Properties

Label 570.4.a.s.1.4
Level $570$
Weight $4$
Character 570.1
Self dual yes
Analytic conductor $33.631$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 570.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(33.6310887033\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\mathbb{Q}[x]/(x^{4} - \cdots)\)
Defining polynomial: \(x^{4} - x^{3} - 410 x^{2} + 4362 x - 12540\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(6.58500\) of defining polynomial
Character \(\chi\) \(=\) 570.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +5.00000 q^{5} +6.00000 q^{6} +36.1008 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +5.00000 q^{5} +6.00000 q^{6} +36.1008 q^{7} +8.00000 q^{8} +9.00000 q^{9} +10.0000 q^{10} -0.930760 q^{11} +12.0000 q^{12} +45.8117 q^{13} +72.2015 q^{14} +15.0000 q^{15} +16.0000 q^{16} -103.133 q^{17} +18.0000 q^{18} +19.0000 q^{19} +20.0000 q^{20} +108.302 q^{21} -1.86152 q^{22} +17.0195 q^{23} +24.0000 q^{24} +25.0000 q^{25} +91.6235 q^{26} +27.0000 q^{27} +144.403 q^{28} -307.261 q^{29} +30.0000 q^{30} +38.1135 q^{31} +32.0000 q^{32} -2.79228 q^{33} -206.267 q^{34} +180.504 q^{35} +36.0000 q^{36} +59.7728 q^{37} +38.0000 q^{38} +137.435 q^{39} +40.0000 q^{40} -269.284 q^{41} +216.605 q^{42} -351.964 q^{43} -3.72304 q^{44} +45.0000 q^{45} +34.0389 q^{46} +472.748 q^{47} +48.0000 q^{48} +960.265 q^{49} +50.0000 q^{50} -309.400 q^{51} +183.247 q^{52} -685.438 q^{53} +54.0000 q^{54} -4.65380 q^{55} +288.806 q^{56} +57.0000 q^{57} -614.522 q^{58} +272.918 q^{59} +60.0000 q^{60} +258.765 q^{61} +76.2269 q^{62} +324.907 q^{63} +64.0000 q^{64} +229.059 q^{65} -5.58456 q^{66} -630.625 q^{67} -412.534 q^{68} +51.0584 q^{69} +361.008 q^{70} +133.460 q^{71} +72.0000 q^{72} +631.242 q^{73} +119.546 q^{74} +75.0000 q^{75} +76.0000 q^{76} -33.6011 q^{77} +274.870 q^{78} +640.921 q^{79} +80.0000 q^{80} +81.0000 q^{81} -538.568 q^{82} +192.203 q^{83} +433.209 q^{84} -515.667 q^{85} -703.929 q^{86} -921.782 q^{87} -7.44608 q^{88} +1574.22 q^{89} +90.0000 q^{90} +1653.84 q^{91} +68.0778 q^{92} +114.340 q^{93} +945.497 q^{94} +95.0000 q^{95} +96.0000 q^{96} -1406.62 q^{97} +1920.53 q^{98} -8.37684 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 8q^{2} + 12q^{3} + 16q^{4} + 20q^{5} + 24q^{6} + 36q^{7} + 32q^{8} + 36q^{9} + O(q^{10}) \) \( 4q + 8q^{2} + 12q^{3} + 16q^{4} + 20q^{5} + 24q^{6} + 36q^{7} + 32q^{8} + 36q^{9} + 40q^{10} + 54q^{11} + 48q^{12} + 46q^{13} + 72q^{14} + 60q^{15} + 64q^{16} + 14q^{17} + 72q^{18} + 76q^{19} + 80q^{20} + 108q^{21} + 108q^{22} + 104q^{23} + 96q^{24} + 100q^{25} + 92q^{26} + 108q^{27} + 144q^{28} + 14q^{29} + 120q^{30} + 30q^{31} + 128q^{32} + 162q^{33} + 28q^{34} + 180q^{35} + 144q^{36} + 30q^{37} + 152q^{38} + 138q^{39} + 160q^{40} - 36q^{41} + 216q^{42} + 102q^{43} + 216q^{44} + 180q^{45} + 208q^{46} + 408q^{47} + 192q^{48} + 480q^{49} + 200q^{50} + 42q^{51} + 184q^{52} - 176q^{53} + 216q^{54} + 270q^{55} + 288q^{56} + 228q^{57} + 28q^{58} + 66q^{59} + 240q^{60} + 60q^{61} + 60q^{62} + 324q^{63} + 256q^{64} + 230q^{65} + 324q^{66} - 152q^{67} + 56q^{68} + 312q^{69} + 360q^{70} + 172q^{71} + 288q^{72} + 284q^{73} + 60q^{74} + 300q^{75} + 304q^{76} - 300q^{77} + 276q^{78} + 554q^{79} + 320q^{80} + 324q^{81} - 72q^{82} - 394q^{83} + 432q^{84} + 70q^{85} + 204q^{86} + 42q^{87} + 432q^{88} - 60q^{89} + 360q^{90} + 32q^{91} + 416q^{92} + 90q^{93} + 816q^{94} + 380q^{95} + 384q^{96} - 922q^{97} + 960q^{98} + 486q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000 0.707107
\(3\) 3.00000 0.577350
\(4\) 4.00000 0.500000
\(5\) 5.00000 0.447214
\(6\) 6.00000 0.408248
\(7\) 36.1008 1.94926 0.974629 0.223826i \(-0.0718549\pi\)
0.974629 + 0.223826i \(0.0718549\pi\)
\(8\) 8.00000 0.353553
\(9\) 9.00000 0.333333
\(10\) 10.0000 0.316228
\(11\) −0.930760 −0.0255122 −0.0127561 0.999919i \(-0.504061\pi\)
−0.0127561 + 0.999919i \(0.504061\pi\)
\(12\) 12.0000 0.288675
\(13\) 45.8117 0.977376 0.488688 0.872459i \(-0.337476\pi\)
0.488688 + 0.872459i \(0.337476\pi\)
\(14\) 72.2015 1.37833
\(15\) 15.0000 0.258199
\(16\) 16.0000 0.250000
\(17\) −103.133 −1.47138 −0.735692 0.677316i \(-0.763143\pi\)
−0.735692 + 0.677316i \(0.763143\pi\)
\(18\) 18.0000 0.235702
\(19\) 19.0000 0.229416
\(20\) 20.0000 0.223607
\(21\) 108.302 1.12540
\(22\) −1.86152 −0.0180399
\(23\) 17.0195 0.154296 0.0771479 0.997020i \(-0.475419\pi\)
0.0771479 + 0.997020i \(0.475419\pi\)
\(24\) 24.0000 0.204124
\(25\) 25.0000 0.200000
\(26\) 91.6235 0.691109
\(27\) 27.0000 0.192450
\(28\) 144.403 0.974629
\(29\) −307.261 −1.96748 −0.983740 0.179601i \(-0.942519\pi\)
−0.983740 + 0.179601i \(0.942519\pi\)
\(30\) 30.0000 0.182574
\(31\) 38.1135 0.220819 0.110409 0.993886i \(-0.464784\pi\)
0.110409 + 0.993886i \(0.464784\pi\)
\(32\) 32.0000 0.176777
\(33\) −2.79228 −0.0147295
\(34\) −206.267 −1.04043
\(35\) 180.504 0.871735
\(36\) 36.0000 0.166667
\(37\) 59.7728 0.265584 0.132792 0.991144i \(-0.457606\pi\)
0.132792 + 0.991144i \(0.457606\pi\)
\(38\) 38.0000 0.162221
\(39\) 137.435 0.564288
\(40\) 40.0000 0.158114
\(41\) −269.284 −1.02573 −0.512867 0.858468i \(-0.671417\pi\)
−0.512867 + 0.858468i \(0.671417\pi\)
\(42\) 216.605 0.795781
\(43\) −351.964 −1.24823 −0.624117 0.781331i \(-0.714541\pi\)
