Properties

Label 43.4.a.b.1.6
Level 43
Weight 4
Character 43.1
Self dual yes
Analytic conductor 2.537
Analytic rank 0
Dimension 6
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 43.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(2.53708213025\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\mathbb{Q}[x]/(x^{6} - \cdots)\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(-4.15251\) of \(x^{6} - 32 x^{4} - 16 x^{3} + 251 x^{2} + 276 x + 60\)
Character \(\chi\) \(=\) 43.1

$q$-expansion

\(f(q)\) \(=\) \(q+5.15251 q^{2} -6.49933 q^{3} +18.5484 q^{4} +17.2665 q^{5} -33.4879 q^{6} -23.3206 q^{7} +54.3507 q^{8} +15.2413 q^{9} +O(q^{10})\) \(q+5.15251 q^{2} -6.49933 q^{3} +18.5484 q^{4} +17.2665 q^{5} -33.4879 q^{6} -23.3206 q^{7} +54.3507 q^{8} +15.2413 q^{9} +88.9661 q^{10} -60.5580 q^{11} -120.552 q^{12} +10.9419 q^{13} -120.160 q^{14} -112.221 q^{15} +131.656 q^{16} -3.57473 q^{17} +78.5308 q^{18} +33.2403 q^{19} +320.267 q^{20} +151.568 q^{21} -312.026 q^{22} +63.7158 q^{23} -353.243 q^{24} +173.134 q^{25} +56.3783 q^{26} +76.4239 q^{27} -432.560 q^{28} -89.3510 q^{29} -578.220 q^{30} +222.839 q^{31} +243.552 q^{32} +393.586 q^{33} -18.4188 q^{34} -402.666 q^{35} +282.701 q^{36} -59.6535 q^{37} +171.271 q^{38} -71.1150 q^{39} +938.449 q^{40} -143.837 q^{41} +780.957 q^{42} -43.0000 q^{43} -1123.25 q^{44} +263.164 q^{45} +328.296 q^{46} +379.013 q^{47} -855.674 q^{48} +200.850 q^{49} +892.073 q^{50} +23.2334 q^{51} +202.955 q^{52} -150.129 q^{53} +393.775 q^{54} -1045.63 q^{55} -1267.49 q^{56} -216.040 q^{57} -460.382 q^{58} +207.310 q^{59} -2081.52 q^{60} -486.557 q^{61} +1148.18 q^{62} -355.435 q^{63} +201.659 q^{64} +188.929 q^{65} +2027.96 q^{66} +1019.41 q^{67} -66.3055 q^{68} -414.110 q^{69} -2074.74 q^{70} +13.8437 q^{71} +828.374 q^{72} +411.158 q^{73} -307.365 q^{74} -1125.25 q^{75} +616.555 q^{76} +1412.25 q^{77} -366.421 q^{78} -1315.13 q^{79} +2273.24 q^{80} -908.218 q^{81} -741.120 q^{82} +813.425 q^{83} +2811.35 q^{84} -61.7233 q^{85} -221.558 q^{86} +580.721 q^{87} -3291.37 q^{88} -350.573 q^{89} +1355.96 q^{90} -255.171 q^{91} +1181.83 q^{92} -1448.30 q^{93} +1952.87 q^{94} +573.946 q^{95} -1582.92 q^{96} -1187.03 q^{97} +1034.88 q^{98} -922.981 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 6q^{2} + 7q^{3} + 22q^{4} + 43q^{5} - 3q^{6} + 8q^{7} + 54q^{8} + 81q^{9} + O(q^{10}) \) \( 6q + 6q^{2} + 7q^{3} + 22q^{4} + 43q^{5} - 3q^{6} + 8q^{7} + 54q^{8} + 81q^{9} + 57q^{10} - 28q^{11} - 157q^{12} + 56q^{13} - 184q^{14} - 124q^{15} - 54q^{16} + 19q^{17} - 81q^{18} - 75q^{19} + 135q^{20} - 18q^{21} - 504q^{22} + 131q^{23} - 567q^{24} + 105q^{25} + 44q^{26} + 238q^{27} - 404q^{28} + 515q^{29} - 396q^{30} + 237q^{31} + 558q^{32} + 540q^{33} - 107q^{34} + 198q^{35} + 73q^{36} + 269q^{37} + 527q^{38} + 290q^{39} + 613q^{40} + 471q^{41} + 362q^{42} - 258q^{43} - 428q^{44} + 334q^{45} - 67q^{46} + 415q^{47} - 989q^{48} + 350q^{49} + 1335q^{50} - 1241q^{51} - 8q^{52} + 450q^{53} + 402q^{54} - 1732q^{55} - 780q^{56} - 1000q^{57} - 1055q^{58} + 356q^{59} - 2732q^{60} - 1328q^{61} + 1603q^{62} - 2290q^{63} + 466q^{64} - 62q^{65} + 156q^{66} - 632q^{67} + 571q^{68} - 1130q^{69} - 1902q^{70} - 144q^{71} + 567q^{72} + 864q^{73} + 1207q^{74} - 2494q^{75} + 1005q^{76} + 2660q^{77} + 2222q^{78} - 1613q^{79} + 2399q^{80} - 102q^{81} + 1673q^{82} - 682q^{83} + 3758q^{84} + 84q^{85} - 258q^{86} + 449q^{87} - 608q^{88} + 3378q^{89} + 930q^{90} - 3900q^{91} + 3491q^{92} + 1879q^{93} + 3197q^{94} - 79q^{95} - 591q^{96} - 55q^{97} + 2398q^{98} - 1612q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.15251 1.82169 0.910844 0.412750i \(-0.135432\pi\)
0.910844 + 0.412750i \(0.135432\pi\)
\(3\) −6.49933 −1.25080 −0.625398 0.780306i \(-0.715063\pi\)
−0.625398 + 0.780306i \(0.715063\pi\)
\(4\) 18.5484 2.31855
\(5\) 17.2665 1.54437 0.772183 0.635400i \(-0.219165\pi\)
0.772183 + 0.635400i \(0.219165\pi\)
\(6\) −33.4879 −2.27856
\(7\) −23.3206 −1.25919 −0.629597 0.776922i \(-0.716780\pi\)
−0.629597 + 0.776922i \(0.716780\pi\)
\(8\) 54.3507 2.40199
\(9\) 15.2413 0.564491
\(10\) 88.9661 2.81336
\(11\) −60.5580 −1.65990 −0.829951 0.557836i \(-0.811632\pi\)
−0.829951 + 0.557836i \(0.811632\pi\)
\(12\) −120.552 −2.90003
\(13\) 10.9419 0.233441 0.116721 0.993165i \(-0.462762\pi\)
0.116721 + 0.993165i \(0.462762\pi\)
\(14\) −120.160 −2.29386
\(15\) −112.221 −1.93169
\(16\) 131.656 2.05712
\(17\) −3.57473 −0.0510000 −0.0255000 0.999675i \(-0.508118\pi\)
−0.0255000 + 0.999675i \(0.508118\pi\)
\(18\) 78.5308 1.02833
\(19\) 33.2403 0.401361 0.200680 0.979657i \(-0.435685\pi\)
0.200680 + 0.979657i \(0.435685\pi\)
\(20\) 320.267 3.58069
\(21\) 151.568 1.57499
\(22\) −312.026 −3.02383
\(23\) 63.7158 0.577637 0.288819 0.957384i \(-0.406738\pi\)
0.288819 + 0.957384i \(0.406738\pi\)
\(24\) −353.243 −3.00440
\(25\) 173.134 1.38507
\(26\) 56.3783 0.425257
\(27\) 76.4239 0.544733
\(28\) −432.560 −2.91950
\(29\) −89.3510 −0.572140 −0.286070 0.958209i \(-0.592349\pi\)
−0.286070 + 0.958209i \(0.592349\pi\)
\(30\) −578.220 −3.51893
\(31\) 222.839 1.29106 0.645532 0.763733i \(-0.276636\pi\)
0.645532 + 0.763733i \(0.276636\pi\)
\(32\) 243.552 1.34545
\(33\) 393.586 2.07620
\(34\) −18.4188 −0.0929061
\(35\) −402.666 −1.94466
\(36\) 282.701 1.30880
