Properties

Label 570.4.a.s.1.3
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 1.3
Root \(12.2089\) of defining polynomial
Character \(\chi\) \(=\) 570.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +5.00000 q^{5} +6.00000 q^{6} +17.1829 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +5.00000 q^{5} +6.00000 q^{6} +17.1829 q^{7} +8.00000 q^{8} +9.00000 q^{9} +10.0000 q^{10} +29.2349 q^{11} +12.0000 q^{12} -69.9219 q^{13} +34.3658 q^{14} +15.0000 q^{15} +16.0000 q^{16} +94.5904 q^{17} +18.0000 q^{18} +19.0000 q^{19} +20.0000 q^{20} +51.5487 q^{21} +58.4699 q^{22} -8.21713 q^{23} +24.0000 q^{24} +25.0000 q^{25} -139.844 q^{26} +27.0000 q^{27} +68.7316 q^{28} +216.520 q^{29} +30.0000 q^{30} -227.097 q^{31} +32.0000 q^{32} +87.7048 q^{33} +189.181 q^{34} +85.9144 q^{35} +36.0000 q^{36} -5.48766 q^{37} +38.0000 q^{38} -209.766 q^{39} +40.0000 q^{40} -423.214 q^{41} +103.097 q^{42} +267.242 q^{43} +116.940 q^{44} +45.0000 q^{45} -16.4343 q^{46} -6.59371 q^{47} +48.0000 q^{48} -47.7483 q^{49} +50.0000 q^{50} +283.771 q^{51} -279.688 q^{52} -206.172 q^{53} +54.0000 q^{54} +146.175 q^{55} +137.463 q^{56} +57.0000 q^{57} +433.040 q^{58} +208.532 q^{59} +60.0000 q^{60} +510.064 q^{61} -454.195 q^{62} +154.646 q^{63} +64.0000 q^{64} -349.610 q^{65} +175.410 q^{66} +1010.47 q^{67} +378.362 q^{68} -24.6514 q^{69} +171.829 q^{70} +334.247 q^{71} +72.0000 q^{72} -866.693 q^{73} -10.9753 q^{74} +75.0000 q^{75} +76.0000 q^{76} +502.341 q^{77} -419.532 q^{78} +502.538 q^{79} +80.0000 q^{80} +81.0000 q^{81} -846.428 q^{82} -478.314 q^{83} +206.195 q^{84} +472.952 q^{85} +534.485 q^{86} +649.559 q^{87} +233.879 q^{88} -1150.25 q^{89} +90.0000 q^{90} -1201.46 q^{91} -32.8685 q^{92} -681.292 q^{93} -13.1874 q^{94} +95.0000 q^{95} +96.0000 q^{96} -1394.30 q^{97} -95.4967 q^{98} +263.114 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 8q^{2} + 12q^{3} + 16q^{4} + 20q^{5} + 24q^{6} + 36q^{7} + 32q^{8} + 36q^{9} + O(q^{10}) \) \( 4q + 8q^{2} + 12q^{3} + 16q^{4} + 20q^{5} + 24q^{6} + 36q^{7} + 32q^{8} + 36q^{9} + 40q^{10} + 54q^{11} + 48q^{12} + 46q^{13} + 72q^{14} + 60q^{15} + 64q^{16} + 14q^{17} + 72q^{18} + 76q^{19} + 80q^{20} + 108q^{21} + 108q^{22} + 104q^{23} + 96q^{24} + 100q^{25} + 92q^{26} + 108q^{27} + 144q^{28} + 14q^{29} + 120q^{30} + 30q^{31} + 128q^{32} + 162q^{33} + 28q^{34} + 180q^{35} + 144q^{36} + 30q^{37} + 152q^{38} + 138q^{39} + 160q^{40} - 36q^{41} + 216q^{42} + 102q^{43} + 216q^{44} + 180q^{45} + 208q^{46} + 408q^{47} + 192q^{48} + 480q^{49} + 200q^{50} + 42q^{51} + 184q^{52} - 176q^{53} + 216q^{54} + 270q^{55} + 288q^{56} + 228q^{57} + 28q^{58} + 66q^{59} + 240q^{60} + 60q^{61} + 60q^{62} + 324q^{63} + 256q^{64} + 230q^{65} + 324q^{66} - 152q^{67} + 56q^{68} + 312q^{69} + 360q^{70} + 172q^{71} + 288q^{72} + 284q^{73} + 60q^{74} + 300q^{75} + 304q^{76} - 300q^{77} + 276q^{78} + 554q^{79} + 320q^{80} + 324q^{81} - 72q^{82} - 394q^{83} + 432q^{84} + 70q^{85} + 204q^{86} + 42q^{87} + 432q^{88} - 60q^{89} + 360q^{90} + 32q^{91} + 416q^{92} + 90q^{93} + 816q^{94} + 380q^{95} + 384q^{96} - 922q^{97} + 960q^{98} + 486q^{99} + O(q^{100}) \)

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
\(7\) 17.1829 0.927789 0.463894 0.885891i \(-0.346452\pi\)
0.463894 + 0.885891i \(0.346452\pi\)
\(8\) 8.00000 0.353553
\(9\) 9.00000 0.333333
\(10\) 10.0000 0.316228
\(11\) 29.2349 0.801333 0.400666 0.916224i \(-0.368779\pi\)
0.400666 + 0.916224i \(0.368779\pi\)
\(12\) 12.0000 0.288675
\(13\) −69.9219 −1.49176 −0.745879 0.666082i \(-0.767970\pi\)
−0.745879 + 0.666082i \(0.767970\pi\)
\(14\) 34.3658 0.656046
\(15\) 15.0000 0.258199
\(16\) 16.0000 0.250000
\(17\) 94.5904 1.34950 0.674751 0.738045i \(-0.264251\pi\)
0.674751 + 0.738045i \(0.264251\pi\)
\(18\) 18.0000 0.235702
\(19\) 19.0000 0.229416
\(20\) 20.0000 0.223607
\(21\) 51.5487 0.535659
\(22\) 58.4699 0.566628
\(23\) −8.21713 −0.0744952 −0.0372476 0.999306i \(-0.511859\pi\)
−0.0372476 + 0.999306i \(0.511859\pi\)
\(24\) 24.0000 0.204124
\(25\) 25.0000 0.200000
\(26\) −139.844 −1.05483
\(27\) 27.0000 0.192450
\(28\) 68.7316 0.463894
\(29\) 216.520 1.38644 0.693219 0.720727i \(-0.256192\pi\)
0.693219 + 0.720727i \(0.256192\pi\)
\(30\) 30.0000 0.182574
\(31\) −227.097 −1.31574 −0.657869 0.753132i \(-0.728542\pi\)
−0.657869 + 0.753132i \(0.728542\pi\)
\(32\) 32.0000 0.176777
\(33\) 87.7048 0.462650
\(34\) 189.181 0.954242
\(35\) 85.9144 0.414920
\(36\) 36.0000 0.166667
\(37\) −5.48766 −0.0243828 −0.0121914 0.999926i \(-0.503881\pi\)
−0.0121914 + 0.999926i \(0.503881\pi\)
\(38\) 38.0000 0.162221
\(39\) −209.766 −0.861267
\(40\) 40.0000 0.158114
