Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,4,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("177.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(10.4433380710\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 49x^{6} + 89x^{5} + 648x^{4} - 1023x^{3} - 1476x^{2} + 1940x - 384 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-5.19624\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.19624 | −1.83715 | −0.918574 | − | 0.395249i | \(-0.870658\pi\) | ||||
−0.918574 | + | 0.395249i | \(0.870658\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 19.0009 | 2.37511 | ||||||||
\(5\) | −8.30102 | −0.742466 | −0.371233 | − | 0.928540i | \(-0.621065\pi\) | ||||
−0.371233 | + | 0.928540i | \(0.621065\pi\) | |||||||
\(6\) | 15.5887 | 1.06068 | ||||||||
\(7\) | 21.5539 | 1.16380 | 0.581900 | − | 0.813260i | \(-0.302309\pi\) | ||||
0.581900 | + | 0.813260i | \(0.302309\pi\) | |||||||
\(8\) | −57.1634 | −2.52629 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 43.1341 | 1.36402 | ||||||||
\(11\) | −28.3746 | −0.777752 | −0.388876 | − | 0.921290i | \(-0.627137\pi\) | ||||
−0.388876 | + | 0.921290i | \(0.627137\pi\) | |||||||
\(12\) | −57.0027 | −1.37127 | ||||||||
\(13\) | −28.2089 | −0.601826 | −0.300913 | − | 0.953652i | \(-0.597291\pi\) | ||||
−0.300913 | + | 0.953652i | \(0.597291\pi\) | |||||||
\(14\) | −111.999 | −2.13807 | ||||||||
\(15\) | 24.9031 | 0.428663 | ||||||||
\(16\) | 145.027 | 2.26605 | ||||||||
\(17\) | 21.8166 | 0.311254 | 0.155627 | − | 0.987816i | \(-0.450260\pi\) | ||||
0.155627 | + | 0.987816i | \(0.450260\pi\) | |||||||
\(18\) | −46.7662 | −0.612383 | ||||||||
\(19\) | −122.388 | −1.47777 | −0.738887 | − | 0.673830i | \(-0.764648\pi\) | ||||
−0.738887 | + | 0.673830i | \(0.764648\pi\) | |||||||
\(20\) | −157.727 | −1.76344 | ||||||||
\(21\) | −64.6617 | −0.671921 | ||||||||
\(22\) | 147.441 | 1.42885 | ||||||||
\(23\) | 82.1571 | 0.744823 | 0.372412 | − | 0.928068i | \(-0.378531\pi\) | ||||
0.372412 | + | 0.928068i | \(0.378531\pi\) | |||||||
\(24\) | 171.490 | 1.45855 | ||||||||
\(25\) | −56.0930 | −0.448744 | ||||||||
\(26\) | 146.580 | 1.10564 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 409.544 | 2.76416 | ||||||||
\(29\) | 86.9209 | 0.556580 | 0.278290 | − | 0.960497i | \(-0.410232\pi\) | ||||
0.278290 | + | 0.960497i | \(0.410232\pi\) | |||||||
\(30\) | −129.402 | −0.787518 | ||||||||
\(31\) | 131.178 | 0.760009 | 0.380004 | − | 0.924985i | \(-0.375922\pi\) | ||||
0.380004 | + | 0.924985i | \(0.375922\pi\) | |||||||
\(32\) | −296.290 | −1.63678 | ||||||||
\(33\) | 85.1239 | 0.449035 | ||||||||
\(34\) | −113.364 | −0.571819 | ||||||||
\(35\) | −178.919 | −0.864083 | ||||||||
\(36\) | 171.008 | 0.791705 | ||||||||
\(37\) | 280.467 | 1.24617 | 0.623087 | − | 0.782152i | \(-0.285878\pi\) | ||||
0.623087 | + | 0.782152i | \(0.285878\pi\) | |||||||
\(38\) | 635.957 | 2.71489 | ||||||||
\(39\) | 84.6266 | 0.347464 | ||||||||
\(40\) | 474.515 | 1.87568 | ||||||||
\(41\) | 381.788 | 1.45427 | 0.727137 | − | 0.686493i | \(-0.240851\pi\) | ||||
0.727137 | + | 0.686493i | \(0.240851\pi\) | |||||||
\(42\) | 335.998 | 1.23442 | ||||||||
\(43\) | 452.501 | 1.60478 | 0.802392 | − | 0.596798i | \(-0.203560\pi\) | ||||
0.802392 | + | 0.596798i | \(0.203560\pi\) | |||||||
\(44\) | −539.144 | −1.84725 | ||||||||
\(45\) | −74.7092 | −0.247489 | ||||||||
\(46\) | −426.908 | −1.36835 | ||||||||
\(47\) | −158.067 | −0.490564 | −0.245282 | − | 0.969452i | \(-0.578881\pi\) | ||||
−0.245282 | + | 0.969452i | \(0.578881\pi\) | |||||||
\(48\) | −435.082 | −1.30831 | ||||||||
\(49\) | 121.570 | 0.354432 | ||||||||
\(50\) | 291.473 | 0.824409 | ||||||||
\(51\) | −65.4499 | −0.179702 | ||||||||
\(52\) | −535.994 | −1.42940 | ||||||||
\(53\) | −162.922 | −0.422245 | −0.211123 | − | 0.977460i | \(-0.567712\pi\) | ||||
−0.211123 | + | 0.977460i | \(0.567712\pi\) | |||||||
\(54\) | 140.298 | 0.353559 | ||||||||
\(55\) | 235.539 | 0.577455 | ||||||||
\(56\) | −1232.09 | −2.94010 | ||||||||
\(57\) | 367.164 | 0.853193 | ||||||||
\(58\) | −451.662 | −1.02252 | ||||||||
\(59\) | −59.0000 | −0.130189 | ||||||||
\(60\) | 473.181 | 1.01812 | ||||||||
\(61\) | −368.344 | −0.773141 | −0.386570 | − | 0.922260i | \(-0.626340\pi\) | ||||
−0.386570 | + | 0.922260i | \(0.626340\pi\) | |||||||
\(62\) | −681.632 | −1.39625 | ||||||||
\(63\) | 193.985 | 0.387934 | ||||||||
\(64\) | 379.374 | 0.740965 | ||||||||
\(65\) | 234.162 | 0.446835 | ||||||||
\(66\) | −442.324 | −0.824945 | ||||||||
\(67\) | 177.950 | 0.324478 | 0.162239 | − | 0.986752i | \(-0.448128\pi\) | ||||
0.162239 | + | 0.986752i | \(0.448128\pi\) | |||||||
\(68\) | 414.536 | 0.739263 | ||||||||
\(69\) | −246.471 | −0.430024 | ||||||||
\(70\) | 929.708 | 1.58745 | ||||||||
\(71\) | 58.9220 | 0.0984894 | 0.0492447 | − | 0.998787i | \(-0.484319\pi\) | ||||
0.0492447 | + | 0.998787i | \(0.484319\pi\) | |||||||
\(72\) | −514.470 | −0.842096 | ||||||||
\(73\) | 880.299 | 1.41139 | 0.705693 | − | 0.708518i | \(-0.250636\pi\) | ||||
0.705693 | + | 0.708518i | \(0.250636\pi\) | |||||||
\(74\) | −1457.37 | −2.28941 | ||||||||
\(75\) | 168.279 | 0.259082 | ||||||||
\(76\) | −2325.48 | −3.50988 | ||||||||
\(77\) | −611.584 | −0.905148 | ||||||||
\(78\) | −439.740 | −0.638343 | ||||||||
\(79\) | −825.284 | −1.17534 | −0.587669 | − | 0.809101i | \(-0.699954\pi\) | ||||
−0.587669 | + | 0.809101i | \(0.699954\pi\) | |||||||
\(80\) | −1203.88 | −1.68247 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −1983.86 | −2.67172 | ||||||||
\(83\) | 1426.68 | 1.88673 | 0.943367 | − | 0.331752i | \(-0.107640\pi\) | ||||
0.943367 | + | 0.331752i | \(0.107640\pi\) | |||||||
\(84\) | −1228.63 | −1.59589 | ||||||||
\(85\) | −181.100 | −0.231095 | ||||||||
\(86\) | −2351.30 | −2.94823 | ||||||||
\(87\) | −260.763 | −0.321341 | ||||||||
\(88\) | 1621.99 | 1.96483 | ||||||||
\(89\) | 1556.78 | 1.85413 | 0.927067 | − | 0.374896i | \(-0.122322\pi\) | ||||
0.927067 | + | 0.374896i | \(0.122322\pi\) | |||||||
\(90\) | 388.207 | 0.454673 | ||||||||
\(91\) | −608.011 | −0.700405 | ||||||||
\(92\) | 1561.06 | 1.76904 | ||||||||
\(93\) | −393.534 | −0.438791 | ||||||||
\(94\) | 821.356 | 0.901238 | ||||||||
\(95\) | 1015.94 | 1.09720 | ||||||||
\(96\) | 888.869 | 0.944998 | ||||||||
\(97\) | 1811.25 | 1.89593 | 0.947964 | − | 0.318377i | \(-0.103138\pi\) | ||||
0.947964 | + | 0.318377i | \(0.103138\pi\) | |||||||
\(98\) | −631.708 | −0.651144 | ||||||||
\(99\) | −255.372 | −0.259251 | ||||||||
\(100\) | −1065.82 | −1.06582 | ||||||||
\(101\) | 1132.95 | 1.11617 | 0.558085 | − | 0.829784i | \(-0.311536\pi\) | ||||
0.558085 | + | 0.829784i | \(0.311536\pi\) | |||||||
\(102\) | 340.093 | 0.330140 | ||||||||
\(103\) | 1479.79 | 1.41561 | 0.707805 | − | 0.706408i | \(-0.249685\pi\) | ||||
0.707805 | + | 0.706408i | \(0.249685\pi\) | |||||||
\(104\) | 1612.51 | 1.52038 | ||||||||
\(105\) | 536.758 | 0.498878 | ||||||||
\(106\) | 846.580 | 0.775727 | ||||||||
\(107\) | 293.850 | 0.265491 | 0.132746 | − | 0.991150i | \(-0.457621\pi\) | ||||
0.132746 | + | 0.991150i | \(0.457621\pi\) | |||||||
\(108\) | −513.025 | −0.457091 | ||||||||
