Properties

Label 1849.4.a.g.1.1
Level $1849$
Weight $4$
Character 1849.1
Self dual yes
Analytic conductor $109.095$
Analytic rank $1$
Dimension $30$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1849 = 43^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1849.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(109.094531601\)
Analytic rank: \(1\)
Dimension: \(30\)
Twist minimal: no (minimal twist has level 43)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1849.1

$q$-expansion

\(f(q)\) \(=\) \(q-5.55308 q^{2} +6.73841 q^{3} +22.8367 q^{4} +8.33670 q^{5} -37.4189 q^{6} -27.2593 q^{7} -82.3895 q^{8} +18.4062 q^{9} +O(q^{10})\) \(q-5.55308 q^{2} +6.73841 q^{3} +22.8367 q^{4} +8.33670 q^{5} -37.4189 q^{6} -27.2593 q^{7} -82.3895 q^{8} +18.4062 q^{9} -46.2944 q^{10} -9.89891 q^{11} +153.883 q^{12} +35.8596 q^{13} +151.373 q^{14} +56.1761 q^{15} +274.822 q^{16} -29.5381 q^{17} -102.211 q^{18} -35.3382 q^{19} +190.383 q^{20} -183.684 q^{21} +54.9695 q^{22} +19.2208 q^{23} -555.174 q^{24} -55.4995 q^{25} -199.131 q^{26} -57.9088 q^{27} -622.513 q^{28} -23.7734 q^{29} -311.950 q^{30} +189.450 q^{31} -866.992 q^{32} -66.7029 q^{33} +164.028 q^{34} -227.253 q^{35} +420.336 q^{36} +353.505 q^{37} +196.236 q^{38} +241.637 q^{39} -686.856 q^{40} +88.4989 q^{41} +1020.01 q^{42} -226.059 q^{44} +153.447 q^{45} -106.735 q^{46} +127.587 q^{47} +1851.86 q^{48} +400.070 q^{49} +308.193 q^{50} -199.040 q^{51} +818.916 q^{52} +556.861 q^{53} +321.572 q^{54} -82.5242 q^{55} +2245.88 q^{56} -238.124 q^{57} +132.015 q^{58} -342.074 q^{59} +1282.88 q^{60} -98.4467 q^{61} -1052.03 q^{62} -501.739 q^{63} +2615.90 q^{64} +298.951 q^{65} +370.407 q^{66} -603.957 q^{67} -674.554 q^{68} +129.518 q^{69} +1261.95 q^{70} +24.3032 q^{71} -1516.47 q^{72} -370.333 q^{73} -1963.04 q^{74} -373.978 q^{75} -807.009 q^{76} +269.837 q^{77} -1341.83 q^{78} -523.511 q^{79} +2291.11 q^{80} -887.180 q^{81} -491.442 q^{82} +628.389 q^{83} -4194.75 q^{84} -246.251 q^{85} -160.195 q^{87} +815.566 q^{88} -1134.03 q^{89} -852.102 q^{90} -977.509 q^{91} +438.940 q^{92} +1276.59 q^{93} -708.500 q^{94} -294.604 q^{95} -5842.15 q^{96} +1630.97 q^{97} -2221.62 q^{98} -182.201 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30q - 6q^{2} - 2q^{3} + 114q^{4} - 27q^{5} + 8q^{6} - 48q^{7} - 90q^{8} + 216q^{9} + O(q^{10}) \) \( 30q - 6q^{2} - 2q^{3} + 114q^{4} - 27q^{5} + 8q^{6} - 48q^{7} - 90q^{8} + 216q^{9} - 27q^{10} + 80q^{11} + 36q^{12} - 13q^{13} + 36q^{14} + 16q^{15} + 318q^{16} + 66q^{17} - 80q^{18} - 254q^{19} - 312q^{20} - 548q^{21} - 305q^{22} - 105q^{23} + 123q^{24} + 523q^{25} - 549q^{26} + 10q^{27} - 578q^{28} - 793q^{29} - 1560q^{30} - 359q^{31} - 676q^{32} - 208q^{33} - 1007q^{34} - 514q^{35} + 776q^{36} - 510q^{37} - 2066q^{38} - 898q^{39} - 1248q^{40} - 270q^{41} + 915q^{42} + 3256q^{44} - 807q^{45} - 1960q^{46} + 1421q^{47} + 632q^{48} + 386q^{49} + 141q^{50} - 209q^{51} + 2825q^{52} - 21q^{53} + 2368q^{54} - 2258q^{55} + 2521q^{56} - 1723q^{57} - 347q^{58} + 1752q^{59} + 2711q^{60} - 1759q^{61} - 395q^{62} - 2204q^{63} + 222q^{64} - 1151q^{65} + 160q^{66} - 3001q^{67} + 1921q^{68} - 1660q^{69} - 1597q^{70} - 727q^{71} - 9100q^{72} - 4623q^{73} - 2649q^{74} - 1027q^{75} - 874q^{76} - 3556q^{77} - 4979q^{78} + 546q^{79} - 5809q^{80} - 410q^{81} + 4397q^{82} - 492q^{83} - 10611q^{84} + 1723q^{85} + 5937q^{87} - 3974q^{88} - 5218q^{89} + 10492q^{90} - 1104q^{91} + 1060q^{92} - 1997q^{93} + 2134q^{94} + 6346q^{95} - 11984q^{96} + 2590q^{97} - 6270q^{98} - 2693q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.55308 −1.96331 −0.981655 0.190664i \(-0.938936\pi\)
−0.981655 + 0.190664i \(0.938936\pi\)
\(3\) 6.73841 1.29681 0.648404 0.761297i \(-0.275437\pi\)
0.648404 + 0.761297i \(0.275437\pi\)
\(4\) 22.8367 2.85459
\(5\) 8.33670 0.745657 0.372829 0.927900i \(-0.378388\pi\)
0.372829 + 0.927900i \(0.378388\pi\)
\(6\) −37.4189 −2.54604
\(7\) −27.2593 −1.47186 −0.735932 0.677055i \(-0.763256\pi\)
−0.735932 + 0.677055i \(0.763256\pi\)
\(8\) −82.3895 −3.64114
\(9\) 18.4062 0.681710
\(10\) −46.2944 −1.46396
\(11\) −9.89891 −0.271330 −0.135665 0.990755i \(-0.543317\pi\)
−0.135665 + 0.990755i \(0.543317\pi\)
\(12\) 153.883 3.70185
\(13\) 35.8596 0.765052 0.382526 0.923945i \(-0.375054\pi\)
0.382526 + 0.923945i \(0.375054\pi\)
\(14\) 151.373 2.88973
\(15\) 56.1761 0.966974
\(16\) 274.822 4.29409
\(17\) −29.5381 −0.421415 −0.210707 0.977549i \(-0.567577\pi\)
−0.210707 + 0.977549i \(0.567577\pi\)
\(18\) −102.211 −1.33841
\(19\) −35.3382 −0.426692 −0.213346 0.976977i \(-0.568436\pi\)
−0.213346 + 0.976977i \(0.568436\pi\)
\(20\) 190.383 2.12854
\(21\) −183.684 −1.90872
\(22\) 54.9695 0.532706
\(23\) 19.2208 0.174253 0.0871265 0.996197i \(-0.472232\pi\)
0.0871265 + 0.996197i \(0.472232\pi\)
\(24\) −555.174 −4.72185
\(25\) −55.4995 −0.443996
\(26\) −199.131 −1.50203
\(27\) −57.9088 −0.412761
\(28\) −622.513 −4.20157
\(29\) −23.7734 −0.152228 −0.0761138 0.997099i \(-0.524251\pi\)
−0.0761138 + 0.997099i \(0.524251\pi\)
\(30\) −311.950 −1.89847
\(31\) 189.450 1.09762 0.548809 0.835948i \(-0.315082\pi\)
0.548809 + 0.835948i \(0.315082\pi\)
\(32\) −866.992 −4.78950
\(33\) −66.7029 −0.351863
\(34\) 164.028 0.827368
