770603 | ||||||||
\(238\) | −5788.02 | −1.57639 | ||||||||
\(239\) | 3999.89 | 1.08256 | 0.541279 | − | 0.840843i | \(-0.317940\pi\) | ||||
0.541279 | + | 0.840843i | \(0.317940\pi\) | |||||||
\(240\) | 8782.88 | 2.36222 | ||||||||
\(241\) | 1352.84 | 0.361593 | 0.180796 | − | 0.983521i | \(-0.442132\pi\) | ||||
0.180796 | + | 0.983521i | \(0.442132\pi\) | |||||||
\(242\) | −628.619 | −0.166980 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 1158.40 | 0.303929 | ||||||||
\(245\) | −2864.39 | −0.746934 | ||||||||
\(246\) | −402.390 | −0.104290 | ||||||||
\(247\) | −42.1839 | −0.0108668 | ||||||||
\(248\) | 2341.33 | 0.599495 | ||||||||
\(249\) | 3929.37 | 1.00006 | ||||||||
\(250\) | −16747.0 | −4.23668 | ||||||||
\(251\) | 4334.84 | 1.09009 | 0.545045 | − | 0.838407i | \(-0.316513\pi\) | ||||
0.545045 | + | 0.838407i | \(0.316513\pi\) | |||||||
\(252\) | −2425.63 | −0.606350 | ||||||||
\(253\) | −1063.19 | −0.264198 | ||||||||
\(254\) | −4121.57 | −1.01815 | ||||||||
\(255\) | −4764.66 | −1.17010 | ||||||||
\(256\) | −5140.38 | −1.25498 | ||||||||
\(257\) | −6384.84 | −1.54971 | −0.774855 | − | 0.632139i | \(-0.782177\pi\) | ||||
−0.774855 | + | 0.632139i | \(0.782177\pi\) | |||||||
\(258\) | −263.240 | −0.0635218 | ||||||||
\(259\) | −2436.48 | −0.584539 | ||||||||
\(260\) | 1354.92 | 0.323187 | ||||||||
\(261\) | −515.873 | −0.122344 | ||||||||
\(262\) | −4283.73 | −1.01011 | ||||||||
\(263\) | −231.068 | −0.0541760 | −0.0270880 | − | 0.999633i | \(-0.508623\pi\) | ||||
−0.0270880 | + | 0.999633i | \(0.508623\pi\) | |||||||
\(264\) | 1884.16 | 0.439251 | ||||||||
\(265\) | −5342.89 | −1.23853 | ||||||||
\(266\) | −881.970 | −0.203297 | ||||||||
\(267\) | 1343.10 | 0.307851 | ||||||||
\(268\) | −9461.95 | −2.15664 | ||||||||
\(269\) | 2380.36 | 0.539529 | 0.269764 | − | 0.962926i | \(-0.413054\pi\) | ||||
0.269764 | + | 0.962926i | \(0.413054\pi\) | |||||||
\(270\) | −2837.94 | −0.639672 | ||||||||
\(271\) | 5017.08 | 1.12460 | 0.562299 | − | 0.826934i | \(-0.309917\pi\) | ||||
0.562299 | + | 0.826934i | \(0.309917\pi\) | |||||||
\(272\) | −11359.3 | −2.53221 | ||||||||
\(273\) | −150.150 | −0.0332875 | ||||||||
\(274\) | −9753.51 | −2.15048 | ||||||||
\(275\) | −3127.63 | −0.685829 | ||||||||
\(276\) | 5506.39 | 1.20089 | ||||||||
\(277\) | 5746.75 | 1.24653 | 0.623265 | − | 0.782011i | \(-0.285806\pi\) | ||||
0.623265 | + | 0.782011i | \(0.285806\pi\) | |||||||
\(278\) | −7364.34 | −1.58879 | ||||||||
\(279\) | −369.064 | −0.0791945 | ||||||||
\(280\) | 16394.4 | 3.49911 | ||||||||
\(281\) | 1962.23 | 0.416571 | 0.208286 | − | 0.978068i | \(-0.433212\pi\) | ||||
0.208286 | + | 0.978068i | \(0.433212\pi\) | |||||||
\(282\) | 3599.12 | 0.760016 | ||||||||
\(283\) | 1538.47 | 0.323154 | 0.161577 | − | 0.986860i | \(-0.448342\pi\) | ||||
0.161577 | + | 0.986860i | \(0.448342\pi\) | |||||||
\(284\) | 12439.4 | 2.59910 | ||||||||
\(285\) | −726.032 | −0.150900 | ||||||||
\(286\) | 201.532 | 0.0416673 | ||||||||
\(287\) | −366.418 | −0.0753623 | ||||||||
\(288\) | −2654.97 | −0.543215 | ||||||||
\(289\) | 1249.37 | 0.254298 | ||||||||
\(290\) | 6024.75 | 1.21995 | ||||||||
\(291\) | 2649.64 | 0.533761 | ||||||||
\(292\) | 13258.3 | 2.65713 | ||||||||
\(293\) | 1389.98 | 0.277144 | 0.138572 | − | 0.990352i | \(-0.455749\pi\) | ||||
0.138572 | + | 0.990352i | \(0.455749\pi\) | |||||||
\(294\) | 2206.57 | 0.437721 | ||||||||
\(295\) | 1840.06 | 0.363161 | ||||||||
\(296\) | −9801.98 | −1.92476 | ||||||||
\(297\) | −297.000 | −0.0580259 | ||||||||
\(298\) | 11541.3 | 2.24353 | ||||||||
\(299\) | 340.853 | 0.0659266 | ||||||||
\(300\) | 16198.4 | 3.11738 | ||||||||
\(301\) | −239.708 | −0.0459021 | ||||||||
\(302\) | 9220.00 | 1.75679 | ||||||||
\(303\) | −836.816 | −0.158659 | ||||||||
\(304\) | −1730.92 | −0.326563 | ||||||||
\(305\) | 1234.15 | 0.231695 | ||||||||
\(306\) | 3670.44 | 0.685704 | ||||||||
\(307\) | −2534.31 | −0.471142 | −0.235571 | − | 0.971857i | \(-0.575696\pi\) | ||||
−0.235571 | + | 0.971857i | \(0.575696\pi\) | |||||||
\(308\) | 2964.65 | 0.548464 | ||||||||
\(309\) | −1249.66 | −0.230067 | ||||||||
\(310\) | 4310.20 | 0.789687 | ||||||||
\(311\) | −7391.61 | −1.34772 | −0.673858 | − | 0.738861i | \(-0.735364\pi\) | ||||
−0.673858 | + | 0.738861i | \(0.735364\pi\) | |||||||
\(312\) | −604.054 | −0.109608 | ||||||||
\(313\) | −1255.43 | −0.226712 | −0.113356 | − | 0.993554i | \(-0.536160\pi\) | ||||
−0.113356 | + | 0.993554i | \(0.536160\pi\) | |||||||
\(314\) | 6300.68 | 1.13238 | ||||||||
\(315\) | −2584.24 | −0.462240 | ||||||||
\(316\) | 17797.5 | 3.16832 | ||||||||
\(317\) | 5649.49 | 1.00097 | 0.500484 | − | 0.865746i | \(-0.333155\pi\) | ||||
0.500484 | + | 0.865746i | \(0.333155\pi\) | |||||||
\(318\) | 4115.88 | 0.725809 | ||||||||
\(319\) | 630.511 | 0.110664 | ||||||||
\(320\) | 7585.77 | 1.32518 | ||||||||
\(321\) | 5079.20 | 0.883157 | ||||||||
\(322\) | 7126.46 | 1.23336 | ||||||||
\(323\) | 939.013 | 0.161759 | ||||||||
\(324\) | 1538.20 | 0.263752 | ||||||||
\(325\) | 1002.70 | 0.171138 | ||||||||
\(326\) | 1046.01 | 0.177709 | ||||||||
\(327\) | −3516.83 | −0.594744 | ||||||||
\(328\) | −1474.10 | −0.248152 | ||||||||
\(329\) | 3277.38 | 0.549203 | ||||||||
\(330\) | 3468.59 | 0.578605 | ||||||||
\(331\) | −861.414 | −0.143044 | −0.0715220 | − | 0.997439i | \(-0.522786\pi\) | ||||
