Properties

Label 2166.4.a.t.1.2
Level $2166$
Weight $4$
Character 2166.1
Self dual yes
Analytic conductor $127.798$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2166 = 2 \cdot 3 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2166.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(127.798137072\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.14457.1
Defining polynomial: \(x^{3} - x^{2} - 32 x - 3\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{3}\cdot 3 \)
Twist minimal: no (minimal twist has level 114)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-0.0940524\) of defining polynomial
Character \(\chi\) \(=\) 2166.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +4.18810 q^{5} -6.00000 q^{6} +3.18810 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +4.18810 q^{5} -6.00000 q^{6} +3.18810 q^{7} -8.00000 q^{8} +9.00000 q^{9} -8.37621 q^{10} +69.4003 q^{11} +12.0000 q^{12} +8.12863 q^{13} -6.37621 q^{14} +12.5643 q^{15} +16.0000 q^{16} -106.084 q^{17} -18.0000 q^{18} +16.7524 q^{20} +9.56431 q^{21} -138.801 q^{22} -176.494 q^{23} -24.0000 q^{24} -107.460 q^{25} -16.2573 q^{26} +27.0000 q^{27} +12.7524 q^{28} +66.2219 q^{29} -25.1286 q^{30} +140.915 q^{31} -32.0000 q^{32} +208.201 q^{33} +212.167 q^{34} +13.3521 q^{35} +36.0000 q^{36} +156.003 q^{37} +24.3859 q^{39} -33.5048 q^{40} +414.563 q^{41} -19.1286 q^{42} +115.850 q^{43} +277.601 q^{44} +37.6929 q^{45} +352.987 q^{46} +620.283 q^{47} +48.0000 q^{48} -332.836 q^{49} +214.920 q^{50} -318.251 q^{51} +32.5145 q^{52} +371.986 q^{53} -54.0000 q^{54} +290.656 q^{55} -25.5048 q^{56} -132.444 q^{58} -91.6929 q^{59} +50.2573 q^{60} +218.621 q^{61} -281.830 q^{62} +28.6929 q^{63} +64.0000 q^{64} +34.0436 q^{65} -416.402 q^{66} +145.342 q^{67} -424.334 q^{68} -529.481 q^{69} -26.7042 q^{70} -887.829 q^{71} -72.0000 q^{72} +199.016 q^{73} -312.006 q^{74} -322.379 q^{75} +221.255 q^{77} -48.7718 q^{78} +389.558 q^{79} +67.0097 q^{80} +81.0000 q^{81} -829.125 q^{82} +380.039 q^{83} +38.2573 q^{84} -444.289 q^{85} -231.701 q^{86} +198.666 q^{87} -555.202 q^{88} +425.799 q^{89} -75.3859 q^{90} +25.9149 q^{91} -705.974 q^{92} +422.744 q^{93} -1240.57 q^{94} -96.0000 q^{96} -419.846 q^{97} +665.672 q^{98} +624.603 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - 6 q^{2} + 9 q^{3} + 12 q^{4} + 10 q^{5} - 18 q^{6} + 7 q^{7} - 24 q^{8} + 27 q^{9} + O(q^{10}) \) \( 3 q - 6 q^{2} + 9 q^{3} + 12 q^{4} + 10 q^{5} - 18 q^{6} + 7 q^{7} - 24 q^{8} + 27 q^{9} - 20 q^{10} - 44 q^{11} + 36 q^{12} + 9 q^{13} - 14 q^{14} + 30 q^{15} + 48 q^{16} - 84 q^{17} - 54 q^{18} + 40 q^{20} + 21 q^{21} + 88 q^{22} - 2 q^{23} - 72 q^{24} - 83 q^{25} - 18 q^{26} + 81 q^{27} + 28 q^{28} - 92 q^{29} - 60 q^{30} + 109 q^{31} - 96 q^{32} - 132 q^{33} + 168 q^{34} + 282 q^{35} + 108 q^{36} - 245 q^{37} + 27 q^{39} - 80 q^{40} + 688 q^{41} - 42 q^{42} - 103 q^{43} - 176 q^{44} + 90 q^{45} + 4 q^{46} + 322 q^{47} + 144 q^{48} - 754 q^{49} + 166 q^{50} - 252 q^{51} + 36 q^{52} + 1322 q^{53} - 162 q^{54} - 248 q^{55} - 56 q^{56} + 184 q^{58} - 252 q^{59} + 120 q^{60} - 435 q^{61} - 218 q^{62} + 63 q^{63} + 192 q^{64} + 1582 q^{65} + 264 q^{66} + 719 q^{67} - 336 q^{68} - 6 q^{69} - 564 q^{70} + 62 q^{71} - 216 q^{72} - 581 q^{73} + 490 q^{74} - 249 q^{75} - 204 q^{77} - 54 q^{78} + 489 q^{79} + 160 q^{80} + 243 q^{81} - 1376 q^{82} + 2496 q^{83} + 84 q^{84} + 1632 q^{85} + 206 q^{86} - 276 q^{87} + 352 q^{88} - 1584 q^{89} - 180 q^{90} + 1573 q^{91} - 8 q^{92} + 327 q^{93} - 644 q^{94} - 288 q^{96} - 974 q^{97} + 1508 q^{98} - 396 q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.00000 −0.707107
\(3\) 3.00000 0.577350
\(4\) 4.00000 0.500000
\(5\) 4.18810 0.374595 0.187298 0.982303i \(-0.440027\pi\)
0.187298 + 0.982303i \(0.440027\pi\)
\(6\) −6.00000 −0.408248
\(7\) 3.18810 0.172141 0.0860707 0.996289i \(-0.472569\pi\)
0.0860707 + 0.996289i \(0.472569\pi\)
\(8\) −8.00000 −0.353553
\(9\) 9.00000 0.333333
\(10\) −8.37621 −0.264879
\(11\) 69.4003 1.90227 0.951135 0.308774i \(-0.0999187\pi\)
0.951135 + 0.308774i \(0.0999187\pi\)
\(12\) 12.0000 0.288675
\(13\) 8.12863 0.173421 0.0867106 0.996234i \(-0.472364\pi\)
0.0867106 + 0.996234i \(0.472364\pi\)
\(14\) −6.37621 −0.121722
\(15\) 12.5643 0.216273
\(16\) 16.0000 0.250000
\(17\) −106.084 −1.51347 −0.756737 0.653720i \(-0.773207\pi\)
−0.756737 + 0.653720i \(0.773207\pi\)
\(18\) −18.0000 −0.235702
\(19\) 0 0
\(20\) 16.7524 0.187298
\(21\) 9.56431 0.0993859
\(22\) −138.801 −1.34511
\(23\) −176.494 −1.60006 −0.800031 0.599958i \(-0.795184\pi\)
−0.800031 + 0.599958i \(0.795184\pi\)
\(24\) −24.0000 −0.204124
\(25\) −107.460 −0.859678
\(26\) −16.2573 −0.122627
\(27\) 27.0000 0.192450
\(28\) 12.7524 0.0860707
\(29\) 66.2219 0.424038 0.212019 0.977266i \(-0.431996\pi\)
0.212019 + 0.977266i \(0.431996\pi\)
\(30\) −25.1286 −0.152928
\(31\) 140.915 0.816421 0.408210 0.912888i \(-0.366153\pi\)
0.408210 + 0.912888i \(0.366153\pi\)
\(32\) −32.0000 −0.176777
\(33\) 208.201 1.09828
\(34\) 212.167 1.07019
\(35\) 13.3521 0.0644834
\(36\) 36.0000 0.166667
\(37\) 156.003 0.693156 0.346578 0.938021i \(-0.387344\pi\)
0.346578 + 0.938021i \(0.387344\pi\)
\(38\) 0 0
\(39\) 24.3859 0.100125
\(40\) −33.5048 −0.132440