\(35\) −227.253 −1.09751
\(36\) 420.336 1.94600
\(37\) 353.505 1.57070 0.785349 0.619053i \(-0.212483\pi\)
0.785349 + 0.619053i \(0.212483\pi\)
\(38\) 196.236 0.837729
\(39\) 241.637 0.992125
\(40\) −686.856 −2.71504
\(41\) 88.4989 0.337103 0.168551 0.985693i \(-0.446091\pi\)
0.168551 + 0.985693i \(0.446091\pi\)
\(42\) 1020.01 3.74742
\(43\) 0 0
\(44\) −226.059 −0.774537
\(45\) 153.447 0.508322
\(46\) −106.735 −0.342113
\(47\) 127.587 0.395967 0.197984 0.980205i \(-0.436561\pi\)
0.197984 + 0.980205i \(0.436561\pi\)
\(48\) 1851.86 5.56861
\(49\) 400.070 1.16638
\(50\) 308.193 0.871701
\(51\) −199.040 −0.546494
\(52\) 818.916 2.18391
\(53\) 556.861 1.44322 0.721611 0.692299i \(-0.243402\pi\)
0.721611 + 0.692299i \(0.243402\pi\)
\(54\) 321.572 0.810378
\(55\) −82.5242 −0.202319
\(56\) 2245.88 5.35926
\(57\) −238.124 −0.553337
\(58\) 132.015 0.298870
\(59\) −342.074 −0.754818 −0.377409 0.926047i \(-0.623185\pi\)
−0.377409 + 0.926047i \(0.623185\pi\)
\(60\) 1282.88 2.76031
\(61\) −98.4467 −0.206636 −0.103318 0.994648i \(-0.532946\pi\)
−0.103318 + 0.994648i \(0.532946\pi\)
\(62\) −1052.03 −2.15496
\(63\) −501.739 −1.00338
\(64\) 2615.90 5.10919
\(65\) 298.951 0.570466
\(66\) 370.407 0.690817
\(67\) −603.957 −1.10127 −0.550635 0.834746i \(-0.685614\pi\)
−0.550635 + 0.834746i \(0.685614\pi\)
\(68\) −674.554 −1.20297
\(69\) 129.518 0.225973
\(70\) 1261.95 2.15475
\(71\) 24.3032 0.0406234 0.0203117 0.999794i \(-0.493534\pi\)
0.0203117 + 0.999794i \(0.493534\pi\)
\(72\) −1516.47 −2.48220
\(73\) −370.333 −0.593755 −0.296878 0.954916i \(-0.595945\pi\)
−0.296878 + 0.954916i \(0.595945\pi\)
\(74\) −1963.04 −3.08377
\(75\) −373.978 −0.575777
\(76\) −807.009 −1.21803
\(77\) 269.837 0.399361
\(78\) −1341.83 −1.94785
\(79\) −523.511 −0.745565 −0.372782 0.927919i \(-0.621596\pi\)
−0.372782 + 0.927919i \(0.621596\pi\)
\(80\) 2291.11 3.20192
\(81\) −887.180 −1.21698
\(82\) −491.442 −0.661837
\(83\) 628.389 0.831020 0.415510 0.909589i \(-0.363603\pi\)
0.415510 + 0.909589i \(0.363603\pi\)
\(84\) −4194.75 −5.44863
\(85\) −246.251 −0.314231
\(86\) 0 0
\(87\) −160.195 −0.197410
\(88\) 815.566 0.987951
\(89\) −1134.03 −1.35064 −0.675320 0.737525i \(-0.735994\pi\)
−0.675320 + 0.737525i \(0.735994\pi\)
\(90\) −852.102 −0.997994
\(91\) −977.509 −1.12605
\(92\) 438.940 0.497421
\(93\) 1276.59 1.42340
\(94\) −708.500 −0.777407
\(95\) −294.604 −0.318166
\(96\) −5842.15 −6.21106
\(97\) 1630.97 1.70721 0.853606 0.520919i \(-0.174411\pi\)
0.853606 + 0.520919i \(0.174411\pi\)
\(98\) −2221.62 −2.28997
\(99\) −182.201 −0.184969
\(100\) −1267.43 −1.26743
\(101\) 1150.29 1.13325 0.566624 0.823976i \(-0.308249\pi\)
0.566624 + 0.823976i \(0.308249\pi\)
\(102\) 1105.29 1.07294
\(103\) −353.790 −0.338446 −0.169223 0.985578i \(-0.554126\pi\)
−0.169223 + 0.985578i \(0.554126\pi\)
\(104\) −2954.46 −2.78566
\(105\) −1531.32 −1.42325
\(106\) −3092.29 −2.83349
\(107\) −1944.51 −1.75685 −0.878426 0.477878i \(-0.841406\pi\)
−0.878426 + 0.477878i \(0.841406\pi\)
\(108\) −1322.45 −1.17826
\(109\) 939.726 0.825775 0.412887 0.910782i \(-0.364520\pi\)
0.412887 + 0.910782i \(0.364520\pi\)
\(110\) 458.264 0.397216
\(111\) 2382.06 2.03689
\(112\) −7491.45 −6.32032
\(113\) −743.611 −0.619053 −0.309527 0.950891i \(-0.600171\pi\)
−0.309527 + 0.950891i \(0.600171\pi\)
\(114\) 1322.32 1.08637
\(115\) 160.238 0.129933
\(116\) −542.905 −0.434547
\(117\) 660.038 0.521543
\(118\) 1899.56 1.48194
\(119\) 805.189 0.620266
\(120\) −4628.32 −3.52088
\(121\) −1233.01 −0.926380
\(122\) 546.682 0.405691
\(123\) 596.342 0.437157
\(124\) 4326.41 3.13325
\(125\) −1504.77 −1.07673
\(126\) 2786.20 1.96996
\(127\) 1005.97 0.702877 0.351439 0.936211i \(-0.385693\pi\)
0.351439 + 0.936211i \(0.385693\pi\)
\(128\) −7590.39 −5.24142
\(129\) 0 0
\(130\) −1660.10 −1.12000
\(131\) −2899.46 −1.93380 −0.966898 0.255163i \(-0.917871\pi\)
−0.966898 + 0.255163i \(0.917871\pi\)
\(132\) −1523.28 −1.00443
\(133\) 963.296 0.628033
\(134\) 3353.82 2.16214
\(135\) −482.768 −0.307778
\(136\) 2433.63 1.53443
\(137\) −1446.49 −0.902058 −0.451029 0.892509i \(-0.648943\pi\)
−0.451029 + 0.892509i \(0.648943\pi\)
\(138\) −719.223 −0.443654
\(139\) −1641.73 −1.00180 −0.500898 0.865506i \(-0.666997\pi\)
−0.500898 + 0.865506i \(0.666997\pi\)
\(140\) −5189.70 −3.13293
\(141\) 859.733 0.513493
\(142\) −134.958 −0.0797563
\(143\) −354.971 −0.207582
\(144\) 5058.42 2.92732
\(145\) −198.191 −0.113510
\(146\) 2056.49 1.16573
\(147\) 2695.83 1.51258
\(148\) 8072.89 4.48370
\(149\) −939.333 −0.516464 −0.258232 0.966083i \(-0.583140\pi\)
−0.258232 + 0.966083i \(0.583140\pi\)
\(150\) 2076.73 1.13043
\(151\) −2062.34 −1.11146 −0.555731 0.831362i \(-0.687562\pi\)
−0.555731 + 0.831362i \(0.687562\pi\)
\(152\) 2911.50 1.55364
\(153\) −543.684 −0.287283
\(154\) −1498.43 −0.784071
\(155\) 1579.38 0.818446
\(156\) 5518.19 2.83211
\(157\) −1914.62 −0.973271 −0.486635 0.873605i \(-0.661776\pi\)
−0.486635 + 0.873605i \(0.661776\pi\)
\(158\) 2907.10 1.46378
\(159\) 3752.36 1.87158
\(160\) −7227.85 −3.57133
\(161\) −523.946 −0.256477
\(162\) 4926.58 2.38931
\(163\) 420.494 0.202059 0.101029 0.994883i \(-0.467786\pi\)
0.101029 + 0.994883i \(0.467786\pi\)
\(164\) 2021.02 0.962290
\(165\) −556.082 −0.262369
\(166\) −3489.49 −1.63155
