Properties

Label 2151.4.a.e.1.10
Level $2151$
Weight $4$
Character 2151.1
Self dual yes
Analytic conductor $126.913$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2151,4,Mod(1,2151)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2151, 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("2151.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2151 = 3^{2} \cdot 239 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2151.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: \(126.913108422\)
Analytic rank: \(0\)
Dimension: \(32\)
Twist minimal: no (minimal twist has level 717)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) \(=\) 2151.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.96284 q^{2} +0.778438 q^{4} -20.0660 q^{5} -4.37640 q^{7} +21.3964 q^{8} +O(q^{10})\) \(q-2.96284 q^{2} +0.778438 q^{4} -20.0660 q^{5} -4.37640 q^{7} +21.3964 q^{8} +59.4524 q^{10} -18.0511 q^{11} +82.1177 q^{13} +12.9666 q^{14} -69.6215 q^{16} +100.079 q^{17} +43.8153 q^{19} -15.6201 q^{20} +53.4826 q^{22} -19.2488 q^{23} +277.645 q^{25} -243.302 q^{26} -3.40676 q^{28} +46.3126 q^{29} +307.269 q^{31} +35.1069 q^{32} -296.518 q^{34} +87.8170 q^{35} -176.784 q^{37} -129.818 q^{38} -429.339 q^{40} +15.7068 q^{41} +483.788 q^{43} -14.0517 q^{44} +57.0312 q^{46} +260.516 q^{47} -323.847 q^{49} -822.618 q^{50} +63.9235 q^{52} -217.305 q^{53} +362.214 q^{55} -93.6391 q^{56} -137.217 q^{58} -176.201 q^{59} +324.738 q^{61} -910.388 q^{62} +452.956 q^{64} -1647.77 q^{65} +1076.40 q^{67} +77.9053 q^{68} -260.188 q^{70} -236.616 q^{71} -343.940 q^{73} +523.783 q^{74} +34.1075 q^{76} +78.9990 q^{77} -326.144 q^{79} +1397.03 q^{80} -46.5369 q^{82} +245.256 q^{83} -2008.18 q^{85} -1433.39 q^{86} -386.228 q^{88} -1457.23 q^{89} -359.380 q^{91} -14.9840 q^{92} -771.869 q^{94} -879.198 q^{95} +762.159 q^{97} +959.508 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 3 q^{2} + 151 q^{4} + 14 q^{5} + 72 q^{7} - 57 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 3 q^{2} + 151 q^{4} + 14 q^{5} + 72 q^{7} - 57 q^{8} + 32 q^{10} - 154 q^{11} + 100 q^{13} - 42 q^{14} + 719 q^{16} - 32 q^{17} + 202 q^{19} + 132 q^{20} + 265 q^{22} - 552 q^{23} + 1086 q^{25} + 280 q^{26} + 390 q^{28} + 154 q^{29} + 560 q^{31} - 444 q^{32} + 156 q^{34} - 394 q^{35} + 914 q^{37} - 111 q^{38} + 257 q^{40} + 914 q^{41} + 1722 q^{43} - 1243 q^{44} + 584 q^{46} - 380 q^{47} + 2446 q^{49} + 454 q^{50} + 1552 q^{52} - 370 q^{53} + 918 q^{55} + 499 q^{56} + 2446 q^{58} - 492 q^{59} + 668 q^{61} - 578 q^{62} + 6475 q^{64} - 736 q^{65} + 4548 q^{67} - 5253 q^{68} + 7793 q^{70} - 258 q^{71} + 3096 q^{73} - 449 q^{74} + 6814 q^{76} - 3804 q^{77} + 2864 q^{79} + 1052 q^{80} + 14145 q^{82} - 2364 q^{83} + 3088 q^{85} - 2811 q^{86} + 8329 q^{88} + 4172 q^{89} + 7350 q^{91} - 13644 q^{92} + 6122 q^{94} - 3336 q^{95} + 6370 q^{97} - 1572 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.96284 −1.04752 −0.523762 0.851865i \(-0.675472\pi\)
−0.523762 + 0.851865i \(0.675472\pi\)
\(3\) 0 0
\(4\) 0.778438 0.0973048
\(5\) −20.0660 −1.79476 −0.897379 0.441260i \(-0.854532\pi\)
−0.897379 + 0.441260i \(0.854532\pi\)
\(6\) 0 0
\(7\) −4.37640 −0.236304 −0.118152 0.992996i \(-0.537697\pi\)
−0.118152 + 0.992996i \(0.537697\pi\)
\(8\) 21.3964 0.945594
\(9\) 0 0
\(10\) 59.4524 1.88005
\(11\) −18.0511 −0.494783 −0.247392 0.968916i \(-0.579573\pi\)
−0.247392 + 0.968916i \(0.579573\pi\)
\(12\) 0 0
\(13\) 82.1177 1.75195 0.875975 0.482357i \(-0.160219\pi\)
0.875975 + 0.482357i \(0.160219\pi\)
\(14\) 12.9666 0.247534
\(15\) 0 0
\(16\) −69.6215 −1.08784
\(17\) 100.079 1.42781 0.713903 0.700245i \(-0.246926\pi\)
0.713903 + 0.700245i \(0.246926\pi\)
\(18\) 0 0
\(19\) 43.8153 0.529048 0.264524 0.964379i \(-0.414785\pi\)
0.264524 + 0.964379i \(0.414785\pi\)
\(20\) −15.6201 −0.174639
\(21\) 0 0
\(22\) 53.4826 0.518297
\(23\) −19.2488 −0.174507 −0.0872533 0.996186i \(-0.527809\pi\)
−0.0872533 + 0.996186i \(0.527809\pi\)
\(24\) 0 0
\(25\) 277.645 2.22116
\(26\) −243.302 −1.83521
\(27\) 0 0
\(28\) −3.40676 −0.0229935
\(29\) 46.3126 0.296553 0.148276 0.988946i \(-0.452627\pi\)
0.148276 + 0.988946i \(0.452627\pi\)
\(30\) 0 0
\(31\) 307.269 1.78023 0.890114 0.455738i \(-0.150625\pi\)
0.890114 + 0.455738i \(0.150625\pi\)
\(32\) 35.1069 0.193940
\(33\) 0 0
\(34\) −296.518 −1.49566
\(35\) 87.8170 0.424108
\(36\) 0 0
\(37\) −176.784 −0.785489 −0.392744 0.919648i \(-0.628474\pi\)
−0.392744 + 0.919648i \(0.628474\pi\)
\(38\) −129.818 −0.554190
\(39\) 0 0
\(40\) −429.339 −1.69711
\(41\) 15.7068 0.0598291 0.0299146 0.999552i \(-0.490476\pi\)
0.0299146 + 0.999552i \(0.490476\pi\)