−0.624117 + 0.781331i \(0.714541\pi\)
\(44\) −3.72304 −0.0127561
\(45\) 45.0000 0.149071
\(46\) 34.0389 0.109104
\(47\) 472.748 1.46718 0.733590 0.679593i \(-0.237843\pi\)
0.733590 + 0.679593i \(0.237843\pi\)
\(48\) 48.0000 0.144338
\(49\) 960.265 2.79961
\(50\) 50.0000 0.141421
\(51\) −309.400 −0.849504
\(52\) 183.247 0.488688
\(53\) −685.438 −1.77646 −0.888228 0.459404i \(-0.848063\pi\)
−0.888228 + 0.459404i \(0.848063\pi\)
\(54\) 54.0000 0.136083
\(55\) −4.65380 −0.0114094
\(56\) 288.806 0.689167
\(57\) 57.0000 0.132453
\(58\) −614.522 −1.39122
\(59\) 272.918 0.602218 0.301109 0.953590i \(-0.402643\pi\)
0.301109 + 0.953590i \(0.402643\pi\)
\(60\) 60.0000 0.129099
\(61\) 258.765 0.543140 0.271570 0.962419i \(-0.412457\pi\)
0.271570 + 0.962419i \(0.412457\pi\)
\(62\) 76.2269 0.156142
\(63\) 324.907 0.649753
\(64\) 64.0000 0.125000
\(65\) 229.059 0.437096
\(66\) −5.58456 −0.0104153
\(67\) −630.625 −1.14990 −0.574948 0.818190i \(-0.694978\pi\)
−0.574948 + 0.818190i \(0.694978\pi\)
\(68\) −412.534 −0.735692
\(69\) 51.0584 0.0890827
\(70\) 361.008 0.616410
\(71\) 133.460 0.223081 0.111540 0.993760i \(-0.464422\pi\)
0.111540 + 0.993760i \(0.464422\pi\)
\(72\) 72.0000 0.117851
\(73\) 631.242 1.01207 0.506036 0.862512i \(-0.331110\pi\)
0.506036 + 0.862512i \(0.331110\pi\)
\(74\) 119.546 0.187796
\(75\) 75.0000 0.115470
\(76\) 76.0000 0.114708
\(77\) −33.6011 −0.0497300
\(78\) 274.870 0.399012
\(79\) 640.921 0.912776 0.456388 0.889781i \(-0.349143\pi\)
0.456388 + 0.889781i \(0.349143\pi\)
\(80\) 80.0000 0.111803
\(81\) 81.0000 0.111111
\(82\) −538.568 −0.725303
\(83\) 192.203 0.254181 0.127091 0.991891i \(-0.459436\pi\)
0.127091 + 0.991891i \(0.459436\pi\)
\(84\) 433.209 0.562702
\(85\) −515.667 −0.658023
\(86\) −703.929 −0.882635
\(87\) −921.782 −1.13592
\(88\) −7.44608 −0.00901994
\(89\) 1574.22 1.87491 0.937456 0.348103i \(-0.113174\pi\)
0.937456 + 0.348103i \(0.113174\pi\)
\(90\) 90.0000 0.105409
\(91\) 1653.84 1.90516
\(92\) 68.0778 0.0771479
\(93\) 114.340 0.127490
\(94\) 945.497 1.03745
\(95\) 95.0000 0.102598
\(96\) 96.0000 0.102062
\(97\) −1406.62 −1.47238 −0.736188 0.676777i \(-0.763376\pi\)
−0.736188 + 0.676777i \(0.763376\pi\)
\(98\) 1920.53 1.97962
\(99\) −8.37684 −0.00850408
\(100\) 100.000 0.100000
\(101\) −993.051 −0.978340 −0.489170 0.872189i \(-0.662700\pi\)
−0.489170 + 0.872189i \(0.662700\pi\)
\(102\) −618.801 −0.600690
\(103\) −597.901 −0.571970 −0.285985 0.958234i \(-0.592321\pi\)
−0.285985 + 0.958234i \(0.592321\pi\)
\(104\) 366.494 0.345555
\(105\) 541.511 0.503296
\(106\) −1370.88 −1.25614
\(107\) 2123.32 1.91840 0.959202 0.282721i \(-0.0912370\pi\)
0.959202 + 0.282721i \(0.0912370\pi\)
\(108\) 108.000 0.0962250
\(109\) −1282.57 −1.12704 −0.563522 0.826101i \(-0.690554\pi\)
−0.563522 + 0.826101i \(0.690554\pi\)
\(110\) −9.30760 −0.00806768
\(111\) 179.318 0.153335
\(112\) 577.612 0.487315
\(113\) −1435.84 −1.19533 −0.597664 0.801746i \(-0.703905\pi\)
−0.597664 + 0.801746i \(0.703905\pi\)
\(114\) 114.000 0.0936586
\(115\) 85.0973 0.0690031
\(116\) −1229.04 −0.983740
\(117\) 412.306 0.325792
\(118\) 545.836 0.425832
\(119\) −3723.20 −2.86811
\(120\) 120.000 0.0912871
\(121\) −1330.13 −0.999349
\(122\) 517.531 0.384058
\(123\) −807.852 −0.592208
\(124\) 152.454 0.110409
\(125\) 125.000 0.0894427
\(126\) 649.814 0.459445
\(127\) −103.018 −0.0719794 −0.0359897 0.999352i \(-0.511458\pi\)
−0.0359897 + 0.999352i \(0.511458\pi\)
\(128\) 128.000 0.0883883
\(129\) −1055.89 −0.720668
\(130\) 458.117 0.309073
\(131\) −263.824 −0.175957 −0.0879787 0.996122i \(-0.528041\pi\)
−0.0879787 + 0.996122i \(0.528041\pi\)
\(132\) −11.1691 −0.00736475
\(133\) 685.915 0.447190
\(134\) −1261.25 −0.813100
\(135\) 135.000 0.0860663
\(136\) −825.068 −0.520213
\(137\) −834.524 −0.520425 −0.260213 0.965551i \(-0.583793\pi\)
−0.260213 + 0.965551i \(0.583793\pi\)
\(138\) 102.117 0.0629910
\(139\) 985.778 0.601529 0.300765 0.953698i \(-0.402758\pi\)
0.300765 + 0.953698i \(0.402758\pi\)
\(140\) 722.015 0.435867
\(141\) 1418.25 0.847077
\(142\) 266.919 0.157742
\(143\) −42.6397 −0.0249351
\(144\) 144.000 0.0833333
\(145\) −1536.30 −0.879883
\(146\) 1262.48 0.715643
\(147\) 2880.80 1.61635
\(148\) 239.091 0.132792
\(149\) 2555.14 1.40487 0.702433 0.711750i \(-0.252097\pi\)
0.702433 + 0.711750i \(0.252097\pi\)
\(150\) 150.000 0.0816497
\(151\) 1527.25 0.823086 0.411543 0.911390i \(-0.364990\pi\)
0.411543 + 0.911390i \(0.364990\pi\)
\(152\) 152.000 0.0811107
\(153\) −928.201 −0.490462
\(154\) −67.2023 −0.0351644
\(155\) 190.567 0.0987531
\(156\) 549.741 0.282144
\(157\) −1159.89 −0.589613 −0.294807 0.955557i \(-0.595255\pi\)
−0.294807 + 0.955557i \(0.595255\pi\)
\(158\) 1281.84 0.645430
\(159\) −2056.31 −1.02564
\(160\) 160.000 0.0790569
\(161\) 614.415 0.300762
\(162\) 162.000 0.0785674
\(163\) 755.501 0.363039 0.181520 0.983387i \(-0.441898\pi\)
0.181520 + 0.983387i \(0.441898\pi\)
\(164\) −1077.14 −0.512867
\(165\) −13.9614 −0.00658723
\(166\) 384.406 0.179733
\(167\) −2545.46 −1.17948 −0.589742 0.807592i \(-0.700770\pi\)
−0.589742 + 0.807592i \(0.700770\pi\)
\(168\) 866.418 0.397891
\(169\) −98.2849 −0.0447360
\(170\) −1031.33 −0.465293
\(171\) 171.000 0.0764719
\(172\) −1407.86 −0.624117
\(173\) 249.551 0.109670 0.0548352 0.998495i \(-0.482537\pi\)