\(167\) 546.523 0.253241 0.126620 0.991951i \(-0.459587\pi\)
0.126620 + 0.991951i \(0.459587\pi\)
\(168\) 15133.7 6.94993
\(169\) −911.087 −0.414696
\(170\) 1367.45 0.616933
\(171\) −650.441 −0.290880
\(172\) 0 0
\(173\) −818.511 −0.359712 −0.179856 0.983693i \(-0.557563\pi\)
−0.179856 + 0.983693i \(0.557563\pi\)
\(174\) 889.574 0.387577
\(175\) 1512.88 0.653501
\(176\) −2720.44 −1.16512
\(177\) −2305.03 −0.978853
\(178\) 6297.36 2.65172
\(179\) −3304.21 −1.37971 −0.689856 0.723947i \(-0.742326\pi\)
−0.689856 + 0.723947i \(0.742326\pi\)
\(180\) 3504.22 1.45105
\(181\) −2609.51 −1.07162 −0.535811 0.844338i \(-0.679994\pi\)
−0.535811 + 0.844338i \(0.679994\pi\)
\(182\) 5428.19 2.21079
\(183\) −663.374 −0.267967
\(184\) −1583.59 −0.634479
\(185\) 2947.06 1.17120
\(186\) −7089.00 −2.79457
\(187\) 292.396 0.114343
\(188\) 2913.67 1.13032
\(189\) 1578.55 0.607528
\(190\) 1635.96 0.624658
\(191\) −1972.83 −0.747377 −0.373688 0.927554i \(-0.621907\pi\)
−0.373688 + 0.927554i \(0.621907\pi\)
\(192\) 17627.0 6.62563
\(193\) −3415.93 −1.27401 −0.637005 0.770860i \(-0.719827\pi\)
−0.637005 + 0.770860i \(0.719827\pi\)
\(194\) −9056.89 −3.35179
\(195\) 2014.45 0.739785
\(196\) 9136.28 3.32955
\(197\) −3185.68 −1.15213 −0.576066 0.817403i \(-0.695413\pi\)
−0.576066 + 0.817403i \(0.695413\pi\)
\(198\) 1011.78 0.363151
\(199\) −893.918 −0.318433 −0.159216 0.987244i \(-0.550897\pi\)
−0.159216 + 0.987244i \(0.550897\pi\)
\(200\) 4572.57 1.61665
\(201\) −4069.71 −1.42814
\(202\) −6387.65 −2.22492
\(203\) 648.045 0.224058
\(204\) −4545.42 −1.56002
\(205\) 737.789 0.251363
\(206\) 1964.62 0.664475
\(207\) 353.782 0.118790
\(208\) 9855.01 3.28520
\(209\) 349.810 0.115774
\(210\) 8503.55 2.79429
\(211\) −2830.29 −0.923436 −0.461718 0.887027i \(-0.652767\pi\)
−0.461718 + 0.887027i \(0.652767\pi\)
\(212\) 12716.9 4.11980
\(213\) 163.765 0.0526807
\(214\) 10798.0 3.44925
\(215\) 0 0
\(216\) 4771.08 1.50292
\(217\) −5164.26 −1.61554
\(218\) −5218.38 −1.62125
\(219\) −2495.45 −0.769986
\(220\) −1884.58 −0.577539
\(221\) −1059.23 −0.322404
\(222\) −13227.8 −3.99906
\(223\) 6086.98 1.82787 0.913934 0.405863i \(-0.133029\pi\)
0.913934 + 0.405863i \(0.133029\pi\)
\(224\) 23633.6 7.04950
\(225\) −1021.53 −0.302676
\(226\) 4129.33 1.21539
\(227\) 3531.47 1.03256 0.516282 0.856418i \(-0.327316\pi\)
0.516282 + 0.856418i \(0.327316\pi\)
\(228\) −5437.96 −1.57955
\(229\) 3675.42 1.06061 0.530303 0.847808i \(-0.322078\pi\)
0.530303 + 0.847808i \(0.322078\pi\)
\(230\) −889.816 −0.255099
\(231\) 1818.28 0.517895
\(232\) 1958.67 0.554281
\(233\) 2445.98 0.687733 0.343866 0.939019i \(-0.388263\pi\)
0.343866 + 0.939019i \(0.388263\pi\)
\(234\) −3665.25 −1.02395
\(235\) 1063.65 0.295256
\(236\) −7811.85 −2.15469
\(237\) −3527.63 −0.966854
\(238\) −4471.28 −1.21777
\(239\) −347.223 −0.0939750 −0.0469875 0.998895i \(-0.514962\pi\)
−0.0469875 + 0.998895i \(0.514962\pi\)
\(240\) 15438.4 4.15227
\(241\) 2750.80 0.735248 0.367624 0.929975i \(-0.380171\pi\)
0.367624 + 0.929975i \(0.380171\pi\)
\(242\) 6847.01 1.81877
\(243\) −4414.64 −1.16543
\(244\) −2248.20 −0.589861
\(245\) 3335.26 0.869723
\(246\) −3311.54 −0.858275
\(247\) −1267.22 −0.326441
\(248\) −15608.7 −3.99657
\(249\) 4234.34 1.07767
\(250\) 8356.11 2.11395
\(251\) −3851.45 −0.968531 −0.484265 0.874921i \(-0.660913\pi\)
−0.484265 + 0.874921i \(0.660913\pi\)
\(252\) −11458.1 −2.86425
\(253\) −190.265 −0.0472801
\(254\) −5586.23 −1.37997
\(255\) −1659.34 −0.407497
\(256\) 21222.8 5.18136
\(257\) −3377.80 −0.819849 −0.409924 0.912119i \(-0.634445\pi\)
−0.409924 + 0.912119i \(0.634445\pi\)
\(258\) 0 0
\(259\) −9636.30 −2.31186
\(260\) 6827.06 1.62845
\(261\) −437.576 −0.103775
\(262\) 16101.0 3.79664
\(263\) −3214.33 −0.753627 −0.376813 0.926289i \(-0.622980\pi\)
−0.376813 + 0.926289i \(0.622980\pi\)
\(264\) 5495.62 1.28118
\(265\) 4642.38 1.07615
\(266\) −5349.26 −1.23302
\(267\) −7641.55 −1.75152
\(268\) −13792.4 −3.14367
\(269\) 1641.68 0.372099 0.186050 0.982540i \(-0.440431\pi\)
0.186050 + 0.982540i \(0.440431\pi\)
\(270\) 2680.85 0.604264
\(271\) 1602.70 0.359252 0.179626 0.983735i \(-0.442511\pi\)
0.179626 + 0.983735i \(0.442511\pi\)
\(272\) −8117.73 −1.80959
\(273\) −6586.85 −1.46027
\(274\) 8032.47 1.77102
\(275\) 549.384 0.120469
\(276\) 2957.76 0.645059
\(277\) −391.521 −0.0849250 −0.0424625 0.999098i \(-0.513520\pi\)
−0.0424625 + 0.999098i \(0.513520\pi\)
\(278\) 9116.65 1.96684
\(279\) 3487.04 0.748257
\(280\) 18723.2 3.99617
\(281\) −613.407 −0.130223 −0.0651117 0.997878i \(-0.520740\pi\)
−0.0651117 + 0.997878i \(0.520740\pi\)
\(282\) −4774.17 −1.00815
\(283\) −3189.48 −0.669947 −0.334973 0.942228i \(-0.608727\pi\)
−0.334973 + 0.942228i \(0.608727\pi\)
\(284\) 555.005 0.115963
\(285\) −1985.16 −0.412600
\(286\) 1971.18 0.407548
\(287\) −2412.42 −0.496169
\(288\) −15958.0 −3.26505
\(289\) −4040.50 −0.822409
\(290\) 1100.57 0.222855
\(291\) 10990.1 2.21393
\(292\) −8457.18 −1.69493
\(293\) −2370.01 −0.472550 −0.236275 0.971686i \(-0.575927\pi\)
−0.236275 + 0.971686i \(0.575927\pi\)
\(294\) −14970.2 −2.96966
\(295\) −2851.77 −0.562835
\(296\) −29125.1 −5.71913
\(297\) 573.234 0.111995
\(298\) 5216.19 1.01398
\(299\) 689.252 0.133313
\(300\) −8540.43 −1.64361