−0.0715220 | + | 0.997439i | \(0.522786\pi\) | |||||||
\(332\) | 24873.1 | 4.11171 | ||||||||
\(333\) | 1545.08 | 0.254264 | ||||||||
\(334\) | −9766.38 | −1.59998 | ||||||||
\(335\) | −10080.7 | −1.64408 | ||||||||
\(336\) | −6161.04 | −1.00033 | ||||||||
\(337\) | 6399.02 | 1.03435 | 0.517177 | − | 0.855879i | \(-0.326983\pi\) | ||||
0.517177 | + | 0.855879i | \(0.326983\pi\) | |||||||
\(338\) | 11349.2 | 1.82638 | ||||||||
\(339\) | 5850.48 | 0.937329 | ||||||||
\(340\) | −30160.5 | −4.81083 | ||||||||
\(341\) | 451.078 | 0.0716341 | ||||||||
\(342\) | 559.297 | 0.0884308 | ||||||||
\(343\) | 6877.29 | 1.08262 | ||||||||
\(344\) | −964.346 | −0.151146 | ||||||||
\(345\) | 5866.46 | 0.915476 | ||||||||
\(346\) | 3926.66 | 0.610112 | ||||||||
\(347\) | 3387.04 | 0.523994 | 0.261997 | − | 0.965069i | \(-0.415619\pi\) | ||||
0.261997 | + | 0.965069i | \(0.415619\pi\) | |||||||
\(348\) | −3265.49 | −0.503014 | ||||||||
\(349\) | −5484.44 | −0.841190 | −0.420595 | − | 0.907249i | \(-0.638179\pi\) | ||||
−0.420595 | + | 0.907249i | \(0.638179\pi\) | |||||||
\(350\) | 20964.2 | 3.20167 | ||||||||
\(351\) | 95.2168 | 0.0144795 | ||||||||
\(352\) | 3244.97 | 0.491356 | ||||||||
\(353\) | 8776.63 | 1.32332 | 0.661661 | − | 0.749803i | \(-0.269852\pi\) | ||||
0.661661 | + | 0.749803i | \(0.269852\pi\) | |||||||
\(354\) | −1417.49 | −0.212821 | ||||||||
\(355\) | 13252.9 | 1.98138 | ||||||||
\(356\) | 8501.85 | 1.26572 | ||||||||
\(357\) | 3342.33 | 0.495503 | ||||||||
\(358\) | −12992.2 | −1.91805 | ||||||||
\(359\) | 704.904 | 0.103631 | 0.0518153 | − | 0.998657i | \(-0.483499\pi\) | ||||
0.0518153 | + | 0.998657i | \(0.483499\pi\) | |||||||
\(360\) | −10396.4 | −1.52205 | ||||||||
\(361\) | −6715.91 | −0.979139 | ||||||||
\(362\) | −1473.48 | −0.213934 | ||||||||
\(363\) | 363.000 | 0.0524864 | ||||||||
\(364\) | −950.454 | −0.136861 | ||||||||
\(365\) | 14125.2 | 2.02561 | ||||||||
\(366\) | −950.722 | −0.135779 | ||||||||
\(367\) | 1966.99 | 0.279771 | 0.139885 | − | 0.990168i | \(-0.455327\pi\) | ||||
0.139885 | + | 0.990168i | \(0.455327\pi\) | |||||||
\(368\) | 13986.1 | 1.98119 | ||||||||
\(369\) | 232.362 | 0.0327813 | ||||||||
\(370\) | −18044.6 | −2.53539 | ||||||||
\(371\) | 3747.94 | 0.524484 | ||||||||
\(372\) | −2336.19 | −0.325607 | ||||||||
\(373\) | −12306.8 | −1.70837 | −0.854187 | − | 0.519965i | \(-0.825945\pi\) | ||||
−0.854187 | + | 0.519965i | \(0.825945\pi\) | |||||||
\(374\) | −4486.10 | −0.620242 | ||||||||
\(375\) | 9670.63 | 1.33170 | ||||||||
\(376\) | 13184.9 | 1.80840 | ||||||||
\(377\) | −202.139 | −0.0276145 | ||||||||
\(378\) | 1990.76 | 0.270883 | ||||||||
\(379\) | −8902.15 | −1.20652 | −0.603262 | − | 0.797543i | \(-0.706133\pi\) | ||||
−0.603262 | + | 0.797543i | \(0.706133\pi\) | |||||||
\(380\) | −4595.81 | −0.620421 | ||||||||
\(381\) | 2380.02 | 0.320032 | ||||||||
\(382\) | −5568.56 | −0.745844 | ||||||||
\(383\) | −7231.26 | −0.964752 | −0.482376 | − | 0.875964i | \(-0.660226\pi\) | ||||
−0.482376 | + | 0.875964i | \(0.660226\pi\) | |||||||
\(384\) | 1236.25 | 0.164289 | ||||||||
\(385\) | 3158.52 | 0.418111 | ||||||||
\(386\) | 17637.7 | 2.32574 | ||||||||
\(387\) | 152.010 | 0.0199666 | ||||||||
\(388\) | 16772.3 | 2.19455 | ||||||||
\(389\) | 12110.5 | 1.57847 | 0.789236 | − | 0.614090i | \(-0.210477\pi\) | ||||
0.789236 | + | 0.614090i | \(0.210477\pi\) | |||||||
\(390\) | −1112.01 | −0.144382 | ||||||||
\(391\) | −7587.38 | −0.981356 | ||||||||
\(392\) | 8083.50 | 1.04153 | ||||||||
\(393\) | 2473.67 | 0.317506 | ||||||||
\(394\) | −17852.2 | −2.28269 | ||||||||
\(395\) | 18961.3 | 2.41531 | ||||||||
\(396\) | −1880.02 | −0.238572 | ||||||||
\(397\) | 632.133 | 0.0799140 | 0.0399570 | − | 0.999201i | \(-0.487278\pi\) | ||||
0.0399570 | + | 0.999201i | \(0.487278\pi\) | |||||||
\(398\) | 16418.3 | 2.06778 | ||||||||
\(399\) | 509.299 | 0.0639018 | ||||||||
\(400\) | 41143.5 | 5.14294 | ||||||||
\(401\) | 3506.63 | 0.436690 | 0.218345 | − | 0.975872i | \(-0.429934\pi\) | ||||
0.218345 | + | 0.975872i | \(0.429934\pi\) | |||||||
\(402\) | 7765.63 | 0.963469 | ||||||||
\(403\) | −144.613 | −0.0178752 | ||||||||
\(404\) | −5297.08 | −0.652325 | ||||||||
\(405\) | 1638.78 | 0.201066 | ||||||||
\(406\) | −4226.26 | −0.516615 | ||||||||
\(407\) | −1888.43 | −0.229991 | ||||||||
\(408\) | 13446.2 | 1.63158 | ||||||||
\(409\) | −7392.68 | −0.893752 | −0.446876 | − | 0.894596i | \(-0.647464\pi\) | ||||
−0.446876 | + | 0.894596i | \(0.647464\pi\) | |||||||
\(410\) | −2713.70 | −0.326879 | ||||||||
\(411\) | 5632.22 | 0.675954 | ||||||||
\(412\) | −7910.40 | −0.945916 | ||||||||
\(413\) | −1290.77 | −0.153789 | ||||||||
\(414\) | −4519.21 | −0.536491 | ||||||||
\(415\) | 26499.6 | 3.13449 | ||||||||
\(416\) | −1040.32 | −0.122610 | ||||||||
\(417\) | 4252.58 | 0.499400 | ||||||||
\(418\) | −683.585 | −0.0799886 | ||||||||
\(419\) | −9993.07 | −1.16514 | −0.582569 | − | 0.812781i | \(-0.697953\pi\) | ||||
−0.582569 | + | 0.812781i | \(0.697953\pi\) | |||||||
\(420\) | −16358.3 | −1.90049 | ||||||||
\(421\) | −2520.43 | −0.291777 | −0.145888 | − | 0.989301i | \(-0.546604\pi\) | ||||
−0.145888 | + | 0.989301i | \(0.546604\pi\) | |||||||
\(422\) | −27481.2 | −3.17006 | ||||||||
\(423\) | −2078.33 | −0.238894 | ||||||||
\(424\) | 15078.0 | 1.72701 | ||||||||
\(425\) | −22320.1 | −2.54749 | ||||||||