\(41\) 414.563 1.57912 0.789559 0.613675i \(-0.210309\pi\)
0.789559 + 0.613675i \(0.210309\pi\)
\(42\) −19.1286 −0.0702765
\(43\) 115.850 0.410861 0.205430 0.978672i \(-0.434141\pi\)
0.205430 + 0.978672i \(0.434141\pi\)
\(44\) 277.601 0.951135
\(45\) 37.6929 0.124865
\(46\) 352.987 1.13142
\(47\) 620.283 1.92505 0.962527 0.271185i \(-0.0874156\pi\)
0.962527 + 0.271185i \(0.0874156\pi\)
\(48\) 48.0000 0.144338
\(49\) −332.836 −0.970367
\(50\) 214.920 0.607884
\(51\) −318.251 −0.873804
\(52\) 32.5145 0.0867106
\(53\) 371.986 0.964078 0.482039 0.876150i \(-0.339896\pi\)
0.482039 + 0.876150i \(0.339896\pi\)
\(54\) −54.0000 −0.136083
\(55\) 290.656 0.712582
\(56\) −25.5048 −0.0608612
\(57\) 0 0
\(58\) −132.444 −0.299840
\(59\) −91.6929 −0.202329 −0.101164 0.994870i \(-0.532257\pi\)
−0.101164 + 0.994870i \(0.532257\pi\)
\(60\) 50.2573 0.108136
\(61\) 218.621 0.458877 0.229438 0.973323i \(-0.426311\pi\)
0.229438 + 0.973323i \(0.426311\pi\)
\(62\) −281.830 −0.577297
\(63\) 28.6929 0.0573805
\(64\) 64.0000 0.125000
\(65\) 34.0436 0.0649628
\(66\) −416.402 −0.776599
\(67\) 145.342 0.265021 0.132510 0.991182i \(-0.457696\pi\)
0.132510 + 0.991182i \(0.457696\pi\)
\(68\) −424.334 −0.756737
\(69\) −529.481 −0.923797
\(70\) −26.7042 −0.0455967
\(71\) −887.829 −1.48403 −0.742014 0.670385i \(-0.766129\pi\)
−0.742014 + 0.670385i \(0.766129\pi\)
\(72\) −72.0000 −0.117851
\(73\) 199.016 0.319083 0.159542 0.987191i \(-0.448998\pi\)
0.159542 + 0.987191i \(0.448998\pi\)
\(74\) −312.006 −0.490135
\(75\) −322.379 −0.496335
\(76\) 0 0
\(77\) 221.255 0.327460
\(78\) −48.7718 −0.0707989
\(79\) 389.558 0.554793 0.277397 0.960755i \(-0.410528\pi\)
0.277397 + 0.960755i \(0.410528\pi\)
\(80\) 67.0097 0.0936489
\(81\) 81.0000 0.111111
\(82\) −829.125 −1.11660
\(83\) 380.039 0.502586 0.251293 0.967911i \(-0.419144\pi\)
0.251293 + 0.967911i \(0.419144\pi\)
\(84\) 38.2573 0.0496930
\(85\) −444.289 −0.566940
\(86\) −231.701 −0.290523
\(87\) 198.666 0.244818
\(88\) −555.202 −0.672554
\(89\) 425.799 0.507130 0.253565 0.967318i \(-0.418397\pi\)
0.253565 + 0.967318i \(0.418397\pi\)
\(90\) −75.3859 −0.0882930
\(91\) 25.9149 0.0298530
\(92\) −705.974 −0.800031
\(93\) 422.744 0.471361
\(94\) −1240.57 −1.36122
\(95\) 0 0
\(96\) −96.0000 −0.102062
\(97\) −419.846 −0.439473 −0.219736 0.975559i \(-0.570520\pi\)
−0.219736 + 0.975559i \(0.570520\pi\)
\(98\) 665.672 0.686153
\(99\) 624.603 0.634090
\(100\) −429.839 −0.429839
\(101\) −1241.71 −1.22331 −0.611657 0.791123i \(-0.709497\pi\)
−0.611657 + 0.791123i \(0.709497\pi\)
\(102\) 636.501 0.617873
\(103\) 593.606 0.567862 0.283931 0.958845i \(-0.408361\pi\)
0.283931 + 0.958845i \(0.408361\pi\)
\(104\) −65.0290 −0.0613137
\(105\) 40.0564 0.0372295
\(106\) −743.971 −0.681706
\(107\) 1778.56 1.60691 0.803457 0.595363i \(-0.202992\pi\)
0.803457 + 0.595363i \(0.202992\pi\)
\(108\) 108.000 0.0962250
\(109\) 1069.99 0.940243 0.470121 0.882602i \(-0.344210\pi\)
0.470121 + 0.882602i \(0.344210\pi\)
\(110\) −581.311 −0.503872
\(111\) 468.009 0.400194
\(112\) 51.0097 0.0430354
\(113\) −583.197 −0.485510 −0.242755 0.970088i \(-0.578051\pi\)
−0.242755 + 0.970088i \(0.578051\pi\)
\(114\) 0 0
\(115\) −739.173 −0.599376
\(116\) 264.887 0.212019
\(117\) 73.1577 0.0578071
\(118\) 183.386 0.143068
\(119\) −338.206 −0.260532
\(120\) −100.515 −0.0764640
\(121\) 3485.40 2.61863
\(122\) −437.241 −0.324475
\(123\) 1243.69 0.911704
\(124\) 563.659 0.408210
\(125\) −973.566 −0.696627
\(126\) −57.3859 −0.0405741
\(127\) −1659.35 −1.15940 −0.579700 0.814830i \(-0.696830\pi\)
−0.579700 + 0.814830i \(0.696830\pi\)
\(128\) −128.000 −0.0883883
\(129\) 347.551 0.237211
\(130\) −68.0871 −0.0459356
\(131\) 597.546 0.398533 0.199267 0.979945i \(-0.436144\pi\)
0.199267 + 0.979945i \(0.436144\pi\)
\(132\) 832.804 0.549138
\(133\) 0 0
\(134\) −290.685 −0.187398
\(135\) 113.079 0.0720909
\(136\) 848.669 0.535094
\(137\) −1777.31 −1.10836 −0.554182 0.832396i \(-0.686969\pi\)
−0.554182 + 0.832396i \(0.686969\pi\)
\(138\) 1058.96 0.653223
\(139\) 163.567 0.0998099 0.0499050 0.998754i \(-0.484108\pi\)
0.0499050 + 0.998754i \(0.484108\pi\)
\(140\) 53.4085 0.0322417
\(141\) 1860.85 1.11143
\(142\) 1775.66 1.04937
\(143\) 564.129 0.329894
\(144\) 144.000 0.0833333
\(145\) 277.344 0.158843
\(146\) −398.032 −0.225626
\(147\) −998.508 −0.560242
\(148\) 624.012 0.346578
\(149\) −1119.80 −0.615688 −0.307844 0.951437i \(-0.599607\pi\)
−0.307844 + 0.951437i \(0.599607\pi\)
\(150\) 644.759 0.350962
\(151\) 2807.15 1.51286 0.756432 0.654073i \(-0.226941\pi\)
0.756432 + 0.654073i \(0.226941\pi\)
\(152\) 0 0
\(153\) −954.752 −0.504491
\(154\) −442.511 −0.231549
\(155\) 590.166 0.305828
\(156\) 97.5436 0.0500624
\(157\) 1003.94 0.510339 0.255170 0.966896i \(-0.417869\pi\)
0.255170 + 0.966896i \(0.417869\pi\)
\(158\) −779.116 −0.392298
\(159\) 1115.96 0.556611
\(160\) −134.019 −0.0662198
\(161\) −562.680 −0.275437
\(162\) −162.000 −0.0785674
\(163\) 1271.99 0.611225 0.305612 0.952156i \(-0.401139\pi\)
0.305612 + 0.952156i \(0.401139\pi\)
\(164\) 1658.25 0.789559
\(165\) 871.967 0.411409
\(166\) −760.077 −0.355382
\(167\) 2984.98 1.38314 0.691572 0.722307i \(-0.256918\pi\)
0.691572 + 0.722307i \(0.256918\pi\)
\(168\) −76.5145 −0.0351382