\(301\) 0 0
\(302\) 11452.3 2.18215
\(303\) 7751.12 1.46960
\(304\) −9711.72 −1.83225
\(305\) −820.720 −0.154080
\(306\) 3019.12 0.564025
\(307\) −1485.87 −0.276232 −0.138116 0.990416i \(-0.544105\pi\)
−0.138116 + 0.990416i \(0.544105\pi\)
\(308\) 6162.20 1.14001
\(309\) −2383.98 −0.438899
\(310\) −8770.45 −1.60686
\(311\) −4799.83 −0.875155 −0.437577 0.899181i \(-0.644163\pi\)
−0.437577 + 0.899181i \(0.644163\pi\)
\(312\) −19908.3 −3.61246
\(313\) −1762.85 −0.318345 −0.159172 0.987251i \(-0.550883\pi\)
−0.159172 + 0.987251i \(0.550883\pi\)
\(314\) 10632.1 1.91083
\(315\) −4182.85 −0.748181
\(316\) −11955.3 −2.12828
\(317\) −4271.00 −0.756730 −0.378365 0.925656i \(-0.623514\pi\)
−0.378365 + 0.925656i \(0.623514\pi\)
\(318\) −20837.1 −3.67449
\(319\) 235.330 0.0413040
\(320\) 21808.0 3.80970
\(321\) −13102.9 −2.27830
\(322\) 2909.52 0.503543
\(323\) 1043.83 0.179814
\(324\) −20260.3 −3.47398
\(325\) −1990.19 −0.339680
\(326\) −2335.03 −0.396704
\(327\) 6332.26 1.07087
\(328\) −7291.38 −1.22744
\(329\) −3477.93 −0.582810
\(330\) 3087.97 0.515112
\(331\) 9623.51 1.59805 0.799027 0.601295i \(-0.205348\pi\)
0.799027 + 0.601295i \(0.205348\pi\)
\(332\) 14350.3 2.37222
\(333\) 6506.67 1.07076
\(334\) −3034.89 −0.497191
\(335\) −5035.01 −0.821170
\(336\) −50480.5 −8.19624
\(337\) 5650.95 0.913432 0.456716 0.889613i \(-0.349026\pi\)
0.456716 + 0.889613i \(0.349026\pi\)
\(338\) 5059.34 0.814177
\(339\) −5010.75 −0.802793
\(340\) −5623.56 −0.897000
\(341\) −1875.34 −0.297817
\(342\) 3611.95 0.571088
\(343\) −1555.68 −0.244895
\(344\) 0 0
\(345\) 1079.75 0.168498
\(346\) 4545.26 0.706227
\(347\) 2258.74 0.349439 0.174720 0.984618i \(-0.444098\pi\)
0.174720 + 0.984618i \(0.444098\pi\)
\(348\) −3658.32 −0.563524
\(349\) 11373.4 1.74442 0.872212 0.489128i \(-0.162685\pi\)
0.872212 + 0.489128i \(0.162685\pi\)
\(350\) −8401.13 −1.28303
\(351\) −2076.59 −0.315784
\(352\) 8582.28 1.29954
\(353\) 6551.13 0.987767 0.493883 0.869528i \(-0.335577\pi\)
0.493883 + 0.869528i \(0.335577\pi\)
\(354\) 12800.0 1.92179
\(355\) 202.608 0.0302911
\(356\) −25897.5 −3.85552
\(357\) 5425.70 0.804365
\(358\) 18348.6 2.70880
\(359\) −4204.66 −0.618144 −0.309072 0.951039i \(-0.600018\pi\)
−0.309072 + 0.951039i \(0.600018\pi\)
\(360\) −12642.4 −1.85087
\(361\) −5610.21 −0.817934
\(362\) 14490.8 2.10393
\(363\) −8308.54 −1.20134
\(364\) −22323.1 −3.21442
\(365\) −3087.35 −0.442738
\(366\) 3683.77 0.526103
\(367\) 4867.39 0.692304 0.346152 0.938178i \(-0.387488\pi\)
0.346152 + 0.938178i \(0.387488\pi\)
\(368\) 5282.30 0.748258
\(369\) 1628.93 0.229806
\(370\) −16365.3 −2.29943
\(371\) −15179.6 −2.12423
\(372\) 29153.1 4.06322
\(373\) −1208.88 −0.167810 −0.0839051 0.996474i \(-0.526739\pi\)
−0.0839051 + 0.996474i \(0.526739\pi\)
\(374\) −1623.70 −0.224490
\(375\) −10139.8 −1.39631
\(376\) −10511.8 −1.44177
\(377\) −852.504 −0.116462
\(378\) −8765.83 −1.19277
\(379\) 2664.41 0.361112 0.180556 0.983565i \(-0.442210\pi\)
0.180556 + 0.983565i \(0.442210\pi\)
\(380\) −6727.79 −0.908233
\(381\) 6778.64 0.911496
\(382\) 10955.3 1.46733
\(383\) 7348.76 0.980428 0.490214 0.871602i \(-0.336919\pi\)
0.490214 + 0.871602i \(0.336919\pi\)
\(384\) −51147.2 −6.79712
\(385\) 2249.55 0.297787
\(386\) 18968.9 2.50128
\(387\) 0 0
\(388\) 37245.9 4.87339
\(389\) 2698.30 0.351695 0.175848 0.984417i \(-0.443733\pi\)
0.175848 + 0.984417i \(0.443733\pi\)
\(390\) −11186.4 −1.45243
\(391\) −567.747 −0.0734328
\(392\) −32961.6 −4.24696
\(393\) −19537.8 −2.50776
\(394\) 17690.3 2.26199
\(395\) −4364.36 −0.555936
\(396\) −4160.87 −0.528009
\(397\) 7999.63 1.01131 0.505655 0.862736i \(-0.331251\pi\)
0.505655 + 0.862736i \(0.331251\pi\)
\(398\) 4964.00 0.625183
\(399\) 6491.08 0.814437
\(400\) −15252.5 −1.90656
\(401\) −1655.91 −0.206215 −0.103107 0.994670i \(-0.532878\pi\)
−0.103107 + 0.994670i \(0.532878\pi\)
\(402\) 22599.4 2.80387
\(403\) 6793.59 0.839734
\(404\) 26268.8 3.23496
\(405\) −7396.15 −0.907451
\(406\) −3598.65 −0.439896
\(407\) −3499.31 −0.426178
\(408\) 16398.8 1.98986
\(409\) 2350.99 0.284227 0.142114 0.989850i \(-0.454610\pi\)
0.142114 + 0.989850i \(0.454610\pi\)
\(410\) −4097.00 −0.493504
\(411\) −9747.04 −1.16980
\(412\) −8079.39 −0.966124
\(413\) 9324.70 1.11099
\(414\) −1964.58 −0.233222
\(415\) 5238.69 0.619656
\(416\) −31090.0 −3.66422
\(417\) −11062.6 −1.29914
\(418\) −1942.52 −0.227301
\(419\) 12597.8 1.46884 0.734421 0.678694i \(-0.237454\pi\)
0.734421 + 0.678694i \(0.237454\pi\)
\(420\) −34970.4 −4.06281
\(421\) 14618.2 1.69228 0.846139 0.532963i \(-0.178921\pi\)
0.846139 + 0.532963i \(0.178921\pi\)
\(422\) 15716.8 1.81299
\(423\) 2348.39 0.269935
\(424\) −45879.5 −5.25497
\(425\) 1639.35 0.187106
\(426\) −909.400 −0.103429
\(427\) 2683.59 0.304140
\(428\) −44406.3 −5.01509
\(429\) −2391.94 −0.269194
\(430\) 0 0
\(431\) −16070.2 −1.79599 −0.897995 0.440005i \(-0.854977\pi\)
−0.897995 + 0.440005i \(0.854977\pi\)
\(432\) −15914.6 −1.77243
\(433\) 4032.84 0.447588 0.223794 0.974636i \(-0.428156\pi\)
0.223794 + 0.974636i \(0.428156\pi\)
\(434\) 28677.6 3.17181
\(435\) −1335.49 −0.147200
\(436\) 21460.3 2.35725
\(437\) −679.230 −0.0743523
\(438\) 13857.5 1.51172
\(439\) 7459.92 0.811031 0.405516 0.914088i \(-0.367092\pi\)