\(41\) −423.214 −1.61207 −0.806035 0.591867i \(-0.798391\pi\)
−0.806035 + 0.591867i \(0.798391\pi\)
\(42\) 103.097 0.378768
\(43\) 267.242 0.947769 0.473885 0.880587i \(-0.342851\pi\)
0.473885 + 0.880587i \(0.342851\pi\)
\(44\) 116.940 0.400666
\(45\) 45.0000 0.149071
\(46\) −16.4343 −0.0526761
\(47\) −6.59371 −0.0204636 −0.0102318 0.999948i \(-0.503257\pi\)
−0.0102318 + 0.999948i \(0.503257\pi\)
\(48\) 48.0000 0.144338
\(49\) −47.7483 −0.139208
\(50\) 50.0000 0.141421
\(51\) 283.771 0.779136
\(52\) −279.688 −0.745879
\(53\) −206.172 −0.534338 −0.267169 0.963650i \(-0.586088\pi\)
−0.267169 + 0.963650i \(0.586088\pi\)
\(54\) 54.0000 0.136083
\(55\) 146.175 0.358367
\(56\) 137.463 0.328023
\(57\) 57.0000 0.132453
\(58\) 433.040 0.980360
\(59\) 208.532 0.460146 0.230073 0.973173i \(-0.426104\pi\)
0.230073 + 0.973173i \(0.426104\pi\)
\(60\) 60.0000 0.129099
\(61\) 510.064 1.07061 0.535303 0.844660i \(-0.320197\pi\)
0.535303 + 0.844660i \(0.320197\pi\)
\(62\) −454.195 −0.930367
\(63\) 154.646 0.309263
\(64\) 64.0000 0.125000
\(65\) −349.610 −0.667134
\(66\) 175.410 0.327143
\(67\) 1010.47 1.84251 0.921257 0.388956i \(-0.127164\pi\)
0.921257 + 0.388956i \(0.127164\pi\)
\(68\) 378.362 0.674751
\(69\) −24.6514 −0.0430098
\(70\) 171.829 0.293393
\(71\) 334.247 0.558701 0.279351 0.960189i \(-0.409881\pi\)
0.279351 + 0.960189i \(0.409881\pi\)
\(72\) 72.0000 0.117851
\(73\) −866.693 −1.38957 −0.694786 0.719217i \(-0.744501\pi\)
−0.694786 + 0.719217i \(0.744501\pi\)
\(74\) −10.9753 −0.0172413
\(75\) 75.0000 0.115470
\(76\) 76.0000 0.114708
\(77\) 502.341 0.743468
\(78\) −419.532 −0.609008
\(79\) 502.538 0.715695 0.357848 0.933780i \(-0.383511\pi\)
0.357848 + 0.933780i \(0.383511\pi\)
\(80\) 80.0000 0.111803
\(81\) 81.0000 0.111111
\(82\) −846.428 −1.13991
\(83\) −478.314 −0.632551 −0.316276 0.948667i \(-0.602432\pi\)
−0.316276 + 0.948667i \(0.602432\pi\)
\(84\) 206.195 0.267830
\(85\) 472.952 0.603516
\(86\) 534.485 0.670174
\(87\) 649.559 0.800461
\(88\) 233.879 0.283314
\(89\) −1150.25 −1.36996 −0.684978 0.728563i \(-0.740188\pi\)
−0.684978 + 0.728563i \(0.740188\pi\)
\(90\) 90.0000 0.105409
\(91\) −1201.46 −1.38404
\(92\) −32.8685 −0.0372476
\(93\) −681.292 −0.759642
\(94\) −13.1874 −0.0144700
\(95\) 95.0000 0.102598
\(96\) 96.0000 0.102062
\(97\) −1394.30 −1.45948 −0.729742 0.683723i \(-0.760360\pi\)
−0.729742 + 0.683723i \(0.760360\pi\)
\(98\) −95.4967 −0.0984349
\(99\) 263.114 0.267111
\(100\) 100.000 0.100000
\(101\) 1962.77 1.93369 0.966847 0.255357i \(-0.0821931\pi\)
0.966847 + 0.255357i \(0.0821931\pi\)
\(102\) 567.542 0.550932
\(103\) 1511.69 1.44612 0.723062 0.690783i \(-0.242734\pi\)
0.723062 + 0.690783i \(0.242734\pi\)
\(104\) −559.375 −0.527416
\(105\) 257.743 0.239554
\(106\) −412.344 −0.377834
\(107\) −1034.13 −0.934332 −0.467166 0.884170i \(-0.654725\pi\)
−0.467166 + 0.884170i \(0.654725\pi\)
\(108\) 108.000 0.0962250
\(109\) −489.446 −0.430096 −0.215048 0.976603i \(-0.568991\pi\)
−0.215048 + 0.976603i \(0.568991\pi\)
\(110\) 292.349 0.253404
\(111\) −16.4630 −0.0140774
\(112\) 274.926 0.231947
\(113\) 598.992 0.498659 0.249329 0.968419i \(-0.419790\pi\)
0.249329 + 0.968419i \(0.419790\pi\)
\(114\) 114.000 0.0936586
\(115\) −41.0857 −0.0333153
\(116\) 866.079 0.693219
\(117\) −629.297 −0.497253
\(118\) 417.065 0.325372
\(119\) 1625.34 1.25205
\(120\) 120.000 0.0912871
\(121\) −476.319 −0.357865
\(122\) 1020.13 0.757033
\(123\) −1269.64 −0.930730
\(124\) −908.389 −0.657869
\(125\) 125.000 0.0894427
\(126\) 309.292 0.218682
\(127\) −1621.31 −1.13282 −0.566411 0.824123i \(-0.691668\pi\)
−0.566411 + 0.824123i \(0.691668\pi\)
\(128\) 128.000 0.0883883
\(129\) 801.727 0.547195
\(130\) −699.219 −0.471735
\(131\) −2133.74 −1.42309 −0.711547 0.702639i \(-0.752005\pi\)
−0.711547 + 0.702639i \(0.752005\pi\)
\(132\) 350.819 0.231325
\(133\) 326.475 0.212849
\(134\) 2020.94 1.30285
\(135\) 135.000 0.0860663
\(136\) 756.723 0.477121
\(137\) 822.308 0.512807 0.256403 0.966570i \(-0.417462\pi\)
0.256403 + 0.966570i \(0.417462\pi\)
\(138\) −49.3028 −0.0304126
\(139\) 423.232 0.258259 0.129130 0.991628i \(-0.458782\pi\)
0.129130 + 0.991628i \(0.458782\pi\)
\(140\) 343.658 0.207460
\(141\) −19.7811 −0.0118147
\(142\) 668.493 0.395061
\(143\) −2044.16 −1.19539
\(144\) 144.000 0.0833333
\(145\) 1082.60 0.620034
\(146\) −1733.39 −0.982576
\(147\) −143.245 −0.0803718
\(148\) −21.9506 −0.0121914
\(149\) −1387.73 −0.763003 −0.381502 0.924368i \(-0.624593\pi\)
−0.381502 + 0.924368i \(0.624593\pi\)
\(150\) 150.000 0.0816497
\(151\) 1687.63 0.909518 0.454759 0.890614i \(-0.349725\pi\)
0.454759 + 0.890614i \(0.349725\pi\)