\(426\) | −10209.3 | −1.16113 | ||||||||
\(427\) | −865.732 | −0.0981164 | ||||||||
\(428\) | 32151.5 | 3.63108 | ||||||||
\(429\) | −116.376 | −0.0130972 | ||||||||
\(430\) | −1775.28 | −0.199097 | ||||||||
\(431\) | 4735.27 | 0.529212 | 0.264606 | − | 0.964357i | \(-0.414758\pi\) | ||||
0.264606 | + | 0.964357i | \(0.414758\pi\) | |||||||
\(432\) | 3907.00 | 0.435128 | ||||||||
\(433\) | 2677.76 | 0.297194 | 0.148597 | − | 0.988898i | \(-0.452524\pi\) | ||||
0.148597 | + | 0.988898i | \(0.452524\pi\) | |||||||
\(434\) | −3023.53 | −0.334411 | ||||||||
\(435\) | −3479.03 | −0.383463 | ||||||||
\(436\) | −22261.7 | −2.44528 | ||||||||
\(437\) | −1156.15 | −0.126559 | ||||||||
\(438\) | −10881.3 | −1.18706 | ||||||||
\(439\) | −3687.05 | −0.400851 | −0.200425 | − | 0.979709i | \(-0.564232\pi\) | ||||
−0.200425 | + | 0.979709i | \(0.564232\pi\) | |||||||
\(440\) | 12706.7 | 1.37675 | ||||||||
\(441\) | −1274.20 | −0.137588 | ||||||||
\(442\) | 1438.22 | 0.154772 | ||||||||
\(443\) | −12049.1 | −1.29226 | −0.646128 | − | 0.763229i | \(-0.723613\pi\) | ||||
−0.646128 | + | 0.763229i | \(0.723613\pi\) | |||||||
\(444\) | 9780.43 | 1.04540 | ||||||||
\(445\) | 9057.79 | 0.964900 | ||||||||
\(446\) | −7394.27 | −0.785042 | ||||||||
\(447\) | −6664.61 | −0.705202 | ||||||||
\(448\) | −5321.29 | −0.561177 | ||||||||
\(449\) | −7912.30 | −0.831635 | −0.415818 | − | 0.909448i | \(-0.636505\pi\) | ||||
−0.415818 | + | 0.909448i | \(0.636505\pi\) | |||||||
\(450\) | −13294.4 | −1.39267 | ||||||||
\(451\) | −283.998 | −0.0296518 | ||||||||
\(452\) | 37033.8 | 3.85381 | ||||||||
\(453\) | −5324.14 | −0.552208 | ||||||||
\(454\) | 21137.2 | 2.18506 | ||||||||
\(455\) | −1012.60 | −0.104333 | ||||||||
\(456\) | 2048.91 | 0.210415 | ||||||||
\(457\) | −8701.19 | −0.890644 | −0.445322 | − | 0.895370i | \(-0.646911\pi\) | ||||
−0.445322 | + | 0.895370i | \(0.646911\pi\) | |||||||
\(458\) | −3320.21 | −0.338741 | ||||||||
\(459\) | −2119.52 | −0.215535 | ||||||||
\(460\) | 37134.9 | 3.76396 | ||||||||
\(461\) | −4328.61 | −0.437318 | −0.218659 | − | 0.975801i | \(-0.570168\pi\) | ||||
−0.218659 | + | 0.975801i | \(0.570168\pi\) | |||||||
\(462\) | −2433.16 | −0.245023 | ||||||||
\(463\) | −6802.73 | −0.682829 | −0.341414 | − | 0.939913i | \(-0.610906\pi\) | ||||
−0.341414 | + | 0.939913i | \(0.610906\pi\) | |||||||
\(464\) | −8294.29 | −0.829855 | ||||||||
\(465\) | −2488.95 | −0.248220 | ||||||||
\(466\) | −19035.8 | −1.89231 | ||||||||
\(467\) | 9079.59 | 0.899686 | 0.449843 | − | 0.893108i | \(-0.351480\pi\) | ||||
0.449843 | + | 0.893108i | \(0.351480\pi\) | |||||||
\(468\) | 602.726 | 0.0595321 | ||||||||
\(469\) | 7071.43 | 0.696222 | ||||||||
\(470\) | 24272.3 | 2.38213 | ||||||||
\(471\) | −3638.36 | −0.355938 | ||||||||
\(472\) | −5192.78 | −0.506392 | ||||||||
\(473\) | −185.789 | −0.0180605 | ||||||||
\(474\) | −14606.8 | −1.41543 | ||||||||
\(475\) | −3401.10 | −0.328533 | ||||||||
\(476\) | 21157.1 | 2.03725 | ||||||||
\(477\) | −2376.74 | −0.228141 | ||||||||
\(478\) | −20780.2 | −1.98842 | ||||||||
\(479\) | −9756.02 | −0.930614 | −0.465307 | − | 0.885149i | \(-0.654056\pi\) | ||||
−0.465307 | + | 0.885149i | \(0.654056\pi\) | |||||||
\(480\) | −17905.1 | −1.70260 | ||||||||
\(481\) | 605.423 | 0.0573906 | ||||||||
\(482\) | −7028.26 | −0.664167 | ||||||||
\(483\) | −4115.22 | −0.387679 | ||||||||
\(484\) | 2297.80 | 0.215797 | ||||||||
\(485\) | 17869.1 | 1.67297 | ||||||||
\(486\) | −1262.43 | −0.117830 | ||||||||
\(487\) | 15102.4 | 1.40525 | 0.702624 | − | 0.711561i | \(-0.252012\pi\) | ||||
0.702624 | + | 0.711561i | \(0.252012\pi\) | |||||||
\(488\) | −3482.85 | −0.323076 | ||||||||
\(489\) | −604.023 | −0.0558586 | ||||||||
\(490\) | 14881.1 | 1.37195 | ||||||||
\(491\) | −6404.28 | −0.588637 | −0.294319 | − | 0.955707i | \(-0.595093\pi\) | ||||
−0.294319 | + | 0.955707i | \(0.595093\pi\) | |||||||
\(492\) | 1470.86 | 0.134780 | ||||||||
\(493\) | 4499.60 | 0.411058 | ||||||||
\(494\) | 219.154 | 0.0199599 | ||||||||
\(495\) | −2002.96 | −0.181871 | ||||||||
\(496\) | −5933.87 | −0.537174 | ||||||||
\(497\) | −9296.65 | −0.839058 | ||||||||
\(498\) | −20413.9 | −1.83688 | ||||||||
\(499\) | 3981.40 | 0.357178 | 0.178589 | − | 0.983924i | \(-0.442847\pi\) | ||||
0.178589 | + | 0.983924i | \(0.442847\pi\) | |||||||
\(500\) | 61215.4 | 5.47528 | ||||||||
\(501\) | 5639.65 | 0.502916 | ||||||||
\(502\) | −22520.4 | −2.00226 | ||||||||
\(503\) | 10949.9 | 0.970641 | 0.485320 | − | 0.874336i | \(-0.338703\pi\) | ||||
0.485320 | + | 0.874336i | \(0.338703\pi\) | |||||||
\(504\) | 7292.91 | 0.644548 | ||||||||
\(505\) | −5643.46 | −0.497288 | ||||||||
\(506\) | 5523.48 | 0.485274 | ||||||||
\(507\) | −6553.69 | −0.574082 | ||||||||
\(508\) | 15065.6 | 1.31581 | ||||||||
\(509\) | 411.376 | 0.0358230 | 0.0179115 | − | 0.999840i | \(-0.494298\pi\) | ||||
0.0179115 | + | 0.999840i | \(0.494298\pi\) | |||||||
\(510\) | 24753.4 | 2.14921 | ||||||||
\(511\) | −9908.61 | −0.857790 | ||||||||
\(512\) | 23408.7 | 2.02056 | ||||||||
\(513\) | −322.969 | −0.0277962 | ||||||||
\(514\) | 33170.5 | 2.84648 | ||||||||
\(515\) | −8427.67 | −0.721102 | ||||||||
\(516\) | 962.226 | 0.0820924 | ||||||||
\(517\) | 2540.18 | 0.216087 | ||||||||
\(518\) | 12658.0 | 1.07367 | ||||||||
\(519\) | −2267.48 | −0.191775 | ||||||||