0.405516 + 0.914088i \(0.367092\pi\)
\(440\) 6799.13 0.736672
\(441\) 7363.75 0.795136
\(442\) 5881.97 0.632980
\(443\) −4510.98 −0.483799 −0.241899 0.970301i \(-0.577770\pi\)
−0.241899 + 0.970301i \(0.577770\pi\)
\(444\) 54398.5 5.81450
\(445\) −9454.06 −1.00711
\(446\) −33801.5 −3.58867
\(447\) −6329.61 −0.669754
\(448\) −71307.7 −7.52003
\(449\) −6496.35 −0.682810 −0.341405 0.939916i \(-0.610903\pi\)
−0.341405 + 0.939916i \(0.610903\pi\)
\(450\) 5672.65 0.594247
\(451\) −876.043 −0.0914662
\(452\) −16981.6 −1.76714
\(453\) −13896.9 −1.44135
\(454\) −19610.6 −2.02725
\(455\) −8149.20 −0.839649
\(456\) 19618.9 2.01478
\(457\) 4452.60 0.455763 0.227881 0.973689i \(-0.426820\pi\)
0.227881 + 0.973689i \(0.426820\pi\)
\(458\) −20409.9 −2.08230
\(459\) 1710.52 0.173944
\(460\) 3659.31 0.370905
\(461\) −17062.6 −1.72383 −0.861913 0.507057i \(-0.830733\pi\)
−0.861913 + 0.507057i \(0.830733\pi\)
\(462\) −10097.0 −1.01679
\(463\) −18830.6 −1.89013 −0.945067 0.326877i \(-0.894004\pi\)
−0.945067 + 0.326877i \(0.894004\pi\)
\(464\) −6533.44 −0.653679
\(465\) 10642.5 1.06137
\(466\) −13582.8 −1.35023
\(467\) 2455.43 0.243305 0.121653 0.992573i \(-0.461181\pi\)
0.121653 + 0.992573i \(0.461181\pi\)
\(468\) 15073.1 1.48879
\(469\) 16463.4 1.62092
\(470\) −5906.55 −0.579679
\(471\) −12901.5 −1.26214
\(472\) 28183.3 2.74839
\(473\) 0 0
\(474\) 19589.2 1.89824
\(475\) 1961.25 0.189449
\(476\) 18387.9 1.77060
\(477\) 10249.7 0.983858
\(478\) 1928.16 0.184502
\(479\) −11404.1 −1.08782 −0.543912 0.839142i \(-0.683057\pi\)
−0.543912 + 0.839142i \(0.683057\pi\)
\(480\) −48704.2 −4.63132
\(481\) 12676.6 1.20167
\(482\) −15275.4 −1.44352
\(483\) −3530.56 −0.332601
\(484\) −28157.9 −2.64443
\(485\) 13596.9 1.27299
\(486\) 24514.9 2.28810
\(487\) −5407.50 −0.503157 −0.251578 0.967837i \(-0.580950\pi\)
−0.251578 + 0.967837i \(0.580950\pi\)
\(488\) 8110.97 0.752390
\(489\) 2833.46 0.262031
\(490\) −18521.0 −1.70754
\(491\) −14996.5 −1.37838 −0.689190 0.724581i \(-0.742033\pi\)
−0.689190 + 0.724581i \(0.742033\pi\)
\(492\) 13618.5 1.24790
\(493\) 702.221 0.0641510
\(494\) 7036.95 0.640906
\(495\) −1518.95 −0.137923
\(496\) 52064.9 4.71327
\(497\) −662.488 −0.0597921
\(498\) −23513.6 −2.11581
\(499\) 10720.9 0.961791 0.480896 0.876778i \(-0.340312\pi\)
0.480896 + 0.876778i \(0.340312\pi\)
\(500\) −34364.0 −3.07361
\(501\) 3682.70 0.328405
\(502\) 21387.4 1.90153
\(503\) −21636.0 −1.91790 −0.958949 0.283579i \(-0.908478\pi\)
−0.958949 + 0.283579i \(0.908478\pi\)
\(504\) 41338.0 3.65346
\(505\) 9589.62 0.845014
\(506\) 1056.56 0.0928256
\(507\) −6139.28 −0.537781
\(508\) 22973.0 2.00643
\(509\) 13204.0 1.14982 0.574908 0.818218i \(-0.305038\pi\)
0.574908 + 0.818218i \(0.305038\pi\)
\(510\) 9214.44 0.800043
\(511\) 10095.0 0.873927
\(512\) −57129.0 −4.93119
\(513\) 2046.39 0.176122
\(514\) 18757.2 1.60962
\(515\) −2949.44 −0.252365
\(516\) 0 0
\(517\) −1262.97 −0.107438
\(518\) 53511.2 4.53889
\(519\) −5515.46 −0.466478
\(520\) −24630.4 −2.07714
\(521\) −12287.5 −1.03325 −0.516626 0.856211i \(-0.672812\pi\)
−0.516626 + 0.856211i \(0.672812\pi\)
\(522\) 2429.90 0.203743
\(523\) 11431.0 0.955721 0.477860 0.878436i \(-0.341413\pi\)
0.477860 + 0.878436i \(0.341413\pi\)
\(524\) −66214.2 −5.52019
\(525\) 10194.4 0.847465
\(526\) 17849.4 1.47960
\(527\) −5595.99 −0.462552
\(528\) −18331.4 −1.51093
\(529\) −11797.6 −0.969636
\(530\) −25779.5 −2.11281
\(531\) −6296.27 −0.514567
\(532\) 21998.5 1.79278
\(533\) 3173.54 0.257901
\(534\) 42434.2 3.43878
\(535\) −16210.8 −1.31001
\(536\) 49759.7 4.00987
\(537\) −22265.1 −1.78922
\(538\) −9116.36 −0.730547
\(539\) −3960.26 −0.316475
\(540\) −11024.8 −0.878580
\(541\) −10071.9 −0.800414 −0.400207 0.916425i \(-0.631062\pi\)
−0.400207 + 0.916425i \(0.631062\pi\)
\(542\) −8899.94 −0.705323
\(543\) −17584.0 −1.38969
\(544\) 25609.4 2.01837
\(545\) 7834.21 0.615745
\(546\) 36577.3 2.86697
\(547\) 3049.29 0.238352 0.119176 0.992873i \(-0.461975\pi\)
0.119176 + 0.992873i \(0.461975\pi\)
\(548\) −33033.1 −2.57501
\(549\) −1812.03 −0.140866
\(550\) −3050.78 −0.236519
\(551\) 840.108 0.0649543
\(552\) −10670.9 −0.822797
\(553\) 14270.6 1.09737
\(554\) 2174.15 0.166734
\(555\) 19858.5 1.51882
\(556\) −37491.7 −2.85971
\(557\) 19978.3 1.51976 0.759882 0.650061i \(-0.225257\pi\)
0.759882 + 0.650061i \(0.225257\pi\)
\(558\) −19363.8 −1.46906
\(559\) 0 0
\(560\) −62454.0 −4.71279
\(561\) 1970.28 0.148280
\(562\) 3406.30 0.255669
\(563\) −7879.14 −0.589815 −0.294908 0.955526i \(-0.595289\pi\)
−0.294908 + 0.955526i \(0.595289\pi\)
\(564\) 19633.5 1.46581
\(565\) −6199.26 −0.461601
\(566\) 17711.4 1.31531
\(567\) 24183.9 1.79123
\(568\) −2002.33 −0.147915
\(569\) 1060.11 0.0781058 0.0390529 0.999237i \(-0.487566\pi\)
0.0390529 + 0.999237i \(0.487566\pi\)
\(570\) 11023.8 0.810062
\(571\) −157.806 −0.0115656 −0.00578281 0.999983i \(-0.501841\pi\)
−0.00578281 + 0.999983i \(0.501841\pi\)
\(572\) −8106.38 −0.592561
\(573\) −13293.7 −0.969204
\(574\) 13396.4 0.974135
\(575\) −1066.74 −0.0773676
\(576\) 48148.8 3.48298
\(577\) 22077.3 1.59288 0.796440 0.604718i \(-0.206714\pi\)
0.796440 + 0.604718i \(0.206714\pi\)
\(578\) 22437.2 1.61465
\(579\) −23017.9 −1.65214
\(580\) −4526.04 −0.324023
\(581\) −17129.4 −1.22315