\(169\) −2130.93 −0.969925
\(170\) 888.578 0.400887
\(171\) 0 0
\(172\) 463.402 0.205430
\(173\) −56.7747 −0.0249509 −0.0124754 0.999922i \(-0.503971\pi\)
−0.0124754 + 0.999922i \(0.503971\pi\)
\(174\) −397.331 −0.173113
\(175\) −342.593 −0.147986
\(176\) 1110.40 0.475568
\(177\) −275.079 −0.116815
\(178\) −851.598 −0.358595
\(179\) 4640.98 1.93790 0.968948 0.247266i \(-0.0795323\pi\)
0.968948 + 0.247266i \(0.0795323\pi\)
\(180\) 150.772 0.0624326
\(181\) −3775.41 −1.55041 −0.775204 0.631711i \(-0.782353\pi\)
−0.775204 + 0.631711i \(0.782353\pi\)
\(182\) −51.8298 −0.0211093
\(183\) 655.862 0.264933
\(184\) 1411.95 0.565708
\(185\) 653.357 0.259653
\(186\) −845.489 −0.333302
\(187\) −7362.23 −2.87904
\(188\) 2481.13 0.962527
\(189\) 86.0788 0.0331286
\(190\) 0 0
\(191\) −2762.53 −1.04654 −0.523271 0.852166i \(-0.675288\pi\)
−0.523271 + 0.852166i \(0.675288\pi\)
\(192\) 192.000 0.0721688
\(193\) −2061.51 −0.768866 −0.384433 0.923153i \(-0.625603\pi\)
−0.384433 + 0.923153i \(0.625603\pi\)
\(194\) 839.691 0.310754
\(195\) 102.131 0.0375063
\(196\) −1331.34 −0.485184
\(197\) 2094.82 0.757614 0.378807 0.925476i \(-0.376334\pi\)
0.378807 + 0.925476i \(0.376334\pi\)
\(198\) −1249.21 −0.448370
\(199\) −1717.36 −0.611762 −0.305881 0.952070i \(-0.598951\pi\)
−0.305881 + 0.952070i \(0.598951\pi\)
\(200\) 859.678 0.303942
\(201\) 436.027 0.153010
\(202\) 2483.42 0.865014
\(203\) 211.122 0.0729945
\(204\) −1273.00 −0.436902
\(205\) 1736.23 0.591530
\(206\) −1187.21 −0.401539
\(207\) −1588.44 −0.533354
\(208\) 130.058 0.0433553
\(209\) 0 0
\(210\) −80.1127 −0.0263252
\(211\) 2291.05 0.747500 0.373750 0.927529i \(-0.378072\pi\)
0.373750 + 0.927529i \(0.378072\pi\)
\(212\) 1487.94 0.482039
\(213\) −2663.49 −0.856804
\(214\) −3557.12 −1.13626
\(215\) 485.194 0.153907
\(216\) −216.000 −0.0680414
\(217\) 449.251 0.140540
\(218\) −2139.98 −0.664852
\(219\) 597.048 0.184223
\(220\) 1162.62 0.356291
\(221\) −862.314 −0.262468
\(222\) −936.019 −0.282980
\(223\) −3256.19 −0.977805 −0.488902 0.872338i \(-0.662603\pi\)
−0.488902 + 0.872338i \(0.662603\pi\)
\(224\) −102.019 −0.0304306
\(225\) −967.138 −0.286559
\(226\) 1166.39 0.343307
\(227\) 998.044 0.291817 0.145909 0.989298i \(-0.453389\pi\)
0.145909 + 0.989298i \(0.453389\pi\)
\(228\) 0 0
\(229\) −1028.59 −0.296816 −0.148408 0.988926i \(-0.547415\pi\)
−0.148408 + 0.988926i \(0.547415\pi\)
\(230\) 1478.35 0.423823
\(231\) 663.766 0.189059
\(232\) −529.775 −0.149920
\(233\) −125.486 −0.0352827 −0.0176414 0.999844i \(-0.505616\pi\)
−0.0176414 + 0.999844i \(0.505616\pi\)
\(234\) −146.315 −0.0408758
\(235\) 2597.81 0.721117
\(236\) −366.772 −0.101164
\(237\) 1168.67 0.320310
\(238\) 676.411 0.184224
\(239\) 3591.03 0.971901 0.485950 0.873986i \(-0.338474\pi\)
0.485950 + 0.873986i \(0.338474\pi\)
\(240\) 201.029 0.0540682
\(241\) 3691.84 0.986773 0.493386 0.869810i \(-0.335759\pi\)
0.493386 + 0.869810i \(0.335759\pi\)
\(242\) −6970.80 −1.85165
\(243\) 243.000 0.0641500
\(244\) 874.482 0.229438
\(245\) −1393.95 −0.363495
\(246\) −2487.38 −0.644672
\(247\) 0 0
\(248\) −1127.32 −0.288648
\(249\) 1140.12 0.290168
\(250\) 1947.13 0.492590
\(251\) 7294.88 1.83446 0.917228 0.398362i \(-0.130421\pi\)
0.917228 + 0.398362i \(0.130421\pi\)
\(252\) 114.772 0.0286902
\(253\) −12248.7 −3.04375
\(254\) 3318.71 0.819820
\(255\) −1332.87 −0.327323
\(256\) 256.000 0.0625000
\(257\) −2303.20 −0.559026 −0.279513 0.960142i \(-0.590173\pi\)
−0.279513 + 0.960142i \(0.590173\pi\)
\(258\) −695.102 −0.167733
\(259\) 497.354 0.119321
\(260\) 136.174 0.0324814
\(261\) 595.997 0.141346
\(262\) −1195.09 −0.281806
\(263\) 7138.38 1.67365 0.836827 0.547467i \(-0.184408\pi\)
0.836827 + 0.547467i \(0.184408\pi\)
\(264\) −1665.61 −0.388299
\(265\) 1557.91 0.361139
\(266\) 0 0
\(267\) 1277.40 0.292792
\(268\) 581.370 0.132510
\(269\) 5446.66 1.23453 0.617265 0.786755i \(-0.288241\pi\)
0.617265 + 0.786755i \(0.288241\pi\)
\(270\) −226.158 −0.0509760
\(271\) −3403.68 −0.762947 −0.381474 0.924380i \(-0.624583\pi\)
−0.381474 + 0.924380i \(0.624583\pi\)
\(272\) −1697.34 −0.378368
\(273\) 77.7448 0.0172356
\(274\) 3554.62 0.783731
\(275\) −7457.74 −1.63534
\(276\) −2117.92 −0.461898
\(277\) −5131.93 −1.11317 −0.556584 0.830791i \(-0.687888\pi\)
−0.556584 + 0.830791i \(0.687888\pi\)
\(278\) −327.134 −0.0705763
\(279\) 1268.23 0.272140
\(280\) −106.817 −0.0227983
\(281\) −3366.68 −0.714731 −0.357365 0.933965i \(-0.616325\pi\)
−0.357365 + 0.933965i \(0.616325\pi\)
\(282\) −3721.70 −0.785900
\(283\) 6685.76 1.40434 0.702168 0.712011i \(-0.252215\pi\)
0.702168 + 0.712011i \(0.252215\pi\)
\(284\) −3551.32 −0.742014
\(285\) 0 0
\(286\) −1128.26 −0.233270
\(287\) 1321.67 0.271832
\(288\) −288.000 −0.0589256
\(289\) 6340.72 1.29060
\(290\) −554.688 −0.112319
\(291\) −1259.54 −0.253730
\(292\) 796.065 0.159542
\(293\) 5625.93 1.12174 0.560871 0.827903i \(-0.310466\pi\)
0.560871 + 0.827903i \(0.310466\pi\)
\(294\) 1997.02 0.396151
\(295\) −384.020 −0.0757915
\(296\) −1248.02 −0.245067
\(297\) 1873.81 0.366092
\(298\) 2239.60 0.435357
\(299\) −1434.65 −0.277485
\(300\) −1289.52 −0.248168
\(301\) 369.343 0.0707262
\(302\) −5614.29 −1.06976
\(303\) −3725.13 −0.706281
\(304\) 0 0
\(305\) 915.606 0.171893
\(306\) 1909.50 0.356729