\(109\) | −801.451 | −0.704267 | −0.352133 | − | 0.935950i | \(-0.614544\pi\) | ||||
−0.352133 | + | 0.935950i | \(0.614544\pi\) | |||||||
\(110\) | −1223.91 | −1.06087 | ||||||||
\(111\) | −841.401 | −0.719479 | ||||||||
\(112\) | 3125.90 | 2.63723 | ||||||||
\(113\) | −1834.04 | −1.52683 | −0.763415 | − | 0.645908i | \(-0.776479\pi\) | ||||
−0.763415 | + | 0.645908i | \(0.776479\pi\) | |||||||
\(114\) | −1907.87 | −1.56744 | ||||||||
\(115\) | −681.988 | −0.553006 | ||||||||
\(116\) | 1651.58 | 1.32194 | ||||||||
\(117\) | −253.880 | −0.200609 | ||||||||
\(118\) | 306.578 | 0.239176 | ||||||||
\(119\) | 470.233 | 0.362237 | ||||||||
\(120\) | −1423.54 | −1.08293 | ||||||||
\(121\) | −525.880 | −0.395102 | ||||||||
\(122\) | 1914.00 | 1.42037 | ||||||||
\(123\) | −1145.36 | −0.839625 | ||||||||
\(124\) | 2492.50 | 1.80511 | ||||||||
\(125\) | 1503.26 | 1.07564 | ||||||||
\(126\) | −1007.99 | −0.712691 | ||||||||
\(127\) | 745.001 | 0.520537 | 0.260268 | − | 0.965536i | \(-0.416189\pi\) | ||||
0.260268 | + | 0.965536i | \(0.416189\pi\) | |||||||
\(128\) | 398.999 | 0.275522 | ||||||||
\(129\) | −1357.50 | −0.926522 | ||||||||
\(130\) | −1216.76 | −0.820902 | ||||||||
\(131\) | −2205.52 | −1.47097 | −0.735485 | − | 0.677541i | \(-0.763046\pi\) | ||||
−0.735485 | + | 0.677541i | \(0.763046\pi\) | |||||||
\(132\) | 1617.43 | 1.06651 | ||||||||
\(133\) | −2637.93 | −1.71983 | ||||||||
\(134\) | −924.669 | −0.596114 | ||||||||
\(135\) | 224.128 | 0.142888 | ||||||||
\(136\) | −1247.11 | −0.786316 | ||||||||
\(137\) | 744.233 | 0.464118 | 0.232059 | − | 0.972702i | \(-0.425454\pi\) | ||||
0.232059 | + | 0.972702i | \(0.425454\pi\) | |||||||
\(138\) | 1280.72 | 0.790018 | ||||||||
\(139\) | 267.712 | 0.163360 | 0.0816801 | − | 0.996659i | \(-0.473971\pi\) | ||||
0.0816801 | + | 0.996659i | \(0.473971\pi\) | |||||||
\(140\) | −3399.63 | −2.05229 | ||||||||
\(141\) | 474.202 | 0.283227 | ||||||||
\(142\) | −306.173 | −0.180940 | ||||||||
\(143\) | 800.416 | 0.468071 | ||||||||
\(144\) | 1305.25 | 0.755351 | ||||||||
\(145\) | −721.533 | −0.413242 | ||||||||
\(146\) | −4574.24 | −2.59292 | ||||||||
\(147\) | −364.711 | −0.204631 | ||||||||
\(148\) | 5329.13 | 2.95981 | ||||||||
\(149\) | −2478.30 | −1.36262 | −0.681308 | − | 0.731997i | \(-0.738589\pi\) | ||||
−0.681308 | + | 0.731997i | \(0.738589\pi\) | |||||||
\(150\) | −874.418 | −0.475973 | ||||||||
\(151\) | 1902.48 | 1.02531 | 0.512655 | − | 0.858595i | \(-0.328662\pi\) | ||||
0.512655 | + | 0.858595i | \(0.328662\pi\) | |||||||
\(152\) | 6996.10 | 3.73328 | ||||||||
\(153\) | 196.350 | 0.103751 | ||||||||
\(154\) | 3177.94 | 1.66289 | ||||||||
\(155\) | −1088.91 | −0.564281 | ||||||||
\(156\) | 1607.98 | 0.825267 | ||||||||
\(157\) | −3638.32 | −1.84949 | −0.924745 | − | 0.380588i | \(-0.875722\pi\) | ||||
−0.924745 | + | 0.380588i | \(0.875722\pi\) | |||||||
\(158\) | 4288.37 | 2.15927 | ||||||||
\(159\) | 488.765 | 0.243783 | ||||||||
\(160\) | 2459.51 | 1.21526 | ||||||||
\(161\) | 1770.81 | 0.866826 | ||||||||
\(162\) | −420.895 | −0.204128 | ||||||||
\(163\) | 1188.42 | 0.571068 | 0.285534 | − | 0.958369i | \(-0.407829\pi\) | ||||
0.285534 | + | 0.958369i | \(0.407829\pi\) | |||||||
\(164\) | 7254.31 | 3.45407 | ||||||||
\(165\) | −706.616 | −0.333394 | ||||||||
\(166\) | −7413.39 | −3.46621 | ||||||||
\(167\) | 1667.69 | 0.772752 | 0.386376 | − | 0.922341i | \(-0.373727\pi\) | ||||
0.386376 | + | 0.922341i | \(0.373727\pi\) | |||||||
\(168\) | 3696.28 | 1.69746 | ||||||||
\(169\) | −1401.26 | −0.637806 | ||||||||
\(170\) | 941.041 | 0.424556 | ||||||||
\(171\) | −1101.49 | −0.492591 | ||||||||
\(172\) | 8597.92 | 3.81154 | ||||||||
\(173\) | 1854.57 | 0.815032 | 0.407516 | − | 0.913198i | \(-0.366395\pi\) | ||||
0.407516 | + | 0.913198i | \(0.366395\pi\) | |||||||
\(174\) | 1354.99 | 0.590352 | ||||||||
\(175\) | −1209.02 | −0.522249 | ||||||||
\(176\) | −4115.10 | −1.76243 | ||||||||
\(177\) | 177.000 | 0.0751646 | ||||||||
\(178\) | −8089.38 | −3.40632 | ||||||||
\(179\) | 3650.51 | 1.52431 | 0.762155 | − | 0.647394i | \(-0.224141\pi\) | ||||
0.762155 | + | 0.647394i | \(0.224141\pi\) | |||||||
\(180\) | −1419.54 | −0.587814 | ||||||||
\(181\) | 912.195 | 0.374602 | 0.187301 | − | 0.982303i | \(-0.440026\pi\) | ||||
0.187301 | + | 0.982303i | \(0.440026\pi\) | |||||||
\(182\) | 3159.37 | 1.28675 | ||||||||
\(183\) | 1105.03 | 0.446373 | ||||||||
\(184\) | −4696.38 | −1.88164 | ||||||||
\(185\) | −2328.16 | −0.925243 | ||||||||
\(186\) | 2044.90 | 0.806124 | ||||||||
\(187\) | −619.039 | −0.242078 | ||||||||
\(188\) | −3003.42 | −1.16514 | ||||||||
\(189\) | −581.955 | −0.223974 | ||||||||
\(190\) | −5279.09 | −2.01571 | ||||||||
\(191\) | 2060.65 | 0.780646 | 0.390323 | − | 0.920678i | \(-0.372363\pi\) | ||||
0.390323 | + | 0.920678i | \(0.372363\pi\) | |||||||
\(192\) | −1138.12 | −0.427796 | ||||||||
\(193\) | −1917.94 | −0.715318 | −0.357659 | − | 0.933852i | \(-0.616425\pi\) | ||||
−0.357659 | + | 0.933852i | \(0.616425\pi\) | |||||||
\(194\) | −9411.71 | −3.48310 | ||||||||
\(195\) | −702.487 | −0.257980 | ||||||||
\(196\) | 2309.94 | 0.841817 | ||||||||
\(197\) | −2490.32 | −0.900651 | −0.450325 | − | 0.892864i | \(-0.648692\pi\) | ||||
−0.450325 | + | 0.892864i | \(0.648692\pi\) | |||||||
\(198\) | 1326.97 | 0.476282 | ||||||||
\(199\) | 3412.12 | 1.21547 | 0.607735 | − | 0.794140i | \(-0.292078\pi\) | ||||
0.607735 | + | 0.794140i | \(0.292078\pi\) | |||||||
\(200\) | 3206.46 | 1.13366 | ||||||||
\(201\) | −533.849 | −0.187337 | ||||||||
\(202\) | −5887.10 | −2.05057 | ||||||||
\(203\) | 1873.48 | 0.647748 | ||||||||
\(204\) | −1243.61 | −0.426814 | ||||||||
\(205\) | −3169.23 | −1.07975 | ||||||||
\(206\) | −7689.34 | −2.60069 | ||||||||
\(207\) | 739.414 | 0.248274 | ||||||||
\(208\) | −4091.06 | −1.36377 | ||||||||
\(209\) | 3472.71 | 1.14934 | ||||||||
\(210\) | −2789.12 | −0.916514 | ||||||||
\(211\) | 892.077 | 0.291057 | 0.145529 | − | 0.989354i | \(-0.453512\pi\) | ||||
0.145529 | + | 0.989354i | \(0.453512\pi\) | |||||||
\(212\) | −3095.66 | −1.00288 | ||||||||
\(213\) | −176.766 | −0.0568629 | ||||||||
\(214\) | −1526.92 | −0.487747 | ||||||||
\(215\) | −3756.22 | −1.19150 | ||||||||
\(216\) | 1543.41 | 0.486184 | ||||||||
\(217\) | 2827.40 | 0.884499 | ||||||||
\(218\) | 4164.53 | 1.29384 | ||||||||
\(219\) | −2640.90 | −0.814864 | ||||||||
\(220\) | 4475.45 | 1.37152 | ||||||||
\(221\) | −615.423 | −0.187320 | ||||||||
\(222\) | 4372.12 | 1.32179 | ||||||||
\(223\) | −2891.35 | −0.868246 | −0.434123 | − | 0.900854i | \(-0.642942\pi\) | ||||
−0.434123 | + | 0.900854i | \(0.642942\pi\) | |||||||
\(224\) | −6386.20 | −1.90489 | ||||||||
\(225\) | −504.837 | −0.149581 | ||||||||
\(226\) | 9530.10 | 2.80501 | ||||||||
\(227\) | −1746.45 | −0.510643 | −0.255321 | − | 0.966856i | \(-0.582181\pi\) | ||||
−0.255321 | + | 0.966856i | \(0.582181\pi\) | |||||||
\(228\) | 6976.44 | 2.02643 | ||||||||
\(229\) | −1195.00 | −0.344837 | −0.172418 | − | 0.985024i | \(-0.555158\pi\) | ||||
−0.172418 | + | 0.985024i | \(0.555158\pi\) | |||||||
\(230\) | 3543.77 | 1.01595 | ||||||||
\(231\) | 1834.75 | 0.522588 | ||||||||
\(232\) | −4968.69 | −1.40608 | ||||||||