\(582\) −61029.1 −4.34662
\(583\) −5512.32 −0.391590
\(584\) 30511.5 2.16194
\(585\) 5502.54 0.388892
\(586\) 13160.8 0.927763
\(587\) −23019.1 −1.61857 −0.809285 0.587416i \(-0.800145\pi\)
−0.809285 + 0.587416i \(0.800145\pi\)
\(588\) 61564.0 4.31778
\(589\) −6694.81 −0.468345
\(590\) 15836.1 1.10502
\(591\) −21466.4 −1.49409
\(592\) 97150.9 6.74473
\(593\) 3709.24 0.256864 0.128432 0.991718i \(-0.459006\pi\)
0.128432 + 0.991718i \(0.459006\pi\)
\(594\) −3183.21 −0.219880
\(595\) 6712.62 0.462505
\(596\) −21451.3 −1.47429
\(597\) −6023.58 −0.412946
\(598\) −3827.47 −0.261734
\(599\) 20702.0 1.41212 0.706059 0.708153i \(-0.250471\pi\)
0.706059 + 0.708153i \(0.250471\pi\)
\(600\) 30811.9 2.09648
\(601\) −19631.3 −1.33241 −0.666205 0.745769i \(-0.732082\pi\)
−0.666205 + 0.745769i \(0.732082\pi\)
\(602\) 0 0
\(603\) −11116.5 −0.750747
\(604\) −47097.0 −3.17277
\(605\) −10279.2 −0.690762
\(606\) −43042.6 −2.88529
\(607\) 321.288 0.0214839 0.0107419 0.999942i \(-0.496581\pi\)
0.0107419 + 0.999942i \(0.496581\pi\)
\(608\) 30638.0 2.04364
\(609\) 4366.79 0.290561
\(610\) 4557.53 0.302506
\(611\) 4575.22 0.302935
\(612\) −12416.0 −0.820074
\(613\) −20803.1 −1.37068 −0.685342 0.728222i \(-0.740347\pi\)
−0.685342 + 0.728222i \(0.740347\pi\)
\(614\) 8251.18 0.542330
\(615\) 4971.52 0.325969
\(616\) −22231.8 −1.45413
\(617\) −18771.8 −1.22484 −0.612418 0.790534i \(-0.709803\pi\)
−0.612418 + 0.790534i \(0.709803\pi\)
\(618\) 13238.4 0.861696
\(619\) −22616.6 −1.46856 −0.734281 0.678846i \(-0.762481\pi\)
−0.734281 + 0.678846i \(0.762481\pi\)
\(620\) 36067.9 2.33633
\(621\) −1113.05 −0.0719248
\(622\) 26653.8 1.71820
\(623\) 30912.9 1.98796
\(624\) 66407.1 4.26028
\(625\) −5607.38 −0.358872
\(626\) 9789.23 0.625010
\(627\) 2357.16 0.150137
\(628\) −43723.7 −2.77829
\(629\) −10441.9 −0.661916
\(630\) 23227.7 1.46891
\(631\) −19599.7 −1.23653 −0.618267 0.785968i \(-0.712165\pi\)
−0.618267 + 0.785968i \(0.712165\pi\)
\(632\) 43131.8 2.71470
\(633\) −19071.6 −1.19752
\(634\) 23717.2 1.48570
\(635\) 8386.47 0.524105
\(636\) 85691.5 5.34259
\(637\) 14346.4 0.892344
\(638\) −1306.81 −0.0810925
\(639\) 447.329 0.0276934
\(640\) −63278.8 −3.90830
\(641\) −21787.1 −1.34249 −0.671247 0.741234i \(-0.734241\pi\)
−0.671247 + 0.741234i \(0.734241\pi\)
\(642\) 72761.6 4.47301
\(643\) −2333.40 −0.143111 −0.0715556 0.997437i \(-0.522796\pi\)
−0.0715556 + 0.997437i \(0.522796\pi\)
\(644\) −11965.2 −0.732136
\(645\) 0 0
\(646\) −5796.45 −0.353031
\(647\) 13759.4 0.836070 0.418035 0.908431i \(-0.362719\pi\)
0.418035 + 0.908431i \(0.362719\pi\)
\(648\) 73094.3 4.43120
\(649\) 3386.16 0.204805
\(650\) 11051.7 0.666897
\(651\) −34798.9 −2.09505
\(652\) 9602.69 0.576795
\(653\) 25853.4 1.54935 0.774673 0.632362i \(-0.217914\pi\)
0.774673 + 0.632362i \(0.217914\pi\)
\(654\) −35163.6 −2.10245
\(655\) −24172.0 −1.44195
\(656\) 24321.4 1.44755
\(657\) −6816.40 −0.404769
\(658\) 19313.2 1.14424
\(659\) −9669.46 −0.571576 −0.285788 0.958293i \(-0.592255\pi\)
−0.285788 + 0.958293i \(0.592255\pi\)
\(660\) −12699.1 −0.748957
\(661\) 16074.9 0.945904 0.472952 0.881088i \(-0.343188\pi\)
0.472952 + 0.881088i \(0.343188\pi\)
\(662\) −53440.1 −3.13748
\(663\) −7137.51 −0.418096
\(664\) −51772.6 −3.02586
\(665\) 8030.71 0.468297
\(666\) −36132.1 −2.10224
\(667\) −456.943 −0.0265261
\(668\) 12480.8 0.722899
\(669\) 41016.6 2.37039
\(670\) 27959.8 1.61221
\(671\) 974.515 0.0560666
\(672\) 159253. 9.14184
\(673\) 22908.2 1.31210 0.656052 0.754716i \(-0.272225\pi\)
0.656052 + 0.754716i \(0.272225\pi\)
\(674\) −31380.2 −1.79335
\(675\) 3213.91 0.183264
\(676\) −20806.2 −1.18379
\(677\) 28243.9 1.60340 0.801698 0.597729i \(-0.203930\pi\)
0.801698 + 0.597729i \(0.203930\pi\)
\(678\) 27825.1 1.57613
\(679\) −44459.0 −2.51278
\(680\) 20288.5 1.14416
\(681\) 23796.5 1.33904
\(682\) 10413.9 0.584707
\(683\) 12213.6 0.684248 0.342124 0.939655i \(-0.388854\pi\)
0.342124 + 0.939655i \(0.388854\pi\)
\(684\) −14853.9 −0.830343
\(685\) −12058.9 −0.672626
\(686\) 8638.84 0.480805
\(687\) 24766.5 1.37540
\(688\) 0 0
\(689\) 19968.8 1.10414
\(690\) −5995.94 −0.330814
\(691\) 31697.9 1.74507 0.872535 0.488551i \(-0.162474\pi\)
0.872535 + 0.488551i \(0.162474\pi\)
\(692\) −18692.1 −1.02683
\(693\) 4966.67 0.272249
\(694\) −12543.0 −0.686058
\(695\) −13686.6 −0.746996
\(696\) 13198.4 0.718796
\(697\) −2614.09 −0.142060
\(698\) −63157.4 −3.42485
\(699\) 16482.0 0.891857
\(700\) 34549.1 1.86548
\(701\) 10100.8 0.544224 0.272112 0.962266i \(-0.412278\pi\)
0.272112 + 0.962266i \(0.412278\pi\)
\(702\) 11531.5 0.619981
\(703\) −12492.2 −0.670205
\(704\) −25894.6 −1.38628
\(705\) 7167.33 0.382890
\(706\) −36379.0 −1.93929
\(707\) −31356.1 −1.66799
\(708\) −52639.4 −2.79422
\(709\) −14326.8 −0.758892 −0.379446 0.925214i \(-0.623885\pi\)
−0.379446 + 0.925214i \(0.623885\pi\)
\(710\) −1125.10 −0.0594709
\(711\) −9635.84 −0.508259
\(712\) 93432.1 4.91786
\(713\) 3641.38 0.191263
\(714\) −30129.3 −1.57922
\(715\) −2959.29 −0.154785
\(716\) −75457.4 −3.93851
\(717\) −2339.73 −0.121867
\(718\) 23348.8 1.21361
\(719\) −13059.9 −0.677402 −0.338701 0.940894i \(-0.609987\pi\)
−0.338701 + 0.940894i \(0.609987\pi\)
\(720\) 42170.5 2.18278
\(721\) 9644.06 0.498146