\(152\) 152.000 0.0811107
\(153\) 851.313 0.449834
\(154\) 1004.68 0.525711
\(155\) −1135.49 −0.588416
\(156\) −839.063 −0.430633
\(157\) −1875.67 −0.953468 −0.476734 0.879048i \(-0.658179\pi\)
−0.476734 + 0.879048i \(0.658179\pi\)
\(158\) 1005.08 0.506073
\(159\) −618.517 −0.308500
\(160\) 160.000 0.0790569
\(161\) −141.194 −0.0691158
\(162\) 162.000 0.0785674
\(163\) 879.526 0.422637 0.211318 0.977417i \(-0.432224\pi\)
0.211318 + 0.977417i \(0.432224\pi\)
\(164\) −1692.86 −0.806035
\(165\) 438.524 0.206903
\(166\) −956.627 −0.447281
\(167\) −3292.23 −1.52551 −0.762756 0.646686i \(-0.776154\pi\)
−0.762756 + 0.646686i \(0.776154\pi\)
\(168\) 412.389 0.189384
\(169\) 2692.07 1.22534
\(170\) 945.904 0.426750
\(171\) 171.000 0.0764719
\(172\) 1068.97 0.473885
\(173\) −1861.03 −0.817868 −0.408934 0.912564i \(-0.634099\pi\)
−0.408934 + 0.912564i \(0.634099\pi\)
\(174\) 1299.12 0.566011
\(175\) 429.572 0.185558
\(176\) 467.759 0.200333
\(177\) 625.597 0.265665
\(178\) −2300.50 −0.968706
\(179\) −2869.30 −1.19811 −0.599055 0.800708i \(-0.704457\pi\)
−0.599055 + 0.800708i \(0.704457\pi\)
\(180\) 180.000 0.0745356
\(181\) −2402.69 −0.986689 −0.493344 0.869834i \(-0.664226\pi\)
−0.493344 + 0.869834i \(0.664226\pi\)
\(182\) −2402.92 −0.978661
\(183\) 1530.19 0.618115
\(184\) −65.7371 −0.0263380
\(185\) −27.4383 −0.0109043
\(186\) −1362.58 −0.537148
\(187\) 2765.34 1.08140
\(188\) −26.3748 −0.0102318
\(189\) 463.938 0.178553
\(190\) 190.000 0.0725476
\(191\) −746.471 −0.282789 −0.141395 0.989953i \(-0.545159\pi\)
−0.141395 + 0.989953i \(0.545159\pi\)
\(192\) 192.000 0.0721688
\(193\) 646.067 0.240958 0.120479 0.992716i \(-0.461557\pi\)
0.120479 + 0.992716i \(0.461557\pi\)
\(194\) −2788.60 −1.03201
\(195\) −1048.83 −0.385170
\(196\) −190.993 −0.0696040
\(197\) 4906.46 1.77447 0.887236 0.461316i \(-0.152623\pi\)
0.887236 + 0.461316i \(0.152623\pi\)
\(198\) 526.229 0.188876
\(199\) −1166.24 −0.415438 −0.207719 0.978189i \(-0.566604\pi\)
−0.207719 + 0.978189i \(0.566604\pi\)
\(200\) 200.000 0.0707107
\(201\) 3031.41 1.06378
\(202\) 3925.54 1.36733
\(203\) 3720.44 1.28632
\(204\) 1135.08 0.389568
\(205\) −2116.07 −0.720940
\(206\) 3023.37 1.02256
\(207\) −73.9542 −0.0248317
\(208\) −1118.75 −0.372939
\(209\) 555.464 0.183838
\(210\) 515.487 0.169390
\(211\) −5519.45 −1.80083 −0.900414 0.435035i \(-0.856736\pi\)
−0.900414 + 0.435035i \(0.856736\pi\)
\(212\) −824.689 −0.267169
\(213\) 1002.74 0.322566
\(214\) −2068.27 −0.660672
\(215\) 1336.21 0.423855
\(216\) 216.000 0.0680414
\(217\) −3902.19 −1.22073
\(218\) −978.893 −0.304124
\(219\) −2600.08 −0.802270
\(220\) 584.699 0.179184
\(221\) −6613.94 −2.01313
\(222\) −32.9259 −0.00995425
\(223\) 1393.07 0.418326 0.209163 0.977881i \(-0.432926\pi\)
0.209163 + 0.977881i \(0.432926\pi\)
\(224\) 549.852 0.164011
\(225\) 225.000 0.0666667
\(226\) 1197.98 0.352605
\(227\) −4179.18 −1.22195 −0.610974 0.791651i \(-0.709222\pi\)
−0.610974 + 0.791651i \(0.709222\pi\)
\(228\) 228.000 0.0662266
\(229\) 2796.83 0.807074 0.403537 0.914963i \(-0.367781\pi\)
0.403537 + 0.914963i \(0.367781\pi\)
\(230\) −82.1713 −0.0235575
\(231\) 1507.02 0.429241
\(232\) 1732.16 0.490180
\(233\) −4967.60 −1.39673 −0.698365 0.715742i \(-0.746089\pi\)
−0.698365 + 0.715742i \(0.746089\pi\)
\(234\) −1258.59 −0.351611
\(235\) −32.9685 −0.00915162
\(236\) 834.129 0.230073
\(237\) 1507.61 0.413207
\(238\) 3250.67 0.885335
\(239\) 4698.63 1.27167 0.635835 0.771825i \(-0.280656\pi\)
0.635835 + 0.771825i \(0.280656\pi\)
\(240\) 240.000 0.0645497
\(241\) −67.0326 −0.0179168 −0.00895840 0.999960i \(-0.502852\pi\)
−0.00895840 + 0.999960i \(0.502852\pi\)
\(242\) −952.638 −0.253049
\(243\) 243.000 0.0641500
\(244\) 2040.26 0.535303
\(245\) −238.742 −0.0622557
\(246\) −2539.28 −0.658125
\(247\) −1328.52 −0.342233
\(248\) −1816.78 −0.465184
\(249\) −1434.94 −0.365204
\(250\) 250.000 0.0632456
\(251\) −5378.10 −1.35244 −0.676221 0.736699i \(-0.736384\pi\)
−0.676221 + 0.736699i \(0.736384\pi\)
\(252\) 618.584 0.154631
\(253\) −240.227 −0.0596955
\(254\) −3242.63 −0.801026
\(255\) 1418.86 0.348440
\(256\) 256.000 0.0625000
\(257\) −2751.52 −0.667840 −0.333920 0.942601i \(-0.608372\pi\)
−0.333920 + 0.942601i \(0.608372\pi\)
\(258\) 1603.45 0.386925
\(259\) −94.2938 −0.0226221
\(260\) −1398.44 −0.333567
\(261\) 1948.68 0.462146
\(262\) −4267.47 −1.00628
\(263\) −1557.63 −0.365201 −0.182600 0.983187i \(-0.558451\pi\)
−0.182600 + 0.983187i \(0.558451\pi\)
\(264\) 701.638 0.163571
\(265\) −1030.86 −0.238963
\(266\) 652.950 0.150507
\(267\) −3450.75 −0.790945
\(268\) 4041.87 0.921257
\(269\) −1660.54 −0.376375 −0.188187 0.982133i \(-0.560261\pi\)
