Properties

Label 1849.4.a.j.1.6
Level $1849$
Weight $4$
Character 1849.1
Self dual yes
Analytic conductor $109.095$
Analytic rank $1$
Dimension $50$
CM no
Inner twists $1$

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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: \(50\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Character \(\chi\) \(=\) 1849.1

$q$-expansion

\(f(q)\) \(=\) \(q-4.32699 q^{2} +4.31725 q^{3} +10.7228 q^{4} -7.58298 q^{5} -18.6807 q^{6} -15.1566 q^{7} -11.7817 q^{8} -8.36138 q^{9} +O(q^{10})\) \(q-4.32699 q^{2} +4.31725 q^{3} +10.7228 q^{4} -7.58298 q^{5} -18.6807 q^{6} -15.1566 q^{7} -11.7817 q^{8} -8.36138 q^{9} +32.8115 q^{10} -4.61811 q^{11} +46.2932 q^{12} +4.43823 q^{13} +65.5824 q^{14} -32.7376 q^{15} -34.8034 q^{16} -58.9409 q^{17} +36.1796 q^{18} +40.0098 q^{19} -81.3111 q^{20} -65.4347 q^{21} +19.9825 q^{22} +205.181 q^{23} -50.8646 q^{24} -67.4984 q^{25} -19.2042 q^{26} -152.664 q^{27} -162.522 q^{28} +248.436 q^{29} +141.655 q^{30} -63.1080 q^{31} +244.848 q^{32} -19.9375 q^{33} +255.037 q^{34} +114.932 q^{35} -89.6578 q^{36} +151.955 q^{37} -173.122 q^{38} +19.1609 q^{39} +89.3405 q^{40} -292.670 q^{41} +283.135 q^{42} -49.5192 q^{44} +63.4042 q^{45} -887.818 q^{46} -100.429 q^{47} -150.255 q^{48} -113.278 q^{49} +292.065 q^{50} -254.462 q^{51} +47.5905 q^{52} +566.570 q^{53} +660.575 q^{54} +35.0190 q^{55} +178.571 q^{56} +172.732 q^{57} -1074.98 q^{58} +730.172 q^{59} -351.040 q^{60} +928.090 q^{61} +273.068 q^{62} +126.730 q^{63} -781.026 q^{64} -33.6550 q^{65} +86.2694 q^{66} -61.7700 q^{67} -632.014 q^{68} +885.819 q^{69} -497.310 q^{70} +66.4400 q^{71} +98.5114 q^{72} +408.464 q^{73} -657.506 q^{74} -291.407 q^{75} +429.019 q^{76} +69.9947 q^{77} -82.9092 q^{78} +583.475 q^{79} +263.913 q^{80} -433.330 q^{81} +1266.38 q^{82} -1149.74 q^{83} -701.646 q^{84} +446.948 q^{85} +1072.56 q^{87} +54.4092 q^{88} -977.540 q^{89} -274.349 q^{90} -67.2684 q^{91} +2200.13 q^{92} -272.453 q^{93} +434.554 q^{94} -303.394 q^{95} +1057.07 q^{96} +254.707 q^{97} +490.153 q^{98} +38.6137 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q + 10q^{2} + 2q^{3} + 186q^{4} - 8q^{5} - 51q^{6} + 6q^{7} + 138q^{8} + 360q^{9} + O(q^{10}) \) \( 50q + 10q^{2} + 2q^{3} + 186q^{4} - 8q^{5} - 51q^{6} + 6q^{7} + 138q^{8} + 360q^{9} - 137q^{10} - 252q^{11} + 48q^{12} - 192q^{13} - 272q^{14} - 314q^{15} + 542q^{16} - 236q^{17} + 386q^{18} - 12q^{19} - 108q^{20} - 408q^{21} - 1235q^{22} - 630q^{23} - 613q^{24} + 1098q^{25} - 1493q^{26} - 10q^{27} + 242q^{28} - 208q^{29} + 48q^{30} - 932q^{31} + 1124q^{32} - 254q^{33} - 765q^{34} - 1452q^{35} + 747q^{36} + 90q^{37} - 1213q^{38} + 1610q^{39} - 1693q^{40} - 1354q^{41} + 16q^{42} - 2704q^{44} - 4508q^{45} - 233q^{46} - 3484q^{47} + 376q^{48} + 1324q^{49} + 408q^{50} - 4054q^{51} - 2176q^{52} - 726q^{53} - 6497q^{54} + 3288q^{55} - 7097q^{56} - 870q^{57} + 275q^{58} - 4370q^{59} - 3891q^{60} - 1172q^{61} + 1546q^{62} + 3686q^{63} + 606q^{64} - 2610q^{65} - 4697q^{66} - 344q^{67} - 3221q^{68} - 136q^{69} + 1310q^{70} - 162q^{71} + 5814q^{72} - 746q^{73} - 4332q^{74} - 236q^{75} - 1338q^{76} - 2024q^{77} - 2782q^{78} - 2656q^{79} + 5713q^{80} - 86q^{81} + 4168q^{82} - 3514q^{83} - 4269q^{84} + 7558q^{85} - 10278q^{87} - 11692q^{88} - 2640q^{89} - 8286q^{90} + 5946q^{91} - 4271q^{92} + 2q^{93} - 9062q^{94} - 12140q^{95} - 700q^{96} - 3864q^{97} + 2826q^{98} - 8174q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.32699 −1.52982 −0.764911 0.644136i \(-0.777217\pi\)
−0.764911 + 0.644136i \(0.777217\pi\)
\(3\) 4.31725 0.830855 0.415427 0.909626i \(-0.363632\pi\)
0.415427 + 0.909626i \(0.363632\pi\)
\(4\) 10.7228 1.34036
\(5\) −7.58298 −0.678242 −0.339121 0.940743i \(-0.610130\pi\)
−0.339121 + 0.940743i \(0.610130\pi\)
\(6\) −18.6807 −1.27106
\(7\) −15.1566 −0.818379 −0.409189 0.912450i \(-0.634188\pi\)
−0.409189 + 0.912450i \(0.634188\pi\)
\(8\) −11.7817 −0.520683
\(9\) −8.36138 −0.309681
\(10\) 32.8115 1.03759
\(11\) −4.61811 −0.126583 −0.0632914 0.997995i \(-0.520160\pi\)
−0.0632914 + 0.997995i \(0.520160\pi\)
\(12\) 46.2932 1.11364
\(13\) 4.43823 0.0946880 0.0473440 0.998879i \(-0.484924\pi\)
0.0473440 + 0.998879i \(0.484924\pi\)
\(14\) 65.5824 1.25197
\(15\) −32.7376 −0.563521
\(16\) −34.8034 −0.543803
\(17\) −58.9409 −0.840898 −0.420449 0.907316i \(-0.638127\pi\)
−0.420449 + 0.907316i \(0.638127\pi\)
\(18\) 36.1796 0.473756
\(19\) 40.0098 0.483099 0.241550 0.970388i \(-0.422344\pi\)
0.241550 + 0.970388i \(0.422344\pi\)
\(20\) −81.3111 −0.909086
\(21\) −65.4347 −0.679953
\(22\) 19.9825 0.193649
\(23\) 205.181 1.86014 0.930071 0.367379i \(-0.119745\pi\)
0.930071 + 0.367379i \(0.119745\pi\)
\(24\) −50.8646 −0.432612
\(25\) −67.4984 −0.539987
\(26\) −19.2042 −0.144856
\(27\) −152.664 −1.08815
\(28\) −162.522 −1.09692
\(29\) 248.436 1.59081 0.795403 0.606081i \(-0.207259\pi\)
0.795403 + 0.606081i \(0.207259\pi\)
\(30\) 141.655 0.862086
\(31\) −63.1080 −0.365630 −0.182815 0.983147i \(-0.558521\pi\)
−0.182815 + 0.983147i \(0.558521\pi\)
\(32\) 244.848 1.35260
\(33\) −19.9375 −0.105172
\(34\) 255.037 1.28642
\(35\) 114.932 0.555059
\(36\) −89.6578 −0.415082
\(37\) 151.955 0.675167 0.337583 0.941296i \(-0.390390\pi\)