\(233\) | −4741.93 | −1.33328 | −0.666640 | − | 0.745380i | \(-0.732268\pi\) | ||||
−0.666640 | + | 0.745380i | \(0.732268\pi\) | |||||||
\(234\) | 1319.22 | 0.368548 | ||||||||
\(235\) | 1312.12 | 0.364227 | ||||||||
\(236\) | −1121.05 | −0.309213 | ||||||||
\(237\) | 2475.85 | 0.678582 | ||||||||
\(238\) | −2443.45 | −0.665483 | ||||||||
\(239\) | −2889.11 | −0.781928 | −0.390964 | − | 0.920406i | \(-0.627858\pi\) | ||||
−0.390964 | + | 0.920406i | \(0.627858\pi\) | |||||||
\(240\) | 3611.63 | 0.971373 | ||||||||
\(241\) | 2648.11 | 0.707799 | 0.353899 | − | 0.935284i | \(-0.384856\pi\) | ||||
0.353899 | + | 0.935284i | \(0.384856\pi\) | |||||||
\(242\) | 2732.60 | 0.725860 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | −6998.87 | −1.83630 | ||||||||
\(245\) | −1009.16 | −0.263154 | ||||||||
\(246\) | 5951.58 | 1.54252 | ||||||||
\(247\) | 3452.42 | 0.889362 | ||||||||
\(248\) | −7498.58 | −1.92000 | ||||||||
\(249\) | −4280.05 | −1.08931 | ||||||||
\(250\) | −7811.29 | −1.97612 | ||||||||
\(251\) | 2327.49 | 0.585299 | 0.292650 | − | 0.956220i | \(-0.405463\pi\) | ||||
0.292650 | + | 0.956220i | \(0.405463\pi\) | |||||||
\(252\) | 3685.89 | 0.921386 | ||||||||
\(253\) | −2331.18 | −0.579288 | ||||||||
\(254\) | −3871.21 | −0.956303 | ||||||||
\(255\) | 543.301 | 0.133423 | ||||||||
\(256\) | −5108.29 | −1.24714 | ||||||||
\(257\) | −4224.97 | −1.02547 | −0.512737 | − | 0.858546i | \(-0.671368\pi\) | ||||
−0.512737 | + | 0.858546i | \(0.671368\pi\) | |||||||
\(258\) | 7053.91 | 1.70216 | ||||||||
\(259\) | 6045.15 | 1.45030 | ||||||||
\(260\) | 4449.30 | 1.06128 | ||||||||
\(261\) | 782.288 | 0.185527 | ||||||||
\(262\) | 11460.4 | 2.70239 | ||||||||
\(263\) | 3245.27 | 0.760881 | 0.380441 | − | 0.924805i | \(-0.375772\pi\) | ||||
0.380441 | + | 0.924805i | \(0.375772\pi\) | |||||||
\(264\) | −4865.97 | −1.13439 | ||||||||
\(265\) | 1352.42 | 0.313503 | ||||||||
\(266\) | 13707.3 | 3.15959 | ||||||||
\(267\) | −4670.33 | −1.07048 | ||||||||
\(268\) | 3381.21 | 0.770672 | ||||||||
\(269\) | −4695.98 | −1.06438 | −0.532191 | − | 0.846624i | \(-0.678631\pi\) | ||||
−0.532191 | + | 0.846624i | \(0.678631\pi\) | |||||||
\(270\) | −1164.62 | −0.262506 | ||||||||
\(271\) | 1442.96 | 0.323444 | 0.161722 | − | 0.986836i | \(-0.448295\pi\) | ||||
0.161722 | + | 0.986836i | \(0.448295\pi\) | |||||||
\(272\) | 3164.01 | 0.705317 | ||||||||
\(273\) | 1824.03 | 0.404379 | ||||||||
\(274\) | −3867.21 | −0.852653 | ||||||||
\(275\) | 1591.62 | 0.349012 | ||||||||
\(276\) | −4683.18 | −1.02136 | ||||||||
\(277\) | 6781.78 | 1.47104 | 0.735519 | − | 0.677504i | \(-0.236938\pi\) | ||||
0.735519 | + | 0.677504i | \(0.236938\pi\) | |||||||
\(278\) | −1391.10 | −0.300117 | ||||||||
\(279\) | 1180.60 | 0.253336 | ||||||||
\(280\) | 10227.6 | 2.18292 | ||||||||
\(281\) | 916.383 | 0.194544 | 0.0972719 | − | 0.995258i | \(-0.468988\pi\) | ||||
0.0972719 | + | 0.995258i | \(0.468988\pi\) | |||||||
\(282\) | −2464.07 | −0.520330 | ||||||||
\(283\) | −1693.18 | −0.355651 | −0.177825 | − | 0.984062i | \(-0.556906\pi\) | ||||
−0.177825 | + | 0.984062i | \(0.556906\pi\) | |||||||
\(284\) | 1119.57 | 0.233924 | ||||||||
\(285\) | −3047.83 | −0.633467 | ||||||||
\(286\) | −4159.15 | −0.859916 | ||||||||
\(287\) | 8229.01 | 1.69248 | ||||||||
\(288\) | −2666.61 | −0.545595 | ||||||||
\(289\) | −4437.03 | −0.903121 | ||||||||
\(290\) | 3749.26 | 0.759186 | ||||||||
\(291\) | −5433.76 | −1.09461 | ||||||||
\(292\) | 16726.5 | 3.35220 | ||||||||
\(293\) | −4712.00 | −0.939515 | −0.469757 | − | 0.882796i | \(-0.655659\pi\) | ||||
−0.469757 | + | 0.882796i | \(0.655659\pi\) | |||||||
\(294\) | 1895.12 | 0.375938 | ||||||||
\(295\) | 489.760 | 0.0966609 | ||||||||
\(296\) | −16032.4 | −3.14820 | ||||||||
\(297\) | 766.115 | 0.149678 | ||||||||
\(298\) | 12877.8 | 2.50333 | ||||||||
\(299\) | −2317.56 | −0.448254 | ||||||||
\(300\) | 3197.45 | 0.615350 | ||||||||
\(301\) | 9753.15 | 1.86765 | ||||||||
\(302\) | −9885.75 | −1.88364 | ||||||||
\(303\) | −3398.86 | −0.644421 | ||||||||
\(304\) | −17749.6 | −3.34871 | ||||||||
\(305\) | 3057.63 | 0.574031 | ||||||||
\(306\) | −1020.28 | −0.190606 | ||||||||
\(307\) | 7720.48 | 1.43528 | 0.717640 | − | 0.696414i | \(-0.245222\pi\) | ||||
0.717640 | + | 0.696414i | \(0.245222\pi\) | |||||||
\(308\) | −11620.6 | −2.14983 | ||||||||
\(309\) | −4439.37 | −0.817303 | ||||||||
\(310\) | 5658.25 | 1.03667 | ||||||||
\(311\) | 5773.53 | 1.05269 | 0.526345 | − | 0.850271i | \(-0.323562\pi\) | ||||
0.526345 | + | 0.850271i | \(0.323562\pi\) | |||||||
\(312\) | −4837.54 | −0.877794 | ||||||||
\(313\) | −9875.96 | −1.78346 | −0.891729 | − | 0.452570i | \(-0.850507\pi\) | ||||
−0.891729 | + | 0.452570i | \(0.850507\pi\) | |||||||
\(314\) | 18905.6 | 3.39779 | ||||||||
\(315\) | −1610.27 | −0.288028 | ||||||||
\(316\) | −15681.1 | −2.79156 | ||||||||
\(317\) | −6005.53 | −1.06405 | −0.532025 | − | 0.846729i | \(-0.678569\pi\) | ||||
−0.532025 | + | 0.846729i | \(0.678569\pi\) | |||||||
\(318\) | −2539.74 | −0.447866 | ||||||||
\(319\) | −2466.35 | −0.432881 | ||||||||
\(320\) | −3149.19 | −0.550141 | ||||||||
\(321\) | −881.551 | −0.153282 | ||||||||
\(322\) | −9201.53 | −1.59249 | ||||||||
\(323\) | −2670.09 | −0.459962 | ||||||||
\(324\) | 1539.07 | 0.263902 | ||||||||
\(325\) | 1582.32 | 0.270066 | ||||||||
\(326\) | −6175.31 | −1.04914 | ||||||||
\(327\) | 2404.35 | 0.406609 | ||||||||
\(328\) | −21824.3 | −3.67391 | ||||||||
\(329\) | −3406.97 | −0.570918 | ||||||||
\(330\) | 3671.74 | 0.612493 | ||||||||
\(331\) | 6895.07 | 1.14498 | 0.572488 | − | 0.819913i | \(-0.305978\pi\) | ||||
0.572488 | + | 0.819913i | \(0.305978\pi\) | |||||||
\(332\) | 27108.3 | 4.48121 | ||||||||
\(333\) | 2524.20 | 0.415392 | ||||||||
\(334\) | −8665.71 | −1.41966 | ||||||||
\(335\) | −1477.16 | −0.240914 | ||||||||
\(336\) | −9377.71 | −1.52261 | ||||||||
\(337\) | 6764.00 | 1.09335 | 0.546675 | − | 0.837345i | \(-0.315893\pi\) | ||||
0.546675 | + | 0.837345i | \(0.315893\pi\) | |||||||
\(338\) | 7281.28 | 1.17174 | ||||||||
\(339\) | 5502.12 | 0.881516 | ||||||||
\(340\) | −3441.07 | −0.548878 | ||||||||
\(341\) | −3722.13 | −0.591098 | ||||||||
\(342\) | 5723.61 | 0.904963 | ||||||||
\(343\) | −4772.67 | −0.751312 | ||||||||
\(344\) | −25866.5 | −4.05415 | ||||||||
\(345\) | 2045.96 | 0.319278 | ||||||||
\(346\) | −9636.81 | −1.49734 | ||||||||
\(347\) | 5474.73 | 0.846971 | 0.423485 | − | 0.905903i | \(-0.360807\pi\) | ||||
0.423485 | + | 0.905903i | \(0.360807\pi\) | |||||||
\(348\) | −4954.73 | −0.763222 | ||||||||
\(349\) | −6375.89 | −0.977919 | −0.488960 | − | 0.872306i | \(-0.662623\pi\) | ||||
−0.488960 | + | 0.872306i | \(0.662623\pi\) | |||||||
\(350\) | 6282.37 | 0.959448 | ||||||||
\(351\) | 761.639 | 0.115821 | ||||||||
\(352\) | 8407.11 | 1.27301 | ||||||||
\(353\) | 4971.14 | 0.749539 | 0.374770 | − | 0.927118i | \(-0.377722\pi\) | ||||
0.374770 | + | 0.927118i | \(0.377722\pi\) | |||||||
\(354\) | −919.734 | −0.138089 | ||||||||
\(355\) | −489.113 | −0.0731251 | ||||||||
\(356\) | 29580.2 | 4.40378 | ||||||||
\(357\) | −1410.70 | −0.209138 | ||||||||
\(358\) | −18968.9 | −2.80039 | ||||||||