0.0548352 + 0.998495i \(0.482537\pi\)
\(174\) −1843.56 −0.803220
\(175\) 902.519 0.389852
\(176\) −14.8922 −0.00637806
\(177\) 818.753 0.347691
\(178\) 3148.44 1.32576
\(179\) 2176.94 0.909008 0.454504 0.890745i \(-0.349817\pi\)
0.454504 + 0.890745i \(0.349817\pi\)
\(180\) 180.000 0.0745356
\(181\) −1829.01 −0.751103 −0.375551 0.926802i \(-0.622547\pi\)
−0.375551 + 0.926802i \(0.622547\pi\)
\(182\) 3307.68 1.34715
\(183\) 776.296 0.313582
\(184\) 136.156 0.0545518
\(185\) 298.864 0.118773
\(186\) 228.681 0.0901488
\(187\) 95.9925 0.0375383
\(188\) 1890.99 0.733590
\(189\) 974.721 0.375135
\(190\) 190.000 0.0725476
\(191\) 1315.52 0.498366 0.249183 0.968456i \(-0.419838\pi\)
0.249183 + 0.968456i \(0.419838\pi\)
\(192\) 192.000 0.0721688
\(193\) 2585.22 0.964189 0.482095 0.876119i \(-0.339876\pi\)
0.482095 + 0.876119i \(0.339876\pi\)
\(194\) −2813.24 −1.04113
\(195\) 687.176 0.252357
\(196\) 3841.06 1.39980
\(197\) −5487.57 −1.98464 −0.992318 0.123713i \(-0.960520\pi\)
−0.992318 + 0.123713i \(0.960520\pi\)
\(198\) −16.7537 −0.00601329
\(199\) −5391.36 −1.92052 −0.960259 0.279111i \(-0.909960\pi\)
−0.960259 + 0.279111i \(0.909960\pi\)
\(200\) 200.000 0.0707107
\(201\) −1891.87 −0.663893
\(202\) −1986.10 −0.691791
\(203\) −11092.3 −3.83512
\(204\) −1237.60 −0.424752
\(205\) −1346.42 −0.458722
\(206\) −1195.80 −0.404444
\(207\) 153.175 0.0514319
\(208\) 732.988 0.244344
\(209\) −17.6844 −0.00585291
\(210\) 1083.02 0.355884
\(211\) −3385.70 −1.10465 −0.552324 0.833629i \(-0.686259\pi\)
−0.552324 + 0.833629i \(0.686259\pi\)
\(212\) −2741.75 −0.888228
\(213\) 400.379 0.128796
\(214\) 4246.64 1.35652
\(215\) −1759.82 −0.558227
\(216\) 216.000 0.0680414
\(217\) 1375.92 0.430433
\(218\) −2565.14 −0.796941
\(219\) 1893.73 0.584320
\(220\) −18.6152 −0.00570471
\(221\) −4724.72 −1.43810
\(222\) 358.637 0.108424
\(223\) 2915.74 0.875572 0.437786 0.899079i \(-0.355763\pi\)
0.437786 + 0.899079i \(0.355763\pi\)
\(224\) 1155.22 0.344583
\(225\) 225.000 0.0666667
\(226\) −2871.67 −0.845225
\(227\) −88.2474 −0.0258026 −0.0129013 0.999917i \(-0.504107\pi\)
−0.0129013 + 0.999917i \(0.504107\pi\)
\(228\) 228.000 0.0662266
\(229\) 3130.32 0.903307 0.451653 0.892194i \(-0.350834\pi\)
0.451653 + 0.892194i \(0.350834\pi\)
\(230\) 170.195 0.0487926
\(231\) −100.803 −0.0287116
\(232\) −2458.09 −0.695609
\(233\) 1590.28 0.447136 0.223568 0.974688i \(-0.428229\pi\)
0.223568 + 0.974688i \(0.428229\pi\)
\(234\) 824.611 0.230370
\(235\) 2363.74 0.656143
\(236\) 1091.67 0.301109
\(237\) 1922.76 0.526991
\(238\) −7446.40 −2.02806
\(239\) −3604.37 −0.975511 −0.487755 0.872980i \(-0.662184\pi\)
−0.487755 + 0.872980i \(0.662184\pi\)
\(240\) 240.000 0.0645497
\(241\) 6388.57 1.70757 0.853784 0.520628i \(-0.174302\pi\)
0.853784 + 0.520628i \(0.174302\pi\)
\(242\) −2660.27 −0.706647
\(243\) 243.000 0.0641500
\(244\) 1035.06 0.271570
\(245\) 4801.33 1.25202
\(246\) −1615.70 −0.418754
\(247\) 870.423 0.224225
\(248\) 304.908 0.0780712
\(249\) 576.609 0.146751
\(250\) 250.000 0.0632456
\(251\) 1386.54 0.348677 0.174338 0.984686i \(-0.444221\pi\)
0.174338 + 0.984686i \(0.444221\pi\)
\(252\) 1299.63 0.324876
\(253\) −15.8410 −0.00393643
\(254\) −206.036 −0.0508971
\(255\) −1547.00 −0.379910
\(256\) 256.000 0.0625000
\(257\) −4775.87 −1.15919 −0.579593 0.814906i \(-0.696788\pi\)
−0.579593 + 0.814906i \(0.696788\pi\)
\(258\) −2111.79 −0.509589
\(259\) 2157.84 0.517691
\(260\) 916.235 0.218548
\(261\) −2765.35 −0.655826
\(262\) −527.648 −0.124421
\(263\) 4723.86 1.10755 0.553775 0.832666i \(-0.313187\pi\)
0.553775 + 0.832666i \(0.313187\pi\)
\(264\) −22.3382 −0.00520767
\(265\) −3427.19 −0.794455
\(266\) 1371.83 0.316211
\(267\) 4722.67 1.08248
\(268\) −2522.50 −0.574948
\(269\) −4038.70 −0.915405 −0.457703 0.889105i \(-0.651328\pi\)
−0.457703 + 0.889105i \(0.651328\pi\)
\(270\) 270.000 0.0608581
\(271\) −7923.94 −1.77618 −0.888090 0.459669i \(-0.847968\pi\)
−0.888090 + 0.459669i \(0.847968\pi\)
\(272\) −1650.14 −0.367846
\(273\) 4961.52 1.09994
\(274\) −1669.05 −0.367996
\(275\) −23.2690 −0.00510245
\(276\) 204.233 0.0445413
\(277\) −3593.69 −0.779510 −0.389755 0.920919i \(-0.627440\pi\)
−0.389755 + 0.920919i \(0.627440\pi\)
\(278\) 1971.56 0.425345
\(279\) 343.021 0.0736062
\(280\) 1444.03 0.308205
\(281\) −3973.82 −0.843623 −0.421812 0.906684i \(-0.638606\pi\)
−0.421812 + 0.906684i \(0.638606\pi\)
\(282\) 2836.49 0.598974
\(283\) 3155.29 0.662765 0.331383 0.943496i \(-0.392485\pi\)
0.331383 + 0.943496i \(0.392485\pi\)
\(284\) 533.838 0.111540
\(285\) 285.000 0.0592349
\(286\) −85.2795 −0.0176317
\(287\) −9721.36 −1.99942
\(288\) 288.000 0.0589256
\(289\) 5723.52 1.16497
\(290\) −3072.61 −0.622172
\(291\) −4219.85 −0.850077
\(292\) 2524.97 0.506036
\(293\) 25.5662 0.00509760 0.00254880 0.999997i \(-0.499189\pi\)
0.00254880 + 0.999997i \(0.499189\pi\)
\(294\) 5761.59 1.14293
\(295\) 1364.59 0.269320
\(296\) 478.183 0.0938980
\(297\) −25.1305 −0.00490983
\(298\) 5110.27 0.993390
\(299\) 779.691 0.150805
\(300\) 300.000 0.0577350
\(301\) −12706.2 −2.43313
\(302\) 3054.50 0.582009
\(303\) −2979.15 −0.564845
\(304\) 304.000 0.0573539
\(305\) 1293.83 0.242899
\(306\) −1856.40 −0.346809
\(307\) −272.811 −0.0507171 −0.0253585 0.999678i \(-0.508073\pi\)