\(37\) −59.6535 −0.265053 −0.132527 0.991179i \(-0.542309\pi\)
−0.132527 + 0.991179i \(0.542309\pi\)
\(38\) 171.271 0.731154
\(39\) −71.1150 −0.291987
\(40\) 938.449 3.70955
\(41\) −143.837 −0.547890 −0.273945 0.961745i \(-0.588329\pi\)
−0.273945 + 0.961745i \(0.588329\pi\)
\(42\) 780.957 2.86915
\(43\) −43.0000 −0.152499
\(44\) −1123.25 −3.84857
\(45\) 263.164 0.871782
\(46\) 328.296 1.05228
\(47\) 379.013 1.17627 0.588135 0.808763i \(-0.299862\pi\)
0.588135 + 0.808763i \(0.299862\pi\)
\(48\) −855.674 −2.57304
\(49\) 200.850 0.585569
\(50\) 892.073 2.52316
\(51\) 23.2334 0.0637906
\(52\) 202.955 0.541245
\(53\) −150.129 −0.389090 −0.194545 0.980894i \(-0.562323\pi\)
−0.194545 + 0.980894i \(0.562323\pi\)
\(54\) 393.775 0.992333
\(55\) −1045.63 −2.56350
\(56\) −1267.49 −3.02457
\(57\) −216.040 −0.502021
\(58\) −460.382 −1.04226
\(59\) 207.310 0.457448 0.228724 0.973491i \(-0.426545\pi\)
0.228724 + 0.973491i \(0.426545\pi\)
\(60\) −2081.52 −4.47871
\(61\) −486.557 −1.02127 −0.510633 0.859799i \(-0.670589\pi\)
−0.510633 + 0.859799i \(0.670589\pi\)
\(62\) 1148.18 2.35192
\(63\) −355.435 −0.710804
\(64\) 201.659 0.393866
\(65\) 188.929 0.360519
\(66\) 2027.96 3.78219
\(67\) 1019.41 1.85882 0.929408 0.369054i \(-0.120318\pi\)
0.929408 + 0.369054i \(0.120318\pi\)
\(68\) −66.3055 −0.118246
\(69\) −414.110 −0.722507
\(70\) −2074.74 −3.54256
\(71\) 13.8437 0.0231400 0.0115700 0.999933i \(-0.496317\pi\)
0.0115700 + 0.999933i \(0.496317\pi\)
\(72\) 828.374 1.35590
\(73\) 411.158 0.659211 0.329605 0.944119i \(-0.393084\pi\)
0.329605 + 0.944119i \(0.393084\pi\)
\(74\) −307.365 −0.482844
\(75\) −1125.25 −1.73244
\(76\) 616.555 0.930575
\(77\) 1412.25 2.09014
\(78\) −366.421 −0.531910
\(79\) −1315.13 −1.87296 −0.936481 0.350718i \(-0.885938\pi\)
−0.936481 + 0.350718i \(0.885938\pi\)
\(80\) 2273.24 3.17695
\(81\) −908.218 −1.24584
\(82\) −741.120 −0.998085
\(83\) 813.425 1.07572 0.537861 0.843033i \(-0.319232\pi\)
0.537861 + 0.843033i \(0.319232\pi\)
\(84\) 2811.35 3.65170
\(85\) −61.7233 −0.0787627
\(86\) −221.558 −0.277805
\(87\) 580.721 0.715630
\(88\) −3291.37 −3.98706
\(89\) −350.573 −0.417535 −0.208768 0.977965i \(-0.566945\pi\)
−0.208768 + 0.977965i \(0.566945\pi\)
\(90\) 1355.96 1.58811
\(91\) −255.171 −0.293948
\(92\) 1181.83 1.33928
\(93\) −1448.30 −1.61486
\(94\) 1952.87 2.14280
\(95\) 573.946 0.619848
\(96\) −1582.92 −1.68288
\(97\) −1187.03 −1.24252 −0.621262 0.783603i \(-0.713380\pi\)
−0.621262 + 0.783603i \(0.713380\pi\)
\(98\) 1034.88 1.06672
\(99\) −922.981 −0.937001
\(100\) 3211.35 3.21135
\(101\) 469.014 0.462066 0.231033 0.972946i \(-0.425790\pi\)
0.231033 + 0.972946i \(0.425790\pi\)
\(102\) 119.710 0.116207
\(103\) −1299.82 −1.24345 −0.621725 0.783235i \(-0.713568\pi\)
−0.621725 + 0.783235i \(0.713568\pi\)
\(104\) 594.700 0.560722
\(105\) 2617.06 2.43237
\(106\) −773.541 −0.708801
\(107\) −1480.92 −1.33800 −0.669000 0.743263i \(-0.733277\pi\)
−0.669000 + 0.743263i \(0.733277\pi\)
\(108\) 1417.54 1.26299
\(109\) 350.586 0.308073 0.154037 0.988065i \(-0.450773\pi\)
0.154037 + 0.988065i \(0.450773\pi\)
\(110\) −5387.61 −4.66990
\(111\) 387.707 0.331528
\(112\) −3070.29 −2.59031
\(113\) 785.106 0.653598 0.326799 0.945094i \(-0.394030\pi\)
0.326799 + 0.945094i \(0.394030\pi\)
\(114\) −1113.15 −0.914525
\(115\) 1100.15 0.892084
\(116\) −1657.32 −1.32653
\(117\) 166.768 0.131776
\(118\) 1068.17 0.833329
\(119\) 83.3649 0.0642189
\(120\) −6099.29 −4.63989
\(121\) 2336.27 1.75528
\(122\) −2506.99 −1.86043
\(123\) 934.841 0.685299
\(124\) 4133.30 2.99340
\(125\) 831.100 0.594687
\(126\) −1831.39 −1.29486
\(127\) −731.562 −0.511147 −0.255573 0.966790i \(-0.582264\pi\)
−0.255573 + 0.966790i \(0.582264\pi\)
\(128\) −909.364 −0.627947
\(129\) 279.471 0.190745
\(130\) 973.458 0.656753
\(131\) 2462.56 1.64240 0.821202 0.570638i \(-0.193304\pi\)
0.821202 + 0.570638i \(0.193304\pi\)
\(132\) 7300.40 4.81377
\(133\) −775.184 −0.505391
\(134\) 5252.52 3.38618
\(135\) 1319.58 0.841267
\(136\) −194.289 −0.122501
\(137\) 2384.64 1.48710 0.743552 0.668678i \(-0.233139\pi\)
0.743552 + 0.668678i \(0.233139\pi\)
\(138\) −2133.71 −1.31618
\(139\) −3086.87 −1.88363 −0.941816 0.336129i \(-0.890882\pi\)
−0.941816 + 0.336129i \(0.890882\pi\)
\(140\) −7468.81 −4.50878
\(141\) −2463.33 −1.47127
\(142\) 71.3297 0.0421539
\(143\) −662.619 −0.387490
\(144\) 2006.60 1.16123
\(145\) −1542.78 −0.883594
\(146\) 2118.50 1.20088
\(147\) −1305.39 −0.732427
\(148\) −1106.48 −0.614539
\(149\) −1445.58 −0.794808 −0.397404 0.917644i \(-0.630089\pi\)
−0.397404 + 0.917644i \(0.630089\pi\)
\(150\) −5797.88 −3.15596
\(151\) −825.878 −0.445093 −0.222546 0.974922i \(-0.571437\pi\)
−0.222546 + 0.974922i \(0.571437\pi\)
\(152\) 1806.64 0.964063
\(153\) −54.4834 −0.0287891
\(154\) 7276.63 3.80758
\(155\) 3847.65 1.99388
\(156\) −1319.07 −0.676987
\(157\) 1187.82 0.603809 0.301904 0.953338i \(-0.402378\pi\)
0.301904 + 0.953338i \(0.402378\pi\)
\(158\) −6776.24 −3.41195
\(159\) 975.737 0.486673
\(160\) 4205.30 2.07786
\(161\) −1485.89 −0.727357
\(162\) −4679.61 −2.26953
\(163\) 1514.60 0.727809 0.363904 0.931436i \(-0.381443\pi\)
0.363904 + 0.931436i \(0.381443\pi\)
\(164\) −2667.94 −1.27031
\(165\) 6795.88 3.20641
\(166\) 4191.18 1.95963
\(167\) −3354.48 −1.55435 −0.777177 0.629282i \(-0.783349\pi\)