\(359\) | 2073.46 | 0.304827 | 0.152414 | − | 0.988317i | \(-0.451295\pi\) | ||||
0.152414 | + | 0.988317i | \(0.451295\pi\) | |||||||
\(360\) | 4270.63 | 0.625228 | ||||||||
\(361\) | 8119.79 | 1.18382 | ||||||||
\(362\) | −4739.98 | −0.688199 | ||||||||
\(363\) | 1577.64 | 0.228112 | ||||||||
\(364\) | −11552.8 | −1.66354 | ||||||||
\(365\) | −7307.38 | −1.04791 | ||||||||
\(366\) | −5742.01 | −0.820053 | ||||||||
\(367\) | −6485.59 | −0.922466 | −0.461233 | − | 0.887279i | \(-0.652593\pi\) | ||||
−0.461233 | + | 0.887279i | \(0.652593\pi\) | |||||||
\(368\) | 11915.0 | 1.68781 | ||||||||
\(369\) | 3436.09 | 0.484758 | ||||||||
\(370\) | 12097.7 | 1.69981 | ||||||||
\(371\) | −3511.59 | −0.491409 | ||||||||
\(372\) | −7477.51 | −1.04218 | ||||||||
\(373\) | −2610.25 | −0.362342 | −0.181171 | − | 0.983452i | \(-0.557989\pi\) | ||||
−0.181171 | + | 0.983452i | \(0.557989\pi\) | |||||||
\(374\) | 3216.67 | 0.444733 | ||||||||
\(375\) | −4509.77 | −0.621023 | ||||||||
\(376\) | 9035.66 | 1.23931 | ||||||||
\(377\) | −2451.94 | −0.334964 | ||||||||
\(378\) | 3023.98 | 0.411473 | ||||||||
\(379\) | −5609.34 | −0.760244 | −0.380122 | − | 0.924936i | \(-0.624118\pi\) | ||||
−0.380122 | + | 0.924936i | \(0.624118\pi\) | |||||||
\(380\) | 19303.9 | 2.60597 | ||||||||
\(381\) | −2235.00 | −0.300532 | ||||||||
\(382\) | −10707.6 | −1.43416 | ||||||||
\(383\) | 2978.80 | 0.397414 | 0.198707 | − | 0.980059i | \(-0.436326\pi\) | ||||
0.198707 | + | 0.980059i | \(0.436326\pi\) | |||||||
\(384\) | −1197.00 | −0.159073 | ||||||||
\(385\) | 5076.77 | 0.672042 | ||||||||
\(386\) | 9966.08 | 1.31415 | ||||||||
\(387\) | 4072.51 | 0.534928 | ||||||||
\(388\) | 34415.5 | 4.50305 | ||||||||
\(389\) | 10137.6 | 1.32132 | 0.660662 | − | 0.750683i | \(-0.270276\pi\) | ||||
0.660662 | + | 0.750683i | \(0.270276\pi\) | |||||||
\(390\) | 3650.29 | 0.473948 | ||||||||
\(391\) | 1792.39 | 0.231829 | ||||||||
\(392\) | −6949.36 | −0.895397 | ||||||||
\(393\) | 6616.56 | 0.849265 | ||||||||
\(394\) | 12940.3 | 1.65463 | ||||||||
\(395\) | 6850.70 | 0.872649 | ||||||||
\(396\) | −4852.29 | −0.615750 | ||||||||
\(397\) | 12921.9 | 1.63359 | 0.816793 | − | 0.576930i | \(-0.195750\pi\) | ||||
0.816793 | + | 0.576930i | \(0.195750\pi\) | |||||||
\(398\) | −17730.2 | −2.23300 | ||||||||
\(399\) | 7913.80 | 0.992947 | ||||||||
\(400\) | −8135.02 | −1.01688 | ||||||||
\(401\) | −9556.68 | −1.19012 | −0.595060 | − | 0.803681i | \(-0.702872\pi\) | ||||
−0.595060 | + | 0.803681i | \(0.702872\pi\) | |||||||
\(402\) | 2774.01 | 0.344167 | ||||||||
\(403\) | −3700.38 | −0.457393 | ||||||||
\(404\) | 21527.1 | 2.65103 | ||||||||
\(405\) | −672.383 | −0.0824962 | ||||||||
\(406\) | −9735.07 | −1.19001 | ||||||||
\(407\) | −7958.14 | −0.969215 | ||||||||
\(408\) | 3741.34 | 0.453980 | ||||||||
\(409\) | 8381.64 | 1.01331 | 0.506657 | − | 0.862148i | \(-0.330881\pi\) | ||||
0.506657 | + | 0.862148i | \(0.330881\pi\) | |||||||
\(410\) | 16468.1 | 1.98366 | ||||||||
\(411\) | −2232.70 | −0.267958 | ||||||||
\(412\) | 28117.3 | 3.36224 | ||||||||
\(413\) | −1271.68 | −0.151514 | ||||||||
\(414\) | −3842.17 | −0.456117 | ||||||||
\(415\) | −11842.9 | −1.40084 | ||||||||
\(416\) | 8358.00 | 0.985059 | ||||||||
\(417\) | −803.137 | −0.0943161 | ||||||||
\(418\) | −18045.0 | −2.11151 | ||||||||
\(419\) | −9005.40 | −1.04998 | −0.524991 | − | 0.851108i | \(-0.675931\pi\) | ||||
−0.524991 | + | 0.851108i | \(0.675931\pi\) | |||||||
\(420\) | 10198.9 | 1.18489 | ||||||||
\(421\) | 754.089 | 0.0872970 | 0.0436485 | − | 0.999047i | \(-0.486102\pi\) | ||||
0.0436485 | + | 0.999047i | \(0.486102\pi\) | |||||||
\(422\) | −4635.45 | −0.534716 | ||||||||
\(423\) | −1422.61 | −0.163521 | ||||||||
\(424\) | 9313.15 | 1.06671 | ||||||||
\(425\) | −1223.76 | −0.139673 | ||||||||
\(426\) | 918.518 | 0.104466 | ||||||||
\(427\) | −7939.24 | −0.899782 | ||||||||
\(428\) | 5583.42 | 0.630572 | ||||||||
\(429\) | −2401.25 | −0.270241 | ||||||||
\(430\) | 19518.2 | 2.18896 | ||||||||
\(431\) | −2505.79 | −0.280046 | −0.140023 | − | 0.990148i | \(-0.544718\pi\) | ||||
−0.140023 | + | 0.990148i | \(0.544718\pi\) | |||||||
\(432\) | −3915.74 | −0.436102 | ||||||||
\(433\) | −176.502 | −0.0195893 | −0.00979465 | − | 0.999952i | \(-0.503118\pi\) | ||||
−0.00979465 | + | 0.999952i | \(0.503118\pi\) | |||||||
\(434\) | −14691.8 | −1.62496 | ||||||||
\(435\) | 2164.60 | 0.238585 | ||||||||
\(436\) | −15228.3 | −1.67271 | ||||||||
\(437\) | −10055.0 | −1.10068 | ||||||||
\(438\) | 13722.7 | 1.49703 | ||||||||
\(439\) | −2223.93 | −0.241782 | −0.120891 | − | 0.992666i | \(-0.538575\pi\) | ||||
−0.120891 | + | 0.992666i | \(0.538575\pi\) | |||||||
\(440\) | −13464.2 | −1.45882 | ||||||||
\(441\) | 1094.13 | 0.118144 | ||||||||
\(442\) | 3197.88 | 0.344135 | ||||||||
\(443\) | −6065.11 | −0.650479 | −0.325239 | − | 0.945632i | \(-0.605445\pi\) | ||||
−0.325239 | + | 0.945632i | \(0.605445\pi\) | |||||||
\(444\) | −15987.4 | −1.70885 | ||||||||
\(445\) | −12922.8 | −1.37663 | ||||||||
\(446\) | 15024.1 | 1.59510 | ||||||||
\(447\) | 7434.89 | 0.786707 | ||||||||
\(448\) | 8176.99 | 0.862336 | ||||||||
\(449\) | −127.588 | −0.0134104 | −0.00670518 | − | 0.999978i | \(-0.502134\pi\) | ||||
−0.00670518 | + | 0.999978i | \(0.502134\pi\) | |||||||
\(450\) | 2623.25 | 0.274803 | ||||||||
\(451\) | −10833.1 | −1.13106 | ||||||||
\(452\) | −34848.4 | −3.62640 | ||||||||
\(453\) | −5707.44 | −0.591962 | ||||||||
\(454\) | 9074.97 | 0.938126 | ||||||||
\(455\) | 5047.11 | 0.520027 | ||||||||
\(456\) | −20988.3 | −2.15541 | ||||||||
\(457\) | 15246.9 | 1.56065 | 0.780327 | − | 0.625372i | \(-0.215053\pi\) | ||||
0.780327 | + | 0.625372i | \(0.215053\pi\) | |||||||
\(458\) | 6209.49 | 0.633517 | ||||||||
\(459\) | −589.049 | −0.0599008 | ||||||||
\(460\) | −12958.4 | −1.31345 | ||||||||
\(461\) | 8148.20 | 0.823210 | 0.411605 | − | 0.911362i | \(-0.364968\pi\) | ||||
0.411605 | + | 0.911362i | \(0.364968\pi\) | |||||||
\(462\) | −9533.81 | −0.960071 | ||||||||
\(463\) | 6518.90 | 0.654340 | 0.327170 | − | 0.944966i | \(-0.393905\pi\) | ||||
0.327170 | + | 0.944966i | \(0.393905\pi\) | |||||||
\(464\) | 12605.9 | 1.26124 | ||||||||
\(465\) | 3266.74 | 0.325788 | ||||||||
\(466\) | 24640.2 | 2.44943 | ||||||||
\(467\) | −263.751 | −0.0261348 | −0.0130674 | − | 0.999915i | \(-0.504160\pi\) | ||||
−0.0130674 | + | 0.999915i | \(0.504160\pi\) | |||||||
\(468\) | −4823.95 | −0.476468 | ||||||||
\(469\) | 3835.51 | 0.377628 | ||||||||
\(470\) | −6818.10 | −0.669139 | ||||||||
\(471\) | 10915.0 | 1.06780 | ||||||||
\(472\) | 3372.64 | 0.328895 | ||||||||
\(473\) | −12839.5 | −1.24812 | ||||||||
\(474\) | −12865.1 | −1.24666 | ||||||||
\(475\) | 6865.10 | 0.663142 | ||||||||
\(476\) | 8934.86 | 0.860354 | ||||||||
\(477\) | −1466.29 | −0.140748 | ||||||||
\(478\) | 15012.5 | 1.43652 | ||||||||
\(479\) | 3204.17 | 0.305642 | 0.152821 | − | 0.988254i | \(-0.451164\pi\) | ||||
0.152821 | + | 0.988254i | \(0.451164\pi\) | |||||||
\(480\) | −7378.52 | −0.701629 | ||||||||
\(481\) | −7911.65 | −0.749980 | ||||||||
\(482\) | −13760.2 | −1.30033 | ||||||||
\(483\) | −5312.42 | −0.500462 | ||||||||