\(42\) 0 0
\(43\) 483.788 1.71574 0.857872 0.513863i \(-0.171786\pi\)
0.857872 + 0.513863i \(0.171786\pi\)
\(44\) −14.0517 −0.0481448
\(45\) 0 0
\(46\) 57.0312 0.182800
\(47\) 260.516 0.808515 0.404258 0.914645i \(-0.367530\pi\)
0.404258 + 0.914645i \(0.367530\pi\)
\(48\) 0 0
\(49\) −323.847 −0.944161
\(50\) −822.618 −2.32671
\(51\) 0 0
\(52\) 63.9235 0.170473
\(53\) −217.305 −0.563190 −0.281595 0.959533i \(-0.590863\pi\)
−0.281595 + 0.959533i \(0.590863\pi\)
\(54\) 0 0
\(55\) 362.214 0.888016
\(56\) −93.6391 −0.223447
\(57\) 0 0
\(58\) −137.217 −0.310646
\(59\) −176.201 −0.388804 −0.194402 0.980922i \(-0.562277\pi\)
−0.194402 + 0.980922i \(0.562277\pi\)
\(60\) 0 0
\(61\) 324.738 0.681614 0.340807 0.940133i \(-0.389300\pi\)
0.340807 + 0.940133i \(0.389300\pi\)
\(62\) −910.388 −1.86483
\(63\) 0 0
\(64\) 452.956 0.884680
\(65\) −1647.77 −3.14433
\(66\) 0 0
\(67\) 1076.40 1.96274 0.981368 0.192138i \(-0.0615421\pi\)
0.981368 + 0.192138i \(0.0615421\pi\)
\(68\) 77.9053 0.138932
\(69\) 0 0
\(70\) −260.188 −0.444263
\(71\) −236.616 −0.395509 −0.197755 0.980252i \(-0.563365\pi\)
−0.197755 + 0.980252i \(0.563365\pi\)
\(72\) 0 0
\(73\) −343.940 −0.551440 −0.275720 0.961238i \(-0.588916\pi\)
−0.275720 + 0.961238i \(0.588916\pi\)
\(74\) 523.783 0.822817
\(75\) 0 0
\(76\) 34.1075 0.0514789
\(77\) 78.9990 0.116919
\(78\) 0 0
\(79\) −326.144 −0.464482 −0.232241 0.972658i \(-0.574606\pi\)
−0.232241 + 0.972658i \(0.574606\pi\)
\(80\) 1397.03 1.95240
\(81\) 0 0
\(82\) −46.5369 −0.0626724
\(83\) 245.256 0.324342 0.162171 0.986763i \(-0.448150\pi\)
0.162171 + 0.986763i \(0.448150\pi\)
\(84\) 0 0
\(85\) −2008.18 −2.56257
\(86\) −1433.39 −1.79728
\(87\) 0 0
\(88\) −386.228 −0.467864
\(89\) −1457.23 −1.73557 −0.867784 0.496941i \(-0.834456\pi\)
−0.867784 + 0.496941i \(0.834456\pi\)
\(90\) 0 0
\(91\) −359.380 −0.413992
\(92\) −14.9840 −0.0169803
\(93\) 0 0
\(94\) −771.869 −0.846938
\(95\) −879.198 −0.949514
\(96\) 0 0
\(97\) 762.159 0.797789 0.398895 0.916997i \(-0.369394\pi\)
0.398895 + 0.916997i \(0.369394\pi\)
\(98\) 959.508 0.989030
\(99\) 0 0
\(100\) 216.129 0.216129
\(101\) −778.397 −0.766865 −0.383432 0.923569i \(-0.625258\pi\)
−0.383432 + 0.923569i \(0.625258\pi\)
\(102\) 0 0
\(103\) 1026.09 0.981588 0.490794 0.871276i \(-0.336707\pi\)
0.490794 + 0.871276i \(0.336707\pi\)
\(104\) 1757.02 1.65663
\(105\) 0 0
\(106\) 643.839 0.589955
\(107\) −1163.26 −1.05100 −0.525498 0.850795i \(-0.676121\pi\)
−0.525498 + 0.850795i \(0.676121\pi\)
\(108\) 0 0
\(109\) −1661.88 −1.46036 −0.730179 0.683256i \(-0.760563\pi\)
−0.730179 + 0.683256i \(0.760563\pi\)
\(110\) −1073.18 −0.930218
\(111\) 0 0
\(112\) 304.692 0.257060
\(113\) 1348.99 1.12303 0.561514 0.827467i \(-0.310219\pi\)
0.561514 + 0.827467i \(0.310219\pi\)
\(114\) 0 0
\(115\) 386.246 0.313197
\(116\) 36.0515 0.0288560
\(117\) 0 0
\(118\) 522.057 0.407282
\(119\) −437.986 −0.337396
\(120\) 0 0
\(121\) −1005.16 −0.755190
\(122\) −962.148 −0.714006
\(123\) 0 0
\(124\) 239.190 0.173225
\(125\) −3062.97 −2.19168
\(126\) 0 0
\(127\) −146.701 −0.102501 −0.0512504 0.998686i \(-0.516321\pi\)
−0.0512504 + 0.998686i \(0.516321\pi\)
\(128\) −1622.89 −1.12066
\(129\) 0 0
\(130\) 4882.09 3.29375
\(131\) 170.987 0.114040 0.0570199 0.998373i \(-0.481840\pi\)
0.0570199 + 0.998373i \(0.481840\pi\)
\(132\) 0 0
\(133\) −191.753 −0.125016
\(134\) −3189.21 −2.05601
\(135\) 0 0
\(136\) 2141.32 1.35013
\(137\) 2473.93 1.54279 0.771396 0.636356i \(-0.219559\pi\)
0.771396 + 0.636356i \(0.219559\pi\)
\(138\) 0 0
\(139\) 1702.66 1.03898 0.519489 0.854477i \(-0.326122\pi\)
0.519489 + 0.854477i \(0.326122\pi\)
\(140\) 68.3601 0.0412677
\(141\) 0 0
\(142\) 701.056 0.414305
\(143\) −1482.32 −0.866835
\(144\) 0 0
\(145\) −929.309 −0.532240
\(146\) 1019.04 0.577647
\(147\) 0 0
\(148\) −137.615 −0.0764318
\(149\) 2686.59 1.47714 0.738571 0.674176i \(-0.235501\pi\)
0.738571 + 0.674176i \(0.235501\pi\)
\(150\) 0 0
\(151\) −2213.88 −1.19313 −0.596565 0.802565i \(-0.703468\pi\)
−0.596565 + 0.802565i \(0.703468\pi\)
\(152\) 937.488 0.500265
\(153\) 0 0
\(154\) −234.062 −0.122475
\(155\) −6165.65 −3.19508
\(156\) 0 0
\(157\) −382.822 −0.194602 −0.0973011 0.995255i \(-0.531021\pi\)
−0.0973011 + 0.995255i \(0.531021\pi\)
\(158\) 966.314 0.486556
\(159\) 0 0
\(160\) −704.455 −0.348075
\(161\) 84.2405 0.0412365
\(162\) 0 0
\(163\) 2175.67 1.04547 0.522736 0.852495i \(-0.324912\pi\)
0.522736 + 0.852495i \(0.324912\pi\)
\(164\) 12.2268 0.00582166
\(165\) 0 0
\(166\) −726.656 −0.339755
\(167\) 106.542 0.0493680 0.0246840 0.999695i \(-0.492142\pi\)
0.0246840 + 0.999695i \(0.492142\pi\)