−0.0253585 + 0.999678i \(0.508073\pi\)
\(308\) −134.405 −0.0248650
\(309\) −1793.70 −0.330227
\(310\) 381.135 0.0698290
\(311\) −3768.46 −0.687105 −0.343553 0.939133i \(-0.611630\pi\)
−0.343553 + 0.939133i \(0.611630\pi\)
\(312\) 1099.48 0.199506
\(313\) −4788.92 −0.864811 −0.432406 0.901679i \(-0.642335\pi\)
−0.432406 + 0.901679i \(0.642335\pi\)
\(314\) −2319.78 −0.416920
\(315\) 1624.53 0.290578
\(316\) 2563.69 0.456388
\(317\) −4040.14 −0.715825 −0.357913 0.933755i \(-0.616511\pi\)
−0.357913 + 0.933755i \(0.616511\pi\)
\(318\) −4112.63 −0.725235
\(319\) 285.986 0.0501948
\(320\) 320.000 0.0559017
\(321\) 6369.97 1.10759
\(322\) 1228.83 0.212671
\(323\) −1959.54 −0.337559
\(324\) 324.000 0.0555556
\(325\) 1145.29 0.195475
\(326\) 1511.00 0.256708
\(327\) −3847.71 −0.650700
\(328\) −2154.27 −0.362652
\(329\) 17066.6 2.85991
\(330\) −27.9228 −0.00465788
\(331\) −9554.49 −1.58659 −0.793297 0.608835i \(-0.791637\pi\)
−0.793297 + 0.608835i \(0.791637\pi\)
\(332\) 768.812 0.127091
\(333\) 537.955 0.0885279
\(334\) −5090.92 −0.834021
\(335\) −3153.12 −0.514249
\(336\) 1732.84 0.281351
\(337\) 1784.39 0.288433 0.144217 0.989546i \(-0.453934\pi\)
0.144217 + 0.989546i \(0.453934\pi\)
\(338\) −196.570 −0.0316331
\(339\) −4307.51 −0.690123
\(340\) −2062.67 −0.329012
\(341\) −35.4745 −0.00563358
\(342\) 342.000 0.0540738
\(343\) 22283.7 3.50790
\(344\) −2815.71 −0.441317
\(345\) 255.292 0.0398390
\(346\) 499.101 0.0775487
\(347\) 364.399 0.0563745 0.0281873 0.999603i \(-0.491027\pi\)
0.0281873 + 0.999603i \(0.491027\pi\)
\(348\) −3687.13 −0.567962
\(349\) 8408.07 1.28961 0.644805 0.764348i \(-0.276939\pi\)
0.644805 + 0.764348i \(0.276939\pi\)
\(350\) 1805.04 0.275667
\(351\) 1236.92 0.188096
\(352\) −29.7843 −0.00450997
\(353\) 8910.59 1.34352 0.671760 0.740769i \(-0.265538\pi\)
0.671760 + 0.740769i \(0.265538\pi\)
\(354\) 1637.51 0.245854
\(355\) 667.298 0.0997648
\(356\) 6296.89 0.937456
\(357\) −11169.6 −1.65590
\(358\) 4353.89 0.642766
\(359\) −5941.53 −0.873488 −0.436744 0.899586i \(-0.643868\pi\)
−0.436744 + 0.899586i \(0.643868\pi\)
\(360\) 360.000 0.0527046
\(361\) 361.000 0.0526316
\(362\) −3658.03 −0.531110
\(363\) −3990.40 −0.576974
\(364\) 6615.35 0.952579
\(365\) 3156.21 0.452612
\(366\) 1552.59 0.221736
\(367\) 8723.39 1.24076 0.620378 0.784303i \(-0.286979\pi\)
0.620378 + 0.784303i \(0.286979\pi\)
\(368\) 272.311 0.0385739
\(369\) −2423.56 −0.341911
\(370\) 597.728 0.0839849
\(371\) −24744.8 −3.46277
\(372\) 457.361 0.0637449
\(373\) 4892.51 0.679155 0.339577 0.940578i \(-0.389716\pi\)
0.339577 + 0.940578i \(0.389716\pi\)
\(374\) 191.985 0.0265436
\(375\) 375.000 0.0516398
\(376\) 3781.99 0.518726
\(377\) −14076.1 −1.92297
\(378\) 1949.44 0.265260
\(379\) 1237.51 0.167722 0.0838609 0.996477i \(-0.473275\pi\)
0.0838609 + 0.996477i \(0.473275\pi\)
\(380\) 380.000 0.0512989
\(381\) −309.054 −0.0415573
\(382\) 2631.05 0.352398
\(383\) −10955.6 −1.46164 −0.730818 0.682573i \(-0.760861\pi\)
−0.730818 + 0.682573i \(0.760861\pi\)
\(384\) 384.000 0.0510310
\(385\) −168.006 −0.0222399
\(386\) 5170.45 0.681785
\(387\) −3167.68 −0.416078
\(388\) −5626.47 −0.736188
\(389\) 5211.34 0.679242 0.339621 0.940562i \(-0.389701\pi\)
0.339621 + 0.940562i \(0.389701\pi\)
\(390\) 1374.35 0.178444
\(391\) −1755.28 −0.227028
\(392\) 7682.12 0.989811
\(393\) −791.472 −0.101589
\(394\) −10975.1 −1.40335
\(395\) 3204.61 0.408206
\(396\) −33.5074 −0.00425204
\(397\) 1136.18 0.143635 0.0718174 0.997418i \(-0.477120\pi\)
0.0718174 + 0.997418i \(0.477120\pi\)
\(398\) −10782.7 −1.35801
\(399\) 2057.74 0.258186
\(400\) 400.000 0.0500000
\(401\) −3873.02 −0.482318 −0.241159 0.970486i \(-0.577528\pi\)
−0.241159 + 0.970486i \(0.577528\pi\)
\(402\) −3783.75 −0.469443
\(403\) 1746.04 0.215823
\(404\) −3972.21 −0.489170
\(405\) 405.000 0.0496904
\(406\) −22184.7 −2.71184
\(407\) −55.6342 −0.00677563
\(408\) −2475.20 −0.300345
\(409\) 5436.39 0.657243 0.328621 0.944462i \(-0.393416\pi\)
0.328621 + 0.944462i \(0.393416\pi\)
\(410\) −2692.84 −0.324366
\(411\) −2503.57 −0.300468
\(412\) −2391.60 −0.285985
\(413\) 9852.54 1.17388
\(414\) 306.350 0.0363679
\(415\) 961.015 0.113673
\(416\) 1465.98 0.172777
\(417\) 2957.33 0.347293
\(418\) −35.3689 −0.00413863
\(419\) 4339.11 0.505917 0.252959 0.967477i \(-0.418596\pi\)
0.252959 + 0.967477i \(0.418596\pi\)
\(420\) 2166.05 0.251648
\(421\) 10397.6 1.20367 0.601836 0.798619i \(-0.294436\pi\)
0.601836 + 0.798619i \(0.294436\pi\)
\(422\) −6771.39 −0.781105
\(423\) 4254.74 0.489060
\(424\) −5483.50 −0.628072
\(425\) −2578.34 −0.294277
\(426\) 800.758 0.0910724
\(427\) 9341.63 1.05872
\(428\) 8493.29 0.959202
\(429\) −127.919 −0.0143963
\(430\) −3519.64 −0.394726
\(431\) −9819.17 −1.09738 −0.548692 0.836024i \(-0.684874\pi\)
−0.548692 + 0.836024i \(0.684874\pi\)
\(432\) 432.000 0.0481125
\(433\) 8198.36 0.909903 0.454952 0.890516i \(-0.349657\pi\)
0.454952 + 0.890516i \(0.349657\pi\)
\(434\) 2751.85 0.304362
\(435\) −4608.91 −0.508001
\(436\) −5130.28 −0.563522
\(437\) 323.370 0.0353979
\(438\) 3787.45 0.413177
\(439\) −849.949 −0.0924052 −0.0462026 0.998932i \(-0.514712\pi\)
−0.0462026 + 0.998932i \(0.514712\pi\)
\(440\) −37.2304 −0.00403384
\(441\) 8642.39 0.933202
\(442\) −9449.45 −1.01689
\(443\) −4275.18 −0.458511 −0.229255 0.973366i \(-0.573629\pi\)