0.337583 + 0.941296i \(0.390390\pi\)
\(38\) −173.122 −0.739056
\(39\) 19.1609 0.0786720
\(40\) 89.3405 0.353150
\(41\) −292.670 −1.11481 −0.557407 0.830239i \(-0.688204\pi\)
−0.557407 + 0.830239i \(0.688204\pi\)
\(42\) 283.135 1.04021
\(43\) 0 0
\(44\) −49.5192 −0.169666
\(45\) 63.4042 0.210039
\(46\) −887.818 −2.84569
\(47\) −100.429 −0.311682 −0.155841 0.987782i \(-0.549809\pi\)
−0.155841 + 0.987782i \(0.549809\pi\)
\(48\) −150.255 −0.451821
\(49\) −113.278 −0.330257
\(50\) 292.065 0.826084
\(51\) −254.462 −0.698664
\(52\) 47.5905 0.126916
\(53\) 566.570 1.46838 0.734192 0.678942i \(-0.237561\pi\)
0.734192 + 0.678942i \(0.237561\pi\)
\(54\) 660.575 1.66468
\(55\) 35.0190 0.0858539
\(56\) 178.571 0.426116
\(57\) 172.732 0.401385
\(58\) −1074.98 −2.43365
\(59\) 730.172 1.61119 0.805596 0.592466i \(-0.201846\pi\)
0.805596 + 0.592466i \(0.201846\pi\)
\(60\) −351.040 −0.755318
\(61\) 928.090 1.94803 0.974014 0.226486i \(-0.0727238\pi\)
0.974014 + 0.226486i \(0.0727238\pi\)
\(62\) 273.068 0.559349
\(63\) 126.730 0.253436
\(64\) −781.026 −1.52544
\(65\) −33.6550 −0.0642214
\(66\) 86.2694 0.160894
\(67\) −61.7700 −0.112633 −0.0563164 0.998413i \(-0.517936\pi\)
−0.0563164 + 0.998413i \(0.517936\pi\)
\(68\) −632.014 −1.12710
\(69\) 885.819 1.54551
\(70\) −497.310 −0.849141
\(71\) 66.4400 0.111056 0.0555280 0.998457i \(-0.482316\pi\)
0.0555280 + 0.998457i \(0.482316\pi\)
\(72\) 98.5114 0.161246
\(73\) 408.464 0.654892 0.327446 0.944870i \(-0.393812\pi\)
0.327446 + 0.944870i \(0.393812\pi\)
\(74\) −657.506 −1.03289
\(75\) −291.407 −0.448651
\(76\) 429.019 0.647525
\(77\) 69.9947 0.103593
\(78\) −82.9092 −0.120354
\(79\) 583.475 0.830962 0.415481 0.909602i \(-0.363613\pi\)
0.415481 + 0.909602i \(0.363613\pi\)
\(80\) 263.913 0.368830
\(81\) −433.330 −0.594417
\(82\) 1266.38 1.70547
\(83\) −1149.74 −1.52049 −0.760246 0.649635i \(-0.774922\pi\)
−0.760246 + 0.649635i \(0.774922\pi\)
\(84\) −701.646 −0.911379
\(85\) 446.948 0.570333
\(86\) 0 0
\(87\) 1072.56 1.32173
\(88\) 54.4092 0.0659096
\(89\) −977.540 −1.16426 −0.582129 0.813096i \(-0.697780\pi\)
−0.582129 + 0.813096i \(0.697780\pi\)
\(90\) −274.349 −0.321322
\(91\) −67.2684 −0.0774906
\(92\) 2200.13 2.49325
\(93\) −272.453 −0.303785
\(94\) 434.554 0.476818
\(95\) −303.394 −0.327658
\(96\) 1057.07 1.12382
\(97\) 254.707 0.266614 0.133307 0.991075i \(-0.457440\pi\)
0.133307 + 0.991075i \(0.457440\pi\)
\(98\) 490.153 0.505234
\(99\) 38.6137 0.0392003
\(100\) −723.775 −0.723775
\(101\) −1396.17 −1.37548 −0.687742 0.725955i \(-0.741398\pi\)
−0.687742 + 0.725955i \(0.741398\pi\)
\(102\) 1101.06 1.06883
\(103\) −770.884 −0.737451 −0.368725 0.929538i \(-0.620206\pi\)
−0.368725 + 0.929538i \(0.620206\pi\)
\(104\) −52.2900 −0.0493025
\(105\) 496.190 0.461173
\(106\) −2451.54 −2.24637
\(107\) −559.189 −0.505223 −0.252611 0.967568i \(-0.581289\pi\)
−0.252611 + 0.967568i \(0.581289\pi\)
\(108\) −1636.99 −1.45851
\(109\) 309.168 0.271678 0.135839 0.990731i \(-0.456627\pi\)
0.135839 + 0.990731i \(0.456627\pi\)
\(110\) −151.527 −0.131341
\(111\) 656.025 0.560966
\(112\) 527.500 0.445036
\(113\) −1649.23 −1.37298 −0.686490 0.727139i \(-0.740850\pi\)
−0.686490 + 0.727139i \(0.740850\pi\)
\(114\) −747.411 −0.614048
\(115\) −1555.89 −1.26163
\(116\) 2663.94 2.13225
\(117\) −37.1098 −0.0293231
\(118\) −3159.45 −2.46484
\(119\) 893.343 0.688173
\(120\) 385.705 0.293416
\(121\) −1309.67 −0.983977
\(122\) −4015.84 −2.98014
\(123\) −1263.53 −0.926249
\(124\) −676.697 −0.490074
\(125\) 1459.71 1.04448
\(126\) −548.359 −0.387712
\(127\) −1484.24 −1.03705 −0.518525 0.855062i \(-0.673519\pi\)
−0.518525 + 0.855062i \(0.673519\pi\)
\(128\) 1420.71 0.981050
\(129\) 0 0
\(130\) 145.625 0.0982474
\(131\) −2344.14 −1.56343 −0.781713 0.623638i \(-0.785654\pi\)
−0.781713 + 0.623638i \(0.785654\pi\)
\(132\) −213.787 −0.140968
\(133\) −606.412 −0.395358
\(134\) 267.278 0.172308
\(135\) 1157.65 0.738032
\(136\) 694.425 0.437842
\(137\) 1016.32 0.633797 0.316899 0.948459i \(-0.397359\pi\)
0.316899 + 0.948459i \(0.397359\pi\)
\(138\) −3832.93 −2.36435
\(139\) 1637.27 0.999073 0.499536 0.866293i \(-0.333504\pi\)
0.499536 + 0.866293i \(0.333504\pi\)
\(140\) 1232.40 0.743976
\(141\) −433.576 −0.258962
\(142\) −287.485 −0.169896
\(143\) −20.4962 −0.0119859
\(144\) 291.004 0.168405
\(145\) −1883.88 −1.07895
\(146\) −1767.42 −1.00187
\(147\) −489.049 −0.274395
\(148\) 1629.39 0.904964
\(149\) 2190.65 1.20446 0.602232 0.798321i \(-0.294278\pi\)
0.602232 + 0.798321i \(0.294278\pi\)
\(150\) 1260.92 0.686356
\(151\) 2993.00 1.61302 0.806512 0.591218i \(-0.201353\pi\)
0.806512 + 0.591218i \(0.201353\pi\)
\(152\) −471.385 −0.251542
\(153\) 492.827 0.260410
\(154\) −302.866 −0.158478
\(155\) 478.546 0.247986
\(156\) 205.460 0.105448
\(157\) 1276.61 0.648948 0.324474 0.945895i \(-0.394813\pi\)
0.324474 + 0.945895i \(0.394813\pi\)
\(158\) −2524.69 −1.27122
\(159\) 2446.02 1.22001
\(160\) −1856.67 −0.917394
\(161\) −3109.85 −1.52230
\(162\) 1875.01 0.909352
\(163\) 1124.07 0.540148 0.270074 0.962840i \(-0.412952\pi\)
0.270074 + 0.962840i \(0.412952\pi\)
\(164\) −3138.26 −1.49425
\(165\) 151.186 0.0713321
\(166\) 4974.93 2.32608
\(167\) 3171.73 1.46968 0.734838 0.678242i \(-0.237258\pi\)