\(168\) 0 0
\(169\) 4546.31 2.06933
\(170\) 5949.94 2.68435
\(171\) 0 0
\(172\) 376.599 0.166950
\(173\) 53.6245 0.0235664 0.0117832 0.999931i \(-0.496249\pi\)
0.0117832 + 0.999931i \(0.496249\pi\)
\(174\) 0 0
\(175\) −1215.09 −0.524868
\(176\) 1256.75 0.538243
\(177\) 0 0
\(178\) 4317.53 1.81805
\(179\) 3374.78 1.40918 0.704588 0.709616i \(-0.251132\pi\)
0.704588 + 0.709616i \(0.251132\pi\)
\(180\) 0 0
\(181\) −671.276 −0.275666 −0.137833 0.990455i \(-0.544014\pi\)
−0.137833 + 0.990455i \(0.544014\pi\)
\(182\) 1064.79 0.433666
\(183\) 0 0
\(184\) −411.854 −0.165012
\(185\) 3547.35 1.40976
\(186\) 0 0
\(187\) −1806.54 −0.706455
\(188\) 202.796 0.0786724
\(189\) 0 0
\(190\) 2604.93 0.994638
\(191\) 2129.32 0.806660 0.403330 0.915054i \(-0.367853\pi\)
0.403330 + 0.915054i \(0.367853\pi\)
\(192\) 0 0
\(193\) 70.6759 0.0263594 0.0131797 0.999913i \(-0.495805\pi\)
0.0131797 + 0.999913i \(0.495805\pi\)
\(194\) −2258.16 −0.835703
\(195\) 0 0
\(196\) −252.095 −0.0918713
\(197\) 18.0688 0.00653477 0.00326739 0.999995i \(-0.498960\pi\)
0.00326739 + 0.999995i \(0.498960\pi\)
\(198\) 0 0
\(199\) −1416.52 −0.504596 −0.252298 0.967650i \(-0.581186\pi\)
−0.252298 + 0.967650i \(0.581186\pi\)
\(200\) 5940.58 2.10031
\(201\) 0 0
\(202\) 2306.27 0.803309
\(203\) −202.683 −0.0700765
\(204\) 0 0
\(205\) −315.173 −0.107379
\(206\) −3040.14 −1.02824
\(207\) 0 0
\(208\) −5717.16 −1.90583
\(209\) −790.915 −0.261764
\(210\) 0 0
\(211\) −3589.96 −1.17129 −0.585646 0.810567i \(-0.699159\pi\)
−0.585646 + 0.810567i \(0.699159\pi\)
\(212\) −169.158 −0.0548011
\(213\) 0 0
\(214\) 3446.56 1.10094
\(215\) −9707.70 −3.07935
\(216\) 0 0
\(217\) −1344.73 −0.420674
\(218\) 4923.88 1.52976
\(219\) 0 0
\(220\) 281.961 0.0864082
\(221\) 8218.25 2.50144
\(222\) 0 0
\(223\) 1859.09 0.558269 0.279135 0.960252i \(-0.409952\pi\)
0.279135 + 0.960252i \(0.409952\pi\)
\(224\) −153.642 −0.0458287
\(225\) 0 0
\(226\) −3996.84 −1.17640
\(227\) 722.980 0.211392 0.105696 0.994399i \(-0.466293\pi\)
0.105696 + 0.994399i \(0.466293\pi\)
\(228\) 0 0
\(229\) −5665.68 −1.63493 −0.817465 0.575979i \(-0.804621\pi\)
−0.817465 + 0.575979i \(0.804621\pi\)
\(230\) −1144.39 −0.328081
\(231\) 0 0
\(232\) 990.920 0.280419
\(233\) −860.058 −0.241821 −0.120910 0.992663i \(-0.538581\pi\)
−0.120910 + 0.992663i \(0.538581\pi\)
\(234\) 0 0
\(235\) −5227.52 −1.45109
\(236\) −137.162 −0.0378325
\(237\) 0 0
\(238\) 1297.68 0.353430
\(239\) 239.000 0.0646846
\(240\) 0 0
\(241\) 2307.55 0.616774 0.308387 0.951261i \(-0.400211\pi\)
0.308387 + 0.951261i \(0.400211\pi\)
\(242\) 2978.12 0.791079
\(243\) 0 0
\(244\) 252.789 0.0663243
\(245\) 6498.32 1.69454
\(246\) 0 0
\(247\) 3598.01 0.926866
\(248\) 6574.43 1.68337
\(249\) 0 0
\(250\) 9075.10 2.29584
\(251\) 182.803 0.0459698 0.0229849 0.999736i \(-0.492683\pi\)
0.0229849 + 0.999736i \(0.492683\pi\)
\(252\) 0 0
\(253\) 347.462 0.0863429
\(254\) 434.652 0.107372
\(255\) 0 0
\(256\) 1184.73 0.289240
\(257\) 2322.56 0.563725 0.281862 0.959455i \(-0.409048\pi\)
0.281862 + 0.959455i \(0.409048\pi\)
\(258\) 0 0
\(259\) 773.677 0.185614
\(260\) −1282.69 −0.305958
\(261\) 0 0
\(262\) −506.608 −0.119459
\(263\) 1496.72 0.350920 0.175460 0.984487i \(-0.443859\pi\)
0.175460 + 0.984487i \(0.443859\pi\)
\(264\) 0 0
\(265\) 4360.43 1.01079
\(266\) 568.135 0.130957
\(267\) 0 0
\(268\) 837.912 0.190984
\(269\) −5169.38 −1.17168 −0.585841 0.810426i \(-0.699236\pi\)
−0.585841 + 0.810426i \(0.699236\pi\)
\(270\) 0 0
\(271\) −3146.26 −0.705246 −0.352623 0.935765i \(-0.614710\pi\)
−0.352623 + 0.935765i \(0.614710\pi\)
\(272\) −6967.65 −1.55322
\(273\) 0 0
\(274\) −7329.88 −1.61611
\(275\) −5011.80 −1.09899
\(276\) 0 0
\(277\) −2778.10 −0.602598 −0.301299 0.953530i \(-0.597420\pi\)
−0.301299 + 0.953530i \(0.597420\pi\)
\(278\) −5044.72 −1.08835
\(279\) 0 0
\(280\) 1878.96 0.401034
\(281\) 5089.72 1.08052 0.540262 0.841497i \(-0.318325\pi\)
0.540262 + 0.841497i \(0.318325\pi\)
\(282\) 0 0
\(283\) −3489.81 −0.733030 −0.366515 0.930412i \(-0.619449\pi\)
−0.366515 + 0.930412i \(0.619449\pi\)
\(284\) −184.191 −0.0384850
\(285\) 0 0
\(286\) 4391.87 0.908030
\(287\) −68.7394 −0.0141378
\(288\) 0 0
\(289\) 5102.79 1.03863
\(290\) 2753.40 0.557534
\(291\) 0 0
\(292\) −267.736 −0.0536578
\(293\) 1983.98 0.395581 0.197791 0.980244i \(-0.436623\pi\)
0.197791 + 0.980244i \(0.436623\pi\)
\(294\) 0 0
\(295\) 3535.66 0.697810
\(296\) −3782.53 −0.742753
\(297\) 0 0
\(298\) −7959.94 −1.54734
\(299\) −1580.67 −0.305727
\(300\) 0 0
\(301\) −2117.25 −0.405437
\(302\) 6559.37 1.24983
\(303\) 0 0
\(304\) −3050.49 −0.575518
\(305\) −6516.20 −1.22333
\(306\) 0 0