\(520\) | −4073.72 | −0.343547 | ||||||||
\(521\) | 1527.57 | 0.128453 | 0.0642264 | − | 0.997935i | \(-0.479542\pi\) | ||||
0.0642264 | + | 0.997935i | \(0.479542\pi\) | |||||||
\(522\) | 2680.06 | 0.224719 | ||||||||
\(523\) | −10845.4 | −0.906760 | −0.453380 | − | 0.891317i | \(-0.649782\pi\) | ||||
−0.453380 | + | 0.891317i | \(0.649782\pi\) | |||||||
\(524\) | 15658.4 | 1.30542 | ||||||||
\(525\) | −12105.9 | −1.00637 | ||||||||
\(526\) | 1200.45 | 0.0995094 | ||||||||
\(527\) | 3219.09 | 0.266083 | ||||||||
\(528\) | −4775.22 | −0.393588 | ||||||||
\(529\) | −2825.09 | −0.232193 | ||||||||
\(530\) | 27757.4 | 2.27491 | ||||||||
\(531\) | 818.536 | 0.0668954 | ||||||||
\(532\) | 3223.88 | 0.262731 | ||||||||
\(533\) | 91.0485 | 0.00739915 | ||||||||
\(534\) | −6977.65 | −0.565454 | ||||||||
\(535\) | 34254.0 | 2.76809 | ||||||||
\(536\) | 28448.4 | 2.29251 | ||||||||
\(537\) | 7502.45 | 0.602895 | ||||||||
\(538\) | −12366.5 | −0.990996 | ||||||||
\(539\) | 1557.35 | 0.124453 | ||||||||
\(540\) | 10373.6 | 0.826680 | ||||||||
\(541\) | −20350.6 | −1.61727 | −0.808634 | − | 0.588312i | \(-0.799793\pi\) | ||||
−0.808634 | + | 0.588312i | \(0.799793\pi\) | |||||||
\(542\) | −26064.8 | −2.06564 | ||||||||
\(543\) | 850.867 | 0.0672453 | ||||||||
\(544\) | 23157.5 | 1.82513 | ||||||||
\(545\) | −23717.4 | −1.86411 | ||||||||
\(546\) | 780.058 | 0.0611418 | ||||||||
\(547\) | 21276.7 | 1.66312 | 0.831559 | − | 0.555437i | \(-0.187449\pi\) | ||||
0.831559 | + | 0.555437i | \(0.187449\pi\) | |||||||
\(548\) | 35652.2 | 2.77917 | ||||||||
\(549\) | 549.000 | 0.0426790 | ||||||||
\(550\) | 16248.7 | 1.25972 | ||||||||
\(551\) | 685.642 | 0.0530115 | ||||||||
\(552\) | −16555.6 | −1.27654 | ||||||||
\(553\) | −13301.0 | −1.02282 | ||||||||
\(554\) | −29855.5 | −2.28960 | ||||||||
\(555\) | 10420.0 | 0.796944 | ||||||||
\(556\) | 26919.0 | 2.05327 | ||||||||
\(557\) | 10163.9 | 0.773172 | 0.386586 | − | 0.922253i | \(-0.373654\pi\) | ||||
0.386586 | + | 0.922253i | \(0.373654\pi\) | |||||||
\(558\) | 1917.36 | 0.145463 | ||||||||
\(559\) | 59.5632 | 0.00450672 | ||||||||
\(560\) | −41549.9 | −3.13536 | ||||||||
\(561\) | 2590.52 | 0.194959 | ||||||||
\(562\) | −10194.2 | −0.765150 | ||||||||
\(563\) | −9195.42 | −0.688349 | −0.344175 | − | 0.938906i | \(-0.611841\pi\) | ||||
−0.344175 | + | 0.938906i | \(0.611841\pi\) | |||||||
\(564\) | −13155.9 | −0.982207 | ||||||||
\(565\) | 39455.4 | 2.93788 | ||||||||
\(566\) | −7992.67 | −0.593563 | ||||||||
\(567\) | −1149.58 | −0.0851460 | ||||||||
\(568\) | −37400.5 | −2.76283 | ||||||||
\(569\) | −10516.8 | −0.774842 | −0.387421 | − | 0.921903i | \(-0.626634\pi\) | ||||
−0.387421 | + | 0.921903i | \(0.626634\pi\) | |||||||
\(570\) | 3771.88 | 0.277170 | ||||||||
\(571\) | 21919.5 | 1.60648 | 0.803241 | − | 0.595654i | \(-0.203107\pi\) | ||||
0.803241 | + | 0.595654i | \(0.203107\pi\) | |||||||
\(572\) | −736.665 | −0.0538488 | ||||||||
\(573\) | 3215.60 | 0.234439 | ||||||||
\(574\) | 1903.62 | 0.138424 | ||||||||
\(575\) | 27481.5 | 1.99314 | ||||||||
\(576\) | 3374.47 | 0.244102 | ||||||||
\(577\) | −3682.02 | −0.265658 | −0.132829 | − | 0.991139i | \(-0.542406\pi\) | ||||
−0.132829 | + | 0.991139i | \(0.542406\pi\) | |||||||
\(578\) | −6490.71 | −0.467090 | ||||||||
\(579\) | −10185.0 | −0.731043 | ||||||||
\(580\) | −22022.4 | −1.57660 | ||||||||
\(581\) | −18589.0 | −1.32737 | ||||||||
\(582\) | −13765.4 | −0.980402 | ||||||||
\(583\) | 2904.91 | 0.206362 | ||||||||
\(584\) | −39862.4 | −2.82452 | ||||||||
\(585\) | 642.139 | 0.0453832 | ||||||||
\(586\) | −7221.21 | −0.509053 | ||||||||
\(587\) | 21123.0 | 1.48525 | 0.742624 | − | 0.669709i | \(-0.233581\pi\) | ||||
0.742624 | + | 0.669709i | \(0.233581\pi\) | |||||||
\(588\) | −8065.73 | −0.565689 | ||||||||
\(589\) | 490.520 | 0.0343150 | ||||||||
\(590\) | −9559.48 | −0.667047 | ||||||||
\(591\) | 10308.9 | 0.717512 | ||||||||
\(592\) | 24842.1 | 1.72467 | ||||||||
\(593\) | 8474.91 | 0.586885 | 0.293442 | − | 0.955977i | \(-0.405199\pi\) | ||||
0.293442 | + | 0.955977i | \(0.405199\pi\) | |||||||
\(594\) | 1542.97 | 0.106581 | ||||||||
\(595\) | 22540.5 | 1.55306 | ||||||||
\(596\) | −42187.2 | −2.89942 | ||||||||
\(597\) | −9480.85 | −0.649958 | ||||||||
\(598\) | −1770.80 | −0.121093 | ||||||||
\(599\) | 9210.29 | 0.628251 | 0.314125 | − | 0.949381i | \(-0.398289\pi\) | ||||
0.314125 | + | 0.949381i | \(0.398289\pi\) | |||||||
\(600\) | −48702.1 | −3.31376 | ||||||||
\(601\) | −19870.6 | −1.34865 | −0.674324 | − | 0.738436i | \(-0.735565\pi\) | ||||
−0.674324 | + | 0.738436i | \(0.735565\pi\) | |||||||
\(602\) | 1245.33 | 0.0843121 | ||||||||
\(603\) | −4484.31 | −0.302845 | ||||||||
\(604\) | −33702.0 | −2.27039 | ||||||||
\(605\) | 2448.06 | 0.164509 | ||||||||
\(606\) | 4347.43 | 0.291423 | ||||||||
\(607\) | 22915.6 | 1.53232 | 0.766158 | − | 0.642652i | \(-0.222166\pi\) | ||||
0.766158 | + | 0.642652i | \(0.222166\pi\) | |||||||
\(608\) | 3528.71 | 0.235375 | ||||||||
\(609\) | 2440.48 | 0.162386 | ||||||||
\(610\) | −6411.64 | −0.425573 | ||||||||
\(611\) | −814.371 | −0.0539213 | ||||||||
\(612\) | −13416.6 | −0.886169 | ||||||||
\(613\) | −17870.8 | −1.17748 | −0.588741 | − | 0.808322i | \(-0.700376\pi\) | ||||
−0.588741 | + | 0.808322i | \(0.700376\pi\) | |||||||
\(614\) | 13166.2 | 0.865384 | ||||||||