0.734838 + 0.678242i \(0.237258\pi\)
\(168\) 770.933 0.354040
\(169\) −2177.30 −0.991034
\(170\) −1933.94 −0.872508
\(171\) −334.537 −0.149607
\(172\) 0 0
\(173\) −364.520 −0.160196 −0.0800982 0.996787i \(-0.525523\pi\)
−0.0800982 + 0.996787i \(0.525523\pi\)
\(174\) −4640.95 −2.02201
\(175\) 1023.05 0.441914
\(176\) 160.726 0.0688361
\(177\) 3152.33 1.33867
\(178\) 4229.81 1.78111
\(179\) −2292.73 −0.957355 −0.478677 0.877991i \(-0.658884\pi\)
−0.478677 + 0.877991i \(0.658884\pi\)
\(180\) 679.873 0.281526
\(181\) 989.703 0.406431 0.203216 0.979134i \(-0.434861\pi\)
0.203216 + 0.979134i \(0.434861\pi\)
\(182\) 291.070 0.118547
\(183\) 4006.79 1.61853
\(184\) −2417.39 −0.968545
\(185\) −1152.27 −0.457927
\(186\) 1178.90 0.464737
\(187\) 272.195 0.106443
\(188\) −1076.88 −0.417764
\(189\) 2313.86 0.890522
\(190\) 1312.78 0.501259
\(191\) −1523.76 −0.577254 −0.288627 0.957442i \(-0.593199\pi\)
−0.288627 + 0.957442i \(0.593199\pi\)
\(192\) −3371.88 −1.26742
\(193\) −794.523 −0.296326 −0.148163 0.988963i \(-0.547336\pi\)
−0.148163 + 0.988963i \(0.547336\pi\)
\(194\) −1102.12 −0.407872
\(195\) −145.297 −0.0533587
\(196\) −1214.66 −0.442661
\(197\) −5363.39 −1.93973 −0.969863 0.243652i \(-0.921655\pi\)
−0.969863 + 0.243652i \(0.921655\pi\)
\(198\) −167.081 −0.0599695
\(199\) 4058.33 1.44566 0.722832 0.691024i \(-0.242840\pi\)
0.722832 + 0.691024i \(0.242840\pi\)
\(200\) 795.247 0.281162
\(201\) −266.676 −0.0935815
\(202\) 6041.21 2.10425
\(203\) −3765.44 −1.30188
\(204\) −2728.56 −0.936458
\(205\) 2219.31 0.756114
\(206\) 3335.61 1.12817
\(207\) −1715.60 −0.576050
\(208\) −154.465 −0.0514916
\(209\) −184.770 −0.0611521
\(210\) −2147.01 −0.705513
\(211\) −1338.34 −0.436658 −0.218329 0.975875i \(-0.570061\pi\)
−0.218329 + 0.975875i \(0.570061\pi\)
\(212\) 6075.24 1.96816
\(213\) 286.838 0.0922715
\(214\) 2419.60 0.772901
\(215\) 0 0
\(216\) 1798.64 0.566584
\(217\) 956.501 0.299224
\(218\) −1337.77 −0.415619
\(219\) 1763.44 0.544120
\(220\) 375.503 0.115075
\(221\) −261.593 −0.0796230
\(222\) −2838.62 −0.858177
\(223\) 334.702 0.100508 0.0502540 0.998736i \(-0.483997\pi\)
0.0502540 + 0.998736i \(0.483997\pi\)
\(224\) −3711.05 −1.10694
\(225\) 564.380 0.167224
\(226\) 7136.22 2.10042
\(227\) −1321.17 −0.386294 −0.193147 0.981170i \(-0.561869\pi\)
−0.193147 + 0.981170i \(0.561869\pi\)
\(228\) 1852.18 0.537999
\(229\) −1838.72 −0.530594 −0.265297 0.964167i \(-0.585470\pi\)
−0.265297 + 0.964167i \(0.585470\pi\)
\(230\) 6732.31 1.93007
\(231\) 302.184 0.0860705
\(232\) −2927.00 −0.828306
\(233\) −2469.71 −0.694403 −0.347202 0.937791i \(-0.612868\pi\)
−0.347202 + 0.937791i \(0.612868\pi\)
\(234\) 160.574 0.0448591
\(235\) 761.550 0.211396
\(236\) 7829.52 2.15957
\(237\) 2519.00 0.690409
\(238\) −3865.48 −1.05278
\(239\) −6493.53 −1.75746 −0.878728 0.477324i \(-0.841607\pi\)
−0.878728 + 0.477324i \(0.841607\pi\)
\(240\) 1139.38 0.306444
\(241\) 546.111 0.145967 0.0729836 0.997333i \(-0.476748\pi\)
0.0729836 + 0.997333i \(0.476748\pi\)
\(242\) 5666.94 1.50531
\(243\) 2251.13 0.594280
\(244\) 9951.76 2.61105
\(245\) 858.985 0.223994
\(246\) 5467.28 1.41700
\(247\) 177.573 0.0457437
\(248\) 743.520 0.190377
\(249\) −4963.73 −1.26331
\(250\) −6316.16 −1.59788
\(251\) 3433.75 0.863493 0.431746 0.901995i \(-0.357898\pi\)
0.431746 + 0.901995i \(0.357898\pi\)
\(252\) 1358.91 0.339694
\(253\) −947.550 −0.235462
\(254\) 6422.31 1.58650
\(255\) 1929.58 0.473864
\(256\) 100.803 0.0246101
\(257\) 485.127 0.117749 0.0588743 0.998265i \(-0.481249\pi\)
0.0588743 + 0.998265i \(0.481249\pi\)
\(258\) 0 0
\(259\) −2303.11 −0.552542
\(260\) −360.878 −0.0860795
\(261\) −2077.27 −0.492642
\(262\) 10143.1 2.39176
\(263\) 1318.47 0.309126 0.154563 0.987983i \(-0.450603\pi\)
0.154563 + 0.987983i \(0.450603\pi\)
\(264\) 234.898 0.0547613
\(265\) −4296.29 −0.995920
\(266\) 2623.94 0.604827
\(267\) −4220.28 −0.967330
\(268\) −662.350 −0.150968
\(269\) −1988.06 −0.450610 −0.225305 0.974288i \(-0.572338\pi\)
−0.225305 + 0.974288i \(0.572338\pi\)
\(270\) −5009.13 −1.12906
\(271\) 7179.43 1.60930 0.804648 0.593752i \(-0.202354\pi\)
0.804648 + 0.593752i \(0.202354\pi\)
\(272\) 2051.34 0.457283
\(273\) −290.414 −0.0643834
\(274\) −4397.61 −0.969597
\(275\) 311.715 0.0683531
\(276\) 9498.50 2.07153
\(277\) −3471.68 −0.753043 −0.376521 0.926408i \(-0.622880\pi\)
−0.376521 + 0.926408i \(0.622880\pi\)
\(278\) −7084.44 −1.52840
\(279\) 527.670 0.113229
\(280\) −1354.10 −0.289010
\(281\) 2360.71 0.501168 0.250584 0.968095i \(-0.419377\pi\)
0.250584 + 0.968095i \(0.419377\pi\)
\(282\) 1876.08 0.396166
\(283\) −3584.19 −0.752854 −0.376427 0.926446i \(-0.622847\pi\)
−0.376427 + 0.926446i \(0.622847\pi\)
\(284\) 712.426 0.148855
\(285\) −1309.83 −0.272236
\(286\) 88.6870 0.0183363
\(287\) 4435.88 0.912340
\(288\) −2047.26 −0.418876
\(289\) −1438.97 −0.292890
\(290\) 8151.55 1.65060
\(291\) 1099.63 0.221518
\(292\) 4379.90 0.877788
\(293\) −218.871 −0.0436403 −0.0218201 0.999762i \(-0.506946\pi\)
−0.0218201 + 0.999762i \(0.506946\pi\)
\(294\) 2116.11 0.419776
\(295\) −5536.88 −1.09278
\(296\) −1790.29 −0.351548
\(297\) 705.018 0.137742
\(298\) −9478.93 −1.84262
\(299\) 910.643 0.176133
\(300\) −3124.72 −0.601352
\(301\) 0 0
\(302\) −12950.7 −2.46764