\(484\) | −9992.20 | −0.938411 | ||||||||
\(485\) | −15035.3 | −1.40766 | ||||||||
\(486\) | 1262.69 | 0.117853 | ||||||||
\(487\) | 5211.90 | 0.484957 | 0.242478 | − | 0.970157i | \(-0.422040\pi\) | ||||
0.242478 | + | 0.970157i | \(0.422040\pi\) | |||||||
\(488\) | 21055.8 | 1.95318 | ||||||||
\(489\) | −3565.26 | −0.329706 | ||||||||
\(490\) | 5243.82 | 0.483453 | ||||||||
\(491\) | −10189.9 | −0.936589 | −0.468295 | − | 0.883572i | \(-0.655131\pi\) | ||||
−0.468295 | + | 0.883572i | \(0.655131\pi\) | |||||||
\(492\) | −21762.9 | −1.99421 | ||||||||
\(493\) | 1896.32 | 0.173237 | ||||||||
\(494\) | −17939.6 | −1.63389 | ||||||||
\(495\) | 2119.85 | 0.192485 | ||||||||
\(496\) | 19024.4 | 1.72222 | ||||||||
\(497\) | 1270.00 | 0.114622 | ||||||||
\(498\) | 22240.2 | 2.00122 | ||||||||
\(499\) | −20602.0 | −1.84824 | −0.924120 | − | 0.382103i | \(-0.875200\pi\) | ||||
−0.924120 | + | 0.382103i | \(0.875200\pi\) | |||||||
\(500\) | 28563.3 | 2.55478 | ||||||||
\(501\) | −5003.07 | −0.446149 | ||||||||
\(502\) | −12094.2 | −1.07528 | ||||||||
\(503\) | −8471.66 | −0.750959 | −0.375480 | − | 0.926831i | \(-0.622522\pi\) | ||||
−0.375480 | + | 0.926831i | \(0.622522\pi\) | |||||||
\(504\) | −11088.8 | −0.980032 | ||||||||
\(505\) | −9404.67 | −0.828718 | ||||||||
\(506\) | 12113.4 | 1.06424 | ||||||||
\(507\) | 4203.78 | 0.368237 | ||||||||
\(508\) | 14155.7 | 1.23633 | ||||||||
\(509\) | 11199.1 | 0.975230 | 0.487615 | − | 0.873059i | \(-0.337867\pi\) | ||||
0.487615 | + | 0.873059i | \(0.337867\pi\) | |||||||
\(510\) | −2823.12 | −0.245118 | ||||||||
\(511\) | 18973.9 | 1.64257 | ||||||||
\(512\) | 23351.9 | 2.01566 | ||||||||
\(513\) | 3304.47 | 0.284398 | ||||||||
\(514\) | 21954.0 | 1.88395 | ||||||||
\(515\) | −12283.8 | −1.05104 | ||||||||
\(516\) | −25793.8 | −2.20060 | ||||||||
\(517\) | 4485.10 | 0.381537 | ||||||||
\(518\) | −31412.1 | −2.66441 | ||||||||
\(519\) | −5563.72 | −0.470559 | ||||||||
\(520\) | −13385.5 | −1.12883 | ||||||||
\(521\) | −3200.10 | −0.269096 | −0.134548 | − | 0.990907i | \(-0.542958\pi\) | ||||
−0.134548 | + | 0.990907i | \(0.542958\pi\) | |||||||
\(522\) | −4064.96 | −0.340840 | ||||||||
\(523\) | 16516.2 | 1.38089 | 0.690443 | − | 0.723386i | \(-0.257415\pi\) | ||||
0.690443 | + | 0.723386i | \(0.257415\pi\) | |||||||
\(524\) | −41906.9 | −3.49372 | ||||||||
\(525\) | 3627.07 | 0.301520 | ||||||||
\(526\) | −16863.2 | −1.39785 | ||||||||
\(527\) | 2861.86 | 0.236555 | ||||||||
\(528\) | 12345.3 | 1.01754 | ||||||||
\(529\) | −5417.21 | −0.445238 | ||||||||
\(530\) | −7027.48 | −0.575951 | ||||||||
\(531\) | −531.000 | −0.0433963 | ||||||||
\(532\) | −50123.2 | −4.08480 | ||||||||
\(533\) | −10769.8 | −0.875219 | ||||||||
\(534\) | 24268.1 | 1.96664 | ||||||||
\(535\) | −2439.26 | −0.197118 | ||||||||
\(536\) | −10172.2 | −0.819724 | ||||||||
\(537\) | −10951.5 | −0.880061 | ||||||||
\(538\) | 24401.4 | 1.95543 | ||||||||
\(539\) | −3449.51 | −0.275660 | ||||||||
\(540\) | 4258.63 | 0.339375 | ||||||||
\(541\) | 20852.2 | 1.65713 | 0.828566 | − | 0.559892i | \(-0.189157\pi\) | ||||
0.828566 | + | 0.559892i | \(0.189157\pi\) | |||||||
\(542\) | −7497.95 | −0.594215 | ||||||||
\(543\) | −2736.58 | −0.216276 | ||||||||
\(544\) | −6464.04 | −0.509455 | ||||||||
\(545\) | 6652.86 | 0.522894 | ||||||||
\(546\) | −9478.11 | −0.742904 | ||||||||
\(547\) | 809.628 | 0.0632856 | 0.0316428 | − | 0.999499i | \(-0.489926\pi\) | ||||
0.0316428 | + | 0.999499i | \(0.489926\pi\) | |||||||
\(548\) | 14141.1 | 1.10233 | ||||||||
\(549\) | −3315.09 | −0.257714 | ||||||||
\(550\) | −8270.43 | −0.641186 | ||||||||
\(551\) | −10638.1 | −0.822499 | ||||||||
\(552\) | 14089.1 | 1.08636 | ||||||||
\(553\) | −17788.1 | −1.36786 | ||||||||
\(554\) | −35239.7 | −2.70251 | ||||||||
\(555\) | 6984.49 | 0.534189 | ||||||||
\(556\) | 5086.78 | 0.387999 | ||||||||
\(557\) | −21643.2 | −1.64641 | −0.823206 | − | 0.567743i | \(-0.807817\pi\) | ||||
−0.823206 | + | 0.567743i | \(0.807817\pi\) | |||||||
\(558\) | −6134.69 | −0.465416 | ||||||||
\(559\) | −12764.5 | −0.965800 | ||||||||
\(560\) | −25948.2 | −1.95806 | ||||||||
\(561\) | 1857.12 | 0.139764 | ||||||||
\(562\) | −4761.74 | −0.357406 | ||||||||
\(563\) | 23646.1 | 1.77010 | 0.885050 | − | 0.465496i | \(-0.154124\pi\) | ||||
0.885050 | + | 0.465496i | \(0.154124\pi\) | |||||||
\(564\) | 9010.27 | 0.672697 | ||||||||
\(565\) | 15224.4 | 1.13362 | ||||||||
\(566\) | 8798.17 | 0.653383 | ||||||||
\(567\) | 1745.87 | 0.129311 | ||||||||
\(568\) | −3368.18 | −0.248813 | ||||||||
\(569\) | −19407.6 | −1.42990 | −0.714948 | − | 0.699177i | \(-0.753550\pi\) | ||||
−0.714948 | + | 0.699177i | \(0.753550\pi\) | |||||||
\(570\) | 15837.3 | 1.16377 | ||||||||
\(571\) | 16659.0 | 1.22094 | 0.610470 | − | 0.792039i | \(-0.290980\pi\) | ||||
0.610470 | + | 0.792039i | \(0.290980\pi\) | |||||||
\(572\) | 15208.6 | 1.11172 | ||||||||
\(573\) | −6181.95 | −0.450706 | ||||||||
\(574\) | −42759.9 | −3.10935 | ||||||||
\(575\) | −4608.44 | −0.334235 | ||||||||
\(576\) | 3414.37 | 0.246988 | ||||||||
\(577\) | −19454.1 | −1.40361 | −0.701805 | − | 0.712369i | \(-0.747622\pi\) | ||||
−0.701805 | + | 0.712369i | \(0.747622\pi\) | |||||||
\(578\) | 23055.9 | 1.65917 | ||||||||
\(579\) | 5753.82 | 0.412989 | ||||||||
\(580\) | −13709.8 | −0.981496 | ||||||||
\(581\) | 30750.6 | 2.19578 | ||||||||
\(582\) | 28235.1 | 2.01097 | ||||||||
\(583\) | 4622.84 | 0.328402 | ||||||||
\(584\) | −50320.8 | −3.56557 | ||||||||
\(585\) | 2107.46 | 0.148945 | ||||||||
\(586\) | 24484.7 | 1.72603 | ||||||||
\(587\) | −2742.52 | −0.192838 | −0.0964190 | − | 0.995341i | \(-0.530739\pi\) | ||||
−0.0964190 | + | 0.995341i | \(0.530739\pi\) | |||||||
\(588\) | −6929.83 | −0.486023 | ||||||||
\(589\) | −16054.6 | −1.12312 | ||||||||
\(590\) | −2544.91 | −0.177580 | ||||||||
\(591\) | 7470.97 | 0.519991 | ||||||||
\(592\) | 40675.4 | 2.82390 | ||||||||
\(593\) | 9829.13 | 0.680664 | 0.340332 | − | 0.940305i | \(-0.389460\pi\) | ||||
0.340332 | + | 0.940305i | \(0.389460\pi\) | |||||||
\(594\) | −3980.92 | −0.274982 | ||||||||
\(595\) | −3903.42 | −0.268949 | ||||||||
\(596\) | −47089.9 | −3.23637 | ||||||||
\(597\) | −10236.3 | −0.701752 | ||||||||
\(598\) | 12042.6 | 0.823509 | ||||||||
\(599\) | 25261.4 | 1.72312 | 0.861562 | − | 0.507653i | \(-0.169487\pi\) | ||||
0.861562 | + | 0.507653i | \(0.169487\pi\) | |||||||
\(600\) | −9619.39 | −0.654517 | ||||||||
\(601\) | 23269.7 | 1.57935 | 0.789677 | − | 0.613523i | \(-0.210248\pi\) | ||||
0.789677 | + | 0.613523i | \(0.210248\pi\) | |||||||
\(602\) | −50679.7 | −3.43115 | ||||||||
\(603\) | 1601.55 | 0.108159 | ||||||||
\(604\) | 36148.9 | 2.43523 | ||||||||
\(605\) | 4365.35 | 0.293350 | ||||||||
\(606\) | 17661.3 | 1.18390 | ||||||||
\(607\) | 11725.1 | 0.784029 | 0.392015 | − | 0.919959i | \(-0.371778\pi\) | ||||
0.392015 | + | 0.919959i | \(0.371778\pi\) | |||||||
\(608\) | 36262.3 | 2.41880 | ||||||||
\(609\) | −5620.45 | −0.373977 | ||||||||
\(610\) | −15888.2 | −1.05458 | ||||||||
\(611\) | 4458.90 | 0.295234 | ||||||||
\(612\) | 3730.82 | 0.246421 | ||||||||
\(613\) | −4075.52 | −0.268530 | −0.134265 | − | 0.990945i | \(-0.542867\pi\) | ||||