−0.777177 + 0.629282i \(0.783349\pi\)
\(168\) 8237.84 3.78312
\(169\) −2077.27 −0.945505
\(170\) −318.030 −0.143481
\(171\) 506.625 0.226565
\(172\) −797.581 −0.353575
\(173\) 1654.64 0.727166 0.363583 0.931562i \(-0.381553\pi\)
0.363583 + 0.931562i \(0.381553\pi\)
\(174\) 2992.17 1.30366
\(175\) −4037.58 −1.74407
\(176\) −7972.81 −3.41462
\(177\) −1347.38 −0.572175
\(178\) −1806.33 −0.760619
\(179\) −1334.05 −0.557049 −0.278524 0.960429i \(-0.589845\pi\)
−0.278524 + 0.960429i \(0.589845\pi\)
\(180\) 4881.27 2.02127
\(181\) 2771.58 1.13817 0.569087 0.822277i \(-0.307297\pi\)
0.569087 + 0.822277i \(0.307297\pi\)
\(182\) −1314.77 −0.535481
\(183\) 3162.29 1.27740
\(184\) 3463.00 1.38748
\(185\) −1030.01 −0.409339
\(186\) −7462.39 −2.94177
\(187\) 216.479 0.0846550
\(188\) 7030.08 2.72724
\(189\) −1782.25 −0.685924
\(190\) 2957.26 1.12917
\(191\) 81.5135 0.0308802 0.0154401 0.999881i \(-0.495085\pi\)
0.0154401 + 0.999881i \(0.495085\pi\)
\(192\) −1310.65 −0.492646
\(193\) 3305.29 1.23275 0.616373 0.787454i \(-0.288601\pi\)
0.616373 + 0.787454i \(0.288601\pi\)
\(194\) −6116.20 −2.26349
\(195\) −1227.91 −0.450936
\(196\) 3725.45 1.35767
\(197\) 2241.99 0.810840 0.405420 0.914131i \(-0.367125\pi\)
0.405420 + 0.914131i \(0.367125\pi\)
\(198\) −4755.67 −1.70692
\(199\) −4074.29 −1.45135 −0.725675 0.688037i \(-0.758472\pi\)
−0.725675 + 0.688037i \(0.758472\pi\)
\(200\) 9409.94 3.32691
\(201\) −6625.48 −2.32500
\(202\) 2416.60 0.841740
\(203\) 2083.72 0.720435
\(204\) 430.941 0.147902
\(205\) −2483.56 −0.846143
\(206\) −6697.36 −2.26518
\(207\) 971.109 0.326071
\(208\) 1440.56 0.480217
\(209\) −2012.97 −0.666220
\(210\) 13484.4 4.43102
\(211\) 4267.62 1.39239 0.696196 0.717851i \(-0.254874\pi\)
0.696196 + 0.717851i \(0.254874\pi\)
\(212\) −2784.65 −0.902125
\(213\) −89.9746 −0.0289435
\(214\) −7630.46 −2.43742
\(215\) −742.461 −0.235514
\(216\) 4153.69 1.30844
\(217\) −5196.73 −1.62570
\(218\) 1806.40 0.561214
\(219\) −2672.25 −0.824538
\(220\) −19394.7 −5.94360
\(221\) −39.1143 −0.0119055
\(222\) 1997.67 0.603940
\(223\) −889.370 −0.267070 −0.133535 0.991044i \(-0.542633\pi\)
−0.133535 + 0.991044i \(0.542633\pi\)
\(224\) −5679.78 −1.69418
\(225\) 2638.78 0.781859
\(226\) 4045.27 1.19065
\(227\) 232.389 0.0679479 0.0339739 0.999423i \(-0.489184\pi\)
0.0339739 + 0.999423i \(0.489184\pi\)
\(228\) −4007.19 −1.16396
\(229\) 851.806 0.245803 0.122902 0.992419i \(-0.460780\pi\)
0.122902 + 0.992419i \(0.460780\pi\)
\(230\) 5668.54 1.62510
\(231\) −9178.67 −2.61434
\(232\) −4856.29 −1.37427
\(233\) −2083.62 −0.585848 −0.292924 0.956136i \(-0.594628\pi\)
−0.292924 + 0.956136i \(0.594628\pi\)
\(234\) 859.276 0.240054
\(235\) 6544.24 1.81659
\(236\) 3845.27 1.06062
\(237\) 8547.48 2.34269
\(238\) 429.539 0.116987
\(239\) 986.983 0.267124 0.133562 0.991040i \(-0.457358\pi\)
0.133562 + 0.991040i \(0.457358\pi\)
\(240\) −14774.5 −3.97372
\(241\) 14.8772 0.00397644 0.00198822 0.999998i \(-0.499367\pi\)
0.00198822 + 0.999998i \(0.499367\pi\)
\(242\) 12037.7 3.19757
\(243\) 3839.36 1.01356
\(244\) −9024.85 −2.36786
\(245\) 3467.99 0.904333
\(246\) 4816.78 1.24840
\(247\) 363.712 0.0936942
\(248\) 12111.4 3.10112
\(249\) −5286.72 −1.34551
\(250\) 4282.26 1.08333
\(251\) −3027.27 −0.761274 −0.380637 0.924725i \(-0.624295\pi\)
−0.380637 + 0.924725i \(0.624295\pi\)
\(252\) −6592.76 −1.64803
\(253\) −3858.50 −0.958822
\(254\) −3769.38 −0.931150
\(255\) 401.160 0.0985161
\(256\) −6298.79 −1.53779
\(257\) 5759.92 1.39803 0.699016 0.715106i \(-0.253622\pi\)
0.699016 + 0.715106i \(0.253622\pi\)
\(258\) 1439.98 0.347477
\(259\) 1391.15 0.333753
\(260\) 3504.32 0.835881
\(261\) −1361.82 −0.322968
\(262\) 12688.4 2.99195
\(263\) 2545.09 0.596719 0.298359 0.954454i \(-0.403561\pi\)
0.298359 + 0.954454i \(0.403561\pi\)
\(264\) 21391.7 4.98700
\(265\) −2592.21 −0.600898
\(266\) −3994.15 −0.920665
\(267\) 2278.49 0.522252
\(268\) 18908.4 4.30976
\(269\) 6757.89 1.53173 0.765866 0.643001i \(-0.222311\pi\)
0.765866 + 0.643001i \(0.222311\pi\)
\(270\) 6799.13 1.53253
\(271\) 2485.54 0.557143 0.278571 0.960415i \(-0.410139\pi\)
0.278571 + 0.960415i \(0.410139\pi\)
\(272\) −470.634 −0.104913
\(273\) 1658.44 0.367669
\(274\) 12286.9 2.70904
\(275\) −10484.6 −2.29908
\(276\) −7681.07 −1.67517
\(277\) −2090.19 −0.453385 −0.226692 0.973966i \(-0.572791\pi\)
−0.226692 + 0.973966i \(0.572791\pi\)
\(278\) −15905.1 −3.43139
\(279\) 3396.34 0.728795
\(280\) −21885.2 −4.67104
\(281\) −6049.22 −1.28422 −0.642111 0.766612i \(-0.721941\pi\)
−0.642111 + 0.766612i \(0.721941\pi\)
\(282\) −12692.3 −2.68020
\(283\) −650.183 −0.136570 −0.0682851 0.997666i \(-0.521753\pi\)
−0.0682851 + 0.997666i \(0.521753\pi\)
\(284\) 256.778 0.0536513
\(285\) −3730.26 −0.775304
\(286\) −3414.16 −0.705885
\(287\) 3354.35 0.689900
\(288\) 3712.04 0.759494
\(289\) −4900.22 −0.997399
\(290\) −7949.21 −1.60963
\(291\) 7714.92 1.55415
\(292\) 7626.31 1.52841
\(293\) −2172.20 −0.433110 −0.216555 0.976270i \(-0.569482\pi\)
−0.216555 + 0.976270i \(0.569482\pi\)
\(294\) −6726.04 −1.33425
\(295\) 3579.53 0.706468
\(296\) −3242.21 −0.636654
\(297\) −4628.08 −0.904203
\(298\) −7448.36 −1.44789
\(299\) 697.171 0.134844
\(300\) −20871.6 −4.01674
\(301\) 1002.79 0.192025
\(302\) −4255.35 −0.810820