\(303\) −6027.60 −1.14283
\(304\) −1392.48 −0.262711
\(305\) −7037.69 −1.32124
\(306\) −2132.46 −0.398381
\(307\) −2450.11 −0.455488 −0.227744 0.973721i \(-0.573135\pi\)
−0.227744 + 0.973721i \(0.573135\pi\)
\(308\) 750.542 0.138851
\(309\) −3328.09 −0.612714
\(310\) −2070.67 −0.379374
\(311\) −818.907 −0.149312 −0.0746559 0.997209i \(-0.523786\pi\)
−0.0746559 + 0.997209i \(0.523786\pi\)
\(312\) −225.749 −0.0409632
\(313\) 1988.86 0.359159 0.179579 0.983743i \(-0.442526\pi\)
0.179579 + 0.983743i \(0.442526\pi\)
\(314\) −5523.89 −0.992775
\(315\) −960.991 −0.171891
\(316\) 6256.51 1.11379
\(317\) −4046.09 −0.716880 −0.358440 0.933553i \(-0.616691\pi\)
−0.358440 + 0.933553i \(0.616691\pi\)
\(318\) −10583.9 −1.86640
\(319\) −1147.30 −0.201369
\(320\) 5922.51 1.03462
\(321\) −2414.16 −0.419767
\(322\) 13456.3 2.32885
\(323\) −2358.22 −0.406237
\(324\) −4646.53 −0.796730
\(325\) −299.574 −0.0511303
\(326\) −4863.85 −0.826330
\(327\) 1334.75 0.225725
\(328\) 3448.16 0.580465
\(329\) 1522.16 0.255074
\(330\) −654.179 −0.109125
\(331\) −11197.4 −1.85940 −0.929702 0.368313i \(-0.879935\pi\)
−0.929702 + 0.368313i \(0.879935\pi\)
\(332\) −12328.5 −2.03800
\(333\) −1270.55 −0.209086
\(334\) −13724.1 −2.24834
\(335\) 468.400 0.0763924
\(336\) 2277.35 0.369760
\(337\) 9070.66 1.46620 0.733102 0.680119i \(-0.238072\pi\)
0.733102 + 0.680119i \(0.238072\pi\)
\(338\) 9421.16 1.51611
\(339\) −7120.15 −1.14075
\(340\) 4792.55 0.764449
\(341\) 291.439 0.0462825
\(342\) 1447.54 0.228871
\(343\) 6915.62 1.08865
\(344\) 0 0
\(345\) −6717.15 −1.04823
\(346\) 1577.28 0.245072
\(347\) 2409.25 0.372724 0.186362 0.982481i \(-0.440330\pi\)
0.186362 + 0.982481i \(0.440330\pi\)
\(348\) 11500.9 1.77159
\(349\) −10646.2 −1.63289 −0.816443 0.577426i \(-0.804057\pi\)
−0.816443 + 0.577426i \(0.804057\pi\)
\(350\) −4426.71 −0.676050
\(351\) −677.557 −0.103035
\(352\) −1130.73 −0.171217
\(353\) 6413.78 0.967056 0.483528 0.875329i \(-0.339355\pi\)
0.483528 + 0.875329i \(0.339355\pi\)
\(354\) −13640.1 −2.04792
\(355\) −503.814 −0.0753229
\(356\) −10482.0 −1.56052
\(357\) 3856.78 0.571772
\(358\) 9920.61 1.46458
\(359\) 3428.56 0.504046 0.252023 0.967721i \(-0.418904\pi\)
0.252023 + 0.967721i \(0.418904\pi\)
\(360\) −747.010 −0.109364
\(361\) −5258.21 −0.766615
\(362\) −4282.44 −0.621768
\(363\) −5654.18 −0.817542
\(364\) −721.309 −0.103865
\(365\) −3097.38 −0.444175
\(366\) −17337.4 −2.47606
\(367\) −10004.5 −1.42297 −0.711483 0.702703i \(-0.751976\pi\)
−0.711483 + 0.702703i \(0.751976\pi\)
\(368\) −7141.00 −1.01155
\(369\) 2447.13 0.345237
\(370\) 4985.85 0.700547
\(371\) −8587.26 −1.20169
\(372\) −2921.47 −0.407180
\(373\) 6168.67 0.856305 0.428153 0.903706i \(-0.359165\pi\)
0.428153 + 0.903706i \(0.359165\pi\)
\(374\) −1177.79 −0.162839
\(375\) 6301.94 0.867815
\(376\) 1183.22 0.162288
\(377\) 1102.62 0.150630
\(378\) −10012.1 −1.36234
\(379\) 12794.7 1.73409 0.867045 0.498230i \(-0.166016\pi\)
0.867045 + 0.498230i \(0.166016\pi\)
\(380\) −3253.24 −0.439179
\(381\) −6407.85 −0.861638
\(382\) 6593.30 0.883096
\(383\) −3461.90 −0.461867 −0.230933 0.972970i \(-0.574178\pi\)
−0.230933 + 0.972970i \(0.574178\pi\)
\(384\) 6133.56 0.815110
\(385\) −530.768 −0.0702610
\(386\) 3437.89 0.453327
\(387\) 0 0
\(388\) 2731.18 0.357358
\(389\) −13493.8 −1.75877 −0.879384 0.476113i \(-0.842045\pi\)
−0.879384 + 0.476113i \(0.842045\pi\)
\(390\) 628.699 0.0816293
\(391\) −12093.6 −1.56419
\(392\) 1334.61 0.171959
\(393\) −10120.2 −1.29898
\(394\) 23207.3 2.96743
\(395\) −4424.48 −0.563594
\(396\) 414.049 0.0525423
\(397\) −8336.42 −1.05389 −0.526943 0.849900i \(-0.676662\pi\)
−0.526943 + 0.849900i \(0.676662\pi\)
\(398\) −17560.3 −2.21161
\(399\) −2618.03 −0.328485
\(400\) 2349.17 0.293647
\(401\) −1635.58 −0.203684 −0.101842 0.994801i \(-0.532474\pi\)
−0.101842 + 0.994801i \(0.532474\pi\)
\(402\) 1153.91 0.143163
\(403\) −280.088 −0.0346208
\(404\) −14970.9 −1.84364
\(405\) 3285.93 0.403159
\(406\) 16293.0 1.99165
\(407\) −701.742 −0.0854646
\(408\) 2998.00 0.363783
\(409\) −13688.6 −1.65490 −0.827452 0.561536i \(-0.810211\pi\)
−0.827452 + 0.561536i \(0.810211\pi\)
\(410\) −9602.94 −1.15672
\(411\) 4387.71 0.526593
\(412\) −8266.07 −0.988446
\(413\) −11066.9 −1.31856
\(414\) 7423.38 0.881255
\(415\) 8718.49 1.03126
\(416\) 1086.69 0.128075
\(417\) 7068.48 0.830084
\(418\) 799.496 0.0935518
\(419\) 253.682 0.0295780 0.0147890 0.999891i \(-0.495292\pi\)
0.0147890 + 0.999891i \(0.495292\pi\)
\(420\) 5320.57 0.618136
\(421\) −11417.5 −1.32174 −0.660872 0.750498i \(-0.729813\pi\)
−0.660872 + 0.750498i \(0.729813\pi\)
\(422\) 5790.96 0.668009
\(423\) 839.724 0.0965219
\(424\) −6675.17 −0.764563
\(425\) 3978.42 0.454074
\(426\) −1241.15 −0.141159
\(427\) −14066.7 −1.59422
\(428\) −5996.10 −0.677178
\(429\) −88.4873 −0.00995852
\(430\) 0 0
\(431\) −4723.09 −0.527850 −0.263925 0.964543i \(-0.585017\pi\)
−0.263925 + 0.964543i \(0.585017\pi\)
\(432\) 5313.21 0.591741
\(433\) −5231.32 −0.580604 −0.290302 0.956935i \(-0.593756\pi\)
−0.290302 + 0.956935i \(0.593756\pi\)
\(434\) −4138.77 −0.457759
\(435\) −8133.19 −0.896452
\(436\) 3315.16 0.364145
\(437\) 8209.27 0.898633
\(438\) −7630.39 −0.832407
\(439\) 12258.1 1.33268 0.666342 0.745646i \(-0.267859\pi\)