\(307\) −2999.10 −0.557549 −0.278775 0.960357i \(-0.589928\pi\)
−0.278775 + 0.960357i \(0.589928\pi\)
\(308\) 61.4958 0.0113768
\(309\) 0 0
\(310\) 18267.9 3.34692
\(311\) 1410.71 0.257216 0.128608 0.991696i \(-0.458949\pi\)
0.128608 + 0.991696i \(0.458949\pi\)
\(312\) 0 0
\(313\) −2855.71 −0.515701 −0.257851 0.966185i \(-0.583014\pi\)
−0.257851 + 0.966185i \(0.583014\pi\)
\(314\) 1134.24 0.203850
\(315\) 0 0
\(316\) −253.883 −0.0451963
\(317\) 9851.39 1.74546 0.872728 0.488207i \(-0.162349\pi\)
0.872728 + 0.488207i \(0.162349\pi\)
\(318\) 0 0
\(319\) −835.993 −0.146729
\(320\) −9089.02 −1.58779
\(321\) 0 0
\(322\) −249.591 −0.0431962
\(323\) 4384.99 0.755378
\(324\) 0 0
\(325\) 22799.5 3.89136
\(326\) −6446.17 −1.09516
\(327\) 0 0
\(328\) 336.069 0.0565741
\(329\) −1140.13 −0.191055
\(330\) 0 0
\(331\) 4100.89 0.680983 0.340492 0.940248i \(-0.389406\pi\)
0.340492 + 0.940248i \(0.389406\pi\)
\(332\) 190.917 0.0315600
\(333\) 0 0
\(334\) −315.667 −0.0517141
\(335\) −21599.1 −3.52264
\(336\) 0 0
\(337\) −7998.17 −1.29284 −0.646422 0.762980i \(-0.723735\pi\)
−0.646422 + 0.762980i \(0.723735\pi\)
\(338\) −13470.0 −2.16767
\(339\) 0 0
\(340\) −1563.25 −0.249350
\(341\) −5546.54 −0.880827
\(342\) 0 0
\(343\) 2918.39 0.459412
\(344\) 10351.3 1.62240
\(345\) 0 0
\(346\) −158.881 −0.0246864
\(347\) 6813.64 1.05411 0.527053 0.849832i \(-0.323297\pi\)
0.527053 + 0.849832i \(0.323297\pi\)
\(348\) 0 0
\(349\) 3694.48 0.566650 0.283325 0.959024i \(-0.408563\pi\)
0.283325 + 0.959024i \(0.408563\pi\)
\(350\) 3600.11 0.549811
\(351\) 0 0
\(352\) −633.718 −0.0959582
\(353\) 5908.53 0.890876 0.445438 0.895313i \(-0.353048\pi\)
0.445438 + 0.895313i \(0.353048\pi\)
\(354\) 0 0
\(355\) 4747.94 0.709844
\(356\) −1134.36 −0.168879
\(357\) 0 0
\(358\) −9998.93 −1.47614
\(359\) −11990.3 −1.76275 −0.881374 0.472420i \(-0.843381\pi\)
−0.881374 + 0.472420i \(0.843381\pi\)
\(360\) 0 0
\(361\) −4939.22 −0.720108
\(362\) 1988.89 0.288767
\(363\) 0 0
\(364\) −279.755 −0.0402834
\(365\) 6901.51 0.989702
\(366\) 0 0
\(367\) 8916.27 1.26819 0.634094 0.773256i \(-0.281373\pi\)
0.634094 + 0.773256i \(0.281373\pi\)
\(368\) 1340.13 0.189835
\(369\) 0 0
\(370\) −10510.2 −1.47676
\(371\) 951.012 0.133084
\(372\) 0 0
\(373\) −12215.6 −1.69571 −0.847854 0.530230i \(-0.822105\pi\)
−0.847854 + 0.530230i \(0.822105\pi\)
\(374\) 5352.48 0.740027
\(375\) 0 0
\(376\) 5574.10 0.764527
\(377\) 3803.08 0.519545
\(378\) 0 0
\(379\) −6784.64 −0.919535 −0.459767 0.888039i \(-0.652067\pi\)
−0.459767 + 0.888039i \(0.652067\pi\)
\(380\) −684.401 −0.0923922
\(381\) 0 0
\(382\) −6308.84 −0.844996
\(383\) 217.768 0.0290534 0.0145267 0.999894i \(-0.495376\pi\)
0.0145267 + 0.999894i \(0.495376\pi\)
\(384\) 0 0
\(385\) −1585.19 −0.209841
\(386\) −209.402 −0.0276121
\(387\) 0 0
\(388\) 593.294 0.0776287
\(389\) 5824.23 0.759126 0.379563 0.925166i \(-0.376074\pi\)
0.379563 + 0.925166i \(0.376074\pi\)
\(390\) 0 0
\(391\) −1926.40 −0.249162
\(392\) −6929.15 −0.892793
\(393\) 0 0
\(394\) −53.5351 −0.00684532
\(395\) 6544.41 0.833633
\(396\) 0 0
\(397\) 10235.3 1.29394 0.646970 0.762515i \(-0.276036\pi\)
0.646970 + 0.762515i \(0.276036\pi\)
\(398\) 4196.94 0.528576
\(399\) 0 0
\(400\) −19330.1 −2.41626
\(401\) −9747.43 −1.21387 −0.606937 0.794750i \(-0.707602\pi\)
−0.606937 + 0.794750i \(0.707602\pi\)
\(402\) 0 0
\(403\) 25232.2 3.11887
\(404\) −605.934 −0.0746196
\(405\) 0 0
\(406\) 600.517 0.0734067
\(407\) 3191.14 0.388647
\(408\) 0 0
\(409\) −1582.88 −0.191365 −0.0956824 0.995412i \(-0.530503\pi\)
−0.0956824 + 0.995412i \(0.530503\pi\)
\(410\) 933.809 0.112482
\(411\) 0 0
\(412\) 798.747 0.0955132
\(413\) 771.128 0.0918759
\(414\) 0 0
\(415\) −4921.31 −0.582115
\(416\) 2882.89 0.339773
\(417\) 0 0
\(418\) 2343.36 0.274204
\(419\) −5163.90 −0.602083 −0.301042 0.953611i \(-0.597334\pi\)
−0.301042 + 0.953611i \(0.597334\pi\)
\(420\) 0 0
\(421\) 3768.50 0.436259 0.218130 0.975920i \(-0.430004\pi\)
0.218130 + 0.975920i \(0.430004\pi\)
\(422\) 10636.5 1.22696
\(423\) 0 0
\(424\) −4649.52 −0.532549
\(425\) 27786.4 3.17138
\(426\) 0 0
\(427\) −1421.19 −0.161068
\(428\) −905.526 −0.102267
\(429\) 0 0
\(430\) 28762.4 3.22569
\(431\) 10345.6 1.15622 0.578108 0.815960i \(-0.303791\pi\)
0.578108 + 0.815960i \(0.303791\pi\)
\(432\) 0 0
\(433\) 15595.8 1.73092 0.865460 0.500978i \(-0.167026\pi\)
0.865460 + 0.500978i \(0.167026\pi\)
\(434\) 3984.23 0.440666
\(435\) 0 0
\(436\) −1293.67 −0.142100
\(437\) −843.392 −0.0923224
\(438\) 0 0
\(439\) −16692.3 −1.81476 −0.907379 0.420314i \(-0.861920\pi\)
−0.907379 + 0.420314i \(0.861920\pi\)
\(440\) 7750.05 0.839703
\(441\) 0 0