\(303\) −3048.28 −0.577950
\(304\) 4376.28 0.825648
\(305\) −8401.16 −1.57721
\(306\) −280.727 −0.0524447
\(307\) 1257.47 0.233771 0.116885 0.993145i \(-0.462709\pi\)
0.116885 + 0.993145i \(0.462709\pi\)
\(308\) 26194.9 4.84609
\(309\) 8447.98 1.55530
\(310\) 19825.1 3.63222
\(311\) −1316.02 −0.239950 −0.119975 0.992777i \(-0.538281\pi\)
−0.119975 + 0.992777i \(0.538281\pi\)
\(312\) −3865.15 −0.701350
\(313\) 3137.09 0.566514 0.283257 0.959044i \(-0.408585\pi\)
0.283257 + 0.959044i \(0.408585\pi\)
\(314\) 6120.24 1.09995
\(315\) −6137.14 −1.09774
\(316\) −24393.6 −4.34256
\(317\) 571.518 0.101261 0.0506303 0.998717i \(-0.483877\pi\)
0.0506303 + 0.998717i \(0.483877\pi\)
\(318\) 5027.50 0.886566
\(319\) 5410.92 0.949696
\(320\) 3481.96 0.608273
\(321\) 9624.99 1.67356
\(322\) −7656.07 −1.32502
\(323\) −118.825 −0.0204694
\(324\) −16846.0 −2.88854
\(325\) 1894.41 0.323332
\(326\) 7804.01 1.32584
\(327\) −2278.57 −0.385337
\(328\) −7817.62 −1.31602
\(329\) −8838.80 −1.48115
\(330\) 35015.8 5.84109
\(331\) −2257.30 −0.374841 −0.187420 0.982280i \(-0.560013\pi\)
−0.187420 + 0.982280i \(0.560013\pi\)
\(332\) 15087.7 2.49412
\(333\) −909.194 −0.149620
\(334\) −17284.0 −2.83155
\(335\) 17601.7 2.87069
\(336\) 19954.8 3.23995
\(337\) −9222.66 −1.49077 −0.745386 0.666633i \(-0.767735\pi\)
−0.745386 + 0.666633i \(0.767735\pi\)
\(338\) −10703.2 −1.72242
\(339\) −5102.66 −0.817517
\(340\) −1144.87 −0.182615
\(341\) −13494.7 −2.14304
\(342\) 2610.39 0.412730
\(343\) 3315.02 0.521849
\(344\) −2337.08 −0.366299
\(345\) −7150.24 −1.11582
\(346\) 8525.54 1.32467
\(347\) 8840.48 1.36767 0.683835 0.729636i \(-0.260311\pi\)
0.683835 + 0.729636i \(0.260311\pi\)
\(348\) 10771.4 1.65922
\(349\) 1431.64 0.219581 0.109791 0.993955i \(-0.464982\pi\)
0.109791 + 0.993955i \(0.464982\pi\)
\(350\) −20803.7 −3.17715
\(351\) 836.222 0.127163
\(352\) −14749.0 −2.23331
\(353\) −8308.06 −1.25267 −0.626336 0.779553i \(-0.715446\pi\)
−0.626336 + 0.779553i \(0.715446\pi\)
\(354\) −6942.37 −1.04232
\(355\) 239.032 0.0357367
\(356\) −6502.56 −0.968076
\(357\) −541.816 −0.0803247
\(358\) −6873.72 −1.01477
\(359\) 11642.2 1.71157 0.855786 0.517330i \(-0.173074\pi\)
0.855786 + 0.517330i \(0.173074\pi\)
\(360\) 14303.2 2.09401
\(361\) −5754.08 −0.838909
\(362\) 14280.6 2.07340
\(363\) −15184.2 −2.19549
\(364\) −4733.02 −0.681532
\(365\) 7099.27 1.01806
\(366\) 16293.8 2.32702
\(367\) 4373.93 0.622119 0.311059 0.950391i \(-0.399316\pi\)
0.311059 + 0.950391i \(0.399316\pi\)
\(368\) 8388.55 1.18827
\(369\) −2192.25 −0.309279
\(370\) −5307.14 −0.745689
\(371\) 3501.09 0.489940
\(372\) −26863.7 −3.74413
\(373\) 7970.63 1.10644 0.553222 0.833034i \(-0.313398\pi\)
0.553222 + 0.833034i \(0.313398\pi\)
\(374\) 1115.41 0.154215
\(375\) −5401.59 −0.743832
\(376\) 20599.6 2.82538
\(377\) −977.669 −0.133561
\(378\) −9183.07 −1.24954
\(379\) −2020.56 −0.273850 −0.136925 0.990581i \(-0.543722\pi\)
−0.136925 + 0.990581i \(0.543722\pi\)
\(380\) 10645.8 1.43715
\(381\) 4754.66 0.639340
\(382\) 420.000 0.0562540
\(383\) 11625.0 1.55094 0.775468 0.631386i \(-0.217514\pi\)
0.775468 + 0.631386i \(0.217514\pi\)
\(384\) 5910.26 0.785434
\(385\) 24384.7 3.22794
\(386\) 17030.5 2.24568
\(387\) −655.375 −0.0860841
\(388\) −22017.6 −2.88086
\(389\) 6212.26 0.809702 0.404851 0.914383i \(-0.367323\pi\)
0.404851 + 0.914383i \(0.367323\pi\)
\(390\) −6326.82 −0.821464
\(391\) −227.767 −0.0294595
\(392\) 10916.4 1.40653
\(393\) −16005.0 −2.05431
\(394\) 11551.9 1.47710
\(395\) −22707.8 −2.89254
\(396\) −17119.8 −2.17248
\(397\) −1647.75 −0.208307 −0.104154 0.994561i \(-0.533213\pi\)
−0.104154 + 0.994561i \(0.533213\pi\)
\(398\) −20992.8 −2.64391
\(399\) 5038.18 0.632141
\(400\) 22794.0 2.84925
\(401\) 6893.37 0.858450 0.429225 0.903198i \(-0.358787\pi\)
0.429225 + 0.903198i \(0.358787\pi\)
\(402\) −34137.8 −4.23543
\(403\) 2438.28 0.301388
\(404\) 8699.46 1.07132
\(405\) −15681.8 −1.92404
\(406\) 10736.4 1.31241
\(407\) 3612.49 0.439962
\(408\) 1262.75 0.153224
\(409\) −2962.23 −0.358125 −0.179062 0.983838i \(-0.557306\pi\)
−0.179062 + 0.983838i \(0.557306\pi\)
\(410\) −12796.6 −1.54141
\(411\) −15498.5 −1.86006
\(412\) −24109.6 −2.88300
\(413\) −4834.59 −0.576016
\(414\) 5003.65 0.594000
\(415\) 14045.0 1.66131
\(416\) 2664.92 0.314083
\(417\) 20062.6 2.35604
\(418\) −10371.8 −1.21365
\(419\) −5520.25 −0.643633 −0.321816 0.946802i \(-0.604293\pi\)
−0.321816 + 0.946802i \(0.604293\pi\)
\(420\) 48542.2 5.63957
\(421\) 11017.9 1.27548 0.637742 0.770250i \(-0.279868\pi\)
0.637742 + 0.770250i \(0.279868\pi\)
\(422\) 21989.0 2.53651
\(423\) 5776.63 0.663994
\(424\) −8159.61 −0.934589
\(425\) −618.906 −0.0706385
\(426\) −463.595 −0.0527260
\(427\) 11346.8 1.28597
\(428\) −27468.7 −3.10222
\(429\) 4306.58 0.484671
\(430\) −3825.54 −0.429033
\(431\) 8825.55 0.986338 0.493169 0.869934i \(-0.335838\pi\)
0.493169 + 0.869934i \(0.335838\pi\)
\(432\) 10061.6 1.12058
\(433\) 4570.88 0.507303 0.253652 0.967296i \(-0.418368\pi\)
0.253652 + 0.967296i \(0.418368\pi\)
\(434\) −26776.2 −2.96152
\(435\) 10027.0 1.10520
\(436\) 6502.80 0.714283
\(437\) 2117.93 0.231841
\(438\) −13768.8 −1.50205
\(439\) −3059.73 −0.332649 −0.166325 0.986071i \(-0.553190\pi\)
−0.166325 + 0.986071i \(0.553190\pi\)
\(440\) −56830.6 −6.15749