\(307\) −5603.54 −1.04173 −0.520865 0.853639i \(-0.674390\pi\)
−0.520865 + 0.853639i \(0.674390\pi\)
\(308\) 885.022 0.163730
\(309\) 1780.82 0.327855
\(310\) −1180.33 −0.216253
\(311\) 6668.20 1.21582 0.607908 0.794008i \(-0.292009\pi\)
0.607908 + 0.794008i \(0.292009\pi\)
\(312\) −195.087 −0.0353995
\(313\) 4491.40 0.811083 0.405541 0.914077i \(-0.367083\pi\)
0.405541 + 0.914077i \(0.367083\pi\)
\(314\) −2007.88 −0.360865
\(315\) 120.169 0.0214945
\(316\) 1558.23 0.277397
\(317\) 1266.05 0.224316 0.112158 0.993690i \(-0.464224\pi\)
0.112158 + 0.993690i \(0.464224\pi\)
\(318\) −2231.91 −0.393583
\(319\) 4595.82 0.806635
\(320\) 268.039 0.0468244
\(321\) 5335.68 0.927752
\(322\) 1125.36 0.194764
\(323\) 0 0
\(324\) 324.000 0.0555556
\(325\) −873.501 −0.149086
\(326\) −2543.97 −0.432201
\(327\) 3209.97 0.542849
\(328\) −3316.50 −0.558302
\(329\) 1977.53 0.331382
\(330\) −1743.93 −0.290910
\(331\) 5068.09 0.841594 0.420797 0.907155i \(-0.361751\pi\)
0.420797 + 0.907155i \(0.361751\pi\)
\(332\) 1520.15 0.251293
\(333\) 1404.03 0.231052
\(334\) −5969.97 −0.978031
\(335\) 608.709 0.0992757
\(336\) 153.029 0.0248465
\(337\) −10744.1 −1.73670 −0.868352 0.495948i \(-0.834821\pi\)
−0.868352 + 0.495948i \(0.834821\pi\)
\(338\) 4261.85 0.685841
\(339\) −1749.59 −0.280309
\(340\) −1777.16 −0.283470
\(341\) 9779.53 1.55305
\(342\) 0 0
\(343\) −2154.64 −0.339182
\(344\) −926.803 −0.145261
\(345\) −2217.52 −0.346050
\(346\) 113.549 0.0176429
\(347\) −4851.34 −0.750528 −0.375264 0.926918i \(-0.622448\pi\)
−0.375264 + 0.926918i \(0.622448\pi\)
\(348\) 794.662 0.122409
\(349\) −7611.35 −1.16741 −0.583705 0.811966i \(-0.698398\pi\)
−0.583705 + 0.811966i \(0.698398\pi\)
\(350\) 685.186 0.104642
\(351\) 219.473 0.0333749
\(352\) −2220.81 −0.336277
\(353\) 5567.64 0.839477 0.419739 0.907645i \(-0.362122\pi\)
0.419739 + 0.907645i \(0.362122\pi\)
\(354\) 550.158 0.0826004
\(355\) −3718.32 −0.555910
\(356\) 1703.20 0.253565
\(357\) −1014.62 −0.150418
\(358\) −9281.96 −1.37030
\(359\) 4341.31 0.638233 0.319116 0.947716i \(-0.396614\pi\)
0.319116 + 0.947716i \(0.396614\pi\)
\(360\) −301.544 −0.0441465
\(361\) 0 0
\(362\) 7550.82 1.09630
\(363\) 10456.2 1.51187
\(364\) 103.660 0.0149265
\(365\) 833.500 0.119527
\(366\) −1311.72 −0.187336
\(367\) −8964.48 −1.27505 −0.637524 0.770431i \(-0.720041\pi\)
−0.637524 + 0.770431i \(0.720041\pi\)
\(368\) −2823.90 −0.400016
\(369\) 3731.06 0.526372
\(370\) −1306.71 −0.183602
\(371\) 1185.93 0.165958
\(372\) 1690.98 0.235680
\(373\) −5048.11 −0.700755 −0.350377 0.936609i \(-0.613947\pi\)
−0.350377 + 0.936609i \(0.613947\pi\)
\(374\) 14724.5 2.03579
\(375\) −2920.70 −0.402198
\(376\) −4962.26 −0.680609
\(377\) 538.293 0.0735371
\(378\) −172.158 −0.0234255
\(379\) 9290.41 1.25915 0.629573 0.776941i \(-0.283230\pi\)
0.629573 + 0.776941i \(0.283230\pi\)
\(380\) 0 0
\(381\) −4978.06 −0.669380
\(382\) 5525.06 0.740017
\(383\) −4162.26 −0.555304 −0.277652 0.960682i \(-0.589556\pi\)
−0.277652 + 0.960682i \(0.589556\pi\)
\(384\) −384.000 −0.0510310
\(385\) 926.641 0.122665
\(386\) 4123.03 0.543670
\(387\) 1042.65 0.136954
\(388\) −1679.38 −0.219736
\(389\) 4185.23 0.545500 0.272750 0.962085i \(-0.412067\pi\)
0.272750 + 0.962085i \(0.412067\pi\)
\(390\) −204.261 −0.0265210
\(391\) 18723.1 2.42165
\(392\) 2662.69 0.343077
\(393\) 1792.64 0.230093
\(394\) −4189.64 −0.535714
\(395\) 1631.51 0.207823
\(396\) 2498.41 0.317045
\(397\) −4529.76 −0.572650 −0.286325 0.958133i \(-0.592434\pi\)
−0.286325 + 0.958133i \(0.592434\pi\)
\(398\) 3434.72 0.432581
\(399\) 0 0
\(400\) −1719.36 −0.214920
\(401\) 9497.05 1.18269 0.591347 0.806417i \(-0.298596\pi\)
0.591347 + 0.806417i \(0.298596\pi\)
\(402\) −872.055 −0.108194
\(403\) 1145.44 0.141585
\(404\) −4966.84 −0.611657
\(405\) 339.236 0.0416217
\(406\) −422.245 −0.0516149
\(407\) 10826.7 1.31857
\(408\) 2546.01 0.308936
\(409\) 5354.44 0.647335 0.323667 0.946171i \(-0.395084\pi\)
0.323667 + 0.946171i \(0.395084\pi\)
\(410\) −3472.46 −0.418275
\(411\) −5331.93 −0.639914
\(412\) 2374.43 0.283931
\(413\) −292.327 −0.0348292
\(414\) 3176.88 0.377138
\(415\) 1591.64 0.188267
\(416\) −260.116 −0.0306568
\(417\) 490.701 0.0576253
\(418\) 0 0
\(419\) 14506.1 1.69134 0.845668 0.533709i \(-0.179202\pi\)
0.845668 + 0.533709i \(0.179202\pi\)
\(420\) 160.225 0.0186148
\(421\) 1263.45 0.146263 0.0731315 0.997322i \(-0.476701\pi\)
0.0731315 + 0.997322i \(0.476701\pi\)
\(422\) −4582.10 −0.528562
\(423\) 5582.55 0.641685
\(424\) −2975.88 −0.340853
\(425\) 11399.7 1.30110
\(426\) 5326.98 0.605852
\(427\) 696.985 0.0789918
\(428\) 7114.24 0.803457
\(429\) 1692.39 0.190464
\(430\) −970.387 −0.108828
\(431\) 8187.62 0.915043 0.457522 0.889198i \(-0.348737\pi\)
0.457522 + 0.889198i \(0.348737\pi\)
\(432\) 432.000 0.0481125
\(433\) 9242.94 1.02584 0.512919 0.858437i \(-0.328564\pi\)
0.512919 + 0.858437i \(0.328564\pi\)
\(434\) −898.502 −0.0993767
\(435\) 832.032 0.0917078
\(436\) 4279.96 0.470121
\(437\) 0 0
\(438\) −1194.10 −0.130265
\(439\) 2043.05 0.222117 0.111059 0.993814i \(-0.464576\pi\)
0.111059 + 0.993814i \(0.464576\pi\)
\(440\) −2325.25 −0.251936
\(441\) −2995.52 −0.323456
\(442\) 1724.63 0.185593
\(443\) −9669.13 −1.03701 −0.518504 0.855075i \(-0.673511\pi\)