\(442\) −24349.4 −2.62032
\(443\) −13601.6 −1.45876 −0.729378 0.684110i \(-0.760191\pi\)
−0.729378 + 0.684110i \(0.760191\pi\)
\(444\) 0 0
\(445\) 29240.7 3.11493
\(446\) −5508.20 −0.584800
\(447\) 0 0
\(448\) −1982.32 −0.209053
\(449\) −14742.7 −1.54955 −0.774777 0.632234i \(-0.782138\pi\)
−0.774777 + 0.632234i \(0.782138\pi\)
\(450\) 0 0
\(451\) −283.526 −0.0296024
\(452\) 1050.10 0.109276
\(453\) 0 0
\(454\) −2142.08 −0.221438
\(455\) 7211.32 0.743016
\(456\) 0 0
\(457\) 16803.5 1.71999 0.859993 0.510306i \(-0.170468\pi\)
0.859993 + 0.510306i \(0.170468\pi\)
\(458\) 16786.5 1.71263
\(459\) 0 0
\(460\) 300.669 0.0304756
\(461\) 4075.01 0.411697 0.205848 0.978584i \(-0.434005\pi\)
0.205848 + 0.978584i \(0.434005\pi\)
\(462\) 0 0
\(463\) 18708.0 1.87783 0.938915 0.344150i \(-0.111833\pi\)
0.938915 + 0.344150i \(0.111833\pi\)
\(464\) −3224.35 −0.322601
\(465\) 0 0
\(466\) 2548.22 0.253313
\(467\) 4242.04 0.420339 0.210170 0.977665i \(-0.432598\pi\)
0.210170 + 0.977665i \(0.432598\pi\)
\(468\) 0 0
\(469\) −4710.77 −0.463802
\(470\) 15488.3 1.52005
\(471\) 0 0
\(472\) −3770.07 −0.367651
\(473\) −8732.91 −0.848921
\(474\) 0 0
\(475\) 12165.1 1.17510
\(476\) −340.945 −0.0328302
\(477\) 0 0
\(478\) −708.119 −0.0677586
\(479\) −7179.42 −0.684835 −0.342418 0.939548i \(-0.611246\pi\)
−0.342418 + 0.939548i \(0.611246\pi\)
\(480\) 0 0
\(481\) −14517.1 −1.37614
\(482\) −6836.91 −0.646085
\(483\) 0 0
\(484\) −782.453 −0.0734836
\(485\) −15293.5 −1.43184
\(486\) 0 0
\(487\) 12366.9 1.15071 0.575356 0.817903i \(-0.304863\pi\)
0.575356 + 0.817903i \(0.304863\pi\)
\(488\) 6948.21 0.644530
\(489\) 0 0
\(490\) −19253.5 −1.77507
\(491\) 7374.98 0.677858 0.338929 0.940812i \(-0.389935\pi\)
0.338929 + 0.940812i \(0.389935\pi\)
\(492\) 0 0
\(493\) 4634.91 0.423420
\(494\) −10660.3 −0.970913
\(495\) 0 0
\(496\) −21392.5 −1.93660
\(497\) 1035.53 0.0934603
\(498\) 0 0
\(499\) −20941.4 −1.87869 −0.939343 0.342980i \(-0.888564\pi\)
−0.939343 + 0.342980i \(0.888564\pi\)
\(500\) −2384.33 −0.213261
\(501\) 0 0
\(502\) −541.617 −0.0481545
\(503\) −677.720 −0.0600757 −0.0300378 0.999549i \(-0.509563\pi\)
−0.0300378 + 0.999549i \(0.509563\pi\)
\(504\) 0 0
\(505\) 15619.3 1.37634
\(506\) −1029.48 −0.0904462
\(507\) 0 0
\(508\) −114.198 −0.00997381
\(509\) 10306.5 0.897503 0.448752 0.893657i \(-0.351869\pi\)
0.448752 + 0.893657i \(0.351869\pi\)
\(510\) 0 0
\(511\) 1505.22 0.130307
\(512\) 9472.98 0.817677
\(513\) 0 0
\(514\) −6881.38 −0.590515
\(515\) −20589.5 −1.76171
\(516\) 0 0
\(517\) −4702.61 −0.400040
\(518\) −2292.28 −0.194435
\(519\) 0 0
\(520\) −35256.3 −2.97326
\(521\) 9265.72 0.779153 0.389576 0.920994i \(-0.372621\pi\)
0.389576 + 0.920994i \(0.372621\pi\)
\(522\) 0 0
\(523\) 596.346 0.0498592 0.0249296 0.999689i \(-0.492064\pi\)
0.0249296 + 0.999689i \(0.492064\pi\)
\(524\) 133.103 0.0110966
\(525\) 0 0
\(526\) −4434.55 −0.367596
\(527\) 30751.1 2.54182
\(528\) 0 0
\(529\) −11796.5 −0.969547
\(530\) −12919.3 −1.05883
\(531\) 0 0
\(532\) −149.268 −0.0121647
\(533\) 1289.81 0.104818
\(534\) 0 0
\(535\) 23342.0 1.88628
\(536\) 23031.1 1.85595
\(537\) 0 0
\(538\) 15316.1 1.22736
\(539\) 5845.80 0.467155
\(540\) 0 0
\(541\) 5386.76 0.428087 0.214043 0.976824i \(-0.431337\pi\)
0.214043 + 0.976824i \(0.431337\pi\)
\(542\) 9321.87 0.738761
\(543\) 0 0
\(544\) 3513.46 0.276908
\(545\) 33347.3 2.62099
\(546\) 0 0
\(547\) 8903.74 0.695972 0.347986 0.937500i \(-0.386866\pi\)
0.347986 + 0.937500i \(0.386866\pi\)
\(548\) 1925.80 0.150121
\(549\) 0 0
\(550\) 14849.2 1.15122
\(551\) 2029.20 0.156891
\(552\) 0 0
\(553\) 1427.34 0.109759
\(554\) 8231.06 0.631235
\(555\) 0 0
\(556\) 1325.42 0.101098
\(557\) 18011.3 1.37013 0.685064 0.728483i \(-0.259774\pi\)
0.685064 + 0.728483i \(0.259774\pi\)
\(558\) 0 0
\(559\) 39727.5 3.00590
\(560\) −6113.95 −0.461360
\(561\) 0 0
\(562\) −15080.0 −1.13187
\(563\) −22166.2 −1.65932 −0.829658 0.558272i \(-0.811465\pi\)
−0.829658 + 0.558272i \(0.811465\pi\)
\(564\) 0 0
\(565\) −27068.8 −2.01556
\(566\) 10339.8 0.767866
\(567\) 0 0
\(568\) −5062.72 −0.373991
\(569\) −20278.7 −1.49407 −0.747035 0.664784i \(-0.768523\pi\)
−0.747035 + 0.664784i \(0.768523\pi\)
\(570\) 0 0
\(571\) 9135.32 0.669529 0.334765 0.942302i \(-0.391343\pi\)
0.334765 + 0.942302i \(0.391343\pi\)
\(572\) −1153.89 −0.0843472
\(573\) 0 0
\(574\) 203.664 0.0148097
\(575\) −5344.33 −0.387607
\(576\) 0 0
\(577\) 15593.3 1.12505 0.562527 0.826779i \(-0.309829\pi\)
0.562527 + 0.826779i \(0.309829\pi\)
\(578\) −15118.8 −1.08799
\(579\) 0 0
\(580\) −723.409 −0.0517895
\(581\) −1073.34 −0.0766431
\(582\) 0 0
\(583\) 3922.59 0.278657