0.666342 + 0.745646i \(0.267859\pi\)
\(440\) −412.584 −0.0447027
\(441\) 947.161 0.102274
\(442\) 1131.91 0.121809
\(443\) −15064.2 −1.61563 −0.807813 0.589439i \(-0.799349\pi\)
−0.807813 + 0.589439i \(0.799349\pi\)
\(444\) 7034.46 0.751893
\(445\) 7412.67 0.789649
\(446\) −1448.25 −0.153759
\(447\) 9457.59 1.00073
\(448\) 11837.7 1.24839
\(449\) −1007.95 −0.105943 −0.0529713 0.998596i \(-0.516869\pi\)
−0.0529713 + 0.998596i \(0.516869\pi\)
\(450\) −2442.07 −0.255822
\(451\) 1351.58 0.141116
\(452\) −17684.5 −1.84028
\(453\) 12921.5 1.34019
\(454\) 5716.67 0.590962
\(455\) 510.095 0.0525574
\(456\) −2035.08 −0.208995
\(457\) 2569.85 0.263047 0.131523 0.991313i \(-0.458013\pi\)
0.131523 + 0.991313i \(0.458013\pi\)
\(458\) 7956.13 0.811715
\(459\) 8998.14 0.915027
\(460\) −16683.5 −1.69103
\(461\) −2634.42 −0.266155 −0.133077 0.991106i \(-0.542486\pi\)
−0.133077 + 0.991106i \(0.542486\pi\)
\(462\) −1307.55 −0.131672
\(463\) −9459.74 −0.949528 −0.474764 0.880113i \(-0.657467\pi\)
−0.474764 + 0.880113i \(0.657467\pi\)
\(464\) −8646.40 −0.865085
\(465\) 2066.00 0.206040
\(466\) 10686.4 1.06231
\(467\) −4529.63 −0.448835 −0.224418 0.974493i \(-0.572048\pi\)
−0.224418 + 0.974493i \(0.572048\pi\)
\(468\) −397.922 −0.0393033
\(469\) 936.221 0.0921763
\(470\) −3295.22 −0.323398
\(471\) 5511.45 0.539181
\(472\) −8602.68 −0.838920
\(473\) 0 0
\(474\) −10899.7 −1.05620
\(475\) −2700.60 −0.260867
\(476\) 9579.17 0.922396
\(477\) −4737.31 −0.454730
\(478\) 28097.5 2.68859
\(479\) −14764.9 −1.40841 −0.704203 0.709999i \(-0.748695\pi\)
−0.704203 + 0.709999i \(0.748695\pi\)
\(480\) −8015.72 −0.762221
\(481\) 674.410 0.0639302
\(482\) −2363.02 −0.223304
\(483\) −13426.0 −1.26481
\(484\) −14043.4 −1.31888
\(485\) −1931.44 −0.180829
\(486\) −9740.62 −0.909143
\(487\) −6246.07 −0.581184 −0.290592 0.956847i \(-0.593852\pi\)
−0.290592 + 0.956847i \(0.593852\pi\)
\(488\) −10934.5 −1.01431
\(489\) 4852.89 0.448784
\(490\) −3716.82 −0.342671
\(491\) −9471.49 −0.870555 −0.435277 0.900296i \(-0.643350\pi\)
−0.435277 + 0.900296i \(0.643350\pi\)
\(492\) −13548.6 −1.24150
\(493\) −14643.0 −1.33771
\(494\) −768.356 −0.0699797
\(495\) −292.807 −0.0265873
\(496\) 2196.37 0.198830
\(497\) −1007.00 −0.0908859
\(498\) 21478.0 1.93264
\(499\) 9708.83 0.870996 0.435498 0.900190i \(-0.356572\pi\)
0.435498 + 0.900190i \(0.356572\pi\)
\(500\) 15652.3 1.39998
\(501\) 13693.2 1.22109
\(502\) −14857.8 −1.32099
\(503\) 5971.16 0.529306 0.264653 0.964344i \(-0.414743\pi\)
0.264653 + 0.964344i \(0.414743\pi\)
\(504\) −1493.10 −0.131960
\(505\) 10587.1 0.932912
\(506\) 4100.04 0.360215
\(507\) −9399.95 −0.823405
\(508\) −15915.3 −1.39002
\(509\) −10850.7 −0.944887 −0.472443 0.881361i \(-0.656628\pi\)
−0.472443 + 0.881361i \(0.656628\pi\)
\(510\) −8349.29 −0.724927
\(511\) −6190.92 −0.535949
\(512\) −11801.9 −1.01870
\(513\) −6108.05 −0.525686
\(514\) −2099.14 −0.180134
\(515\) 5845.60 0.500170
\(516\) 0 0
\(517\) 463.791 0.0394536
\(518\) 9965.54 0.845291
\(519\) −1573.72 −0.133100
\(520\) 396.514 0.0334390
\(521\) −13234.7 −1.11290 −0.556450 0.830881i \(-0.687837\pi\)
−0.556450 + 0.830881i \(0.687837\pi\)
\(522\) 8988.31 0.753655
\(523\) −15760.1 −1.31767 −0.658836 0.752286i \(-0.728951\pi\)
−0.658836 + 0.752286i \(0.728951\pi\)
\(524\) −25135.9 −2.09555
\(525\) 4416.74 0.367166
\(526\) −5705.00 −0.472908
\(527\) 3719.64 0.307457
\(528\) 693.892 0.0571928
\(529\) 29932.4 2.46013
\(530\) 18590.0 1.52358
\(531\) −6105.24 −0.498955
\(532\) −6502.46 −0.529920
\(533\) −1298.94 −0.105560
\(534\) 18261.1 1.47984
\(535\) 4240.32 0.342663
\(536\) 727.756 0.0586461
\(537\) −9898.27 −0.795423
\(538\) 8602.31 0.689353
\(539\) 523.130 0.0418048
\(540\) 12413.3 0.989226
\(541\) −8717.14 −0.692753 −0.346376 0.938096i \(-0.612588\pi\)
−0.346376 + 0.938096i \(0.612588\pi\)
\(542\) −31065.3 −2.46194
\(543\) 4272.79 0.337685
\(544\) −14431.5 −1.13740
\(545\) −2344.41 −0.184263
\(546\) 1256.62 0.0984952
\(547\) 13375.8 1.04553 0.522766 0.852476i \(-0.324900\pi\)
0.522766 + 0.852476i \(0.324900\pi\)
\(548\) 10897.9 0.849514
\(549\) −7760.11 −0.603267
\(550\) −1348.79 −0.104568
\(551\) 9939.88 0.768517
\(552\) −10436.5 −0.804720
\(553\) −8843.48 −0.680042
\(554\) 15021.9 1.15202
\(555\) −4974.63 −0.380471
\(556\) 17556.2 1.33911
\(557\) 18892.9 1.43720 0.718598 0.695426i \(-0.244784\pi\)
0.718598 + 0.695426i \(0.244784\pi\)
\(558\) −2283.22 −0.173220
\(559\) 0 0
\(560\) −4000.02 −0.301843
\(561\) 1175.13 0.0884389
\(562\) −10214.8 −0.766698
\(563\) −24531.2 −1.83635 −0.918177 0.396170i \(-0.870339\pi\)
−0.918177 + 0.396170i \(0.870339\pi\)
\(564\) −4649.17 −0.347102
\(565\) 12506.1 0.931214
\(566\) 15508.7 1.15173
\(567\) 6567.80 0.486458
\(568\) −782.778 −0.0578251
\(569\) 18497.1 1.36281 0.681403 0.731908i \(-0.261370\pi\)
0.681403 + 0.731908i \(0.261370\pi\)
\(570\) 5667.60 0.416473
\(571\) −4775.61 −0.350006 −0.175003 0.984568i \(-0.555993\pi\)
−0.175003 + 0.984568i \(0.555993\pi\)
\(572\) −219.778 −0.0160653
\(573\) −6578.46 −0.479614
\(574\) −19194.0 −1.39572
\(575\) −13849.4 −1.00445
\(576\) 6530.46 0.472400
\(577\) −17822.1 −1.28586 −0.642932 0.765923i \(-0.722282\pi\)
−0.642932 + 0.765923i \(0.722282\pi\)
\(578\) 6226.41 0.448070