−0.518504 + 0.855075i \(0.673511\pi\)
\(444\) 1872.04 0.200097
\(445\) 1783.29 0.189969
\(446\) 6512.38 0.691412
\(447\) −3359.40 −0.355467
\(448\) 204.039 0.0215177
\(449\) 13227.2 1.39027 0.695134 0.718881i \(-0.255345\pi\)
0.695134 + 0.718881i \(0.255345\pi\)
\(450\) 1934.28 0.202628
\(451\) 28770.8 3.00391
\(452\) −2332.79 −0.242755
\(453\) 8421.44 0.873452
\(454\) −1996.09 −0.206346
\(455\) 108.534 0.0111828
\(456\) 0 0
\(457\) −5380.98 −0.550791 −0.275396 0.961331i \(-0.588809\pi\)
−0.275396 + 0.961331i \(0.588809\pi\)
\(458\) 2057.17 0.209880
\(459\) −2864.26 −0.291268
\(460\) −2956.69 −0.299688
\(461\) −2844.67 −0.287396 −0.143698 0.989622i \(-0.545899\pi\)
−0.143698 + 0.989622i \(0.545899\pi\)
\(462\) −1327.53 −0.133685
\(463\) 6625.39 0.665028 0.332514 0.943098i \(-0.392103\pi\)
0.332514 + 0.943098i \(0.392103\pi\)
\(464\) 1059.55 0.106009
\(465\) 1770.50 0.176570
\(466\) 250.972 0.0249487
\(467\) −18635.1 −1.84653 −0.923264 0.384167i \(-0.874489\pi\)
−0.923264 + 0.384167i \(0.874489\pi\)
\(468\) 292.631 0.0289035
\(469\) 463.367 0.0456211
\(470\) −5195.62 −0.509906
\(471\) 3011.83 0.294645
\(472\) 733.544 0.0715341
\(473\) 8040.05 0.781569
\(474\) −2337.35 −0.226493
\(475\) 0 0
\(476\) −1352.82 −0.130266
\(477\) 3347.87 0.321359
\(478\) −7182.05 −0.687237
\(479\) 1556.62 0.148484 0.0742420 0.997240i \(-0.476346\pi\)
0.0742420 + 0.997240i \(0.476346\pi\)
\(480\) −402.058 −0.0382320
\(481\) 1268.09 0.120208
\(482\) −7383.68 −0.697754
\(483\) −1688.04 −0.159024
\(484\) 13941.6 1.30932
\(485\) −1758.36 −0.164625
\(486\) −486.000 −0.0453609
\(487\) −19339.5 −1.79950 −0.899751 0.436405i \(-0.856252\pi\)
−0.899751 + 0.436405i \(0.856252\pi\)
\(488\) −1748.96 −0.162238
\(489\) 3815.96 0.352891
\(490\) 2787.90 0.257030
\(491\) −6838.25 −0.628525 −0.314262 0.949336i \(-0.601757\pi\)
−0.314262 + 0.949336i \(0.601757\pi\)
\(492\) 4974.75 0.455852
\(493\) −7025.05 −0.641770
\(494\) 0 0
\(495\) 2615.90 0.237527
\(496\) 2254.64 0.204105
\(497\) −2830.49 −0.255463
\(498\) −2280.23 −0.205180
\(499\) −18115.0 −1.62513 −0.812563 0.582874i \(-0.801928\pi\)
−0.812563 + 0.582874i \(0.801928\pi\)
\(500\) −3894.26 −0.348314
\(501\) 8954.95 0.798559
\(502\) −14589.8 −1.29716
\(503\) −5831.85 −0.516957 −0.258478 0.966017i \(-0.583221\pi\)
−0.258478 + 0.966017i \(0.583221\pi\)
\(504\) −229.544 −0.0202871
\(505\) −5200.41 −0.458248
\(506\) 24497.4 2.15226
\(507\) −6392.78 −0.559987
\(508\) −6637.41 −0.579700
\(509\) −9914.65 −0.863377 −0.431689 0.902023i \(-0.642082\pi\)
−0.431689 + 0.902023i \(0.642082\pi\)
\(510\) 2665.73 0.231452
\(511\) 634.484 0.0549275
\(512\) −512.000 −0.0441942
\(513\) 0 0
\(514\) 4606.40 0.395291
\(515\) 2486.09 0.212718
\(516\) 1390.20 0.118605
\(517\) 43047.8 3.66197
\(518\) −994.709 −0.0843726
\(519\) −170.324 −0.0144054
\(520\) −272.348 −0.0229678
\(521\) 5851.91 0.492086 0.246043 0.969259i \(-0.420869\pi\)
0.246043 + 0.969259i \(0.420869\pi\)
\(522\) −1191.99 −0.0999466
\(523\) −6894.09 −0.576401 −0.288200 0.957570i \(-0.593057\pi\)
−0.288200 + 0.957570i \(0.593057\pi\)
\(524\) 2390.19 0.199267
\(525\) −1027.78 −0.0854399
\(526\) −14276.8 −1.18345
\(527\) −14948.7 −1.23563
\(528\) 3331.21 0.274569
\(529\) 18983.0 1.56020
\(530\) −3115.83 −0.255364
\(531\) −825.236 −0.0674430
\(532\) 0 0
\(533\) 3369.83 0.273853
\(534\) −2554.79 −0.207035
\(535\) 7448.79 0.601943
\(536\) −1162.74 −0.0936991
\(537\) 13922.9 1.11884
\(538\) −10893.3 −0.872945
\(539\) −23098.9 −1.84590
\(540\) 452.315 0.0360455
\(541\) −5624.99 −0.447019 −0.223509 0.974702i \(-0.571751\pi\)
−0.223509 + 0.974702i \(0.571751\pi\)
\(542\) 6807.36 0.539485
\(543\) −11326.2 −0.895129
\(544\) 3394.67 0.267547
\(545\) 4481.23 0.352211
\(546\) −155.490 −0.0121874
\(547\) −3596.14 −0.281096 −0.140548 0.990074i \(-0.544886\pi\)
−0.140548 + 0.990074i \(0.544886\pi\)
\(548\) −7109.24 −0.554182
\(549\) 1967.59 0.152959
\(550\) 14915.5 1.15636
\(551\) 0 0
\(552\) 4235.85 0.326611
\(553\) 1241.95 0.0955029
\(554\) 10263.9 0.787129
\(555\) 1960.07 0.149911
\(556\) 654.269 0.0499050
\(557\) 18381.5 1.39829 0.699145 0.714980i \(-0.253564\pi\)
0.699145 + 0.714980i \(0.253564\pi\)
\(558\) −2536.47 −0.192432
\(559\) 941.705 0.0712520
\(560\) 213.634 0.0161209
\(561\) −22086.7 −1.66221
\(562\) 6733.36 0.505391
\(563\) −5578.33 −0.417582 −0.208791 0.977960i \(-0.566953\pi\)
−0.208791 + 0.977960i \(0.566953\pi\)
\(564\) 7443.39 0.555715
\(565\) −2442.49 −0.181870
\(566\) −13371.5 −0.993016
\(567\) 258.236 0.0191268
\(568\) 7102.63 0.524683
\(569\) −16981.3 −1.25113 −0.625564 0.780173i \(-0.715131\pi\)
−0.625564 + 0.780173i \(0.715131\pi\)
\(570\) 0 0
\(571\) −19520.5 −1.43066 −0.715332 0.698785i \(-0.753724\pi\)
−0.715332 + 0.698785i \(0.753724\pi\)
\(572\) 2256.52 0.164947
\(573\) −8287.59 −0.604221
\(574\) −2643.34 −0.192214
\(575\) 18966.0 1.37554
\(576\) 576.000 0.0416667
\(577\) 6371.35 0.459693 0.229846 0.973227i \(-0.426178\pi\)
0.229846 + 0.973227i \(0.426178\pi\)
\(578\) −12681.4 −0.912593
\(579\) −6184.54 −0.443905
\(580\) 1109.38 0.0794213
\(581\) 1211.60 0.0865159
\(582\) 2519.07 0.179414
\(583\) 25815.9 1.83394
\(584\) −1592.13 −0.112813
\(585\) 306.392 0.0216543
\(586\) −11251.9 −0.793191