−0.188187 + 0.982133i \(0.560261\pi\)
\(270\) 270.000 0.0608581
\(271\) 1880.00 0.421409 0.210704 0.977550i \(-0.432424\pi\)
0.210704 + 0.977550i \(0.432424\pi\)
\(272\) 1513.45 0.337376
\(273\) −3604.38 −0.799074
\(274\) 1644.62 0.362609
\(275\) 730.873 0.160267
\(276\) −98.6056 −0.0215049
\(277\) −8624.73 −1.87079 −0.935397 0.353599i \(-0.884958\pi\)
−0.935397 + 0.353599i \(0.884958\pi\)
\(278\) 846.464 0.182617
\(279\) −2043.88 −0.438579
\(280\) 687.316 0.146696
\(281\) −928.020 −0.197014 −0.0985071 0.995136i \(-0.531407\pi\)
−0.0985071 + 0.995136i \(0.531407\pi\)
\(282\) −39.5623 −0.00835425
\(283\) −2306.23 −0.484420 −0.242210 0.970224i \(-0.577872\pi\)
−0.242210 + 0.970224i \(0.577872\pi\)
\(284\) 1336.99 0.279351
\(285\) 285.000 0.0592349
\(286\) −4088.32 −0.845272
\(287\) −7272.04 −1.49566
\(288\) 288.000 0.0589256
\(289\) 4034.34 0.821156
\(290\) 2165.20 0.438430
\(291\) −4182.91 −0.842633
\(292\) −3466.77 −0.694786
\(293\) 2760.03 0.550317 0.275158 0.961399i \(-0.411270\pi\)
0.275158 + 0.961399i \(0.411270\pi\)
\(294\) −286.490 −0.0568314
\(295\) 1042.66 0.205783
\(296\) −43.9012 −0.00862064
\(297\) 789.343 0.154217
\(298\) −2775.46 −0.539525
\(299\) 574.558 0.111129
\(300\) 300.000 0.0577350
\(301\) 4592.00 0.879330
\(302\) 3375.26 0.643127
\(303\) 5888.31 1.11642
\(304\) 304.000 0.0573539
\(305\) 2550.32 0.478790
\(306\) 1702.63 0.318081
\(307\) 5771.80 1.07301 0.536505 0.843897i \(-0.319744\pi\)
0.536505 + 0.843897i \(0.319744\pi\)
\(308\) 2009.36 0.371734
\(309\) 4535.06 0.834920
\(310\) −2270.97 −0.416073
\(311\) −6175.04 −1.12590 −0.562949 0.826491i \(-0.690333\pi\)
−0.562949 + 0.826491i \(0.690333\pi\)
\(312\) −1678.13 −0.304504
\(313\) 11040.3 1.99372 0.996862 0.0791558i \(-0.0252224\pi\)
0.996862 + 0.0791558i \(0.0252224\pi\)
\(314\) −3751.33 −0.674203
\(315\) 773.230 0.138307
\(316\) 2010.15 0.357848
\(317\) −1426.52 −0.252748 −0.126374 0.991983i \(-0.540334\pi\)
−0.126374 + 0.991983i \(0.540334\pi\)
\(318\) −1237.03 −0.218143
\(319\) 6329.94 1.11100
\(320\) 320.000 0.0559017
\(321\) −3102.40 −0.539437
\(322\) −282.388 −0.0488723
\(323\) 1797.22 0.309597
\(324\) 324.000 0.0555556
\(325\) −1748.05 −0.298352
\(326\) 1759.05 0.298849
\(327\) −1468.34 −0.248316
\(328\) −3385.71 −0.569953
\(329\) −113.299 −0.0189859
\(330\) 877.048 0.146303
\(331\) −900.393 −0.149517 −0.0747584 0.997202i \(-0.523819\pi\)
−0.0747584 + 0.997202i \(0.523819\pi\)
\(332\) −1913.25 −0.316276
\(333\) −49.3889 −0.00812761
\(334\) −6584.46 −1.07870
\(335\) 5052.34 0.823997
\(336\) 824.779 0.133915
\(337\) 7663.82 1.23880 0.619399 0.785076i \(-0.287376\pi\)
0.619399 + 0.785076i \(0.287376\pi\)
\(338\) 5384.15 0.866447
\(339\) 1796.98 0.287901
\(340\) 1891.81 0.301758
\(341\) −6639.17 −1.05434
\(342\) 342.000 0.0540738
\(343\) −6714.19 −1.05694
\(344\) 2137.94 0.335087
\(345\) −123.257 −0.0192346
\(346\) −3722.05 −0.578320
\(347\) −10905.5 −1.68714 −0.843569 0.537021i \(-0.819549\pi\)
−0.843569 + 0.537021i \(0.819549\pi\)
\(348\) 2598.24 0.400230
\(349\) −2473.62 −0.379397 −0.189699 0.981842i \(-0.560751\pi\)
−0.189699 + 0.981842i \(0.560751\pi\)
\(350\) 859.144 0.131209
\(351\) −1887.89 −0.287089
\(352\) 935.518 0.141657
\(353\) −4926.69 −0.742836 −0.371418 0.928466i \(-0.621128\pi\)
−0.371418 + 0.928466i \(0.621128\pi\)
\(354\) 1251.19 0.187854
\(355\) 1671.23 0.249859
\(356\) −4601.00 −0.684978
\(357\) 4876.01 0.722873
\(358\) −5738.61 −0.847192
\(359\) 7595.97 1.11671 0.558356 0.829601i \(-0.311432\pi\)
0.558356 + 0.829601i \(0.311432\pi\)
\(360\) 360.000 0.0527046
\(361\) 361.000 0.0526316
\(362\) −4805.38 −0.697694
\(363\) −1428.96 −0.206614
\(364\) −4805.84 −0.692018
\(365\) −4333.47 −0.621435
\(366\) 3060.38 0.437073
\(367\) 5177.70 0.736441 0.368221 0.929738i \(-0.379967\pi\)
0.368221 + 0.929738i \(0.379967\pi\)
\(368\) −131.474 −0.0186238
\(369\) −3808.92 −0.537357
\(370\) −54.8766 −0.00771053
\(371\) −3542.63 −0.495753
\(372\) −2725.17 −0.379821
\(373\) 4912.63 0.681947 0.340974 0.940073i \(-0.389243\pi\)
0.340974 + 0.940073i \(0.389243\pi\)
\(374\) 5530.69 0.764666
\(375\) 375.000 0.0516398
\(376\) −52.7497 −0.00723499
\(377\) −15139.5 −2.06823
\(378\) 927.876 0.126256
\(379\) −6166.88 −0.835809 −0.417904 0.908491i \(-0.637235\pi\)
−0.417904 + 0.908491i \(0.637235\pi\)
\(380\) 380.000 0.0512989
\(381\) −4863.94 −0.654035
\(382\) −1492.94 −0.199962
\(383\) −6827.55 −0.910891 −0.455446 0.890264i \(-0.650520\pi\)
−0.455446 + 0.890264i \(0.650520\pi\)
\(384\) 384.000 0.0510310
\(385\) 2511.70 0.332489
\(386\) 1292.13 0.170383
\(387\) 2405.18 0.315923
\(388\) −5577.21 −0.729742