−0.229255 + 0.973366i \(0.573629\pi\)
\(444\) 717.274 0.0766674
\(445\) 7871.11 0.838486
\(446\) 5831.48 0.619123
\(447\) 7665.41 0.811100
\(448\) 2310.45 0.243657
\(449\) 15175.3 1.59503 0.797515 0.603299i \(-0.206147\pi\)
0.797515 + 0.603299i \(0.206147\pi\)
\(450\) 450.000 0.0471405
\(451\) 250.639 0.0261688
\(452\) −5743.35 −0.597664
\(453\) 4581.75 0.475209
\(454\) −176.495 −0.0182452
\(455\) 8269.19 0.852013
\(456\) 456.000 0.0468293
\(457\) 5141.61 0.526290 0.263145 0.964756i \(-0.415240\pi\)
0.263145 + 0.964756i \(0.415240\pi\)
\(458\) 6260.64 0.638734
\(459\) −2784.60 −0.283168
\(460\) 340.389 0.0345016
\(461\) −1294.65 −0.130798 −0.0653992 0.997859i \(-0.520832\pi\)
−0.0653992 + 0.997859i \(0.520832\pi\)
\(462\) −201.607 −0.0203022
\(463\) −12898.4 −1.29469 −0.647344 0.762198i \(-0.724120\pi\)
−0.647344 + 0.762198i \(0.724120\pi\)
\(464\) −4916.17 −0.491870
\(465\) 571.702 0.0570151
\(466\) 3180.56 0.316173
\(467\) 10324.8 1.02307 0.511535 0.859262i \(-0.329077\pi\)
0.511535 + 0.859262i \(0.329077\pi\)
\(468\) 1649.22 0.162896
\(469\) −22766.0 −2.24145
\(470\) 4727.48 0.463963
\(471\) −3479.67 −0.340413
\(472\) 2183.34 0.212916
\(473\) 327.594 0.0318453
\(474\) 3845.53 0.372639
\(475\) 475.000 0.0458831
\(476\) −14892.8 −1.43405
\(477\) −6168.94 −0.592152
\(478\) −7208.73 −0.689790
\(479\) 5406.05 0.515676 0.257838 0.966188i \(-0.416990\pi\)
0.257838 + 0.966188i \(0.416990\pi\)
\(480\) 480.000 0.0456435
\(481\) 2738.30 0.259575
\(482\) 12777.1 1.20743
\(483\) 1843.25 0.173645
\(484\) −5320.53 −0.499675
\(485\) −7033.09 −0.658466
\(486\) 486.000 0.0453609
\(487\) 15664.5 1.45755 0.728773 0.684756i \(-0.240091\pi\)
0.728773 + 0.684756i \(0.240091\pi\)
\(488\) 2070.12 0.192029
\(489\) 2266.50 0.209601
\(490\) 9602.65 0.885313
\(491\) −9832.59 −0.903745 −0.451872 0.892083i \(-0.649244\pi\)
−0.451872 + 0.892083i \(0.649244\pi\)
\(492\) −3231.41 −0.296104
\(493\) 31688.9 2.89492
\(494\) 1740.85 0.158551
\(495\) −41.8842 −0.00380314
\(496\) 609.815 0.0552047
\(497\) 4817.99 0.434842
\(498\) 1153.22 0.103769
\(499\) 12193.9 1.09393 0.546966 0.837155i \(-0.315783\pi\)
0.546966 + 0.837155i \(0.315783\pi\)
\(500\) 500.000 0.0447214
\(501\) −7636.38 −0.680975
\(502\) 2773.09 0.246552
\(503\) 20823.3 1.84585 0.922926 0.384977i \(-0.125791\pi\)
0.922926 + 0.384977i \(0.125791\pi\)
\(504\) 2599.26 0.229722
\(505\) −4965.26 −0.437527
\(506\) −31.6821 −0.00278348
\(507\) −294.855 −0.0258283
\(508\) −412.073 −0.0359897
\(509\) 262.903 0.0228939 0.0114469 0.999934i \(-0.496356\pi\)
0.0114469 + 0.999934i \(0.496356\pi\)
\(510\) −3094.00 −0.268637
\(511\) 22788.3 1.97279
\(512\) 512.000 0.0441942
\(513\) 513.000 0.0441511
\(514\) −9551.75 −0.819668
\(515\) −2989.51 −0.255793
\(516\) −4223.57 −0.360334
\(517\) −440.015 −0.0374310
\(518\) 4315.69 0.366063
\(519\) 748.652 0.0633182
\(520\) 1832.47 0.154537
\(521\) −13595.2 −1.14321 −0.571607 0.820527i \(-0.693680\pi\)
−0.571607 + 0.820527i \(0.693680\pi\)
\(522\) −5530.69 −0.463739
\(523\) 16842.1 1.40813 0.704066 0.710134i \(-0.251366\pi\)
0.704066 + 0.710134i \(0.251366\pi\)
\(524\) −1055.30 −0.0879787
\(525\) 2707.56 0.225081
\(526\) 9447.72 0.783156
\(527\) −3930.77 −0.324909
\(528\) −44.6765 −0.00368238
\(529\) −11877.3 −0.976193
\(530\) −6854.38 −0.561764
\(531\) 2456.26 0.200739
\(532\) 2743.66 0.223595
\(533\) −12336.4 −1.00253
\(534\) 9445.33 0.765430
\(535\) 10616.6 0.857937
\(536\) −5045.00 −0.406550
\(537\) 6530.83 0.524816
\(538\) −8077.41 −0.647289
\(539\) −893.776 −0.0714243
\(540\) 540.000 0.0430331
\(541\) 11469.7 0.911500 0.455750 0.890108i \(-0.349371\pi\)
0.455750 + 0.890108i \(0.349371\pi\)
\(542\) −15847.9 −1.25595
\(543\) −5487.04 −0.433649
\(544\) −3300.27 −0.260107
\(545\) −6412.85 −0.504030
\(546\) 9923.03 0.777778
\(547\) 7568.23 0.591580 0.295790 0.955253i \(-0.404417\pi\)
0.295790 + 0.955253i \(0.404417\pi\)
\(548\) −3338.10 −0.260213
\(549\) 2328.89 0.181047
\(550\) −46.5380 −0.00360798
\(551\) −5837.95 −0.451371
\(552\) 408.467 0.0314955
\(553\) 23137.7 1.77924
\(554\) −7187.39 −0.551197
\(555\) 896.592 0.0685734
\(556\) 3943.11 0.300765
\(557\) 10701.2 0.814051 0.407025 0.913417i \(-0.366566\pi\)
0.407025 + 0.913417i \(0.366566\pi\)
\(558\) 686.042 0.0520475
\(559\) −16124.1 −1.21999
\(560\) 2888.06 0.217934
\(561\) 287.978 0.0216728
\(562\) −7947.64 −0.596532
\(563\) 12327.0 0.922772 0.461386 0.887200i \(-0.347352\pi\)
0.461386 + 0.887200i \(0.347352\pi\)
\(564\) 5672.98 0.423538
\(565\) −7179.18 −0.534567
\(566\) 6310.58 0.468646
\(567\) 2924.16 0.216584
\(568\) 1067.68 0.0788710
\(569\) 18887.8 1.39160 0.695799 0.718236i \(-0.255050\pi\)
0.695799 + 0.718236i \(0.255050\pi\)
\(570\) 570.000 0.0418854
\(571\) −15534.3 −1.13851 −0.569256 0.822161i \(-0.692769\pi\)
−0.569256 + 0.822161i \(0.692769\pi\)
\(572\) −170.559 −0.0124675
\(573\) 3946.57 0.287732
\(574\) −19442.7 −1.41380
\(575\) 425.486 0.0308591
\(576\) 576.000 0.0416667
\(577\) 5670.77 0.409146 0.204573 0.978851i \(-0.434419\pi\)
0.204573 + 0.978851i \(0.434419\pi\)
\(578\) 11447.0 0.823761
\(579\) 7755.67 0.556675
\(580\) −6145.22 −0.439942
\(581\) 6938.68 0.495464
\(582\) −8439.71 −0.601095
\(583\) 637.978 0.0453214
\(584\) 5049.93 0.357821
\(585\) 2061.53 0.145699