\(587\) 10759.0 0.756513 0.378257 0.925701i \(-0.376524\pi\)
0.378257 + 0.925701i \(0.376524\pi\)
\(588\) −3994.03 −0.280121
\(589\) 0 0
\(590\) 768.039 0.0535927
\(591\) 6284.47 0.437408
\(592\) 2496.05 0.173289
\(593\) 3611.76 0.250113 0.125057 0.992150i \(-0.460089\pi\)
0.125057 + 0.992150i \(0.460089\pi\)
\(594\) −3747.62 −0.258866
\(595\) −1416.44 −0.0975939
\(596\) −4479.19 −0.307844
\(597\) −5152.09 −0.353201
\(598\) 2869.30 0.196211
\(599\) 9180.23 0.626201 0.313100 0.949720i \(-0.398632\pi\)
0.313100 + 0.949720i \(0.398632\pi\)
\(600\) 2579.03 0.175481
\(601\) −12700.4 −0.862000 −0.431000 0.902352i \(-0.641839\pi\)
−0.431000 + 0.902352i \(0.641839\pi\)
\(602\) −738.686 −0.0500110
\(603\) 1308.08 0.0883403
\(604\) 11228.6 0.756432
\(605\) 14597.2 0.980928
\(606\) 7450.26 0.499416
\(607\) 24227.5 1.62004 0.810019 0.586404i \(-0.199457\pi\)
0.810019 + 0.586404i \(0.199457\pi\)
\(608\) 0 0
\(609\) 633.367 0.0421434
\(610\) −1831.21 −0.121547
\(611\) 5042.05 0.333845
\(612\) −3819.01 −0.252246
\(613\) −16213.5 −1.06828 −0.534141 0.845396i \(-0.679365\pi\)
−0.534141 + 0.845396i \(0.679365\pi\)
\(614\) 11207.1 0.736614
\(615\) 5208.70 0.341520
\(616\) −1770.04 −0.115774
\(617\) −21515.3 −1.40385 −0.701924 0.712252i \(-0.747675\pi\)
−0.701924 + 0.712252i \(0.747675\pi\)
\(618\) −3561.64 −0.231829
\(619\) −15878.5 −1.03103 −0.515516 0.856880i \(-0.672400\pi\)
−0.515516 + 0.856880i \(0.672400\pi\)
\(620\) 2360.66 0.152914
\(621\) −4765.33 −0.307932
\(622\) −13336.4 −0.859712
\(623\) 1357.49 0.0872982
\(624\) 390.174 0.0250312
\(625\) 9355.08 0.598725
\(626\) −8982.80 −0.573522
\(627\) 0 0
\(628\) 4015.77 0.255170
\(629\) −16549.4 −1.04907
\(630\) −240.338 −0.0151989
\(631\) 5559.75 0.350761 0.175380 0.984501i \(-0.443884\pi\)
0.175380 + 0.984501i \(0.443884\pi\)
\(632\) −3116.46 −0.196149
\(633\) 6873.16 0.431569
\(634\) −2532.09 −0.158616
\(635\) −6949.55 −0.434306
\(636\) 4463.83 0.278305
\(637\) −2705.50 −0.168282
\(638\) −9191.64 −0.570377
\(639\) −7990.46 −0.494676
\(640\) −536.077 −0.0331099
\(641\) 20486.9 1.26238 0.631190 0.775628i \(-0.282567\pi\)
0.631190 + 0.775628i \(0.282567\pi\)
\(642\) −10671.4 −0.656020
\(643\) −4102.30 −0.251600 −0.125800 0.992056i \(-0.540150\pi\)
−0.125800 + 0.992056i \(0.540150\pi\)
\(644\) −2250.72 −0.137719
\(645\) 1455.58 0.0888580
\(646\) 0 0
\(647\) 22860.4 1.38908 0.694539 0.719455i \(-0.255608\pi\)
0.694539 + 0.719455i \(0.255608\pi\)
\(648\) −648.000 −0.0392837
\(649\) −6363.52 −0.384884
\(650\) 1747.00 0.105420
\(651\) 1347.75 0.0811408
\(652\) 5087.94 0.305612
\(653\) 26388.5 1.58141 0.790706 0.612197i \(-0.209714\pi\)
0.790706 + 0.612197i \(0.209714\pi\)
\(654\) −6419.94 −0.383853
\(655\) 2502.59 0.149289
\(656\) 6633.00 0.394779
\(657\) 1791.15 0.106361
\(658\) −3955.05 −0.234322
\(659\) −3223.29 −0.190534 −0.0952668 0.995452i \(-0.530370\pi\)
−0.0952668 + 0.995452i \(0.530370\pi\)
\(660\) 3487.87 0.205705
\(661\) 27480.2 1.61703 0.808513 0.588478i \(-0.200273\pi\)
0.808513 + 0.588478i \(0.200273\pi\)
\(662\) −10136.2 −0.595097
\(663\) −2586.94 −0.151536
\(664\) −3040.31 −0.177691
\(665\) 0 0
\(666\) −2808.06 −0.163378
\(667\) −11687.7 −0.678487
\(668\) 11939.9 0.691572
\(669\) −9768.56 −0.564536
\(670\) −1217.42 −0.0701985
\(671\) 15172.3 0.872908
\(672\) −306.058 −0.0175691
\(673\) 2165.00 0.124004 0.0620020 0.998076i \(-0.480251\pi\)
0.0620020 + 0.998076i \(0.480251\pi\)
\(674\) 21488.2 1.22804
\(675\) −2901.41 −0.165445
\(676\) −8523.70 −0.484963
\(677\) −11999.0 −0.681179 −0.340589 0.940212i \(-0.610627\pi\)
−0.340589 + 0.940212i \(0.610627\pi\)
\(678\) 3499.18 0.198209
\(679\) −1338.51 −0.0756515
\(680\) 3554.31 0.200444
\(681\) 2994.13 0.168481
\(682\) −19559.1 −1.09817
\(683\) −5234.35 −0.293246 −0.146623 0.989192i \(-0.546840\pi\)
−0.146623 + 0.989192i \(0.546840\pi\)
\(684\) 0 0
\(685\) −7443.56 −0.415188
\(686\) 4309.27 0.239838
\(687\) −3085.76 −0.171367
\(688\) 1853.61 0.102715
\(689\) 3023.73 0.167192
\(690\) 4435.04 0.244694
\(691\) −5160.63 −0.284109 −0.142055 0.989859i \(-0.545371\pi\)
−0.142055 + 0.989859i \(0.545371\pi\)
\(692\) −227.099 −0.0124754
\(693\) 1991.30 0.109153
\(694\) 9702.67 0.530704
\(695\) 685.036 0.0373884
\(696\) −1589.32 −0.0865563
\(697\) −43978.3 −2.38995
\(698\) 15222.7 0.825484
\(699\) −376.459 −0.0203705
\(700\) −1370.37 −0.0739931
\(701\) −3315.03 −0.178612 −0.0893059 0.996004i \(-0.528465\pi\)
−0.0893059 + 0.996004i \(0.528465\pi\)
\(702\) −438.946 −0.0235996
\(703\) 0 0
\(704\) 4441.62 0.237784
\(705\) 7793.43 0.416337
\(706\) −11135.3 −0.593600
\(707\) −3958.70 −0.210583
\(708\) −1100.32 −0.0584073
\(709\) −18333.2 −0.971111 −0.485555 0.874206i \(-0.661383\pi\)
−0.485555 + 0.874206i \(0.661383\pi\)
\(710\) 7436.64 0.393088
\(711\) 3506.02 0.184931
\(712\) −3406.39 −0.179298
\(713\) −24870.6 −1.30632
\(714\) 2029.23 0.106362
\(715\) 2362.63 0.123577
\(716\) 18563.9 0.968948
\(717\) 10773.1 0.561127
\(718\) −8682.62 −0.451299
\(719\) 9747.00 0.505566 0.252783 0.967523i \(-0.418654\pi\)
0.252783 + 0.967523i \(0.418654\pi\)
\(720\) 603.087 0.0312163
\(721\) 1892.48 0.0977526
\(722\) 0 0
\(723\) 11075.5 0.569713
\(724\) −15101.6 −0.775204
\(725\) −7116.19 −0.364536
\(726\) −20912.4 −1.06905