\(615\) | 1567.04 | 0.102747 | ||||||||
\(616\) | −8913.56 | −0.583015 | ||||||||
\(617\) | 19689.7 | 1.28473 | 0.642365 | − | 0.766399i | \(-0.277954\pi\) | ||||
0.642365 | + | 0.766399i | \(0.277954\pi\) | |||||||
\(618\) | 6492.24 | 0.422583 | ||||||||
\(619\) | −3004.27 | −0.195076 | −0.0975378 | − | 0.995232i | \(-0.531097\pi\) | ||||
−0.0975378 | + | 0.995232i | \(0.531097\pi\) | |||||||
\(620\) | −15755.2 | −1.02055 | ||||||||
\(621\) | 2609.65 | 0.168634 | ||||||||
\(622\) | 38400.9 | 2.47546 | ||||||||
\(623\) | −6353.89 | −0.408609 | ||||||||
\(624\) | 1530.91 | 0.0982139 | ||||||||
\(625\) | 29677.2 | 1.89934 | ||||||||
\(626\) | 6522.20 | 0.416421 | ||||||||
\(627\) | 394.740 | 0.0251426 | ||||||||
\(628\) | −23031.0 | −1.46343 | ||||||||
\(629\) | −13476.7 | −0.854293 | ||||||||
\(630\) | 13425.6 | 0.849033 | ||||||||
\(631\) | 21673.9 | 1.36739 | 0.683697 | − | 0.729766i | \(-0.260371\pi\) | ||||
0.683697 | + | 0.729766i | \(0.260371\pi\) | |||||||
\(632\) | −53510.2 | −3.36791 | ||||||||
\(633\) | 15869.2 | 0.996435 | ||||||||
\(634\) | −29350.2 | −1.83856 | ||||||||
\(635\) | 16050.8 | 1.00308 | ||||||||
\(636\) | −15044.9 | −0.937999 | ||||||||
\(637\) | −499.280 | −0.0310553 | ||||||||
\(638\) | −3275.63 | −0.203266 | ||||||||
\(639\) | 5895.43 | 0.364976 | ||||||||
\(640\) | 8337.21 | 0.514933 | ||||||||
\(641\) | −7667.71 | −0.472475 | −0.236237 | − | 0.971695i | \(-0.575914\pi\) | ||||
−0.236237 | + | 0.971695i | \(0.575914\pi\) | |||||||
\(642\) | −26387.5 | −1.62217 | ||||||||
\(643\) | −27570.3 | −1.69093 | −0.845463 | − | 0.534035i | \(-0.820675\pi\) | ||||
−0.845463 | + | 0.534035i | \(0.820675\pi\) | |||||||
\(644\) | −26049.5 | −1.59393 | ||||||||
\(645\) | 1025.15 | 0.0625816 | ||||||||
\(646\) | −4878.36 | −0.297115 | ||||||||
\(647\) | 10873.6 | 0.660719 | 0.330360 | − | 0.943855i | \(-0.392830\pi\) | ||||
0.330360 | + | 0.943855i | \(0.392830\pi\) | |||||||
\(648\) | −4624.76 | −0.280367 | ||||||||
\(649\) | −1000.43 | −0.0605091 | ||||||||
\(650\) | −5209.24 | −0.314343 | ||||||||
\(651\) | 1745.96 | 0.105114 | ||||||||
\(652\) | −3823.49 | −0.229662 | ||||||||
\(653\) | −2866.96 | −0.171811 | −0.0859057 | − | 0.996303i | \(-0.527378\pi\) | ||||
−0.0859057 | + | 0.996303i | \(0.527378\pi\) | |||||||
\(654\) | 18270.6 | 1.09241 | ||||||||
\(655\) | 16682.3 | 0.995163 | ||||||||
\(656\) | 3735.96 | 0.222355 | ||||||||
\(657\) | 6283.50 | 0.373124 | ||||||||
\(658\) | −17026.6 | −1.00876 | ||||||||
\(659\) | −5297.83 | −0.313162 | −0.156581 | − | 0.987665i | \(-0.550047\pi\) | ||||
−0.156581 | + | 0.987665i | \(0.550047\pi\) | |||||||
\(660\) | −12678.8 | −0.747760 | ||||||||
\(661\) | 27215.1 | 1.60143 | 0.800716 | − | 0.599044i | \(-0.204453\pi\) | ||||
0.800716 | + | 0.599044i | \(0.204453\pi\) | |||||||
\(662\) | 4475.22 | 0.262741 | ||||||||
\(663\) | −830.509 | −0.0486490 | ||||||||
\(664\) | −74783.7 | −4.37074 | ||||||||
\(665\) | 3434.69 | 0.200288 | ||||||||
\(666\) | −8027.01 | −0.467028 | ||||||||
\(667\) | −5540.10 | −0.321610 | ||||||||
\(668\) | 35699.2 | 2.06773 | ||||||||
\(669\) | 4269.86 | 0.246760 | ||||||||
\(670\) | 52371.2 | 3.01981 | ||||||||
\(671\) | −671.000 | −0.0386046 | ||||||||
\(672\) | 12560.1 | 0.721006 | ||||||||
\(673\) | 22581.3 | 1.29338 | 0.646691 | − | 0.762752i | \(-0.276152\pi\) | ||||
0.646691 | + | 0.762752i | \(0.276152\pi\) | |||||||
\(674\) | −33244.2 | −1.89988 | ||||||||
\(675\) | 7676.90 | 0.437754 | ||||||||
\(676\) | −41485.1 | −2.36033 | ||||||||
\(677\) | −5985.20 | −0.339778 | −0.169889 | − | 0.985463i | \(-0.554341\pi\) | ||||
−0.169889 | + | 0.985463i | \(0.554341\pi\) | |||||||
\(678\) | −30394.4 | −1.72167 | ||||||||
\(679\) | −12534.8 | −0.708458 | ||||||||
\(680\) | 90680.7 | 5.11389 | ||||||||
\(681\) | −12205.8 | −0.686825 | ||||||||
\(682\) | −2343.44 | −0.131576 | ||||||||
\(683\) | 9712.88 | 0.544148 | 0.272074 | − | 0.962276i | \(-0.412290\pi\) | ||||
0.272074 | + | 0.962276i | \(0.412290\pi\) | |||||||
\(684\) | −2044.41 | −0.114284 | ||||||||
\(685\) | 37983.5 | 2.11865 | ||||||||
\(686\) | −35728.9 | −1.98854 | ||||||||
\(687\) | 1917.28 | 0.106475 | ||||||||
\(688\) | 2444.04 | 0.135433 | ||||||||
\(689\) | −931.299 | −0.0514944 | ||||||||
\(690\) | −30477.4 | −1.68153 | ||||||||
\(691\) | 20436.0 | 1.12507 | 0.562533 | − | 0.826775i | \(-0.309827\pi\) | ||||
0.562533 | + | 0.826775i | \(0.309827\pi\) | |||||||
\(692\) | −14353.2 | −0.788478 | ||||||||
\(693\) | 1405.04 | 0.0770174 | ||||||||
\(694\) | −17596.4 | −0.962463 | ||||||||
\(695\) | 28679.3 | 1.56528 | ||||||||
\(696\) | 9818.06 | 0.534702 | ||||||||
\(697\) | −2026.74 | −0.110141 | ||||||||
\(698\) | 28492.8 | 1.54508 | ||||||||
\(699\) | 10992.3 | 0.594805 | ||||||||
\(700\) | −76630.8 | −4.13768 | ||||||||
\(701\) | −13067.5 | −0.704069 | −0.352035 | − | 0.935987i | \(-0.614510\pi\) | ||||
−0.352035 | + | 0.935987i | \(0.614510\pi\) | |||||||
\(702\) | −494.670 | −0.0265956 | ||||||||
\(703\) | −2053.56 | −0.110173 | ||||||||
\(704\) | −4124.35 | −0.220799 | ||||||||
\(705\) | −14016.2 | −0.748767 | ||||||||
\(706\) | −45596.4 | −2.43065 | ||||||||
\(707\) | 3958.79 | 0.210588 | ||||||||
\(708\) | 5181.36 | 0.275039 | ||||||||
\(709\) | −26035.0 | −1.37908 | −0.689539 | − | 0.724249i | \(-0.742187\pi\) | ||||
−0.689539 | + | 0.724249i | \(0.742187\pi\) | |||||||