\(586\) 51.1325 0.00360455
\(587\) −8951.67 −0.629429 −0.314715 0.949186i \(-0.601909\pi\)
−0.314715 + 0.949186i \(0.601909\pi\)
\(588\) 11523.2 0.808177
\(589\) 724.156 0.0506593
\(590\) 2729.18 0.190438
\(591\) −16462.7 −1.14583
\(592\) 956.365 0.0663959
\(593\) 16888.6 1.16953 0.584765 0.811203i \(-0.301187\pi\)
0.584765 + 0.811203i \(0.301187\pi\)
\(594\) −50.2610 −0.00347178
\(595\) −18616.0 −1.28266
\(596\) 10220.5 0.702433
\(597\) −16174.1 −1.10881
\(598\) 1559.38 0.106635
\(599\) −4473.77 −0.305164 −0.152582 0.988291i \(-0.548759\pi\)
−0.152582 + 0.988291i \(0.548759\pi\)
\(600\) 600.000 0.0408248
\(601\) −19271.9 −1.30802 −0.654009 0.756487i \(-0.726914\pi\)
−0.654009 + 0.756487i \(0.726914\pi\)
\(602\) −25412.4 −1.72048
\(603\) −5675.62 −0.383299
\(604\) 6109.00 0.411543
\(605\) −6650.67 −0.446923
\(606\) −5958.31 −0.399406
\(607\) 9000.09 0.601816 0.300908 0.953653i \(-0.402710\pi\)
0.300908 + 0.953653i \(0.402710\pi\)
\(608\) 608.000 0.0405554
\(609\) −33277.0 −2.21421
\(610\) 2587.65 0.171756
\(611\) 21657.4 1.43399
\(612\) −3712.81 −0.245231
\(613\) −11357.5 −0.748328 −0.374164 0.927363i \(-0.622070\pi\)
−0.374164 + 0.927363i \(0.622070\pi\)
\(614\) −545.622 −0.0358624
\(615\) −4039.26 −0.264843
\(616\) −268.809 −0.0175822
\(617\) 7071.80 0.461426 0.230713 0.973022i \(-0.425894\pi\)
0.230713 + 0.973022i \(0.425894\pi\)
\(618\) −3587.41 −0.233506
\(619\) −19272.4 −1.25141 −0.625706 0.780059i \(-0.715189\pi\)
−0.625706 + 0.780059i \(0.715189\pi\)
\(620\) 762.269 0.0493766
\(621\) 459.525 0.0296942
\(622\) −7536.92 −0.485857
\(623\) 56830.6 3.65469
\(624\) 2198.96 0.141072
\(625\) 625.000 0.0400000
\(626\) −9577.84 −0.611514
\(627\) −53.0533 −0.00337918
\(628\) −4639.56 −0.294807
\(629\) −6164.58 −0.390776
\(630\) 3249.07 0.205470
\(631\) 30363.6 1.91562 0.957810 0.287403i \(-0.0927918\pi\)
0.957810 + 0.287403i \(0.0927918\pi\)
\(632\) 5127.37 0.322715
\(633\) −10157.1 −0.637769
\(634\) −8080.27 −0.506165
\(635\) −515.091 −0.0321902
\(636\) −8225.25 −0.512818
\(637\) 43991.4 2.73627
\(638\) 571.972 0.0354931
\(639\) 1201.14 0.0743603
\(640\) 640.000 0.0395285
\(641\) 4344.27 0.267688 0.133844 0.991002i \(-0.457268\pi\)
0.133844 + 0.991002i \(0.457268\pi\)
\(642\) 12739.9 0.783185
\(643\) −19953.3 −1.22376 −0.611882 0.790949i \(-0.709587\pi\)
−0.611882 + 0.790949i \(0.709587\pi\)
\(644\) 2457.66 0.150381
\(645\) −5279.47 −0.322293
\(646\) −3919.07 −0.238690
\(647\) 2474.77 0.150376 0.0751880 0.997169i \(-0.476044\pi\)
0.0751880 + 0.997169i \(0.476044\pi\)
\(648\) 648.000 0.0392837
\(649\) −254.021 −0.0153639
\(650\) 2290.59 0.138222
\(651\) 4127.77 0.248510
\(652\) 3022.00 0.181520
\(653\) 30781.5 1.84468 0.922339 0.386382i \(-0.126275\pi\)
0.922339 + 0.386382i \(0.126275\pi\)
\(654\) −7695.42 −0.460114
\(655\) −1319.12 −0.0786905
\(656\) −4308.54 −0.256433
\(657\) 5681.18 0.337357
\(658\) 34133.2 2.02226
\(659\) 13752.5 0.812930 0.406465 0.913666i \(-0.366761\pi\)
0.406465 + 0.913666i \(0.366761\pi\)
\(660\) −55.8456 −0.00329362
\(661\) 2059.46 0.121186 0.0605928 0.998163i \(-0.480701\pi\)
0.0605928 + 0.998163i \(0.480701\pi\)
\(662\) −19109.0 −1.12189
\(663\) −14174.2 −0.830285
\(664\) 1537.62 0.0898666
\(665\) 3429.57 0.199990
\(666\) 1075.91 0.0625986
\(667\) −5229.41 −0.303574
\(668\) −10181.8 −0.589742
\(669\) 8747.23 0.505512
\(670\) −6306.25 −0.363629
\(671\) −240.848 −0.0138567
\(672\) 3465.67 0.198945
\(673\) −22647.6 −1.29718 −0.648588 0.761139i \(-0.724640\pi\)
−0.648588 + 0.761139i \(0.724640\pi\)
\(674\) 3568.78 0.203953
\(675\) 675.000 0.0384900
\(676\) −393.140 −0.0223680
\(677\) 19995.2 1.13512 0.567562 0.823331i \(-0.307887\pi\)
0.567562 + 0.823331i \(0.307887\pi\)
\(678\) −8615.02 −0.487991
\(679\) −50780.0 −2.87004
\(680\) −4125.34 −0.232646
\(681\) −264.742 −0.0148971
\(682\) −70.9490 −0.00398354
\(683\) −16395.8 −0.918550 −0.459275 0.888294i \(-0.651891\pi\)
−0.459275 + 0.888294i \(0.651891\pi\)
\(684\) 684.000 0.0382360
\(685\) −4172.62 −0.232741
\(686\) 44567.5 2.48046
\(687\) 9390.95 0.521524
\(688\) −5631.43 −0.312058
\(689\) −31401.1 −1.73626
\(690\) 510.584 0.0281704
\(691\) −8258.78 −0.454673 −0.227336 0.973816i \(-0.573002\pi\)
−0.227336 + 0.973816i \(0.573002\pi\)
\(692\) 998.202 0.0548352
\(693\) −302.410 −0.0165767
\(694\) 728.798 0.0398628
\(695\) 4928.89 0.269012
\(696\) −7374.26 −0.401610
\(697\) 27772.2 1.50925
\(698\) 16816.1 0.911891
\(699\) 4770.84 0.258154
\(700\) 3610.08 0.194926
\(701\) −12578.1 −0.677701 −0.338851 0.940840i \(-0.610038\pi\)
−0.338851 + 0.940840i \(0.610038\pi\)
\(702\) 2473.83 0.133004
\(703\) 1135.68 0.0609290
\(704\) −59.5686 −0.00318903
\(705\) 7091.23 0.378824
\(706\) 17821.2 0.950013
\(707\) −35849.9 −1.90704
\(708\) 3275.01 0.173845
\(709\) −18242.9 −0.966329 −0.483164 0.875530i \(-0.660513\pi\)
−0.483164 + 0.875530i \(0.660513\pi\)
\(710\) 1334.60 0.0705444
\(711\) 5768.29 0.304259
\(712\) 12593.8 0.662882
\(713\) 648.670 0.0340714
\(714\) −22339.2 −1.17090
\(715\) −213.199 −0.0111513
\(716\) 8707.77 0.454504
\(717\) −10813.1 −0.563211
\(718\) −11883.1 −0.617649
\(719\) −2709.59 −0.140543 −0.0702717 0.997528i \(-0.522387\pi\)
−0.0702717 + 0.997528i \(0.522387\pi\)
\(720\) 720.000 0.0372678
\(721\) −21584.7 −1.11492