\(727\) 32723.6 1.66939 0.834697 0.550709i \(-0.185643\pi\)
0.834697 + 0.550709i \(0.185643\pi\)
\(728\) −207.319 −0.0105546
\(729\) 729.000 0.0370370
\(730\) −1667.00 −0.0845185
\(731\) −12289.8 −0.621827
\(732\) 2623.45 0.132466
\(733\) 36938.2 1.86131 0.930657 0.365894i \(-0.119237\pi\)
0.930657 + 0.365894i \(0.119237\pi\)
\(734\) 17929.0 0.901594
\(735\) −4181.86 −0.209864
\(736\) 5647.79 0.282854
\(737\) 10086.8 0.504142
\(738\) −7462.13 −0.372202
\(739\) −9987.19 −0.497138 −0.248569 0.968614i \(-0.579960\pi\)
−0.248569 + 0.968614i \(0.579960\pi\)
\(740\) 2613.43 0.129826
\(741\) 0 0
\(742\) −2371.86 −0.117350
\(743\) −21739.8 −1.07343 −0.536713 0.843765i \(-0.680334\pi\)
−0.536713 + 0.843765i \(0.680334\pi\)
\(744\) −3381.96 −0.166651
\(745\) −4689.83 −0.230634
\(746\) 10096.2 0.495508
\(747\) 3420.35 0.167529
\(748\) −29448.9 −1.43952
\(749\) 5670.23 0.276617
\(750\) 5841.40 0.284397
\(751\) 38067.4 1.84967 0.924833 0.380374i \(-0.124205\pi\)
0.924833 + 0.380374i \(0.124205\pi\)
\(752\) 9924.53 0.481264
\(753\) 21884.6 1.05912
\(754\) −1076.59 −0.0519986
\(755\) 11756.6 0.566712
\(756\) 344.315 0.0165643
\(757\) −11365.2 −0.545675 −0.272838 0.962060i \(-0.587962\pi\)
−0.272838 + 0.962060i \(0.587962\pi\)
\(758\) −18580.8 −0.890351
\(759\) −36746.1 −1.75731
\(760\) 0 0
\(761\) 24549.3 1.16940 0.584699 0.811250i \(-0.301213\pi\)
0.584699 + 0.811250i \(0.301213\pi\)
\(762\) 9956.12 0.473323
\(763\) 3411.24 0.161855
\(764\) −11050.1 −0.523271
\(765\) −3998.60 −0.188980
\(766\) 8324.51 0.392659
\(767\) −745.338 −0.0350881
\(768\) 768.000 0.0360844
\(769\) 14222.5 0.666941 0.333471 0.942760i \(-0.391780\pi\)
0.333471 + 0.942760i \(0.391780\pi\)
\(770\) −1853.28 −0.0867372
\(771\) −6909.60 −0.322754
\(772\) −8246.06 −0.384433
\(773\) −16082.6 −0.748319 −0.374159 0.927364i \(-0.622069\pi\)
−0.374159 + 0.927364i \(0.622069\pi\)
\(774\) −2085.31 −0.0968409
\(775\) −15142.7 −0.701859
\(776\) 3358.77 0.155377
\(777\) 1492.06 0.0688899
\(778\) −8370.46 −0.385727
\(779\) 0 0
\(780\) 408.523 0.0187531
\(781\) −61615.6 −2.82302
\(782\) −37446.1 −1.71237
\(783\) 1787.99 0.0816061
\(784\) −5325.38 −0.242592
\(785\) 4204.61 0.191171
\(786\) −3585.28 −0.162701
\(787\) −30058.0 −1.36144 −0.680720 0.732544i \(-0.738333\pi\)
−0.680720 + 0.732544i \(0.738333\pi\)
\(788\) 8379.29 0.378807
\(789\) 21415.1 0.966285
\(790\) −3263.02 −0.146953
\(791\) −1859.29 −0.0835764
\(792\) −4996.82 −0.224185
\(793\) 1777.09 0.0795790
\(794\) 9059.52 0.404925
\(795\) 4673.74 0.208504
\(796\) −6869.45 −0.305881
\(797\) 20008.2 0.889243 0.444621 0.895719i \(-0.353338\pi\)
0.444621 + 0.895719i \(0.353338\pi\)
\(798\) 0 0
\(799\) −65801.8 −2.91352
\(800\) 3438.71 0.151971
\(801\) 3832.19 0.169043
\(802\) −18994.1 −0.836291
\(803\) 13811.8 0.606983
\(804\) 1744.11 0.0765050
\(805\) −2356.56 −0.103178
\(806\) −2290.89 −0.100116
\(807\) 16340.0 0.712757
\(808\) 9933.68 0.432507
\(809\) 35302.3 1.53419 0.767097 0.641532i \(-0.221701\pi\)
0.767097 + 0.641532i \(0.221701\pi\)
\(810\) −678.473 −0.0294310
\(811\) −10980.8 −0.475446 −0.237723 0.971333i \(-0.576401\pi\)
−0.237723 + 0.971333i \(0.576401\pi\)
\(812\) 844.489 0.0364972
\(813\) −10211.0 −0.440488
\(814\) −21653.3 −0.932369
\(815\) 5327.21 0.228962
\(816\) −5092.01 −0.218451
\(817\) 0 0
\(818\) −10708.9 −0.457735
\(819\) 233.234 0.00995100
\(820\) 6944.93 0.295765
\(821\) −5626.68 −0.239187 −0.119594 0.992823i \(-0.538159\pi\)
−0.119594 + 0.992823i \(0.538159\pi\)
\(822\) 10663.9 0.452487
\(823\) 28766.3 1.21838 0.609191 0.793023i \(-0.291494\pi\)
0.609191 + 0.793023i \(0.291494\pi\)
\(824\) −4748.85 −0.200769
\(825\) −22373.2 −0.944164
\(826\) 584.653 0.0246280
\(827\) −44482.4 −1.87038 −0.935191 0.354145i \(-0.884772\pi\)
−0.935191 + 0.354145i \(0.884772\pi\)
\(828\) −6353.77 −0.266677
\(829\) −23302.5 −0.976271 −0.488136 0.872768i \(-0.662323\pi\)
−0.488136 + 0.872768i \(0.662323\pi\)
\(830\) −3183.28 −0.133125
\(831\) −15395.8 −0.642688
\(832\) 520.232 0.0216777
\(833\) 35308.4 1.46862
\(834\) −981.403 −0.0407472
\(835\) 12501.4 0.518120
\(836\) 0 0
\(837\) 3804.70 0.157120
\(838\) −29012.2 −1.19596
\(839\) 27683.7 1.13915 0.569575 0.821939i \(-0.307108\pi\)
0.569575 + 0.821939i \(0.307108\pi\)
\(840\) −320.451 −0.0131626
\(841\) −20003.7 −0.820192
\(842\) −2526.90 −0.103424
\(843\) −10100.0 −0.412650
\(844\) 9164.21 0.373750
\(845\) −8924.54 −0.363330
\(846\) −11165.1 −0.453740
\(847\) 11111.8 0.450776
\(848\) 5951.77 0.241020
\(849\) 20057.3 0.810794
\(850\) −22799.4 −0.920017
\(851\) −27533.5 −1.10909
\(852\) −10654.0 −0.428402
\(853\) −30609.5 −1.22866 −0.614331 0.789049i \(-0.710574\pi\)
−0.614331 + 0.789049i \(0.710574\pi\)
\(854\) −1393.97 −0.0558556
\(855\) 0 0
\(856\) −14228.5 −0.568130
\(857\) −10918.3 −0.435194 −0.217597 0.976039i \(-0.569822\pi\)
−0.217597 + 0.976039i \(0.569822\pi\)
\(858\) −3384.78 −0.134679
\(859\) 14639.5 0.581482 0.290741 0.956802i \(-0.406098\pi\)
0.290741 + 0.956802i \(0.406098\pi\)
\(860\) 1940.77 0.0769533
\(861\) 3965.01 0.156942
\(862\) −16375.2 −0.647033
\(863\) 22775.2 0.898353 0.449176 0.893443i \(-0.351717\pi\)
0.449176 + 0.893443i \(0.351717\pi\)
\(864\) −864.000 −0.0340207
\(865\) −237.778 −0.00934648
\(866\) −18485.9 −0.725377