\(389\) 1891.05 0.246479 0.123239 0.992377i \(-0.460672\pi\)
0.123239 + 0.992377i \(0.460672\pi\)
\(390\) −2097.66 −0.272356
\(391\) −777.262 −0.100531
\(392\) −381.987 −0.0492175
\(393\) −6401.21 −0.821624
\(394\) 9812.92 1.25474
\(395\) 2512.69 0.320069
\(396\) 1052.46 0.133555
\(397\) 9658.62 1.22104 0.610519 0.792001i \(-0.290961\pi\)
0.610519 + 0.792001i \(0.290961\pi\)
\(398\) −2332.47 −0.293759
\(399\) 979.425 0.122889
\(400\) 400.000 0.0500000
\(401\) 2062.75 0.256880 0.128440 0.991717i \(-0.459003\pi\)
0.128440 + 0.991717i \(0.459003\pi\)
\(402\) 6062.81 0.752203
\(403\) 15879.1 1.96276
\(404\) 7851.08 0.966847
\(405\) 405.000 0.0496904
\(406\) 7440.87 0.909567
\(407\) −160.431 −0.0195388
\(408\) 2270.17 0.275466
\(409\) −6421.95 −0.776394 −0.388197 0.921576i \(-0.626902\pi\)
−0.388197 + 0.921576i \(0.626902\pi\)
\(410\) −4232.14 −0.509782
\(411\) 2466.92 0.296069
\(412\) 6046.74 0.723062
\(413\) 3583.19 0.426918
\(414\) −147.908 −0.0175587
\(415\) −2391.57 −0.282885
\(416\) −2237.50 −0.263708
\(417\) 1269.70 0.149106
\(418\) 1110.93 0.129993
\(419\) 3671.43 0.428070 0.214035 0.976826i \(-0.431339\pi\)
0.214035 + 0.976826i \(0.431339\pi\)
\(420\) 1030.97 0.119777
\(421\) −5940.10 −0.687655 −0.343827 0.939033i \(-0.611723\pi\)
−0.343827 + 0.939033i \(0.611723\pi\)
\(422\) −11038.9 −1.27338
\(423\) −59.3434 −0.00682122
\(424\) −1649.38 −0.188917
\(425\) 2364.76 0.269900
\(426\) 2005.48 0.228089
\(427\) 8764.37 0.993297
\(428\) −4136.53 −0.467166
\(429\) −6132.49 −0.690161
\(430\) 2672.42 0.299711
\(431\) −17677.0 −1.97557 −0.987785 0.155825i \(-0.950196\pi\)
−0.987785 + 0.155825i \(0.950196\pi\)
\(432\) 432.000 0.0481125
\(433\) 13703.0 1.52084 0.760421 0.649430i \(-0.224993\pi\)
0.760421 + 0.649430i \(0.224993\pi\)
\(434\) −7804.38 −0.863184
\(435\) 3247.80 0.357977
\(436\) −1957.79 −0.215048
\(437\) −156.126 −0.0170904
\(438\) −5200.16 −0.567290
\(439\) −2745.97 −0.298538 −0.149269 0.988797i \(-0.547692\pi\)
−0.149269 + 0.988797i \(0.547692\pi\)
\(440\) 1169.40 0.126702
\(441\) −429.735 −0.0464027
\(442\) −13227.9 −1.42350
\(443\) 8941.76 0.958997 0.479499 0.877543i \(-0.340819\pi\)
0.479499 + 0.877543i \(0.340819\pi\)
\(444\) −65.8519 −0.00703872
\(445\) −5751.24 −0.612663
\(446\) 2786.14 0.295801
\(447\) −4163.20 −0.440520
\(448\) 1099.70 0.115974
\(449\) 8770.30 0.921818 0.460909 0.887448i \(-0.347524\pi\)
0.460909 + 0.887448i \(0.347524\pi\)
\(450\) 450.000 0.0471405
\(451\) −12372.6 −1.29181
\(452\) 2395.97 0.249329
\(453\) 5062.89 0.525111
\(454\) −8358.36 −0.864047
\(455\) −6007.30 −0.618960
\(456\) 456.000 0.0468293
\(457\) 14319.3 1.46571 0.732856 0.680384i \(-0.238187\pi\)
0.732856 + 0.680384i \(0.238187\pi\)
\(458\) 5593.67 0.570688
\(459\) 2553.94 0.259712
\(460\) −164.343 −0.0166576
\(461\) 2579.44 0.260599 0.130300 0.991475i \(-0.458406\pi\)
0.130300 + 0.991475i \(0.458406\pi\)
\(462\) 3014.04 0.303519
\(463\) 19134.6 1.92065 0.960324 0.278888i \(-0.0899657\pi\)
0.960324 + 0.278888i \(0.0899657\pi\)
\(464\) 3464.32 0.346610
\(465\) −3406.46 −0.339722
\(466\) −9935.20 −0.987637
\(467\) 12280.1 1.21682 0.608409 0.793624i \(-0.291808\pi\)
0.608409 + 0.793624i \(0.291808\pi\)
\(468\) −2517.19 −0.248626
\(469\) 17362.8 1.70946
\(470\) −65.9371 −0.00647117
\(471\) −5627.00 −0.550485
\(472\) 1668.26 0.162686
\(473\) 7812.81 0.759479
\(474\) 3015.23 0.292181
\(475\) 475.000 0.0458831
\(476\) 6501.34 0.626027
\(477\) −1855.55 −0.178113
\(478\) 9397.26 0.899206
\(479\) 1427.43 0.136160 0.0680802 0.997680i \(-0.478313\pi\)
0.0680802 + 0.997680i \(0.478313\pi\)
\(480\) 480.000 0.0456435
\(481\) 383.707 0.0363733
\(482\) −134.065 −0.0126691
\(483\) −423.582 −0.0399041
\(484\) −1905.28 −0.178933
\(485\) −6971.51 −0.652701
\(486\) 486.000 0.0453609
\(487\) 14257.2 1.32660 0.663301 0.748353i \(-0.269155\pi\)
0.663301 + 0.748353i \(0.269155\pi\)
\(488\) 4080.51 0.378517
\(489\) 2638.58 0.244010
\(490\) −477.483 −0.0440214
\(491\) −17429.3 −1.60198 −0.800990 0.598678i \(-0.795693\pi\)
−0.800990 + 0.598678i \(0.795693\pi\)
\(492\) −5078.57 −0.465365
\(493\) 20480.7 1.87100
\(494\) −2657.03 −0.241995
\(495\) 1315.57 0.119456
\(496\) −3633.56 −0.328935
\(497\) 5743.32 0.518357
\(498\) −2869.88 −0.258238
\(499\) −6280.73 −0.563455 −0.281728 0.959494i \(-0.590907\pi\)
−0.281728 + 0.959494i \(0.590907\pi\)
\(500\) 500.000 0.0447214
\(501\) −9876.69 −0.880755
\(502\) −10756.2 −0.956321
\(503\) 6433.48 0.570288 0.285144 0.958485i \(-0.407959\pi\)
0.285144 + 0.958485i \(0.407959\pi\)
\(504\) 1237.17 0.109341
\(505\) 9813.86 0.864774
\(506\) −480.455 −0.0422111
\(507\) 8076.22 0.707451
\(508\) −6485.26 −0.566411