\(441\) 3061.21 0.330549
\(442\) −201.537 −0.0216881
\(443\) −2764.55 −0.296496 −0.148248 0.988950i \(-0.547363\pi\)
−0.148248 + 0.988950i \(0.547363\pi\)
\(444\) 7191.35 0.768663
\(445\) −6053.18 −0.644828
\(446\) −4582.49 −0.486518
\(447\) 9395.29 0.994143
\(448\) −4702.82 −0.495954
\(449\) 7567.33 0.795377 0.397688 0.917521i \(-0.369812\pi\)
0.397688 + 0.917521i \(0.369812\pi\)
\(450\) 13596.3 1.42430
\(451\) 8710.46 0.909444
\(452\) 14562.4 1.51540
\(453\) 5367.65 0.556720
\(454\) 1197.38 0.123780
\(455\) −4405.93 −0.453963
\(456\) −11741.9 −1.20585
\(457\) −8079.05 −0.826963 −0.413482 0.910512i \(-0.635687\pi\)
−0.413482 + 0.910512i \(0.635687\pi\)
\(458\) 4388.94 0.447777
\(459\) −273.195 −0.0277813
\(460\) 20406.0 2.06834
\(461\) 14466.4 1.46154 0.730770 0.682624i \(-0.239161\pi\)
0.730770 + 0.682624i \(0.239161\pi\)
\(462\) −47293.2 −4.76251
\(463\) −7966.79 −0.799672 −0.399836 0.916587i \(-0.630933\pi\)
−0.399836 + 0.916587i \(0.630933\pi\)
\(464\) −11763.6 −1.17696
\(465\) −25007.2 −2.49393
\(466\) −10735.9 −1.06723
\(467\) 6737.29 0.667590 0.333795 0.942646i \(-0.391671\pi\)
0.333795 + 0.942646i \(0.391671\pi\)
\(468\) 3093.29 0.305528
\(469\) −23773.2 −2.34061
\(470\) 33719.3 3.30927
\(471\) −7720.00 −0.755242
\(472\) 11267.4 1.09878
\(473\) 2603.99 0.253133
\(474\) 44041.0 4.26766
\(475\) 5755.02 0.555912
\(476\) 1546.28 0.148895
\(477\) −2288.15 −0.219638
\(478\) 5085.44 0.486616
\(479\) −18115.7 −1.72803 −0.864014 0.503468i \(-0.832057\pi\)
−0.864014 + 0.503468i \(0.832057\pi\)
\(480\) −27331.6 −2.59899
\(481\) −652.722 −0.0618743
\(482\) 76.6548 0.00724384
\(483\) 9657.28 0.909776
\(484\) 43334.1 4.06969
\(485\) −20496.0 −1.91891
\(486\) 19782.4 1.84639
\(487\) −14966.4 −1.39260 −0.696298 0.717753i \(-0.745171\pi\)
−0.696298 + 0.717753i \(0.745171\pi\)
\(488\) −26444.7 −2.45307
\(489\) −9843.90 −0.910341
\(490\) 17868.8 1.64741
\(491\) −15713.8 −1.44430 −0.722151 0.691736i \(-0.756846\pi\)
−0.722151 + 0.691736i \(0.756846\pi\)
\(492\) 17339.8 1.58890
\(493\) 319.406 0.0291791
\(494\) 1874.03 0.170682
\(495\) −15936.7 −1.44707
\(496\) 29338.0 2.65588
\(497\) −322.843 −0.0291378
\(498\) −27239.9 −2.45110
\(499\) −15391.5 −1.38080 −0.690398 0.723430i \(-0.742565\pi\)
−0.690398 + 0.723430i \(0.742565\pi\)
\(500\) 15415.6 1.37881
\(501\) 21801.8 1.94418
\(502\) −15598.1 −1.38680
\(503\) −12150.9 −1.07710 −0.538548 0.842595i \(-0.681027\pi\)
−0.538548 + 0.842595i \(0.681027\pi\)
\(504\) −19318.2 −1.70734
\(505\) 8098.25 0.713599
\(506\) −19881.0 −1.74667
\(507\) 13500.9 1.18263
\(508\) −13569.3 −1.18512
\(509\) 16646.6 1.44960 0.724799 0.688960i \(-0.241933\pi\)
0.724799 + 0.688960i \(0.241933\pi\)
\(510\) 2066.98 0.179466
\(511\) −9588.44 −0.830074
\(512\) −25179.7 −2.17343
\(513\) 2540.35 0.218634
\(514\) 29678.1 2.54678
\(515\) −22443.5 −1.92034
\(516\) 5183.74 0.442251
\(517\) −22952.3 −1.95249
\(518\) 7167.94 0.607995
\(519\) −10754.0 −0.909536
\(520\) 10268.4 0.865961
\(521\) 16675.9 1.40227 0.701135 0.713028i \(-0.252677\pi\)
0.701135 + 0.713028i \(0.252677\pi\)
\(522\) −7016.81 −0.588347
\(523\) 14326.5 1.19781 0.598903 0.800821i \(-0.295603\pi\)
0.598903 + 0.800821i \(0.295603\pi\)
\(524\) 45676.5 3.80799
\(525\) 26241.5 2.18148
\(526\) 13113.6 1.08704
\(527\) −796.588 −0.0658443
\(528\) 51817.9 4.27099
\(529\) −8107.30 −0.666335
\(530\) −13356.4 −1.09465
\(531\) 3159.67 0.258226
\(532\) −14378.4 −1.17177
\(533\) −1573.84 −0.127900
\(534\) 11739.9 0.951380
\(535\) −25570.4 −2.06636
\(536\) 55405.6 4.46485
\(537\) 8670.44 0.696754
\(538\) 34820.1 2.79034
\(539\) −12163.1 −0.971987
\(540\) 24476.0 1.95052
\(541\) −8159.73 −0.648455 −0.324228 0.945979i \(-0.605104\pi\)
−0.324228 + 0.945979i \(0.605104\pi\)
\(542\) 12806.8 1.01494
\(543\) −18013.4 −1.42362
\(544\) −870.633 −0.0686178
\(545\) 6053.40 0.475778
\(546\) 8545.15 0.669778
\(547\) −6089.67 −0.476006 −0.238003 0.971264i \(-0.576493\pi\)
−0.238003 + 0.971264i \(0.576493\pi\)
\(548\) 44231.2 3.44793
\(549\) −7415.74 −0.576496
\(550\) −54022.2 −4.18821
\(551\) −2970.06 −0.229635
\(552\) −22507.2 −1.73545
\(553\) 30669.7 2.35842
\(554\) −10769.8 −0.825926
\(555\) 6694.37 0.512000
\(556\) −57256.5 −4.36729
\(557\) 4160.66 0.316504 0.158252 0.987399i \(-0.449414\pi\)
0.158252 + 0.987399i \(0.449414\pi\)
\(558\) 17499.7 1.32764
\(559\) −470.501 −0.0355995
\(560\) −53013.3 −4.00039
\(561\) −1406.97 −0.105886
\(562\) −31168.7 −2.33945
\(563\) 7731.24 0.578744 0.289372 0.957217i \(-0.406554\pi\)
0.289372 + 0.957217i \(0.406554\pi\)
\(564\) −45690.8 −3.41122
\(565\) 13556.1 1.00939
\(566\) −3350.08 −0.248788
\(567\) 21180.2 1.56875
\(568\) 752.414 0.0555820
\(569\) 9134.32 0.672989 0.336494 0.941685i \(-0.390759\pi\)
0.336494 + 0.941685i \(0.390759\pi\)
\(570\) −19220.2 −1.41236
\(571\) 10421.5 0.763797 0.381898 0.924204i \(-0.375270\pi\)
0.381898 + 0.924204i \(0.375270\pi\)
\(572\) −12290.5 −0.898414
\(573\) −529.783 −0.0386248
\(574\) 17283.4 1.25678
\(575\) 11031.3 0.800067
\(576\) 3073.54 0.222334
\(577\) 806.571 0.0581941 0.0290971 0.999577i \(-0.490737\pi\)
0.0290971 + 0.999577i \(0.490737\pi\)
\(578\) −25248.5 −1.81695
\(579\) −21482.2 −1.54191
\(580\) −28616.1 −2.04866
\(581\) −18969.6 −1.35454
\(582\) 39751.2 2.83117
\(583\) 9091.50 0.645852
\(584\) 22346.7 1.58341