−0.134265 | + | 0.990945i | \(0.542867\pi\) | |||||||
\(614\) | −40117.5 | −2.63682 | ||||||||
\(615\) | 9507.69 | 0.623393 | ||||||||
\(616\) | 34960.2 | 2.28667 | ||||||||
\(617\) | −2326.85 | −0.151824 | −0.0759121 | − | 0.997115i | \(-0.524187\pi\) | ||||
−0.0759121 | + | 0.997115i | \(0.524187\pi\) | |||||||
\(618\) | 23068.0 | 1.50151 | ||||||||
\(619\) | 27579.3 | 1.79080 | 0.895400 | − | 0.445263i | \(-0.146890\pi\) | ||||
0.895400 | + | 0.445263i | \(0.146890\pi\) | |||||||
\(620\) | −20690.3 | −1.34023 | ||||||||
\(621\) | −2218.24 | −0.143341 | ||||||||
\(622\) | −30000.6 | −1.93395 | ||||||||
\(623\) | 33554.6 | 2.15784 | ||||||||
\(624\) | 12273.2 | 0.787372 | ||||||||
\(625\) | −5466.95 | −0.349885 | ||||||||
\(626\) | 51317.8 | 3.27648 | ||||||||
\(627\) | −10418.1 | −0.663573 | ||||||||
\(628\) | −69131.5 | −4.39275 | ||||||||
\(629\) | 6118.84 | 0.387876 | ||||||||
\(630\) | 8367.37 | 0.529149 | ||||||||
\(631\) | −4818.78 | −0.304013 | −0.152007 | − | 0.988379i | \(-0.548574\pi\) | ||||
−0.152007 | + | 0.988379i | \(0.548574\pi\) | |||||||
\(632\) | 47176.0 | 2.96924 | ||||||||
\(633\) | −2676.23 | −0.168042 | ||||||||
\(634\) | 31206.2 | 1.95482 | ||||||||
\(635\) | −6184.27 | −0.386481 | ||||||||
\(636\) | 9286.98 | 0.579014 | ||||||||
\(637\) | −3429.36 | −0.213306 | ||||||||
\(638\) | 12815.7 | 0.795266 | ||||||||
\(639\) | 530.298 | 0.0328298 | ||||||||
\(640\) | −3312.10 | −0.204566 | ||||||||
\(641\) | −16896.8 | −1.04116 | −0.520580 | − | 0.853813i | \(-0.674284\pi\) | ||||
−0.520580 | + | 0.853813i | \(0.674284\pi\) | |||||||
\(642\) | 4580.75 | 0.281601 | ||||||||
\(643\) | −30887.2 | −1.89436 | −0.947180 | − | 0.320702i | \(-0.896081\pi\) | ||||
−0.947180 | + | 0.320702i | \(0.896081\pi\) | |||||||
\(644\) | 33646.9 | 2.05881 | ||||||||
\(645\) | 11268.7 | 0.687911 | ||||||||
\(646\) | 13874.4 | 0.845019 | ||||||||
\(647\) | −4782.21 | −0.290585 | −0.145292 | − | 0.989389i | \(-0.546412\pi\) | ||||
−0.145292 | + | 0.989389i | \(0.546412\pi\) | |||||||
\(648\) | −4630.23 | −0.280699 | ||||||||
\(649\) | 1674.10 | 0.101255 | ||||||||
\(650\) | −8222.11 | −0.496150 | ||||||||
\(651\) | −8482.19 | −0.510666 | ||||||||
\(652\) | 22581.0 | 1.35635 | ||||||||
\(653\) | −33078.5 | −1.98233 | −0.991164 | − | 0.132639i | \(-0.957655\pi\) | ||||
−0.991164 | + | 0.132639i | \(0.957655\pi\) | |||||||
\(654\) | −12493.6 | −0.747000 | ||||||||
\(655\) | 18308.1 | 1.09215 | ||||||||
\(656\) | 55369.6 | 3.29546 | ||||||||
\(657\) | 7922.69 | 0.470462 | ||||||||
\(658\) | 17703.4 | 1.04886 | ||||||||
\(659\) | 10359.2 | 0.612351 | 0.306175 | − | 0.951975i | \(-0.400951\pi\) | ||||
0.306175 | + | 0.951975i | \(0.400951\pi\) | |||||||
\(660\) | −13426.3 | −0.791848 | ||||||||
\(661\) | −14606.6 | −0.859502 | −0.429751 | − | 0.902947i | \(-0.641399\pi\) | ||||
−0.429751 | + | 0.902947i | \(0.641399\pi\) | |||||||
\(662\) | −35828.4 | −2.10349 | ||||||||
\(663\) | 1846.27 | 0.108149 | ||||||||
\(664\) | −81554.0 | −4.76643 | ||||||||
\(665\) | 21897.6 | 1.27692 | ||||||||
\(666\) | −13116.4 | −0.763136 | ||||||||
\(667\) | 7141.17 | 0.414553 | ||||||||
\(668\) | 31687.6 | 1.83538 | ||||||||
\(669\) | 8674.04 | 0.501282 | ||||||||
\(670\) | 7675.70 | 0.442594 | ||||||||
\(671\) | 10451.6 | 0.601312 | ||||||||
\(672\) | 19158.6 | 1.09979 | ||||||||
\(673\) | 4901.10 | 0.280719 | 0.140359 | − | 0.990101i | \(-0.455174\pi\) | ||||
0.140359 | + | 0.990101i | \(0.455174\pi\) | |||||||
\(674\) | −35147.4 | −2.00865 | ||||||||
\(675\) | 1514.51 | 0.0863608 | ||||||||
\(676\) | −26625.2 | −1.51486 | ||||||||
\(677\) | −7783.32 | −0.441857 | −0.220929 | − | 0.975290i | \(-0.570909\pi\) | ||||
−0.220929 | + | 0.975290i | \(0.570909\pi\) | |||||||
\(678\) | −28590.3 | −1.61948 | ||||||||
\(679\) | 39039.6 | 2.20648 | ||||||||
\(680\) | 10352.3 | 0.583813 | ||||||||
\(681\) | 5239.35 | 0.294820 | ||||||||
\(682\) | 19341.1 | 1.08594 | ||||||||
\(683\) | −5065.20 | −0.283770 | −0.141885 | − | 0.989883i | \(-0.545316\pi\) | ||||
−0.141885 | + | 0.989883i | \(0.545316\pi\) | |||||||
\(684\) | −20929.3 | −1.16996 | ||||||||
\(685\) | −6177.89 | −0.344592 | ||||||||
\(686\) | 24800.0 | 1.38027 | ||||||||
\(687\) | 3584.99 | 0.199092 | ||||||||
\(688\) | 65624.9 | 3.63652 | ||||||||
\(689\) | 4595.83 | 0.254118 | ||||||||
\(690\) | −10631.3 | −0.586562 | ||||||||
\(691\) | −987.814 | −0.0543824 | −0.0271912 | − | 0.999630i | \(-0.508656\pi\) | ||||
−0.0271912 | + | 0.999630i | \(0.508656\pi\) | |||||||
\(692\) | 35238.6 | 1.93579 | ||||||||
\(693\) | −5504.25 | −0.301716 | ||||||||
\(694\) | −28448.0 | −1.55601 | ||||||||
\(695\) | −2222.29 | −0.121289 | ||||||||
\(696\) | 14906.1 | 0.811801 | ||||||||
\(697\) | 8329.32 | 0.452648 | ||||||||
\(698\) | 33130.7 | 1.79658 | ||||||||
\(699\) | 14225.8 | 0.769769 | ||||||||
\(700\) | −22972.5 | −1.24040 | ||||||||
\(701\) | 24301.9 | 1.30937 | 0.654685 | − | 0.755902i | \(-0.272801\pi\) | ||||
0.654685 | + | 0.755902i | \(0.272801\pi\) | |||||||
\(702\) | −3957.66 | −0.212781 | ||||||||
\(703\) | −34325.7 | −1.84156 | ||||||||
\(704\) | −10764.6 | −0.576287 | ||||||||
\(705\) | −3936.36 | −0.210287 | ||||||||
\(706\) | −25831.3 | −1.37701 | ||||||||
\(707\) | 24419.6 | 1.29900 | ||||||||
\(708\) | 3363.16 | 0.178524 | ||||||||
\(709\) | 19625.0 | 1.03954 | 0.519769 | − | 0.854307i | \(-0.326018\pi\) | ||||
0.519769 | + | 0.854307i | \(0.326018\pi\) | |||||||
\(710\) | 2541.55 | 0.134342 | ||||||||
\(711\) | −7427.56 | −0.391779 | ||||||||
\(712\) | −88990.5 | −4.68408 | ||||||||
\(713\) | 10777.2 | 0.566072 | ||||||||
\(714\) | 7330.34 | 0.384217 | ||||||||
\(715\) | −6644.27 | −0.347527 | ||||||||
\(716\) | 69362.9 | 3.62041 | ||||||||
\(717\) | 8667.32 | 0.451446 | ||||||||
\(718\) | −10774.2 | −0.560012 | ||||||||
\(719\) | −12274.5 | −0.636663 | −0.318331 | − | 0.947979i | \(-0.603123\pi\) | ||||
−0.318331 | + | 0.947979i | \(0.603123\pi\) | |||||||
\(720\) | −10834.9 | −0.560822 | ||||||||
\(721\) | 31895.2 | 1.64749 | ||||||||
\(722\) | −42192.4 | −2.17484 | ||||||||
\(723\) | −7944.32 | −0.408648 | ||||||||
\(724\) | 17332.5 | 0.889722 | ||||||||
\(725\) | −4875.65 | −0.249762 | ||||||||
\(726\) | −8197.80 | −0.419076 | ||||||||
\(727\) | 9818.35 | 0.500884 | 0.250442 | − | 0.968132i | \(-0.419424\pi\) | ||||
0.250442 | + | 0.968132i | \(0.419424\pi\) | |||||||
\(728\) | 34755.9 | 1.76942 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 37970.9 | 1.92516 | ||||||||
\(731\) | 9872.04 | 0.499495 | ||||||||
\(732\) | 20996.6 | 1.06019 | ||||||||
\(733\) | −36133.7 | −1.82078 | −0.910388 | − | 0.413756i | \(-0.864217\pi\) | ||||
−0.910388 | + | 0.413756i | \(0.864217\pi\) | |||||||
\(734\) | 33700.7 | 1.69471 | ||||||||
\(735\) | 3027.47 | 0.151932 | ||||||||
\(736\) | −24342.3 | −1.21912 | ||||||||
\(737\) | −5049.26 | −0.252363 | ||||||||
\(738\) | −17854.7 | −0.890572 | ||||||||
\(739\) | 15833.8 | 0.788166 | 0.394083 | − | 0.919075i | \(-0.371062\pi\) | ||||
0.394083 | + | 0.919075i | \(0.371062\pi\) | |||||||
\(740\) | −44237.2 | −2.19756 | ||||||||
\(741\) | −10357.3 | −0.513473 | ||||||||
\(742\) | 18247.1 | 0.902792 | ||||||||