\(509\) 18989.4 1.65362 0.826808 0.562485i \(-0.190155\pi\)
0.826808 + 0.562485i \(0.190155\pi\)
\(510\) 2837.71 0.246384
\(511\) −14892.3 −1.28923
\(512\) 512.000 0.0441942
\(513\) 513.000 0.0441511
\(514\) −5503.03 −0.472234
\(515\) 7558.43 0.646726
\(516\) 3206.91 0.273597
\(517\) −192.767 −0.0163982
\(518\) −188.588 −0.0159963
\(519\) −5583.08 −0.472197
\(520\) −2796.88 −0.235868
\(521\) 7232.61 0.608189 0.304094 0.952642i \(-0.401646\pi\)
0.304094 + 0.952642i \(0.401646\pi\)
\(522\) 3897.36 0.326787
\(523\) 7864.04 0.657496 0.328748 0.944418i \(-0.393373\pi\)
0.328748 + 0.944418i \(0.393373\pi\)
\(524\) −8534.94 −0.711547
\(525\) 1288.72 0.107132
\(526\) −3115.27 −0.258236
\(527\) −21481.2 −1.77559
\(528\) 1403.28 0.115662
\(529\) −12099.5 −0.994450
\(530\) −2061.72 −0.168973
\(531\) 1876.79 0.153382
\(532\) 1305.90 0.106425
\(533\) 29591.9 2.40482
\(534\) −6901.49 −0.559282
\(535\) −5170.67 −0.417846
\(536\) 8083.75 0.651427
\(537\) −8607.91 −0.691729
\(538\) −3321.08 −0.266137
\(539\) −1395.92 −0.111552
\(540\) 540.000 0.0430331
\(541\) 19267.3 1.53117 0.765587 0.643332i \(-0.222449\pi\)
0.765587 + 0.643332i \(0.222449\pi\)
\(542\) 3760.00 0.297981
\(543\) −7208.08 −0.569665
\(544\) 3026.89 0.238561
\(545\) −2447.23 −0.192345
\(546\) −7208.76 −0.565030
\(547\) 7054.21 0.551401 0.275700 0.961244i \(-0.411090\pi\)
0.275700 + 0.961244i \(0.411090\pi\)
\(548\) 3289.23 0.256403
\(549\) 4590.57 0.356869
\(550\) 1461.75 0.113326
\(551\) 4113.88 0.318071
\(552\) −197.211 −0.0152063
\(553\) 8635.05 0.664014
\(554\) −17249.5 −1.32285
\(555\) −82.3148 −0.00629562
\(556\) 1692.93 0.129130
\(557\) 7105.83 0.540546 0.270273 0.962784i \(-0.412886\pi\)
0.270273 + 0.962784i \(0.412886\pi\)
\(558\) −4087.75 −0.310122
\(559\) −18686.1 −1.41384
\(560\) 1374.63 0.103730
\(561\) 8296.03 0.624347
\(562\) −1856.04 −0.139310
\(563\) 1180.00 0.0883323 0.0441661 0.999024i \(-0.485937\pi\)
0.0441661 + 0.999024i \(0.485937\pi\)
\(564\) −79.1245 −0.00590735
\(565\) 2994.96 0.223007
\(566\) −4612.45 −0.342537
\(567\) 1391.81 0.103088
\(568\) 2673.97 0.197531
\(569\) 2692.66 0.198387 0.0991936 0.995068i \(-0.468374\pi\)
0.0991936 + 0.995068i \(0.468374\pi\)
\(570\) 570.000 0.0418854
\(571\) −10754.0 −0.788160 −0.394080 0.919076i \(-0.628937\pi\)
−0.394080 + 0.919076i \(0.628937\pi\)
\(572\) −8176.65 −0.597697
\(573\) −2239.41 −0.163268
\(574\) −14544.1 −1.05759
\(575\) −205.428 −0.0148990
\(576\) 576.000 0.0416667
\(577\) 16146.3 1.16495 0.582476 0.812848i \(-0.302084\pi\)
0.582476 + 0.812848i \(0.302084\pi\)
\(578\) 8068.68 0.580645
\(579\) 1938.20 0.139117
\(580\) 4330.40 0.310017
\(581\) −8218.81 −0.586874
\(582\) −8365.81 −0.595832
\(583\) −6027.43 −0.428183
\(584\) −6933.54 −0.491288
\(585\) −3146.49 −0.222378
\(586\) 5520.06 0.389133
\(587\) 19339.4 1.35984 0.679918 0.733288i \(-0.262015\pi\)
0.679918 + 0.733288i \(0.262015\pi\)
\(588\) −572.980 −0.0401859
\(589\) −4314.85 −0.301851
\(590\) 2085.32 0.145511
\(591\) 14719.4 1.02449
\(592\) −87.8025 −0.00609571
\(593\) 15453.7 1.07016 0.535082 0.844800i \(-0.320281\pi\)
0.535082 + 0.844800i \(0.320281\pi\)
\(594\) 1578.69 0.109048
\(595\) 8126.68 0.559935
\(596\) −5550.93 −0.381502
\(597\) −3498.71 −0.239853
\(598\) 1149.12 0.0785800
\(599\) 15789.0 1.07700 0.538500 0.842626i \(-0.318991\pi\)
0.538500 + 0.842626i \(0.318991\pi\)
\(600\) 600.000 0.0408248
\(601\) −4673.39 −0.317191 −0.158595 0.987344i \(-0.550697\pi\)
−0.158595 + 0.987344i \(0.550697\pi\)
\(602\) 9183.99 0.621780
\(603\) 9094.22 0.614171
\(604\) 6750.51 0.454759
\(605\) −2381.59 −0.160042
\(606\) 11776.6 0.789427
\(607\) 10101.9 0.675488 0.337744 0.941238i \(-0.390336\pi\)
0.337744 + 0.941238i \(0.390336\pi\)
\(608\) 608.000 0.0405554
\(609\) 11161.3 0.742658
\(610\) 5100.64 0.338555
\(611\) 461.045 0.0305268
\(612\) 3405.25 0.224917
\(613\) −8592.15 −0.566123 −0.283062 0.959102i \(-0.591350\pi\)
−0.283062 + 0.959102i \(0.591350\pi\)
\(614\) 11543.6 0.758732
\(615\) −6348.21 −0.416235
\(616\) 4018.72 0.262856
\(617\) −14952.7 −0.975646 −0.487823 0.872943i \(-0.662209\pi\)
−0.487823 + 0.872943i \(0.662209\pi\)
\(618\) 9070.11 0.590378
\(619\) −25121.9 −1.63124 −0.815618 0.578591i \(-0.803603\pi\)
−0.815618 + 0.578591i \(0.803603\pi\)
\(620\) −4541.95 −0.294208
\(621\) −221.863 −0.0143366
\(622\) −12350.1 −0.796131
\(623\) −19764.6 −1.27103
\(624\) −3356.25 −0.215317
\(625\) 625.000 0.0400000
\(626\) 22080.6 1.40978
\(627\) 1666.39 0.106139
\(628\) −7502.66 −0.476734
\(629\) −519.080 −0.0329047
\(630\) 1546.46 0.0977975
\(631\) 18777.7 1.18468 0.592338 0.805690i \(-0.298205\pi\)
0.592338 + 0.805690i \(0.298205\pi\)
\(632\) 4020.30 0.253037