\(584\) −7359.07 −0.521439
\(585\) 0 0
\(586\) −5878.22 −0.414380
\(587\) 20628.7 1.45049 0.725246 0.688490i \(-0.241726\pi\)
0.725246 + 0.688490i \(0.241726\pi\)
\(588\) 0 0
\(589\) 13463.1 0.941826
\(590\) −10475.6 −0.730972
\(591\) 0 0
\(592\) 12308.0 0.854483
\(593\) −24665.1 −1.70805 −0.854026 0.520231i \(-0.825846\pi\)
−0.854026 + 0.520231i \(0.825846\pi\)
\(594\) 0 0
\(595\) 8788.63 0.605544
\(596\) 2091.34 0.143733
\(597\) 0 0
\(598\) 4683.26 0.320256
\(599\) −4775.77 −0.325764 −0.162882 0.986646i \(-0.552079\pi\)
−0.162882 + 0.986646i \(0.552079\pi\)
\(600\) 0 0
\(601\) 11733.3 0.796359 0.398180 0.917307i \(-0.369642\pi\)
0.398180 + 0.917307i \(0.369642\pi\)
\(602\) 6273.09 0.424704
\(603\) 0 0
\(604\) −1723.37 −0.116097
\(605\) 20169.5 1.35538
\(606\) 0 0
\(607\) 24208.3 1.61876 0.809378 0.587288i \(-0.199804\pi\)
0.809378 + 0.587288i \(0.199804\pi\)
\(608\) 1538.22 0.102604
\(609\) 0 0
\(610\) 19306.5 1.28147
\(611\) 21393.0 1.41648
\(612\) 0 0
\(613\) −3338.26 −0.219953 −0.109976 0.993934i \(-0.535078\pi\)
−0.109976 + 0.993934i \(0.535078\pi\)
\(614\) 8885.86 0.584046
\(615\) 0 0
\(616\) 1690.29 0.110558
\(617\) 19730.0 1.28736 0.643679 0.765295i \(-0.277407\pi\)
0.643679 + 0.765295i \(0.277407\pi\)
\(618\) 0 0
\(619\) −12280.2 −0.797385 −0.398692 0.917085i \(-0.630536\pi\)
−0.398692 + 0.917085i \(0.630536\pi\)
\(620\) −4799.58 −0.310896
\(621\) 0 0
\(622\) −4179.72 −0.269439
\(623\) 6377.41 0.410121
\(624\) 0 0
\(625\) 26756.0 1.71238
\(626\) 8461.03 0.540209
\(627\) 0 0
\(628\) −298.003 −0.0189357
\(629\) −17692.3 −1.12153
\(630\) 0 0
\(631\) 797.287 0.0503003 0.0251502 0.999684i \(-0.491994\pi\)
0.0251502 + 0.999684i \(0.491994\pi\)
\(632\) −6978.29 −0.439211
\(633\) 0 0
\(634\) −29188.1 −1.82841
\(635\) 2943.70 0.183964
\(636\) 0 0
\(637\) −26593.6 −1.65412
\(638\) 2476.92 0.153702
\(639\) 0 0
\(640\) 32565.0 2.01132
\(641\) −23898.3 −1.47258 −0.736292 0.676664i \(-0.763425\pi\)
−0.736292 + 0.676664i \(0.763425\pi\)
\(642\) 0 0
\(643\) −17199.9 −1.05490 −0.527449 0.849587i \(-0.676851\pi\)
−0.527449 + 0.849587i \(0.676851\pi\)
\(644\) 65.5760 0.00401251
\(645\) 0 0
\(646\) −12992.0 −0.791276
\(647\) 22371.5 1.35937 0.679686 0.733503i \(-0.262116\pi\)
0.679686 + 0.733503i \(0.262116\pi\)
\(648\) 0 0
\(649\) 3180.63 0.192374
\(650\) −67551.4 −4.07628
\(651\) 0 0
\(652\) 1693.63 0.101729
\(653\) −2778.94 −0.166536 −0.0832682 0.996527i \(-0.526536\pi\)
−0.0832682 + 0.996527i \(0.526536\pi\)
\(654\) 0 0
\(655\) −3431.03 −0.204674
\(656\) −1093.53 −0.0650843
\(657\) 0 0
\(658\) 3378.01 0.200135
\(659\) 26408.2 1.56103 0.780514 0.625138i \(-0.214957\pi\)
0.780514 + 0.625138i \(0.214957\pi\)
\(660\) 0 0
\(661\) 2574.95 0.151519 0.0757595 0.997126i \(-0.475862\pi\)
0.0757595 + 0.997126i \(0.475862\pi\)
\(662\) −12150.3 −0.713346
\(663\) 0 0
\(664\) 5247.59 0.306696
\(665\) 3847.73 0.224374
\(666\) 0 0
\(667\) −891.461 −0.0517504
\(668\) 82.9362 0.00480374
\(669\) 0 0
\(670\) 63994.7 3.69004
\(671\) −5861.88 −0.337251
\(672\) 0 0
\(673\) 25686.4 1.47123 0.735614 0.677401i \(-0.236894\pi\)
0.735614 + 0.677401i \(0.236894\pi\)
\(674\) 23697.3 1.35428
\(675\) 0 0
\(676\) 3539.02 0.201355
\(677\) 9283.47 0.527020 0.263510 0.964657i \(-0.415120\pi\)
0.263510 + 0.964657i \(0.415120\pi\)
\(678\) 0 0
\(679\) −3335.52 −0.188521
\(680\) −42967.8 −2.42315
\(681\) 0 0
\(682\) 16433.5 0.922686
\(683\) −1759.49 −0.0985722 −0.0492861 0.998785i \(-0.515695\pi\)
−0.0492861 + 0.998785i \(0.515695\pi\)
\(684\) 0 0
\(685\) −49642.0 −2.76894
\(686\) −8646.74 −0.481245
\(687\) 0 0
\(688\) −33682.1 −1.86645
\(689\) −17844.5 −0.986680
\(690\) 0 0
\(691\) 5318.04 0.292775 0.146388 0.989227i \(-0.453235\pi\)
0.146388 + 0.989227i \(0.453235\pi\)
\(692\) 41.7433 0.00229313
\(693\) 0 0
\(694\) −20187.7 −1.10420
\(695\) −34165.7 −1.86472
\(696\) 0 0
\(697\) 1571.92 0.0854244
\(698\) −10946.2 −0.593579
\(699\) 0 0
\(700\) −945.869 −0.0510721
\(701\) −1243.51 −0.0669994 −0.0334997 0.999439i \(-0.510665\pi\)
−0.0334997 + 0.999439i \(0.510665\pi\)
\(702\) 0 0
\(703\) −7745.83 −0.415561
\(704\) −8176.36 −0.437725
\(705\) 0 0
\(706\) −17506.0 −0.933214
\(707\) 3406.58 0.181213
\(708\) 0 0
\(709\) 25289.1 1.33957 0.669783 0.742557i \(-0.266387\pi\)
0.669783 + 0.742557i \(0.266387\pi\)
\(710\) −14067.4 −0.743578
\(711\) 0 0
\(712\) −31179.3 −1.64114
\(713\) −5914.55 −0.310661
\(714\) 0 0
\(715\) 29744.1 1.55576
\(716\) 2627.05 0.137120
\(717\) 0 0
\(718\) 35525.5 1.84652
\(719\) −23122.3 −1.19932 −0.599662 0.800253i \(-0.704698\pi\)
−0.599662 + 0.800253i \(0.704698\pi\)
\(720\) 0 0
\(721\) −4490.58 −0.231953