\(722\) 722.000 0.0372161
\(723\) 19165.7 0.985865
\(724\) −7316.06 −0.375551
\(725\) −7681.52 −0.393496
\(726\) −7980.80 −0.407983
\(727\) −4649.35 −0.237187 −0.118594 0.992943i \(-0.537839\pi\)
−0.118594 + 0.992943i \(0.537839\pi\)
\(728\) 13230.7 0.673575
\(729\) 729.000 0.0370370
\(730\) 6312.42 0.320045
\(731\) 36299.3 1.83663
\(732\) 3105.18 0.156791
\(733\) −7179.88 −0.361794 −0.180897 0.983502i \(-0.557900\pi\)
−0.180897 + 0.983502i \(0.557900\pi\)
\(734\) 17446.8 0.877347
\(735\) 14404.0 0.722855
\(736\) 544.623 0.0272759
\(737\) 586.960 0.0293364
\(738\) −4847.11 −0.241768
\(739\) −31181.9 −1.55216 −0.776079 0.630635i \(-0.782794\pi\)
−0.776079 + 0.630635i \(0.782794\pi\)
\(740\) 1195.46 0.0593863
\(741\) 2611.27 0.129457
\(742\) −49489.7 −2.44855
\(743\) 2085.25 0.102961 0.0514807 0.998674i \(-0.483606\pi\)
0.0514807 + 0.998674i \(0.483606\pi\)
\(744\) 914.723 0.0450744
\(745\) 12775.7 0.628275
\(746\) 9785.02 0.480235
\(747\) 1729.83 0.0847270
\(748\) 383.970 0.0187692
\(749\) 76653.5 3.73947
\(750\) 750.000 0.0365148
\(751\) −34782.8 −1.69007 −0.845034 0.534713i \(-0.820420\pi\)
−0.845034 + 0.534713i \(0.820420\pi\)
\(752\) 7563.97 0.366795
\(753\) 4159.63 0.201309
\(754\) −28152.3 −1.35974
\(755\) 7636.26 0.368095
\(756\) 3898.88 0.187567
\(757\) 17185.7 0.825133 0.412566 0.910928i \(-0.364632\pi\)
0.412566 + 0.910928i \(0.364632\pi\)
\(758\) 2475.02 0.118597
\(759\) −47.5231 −0.00227270
\(760\) 760.000 0.0362738
\(761\) 20792.1 0.990425 0.495213 0.868772i \(-0.335090\pi\)
0.495213 + 0.868772i \(0.335090\pi\)
\(762\) −618.109 −0.0293855
\(763\) −46301.7 −2.19690
\(764\) 5262.09 0.249183
\(765\) −4641.01 −0.219341
\(766\) −21911.2 −1.03353
\(767\) 12502.8 0.588594
\(768\) 768.000 0.0360844
\(769\) 19857.3 0.931174 0.465587 0.885002i \(-0.345843\pi\)
0.465587 + 0.885002i \(0.345843\pi\)
\(770\) −336.011 −0.0157260
\(771\) −14327.6 −0.669256
\(772\) 10340.9 0.482095
\(773\) −21528.0 −1.00169 −0.500847 0.865536i \(-0.666978\pi\)
−0.500847 + 0.865536i \(0.666978\pi\)
\(774\) −6335.36 −0.294212
\(775\) 952.836 0.0441637
\(776\) −11252.9 −0.520563
\(777\) 6473.53 0.298889
\(778\) 10422.7 0.480297
\(779\) −5116.40 −0.235320
\(780\) 2748.70 0.126179
\(781\) −124.219 −0.00569129
\(782\) −3510.55 −0.160533
\(783\) −8296.04 −0.378642
\(784\) 15364.2 0.699902
\(785\) −5799.45 −0.263683
\(786\) −1582.94 −0.0718343
\(787\) −39904.4 −1.80742 −0.903710 0.428145i \(-0.859167\pi\)
−0.903710 + 0.428145i \(0.859167\pi\)
\(788\) −21950.3 −0.992318
\(789\) 14171.6 0.639444
\(790\) 6409.21 0.288645
\(791\) −51834.8 −2.33000
\(792\) −67.0147 −0.00300665
\(793\) 11854.5 0.530852
\(794\) 2272.35 0.101565
\(795\) −10281.6 −0.458679
\(796\) −21565.4 −0.960259
\(797\) 30219.8 1.34309 0.671543 0.740966i \(-0.265632\pi\)
0.671543 + 0.740966i \(0.265632\pi\)
\(798\) 4115.49 0.182565
\(799\) −48756.2 −2.15879
\(800\) 800.000 0.0353553
\(801\) 14168.0 0.624971
\(802\) −7746.04 −0.341050
\(803\) −587.535 −0.0258202
\(804\) −7567.50 −0.331947
\(805\) 3072.08 0.134505
\(806\) 3492.09 0.152610
\(807\) −12116.1 −0.528510
\(808\) −7944.41 −0.345895
\(809\) 34900.3 1.51673 0.758363 0.651833i \(-0.226000\pi\)
0.758363 + 0.651833i \(0.226000\pi\)
\(810\) 810.000 0.0351364
\(811\) −36071.1 −1.56181 −0.780905 0.624650i \(-0.785242\pi\)
−0.780905 + 0.624650i \(0.785242\pi\)
\(812\) −44369.4 −1.91756
\(813\) −23771.8 −1.02548
\(814\) −111.268 −0.00479110
\(815\) 3777.51 0.162356
\(816\) −4950.41 −0.212376
\(817\) −6687.32 −0.286365
\(818\) 10872.8 0.464741
\(819\) 14884.5 0.635053
\(820\) −5385.68 −0.229361
\(821\) 3695.95 0.157113 0.0785563 0.996910i \(-0.474969\pi\)
0.0785563 + 0.996910i \(0.474969\pi\)
\(822\) −5007.15 −0.212463
\(823\) 33632.8 1.42450 0.712250 0.701925i \(-0.247676\pi\)
0.712250 + 0.701925i \(0.247676\pi\)
\(824\) −4783.21 −0.202222
\(825\) −69.8070 −0.00294590
\(826\) 19705.1 0.830057
\(827\) −9896.52 −0.416125 −0.208063 0.978116i \(-0.566716\pi\)
−0.208063 + 0.978116i \(0.566716\pi\)
\(828\) 612.700 0.0257160
\(829\) 2514.76 0.105357 0.0526787 0.998612i \(-0.483224\pi\)
0.0526787 + 0.998612i \(0.483224\pi\)
\(830\) 1922.03 0.0803791
\(831\) −10781.1 −0.450050
\(832\) 2931.95 0.122172
\(833\) −99035.5 −4.11930
\(834\) 5914.67 0.245573
\(835\) −12727.3 −0.527481
\(836\) −70.7378 −0.00292646
\(837\) 1029.06 0.0424966
\(838\) 8678.22 0.357738
\(839\) −17494.6 −0.719880 −0.359940 0.932975i \(-0.617203\pi\)
−0.359940 + 0.932975i \(0.617203\pi\)
\(840\) 4332.09 0.177942
\(841\) 70020.2 2.87097
\(842\) 20795.1 0.851125
\(843\) −11921.5 −0.487066
\(844\) −13542.8 −0.552324
\(845\) −491.425 −0.0200065
\(846\) 8509.47 0.345818
\(847\) −48018.8 −1.94799
\(848\) −10967.0 −0.444114
\(849\) 9465.87 0.382648
\(850\) −5156.67 −0.208085
\(851\) 1017.30 0.0409784
\(852\) 1601.52 0.0643979
\(853\) −17651.5 −0.708531 −0.354266 0.935145i \(-0.615269\pi\)
−0.354266 + 0.935145i \(0.615269\pi\)
\(854\) 18683.3 0.748627
\(855\) 855.000 0.0341993
\(856\) 16986.6 0.678258
\(857\) −10617.1 −0.423188 −0.211594 0.977358i \(-0.567865\pi\)
−0.211594 + 0.977358i \(0.567865\pi\)
\(858\) −255.838 −0.0101797
\(859\) −940.655 −0.0373629 −0.0186814 0.999825i \(-0.505947\pi\)
−0.0186814 + 0.999825i \(0.505947\pi\)
\(860\) −7039.29 −0.279114
\(861\) −29164.1 −1.15437