\(585\) 2879.51 0.203510
\(586\) −11192.3 −0.788992
\(587\) 11514.2 0.809614 0.404807 0.914402i \(-0.367339\pi\)
0.404807 + 0.914402i \(0.367339\pi\)
\(588\) −24212.9 −1.69817
\(589\) 7407.23 0.518183
\(590\) 18443.6 1.28696
\(591\) −14571.5 −1.01420
\(592\) −7853.72 −0.545246
\(593\) 2702.41 0.187141 0.0935706 0.995613i \(-0.470172\pi\)
0.0935706 + 0.995613i \(0.470172\pi\)
\(594\) −23846.2 −1.64718
\(595\) 1439.42 0.0991775
\(596\) −26813.1 −1.84280
\(597\) 26480.1 1.81534
\(598\) 3592.18 0.245644
\(599\) −27360.1 −1.86628 −0.933142 0.359507i \(-0.882945\pi\)
−0.933142 + 0.359507i \(0.882945\pi\)
\(600\) −61158.3 −4.16129
\(601\) −11506.8 −0.780985 −0.390492 0.920606i \(-0.627695\pi\)
−0.390492 + 0.920606i \(0.627695\pi\)
\(602\) 5166.87 0.349810
\(603\) 15537.1 1.04929
\(604\) −15318.7 −1.03197
\(605\) 40339.4 2.71079
\(606\) −15706.3 −1.05285
\(607\) 8189.12 0.547588 0.273794 0.961788i \(-0.411721\pi\)
0.273794 + 0.961788i \(0.411721\pi\)
\(608\) 8095.75 0.540010
\(609\) −13542.8 −0.901117
\(610\) −43287.1 −2.87318
\(611\) 4147.12 0.274590
\(612\) −1010.58 −0.0667488
\(613\) −24210.1 −1.59517 −0.797583 0.603209i \(-0.793889\pi\)
−0.797583 + 0.603209i \(0.793889\pi\)
\(614\) 6479.14 0.425858
\(615\) 16141.5 1.05835
\(616\) 76756.8 5.02048
\(617\) −8779.45 −0.572848 −0.286424 0.958103i \(-0.592467\pi\)
−0.286424 + 0.958103i \(0.592467\pi\)
\(618\) 43528.3 2.83328
\(619\) −6089.56 −0.395412 −0.197706 0.980261i \(-0.563349\pi\)
−0.197706 + 0.980261i \(0.563349\pi\)
\(620\) 71367.8 4.62290
\(621\) 4869.40 0.314658
\(622\) −6780.79 −0.437114
\(623\) 8175.57 0.525758
\(624\) −9362.69 −0.600653
\(625\) −7291.47 −0.466654
\(626\) 16163.9 1.03201
\(627\) 13082.9 0.833305
\(628\) 22032.1 1.39996
\(629\) 213.245 0.0135177
\(630\) −31621.7 −1.99974
\(631\) 13768.3 0.868634 0.434317 0.900760i \(-0.356990\pi\)
0.434317 + 0.900760i \(0.356990\pi\)
\(632\) −71478.5 −4.49883
\(633\) −27736.6 −1.74160
\(634\) 2944.75 0.184465
\(635\) −12631.5 −0.789398
\(636\) 18098.3 1.12837
\(637\) 2197.68 0.136696
\(638\) 27879.8 1.73005
\(639\) 210.995 0.0130623
\(640\) −15701.6 −0.969780
\(641\) 393.612 0.0242539 0.0121269 0.999926i \(-0.496140\pi\)
0.0121269 + 0.999926i \(0.496140\pi\)
\(642\) 49592.9 3.04871
\(643\) −29944.9 −1.83656 −0.918281 0.395929i \(-0.870423\pi\)
−0.918281 + 0.395929i \(0.870423\pi\)
\(644\) −27560.9 −1.68641
\(645\) 4825.50 0.294580
\(646\) −612.249 −0.0372889
\(647\) −8372.05 −0.508716 −0.254358 0.967110i \(-0.581864\pi\)
−0.254358 + 0.967110i \(0.581864\pi\)
\(648\) −49362.3 −2.99249
\(649\) −12554.3 −0.759320
\(650\) 9760.97 0.589010
\(651\) 33775.3 2.03342
\(652\) 28093.4 1.68746
\(653\) 7203.34 0.431682 0.215841 0.976429i \(-0.430751\pi\)
0.215841 + 0.976429i \(0.430751\pi\)
\(654\) −11740.4 −0.701964
\(655\) 42519.9 2.53647
\(656\) −18936.9 −1.12708
\(657\) 6266.56 0.372119
\(658\) −45542.0 −2.69820
\(659\) −28054.8 −1.65836 −0.829182 0.558979i \(-0.811193\pi\)
−0.829182 + 0.558979i \(0.811193\pi\)
\(660\) 126053. 7.43423
\(661\) −11582.1 −0.681531 −0.340766 0.940148i \(-0.610686\pi\)
−0.340766 + 0.940148i \(0.610686\pi\)
\(662\) −11630.8 −0.682843
\(663\) 254.217 0.0148914
\(664\) 44210.2 2.58387
\(665\) −13384.8 −0.780509
\(666\) −4684.64 −0.272561
\(667\) −5693.07 −0.330489
\(668\) −62220.1 −3.60385
\(669\) 5780.31 0.334050
\(670\) 90692.9 5.22951
\(671\) 29464.9 1.69520
\(672\) 36914.7 2.11907
\(673\) 9582.65 0.548862 0.274431 0.961607i \(-0.411511\pi\)
0.274431 + 0.961607i \(0.411511\pi\)
\(674\) −47519.9 −2.71572
\(675\) 13231.5 0.754492
\(676\) −38530.1 −2.19220
\(677\) 8247.63 0.468216 0.234108 0.972211i \(-0.424783\pi\)
0.234108 + 0.972211i \(0.424783\pi\)
\(678\) −26291.5 −1.48926
\(679\) 27682.3 1.56458
\(680\) −3354.70 −0.189187
\(681\) −1510.37 −0.0849890
\(682\) −69531.5 −3.90395
\(683\) 23171.1 1.29812 0.649061 0.760736i \(-0.275162\pi\)
0.649061 + 0.760736i \(0.275162\pi\)
\(684\) 9397.08 0.525301
\(685\) 41174.4 2.29663
\(686\) 17080.7 0.950647
\(687\) −5536.16 −0.307450
\(688\) −5661.20 −0.313708
\(689\) −1642.69 −0.0908297
\(690\) −36841.7 −2.03267
\(691\) 24019.8 1.32237 0.661185 0.750223i \(-0.270054\pi\)
0.661185 + 0.750223i \(0.270054\pi\)
\(692\) 30690.8 1.68597
\(693\) 21524.5 1.17987
\(694\) 45550.7 2.49147
\(695\) −53299.6 −2.90902
\(696\) 31562.6 1.71893
\(697\) 514.177 0.0279424
\(698\) 7376.54 0.400009
\(699\) 13542.1 0.732776
\(700\) −74890.6 −4.04371
\(701\) −756.339 −0.0407511 −0.0203755 0.999792i \(-0.506486\pi\)
−0.0203755 + 0.999792i \(0.506486\pi\)
\(702\) 4308.64 0.231651
\(703\) −1982.90 −0.106382
\(704\) −12212.1 −0.653779
\(705\) −42533.2 −2.27219
\(706\) −42807.4 −2.28198
\(707\) −10937.7 −0.581830
\(708\) −24991.7 −1.32662
\(709\) −26580.1 −1.40795 −0.703975 0.710224i \(-0.748594\pi\)
−0.703975 + 0.710224i \(0.748594\pi\)
\(710\) 1231.62 0.0651011
\(711\) −20044.3 −1.05727
\(712\) −19053.9 −1.00291
\(713\) 14198.3 0.745767
\(714\) −2791.71 −0.146327
\(715\) −11441.1 −0.598426
\(716\) −24744.5 −1.29154
\(717\) −6414.72 −0.334118
\(718\) 59986.8 3.11795
\(719\) 14125.2 0.732656 0.366328 0.930486i \(-0.380615\pi\)
0.366328 + 0.930486i \(0.380615\pi\)
\(720\) 34647.1 1.79336
\(721\) 30312.7 1.56575
\(722\) −29648.0 −1.52823
\(723\) −96.6916 −0.00497372
\(724\) 51408.3 2.63891