\(722\) 14634.1 0.754330
\(723\) 0 0
\(724\) −522.547 −0.0268236
\(725\) 12858.4 0.658690
\(726\) 0 0
\(727\) −24532.7 −1.25154 −0.625769 0.780009i \(-0.715215\pi\)
−0.625769 + 0.780009i \(0.715215\pi\)
\(728\) −7689.42 −0.391468
\(729\) 0 0
\(730\) −20448.1 −1.03674
\(731\) 48417.0 2.44975
\(732\) 0 0
\(733\) −22966.4 −1.15728 −0.578638 0.815585i \(-0.696416\pi\)
−0.578638 + 0.815585i \(0.696416\pi\)
\(734\) −26417.5 −1.32846
\(735\) 0 0
\(736\) −675.765 −0.0338438
\(737\) −19430.2 −0.971129
\(738\) 0 0
\(739\) −27171.0 −1.35250 −0.676252 0.736671i \(-0.736397\pi\)
−0.676252 + 0.736671i \(0.736397\pi\)
\(740\) 2761.39 0.137177
\(741\) 0 0
\(742\) −2817.70 −0.139408
\(743\) −13694.7 −0.676192 −0.338096 0.941112i \(-0.609783\pi\)
−0.338096 + 0.941112i \(0.609783\pi\)
\(744\) 0 0
\(745\) −53909.1 −2.65111
\(746\) 36192.8 1.77629
\(747\) 0 0
\(748\) −1406.28 −0.0687414
\(749\) 5090.90 0.248354
\(750\) 0 0
\(751\) 1219.25 0.0592424 0.0296212 0.999561i \(-0.490570\pi\)
0.0296212 + 0.999561i \(0.490570\pi\)
\(752\) −18137.6 −0.879532
\(753\) 0 0
\(754\) −11267.9 −0.544236
\(755\) 44423.7 2.14138
\(756\) 0 0
\(757\) 1138.49 0.0546620 0.0273310 0.999626i \(-0.491299\pi\)
0.0273310 + 0.999626i \(0.491299\pi\)
\(758\) 20101.8 0.963234
\(759\) 0 0
\(760\) −18811.6 −0.897855
\(761\) 16423.4 0.782325 0.391162 0.920322i \(-0.372073\pi\)
0.391162 + 0.920322i \(0.372073\pi\)
\(762\) 0 0
\(763\) 7273.05 0.345088
\(764\) 1657.54 0.0784919
\(765\) 0 0
\(766\) −645.214 −0.0304341
\(767\) −14469.2 −0.681166
\(768\) 0 0
\(769\) −23857.4 −1.11875 −0.559376 0.828914i \(-0.688959\pi\)
−0.559376 + 0.828914i \(0.688959\pi\)
\(770\) 4696.68 0.219814
\(771\) 0 0
\(772\) 55.0168 0.00256489
\(773\) −5404.60 −0.251475 −0.125737 0.992064i \(-0.540130\pi\)
−0.125737 + 0.992064i \(0.540130\pi\)
\(774\) 0 0
\(775\) 85311.5 3.95417
\(776\) 16307.4 0.754385
\(777\) 0 0
\(778\) −17256.3 −0.795202
\(779\) 688.199 0.0316525
\(780\) 0 0
\(781\) 4271.18 0.195691
\(782\) 5707.62 0.261003
\(783\) 0 0
\(784\) 22546.7 1.02709
\(785\) 7681.71 0.349264
\(786\) 0 0
\(787\) 31446.3 1.42432 0.712161 0.702017i \(-0.247717\pi\)
0.712161 + 0.702017i \(0.247717\pi\)
\(788\) 14.0655 0.000635864 0
\(789\) 0 0
\(790\) −19390.1 −0.873250
\(791\) −5903.72 −0.265376
\(792\) 0 0
\(793\) 26666.7 1.19415
\(794\) −30325.5 −1.35543
\(795\) 0 0
\(796\) −1102.68 −0.0490996
\(797\) −36126.4 −1.60560 −0.802801 0.596248i \(-0.796658\pi\)
−0.802801 + 0.596248i \(0.796658\pi\)
\(798\) 0 0
\(799\) 26072.2 1.15440
\(800\) 9747.23 0.430771
\(801\) 0 0
\(802\) 28880.1 1.27156
\(803\) 6208.50 0.272843
\(804\) 0 0
\(805\) −1690.37 −0.0740096
\(806\) −74759.0 −3.26709
\(807\) 0 0
\(808\) −16654.8 −0.725143
\(809\) 39760.7 1.72795 0.863976 0.503533i \(-0.167967\pi\)
0.863976 + 0.503533i \(0.167967\pi\)
\(810\) 0 0
\(811\) −24265.4 −1.05065 −0.525323 0.850903i \(-0.676056\pi\)
−0.525323 + 0.850903i \(0.676056\pi\)
\(812\) −157.776 −0.00681878
\(813\) 0 0
\(814\) −9454.86 −0.407116
\(815\) −43657.1 −1.87637
\(816\) 0 0
\(817\) 21197.3 0.907711
\(818\) 4689.81 0.200459
\(819\) 0 0
\(820\) −245.343 −0.0104485
\(821\) −30503.1 −1.29667 −0.648334 0.761356i \(-0.724534\pi\)
−0.648334 + 0.761356i \(0.724534\pi\)
\(822\) 0 0
\(823\) −39552.4 −1.67523 −0.837613 0.546264i \(-0.816049\pi\)
−0.837613 + 0.546264i \(0.816049\pi\)
\(824\) 21954.6 0.928184
\(825\) 0 0
\(826\) −2284.73 −0.0962421
\(827\) −25903.8 −1.08920 −0.544598 0.838698i \(-0.683318\pi\)
−0.544598 + 0.838698i \(0.683318\pi\)
\(828\) 0 0
\(829\) 30363.1 1.27208 0.636039 0.771657i \(-0.280572\pi\)
0.636039 + 0.771657i \(0.280572\pi\)
\(830\) 14581.1 0.609779
\(831\) 0 0
\(832\) 37195.7 1.54991
\(833\) −32410.3 −1.34808
\(834\) 0 0
\(835\) −2137.87 −0.0886036
\(836\) −615.678 −0.0254709
\(837\) 0 0
\(838\) 15299.8 0.630696
\(839\) −43564.3 −1.79262 −0.896310 0.443428i \(-0.853762\pi\)
−0.896310 + 0.443428i \(0.853762\pi\)
\(840\) 0 0
\(841\) −22244.1 −0.912056
\(842\) −11165.5 −0.456992
\(843\) 0 0
\(844\) −2794.56 −0.113972
\(845\) −91226.3 −3.71394
\(846\) 0 0
\(847\) 4398.98 0.178454
\(848\) 15129.1 0.612659
\(849\) 0 0
\(850\) −82326.7 −3.32210
\(851\) 3402.88 0.137073
\(852\) 0 0
\(853\) −12912.3 −0.518299 −0.259149 0.965837i \(-0.583442\pi\)
−0.259149 + 0.965837i \(0.583442\pi\)
\(854\) 4210.75 0.168722
\(855\) 0 0
\(856\) −24889.5 −0.993816
\(857\) −11738.7 −0.467897 −0.233948 0.972249i \(-0.575165\pi\)
−0.233948 + 0.972249i \(0.575165\pi\)
\(858\) 0 0
\(859\) −41876.5 −1.66334 −0.831670 0.555271i \(-0.812615\pi\)
−0.831670 + 0.555271i \(0.812615\pi\)
\(860\) −7556.84 −0.299635
\(861\) 0 0
\(862\) −30652.3 −1.21116