\(722\) 31153.9 1.60586
\(723\) 18536.0 0.953475
\(724\) −59592.7 −3.05904
\(725\) 1319.41 0.0675884
\(726\) 46138.0 2.35860
\(727\) 6978.02 0.355984 0.177992 0.984032i \(-0.443040\pi\)
0.177992 + 0.984032i \(0.443040\pi\)
\(728\) 80536.5 4.10011
\(729\) −5793.82 −0.294357
\(730\) 17144.3 0.869232
\(731\) 0 0
\(732\) −15149.3 −0.764937
\(733\) 11737.8 0.591469 0.295734 0.955270i \(-0.404436\pi\)
0.295734 + 0.955270i \(0.404436\pi\)
\(734\) −27029.0 −1.35921
\(735\) 22474.4 1.12786
\(736\) −16664.3 −0.834585
\(737\) 5978.52 0.298808
\(738\) −9045.56 −0.451181
\(739\) 7982.37 0.397343 0.198671 0.980066i \(-0.436337\pi\)
0.198671 + 0.980066i \(0.436337\pi\)
\(740\) 67301.3 3.34330
\(741\) −8539.02 −0.423332
\(742\) 84293.8 4.17052
\(743\) −36108.3 −1.78289 −0.891444 0.453131i \(-0.850307\pi\)
−0.891444 + 0.453131i \(0.850307\pi\)
\(744\) −105177. −5.18279
\(745\) −7830.93 −0.385105
\(746\) 6712.99 0.329464
\(747\) 11566.2 0.566514
\(748\) 6677.35 0.326401
\(749\) 53006.1 2.58585
\(750\) 56306.9 2.74138
\(751\) 14327.0 0.696138 0.348069 0.937469i \(-0.386838\pi\)
0.348069 + 0.937469i \(0.386838\pi\)
\(752\) 35063.7 1.70032
\(753\) −25952.6 −1.25600
\(754\) 4734.02 0.228651
\(755\) −17193.1 −0.828769
\(756\) 36049.0 1.73424
\(757\) 19278.0 0.925589 0.462794 0.886466i \(-0.346847\pi\)
0.462794 + 0.886466i \(0.346847\pi\)
\(758\) −14795.7 −0.708975
\(759\) −1282.08 −0.0613132
\(760\) 24272.3 1.15849
\(761\) −1332.42 −0.0634692 −0.0317346 0.999496i \(-0.510103\pi\)
−0.0317346 + 0.999496i \(0.510103\pi\)
\(762\) −37642.3 −1.78955
\(763\) −25616.3 −1.21543
\(764\) −45052.9 −2.13345
\(765\) −4532.53 −0.214214
\(766\) −40808.3 −1.92489
\(767\) −12266.6 −0.577475
\(768\) 143008. 6.71922
\(769\) 17605.9 0.825599 0.412800 0.910822i \(-0.364551\pi\)
0.412800 + 0.910822i \(0.364551\pi\)
\(770\) −12492.0 −0.584648
\(771\) −22761.0 −1.06319
\(772\) −78008.5 −3.63677
\(773\) −16456.0 −0.765694 −0.382847 0.923812i \(-0.625056\pi\)
−0.382847 + 0.923812i \(0.625056\pi\)
\(774\) 0 0
\(775\) −10514.3 −0.487337
\(776\) −134375. −6.21619
\(777\) −64933.3 −2.99803
\(778\) −14983.9 −0.690487
\(779\) −3127.40 −0.143839
\(780\) 46003.5 2.11178
\(781\) −240.575 −0.0110224
\(782\) 3152.75 0.144171
\(783\) 1376.69 0.0628336
\(784\) 109948. 5.00856
\(785\) −15961.6 −0.725726
\(786\) 108495. 4.92351
\(787\) −8543.07 −0.386948 −0.193474 0.981105i \(-0.561975\pi\)
−0.193474 + 0.981105i \(0.561975\pi\)
\(788\) −72750.4 −3.28886
\(789\) −21659.5 −0.977309
\(790\) 24235.6 1.09147
\(791\) 20270.3 0.911162
\(792\) 15011.4 0.673496
\(793\) −3530.26 −0.158087
\(794\) −44422.6 −1.98552
\(795\) 31282.3 1.39556
\(796\) −20414.1 −0.908995
\(797\) 13935.4 0.619345 0.309672 0.950843i \(-0.399781\pi\)
0.309672 + 0.950843i \(0.399781\pi\)
\(798\) −36045.5 −1.59899
\(799\) −3768.68 −0.166866
\(800\) 48117.6 2.12652
\(801\) −20873.1 −0.920744
\(802\) 9195.38 0.404863
\(803\) 3665.89 0.161104
\(804\) −92938.8 −4.07674
\(805\) −4367.98 −0.191244
\(806\) −37725.4 −1.64866
\(807\) 11062.3 0.482541
\(808\) −94771.8 −4.12631
\(809\) 28901.8 1.25604 0.628019 0.778198i \(-0.283866\pi\)
0.628019 + 0.778198i \(0.283866\pi\)
\(810\) 41071.4 1.78161
\(811\) 22920.0 0.992391 0.496196 0.868211i \(-0.334730\pi\)
0.496196 + 0.868211i \(0.334730\pi\)
\(812\) 14799.2 0.639595
\(813\) 10799.7 0.465881
\(814\) 19432.0 0.836721
\(815\) 3505.53 0.150667
\(816\) −54700.6 −2.34670
\(817\) 0 0
\(818\) −13055.2 −0.558027
\(819\) −17992.2 −0.767641
\(820\) 16848.7 0.717538
\(821\) −11385.2 −0.483980 −0.241990 0.970279i \(-0.577800\pi\)
−0.241990 + 0.970279i \(0.577800\pi\)
\(822\) 54126.1 2.29667
\(823\) 18547.7 0.785580 0.392790 0.919628i \(-0.371510\pi\)
0.392790 + 0.919628i \(0.371510\pi\)
\(824\) 29148.6 1.23233
\(825\) 3701.98 0.156226
\(826\) −51780.8 −2.18122
\(827\) 35248.8 1.48213 0.741065 0.671434i \(-0.234321\pi\)
0.741065 + 0.671434i \(0.234321\pi\)
\(828\) 8079.21 0.339097
\(829\) −14809.3 −0.620444 −0.310222 0.950664i \(-0.600403\pi\)
−0.310222 + 0.950664i \(0.600403\pi\)
\(830\) −29090.9 −1.21658
\(831\) −2638.23 −0.110131
\(832\) 93805.4 3.90879
\(833\) −11817.3 −0.491532
\(834\) 61431.7 2.55061
\(835\) 4556.20 0.188831
\(836\) 7988.51 0.330489
\(837\) −10970.8 −0.453054
\(838\) −69956.9 −2.88379
\(839\) −3415.56 −0.140546 −0.0702730 0.997528i \(-0.522387\pi\)
−0.0702730 + 0.997528i \(0.522387\pi\)
\(840\) 126165. 5.18226
\(841\) −23823.8 −0.976827
\(842\) −81176.2 −3.32247
\(843\) −4133.39 −0.168875
\(844\) −64634.5 −2.63603
\(845\) −7595.46 −0.309221
\(846\) −13040.8 −0.529966
\(847\) 33611.0 1.36351
\(848\) 153038. 6.19733
\(849\) −21492.0 −0.868792
\(850\) −9103.45 −0.367348
\(851\) 6794.66 0.273699
\(852\) 3739.85 0.150382
\(853\) −14467.2 −0.580712 −0.290356 0.956919i \(-0.593774\pi\)
−0.290356 + 0.956919i \(0.593774\pi\)
\(854\) −14902.2 −0.597122
\(855\) −5422.53 −0.216897
\(856\) 160207. 6.39694
\(857\) −1495.92 −0.0596262 −0.0298131 0.999555i \(-0.509491\pi\)
−0.0298131 + 0.999555i \(0.509491\pi\)
\(858\) 13282.6 0.528511
\(859\) −14786.2 −0.587309 −0.293655 0.955912i \(-0.594872\pi\)
−0.293655 + 0.955912i \(0.594872\pi\)
\(860\) 0 0
\(861\) −16255.9 −0.643436
\(862\) 89238.9 3.52609
\(863\) −27686.3 −1.09207 −0.546033 0.837763i \(-0.683863\pi\)