\(633\) −16558.3 −1.03971
\(634\) −2853.03 −0.178720
\(635\) −8106.57 −0.506613
\(636\) −2474.07 −0.154250
\(637\) 3338.66 0.207665
\(638\) 12659.9 0.785595
\(639\) 3008.22 0.186234
\(640\) 640.000 0.0395285
\(641\) 25392.7 1.56466 0.782332 0.622862i \(-0.214030\pi\)
0.782332 + 0.622862i \(0.214030\pi\)
\(642\) −6204.80 −0.381439
\(643\) 215.451 0.0132139 0.00660696 0.999978i \(-0.497897\pi\)
0.00660696 + 0.999978i \(0.497897\pi\)
\(644\) −564.776 −0.0345579
\(645\) 4008.64 0.244713
\(646\) 3594.43 0.218918
\(647\) −19929.7 −1.21100 −0.605501 0.795844i \(-0.707027\pi\)
−0.605501 + 0.795844i \(0.707027\pi\)
\(648\) 648.000 0.0392837
\(649\) 6096.43 0.368730
\(650\) −3496.10 −0.210966
\(651\) −11706.6 −0.704787
\(652\) 3518.11 0.211318
\(653\) 18648.1 1.11754 0.558771 0.829322i \(-0.311273\pi\)
0.558771 + 0.829322i \(0.311273\pi\)
\(654\) −2936.68 −0.175586
\(655\) −10668.7 −0.636427
\(656\) −6771.42 −0.403018
\(657\) −7800.24 −0.463191
\(658\) −226.598 −0.0134251
\(659\) −8105.95 −0.479155 −0.239577 0.970877i \(-0.577009\pi\)
−0.239577 + 0.970877i \(0.577009\pi\)
\(660\) 1754.10 0.103452
\(661\) −4872.33 −0.286704 −0.143352 0.989672i \(-0.545788\pi\)
−0.143352 + 0.989672i \(0.545788\pi\)
\(662\) −1800.79 −0.105724
\(663\) −19841.8 −1.16228
\(664\) −3826.51 −0.223641
\(665\) 1632.37 0.0951891
\(666\) −98.7778 −0.00574709
\(667\) −1779.17 −0.103283
\(668\) −13168.9 −0.762756
\(669\) 4179.20 0.241521
\(670\) 10104.7 0.582654
\(671\) 14911.7 0.857912
\(672\) 1649.56 0.0946920
\(673\) 12953.6 0.741937 0.370969 0.928645i \(-0.379026\pi\)
0.370969 + 0.928645i \(0.379026\pi\)
\(674\) 15327.6 0.875962
\(675\) 675.000 0.0384900
\(676\) 10768.3 0.612671
\(677\) 6098.11 0.346188 0.173094 0.984905i \(-0.444624\pi\)
0.173094 + 0.984905i \(0.444624\pi\)
\(678\) 3593.95 0.203577
\(679\) −23958.1 −1.35409
\(680\) 3783.62 0.213375
\(681\) −12537.5 −0.705491
\(682\) −13278.3 −0.745534
\(683\) 27530.4 1.54234 0.771171 0.636628i \(-0.219671\pi\)
0.771171 + 0.636628i \(0.219671\pi\)
\(684\) 684.000 0.0382360
\(685\) 4111.54 0.229334
\(686\) −13428.4 −0.747373
\(687\) 8390.50 0.465965
\(688\) 4275.88 0.236942
\(689\) 14416.0 0.797103
\(690\) −246.514 −0.0136009
\(691\) −26669.7 −1.46825 −0.734127 0.679012i \(-0.762408\pi\)
−0.734127 + 0.679012i \(0.762408\pi\)
\(692\) −7444.11 −0.408934
\(693\) 4521.06 0.247823
\(694\) −21811.0 −1.19299
\(695\) 2116.16 0.115497
\(696\) 5196.47 0.283006
\(697\) −40032.0 −2.17549
\(698\) −4947.23 −0.268274
\(699\) −14902.8 −0.806403
\(700\) 1718.29 0.0927789
\(701\) −5377.33 −0.289727 −0.144864 0.989452i \(-0.546274\pi\)
−0.144864 + 0.989452i \(0.546274\pi\)
\(702\) −3775.78 −0.203003
\(703\) −104.265 −0.00559381
\(704\) 1871.04 0.100167
\(705\) −98.9056 −0.00528369
\(706\) −9853.38 −0.525265
\(707\) 33726.1 1.79406
\(708\) 2502.39 0.132833
\(709\) −14906.2 −0.789580 −0.394790 0.918771i \(-0.629183\pi\)
−0.394790 + 0.918771i \(0.629183\pi\)
\(710\) 3342.47 0.176677
\(711\) 4522.84 0.238565
\(712\) −9201.99 −0.484353
\(713\) 1866.09 0.0980162
\(714\) 9752.02 0.511149
\(715\) −10220.8 −0.534597
\(716\) −11477.2 −0.599055
\(717\) 14095.9 0.734199
\(718\) 15191.9 0.789635
\(719\) −17007.1 −0.882140 −0.441070 0.897473i \(-0.645401\pi\)
−0.441070 + 0.897473i \(0.645401\pi\)
\(720\) 720.000 0.0372678
\(721\) 25975.1 1.34170
\(722\) 722.000 0.0372161
\(723\) −201.098 −0.0103443
\(724\) −9610.77 −0.493344
\(725\) 5412.99 0.277288
\(726\) −2857.91 −0.146098
\(727\) 25491.3 1.30044 0.650221 0.759745i \(-0.274676\pi\)
0.650221 + 0.759745i \(0.274676\pi\)
\(728\) −9611.68 −0.489331
\(729\) 729.000 0.0370370
\(730\) −8666.93 −0.439421
\(731\) 25278.6 1.27902
\(732\) 6120.77 0.309057
\(733\) −18043.7 −0.909223 −0.454611 0.890690i \(-0.650222\pi\)
−0.454611 + 0.890690i \(0.650222\pi\)
\(734\) 10355.4 0.520743
\(735\) −716.225 −0.0359433
\(736\) −262.948 −0.0131690
\(737\) 29541.0 1.47647
\(738\) −7617.85 −0.379969
\(739\) −4482.52 −0.223129 −0.111564 0.993757i \(-0.535586\pi\)
−0.111564 + 0.993757i \(0.535586\pi\)
\(740\) −109.753 −0.00545217
\(741\) −3985.55 −0.197588
\(742\) −7085.27 −0.350550
\(743\) −1934.60 −0.0955230 −0.0477615 0.998859i \(-0.515209\pi\)
−0.0477615 + 0.998859i \(0.515209\pi\)
\(744\) −5450.34 −0.268574
\(745\) −6938.66 −0.341225
\(746\) 9825.26 0.482210
\(747\) −4304.82 −0.210850
\(748\) 11061.4 0.540700
\(749\) −17769.4 −0.866862
\(750\) 750.000 0.0365148
\(751\) 6102.74 0.296528 0.148264 0.988948i \(-0.452632\pi\)
0.148264 + 0.988948i \(0.452632\pi\)
\(752\) −105.499 −0.00511591
\(753\) −16134.3 −0.780833
\(754\) −30279.0 −1.46246
\(755\) 8438.14 0.406749
\(756\) 1855.75 0.0892765