\(863\) 17201.8 0.678514 0.339257 0.940694i \(-0.389824\pi\)
0.339257 + 0.940694i \(0.389824\pi\)
\(864\) 0 0
\(865\) −1076.03 −0.0422961
\(866\) −46208.0 −1.81318
\(867\) 0 0
\(868\) −1046.79 −0.0409336
\(869\) 5887.26 0.229818
\(870\) 0 0
\(871\) 88391.5 3.43861
\(872\) −35558.1 −1.38091
\(873\) 0 0
\(874\) 2498.84 0.0967099
\(875\) 13404.8 0.517903
\(876\) 0 0
\(877\) −33863.8 −1.30388 −0.651938 0.758272i \(-0.726044\pi\)
−0.651938 + 0.758272i \(0.726044\pi\)
\(878\) 49456.6 1.90100
\(879\) 0 0
\(880\) −25217.9 −0.966017
\(881\) 28690.0 1.09715 0.548575 0.836101i \(-0.315170\pi\)
0.548575 + 0.836101i \(0.315170\pi\)
\(882\) 0 0
\(883\) −40094.8 −1.52808 −0.764042 0.645166i \(-0.776788\pi\)
−0.764042 + 0.645166i \(0.776788\pi\)
\(884\) 6397.40 0.243402
\(885\) 0 0
\(886\) 40299.3 1.52808
\(887\) −22456.6 −0.850079 −0.425039 0.905175i \(-0.639740\pi\)
−0.425039 + 0.905175i \(0.639740\pi\)
\(888\) 0 0
\(889\) 642.022 0.0242213
\(890\) −86635.6 −3.26296
\(891\) 0 0
\(892\) 1447.19 0.0543223
\(893\) 11414.6 0.427744
\(894\) 0 0
\(895\) −67718.3 −2.52913
\(896\) 7102.44 0.264817
\(897\) 0 0
\(898\) 43680.2 1.62319
\(899\) 14230.4 0.527931
\(900\) 0 0
\(901\) −21747.6 −0.804126
\(902\) 840.042 0.0310092
\(903\) 0 0
\(904\) 28863.4 1.06193
\(905\) 13469.8 0.494754
\(906\) 0 0
\(907\) 7459.02 0.273068 0.136534 0.990635i \(-0.456404\pi\)
0.136534 + 0.990635i \(0.456404\pi\)
\(908\) 562.795 0.0205694
\(909\) 0 0
\(910\) −21366.0 −0.778326
\(911\) 48552.9 1.76578 0.882892 0.469576i \(-0.155593\pi\)
0.882892 + 0.469576i \(0.155593\pi\)
\(912\) 0 0
\(913\) −4427.15 −0.160479
\(914\) −49786.1 −1.80172
\(915\) 0 0
\(916\) −4410.38 −0.159086
\(917\) −748.309 −0.0269480
\(918\) 0 0
\(919\) 22652.3 0.813090 0.406545 0.913631i \(-0.366733\pi\)
0.406545 + 0.913631i \(0.366733\pi\)
\(920\) 8264.27 0.296157
\(921\) 0 0
\(922\) −12073.6 −0.431262
\(923\) −19430.4 −0.692912
\(924\) 0 0
\(925\) −49083.1 −1.74469
\(926\) −55428.9 −1.96707
\(927\) 0 0
\(928\) 1625.89 0.0575134
\(929\) −11545.0 −0.407727 −0.203864 0.978999i \(-0.565350\pi\)
−0.203864 + 0.978999i \(0.565350\pi\)
\(930\) 0 0
\(931\) −14189.5 −0.499507
\(932\) −669.502 −0.0235303
\(933\) 0 0
\(934\) −12568.5 −0.440315
\(935\) 36250.0 1.26792
\(936\) 0 0
\(937\) −43731.1 −1.52469 −0.762344 0.647172i \(-0.775952\pi\)
−0.762344 + 0.647172i \(0.775952\pi\)
\(938\) 13957.3 0.485843
\(939\) 0 0
\(940\) −4069.30 −0.141198
\(941\) 29756.4 1.03085 0.515426 0.856934i \(-0.327634\pi\)
0.515426 + 0.856934i \(0.327634\pi\)
\(942\) 0 0
\(943\) −302.338 −0.0104406
\(944\) 12267.4 0.422956
\(945\) 0 0
\(946\) 25874.2 0.889265
\(947\) 14137.3 0.485112 0.242556 0.970137i \(-0.422014\pi\)
0.242556 + 0.970137i \(0.422014\pi\)
\(948\) 0 0
\(949\) −28243.6 −0.966096
\(950\) −36043.2 −1.23094
\(951\) 0 0
\(952\) −9371.30 −0.319039
\(953\) 32201.4 1.09455 0.547274 0.836953i \(-0.315665\pi\)
0.547274 + 0.836953i \(0.315665\pi\)
\(954\) 0 0
\(955\) −42726.9 −1.44776
\(956\) 186.047 0.00629412
\(957\) 0 0
\(958\) 21271.5 0.717381
\(959\) −10826.9 −0.364567
\(960\) 0 0
\(961\) 64622.9 2.16921
\(962\) 43011.8 1.44153
\(963\) 0 0
\(964\) 1796.29 0.0600150
\(965\) −1418.18 −0.0473087
\(966\) 0 0
\(967\) 4397.57 0.146242 0.0731211 0.997323i \(-0.476704\pi\)
0.0731211 + 0.997323i \(0.476704\pi\)
\(968\) −21506.7 −0.714103
\(969\) 0 0
\(970\) 45312.2 1.49988
\(971\) 4180.99 0.138182 0.0690908 0.997610i \(-0.477990\pi\)
0.0690908 + 0.997610i \(0.477990\pi\)
\(972\) 0 0
\(973\) −7451.54 −0.245514
\(974\) −36641.1 −1.20540
\(975\) 0 0
\(976\) −22608.8 −0.741485
\(977\) 47905.2 1.56870 0.784351 0.620317i \(-0.212996\pi\)
0.784351 + 0.620317i \(0.212996\pi\)
\(978\) 0 0
\(979\) 26304.5 0.858730
\(980\) 5058.54 0.164887
\(981\) 0 0
\(982\) −21850.9 −0.710072
\(983\) 38331.6 1.24373 0.621866 0.783124i \(-0.286375\pi\)
0.621866 + 0.783124i \(0.286375\pi\)
\(984\) 0 0
\(985\) −362.569 −0.0117283
\(986\) −13732.5 −0.443542
\(987\) 0 0
\(988\) 2800.83 0.0901885
\(989\) −9312.34 −0.299409
\(990\) 0 0
\(991\) −44623.8 −1.43039 −0.715197 0.698923i \(-0.753663\pi\)
−0.715197 + 0.698923i \(0.753663\pi\)
\(992\) 10787.2 0.345257
\(993\) 0 0
\(994\) −3068.11 −0.0979018
\(995\) 28424.0 0.905628
\(996\) 0 0
\(997\) −54629.3 −1.73533 −0.867667 0.497146i \(-0.834381\pi\)
−0.867667 + 0.497146i \(0.834381\pi\)
\(998\) 62046.0 1.96797
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (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 2151.4.a.e.1.10 32
3.2 odd 2 717.4.a.c.1.23 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
717.4.a.c.1.23 32 3.2 odd 2
2151.4.a.e.1.10 32 1.1 even 1 trivial