−0.546033 + 0.837763i \(0.683863\pi\)
\(864\) 50206.5 1.97692
\(865\) −6823.68 −0.268222
\(866\) −22394.7 −0.878755
\(867\) −27226.5 −1.06651
\(868\) −117935. −4.61171
\(869\) 5182.19 0.202294
\(870\) 7416.11 0.289000
\(871\) −21657.7 −0.842529
\(872\) −77423.6 −3.00676
\(873\) 30019.8 1.16382
\(874\) 3771.82 0.145977
\(875\) 41019.0 1.58479
\(876\) −56987.9 −2.19800
\(877\) 1957.85 0.0753843 0.0376921 0.999289i \(-0.487999\pi\)
0.0376921 + 0.999289i \(0.487999\pi\)
\(878\) −41425.6 −1.59231
\(879\) −15970.1 −0.612807
\(880\) −22679.5 −0.868778
\(881\) 14947.8 0.571629 0.285815 0.958285i \(-0.407736\pi\)
0.285815 + 0.958285i \(0.407736\pi\)
\(882\) −40891.5 −1.56110
\(883\) −6284.37 −0.239509 −0.119754 0.992804i \(-0.538211\pi\)
−0.119754 + 0.992804i \(0.538211\pi\)
\(884\) −24189.3 −0.920332
\(885\) −19216.4 −0.729889
\(886\) 25049.8 0.949848
\(887\) 42767.5 1.61893 0.809465 0.587168i \(-0.199757\pi\)
0.809465 + 0.587168i \(0.199757\pi\)
\(888\) −196257. −7.41661
\(889\) −27422.0 −1.03454
\(890\) 52499.2 1.97728
\(891\) 8782.11 0.330204
\(892\) 139007. 5.21781
\(893\) −4508.69 −0.168956
\(894\) 35148.8 1.31494
\(895\) −27546.2 −1.02879
\(896\) 206909. 7.71466
\(897\) 4644.46 0.172881
\(898\) 36074.8 1.34057
\(899\) −4503.85 −0.167088
\(900\) −23328.4 −0.864016
\(901\) −16448.6 −0.608195
\(902\) 4864.74 0.179577
\(903\) 0 0
\(904\) 61265.7 2.25406
\(905\) −21754.7 −0.799062
\(906\) 77170.5 2.82982
\(907\) 21527.8 0.788112 0.394056 0.919086i \(-0.371072\pi\)
0.394056 + 0.919086i \(0.371072\pi\)
\(908\) 80647.3 2.94755
\(909\) 21172.4 0.772546
\(910\) 45253.1 1.64849
\(911\) 11639.2 0.423299 0.211650 0.977346i \(-0.432116\pi\)
0.211650 + 0.977346i \(0.432116\pi\)
\(912\) −65441.5 −2.37608
\(913\) −6220.36 −0.225481
\(914\) −24725.6 −0.894804
\(915\) −5530.35 −0.199812
\(916\) 83934.5 3.02759
\(917\) 79037.4 2.84629
\(918\) −9498.65 −0.341506
\(919\) 38878.1 1.39551 0.697753 0.716338i \(-0.254183\pi\)
0.697753 + 0.716338i \(0.254183\pi\)
\(920\) −13201.9 −0.473103
\(921\) −10012.4 −0.358220
\(922\) 94749.9 3.38440
\(923\) 871.504 0.0310790
\(924\) 41523.4 1.47838
\(925\) −19619.3 −0.697383
\(926\) 104568. 3.71092
\(927\) −6511.91 −0.230722
\(928\) 20611.3 0.729094
\(929\) −21729.0 −0.767391 −0.383695 0.923460i \(-0.625349\pi\)
−0.383695 + 0.923460i \(0.625349\pi\)
\(930\) −59098.9 −2.08379
\(931\) −14137.8 −0.497687
\(932\) 55858.3 1.96320
\(933\) −32343.2 −1.13491
\(934\) −13635.2 −0.477684
\(935\) 2437.61 0.0852604
\(936\) −54380.2 −1.89901
\(937\) 2387.68 0.0832466 0.0416233 0.999133i \(-0.486747\pi\)
0.0416233 + 0.999133i \(0.486747\pi\)
\(938\) −91422.9 −3.18237
\(939\) −11878.8 −0.412832
\(940\) 24290.3 0.842834
\(941\) −32184.8 −1.11498 −0.557489 0.830185i \(-0.688235\pi\)
−0.557489 + 0.830185i \(0.688235\pi\)
\(942\) 71643.1 2.47798
\(943\) 1701.02 0.0587411
\(944\) −94009.4 −3.24126
\(945\) 13159.9 0.453008
\(946\) 0 0
\(947\) −38920.2 −1.33552 −0.667760 0.744376i \(-0.732747\pi\)
−0.667760 + 0.744376i \(0.732747\pi\)
\(948\) −80559.6 −2.75997
\(949\) −13280.0 −0.454254
\(950\) −10891.0 −0.371948
\(951\) −28779.8 −0.981333
\(952\) −66339.2 −2.25847
\(953\) −22243.3 −0.756067 −0.378034 0.925792i \(-0.623400\pi\)
−0.378034 + 0.925792i \(0.623400\pi\)
\(954\) −56917.3 −1.93162
\(955\) −16446.9 −0.557287
\(956\) −7929.44 −0.268260
\(957\) 1585.75 0.0535633
\(958\) 63328.0 2.13574
\(959\) 39430.3 1.32771
\(960\) 146951. 4.94045
\(961\) 6100.13 0.204764
\(962\) −70394.0 −2.35924
\(963\) −35791.0 −1.19766
\(964\) 62819.3 2.09883
\(965\) −28477.5 −0.949974
\(966\) 19605.5 0.652999
\(967\) −28555.0 −0.949603 −0.474801 0.880093i \(-0.657480\pi\)
−0.474801 + 0.880093i \(0.657480\pi\)
\(968\) 101587. 3.37307
\(969\) 7033.73 0.233185
\(970\) −75504.6 −2.49928
\(971\) −20068.7 −0.663269 −0.331634 0.943408i \(-0.607600\pi\)
−0.331634 + 0.943408i \(0.607600\pi\)
\(972\) −100816. −3.32682
\(973\) 44752.4 1.47451
\(974\) 30028.3 0.987853
\(975\) −13410.7 −0.440499
\(976\) −27055.3 −0.887314
\(977\) 2742.71 0.0898128 0.0449064 0.998991i \(-0.485701\pi\)
0.0449064 + 0.998991i \(0.485701\pi\)
\(978\) −15734.4 −0.514449
\(979\) 11225.7 0.366469
\(980\) 76166.4 2.48270
\(981\) 17296.8 0.562939
\(982\) 83277.0 2.70619
\(983\) −52945.4 −1.71790 −0.858950 0.512059i \(-0.828883\pi\)
−0.858950 + 0.512059i \(0.828883\pi\)
\(984\) −49132.3 −1.59175
\(985\) −26558.0 −0.859095
\(986\) −3899.49 −0.125948
\(987\) −23435.7 −0.755792
\(988\) −28939.1 −0.931856
\(989\) 0 0
\(990\) 8434.88 0.270786
\(991\) 7835.58 0.251166 0.125583 0.992083i \(-0.459920\pi\)
0.125583 + 0.992083i \(0.459920\pi\)
\(992\) −164251. −5.25704
\(993\) 64847.2 2.07237
\(994\) 3678.85 0.117390
\(995\) −7452.32 −0.237442
\(996\) 96698.4 3.07631
\(997\) −35826.3 −1.13804 −0.569022 0.822322i \(-0.692678\pi\)
−0.569022 + 0.822322i \(0.692678\pi\)
\(998\) −59534.1 −1.88829
\(999\) −20471.0 −0.648323
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 1849.4.a.g.1.1 30
43.8 odd 14 43.4.e.a.21.1 60
43.27 odd 14 43.4.e.a.41.1 yes 60
43.42 odd 2 1849.4.a.h.1.30 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.4.e.a.21.1 60 43.8 odd 14
43.4.e.a.41.1 yes 60 43.27 odd 14
1849.4.a.g.1.1 30 1.1 even 1 trivial
1849.4.a.h.1.30 30 43.42 odd 2