\(579\) −3430.15 −0.246204
\(580\) −20200.6 −1.44618
\(581\) 17426.2 1.24434
\(582\) −4758.10 −0.338883
\(583\) −2616.48 −0.185872
\(584\) −4812.41 −0.340991
\(585\) 281.403 0.0198881
\(586\) 947.054 0.0667618
\(587\) −8344.83 −0.586760 −0.293380 0.955996i \(-0.594780\pi\)
−0.293380 + 0.955996i \(0.594780\pi\)
\(588\) −5244.00 −0.367787
\(589\) −2524.94 −0.176635
\(590\) 23958.0 1.67176
\(591\) −23155.1 −1.61163
\(592\) −5288.53 −0.367158
\(593\) 12261.2 0.849084 0.424542 0.905408i \(-0.360435\pi\)
0.424542 + 0.905408i \(0.360435\pi\)
\(594\) −3050.60 −0.210720
\(595\) −6774.20 −0.466748
\(596\) 23490.0 1.61441
\(597\) 17520.8 1.20114
\(598\) −3940.34 −0.269452
\(599\) 20681.9 1.41075 0.705374 0.708835i \(-0.250779\pi\)
0.705374 + 0.708835i \(0.250779\pi\)
\(600\) 3433.28 0.233605
\(601\) −7757.58 −0.526519 −0.263260 0.964725i \(-0.584798\pi\)
−0.263260 + 0.964725i \(0.584798\pi\)
\(602\) 0 0
\(603\) 516.482 0.0348802
\(604\) 32093.4 2.16203
\(605\) 9931.22 0.667375
\(606\) 26081.4 1.74832
\(607\) −1766.42 −0.118116 −0.0590582 0.998255i \(-0.518810\pi\)
−0.0590582 + 0.998255i \(0.518810\pi\)
\(608\) 9796.31 0.653442
\(609\) −16256.3 −1.08167
\(610\) 30452.0 2.02126
\(611\) −445.726 −0.0295125
\(612\) 5284.51 0.349042
\(613\) 10071.3 0.663584 0.331792 0.943352i \(-0.392347\pi\)
0.331792 + 0.943352i \(0.392347\pi\)
\(614\) 10601.6 0.696816
\(615\) 9581.32 0.628221
\(616\) −824.658 −0.0539390
\(617\) 21039.4 1.37280 0.686399 0.727225i \(-0.259191\pi\)
0.686399 + 0.727225i \(0.259191\pi\)
\(618\) 14400.6 0.937344
\(619\) 9690.78 0.629249 0.314625 0.949216i \(-0.398121\pi\)
0.314625 + 0.949216i \(0.398121\pi\)
\(620\) 5131.38 0.332389
\(621\) −31323.8 −2.02412
\(622\) 3543.40 0.228420
\(623\) 14816.2 0.952804
\(624\) −666.865 −0.0427820
\(625\) −2631.66 −0.168426
\(626\) −8605.76 −0.549449
\(627\) −797.696 −0.0508085
\(628\) 13688.9 0.869821
\(629\) −8956.34 −0.567747
\(630\) 4158.20 0.262963
\(631\) 20307.8 1.28121 0.640603 0.767872i \(-0.278684\pi\)
0.640603 + 0.767872i \(0.278684\pi\)
\(632\) −6874.34 −0.432668
\(633\) −5777.92 −0.362799
\(634\) 17507.4 1.09670
\(635\) 11255.0 0.703372
\(636\) 26228.3 1.63525
\(637\) −502.754 −0.0312713
\(638\) 4964.37 0.308058
\(639\) −555.531 −0.0343919
\(640\) −10773.2 −0.665390
\(641\) −29060.8 −1.79069 −0.895344 0.445374i \(-0.853071\pi\)
−0.895344 + 0.445374i \(0.853071\pi\)
\(642\) 10446.0 0.642168
\(643\) 13231.3 0.811494 0.405747 0.913985i \(-0.367011\pi\)
0.405747 + 0.913985i \(0.367011\pi\)
\(644\) −33346.4 −2.04042
\(645\) 0 0
\(646\) 10204.0 0.621471
\(647\) −25154.9 −1.52850 −0.764252 0.644918i \(-0.776891\pi\)
−0.764252 + 0.644918i \(0.776891\pi\)
\(648\) 5105.37 0.309503
\(649\) −3372.01 −0.203949
\(650\) 1296.25 0.0782203
\(651\) 4129.45 0.248611
\(652\) 12053.2 0.723990
\(653\) 6734.12 0.403563 0.201781 0.979431i \(-0.435327\pi\)
0.201781 + 0.979431i \(0.435327\pi\)
\(654\) −5775.46 −0.345319
\(655\) 17775.6 1.06038
\(656\) 10185.9 0.606239
\(657\) −3415.32 −0.202807
\(658\) −6586.36 −0.390217
\(659\) −3685.41 −0.217850 −0.108925 0.994050i \(-0.534741\pi\)
−0.108925 + 0.994050i \(0.534741\pi\)
\(660\) 1621.14 0.0956103
\(661\) 3938.81 0.231773 0.115887 0.993262i \(-0.463029\pi\)
0.115887 + 0.993262i \(0.463029\pi\)
\(662\) 48450.9 2.84456
\(663\) −1129.36 −0.0661551
\(664\) 13546.0 0.791695
\(665\) 4598.41 0.268149
\(666\) 5497.66 0.319865
\(667\) 50974.4 2.95913
\(668\) 34010.0 1.96989
\(669\) 1444.99 0.0835076
\(670\) −2026.76 −0.116867
\(671\) −4286.02 −0.246587
\(672\) −16021.5 −0.919708
\(673\) −31975.1 −1.83143 −0.915714 0.401831i \(-0.868374\pi\)
−0.915714 + 0.401831i \(0.868374\pi\)
\(674\) −39248.7 −2.24303
\(675\) 10304.6 0.587589
\(676\) −23346.9 −1.32834
\(677\) −10683.3 −0.606487 −0.303244 0.952913i \(-0.598070\pi\)
−0.303244 + 0.952913i \(0.598070\pi\)
\(678\) 30808.8 1.74514
\(679\) −3860.49 −0.218191
\(680\) −5265.81 −0.296963
\(681\) −5703.80 −0.320954
\(682\) −1261.06 −0.0708039
\(683\) −15614.9 −0.874800 −0.437400 0.899267i \(-0.644101\pi\)
−0.437400 + 0.899267i \(0.644101\pi\)
\(684\) −3587.19 −0.200526
\(685\) −7706.75 −0.429868
\(686\) −29923.8 −1.66545
\(687\) −7938.21 −0.440847
\(688\) 0 0
\(689\) 2514.57 0.139038
\(690\) 29065.0 1.60360
\(691\) −25222.6 −1.38858 −0.694292 0.719693i \(-0.744283\pi\)
−0.694292 + 0.719693i \(0.744283\pi\)
\(692\) −3908.70 −0.214720
\(693\) −585.252 −0.0320807
\(694\) −10424.8 −0.570201
\(695\) −12415.4 −0.677614
\(696\) −12636.6 −0.688202
\(697\) 17250.2 0.937445
\(698\) 46065.9 2.49802
\(699\) −10662.3 −0.576948
\(700\) 10970.0 0.592322
\(701\) −4178.65 −0.225143 −0.112572 0.993644i \(-0.535909\pi\)
−0.112572 + 0.993644i \(0.535909\pi\)
\(702\) 2931.78 0.157625
\(703\) 6079.68 0.326173
\(704\) 3606.86 0.193095
\(705\) 3287.80 0.175639
\(706\) −27752.3 −1.47942
\(707\) 21161.1 1.12567
\(708\) 33802.0 1.79429
\(709\) −27765.1 −1.47072 −0.735360 0.677677i \(-0.762987\pi\)
−0.735360 + 0.677677i \(0.762987\pi\)
\(710\) 2180.00 0.115231
\(711\) −4878.65 −0.257333
\(712\) 11517.1 0.606210
\(713\) −12948.6 −0.680124
\(714\) −16688.3 −0.874709
\(715\) 155.423 0.00812933
\(716\) −24584.6 −1.28320
\(717\) −28034.2 −1.46019
\(718\) −14835.4 −0.771101
\(719\) −25705.2 −1.33330 −0.666649 0.745372i \(-0.732272\pi\)