\(862\) −19638.3 −0.775968
\(863\) −34694.3 −1.36849 −0.684246 0.729251i \(-0.739869\pi\)
−0.684246 + 0.729251i \(0.739869\pi\)
\(864\) 864.000 0.0340207
\(865\) 1247.75 0.0490461
\(866\) 16396.7 0.643399
\(867\) 17170.5 0.672598
\(868\) 5503.70 0.215216
\(869\) −596.544 −0.0232870
\(870\) −9217.82 −0.359211
\(871\) −28890.0 −1.12388
\(872\) −10260.6 −0.398470
\(873\) −12659.6 −0.490792
\(874\) 646.739 0.0250301
\(875\) 4512.60 0.174347
\(876\) 7574.90 0.292160
\(877\) −30130.8 −1.16014 −0.580072 0.814565i \(-0.696976\pi\)
−0.580072 + 0.814565i \(0.696976\pi\)
\(878\) −1699.90 −0.0653403
\(879\) 76.6987 0.00294310
\(880\) −74.4608 −0.00285236
\(881\) −5044.75 −0.192919 −0.0964597 0.995337i \(-0.530752\pi\)
−0.0964597 + 0.995337i \(0.530752\pi\)
\(882\) 17284.8 0.659874
\(883\) 15728.5 0.599440 0.299720 0.954027i \(-0.403107\pi\)
0.299720 + 0.954027i \(0.403107\pi\)
\(884\) −18898.9 −0.719048
\(885\) 4093.77 0.155492
\(886\) −8550.37 −0.324216
\(887\) −16440.5 −0.622342 −0.311171 0.950354i \(-0.600721\pi\)
−0.311171 + 0.950354i \(0.600721\pi\)
\(888\) 1434.55 0.0542120
\(889\) −3719.03 −0.140306
\(890\) 15742.2 0.592899
\(891\) −75.3916 −0.00283469
\(892\) 11663.0 0.437786
\(893\) 8982.22 0.336594
\(894\) 15330.8 0.573534
\(895\) 10884.7 0.406521
\(896\) 4620.90 0.172292
\(897\) 2339.07 0.0870673
\(898\) 30350.7 1.12786
\(899\) −11710.8 −0.434456
\(900\) 900.000 0.0333333
\(901\) 70691.6 2.61385
\(902\) 501.278 0.0185041
\(903\) −38118.5 −1.40477
\(904\) −11486.7 −0.422613
\(905\) −9145.07 −0.335903
\(906\) 9163.51 0.336023
\(907\) −27363.4 −1.00175 −0.500874 0.865520i \(-0.666988\pi\)
−0.500874 + 0.865520i \(0.666988\pi\)
\(908\) −352.990 −0.0129013
\(909\) −8937.46 −0.326113
\(910\) 16538.4 0.602464
\(911\) −15939.3 −0.579684 −0.289842 0.957075i \(-0.593603\pi\)
−0.289842 + 0.957075i \(0.593603\pi\)
\(912\) 912.000 0.0331133
\(913\) −178.895 −0.00648473
\(914\) 10283.2 0.372143
\(915\) 3881.48 0.140238
\(916\) 12521.3 0.451653
\(917\) −9524.25 −0.342986
\(918\) −5569.21 −0.200230
\(919\) 26217.5 0.941061 0.470530 0.882384i \(-0.344063\pi\)
0.470530 + 0.882384i \(0.344063\pi\)
\(920\) 680.778 0.0243963
\(921\) −818.433 −0.0292815
\(922\) −2589.31 −0.0924884
\(923\) 6114.02 0.218034
\(924\) −403.214 −0.0143558
\(925\) 1494.32 0.0531167
\(926\) −25796.8 −0.915482
\(927\) −5381.11 −0.190657
\(928\) −9832.34 −0.347804
\(929\) 20817.0 0.735181 0.367591 0.929988i \(-0.380183\pi\)
0.367591 + 0.929988i \(0.380183\pi\)
\(930\) 1143.40 0.0403158
\(931\) 18245.0 0.642274
\(932\) 6361.12 0.223568
\(933\) −11305.4 −0.396700
\(934\) 20649.6 0.723420
\(935\) 479.963 0.0167877
\(936\) 3298.44 0.115185
\(937\) −37517.5 −1.30805 −0.654025 0.756473i \(-0.726921\pi\)
−0.654025 + 0.756473i \(0.726921\pi\)
\(938\) −45532.1 −1.58494
\(939\) −14366.8 −0.499299
\(940\) 9454.97 0.328071
\(941\) −26725.6 −0.925856 −0.462928 0.886396i \(-0.653201\pi\)
−0.462928 + 0.886396i \(0.653201\pi\)
\(942\) −6959.34 −0.240709
\(943\) −4583.07 −0.158266
\(944\) 4366.68 0.150555
\(945\) 4873.60 0.167765
\(946\) 655.189 0.0225180
\(947\) 25719.8 0.882557 0.441279 0.897370i \(-0.354525\pi\)
0.441279 + 0.897370i \(0.354525\pi\)
\(948\) 7691.06 0.263496
\(949\) 28918.3 0.989175
\(950\) 950.000 0.0324443
\(951\) −12120.4 −0.413282
\(952\) −29785.6 −1.01403
\(953\) −4559.63 −0.154985 −0.0774926 0.996993i \(-0.524691\pi\)
−0.0774926 + 0.996993i \(0.524691\pi\)
\(954\) −12337.9 −0.418714
\(955\) 6577.62 0.222876
\(956\) −14417.5 −0.487755
\(957\) 857.958 0.0289800
\(958\) 10812.1 0.364638
\(959\) −30127.0 −1.01444
\(960\) 960.000 0.0322749
\(961\) −28338.4 −0.951239
\(962\) 5476.59 0.183547
\(963\) 19109.9 0.639468
\(964\) 25554.3 0.853784
\(965\) 12926.1 0.431199
\(966\) 3686.49 0.122786
\(967\) 53457.4 1.77774 0.888869 0.458161i \(-0.151492\pi\)
0.888869 + 0.458161i \(0.151492\pi\)
\(968\) −10641.1 −0.353323
\(969\) −5878.61 −0.194890
\(970\) −14066.2 −0.465606
\(971\) 12095.4 0.399753 0.199876 0.979821i \(-0.435946\pi\)
0.199876 + 0.979821i \(0.435946\pi\)
\(972\) 972.000 0.0320750
\(973\) 35587.3 1.17254
\(974\) 31328.9 1.03064
\(975\) 3435.88 0.112858
\(976\) 4140.25 0.135785
\(977\) −24895.5 −0.815227 −0.407614 0.913155i \(-0.633639\pi\)
−0.407614 + 0.913155i \(0.633639\pi\)
\(978\) 4533.01 0.148210
\(979\) −1465.22 −0.0478332
\(980\) 19205.3 0.626011
\(981\) −11543.1 −0.375682
\(982\) −19665.2 −0.639044
\(983\) 10329.2 0.335146 0.167573 0.985860i \(-0.446407\pi\)
0.167573 + 0.985860i \(0.446407\pi\)
\(984\) −6462.82 −0.209377
\(985\) −27437.9 −0.887556
\(986\) 63377.7 2.04702
\(987\) 51199.7 1.65117
\(988\) 3481.69 0.112113
\(989\) −5990.24 −0.192597
\(990\) −83.7684 −0.00268923
\(991\) −44011.4 −1.41076 −0.705382 0.708827i \(-0.749225\pi\)
−0.705382 + 0.708827i \(0.749225\pi\)
\(992\) 1219.63 0.0390356
\(993\) −28663.5 −0.916020
\(994\) 9635.99 0.307480
\(995\) −26956.8 −0.858882
\(996\) 2306.44 0.0733757
\(997\) −11358.7 −0.360815 −0.180407 0.983592i \(-0.557742\pi\)
−0.180407 + 0.983592i \(0.557742\pi\)
\(998\) 24387.7 0.773527
\(999\) 1613.87 0.0511116
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 570.4.a.s.1.4 4
3.2 odd 2 1710.4.a.bc.1.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
570.4.a.s.1.4 4 1.1 even 1 trivial
1710.4.a.bc.1.4 4 3.2 odd 2