\(743\) | 23888.6 | 1.17953 | 0.589764 | − | 0.807576i | \(-0.299221\pi\) | ||||
0.589764 | + | 0.807576i | \(0.299221\pi\) | |||||||
\(744\) | 22495.7 | 1.10851 | ||||||||
\(745\) | 20572.4 | 1.01170 | ||||||||
\(746\) | 13563.5 | 0.665676 | ||||||||
\(747\) | 12840.2 | 0.628911 | ||||||||
\(748\) | −11762.3 | −0.574963 | ||||||||
\(749\) | 6333.62 | 0.308979 | ||||||||
\(750\) | 23433.9 | 1.14091 | ||||||||
\(751\) | −29824.3 | −1.44914 | −0.724571 | − | 0.689200i | \(-0.757962\pi\) | ||||
−0.724571 | + | 0.689200i | \(0.757962\pi\) | |||||||
\(752\) | −22924.1 | −1.11164 | ||||||||
\(753\) | −6982.48 | −0.337923 | ||||||||
\(754\) | 12740.9 | 0.615378 | ||||||||
\(755\) | −15792.5 | −0.761257 | ||||||||
\(756\) | −11057.7 | −0.531963 | ||||||||
\(757\) | 7136.54 | 0.342645 | 0.171322 | − | 0.985215i | \(-0.445196\pi\) | ||||
0.171322 | + | 0.985215i | \(0.445196\pi\) | |||||||
\(758\) | 29147.5 | 1.39668 | ||||||||
\(759\) | 6993.53 | 0.334452 | ||||||||
\(760\) | −58074.8 | −2.77184 | ||||||||
\(761\) | −19820.8 | −0.944157 | −0.472079 | − | 0.881557i | \(-0.656496\pi\) | ||||
−0.472079 | + | 0.881557i | \(0.656496\pi\) | |||||||
\(762\) | 11613.6 | 0.552122 | ||||||||
\(763\) | −17274.4 | −0.819626 | ||||||||
\(764\) | 39154.2 | 1.85412 | ||||||||
\(765\) | −1629.90 | −0.0770318 | ||||||||
\(766\) | −15478.5 | −0.730108 | ||||||||
\(767\) | 1664.32 | 0.0783510 | ||||||||
\(768\) | 15324.9 | 0.720037 | ||||||||
\(769\) | 23969.6 | 1.12401 | 0.562006 | − | 0.827133i | \(-0.310030\pi\) | ||||
0.562006 | + | 0.827133i | \(0.310030\pi\) | |||||||
\(770\) | −26380.1 | −1.23464 | ||||||||
\(771\) | 12674.9 | 0.592057 | ||||||||
\(772\) | −36442.6 | −1.69896 | ||||||||
\(773\) | 41618.3 | 1.93649 | 0.968245 | − | 0.250004i | \(-0.0804320\pi\) | ||||
0.968245 | + | 0.250004i | \(0.0804320\pi\) | |||||||
\(774\) | −21161.7 | −0.982742 | ||||||||
\(775\) | −7358.17 | −0.341049 | ||||||||
\(776\) | −103537. | −4.78966 | ||||||||
\(777\) | −18135.5 | −0.837331 | ||||||||
\(778\) | −52677.2 | −2.42747 | ||||||||
\(779\) | −46726.2 | −2.14909 | ||||||||
\(780\) | −13347.9 | −0.612733 | ||||||||
\(781\) | −1671.89 | −0.0766004 | ||||||||
\(782\) | −9313.70 | −0.425904 | ||||||||
\(783\) | −2346.86 | −0.107114 | ||||||||
\(784\) | 17631.0 | 0.803161 | ||||||||
\(785\) | 30201.8 | 1.37318 | ||||||||
\(786\) | −34381.2 | −1.56023 | ||||||||
\(787\) | 17130.9 | 0.775920 | 0.387960 | − | 0.921676i | \(-0.373180\pi\) | ||||
0.387960 | + | 0.921676i | \(0.373180\pi\) | |||||||
\(788\) | −47318.4 | −2.13915 | ||||||||
\(789\) | −9735.80 | −0.439295 | ||||||||
\(790\) | −35597.9 | −1.60319 | ||||||||
\(791\) | −39530.7 | −1.77693 | ||||||||
\(792\) | 14597.9 | 0.654942 | ||||||||
\(793\) | 10390.6 | 0.465296 | ||||||||
\(794\) | −67145.5 | −3.00114 | ||||||||
\(795\) | −4057.25 | −0.181001 | ||||||||
\(796\) | 64833.3 | 2.88688 | ||||||||
\(797\) | −3545.01 | −0.157554 | −0.0787770 | − | 0.996892i | \(-0.525102\pi\) | ||||
−0.0787770 | + | 0.996892i | \(0.525102\pi\) | |||||||
\(798\) | −41122.0 | −1.82419 | ||||||||
\(799\) | −3448.50 | −0.152690 | ||||||||
\(800\) | 16619.8 | 0.734497 | ||||||||
\(801\) | 14011.0 | 0.618045 | ||||||||
\(802\) | 49658.8 | 2.18643 | ||||||||
\(803\) | −24978.1 | −1.09771 | ||||||||
\(804\) | −10143.6 | −0.444948 | ||||||||
\(805\) | −14699.5 | −0.643589 | ||||||||
\(806\) | 19228.1 | 0.840298 | ||||||||
\(807\) | 14087.9 | 0.614521 | ||||||||
\(808\) | −64763.4 | −2.81976 | ||||||||
\(809\) | −11108.5 | −0.482763 | −0.241381 | − | 0.970430i | \(-0.577600\pi\) | ||||
−0.241381 | + | 0.970430i | \(0.577600\pi\) | |||||||
\(810\) | 3493.86 | 0.151558 | ||||||||
\(811\) | −11416.7 | −0.494320 | −0.247160 | − | 0.968975i | \(-0.579497\pi\) | ||||
−0.247160 | + | 0.968975i | \(0.579497\pi\) | |||||||
\(812\) | 35597.9 | 1.53847 | ||||||||
\(813\) | −4328.87 | −0.186741 | ||||||||
\(814\) | 41352.4 | 1.78059 | ||||||||
\(815\) | −9865.09 | −0.423999 | ||||||||
\(816\) | −9492.02 | −0.407215 | ||||||||
\(817\) | −55380.6 | −2.37151 | ||||||||
\(818\) | −43553.0 | −1.86161 | ||||||||
\(819\) | −5472.10 | −0.233468 | ||||||||
\(820\) | −60218.2 | −2.56453 | ||||||||
\(821\) | 27265.7 | 1.15905 | 0.579524 | − | 0.814955i | \(-0.303238\pi\) | ||||
0.579524 | + | 0.814955i | \(0.303238\pi\) | |||||||
\(822\) | 11601.6 | 0.492279 | ||||||||
\(823\) | 18672.1 | 0.790849 | 0.395424 | − | 0.918499i | \(-0.370598\pi\) | ||||
0.395424 | + | 0.918499i | \(0.370598\pi\) | |||||||
\(824\) | −84589.7 | −3.57624 | ||||||||
\(825\) | −4774.85 | −0.201502 | ||||||||
\(826\) | 6607.95 | 0.278354 | ||||||||
\(827\) | 33292.9 | 1.39989 | 0.699945 | − | 0.714197i | \(-0.253208\pi\) | ||||
0.699945 | + | 0.714197i | \(0.253208\pi\) | |||||||
\(828\) | 14049.5 | 0.589680 | ||||||||
\(829\) | 21571.9 | 0.903768 | 0.451884 | − | 0.892077i | \(-0.350752\pi\) | ||||
0.451884 | + | 0.892077i | \(0.350752\pi\) | |||||||
\(830\) | 61538.7 | 2.57354 | ||||||||
\(831\) | −20345.3 | −0.849304 | ||||||||
\(832\) | −10701.7 | −0.445932 | ||||||||
\(833\) | 2652.25 | 0.110318 | ||||||||
\(834\) | 4173.29 | 0.173273 | ||||||||
\(835\) | −13843.5 | −0.573743 | ||||||||
\(836\) | 65984.7 | 2.72982 | ||||||||
\(837\) | −3541.81 | −0.146264 | ||||||||
\(838\) | 46794.2 | 1.92897 | ||||||||
\(839\) | 24952.4 | 1.02676 | 0.513381 | − | 0.858161i | \(-0.328393\pi\) | ||||
0.513381 | + | 0.858161i | \(0.328393\pi\) | |||||||
\(840\) | −30682.9 | −1.26031 | ||||||||
\(841\) | −16833.8 | −0.690219 | ||||||||
\(842\) | −3918.43 | −0.160378 | ||||||||
\(843\) | −2749.15 | −0.112320 | ||||||||
\(844\) | 16950.3 | 0.691294 | ||||||||
\(845\) | 11631.9 | 0.473549 | ||||||||
\(846\) | 7392.20 | 0.300413 | ||||||||
\(847\) | −11334.8 | −0.459820 | ||||||||
\(848\) | −23628.1 | −0.956830 | ||||||||
\(849\) | 5079.54 | 0.205335 | ||||||||
\(850\) | 6358.95 | 0.256600 | ||||||||
\(851\) | 23042.3 | 0.928180 | ||||||||
\(852\) | −3358.71 | −0.135056 | ||||||||
\(853\) | 22193.3 | 0.890836 | 0.445418 | − | 0.895323i | \(-0.353055\pi\) | ||||
0.445418 | + | 0.895323i | \(0.353055\pi\) | |||||||
\(854\) | 41254.2 | 1.65303 | ||||||||
\(855\) | 9143.50 | 0.365732 | ||||||||
\(856\) | −16797.5 | −0.670708 | ||||||||
\(857\) | 5155.43 | 0.205491 | 0.102746 | − | 0.994708i | \(-0.467237\pi\) | ||||
0.102746 | + | 0.994708i | \(0.467237\pi\) | |||||||
\(858\) | 12477.5 | 0.496473 | ||||||||
\(859\) | −18059.6 | −0.717327 | −0.358664 | − | 0.933467i | \(-0.616767\pi\) | ||||
−0.358664 | + | 0.933467i | \(0.616767\pi\) | |||||||
\(860\) | −71371.6 | −2.82994 | ||||||||
\(861\) | −24687.0 | −0.977156 | ||||||||
\(862\) | 13020.7 | 0.514486 | ||||||||
\(863\) | −3135.68 | −0.123685 | −0.0618423 | − | 0.998086i | \(-0.519698\pi\) | ||||
−0.0618423 | + | 0.998086i | \(0.519698\pi\) | |||||||
\(864\) | 7999.82 | 0.314999 | ||||||||
\(865\) | −15394.9 | −0.605134 | ||||||||
\(866\) | 917.149 | 0.0359884 | ||||||||
\(867\) | 13311.1 | 0.521417 | ||||||||
\(868\) | 53723.1 | 2.10078 | ||||||||
\(869\) | 23417.1 | 0.914122 | ||||||||
\(870\) | −11247.8 | −0.438316 | ||||||||
\(871\) | −5019.76 | −0.195279 | ||||||||
\(872\) | 45813.6 | 1.77918 | ||||||||
\(873\) | 16301.3 | 0.631976 | ||||||||