−0.666649 + 0.745372i \(0.732272\pi\)
\(720\) −2206.68 −0.114220
\(721\) 11684.0 0.603514
\(722\) 22752.2 1.17278
\(723\) 2357.69 0.121277
\(724\) 10612.4 0.544763
\(725\) −16769.0 −0.859015
\(726\) 24465.6 1.25069
\(727\) 27877.2 1.42216 0.711080 0.703111i \(-0.248207\pi\)
0.711080 + 0.703111i \(0.248207\pi\)
\(728\) 792.538 0.0403481
\(729\) 21418.6 1.08818
\(730\) 13402.3 0.679509
\(731\) 0 0
\(732\) 42964.2 2.16940
\(733\) 1914.75 0.0964841 0.0482420 0.998836i \(-0.484638\pi\)
0.0482420 + 0.998836i \(0.484638\pi\)
\(734\) 43289.2 2.17689
\(735\) 3708.45 0.186106
\(736\) 50238.2 2.51604
\(737\) 285.260 0.0142574
\(738\) −10588.7 −0.528151
\(739\) −397.742 −0.0197986 −0.00989932 0.999951i \(-0.503151\pi\)
−0.00989932 + 0.999951i \(0.503151\pi\)
\(740\) −12355.6 −0.613785
\(741\) 766.626 0.0380064
\(742\) 37157.0 1.83838
\(743\) 9023.68 0.445554 0.222777 0.974869i \(-0.428488\pi\)
0.222777 + 0.974869i \(0.428488\pi\)
\(744\) 3209.96 0.158176
\(745\) −16611.7 −0.816919
\(746\) −26691.8 −1.30999
\(747\) 9613.45 0.470867
\(748\) 2918.71 0.142672
\(749\) 8475.39 0.413463
\(750\) −27268.4 −1.32760
\(751\) 19915.2 0.967665 0.483832 0.875161i \(-0.339244\pi\)
0.483832 + 0.875161i \(0.339244\pi\)
\(752\) 3495.26 0.169493
\(753\) 14824.4 0.717437
\(754\) −4771.01 −0.230438
\(755\) −22695.8 −1.09402
\(756\) 24811.2 1.19362
\(757\) 24897.3 1.19539 0.597694 0.801724i \(-0.296084\pi\)
0.597694 + 0.801724i \(0.296084\pi\)
\(758\) −55362.6 −2.65285
\(759\) −4090.81 −0.195635
\(760\) 3574.50 0.170606
\(761\) 34554.9 1.64601 0.823006 0.568033i \(-0.192295\pi\)
0.823006 + 0.568033i \(0.192295\pi\)
\(762\) 27726.7 1.31815
\(763\) −4685.93 −0.222335
\(764\) −16339.1 −0.773726
\(765\) −3737.10 −0.176621
\(766\) 14979.6 0.706574
\(767\) 3240.67 0.152560
\(768\) 435.191 0.0204474
\(769\) −12520.7 −0.587138 −0.293569 0.955938i \(-0.594843\pi\)
−0.293569 + 0.955938i \(0.594843\pi\)
\(770\) 2296.63 0.107487
\(771\) 2094.41 0.0978319
\(772\) −8519.54 −0.397183
\(773\) 23875.0 1.11090 0.555450 0.831550i \(-0.312546\pi\)
0.555450 + 0.831550i \(0.312546\pi\)
\(774\) 0 0
\(775\) 4259.69 0.197435
\(776\) −3000.89 −0.138822
\(777\) −9943.10 −0.459082
\(778\) 58387.4 2.69060
\(779\) −11709.7 −0.538566
\(780\) −1558.00 −0.0715196
\(781\) −306.827 −0.0140578
\(782\) 52328.8 2.39293
\(783\) −37927.2 −1.73104
\(784\) 3942.46 0.179594
\(785\) −9680.53 −0.440144
\(786\) 43790.2 1.98721
\(787\) 3612.43 0.163620 0.0818102 0.996648i \(-0.473930\pi\)
0.0818102 + 0.996648i \(0.473930\pi\)
\(788\) −57510.8 −2.59992
\(789\) 5692.15 0.256839
\(790\) 19144.7 0.862198
\(791\) 24996.7 1.12362
\(792\) −454.936 −0.0204109
\(793\) 4119.08 0.184455
\(794\) 36071.6 1.61226
\(795\) −18548.1 −0.827465
\(796\) 43516.8 1.93770
\(797\) 14565.8 0.647363 0.323682 0.946166i \(-0.395079\pi\)
0.323682 + 0.946166i \(0.395079\pi\)
\(798\) 11328.2 0.502524
\(799\) 5919.36 0.262093
\(800\) −16526.8 −0.730389
\(801\) 8173.58 0.360549
\(802\) 7077.16 0.311600
\(803\) −1886.33 −0.0828981
\(804\) −2859.53 −0.125433
\(805\) 23581.9 1.03249
\(806\) 1211.94 0.0529636
\(807\) −8582.94 −0.374391
\(808\) 16449.3 0.716192
\(809\) −22200.5 −0.964806 −0.482403 0.875949i \(-0.660236\pi\)
−0.482403 + 0.875949i \(0.660236\pi\)
\(810\) −14218.2 −0.616761
\(811\) −805.377 −0.0348713 −0.0174356 0.999848i \(-0.505550\pi\)
−0.0174356 + 0.999848i \(0.505550\pi\)
\(812\) −40376.2 −1.74498
\(813\) 30995.4 1.33709
\(814\) 3036.43 0.130746
\(815\) −8523.81 −0.366351
\(816\) 8856.15 0.379935
\(817\) 0 0
\(818\) 59230.3 2.53171
\(819\) 562.457 0.0239974
\(820\) 23797.3 1.01346
\(821\) −30715.5 −1.30570 −0.652848 0.757489i \(-0.726426\pi\)
−0.652848 + 0.757489i \(0.726426\pi\)
\(822\) −18985.6 −0.805594
\(823\) −10776.3 −0.456424 −0.228212 0.973611i \(-0.573288\pi\)
−0.228212 + 0.973611i \(0.573288\pi\)
\(824\) 9082.34 0.383978
\(825\) 1345.75 0.0567915
\(826\) 47886.4 2.01717
\(827\) −26112.2 −1.09796 −0.548978 0.835837i \(-0.684983\pi\)
−0.548978 + 0.835837i \(0.684983\pi\)
\(828\) −18396.1 −0.772112
\(829\) 44126.9 1.84872 0.924362 0.381518i \(-0.124598\pi\)
0.924362 + 0.381518i \(0.124598\pi\)
\(830\) −37724.8 −1.57765
\(831\) −14988.1 −0.625669
\(832\) −3466.38 −0.144441
\(833\) 6676.71 0.277712
\(834\) −30585.3 −1.26988
\(835\) −24051.2 −0.996797
\(836\) −1981.26 −0.0819655
\(837\) 9634.30 0.397862
\(838\) −1097.68 −0.0452491
\(839\) 2366.99 0.0973986 0.0486993 0.998813i \(-0.484492\pi\)
0.0486993 + 0.998813i \(0.484492\pi\)
\(840\) −5845.97 −0.240125
\(841\) 37331.4 1.53066
\(842\) 49403.4 2.02203
\(843\) 10191.8 0.416398
\(844\) −14350.8 −0.585277
\(845\) 16510.4 0.672161
\(846\) −3633.48 −0.147661
\(847\) 19850.2 0.805265
\(848\) −19718.5 −0.798511
\(849\) −15473.8 −0.625512
\(850\) −17214.6 −0.694653
\(851\) 31178.3 1.25591
\(852\) 3075.72 0.123677
\(853\) −24301.3 −0.975452 −0.487726 0.872997i \(-0.662173\pi\)
−0.487726 + 0.872997i \(0.662173\pi\)
\(854\) 60866.4 2.43888
\(855\) 2536.79 0.101469
\(856\) 6588.21 0.263061
\(857\) −40357.3 −1.60861 −0.804304 0.594218i \(-0.797462\pi\)
−0.804304 + 0.594218i \(0.797462\pi\)
\(858\) 382.884 0.0152348
\(859\) 10352.8 0.411212 0.205606 0.978635i \(-0.434083\pi\)
0.205606 + 0.978635i \(0.434083\pi\)
\(860\) 0 0