\(710\) | −68851.2 | −3.63935 | ||||||||
\(711\) | 8434.79 | 0.444908 | ||||||||
\(712\) | −25561.7 | −1.34546 | ||||||||
\(713\) | −3963.48 | −0.208182 | ||||||||
\(714\) | −17364.1 | −0.910131 | ||||||||
\(715\) | −784.836 | −0.0410506 | ||||||||
\(716\) | 47490.8 | 2.47879 | ||||||||
\(717\) | 11999.7 | 0.625015 | ||||||||
\(718\) | −3662.12 | −0.190347 | ||||||||
\(719\) | −2941.21 | −0.152557 | −0.0762785 | − | 0.997087i | \(-0.524304\pi\) | ||||
−0.0762785 | + | 0.997087i | \(0.524304\pi\) | |||||||
\(720\) | 26348.6 | 1.36383 | ||||||||
\(721\) | 5911.87 | 0.305367 | ||||||||
\(722\) | 34890.5 | 1.79846 | ||||||||
\(723\) | 4058.51 | 0.208766 | ||||||||
\(724\) | 5386.02 | 0.276478 | ||||||||
\(725\) | −16297.5 | −0.834863 | ||||||||
\(726\) | −1885.86 | −0.0964060 | ||||||||
\(727\) | 2186.49 | 0.111544 | 0.0557719 | − | 0.998444i | \(-0.482238\pi\) | ||||
0.0557719 | + | 0.998444i | \(0.482238\pi\) | |||||||
\(728\) | 2857.64 | 0.145483 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −73383.4 | −3.72060 | ||||||||
\(731\) | −1325.87 | −0.0670851 | ||||||||
\(732\) | 3475.19 | 0.175474 | ||||||||
\(733\) | 12452.5 | 0.627479 | 0.313740 | − | 0.949509i | \(-0.398418\pi\) | ||||
0.313740 | + | 0.949509i | \(0.398418\pi\) | |||||||
\(734\) | −10218.9 | −0.513878 | ||||||||
\(735\) | −8593.16 | −0.431243 | ||||||||
\(736\) | −28512.5 | −1.42797 | ||||||||
\(737\) | 5480.82 | 0.273933 | ||||||||
\(738\) | −1207.17 | −0.0602121 | ||||||||
\(739\) | −1009.12 | −0.0502313 | −0.0251157 | − | 0.999685i | \(-0.507995\pi\) | ||||
−0.0251157 | + | 0.999685i | \(0.507995\pi\) | |||||||
\(740\) | 65958.9 | 3.27662 | ||||||||
\(741\) | −126.552 | −0.00627395 | ||||||||
\(742\) | −19471.3 | −0.963362 | ||||||||
\(743\) | −5922.18 | −0.292414 | −0.146207 | − | 0.989254i | \(-0.546707\pi\) | ||||
−0.146207 | + | 0.989254i | \(0.546707\pi\) | |||||||
\(744\) | 7024.00 | 0.346119 | ||||||||
\(745\) | −44945.9 | −2.21032 | ||||||||
\(746\) | 63936.5 | 3.13791 | ||||||||
\(747\) | 11788.1 | 0.577383 | ||||||||
\(748\) | 16398.1 | 0.801570 | ||||||||
\(749\) | −24028.6 | −1.17221 | ||||||||
\(750\) | −50240.9 | −2.44605 | ||||||||
\(751\) | −28675.3 | −1.39331 | −0.696654 | − | 0.717407i | \(-0.745329\pi\) | ||||
−0.696654 | + | 0.717407i | \(0.745329\pi\) | |||||||
\(752\) | −33415.8 | −1.62041 | ||||||||
\(753\) | 13004.5 | 0.629364 | ||||||||
\(754\) | 1050.15 | 0.0507218 | ||||||||
\(755\) | −35905.8 | −1.73079 | ||||||||
\(756\) | −7276.88 | −0.350076 | ||||||||
\(757\) | 17950.6 | 0.861856 | 0.430928 | − | 0.902386i | \(-0.358186\pi\) | ||||
0.430928 | + | 0.902386i | \(0.358186\pi\) | |||||||
\(758\) | 46248.5 | 2.21612 | ||||||||
\(759\) | −3189.57 | −0.152535 | ||||||||
\(760\) | 13817.8 | 0.659506 | ||||||||
\(761\) | 30285.6 | 1.44264 | 0.721321 | − | 0.692600i | \(-0.243535\pi\) | ||||
0.721321 | + | 0.692600i | \(0.243535\pi\) | |||||||
\(762\) | −12364.7 | −0.587829 | ||||||||
\(763\) | 16637.3 | 0.789400 | ||||||||
\(764\) | 20354.9 | 0.963892 | ||||||||
\(765\) | −14294.0 | −0.675555 | ||||||||
\(766\) | 37567.9 | 1.77204 | ||||||||
\(767\) | 320.734 | 0.0150991 | ||||||||
\(768\) | −15421.1 | −0.724561 | ||||||||
\(769\) | −34159.7 | −1.60186 | −0.800931 | − | 0.598757i | \(-0.795662\pi\) | ||||
−0.800931 | + | 0.598757i | \(0.795662\pi\) | |||||||
\(770\) | −16409.1 | −0.767979 | ||||||||
\(771\) | −19154.5 | −0.894725 | ||||||||
\(772\) | −64471.4 | −3.00567 | ||||||||
\(773\) | 26424.3 | 1.22952 | 0.614759 | − | 0.788715i | \(-0.289253\pi\) | ||||
0.614759 | + | 0.788715i | \(0.289253\pi\) | |||||||
\(774\) | −789.720 | −0.0366743 | ||||||||
\(775\) | −11659.5 | −0.540416 | ||||||||
\(776\) | −50427.7 | −2.33280 | ||||||||
\(777\) | −7309.44 | −0.337484 | ||||||||
\(778\) | −62916.4 | −2.89931 | ||||||||
\(779\) | −308.831 | −0.0142041 | ||||||||
\(780\) | 4064.76 | 0.186592 | ||||||||
\(781\) | −7205.52 | −0.330133 | ||||||||
\(782\) | 39417.9 | 1.80254 | ||||||||
\(783\) | −1547.62 | −0.0706352 | ||||||||
\(784\) | −20486.8 | −0.933254 | ||||||||
\(785\) | −24537.0 | −1.11562 | ||||||||
\(786\) | −12851.2 | −0.583189 | ||||||||
\(787\) | 25200.9 | 1.14144 | 0.570720 | − | 0.821145i | \(-0.306664\pi\) | ||||
0.570720 | + | 0.821145i | \(0.306664\pi\) | |||||||
\(788\) | 65255.4 | 2.95004 | ||||||||
\(789\) | −693.205 | −0.0312785 | ||||||||
\(790\) | −98507.9 | −4.43640 | ||||||||
\(791\) | −27677.3 | −1.24411 | ||||||||
\(792\) | 5652.49 | 0.253602 | ||||||||
\(793\) | 215.119 | 0.00963318 | ||||||||
\(794\) | −3284.06 | −0.146784 | ||||||||
\(795\) | −16028.7 | −0.715067 | ||||||||
\(796\) | −60014.1 | −2.67229 | ||||||||
\(797\) | −4756.15 | −0.211382 | −0.105691 | − | 0.994399i | \(-0.533705\pi\) | ||||
−0.105691 | + | 0.994399i | \(0.533705\pi\) | |||||||
\(798\) | −2645.91 | −0.117374 | ||||||||
\(799\) | 18127.9 | 0.802650 | ||||||||
\(800\) | −83876.4 | −3.70685 | ||||||||
\(801\) | 4029.29 | 0.177738 | ||||||||
\(802\) | −18217.6 | −0.802103 | ||||||||
\(803\) | −7679.83 | −0.337503 | ||||||||
\(804\) | −28385.9 | −1.24514 | ||||||||
\(805\) | −27752.9 | −1.21511 | ||||||||
\(806\) | 751.295 | 0.0328328 | ||||||||
\(807\) | 7141.09 | 0.311497 | ||||||||
\(808\) | 15926.2 | 0.693420 | ||||||||
\(809\) | −26343.8 | −1.14487 | −0.572435 | − | 0.819950i | \(-0.694001\pi\) | ||||