\(867\) 19022.2 0.745129
\(868\) 1797.00 0.0702700
\(869\) 27035.4 1.05537
\(870\) −1664.06 −0.0648472
\(871\) 1181.43 0.0459603
\(872\) −8559.92 −0.332426
\(873\) −3778.61 −0.146491
\(874\) 0 0
\(875\) −3103.83 −0.119918
\(876\) 2388.19 0.0921114
\(877\) −805.908 −0.0310303 −0.0155152 0.999880i \(-0.504939\pi\)
−0.0155152 + 0.999880i \(0.504939\pi\)
\(878\) −4086.10 −0.157061
\(879\) 16877.8 0.647638
\(880\) 4650.49 0.178146
\(881\) −901.690 −0.0344821 −0.0172410 0.999851i \(-0.505488\pi\)
−0.0172410 + 0.999851i \(0.505488\pi\)
\(882\) 5991.05 0.228718
\(883\) −25406.3 −0.968279 −0.484140 0.874991i \(-0.660867\pi\)
−0.484140 + 0.874991i \(0.660867\pi\)
\(884\) −3449.26 −0.131234
\(885\) −1152.06 −0.0437582
\(886\) 19338.3 0.733275
\(887\) −28560.5 −1.08114 −0.540568 0.841300i \(-0.681791\pi\)
−0.540568 + 0.841300i \(0.681791\pi\)
\(888\) −3744.07 −0.141490
\(889\) −5290.19 −0.199581
\(890\) −3566.58 −0.134328
\(891\) 5621.42 0.211363
\(892\) −13024.8 −0.488902
\(893\) 0 0
\(894\) 6718.79 0.251353
\(895\) 19436.9 0.725927
\(896\) −408.077 −0.0152153
\(897\) −4303.95 −0.160206
\(898\) −26454.4 −0.983067
\(899\) 9331.64 0.346193
\(900\) −3868.55 −0.143280
\(901\) −39461.6 −1.45911
\(902\) −57541.6 −2.12408
\(903\) 1108.03 0.0408338
\(904\) 4665.58 0.171654
\(905\) −15811.8 −0.580776
\(906\) −16842.9 −0.617624
\(907\) 40905.4 1.49751 0.748755 0.662847i \(-0.230652\pi\)
0.748755 + 0.662847i \(0.230652\pi\)
\(908\) 3992.18 0.145909
\(909\) −11175.4 −0.407772
\(910\) −217.069 −0.00790743
\(911\) −30047.9 −1.09279 −0.546395 0.837527i \(-0.684000\pi\)
−0.546395 + 0.837527i \(0.684000\pi\)
\(912\) 0 0
\(913\) 26374.8 0.956055
\(914\) 10762.0 0.389468
\(915\) 2746.82 0.0992426
\(916\) −4114.34 −0.148408
\(917\) 1905.04 0.0686041
\(918\) 5728.51 0.205958
\(919\) −49600.1 −1.78036 −0.890182 0.455605i \(-0.849423\pi\)
−0.890182 + 0.455605i \(0.849423\pi\)
\(920\) 5913.39 0.211912
\(921\) −16810.6 −0.601443
\(922\) 5689.33 0.203219
\(923\) −7216.84 −0.257362
\(924\) 2655.07 0.0945295
\(925\) −16764.1 −0.595891
\(926\) −13250.8 −0.470246
\(927\) 5342.46 0.189287
\(928\) −2119.10 −0.0749600
\(929\) 27556.8 0.973205 0.486603 0.873623i \(-0.338236\pi\)
0.486603 + 0.873623i \(0.338236\pi\)
\(930\) −3541.00 −0.124854
\(931\) 0 0
\(932\) −501.945 −0.0176414
\(933\) 20004.6 0.701952
\(934\) 37270.1 1.30569
\(935\) −30833.8 −1.07847
\(936\) −585.261 −0.0204379
\(937\) −26880.8 −0.937202 −0.468601 0.883410i \(-0.655242\pi\)
−0.468601 + 0.883410i \(0.655242\pi\)
\(938\) −926.734 −0.0322590
\(939\) 13474.2 0.468279
\(940\) 10391.2 0.360558
\(941\) 6411.34 0.222108 0.111054 0.993814i \(-0.464577\pi\)
0.111054 + 0.993814i \(0.464577\pi\)
\(942\) −6023.65 −0.208345
\(943\) −73167.6 −2.52669
\(944\) −1467.09 −0.0505822
\(945\) 360.507 0.0124098
\(946\) −16080.1 −0.552653
\(947\) −1989.83 −0.0682796 −0.0341398 0.999417i \(-0.510869\pi\)
−0.0341398 + 0.999417i \(0.510869\pi\)
\(948\) 4674.69 0.160155
\(949\) 1617.73 0.0553358
\(950\) 0 0
\(951\) 3798.14 0.129509
\(952\) 2705.64 0.0921118
\(953\) 38266.4 1.30070 0.650351 0.759633i \(-0.274622\pi\)
0.650351 + 0.759633i \(0.274622\pi\)
\(954\) −6695.74 −0.227235
\(955\) −11569.8 −0.392030
\(956\) 14364.1 0.485950
\(957\) 13787.5 0.465711
\(958\) −3113.24 −0.104994
\(959\) −5666.25 −0.190795
\(960\) 804.116 0.0270341
\(961\) −9934.01 −0.333457
\(962\) −2536.18 −0.0849998
\(963\) 16007.0 0.535638
\(964\) 14767.4 0.493386
\(965\) −8633.84 −0.288014
\(966\) 3376.08 0.112447
\(967\) 220.116 0.00732002 0.00366001 0.999993i \(-0.498835\pi\)
0.00366001 + 0.999993i \(0.498835\pi\)
\(968\) −27883.2 −0.925827
\(969\) 0 0
\(970\) 3516.72 0.116407
\(971\) −2175.36 −0.0718955 −0.0359478 0.999354i \(-0.511445\pi\)
−0.0359478 + 0.999354i \(0.511445\pi\)
\(972\) 972.000 0.0320750
\(973\) 521.469 0.0171814
\(974\) 38679.0 1.27244
\(975\) −2620.50 −0.0860751
\(976\) 3497.93 0.114719
\(977\) −13707.7 −0.448872 −0.224436 0.974489i \(-0.572054\pi\)
−0.224436 + 0.974489i \(0.572054\pi\)
\(978\) −7631.91 −0.249531
\(979\) 29550.6 0.964699
\(980\) −5575.81 −0.181748
\(981\) 9629.91 0.313414
\(982\) 13676.5 0.444434
\(983\) 18885.7 0.612779 0.306389 0.951906i \(-0.400879\pi\)
0.306389 + 0.951906i \(0.400879\pi\)
\(984\) −9949.50 −0.322336
\(985\) 8773.33 0.283799
\(986\) 14050.1 0.453800
\(987\) 5932.58 0.191323
\(988\) 0 0
\(989\) −20446.8 −0.657403
\(990\) −5231.80 −0.167957
\(991\) 40655.0 1.30318 0.651589 0.758572i \(-0.274103\pi\)
0.651589 + 0.758572i \(0.274103\pi\)
\(992\) −4509.27 −0.144324
\(993\) 15204.3 0.485894
\(994\) 5660.99 0.180639
\(995\) −7192.49 −0.229163
\(996\) 4560.46 0.145084
\(997\) −16433.3 −0.522014 −0.261007 0.965337i \(-0.584055\pi\)
−0.261007 + 0.965337i \(0.584055\pi\)
\(998\) 36229.9 1.14914
\(999\) 4212.08 0.133398
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 2166.4.a.t.1.2 3
19.8 odd 6 114.4.e.d.7.2 6
19.12 odd 6 114.4.e.d.49.2 yes 6
19.18 odd 2 2166.4.a.u.1.2 3
57.8 even 6 342.4.g.h.235.2 6
57.50 even 6 342.4.g.h.163.2 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
114.4.e.d.7.2 6 19.8 odd 6
114.4.e.d.49.2 yes 6 19.12 odd 6
342.4.g.h.163.2 6 57.50 even 6
342.4.g.h.235.2 6 57.8 even 6
2166.4.a.t.1.2 3 1.1 even 1 trivial
2166.4.a.u.1.2 3 19.18 odd 2