\(861\) 19150.8 0.758022
\(862\) 20436.8 0.807516
\(863\) 15149.6 0.597563 0.298781 0.954322i \(-0.403420\pi\)
0.298781 + 0.954322i \(0.403420\pi\)
\(864\) −37379.4 −1.47184
\(865\) 2764.15 0.108652
\(866\) 22635.9 0.888220
\(867\) −6212.39 −0.243349
\(868\) 10256.4 0.401066
\(869\) −2694.55 −0.105186
\(870\) 35192.2 1.37141
\(871\) −274.149 −0.0106650
\(872\) −3642.53 −0.141458
\(873\) −2129.70 −0.0825653
\(874\) −35521.4 −1.37475
\(875\) −22124.2 −0.854784
\(876\) 18909.1 0.729314
\(877\) 19411.3 0.747405 0.373703 0.927549i \(-0.378088\pi\)
0.373703 + 0.927549i \(0.378088\pi\)
\(878\) −53040.8 −2.03877
\(879\) −944.921 −0.0362587
\(880\) −1218.78 −0.0466876
\(881\) −44659.5 −1.70785 −0.853926 0.520394i \(-0.825785\pi\)
−0.853926 + 0.520394i \(0.825785\pi\)
\(882\) −4098.36 −0.156461
\(883\) 21280.2 0.811024 0.405512 0.914090i \(-0.367093\pi\)
0.405512 + 0.914090i \(0.367093\pi\)
\(884\) −2805.03 −0.106723
\(885\) −23904.1 −0.907940
\(886\) 65182.7 2.47162
\(887\) −12849.9 −0.486423 −0.243211 0.969973i \(-0.578201\pi\)
−0.243211 + 0.969973i \(0.578201\pi\)
\(888\) −7729.11 −0.292085
\(889\) 22496.1 0.848700
\(890\) −32074.5 −1.20802
\(891\) 2001.16 0.0752430
\(892\) 3588.96 0.134717
\(893\) −4018.14 −0.150573
\(894\) −40922.9 −1.53095
\(895\) 17385.7 0.649319
\(896\) −21533.1 −0.802870
\(897\) 3931.47 0.146341
\(898\) 4361.40 0.162073
\(899\) −15678.3 −0.581646
\(900\) 6051.76 0.224139
\(901\) −33394.1 −1.23476
\(902\) −5848.28 −0.215883
\(903\) 0 0
\(904\) 19430.8 0.714888
\(905\) −7504.90 −0.275659
\(906\) −55911.2 −2.05025
\(907\) 38267.7 1.40094 0.700472 0.713680i \(-0.252973\pi\)
0.700472 + 0.713680i \(0.252973\pi\)
\(908\) −14166.6 −0.517772
\(909\) 11673.9 0.425961
\(910\) −2207.18 −0.0804035
\(911\) −33801.3 −1.22929 −0.614646 0.788803i \(-0.710701\pi\)
−0.614646 + 0.788803i \(0.710701\pi\)
\(912\) −6011.67 −0.218274
\(913\) 5309.64 0.192468
\(914\) −11119.7 −0.402415
\(915\) −30383.4 −1.09775
\(916\) −19716.3 −0.711185
\(917\) 35529.2 1.27947
\(918\) −38934.9 −1.39983
\(919\) 18924.2 0.679274 0.339637 0.940557i \(-0.389696\pi\)
0.339637 + 0.940557i \(0.389696\pi\)
\(920\) 18331.0 0.656908
\(921\) −10577.7 −0.378445
\(922\) 11399.1 0.407170
\(923\) 294.876 0.0105157
\(924\) 3240.28 0.115365
\(925\) −10256.7 −0.364582
\(926\) 40932.2 1.45261
\(927\) 6445.65 0.228374
\(928\) 60828.9 2.15173
\(929\) 47171.0 1.66591 0.832955 0.553340i \(-0.186647\pi\)
0.832955 + 0.553340i \(0.186647\pi\)
\(930\) −8939.58 −0.315205
\(931\) −4532.23 −0.159547
\(932\) −26482.3 −0.930747
\(933\) −3535.42 −0.124056
\(934\) 19599.6 0.686638
\(935\) −2064.05 −0.0721944
\(936\) 437.217 0.0152680
\(937\) 39747.2 1.38579 0.692894 0.721039i \(-0.256335\pi\)
0.692894 + 0.721039i \(0.256335\pi\)
\(938\) −4051.02 −0.141013
\(939\) 8586.38 0.298409
\(940\) 8165.98 0.283346
\(941\) 9781.20 0.338850 0.169425 0.985543i \(-0.445809\pi\)
0.169425 + 0.985543i \(0.445809\pi\)
\(942\) −23848.0 −0.824852
\(943\) −60050.5 −2.07371
\(944\) −25412.4 −0.876170
\(945\) −17546.0 −0.603990
\(946\) 0 0
\(947\) 33077.2 1.13502 0.567511 0.823366i \(-0.307906\pi\)
0.567511 + 0.823366i \(0.307906\pi\)
\(948\) 27010.9 0.925393
\(949\) 1812.86 0.0620104
\(950\) 11685.5 0.399081
\(951\) −17468.0 −0.595623
\(952\) −10525.1 −0.358320
\(953\) −4221.07 −0.143477 −0.0717386 0.997423i \(-0.522855\pi\)
−0.0717386 + 0.997423i \(0.522855\pi\)
\(954\) 20498.3 0.695657
\(955\) 11554.7 0.391518
\(956\) −69629.2 −2.35561
\(957\) −4953.19 −0.167308
\(958\) 63887.6 2.15461
\(959\) −15404.0 −0.518686
\(960\) 25568.9 0.859618
\(961\) −25808.4 −0.866315
\(962\) −2918.16 −0.0978019
\(963\) 4675.59 0.156458
\(964\) 5855.86 0.195648
\(965\) 6024.85 0.200981
\(966\) 58094.1 1.93493
\(967\) 17701.1 0.588655 0.294328 0.955705i \(-0.404904\pi\)
0.294328 + 0.955705i \(0.404904\pi\)
\(968\) 15430.2 0.512340
\(969\) −10181.0 −0.337524
\(970\) 8357.32 0.276636
\(971\) 22881.9 0.756248 0.378124 0.925755i \(-0.376569\pi\)
0.378124 + 0.925755i \(0.376569\pi\)
\(972\) 24138.5 0.796547
\(973\) −24815.4 −0.817620
\(974\) 27026.7 0.889108
\(975\) −1293.33 −0.0424819
\(976\) −32300.7 −1.05934
\(977\) 27596.4 0.903671 0.451835 0.892101i \(-0.350769\pi\)
0.451835 + 0.892101i \(0.350769\pi\)
\(978\) −20998.4 −0.686560
\(979\) 4514.38 0.147375
\(980\) 9210.76 0.300232
\(981\) −2585.07 −0.0841334
\(982\) 40983.0 1.33179
\(983\) −13288.7 −0.431175 −0.215587 0.976485i \(-0.569167\pi\)
−0.215587 + 0.976485i \(0.569167\pi\)
\(984\) 14886.5 0.482282
\(985\) 40670.5 1.31560
\(986\) 63360.3 2.04645
\(987\) 6571.53 0.211929
\(988\) 1904.09 0.0613128
\(989\) 0 0
\(990\) 1266.97 0.0406738
\(991\) −43350.5 −1.38958 −0.694789 0.719213i \(-0.744502\pi\)
−0.694789 + 0.719213i \(0.744502\pi\)
\(992\) −15451.8 −0.494553
\(993\) −48341.8 −1.54489
\(994\) 4357.30 0.139039
\(995\) −30774.2 −0.980510
\(996\) −53225.3 −1.69328
\(997\) −45404.7 −1.44231 −0.721154 0.692775i \(-0.756388\pi\)
−0.721154 + 0.692775i \(0.756388\pi\)
\(998\) −42010.0 −1.33247
\(999\) −23198.0 −0.734686
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.j.1.6 yes 50
43.42 odd 2 1849.4.a.i.1.45 50
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1849.4.a.i.1.45 50 43.42 odd 2
1849.4.a.j.1.6 yes 50 1.1 even 1 trivial