\(874\) | 52248.4 | 2.02211 | ||||||||
\(875\) | 32401.0 | 1.25183 | ||||||||
\(876\) | −50179.4 | −1.93539 | ||||||||
\(877\) | 24764.4 | 0.953516 | 0.476758 | − | 0.879035i | \(-0.341812\pi\) | ||||
0.476758 | + | 0.879035i | \(0.341812\pi\) | |||||||
\(878\) | 11556.1 | 0.444190 | ||||||||
\(879\) | 14136.0 | 0.542429 | ||||||||
\(880\) | 34159.5 | 1.30854 | ||||||||
\(881\) | −24195.2 | −0.925265 | −0.462633 | − | 0.886550i | \(-0.653095\pi\) | ||||
−0.462633 | + | 0.886550i | \(0.653095\pi\) | |||||||
\(882\) | −5685.37 | −0.217048 | ||||||||
\(883\) | −26387.8 | −1.00569 | −0.502843 | − | 0.864378i | \(-0.667713\pi\) | ||||
−0.502843 | + | 0.864378i | \(0.667713\pi\) | |||||||
\(884\) | −11693.6 | −0.444907 | ||||||||
\(885\) | −1469.28 | −0.0558072 | ||||||||
\(886\) | 31515.8 | 1.19503 | ||||||||
\(887\) | 45619.8 | 1.72690 | 0.863452 | − | 0.504431i | \(-0.168298\pi\) | ||||
0.863452 | + | 0.504431i | \(0.168298\pi\) | |||||||
\(888\) | 48097.3 | 1.81761 | ||||||||
\(889\) | 16057.7 | 0.605801 | ||||||||
\(890\) | 67150.1 | 2.52908 | ||||||||
\(891\) | −2298.35 | −0.0864169 | ||||||||
\(892\) | −54938.2 | −2.06218 | ||||||||
\(893\) | 19345.5 | 0.724942 | ||||||||
\(894\) | −38633.5 | −1.44530 | ||||||||
\(895\) | −30302.9 | −1.13175 | ||||||||
\(896\) | 8599.98 | 0.320653 | ||||||||
\(897\) | 6952.68 | 0.258799 | ||||||||
\(898\) | 662.978 | 0.0246368 | ||||||||
\(899\) | 11402.1 | 0.423005 | ||||||||
\(900\) | −9592.36 | −0.355273 | ||||||||
\(901\) | −3554.40 | −0.131425 | ||||||||
\(902\) | 56291.3 | 2.07793 | ||||||||
\(903\) | −29259.4 | −1.07829 | ||||||||
\(904\) | 104840. | 3.85721 | ||||||||
\(905\) | −7572.15 | −0.278129 | ||||||||
\(906\) | 29657.2 | 1.08752 | ||||||||
\(907\) | −28604.5 | −1.04719 | −0.523593 | − | 0.851968i | \(-0.675409\pi\) | ||||
−0.523593 | + | 0.851968i | \(0.675409\pi\) | |||||||
\(908\) | −33184.1 | −1.21283 | ||||||||
\(909\) | 10196.6 | 0.372056 | ||||||||
\(910\) | −26226.0 | −0.955367 | ||||||||
\(911\) | 23089.0 | 0.839706 | 0.419853 | − | 0.907592i | \(-0.362082\pi\) | ||||
0.419853 | + | 0.907592i | \(0.362082\pi\) | |||||||
\(912\) | 53248.7 | 1.93338 | ||||||||
\(913\) | −40481.6 | −1.46741 | ||||||||
\(914\) | −79226.4 | −2.86715 | ||||||||
\(915\) | −9172.89 | −0.331417 | ||||||||
\(916\) | −22706.0 | −0.819027 | ||||||||
\(917\) | −47537.5 | −1.71192 | ||||||||
\(918\) | 3060.84 | 0.110047 | ||||||||
\(919\) | −14323.8 | −0.514145 | −0.257072 | − | 0.966392i | \(-0.582758\pi\) | ||||
−0.257072 | + | 0.966392i | \(0.582758\pi\) | |||||||
\(920\) | 38984.7 | 1.39705 | ||||||||
\(921\) | −23161.4 | −0.828659 | ||||||||
\(922\) | −42340.0 | −1.51236 | ||||||||
\(923\) | −1662.12 | −0.0592735 | ||||||||
\(924\) | 34861.9 | 1.24121 | ||||||||
\(925\) | −15732.2 | −0.559213 | ||||||||
\(926\) | −33873.8 | −1.20212 | ||||||||
\(927\) | 13318.1 | 0.471870 | ||||||||
\(928\) | −25753.8 | −0.911001 | ||||||||
\(929\) | −34587.5 | −1.22151 | −0.610753 | − | 0.791821i | \(-0.709133\pi\) | ||||
−0.610753 | + | 0.791821i | \(0.709133\pi\) | |||||||
\(930\) | −16974.7 | −0.598520 | ||||||||
\(931\) | −14878.7 | −0.523770 | ||||||||
\(932\) | −90101.0 | −3.16669 | ||||||||
\(933\) | −17320.6 | −0.607771 | ||||||||
\(934\) | 1370.51 | 0.0480134 | ||||||||
\(935\) | 5138.66 | 0.179735 | ||||||||
\(936\) | 14512.6 | 0.506795 | ||||||||
\(937\) | 30905.7 | 1.07753 | 0.538765 | − | 0.842456i | \(-0.318891\pi\) | ||||
0.538765 | + | 0.842456i | \(0.318891\pi\) | |||||||
\(938\) | −19930.2 | −0.693758 | ||||||||
\(939\) | 29627.9 | 1.02968 | ||||||||
\(940\) | 24931.5 | 0.865081 | ||||||||
\(941\) | −20269.1 | −0.702184 | −0.351092 | − | 0.936341i | \(-0.614189\pi\) | ||||
−0.351092 | + | 0.936341i | \(0.614189\pi\) | |||||||
\(942\) | −56716.8 | −1.96171 | ||||||||
\(943\) | 31366.6 | 1.08318 | ||||||||
\(944\) | −8556.61 | −0.295015 | ||||||||
\(945\) | 4830.82 | 0.166293 | ||||||||
\(946\) | 66717.3 | 2.29299 | ||||||||
\(947\) | 3806.38 | 0.130613 | 0.0653066 | − | 0.997865i | \(-0.479197\pi\) | ||||
0.0653066 | + | 0.997865i | \(0.479197\pi\) | |||||||
\(948\) | 47043.4 | 1.61171 | ||||||||
\(949\) | −24832.2 | −0.849408 | ||||||||
\(950\) | −35672.7 | −1.21829 | ||||||||
\(951\) | 18016.6 | 0.614330 | ||||||||
\(952\) | −26880.1 | −0.915115 | ||||||||
\(953\) | −58087.5 | −1.97444 | −0.987219 | − | 0.159370i | \(-0.949054\pi\) | ||||
−0.987219 | + | 0.159370i | \(0.949054\pi\) | |||||||
\(954\) | 7619.22 | 0.258576 | ||||||||
\(955\) | −17105.5 | −0.579603 | ||||||||
\(956\) | −54895.6 | −1.85717 | ||||||||
\(957\) | 7399.05 | 0.249924 | ||||||||
\(958\) | −16649.6 | −0.561509 | ||||||||
\(959\) | 16041.1 | 0.540140 | ||||||||
\(960\) | 9447.58 | 0.317624 | ||||||||
\(961\) | −12583.3 | −0.422387 | ||||||||
\(962\) | 41110.8 | 1.37782 | ||||||||
\(963\) | 2644.65 | 0.0884971 | ||||||||
\(964\) | 50316.4 | 1.68110 | ||||||||
\(965\) | 15920.9 | 0.531100 | ||||||||
\(966\) | 27604.6 | 0.919423 | ||||||||
\(967\) | −9873.60 | −0.328349 | −0.164175 | − | 0.986431i | \(-0.552496\pi\) | ||||
−0.164175 | + | 0.986431i | \(0.552496\pi\) | |||||||
\(968\) | 30061.1 | 0.998141 | ||||||||
\(969\) | 8010.27 | 0.265559 | ||||||||
\(970\) | 78126.9 | 2.58609 | ||||||||
\(971\) | 55181.6 | 1.82375 | 0.911875 | − | 0.410468i | \(-0.134634\pi\) | ||||
0.911875 | + | 0.410468i | \(0.134634\pi\) | |||||||
\(972\) | −4617.22 | −0.152364 | ||||||||
\(973\) | 5770.24 | 0.190119 | ||||||||
\(974\) | −27082.3 | −0.890937 | ||||||||
\(975\) | −4746.96 | −0.155922 | ||||||||
\(976\) | −53419.9 | −1.75198 | ||||||||
\(977\) | 14494.0 | 0.474620 | 0.237310 | − | 0.971434i | \(-0.423734\pi\) | ||||
0.237310 | + | 0.971434i | \(0.423734\pi\) | |||||||
\(978\) | 18525.9 | 0.605720 | ||||||||
\(979\) | −44172.9 | −1.44206 | ||||||||
\(980\) | −19174.9 | −0.625020 | ||||||||
\(981\) | −7213.06 | −0.234756 | ||||||||
\(982\) | 52949.4 | 1.72065 | ||||||||
\(983\) | −38986.8 | −1.26499 | −0.632495 | − | 0.774564i | \(-0.717969\pi\) | ||||
−0.632495 | + | 0.774564i | \(0.717969\pi\) | |||||||
\(984\) | 65472.8 | 2.12114 | ||||||||
\(985\) | 20672.2 | 0.668703 | ||||||||
\(986\) | −9853.74 | −0.318263 | ||||||||
\(987\) | 10220.9 | 0.329620 | ||||||||
\(988\) | 65599.2 | 2.11234 | ||||||||
\(989\) | 37176.1 | 1.19528 | ||||||||
\(990\) | −11015.2 | −0.353623 | ||||||||
\(991\) | −48817.5 | −1.56482 | −0.782412 | − | 0.622762i | \(-0.786011\pi\) | ||||
−0.782412 | + | 0.622762i | \(0.786011\pi\) | |||||||
\(992\) | −38866.7 | −1.24397 | ||||||||
\(993\) | −20685.2 | −0.661052 | ||||||||
\(994\) | −6599.21 | −0.210578 | ||||||||
\(995\) | −28324.1 | −0.902445 | ||||||||
\(996\) | −81324.9 | −2.58723 | ||||||||
\(997\) | −14978.6 | −0.475806 | −0.237903 | − | 0.971289i | \(-0.576460\pi\) | ||||
−0.237903 | + | 0.971289i | \(0.576460\pi\) | |||||||
\(998\) | 107053. | 3.39549 | ||||||||
\(999\) | −7572.60 | −0.239826 |
(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 | 177.4.a.c.1.1 | ✓ | 8 | |
3.2 | odd | 2 | 531.4.a.f.1.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.4.a.c.1.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
531.4.a.f.1.8 | 8 | 3.2 | odd | 2 |