−0.572435 | + | 0.819950i | \(0.694001\pi\) | |||||||
\(810\) | −8513.81 | −0.369315 | ||||||||
\(811\) | 27595.0 | 1.19481 | 0.597406 | − | 0.801939i | \(-0.296198\pi\) | ||||
0.597406 | + | 0.801939i | \(0.296198\pi\) | |||||||
\(812\) | 15448.3 | 0.667648 | ||||||||
\(813\) | 15051.3 | 0.649287 | ||||||||
\(814\) | 9810.79 | 0.422442 | ||||||||
\(815\) | −4073.51 | −0.175078 | ||||||||
\(816\) | −34078.0 | −1.46197 | ||||||||
\(817\) | −202.035 | −0.00865153 | ||||||||
\(818\) | 38406.5 | 1.64163 | ||||||||
\(819\) | −450.449 | −0.0192185 | ||||||||
\(820\) | 9919.45 | 0.422442 | ||||||||
\(821\) | −14264.7 | −0.606386 | −0.303193 | − | 0.952929i | \(-0.598053\pi\) | ||||
−0.303193 | + | 0.952929i | \(0.598053\pi\) | |||||||
\(822\) | −29260.5 | −1.24158 | ||||||||
\(823\) | 8243.99 | 0.349171 | 0.174585 | − | 0.984642i | \(-0.444141\pi\) | ||||
0.174585 | + | 0.984642i | \(0.444141\pi\) | |||||||
\(824\) | 23783.5 | 1.00551 | ||||||||
\(825\) | −9382.88 | −0.395964 | ||||||||
\(826\) | 6705.81 | 0.282476 | ||||||||
\(827\) | 38487.5 | 1.61831 | 0.809155 | − | 0.587596i | \(-0.199925\pi\) | ||||
0.809155 | + | 0.587596i | \(0.199925\pi\) | |||||||
\(828\) | 16519.2 | 0.693334 | ||||||||
\(829\) | −25969.6 | −1.08801 | −0.544007 | − | 0.839081i | \(-0.683093\pi\) | ||||
−0.544007 | + | 0.839081i | \(0.683093\pi\) | |||||||
\(830\) | −137671. | −5.75737 | ||||||||
\(831\) | 17240.2 | 0.719684 | ||||||||
\(832\) | 1322.25 | 0.0550970 | ||||||||
\(833\) | 11114.0 | 0.462276 | ||||||||
\(834\) | −22093.0 | −0.917289 | ||||||||
\(835\) | 38033.6 | 1.57630 | ||||||||
\(836\) | 2498.72 | 0.103373 | ||||||||
\(837\) | −1107.19 | −0.0457230 | ||||||||
\(838\) | 51916.0 | 2.14010 | ||||||||
\(839\) | 18635.0 | 0.766806 | 0.383403 | − | 0.923581i | \(-0.374752\pi\) | ||||
0.383403 | + | 0.923581i | \(0.374752\pi\) | |||||||
\(840\) | 49183.1 | 2.02021 | ||||||||
\(841\) | −21103.5 | −0.865288 | ||||||||
\(842\) | 13094.1 | 0.535930 | ||||||||
\(843\) | 5886.68 | 0.240508 | ||||||||
\(844\) | 100453. | 4.09682 | ||||||||
\(845\) | −44197.9 | −1.79935 | ||||||||
\(846\) | 10797.4 | 0.438795 | ||||||||
\(847\) | −1717.27 | −0.0696649 | ||||||||
\(848\) | −38213.6 | −1.54748 | ||||||||
\(849\) | 4615.41 | 0.186573 | ||||||||
\(850\) | 115957. | 4.67918 | ||||||||
\(851\) | 16593.1 | 0.668394 | ||||||||
\(852\) | 37318.3 | 1.50059 | ||||||||
\(853\) | 35743.1 | 1.43472 | 0.717362 | − | 0.696701i | \(-0.245350\pi\) | ||||
0.717362 | + | 0.696701i | \(0.245350\pi\) | |||||||
\(854\) | 4497.65 | 0.180218 | ||||||||
\(855\) | −2178.09 | −0.0871220 | ||||||||
\(856\) | −96667.1 | −3.85983 | ||||||||
\(857\) | 11207.6 | 0.446727 | 0.223363 | − | 0.974735i | \(-0.428296\pi\) | ||||
0.223363 | + | 0.974735i | \(0.428296\pi\) | |||||||
\(858\) | 604.597 | 0.0240566 | ||||||||
\(859\) | 42173.7 | 1.67514 | 0.837572 | − | 0.546328i | \(-0.183975\pi\) | ||||
0.837572 | + | 0.546328i | \(0.183975\pi\) | |||||||
\(860\) | 6489.22 | 0.257303 | ||||||||
\(861\) | −1099.25 | −0.0435105 | ||||||||
\(862\) | −24600.7 | −0.972046 | ||||||||
\(863\) | −27461.7 | −1.08320 | −0.541602 | − | 0.840635i | \(-0.682182\pi\) | ||||
−0.541602 | + | 0.840635i | \(0.682182\pi\) | |||||||
\(864\) | −7964.92 | −0.313625 | ||||||||
\(865\) | −15291.8 | −0.601082 | ||||||||
\(866\) | −13911.5 | −0.545879 | ||||||||
\(867\) | 3748.10 | 0.146819 | ||||||||
\(868\) | 11052.0 | 0.432176 | ||||||||
\(869\) | −10309.2 | −0.402434 | ||||||||
\(870\) | 18074.2 | 0.704338 | ||||||||
\(871\) | −1757.13 | −0.0683558 | ||||||||
\(872\) | 66932.2 | 2.59932 | ||||||||
\(873\) | 7948.91 | 0.308167 | ||||||||
\(874\) | 6006.45 | 0.232461 | ||||||||
\(875\) | −45749.6 | −1.76756 | ||||||||
\(876\) | 39774.8 | 1.53409 | ||||||||
\(877\) | −1472.63 | −0.0567016 | −0.0283508 | − | 0.999598i | \(-0.509026\pi\) | ||||
−0.0283508 | + | 0.999598i | \(0.509026\pi\) | |||||||
\(878\) | 19155.0 | 0.736275 | ||||||||
\(879\) | 4169.93 | 0.160009 | ||||||||
\(880\) | −32203.9 | −1.23363 | ||||||||
\(881\) | 33279.2 | 1.27265 | 0.636326 | − | 0.771421i | \(-0.280454\pi\) | ||||
0.636326 | + | 0.771421i | \(0.280454\pi\) | |||||||
\(882\) | 6619.72 | 0.252718 | ||||||||
\(883\) | −5560.78 | −0.211931 | −0.105966 | − | 0.994370i | \(-0.533793\pi\) | ||||
−0.105966 | + | 0.994370i | \(0.533793\pi\) | |||||||
\(884\) | −5257.16 | −0.200020 | ||||||||
\(885\) | 5520.18 | 0.209671 | ||||||||
\(886\) | 62597.4 | 2.37359 | ||||||||
\(887\) | −50200.0 | −1.90028 | −0.950142 | − | 0.311817i | \(-0.899062\pi\) | ||||
−0.950142 | + | 0.311817i | \(0.899062\pi\) | |||||||
\(888\) | −29405.9 | −1.11126 | ||||||||
\(889\) | −11259.4 | −0.424777 | ||||||||
\(890\) | −47057.1 | −1.77231 | ||||||||
\(891\) | −891.000 | −0.0335013 | ||||||||
\(892\) | 27028.4 | 1.01455 | ||||||||
\(893\) | 2762.30 | 0.103513 | ||||||||
\(894\) | 34624.0 | 1.29530 | ||||||||
\(895\) | 50596.3 | 1.88966 | ||||||||
\(896\) | −5848.41 | −0.218060 | ||||||||
\(897\) | 1022.56 | 0.0380627 | ||||||||
\(898\) | 41106.0 | 1.52753 | ||||||||
\(899\) | 2350.49 | 0.0872005 | ||||||||
\(900\) | 48595.1 | 1.79982 | ||||||||
\(901\) | 20730.7 | 0.766524 | ||||||||
\(902\) | 1475.43 | 0.0544639 | ||||||||
\(903\) | −719.123 | −0.0265016 | ||||||||
\(904\) | −111346. | −4.09659 | ||||||||
\(905\) | 5738.22 | 0.210768 | ||||||||
\(906\) | 27660.0 | 1.01428 | ||||||||