\(725\) −15469.6 −0.792453
\(726\) −78236.8 −3.99951
\(727\) −19206.2 −0.979805 −0.489903 0.871777i \(-0.662968\pi\)
−0.489903 + 0.871777i \(0.662968\pi\)
\(728\) −13868.8 −0.706058
\(729\) −431.393 −0.0219170
\(730\) 36579.1 1.85459
\(731\) 153.713 0.00777742
\(732\) 58655.5 2.96170
\(733\) −29831.4 −1.50320 −0.751602 0.659617i \(-0.770718\pi\)
−0.751602 + 0.659617i \(0.770718\pi\)
\(734\) 22536.8 1.13331
\(735\) −22539.6 −1.13114
\(736\) 15518.1 0.777181
\(737\) −61733.4 −3.08545
\(738\) −11295.6 −0.563411
\(739\) 11720.8 0.583431 0.291715 0.956505i \(-0.405774\pi\)
0.291715 + 0.956505i \(0.405774\pi\)
\(740\) −19105.0 −0.949073
\(741\) −2363.89 −0.117192
\(742\) 18039.4 0.892518
\(743\) 4257.57 0.210222 0.105111 0.994460i \(-0.466480\pi\)
0.105111 + 0.994460i \(0.466480\pi\)
\(744\) −78716.3 −3.87887
\(745\) −24960.1 −1.22747
\(746\) 41068.8 2.01560
\(747\) 12397.6 0.607236
\(748\) 4015.33 0.196277
\(749\) 34535.9 1.68480
\(750\) −27831.8 −1.35503
\(751\) −16414.4 −0.797564 −0.398782 0.917046i \(-0.630567\pi\)
−0.398782 + 0.917046i \(0.630567\pi\)
\(752\) 49899.2 2.41973
\(753\) 19675.2 0.952199
\(754\) −5037.45 −0.243307
\(755\) −14260.1 −0.687386
\(756\) −33057.9 −1.59035
\(757\) −22813.5 −1.09534 −0.547668 0.836696i \(-0.684484\pi\)
−0.547668 + 0.836696i \(0.684484\pi\)
\(758\) −10410.9 −0.498869
\(759\) 25077.7 1.19929
\(760\) 31194.4 1.48887
\(761\) 1695.44 0.0807617 0.0403808 0.999184i \(-0.487143\pi\)
0.0403808 + 0.999184i \(0.487143\pi\)
\(762\) 24498.5 1.16468
\(763\) −8175.86 −0.387924
\(764\) 1511.95 0.0715972
\(765\) −940.741 −0.0444609
\(766\) 59897.9 2.82532
\(767\) 2268.36 0.106787
\(768\) 40937.9 1.92346
\(769\) 21604.9 1.01313 0.506563 0.862203i \(-0.330916\pi\)
0.506563 + 0.862203i \(0.330916\pi\)
\(770\) 125642. 5.88030
\(771\) −37435.6 −1.74865
\(772\) 61307.8 2.85818
\(773\) 34435.4 1.60227 0.801136 0.598482i \(-0.204229\pi\)
0.801136 + 0.598482i \(0.204229\pi\)
\(774\) −3376.83 −0.156818
\(775\) 38580.9 1.78821
\(776\) −64516.1 −2.98453
\(777\) −9041.57 −0.417457
\(778\) 32008.8 1.47503
\(779\) −4781.18 −0.219902
\(780\) −22775.8 −1.04552
\(781\) −838.345 −0.0384102
\(782\) −1173.57 −0.0536660
\(783\) −6828.54 −0.311663
\(784\) 26443.1 1.20459
\(785\) 20509.5 0.932502
\(786\) −82465.9 −3.74232
\(787\) −12352.5 −0.559490 −0.279745 0.960074i \(-0.590250\pi\)
−0.279745 + 0.960074i \(0.590250\pi\)
\(788\) 41585.4 1.87997
\(789\) −16541.4 −0.746374
\(790\) −117002. −5.26931
\(791\) −18309.1 −0.823006
\(792\) −50164.7 −2.25066
\(793\) −5323.85 −0.238406
\(794\) −8490.03 −0.379471
\(795\) 16847.6 0.751601
\(796\) −75571.5 −3.36503
\(797\) 29811.8 1.32495 0.662477 0.749083i \(-0.269505\pi\)
0.662477 + 0.749083i \(0.269505\pi\)
\(798\) 25959.3 1.15156
\(799\) −1354.87 −0.0599897
\(800\) 42167.0 1.86354
\(801\) −5343.17 −0.235695
\(802\) 35518.2 1.56383
\(803\) −24898.9 −1.09423
\(804\) −122892. −5.39063
\(805\) −25656.2 −1.12331
\(806\) 12563.3 0.549035
\(807\) −43921.7 −1.91588
\(808\) 25491.3 1.10988
\(809\) −1273.45 −0.0553424 −0.0276712 0.999617i \(-0.508809\pi\)
−0.0276712 + 0.999617i \(0.508809\pi\)
\(810\) −80800.6 −3.50499
\(811\) 37825.5 1.63777 0.818886 0.573956i \(-0.194592\pi\)
0.818886 + 0.573956i \(0.194592\pi\)
\(812\) 38649.6 1.67036
\(813\) −16154.3 −0.696872
\(814\) 18613.4 0.801475
\(815\) 26152.0 1.12400
\(816\) 3058.80 0.131225
\(817\) −1429.33 −0.0612070
\(818\) −15262.9 −0.652391
\(819\) −3889.14 −0.165931
\(820\) −46066.1 −1.96182
\(821\) 189.193 0.00804247 0.00402124 0.999992i \(-0.498720\pi\)
0.00402124 + 0.999992i \(0.498720\pi\)
\(822\) −79856.4 −3.38846
\(823\) 26388.5 1.11767 0.558837 0.829278i \(-0.311248\pi\)
0.558837 + 0.829278i \(0.311248\pi\)
\(824\) −70646.4 −2.98675
\(825\) 68143.0 2.87568
\(826\) −24910.3 −1.04932
\(827\) −37247.2 −1.56616 −0.783079 0.621923i \(-0.786352\pi\)
−0.783079 + 0.621923i \(0.786352\pi\)
\(828\) 18012.5 0.756012
\(829\) −18429.8 −0.772128 −0.386064 0.922472i \(-0.626166\pi\)
−0.386064 + 0.922472i \(0.626166\pi\)
\(830\) 72367.2 3.02639
\(831\) 13584.9 0.567092
\(832\) 2206.54 0.0919445
\(833\) −717.985 −0.0298640
\(834\) 103373. 4.29197
\(835\) −57920.2 −2.40049
\(836\) −37337.3 −1.54466
\(837\) 17030.2 0.703285
\(838\) −28443.2 −1.17250
\(839\) 24344.3 1.00174 0.500870 0.865523i \(-0.333014\pi\)
0.500870 + 0.865523i \(0.333014\pi\)
\(840\) 142239. 5.84252
\(841\) −16405.4 −0.672656
\(842\) 56769.8 2.32354
\(843\) 39315.9 1.60630
\(844\) 79157.5 3.22833
\(845\) −35867.4 −1.46021
\(846\) 29764.2 1.20959
\(847\) −54483.3 −2.21023
\(848\) −19765.3 −0.800406
\(849\) 4225.75 0.170822
\(850\) −3188.92 −0.128681
\(851\) −3800.87 −0.153105
\(852\) −1668.88 −0.0671068
\(853\) 14146.8 0.567852 0.283926 0.958846i \(-0.408363\pi\)
0.283926 + 0.958846i \(0.408363\pi\)
\(854\) 58464.5 2.34264
\(855\) 8747.66 0.349899
\(856\) −80489.1 −3.21386
\(857\) 8682.05 0.346060 0.173030 0.984917i \(-0.444644\pi\)
0.173030 + 0.984917i \(0.444644\pi\)
\(858\) 22189.7 0.882919
\(859\) −25428.8 −1.01003 −0.505017 0.863110i \(-0.668514\pi\)
−0.505017 + 0.863110i \(0.668514\pi\)
\(860\) −13771.5 −0.546050
\(861\) −21801.0 −0.862924
\(862\) 45473.7 1.79680
\(863\) −39552.6 −1.56012 −0.780062 0.625703i \(-0.784812\pi\)
−0.780062 + 0.625703i \(0.784812\pi\)
\(864\) 18613.2 0.732909
\(865\) 28569.9 1.12301
\(866\) 23551.5 0.924148
\(867\) 31848.1 1.24754
\(868\) −96391.0 −3.76927
\(869\) 79641.9 3.10894
\(870\) 51664.5 2.01332
\(871\) 11154.3 0.433924
\(872\) 19054.6 0.739988
\(873\) −18091.9 −0.701395
\(874\) 10912.7 0.422342
\(875\) −19381.8 −0.748826
\(876\) −49565.9 −1.91173
\(877\) 1955.60 0.0752975 0.0376487 0.999291i \(-0.488013\pi\)
0.0376487 + 0.999291i \(0.488013\pi\)
\(878\) −15765.3 −0.605983
\(879\) 14117.8 0.541733
\(880\) −137663. −5.27343
\(881\) 3037.09 0.116143 0.0580716 0.998312i \(-0.481505\pi\)
0.0580716 + 0.998312i \(0.481505\pi\)
\(882\) 15772.9 0.602157
\(883\) 15702.3 0.598443 0.299222 0.954184i \(-0.403273\pi\)
0.299222 + 0.954184i \(0.403273\pi\)
\(884\) −725.508 −0.0276035
\(885\) −23264.5 −0.883648
\(886\) −14244.4 −0.540123
\(887\) 2964.83 0.112231 0.0561157 0.998424i \(-0.482128\pi\)
0.0561157 + 0.998424i \(0.482128\pi\)
\(888\) 21072.2 0.796324
\(889\) 17060.5 0.643633
\(890\) −31189.1 −1.17467
\(891\) 54999.9 2.06797
\(892\) −16496.4 −0.619215
\(893\) 12598.5 0.472109
\(894\) 48409.3 1.81102
\(895\) −23034.5 −0.860287
\(896\) 21206.9 0.790707
\(897\) −4531.14 −0.168663
\(898\) 38990.8 1.44893
\(899\) −19910.9 −0.738670
\(900\) 48945.0 1.81278
\(901\) 536.670 0.0198436
\(902\) 44880.7 1.65672
\(903\) −6517.43 −0.240184
\(904\) 42671.1 1.56993
\(905\) 47855.5 1.75776
\(906\) 27656.9 1.01417
\(907\) 47065.4 1.72302 0.861511 0.507738i \(-0.169518\pi\)
0.861511 + 0.507738i \(0.169518\pi\)
\(908\) 4310.43 0.157540
\(909\) 7148.37 0.260832
\(910\) −22701.6 −0.826979
\(911\) −40218.3 −1.46267 −0.731335 0.682018i \(-0.761102\pi\)
−0.731335 + 0.682018i \(0.761102\pi\)
\(912\) −28442.9 −1.03272
\(913\) −49259.4 −1.78559
\(914\) −41627.4 −1.50647
\(915\) 54601.9 1.97277
\(916\) 15799.6 0.569906
\(917\) −57428.4 −2.06810
\(918\) −1407.64 −0.0506090
\(919\) −13015.3 −0.467175 −0.233587 0.972336i \(-0.575047\pi\)
−0.233587 + 0.972336i \(0.575047\pi\)
\(920\) 59794.0 2.14277
\(921\) −8172.72 −0.292400
\(922\) 74538.6 2.66247
\(923\) 151.476 0.00540184
\(924\) −170250. −6.06147
\(925\) −10328.0 −0.367117
\(926\) −41049.0 −1.45675
\(927\) −19811.0 −0.701917
\(928\) −21761.6 −0.769784
\(929\) −17365.8 −0.613298 −0.306649 0.951823i \(-0.599208\pi\)
−0.306649 + 0.951823i \(0.599208\pi\)
\(930\) −128850. −4.54317
\(931\) 6676.32 0.235024
\(932\) −38647.8 −1.35832
\(933\) 8553.22 0.300128
\(934\) 34714.0 1.21614
\(935\) 3737.84 0.130738
\(936\) 9063.98 0.316523
\(937\) −41655.6 −1.45232 −0.726162 0.687523i \(-0.758698\pi\)
−0.726162 + 0.687523i \(0.758698\pi\)
\(938\) −122492. −4.26386
\(939\) −20389.0 −0.708593
\(940\) 121385. 4.21186
\(941\) −11377.5 −0.394149 −0.197075 0.980388i \(-0.563144\pi\)
−0.197075 + 0.980388i \(0.563144\pi\)
\(942\) −39777.4 −1.37582
\(943\) −9164.66 −0.316482
\(944\) 27293.5 0.941027
\(945\) −30773.3 −1.05932
\(946\) 13417.1 0.461129
\(947\) 39835.0 1.36691 0.683455 0.729992i \(-0.260476\pi\)
0.683455 + 0.729992i \(0.260476\pi\)
\(948\) 158542. 5.43165
\(949\) 4498.84 0.153887
\(950\) 29652.8 1.01270
\(951\) −3714.48 −0.126656
\(952\) 4530.94 0.154253
\(953\) 16468.3 0.559769 0.279885 0.960034i \(-0.409704\pi\)
0.279885 + 0.960034i \(0.409704\pi\)
\(954\) −11789.7 −0.400112
\(955\) 1407.46 0.0476903
\(956\) 18306.9 0.619340
\(957\) −35167.3 −1.18788
\(958\) −93341.2 −3.14793
\(959\) −55611.2 −1.87255
\(960\) −22630.4 −0.760826
\(961\) 19866.1 0.666848
\(962\) −3363.16 −0.112716
\(963\) −22571.1 −0.755289
\(964\) 275.948 0.00921958
\(965\) 57070.9 1.90381
\(966\) 49759.3 1.65733
\(967\) 55135.3 1.83354 0.916770 0.399416i \(-0.130787\pi\)
0.916770 + 0.399416i \(0.130787\pi\)
\(968\) 126978. 4.21615
\(969\) 772.284 0.0256030
\(970\) −105606. −3.49566
\(971\) −13040.1 −0.430975 −0.215488 0.976507i \(-0.569134\pi\)
−0.215488 + 0.976507i \(0.569134\pi\)
\(972\) 71214.0 2.34999
\(973\) 71987.6 2.37186
\(974\) −77114.7 −2.53687
\(975\) −12312.4 −0.404423
\(976\) −64058.0 −2.10087
\(977\) −45144.9 −1.47831 −0.739157 0.673534i \(-0.764776\pi\)
−0.739157 + 0.673534i \(0.764776\pi\)
\(978\) −50720.8 −1.65836
\(979\) 21230.0 0.693068
\(980\) 64325.6 2.09674
\(981\) 5343.37 0.173905
\(982\) −80965.4 −2.63107
\(983\) −26573.6 −0.862225 −0.431113 0.902298i \(-0.641879\pi\)
−0.431113 + 0.902298i \(0.641879\pi\)
\(984\) 50809.3 1.64608
\(985\) 38711.5 1.25223
\(986\) 1645.74 0.0531553
\(987\) 57446.3 1.85262
\(988\) 6746.28 0.217235
\(989\) −2739.78 −0.0880889
\(990\) −82114.0 −2.63612
\(991\) 20658.0 0.662183 0.331092 0.943599i \(-0.392583\pi\)
0.331092 + 0.943599i \(0.392583\pi\)
\(992\) 54272.8 1.73706
\(993\) 14670.9 0.468850
\(994\) −1663.45 −0.0530800
\(995\) −70348.9 −2.24142
\(996\) −98060.1 −3.11963
\(997\) −27284.2 −0.866701 −0.433350 0.901226i \(-0.642669\pi\)
−0.433350 + 0.901226i \(0.642669\pi\)
\(998\) −79304.8 −2.51538
\(999\) −4558.95 −0.144383
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 43.4.a.b.1.6 6
3.2 odd 2 387.4.a.h.1.1 6
4.3 odd 2 688.4.a.i.1.5 6
5.4 even 2 1075.4.a.b.1.1 6
7.6 odd 2 2107.4.a.c.1.6 6
43.42 odd 2 1849.4.a.c.1.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.4.a.b.1.6 6 1.1 even 1 trivial
387.4.a.h.1.1 6 3.2 odd 2
688.4.a.i.1.5 6 4.3 odd 2
1075.4.a.b.1.1 6 5.4 even 2
1849.4.a.c.1.1 6 43.42 odd 2
2107.4.a.c.1.6 6 7.6 odd 2