\(907\) | −6586.91 | −0.241141 | −0.120570 | − | 0.992705i | \(-0.538472\pi\) | ||||
−0.120570 | + | 0.992705i | \(0.538472\pi\) | |||||||
\(908\) | −77263.3 | −2.82387 | ||||||||
\(909\) | −2510.45 | −0.0916021 | ||||||||
\(910\) | 5260.69 | 0.191637 | ||||||||
\(911\) | 23707.7 | 0.862208 | 0.431104 | − | 0.902302i | \(-0.358124\pi\) | ||||
0.431104 | + | 0.902302i | \(0.358124\pi\) | |||||||
\(912\) | −5192.76 | −0.188541 | ||||||||
\(913\) | −14407.7 | −0.522262 | ||||||||
\(914\) | 45204.4 | 1.63592 | ||||||||
\(915\) | 3702.44 | 0.133769 | ||||||||
\(916\) | 12136.4 | 0.437772 | ||||||||
\(917\) | −11702.4 | −0.421424 | ||||||||
\(918\) | 11011.3 | 0.395891 | ||||||||
\(919\) | 20270.2 | 0.727586 | 0.363793 | − | 0.931480i | \(-0.381482\pi\) | ||||
0.363793 | + | 0.931480i | \(0.381482\pi\) | |||||||
\(920\) | −111650. | −4.00108 | ||||||||
\(921\) | −7602.92 | −0.272014 | ||||||||
\(922\) | 22488.0 | 0.803257 | ||||||||
\(923\) | 2310.06 | 0.0823796 | ||||||||
\(924\) | 8893.96 | 0.316656 | ||||||||
\(925\) | 48812.5 | 1.73508 | ||||||||
\(926\) | 35341.6 | 1.25421 | ||||||||
\(927\) | −3748.98 | −0.132829 | ||||||||
\(928\) | 16909.0 | 0.598130 | ||||||||
\(929\) | −34261.8 | −1.21000 | −0.605001 | − | 0.796225i | \(-0.706827\pi\) | ||||
−0.605001 | + | 0.796225i | \(0.706827\pi\) | |||||||
\(930\) | 12930.6 | 0.455926 | ||||||||
\(931\) | 1693.53 | 0.0596167 | ||||||||
\(932\) | 69582.0 | 2.44553 | ||||||||
\(933\) | −22174.8 | −0.778104 | ||||||||
\(934\) | −47170.3 | −1.65253 | ||||||||
\(935\) | 17470.4 | 0.611063 | ||||||||
\(936\) | −1812.16 | −0.0632824 | ||||||||
\(937\) | −17501.4 | −0.610189 | −0.305095 | − | 0.952322i | \(-0.598688\pi\) | ||||
−0.305095 | + | 0.952322i | \(0.598688\pi\) | |||||||
\(938\) | −36737.5 | −1.27881 | ||||||||
\(939\) | −3766.28 | −0.130892 | ||||||||
\(940\) | −88723.1 | −3.07854 | ||||||||
\(941\) | 47973.9 | 1.66196 | 0.830980 | − | 0.556303i | \(-0.187781\pi\) | ||||
0.830980 | + | 0.556303i | \(0.187781\pi\) | |||||||
\(942\) | 18902.0 | 0.653781 | ||||||||
\(943\) | 2495.41 | 0.0861735 | ||||||||
\(944\) | 13160.6 | 0.453750 | ||||||||
\(945\) | −7752.72 | −0.266874 | ||||||||
\(946\) | 965.214 | 0.0331732 | ||||||||
\(947\) | −25129.6 | −0.862305 | −0.431153 | − | 0.902279i | \(-0.641893\pi\) | ||||
−0.431153 | + | 0.902279i | \(0.641893\pi\) | |||||||
\(948\) | 53392.6 | 1.82923 | ||||||||
\(949\) | 2462.12 | 0.0842188 | ||||||||
\(950\) | 17669.4 | 0.603444 | ||||||||
\(951\) | 16948.5 | 0.577909 | ||||||||
\(952\) | −63611.0 | −2.16559 | ||||||||
\(953\) | −37420.9 | −1.27196 | −0.635982 | − | 0.771704i | \(-0.719405\pi\) | ||||
−0.635982 | + | 0.771704i | \(0.719405\pi\) | |||||||
\(954\) | 12347.6 | 0.419046 | ||||||||
\(955\) | 21685.9 | 0.734806 | ||||||||
\(956\) | 75958.4 | 2.56974 | ||||||||
\(957\) | 1891.53 | 0.0638919 | ||||||||
\(958\) | 50684.5 | 1.70933 | ||||||||
\(959\) | −26644.8 | −0.897190 | ||||||||
\(960\) | 22757.3 | 0.765093 | ||||||||
\(961\) | −28109.4 | −0.943554 | ||||||||
\(962\) | −3145.29 | −0.105414 | ||||||||
\(963\) | 15237.6 | 0.509891 | ||||||||
\(964\) | 25690.5 | 0.858337 | ||||||||
\(965\) | −68687.2 | −2.29132 | ||||||||
\(966\) | 21379.4 | 0.712081 | ||||||||
\(967\) | −46220.4 | −1.53707 | −0.768536 | − | 0.639806i | \(-0.779015\pi\) | ||||
−0.768536 | + | 0.639806i | \(0.779015\pi\) | |||||||
\(968\) | −6908.60 | −0.229391 | ||||||||
\(969\) | 2817.04 | 0.0933914 | ||||||||
\(970\) | −92833.3 | −3.07288 | ||||||||
\(971\) | 24103.9 | 0.796632 | 0.398316 | − | 0.917248i | \(-0.369595\pi\) | ||||
0.398316 | + | 0.917248i | \(0.369595\pi\) | |||||||
\(972\) | 4614.60 | 0.152277 | ||||||||
\(973\) | −20118.0 | −0.662851 | ||||||||
\(974\) | −78460.1 | −2.58113 | ||||||||
\(975\) | 3008.11 | 0.0988066 | ||||||||
\(976\) | 8826.92 | 0.289490 | ||||||||
\(977\) | −12247.8 | −0.401066 | −0.200533 | − | 0.979687i | \(-0.564267\pi\) | ||||
−0.200533 | + | 0.979687i | \(0.564267\pi\) | |||||||
\(978\) | 3138.02 | 0.102600 | ||||||||
\(979\) | −4924.69 | −0.160770 | ||||||||
\(980\) | −54395.0 | −1.77305 | ||||||||
\(981\) | −10550.5 | −0.343375 | ||||||||
\(982\) | 33271.5 | 1.08120 | ||||||||
\(983\) | 22411.3 | 0.727172 | 0.363586 | − | 0.931561i | \(-0.381552\pi\) | ||||
0.363586 | + | 0.931561i | \(0.381552\pi\) | |||||||
\(984\) | −4422.31 | −0.143270 | ||||||||
\(985\) | 69522.5 | 2.24891 | ||||||||
\(986\) | −23376.3 | −0.755024 | ||||||||
\(987\) | 9832.13 | 0.317082 | ||||||||
\(988\) | −801.078 | −0.0257952 | ||||||||
\(989\) | 1632.47 | 0.0524870 | ||||||||
\(990\) | 10405.8 | 0.334058 | ||||||||
\(991\) | −11091.1 | −0.355521 | −0.177760 | − | 0.984074i | \(-0.556885\pi\) | ||||
−0.177760 | + | 0.984074i | \(0.556885\pi\) | |||||||
\(992\) | 12097.0 | 0.387177 | ||||||||
\(993\) | −2584.24 | −0.0825865 | ||||||||
\(994\) | 48298.0 | 1.54117 | ||||||||
\(995\) | −63938.5 | −2.03717 | ||||||||
\(996\) | 74619.3 | 2.37390 | ||||||||
\(997\) | −13750.9 | −0.436805 | −0.218402 | − | 0.975859i | \(-0.570085\pi\) | ||||
−0.218402 | + | 0.975859i | \(0.570085\pi\) | |||||||
\(998\) | −20684.2 | −0.656058 | ||||||||
\(999\) | 4635.25 | 0.146800 |
(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.h.1.2 | ✓ | 39 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2013.4.a.h.1.2 | ✓ | 39 | 1.1 | even | 1 | trivial |