\(757\) −40052.0 −1.92301 −0.961503 0.274796i \(-0.911390\pi\)
−0.961503 + 0.274796i \(0.911390\pi\)
\(758\) −12333.8 −0.591006
\(759\) −720.682 −0.0344652
\(760\) 760.000 0.0362738
\(761\) −10449.7 −0.497770 −0.248885 0.968533i \(-0.580064\pi\)
−0.248885 + 0.968533i \(0.580064\pi\)
\(762\) −9727.88 −0.462472
\(763\) −8410.10 −0.399038
\(764\) −2985.88 −0.141395
\(765\) 4256.57 0.201172
\(766\) −13655.1 −0.644097
\(767\) −14581.0 −0.686426
\(768\) 768.000 0.0360844
\(769\) 6903.59 0.323732 0.161866 0.986813i \(-0.448249\pi\)
0.161866 + 0.986813i \(0.448249\pi\)
\(770\) 5023.41 0.235105
\(771\) −8254.55 −0.385578
\(772\) 2584.27 0.120479
\(773\) −26849.0 −1.24928 −0.624639 0.780914i \(-0.714754\pi\)
−0.624639 + 0.780914i \(0.714754\pi\)
\(774\) 4810.36 0.223391
\(775\) −5677.43 −0.263148
\(776\) −11154.4 −0.516005
\(777\) −282.881 −0.0130609
\(778\) 3782.11 0.174287
\(779\) −8041.06 −0.369834
\(780\) −4195.32 −0.192585
\(781\) 9771.68 0.447706
\(782\) −1554.52 −0.0710865
\(783\) 5846.03 0.266820
\(784\) −763.973 −0.0348020
\(785\) −9378.33 −0.426404
\(786\) −12802.4 −0.580976
\(787\) 13804.1 0.625239 0.312620 0.949878i \(-0.398793\pi\)
0.312620 + 0.949878i \(0.398793\pi\)
\(788\) 19625.8 0.887236
\(789\) −4672.90 −0.210849
\(790\) 5025.38 0.226323
\(791\) 10292.4 0.462650
\(792\) 2104.91 0.0944380
\(793\) −35664.6 −1.59709
\(794\) 19317.2 0.863405
\(795\) −3092.58 −0.137966
\(796\) −4664.94 −0.207719
\(797\) 14190.6 0.630684 0.315342 0.948978i \(-0.397881\pi\)
0.315342 + 0.948978i \(0.397881\pi\)
\(798\) 1958.85 0.0868954
\(799\) −623.702 −0.0276157
\(800\) 800.000 0.0353553
\(801\) −10352.2 −0.456652
\(802\) 4125.50 0.181642
\(803\) −25337.7 −1.11351
\(804\) 12125.6 0.531888
\(805\) −705.970 −0.0309095
\(806\) 31758.2 1.38788
\(807\) −4981.62 −0.217300
\(808\) 15702.2 0.683664
\(809\) 23720.0 1.03084 0.515422 0.856937i \(-0.327635\pi\)
0.515422 + 0.856937i \(0.327635\pi\)
\(810\) 810.000 0.0351364
\(811\) 23359.2 1.01141 0.505704 0.862707i \(-0.331233\pi\)
0.505704 + 0.862707i \(0.331233\pi\)
\(812\) 14881.7 0.643161
\(813\) 5639.99 0.243300
\(814\) −320.862 −0.0138160
\(815\) 4397.63 0.189009
\(816\) 4540.34 0.194784
\(817\) 5077.61 0.217433
\(818\) −12843.9 −0.548994
\(819\) −10813.1 −0.461345
\(820\) −8464.28 −0.360470
\(821\) −13199.5 −0.561103 −0.280551 0.959839i \(-0.590517\pi\)
−0.280551 + 0.959839i \(0.590517\pi\)
\(822\) 4933.85 0.209352
\(823\) −11817.2 −0.500513 −0.250256 0.968180i \(-0.580515\pi\)
−0.250256 + 0.968180i \(0.580515\pi\)
\(824\) 12093.5 0.511282
\(825\) 2192.62 0.0925300
\(826\) 7166.38 0.301877
\(827\) −33124.4 −1.39280 −0.696402 0.717652i \(-0.745217\pi\)
−0.696402 + 0.717652i \(0.745217\pi\)
\(828\) −295.817 −0.0124159
\(829\) 21452.5 0.898764 0.449382 0.893340i \(-0.351644\pi\)
0.449382 + 0.893340i \(0.351644\pi\)
\(830\) −4783.14 −0.200030
\(831\) −25874.2 −1.08010
\(832\) −4475.00 −0.186470
\(833\) −4516.53 −0.187862
\(834\) 2539.39 0.105434
\(835\) −16461.2 −0.682230
\(836\) 2221.85 0.0919192
\(837\) −6131.63 −0.253214
\(838\) 7342.86 0.302691
\(839\) −4748.27 −0.195386 −0.0976928 0.995217i \(-0.531146\pi\)
−0.0976928 + 0.995217i \(0.531146\pi\)
\(840\) 2061.95 0.0846951
\(841\) 22491.8 0.922212
\(842\) −11880.2 −0.486245
\(843\) −2784.06 −0.113746
\(844\) −22077.8 −0.900414
\(845\) 13460.4 0.547989
\(846\) −118.687 −0.00482333
\(847\) −8184.53 −0.332024
\(848\) −3298.76 −0.133585
\(849\) −6918.68 −0.279680
\(850\) 4729.52 0.190848
\(851\) 45.0928 0.00181641
\(852\) 4010.96 0.161283
\(853\) 16832.9 0.675672 0.337836 0.941205i \(-0.390305\pi\)
0.337836 + 0.941205i \(0.390305\pi\)
\(854\) 17528.7 0.702367
\(855\) 855.000 0.0341993
\(856\) −8273.07 −0.330336
\(857\) 22016.2 0.877548 0.438774 0.898597i \(-0.355413\pi\)
0.438774 + 0.898597i \(0.355413\pi\)
\(858\) −12265.0 −0.488018
\(859\) −44154.2 −1.75381 −0.876904 0.480666i \(-0.840395\pi\)
−0.876904 + 0.480666i \(0.840395\pi\)
\(860\) 5344.85 0.211928
\(861\) −21816.1 −0.863520
\(862\) −35354.0 −1.39694
\(863\) 18091.3 0.713598 0.356799 0.934181i \(-0.383868\pi\)
0.356799 + 0.934181i \(0.383868\pi\)
\(864\) 864.000 0.0340207
\(865\) −9305.13 −0.365762
\(866\) 27406.0 1.07540
\(867\) 12103.0 0.474095
\(868\) −15608.8 −0.610363
\(869\) 14691.7 0.573510
\(870\) 6495.59 0.253128
\(871\) −70653.9 −2.74858
\(872\) −3915.57 −0.152062
\(873\) −12548.7 −0.486495
\(874\) −312.251 −0.0120847
\(875\) 2147.86 0.0829840
\(876\) −10400.3 −0.401135
\(877\) 17188.7 0.661825 0.330913 0.943661i \(-0.392643\pi\)
0.330913 + 0.943661i \(0.392643\pi\)
\(878\) −5491.94 −0.211098
\(879\) 8280.09 0.317725
\(880\) 2338.79 0.0895918
\(881\) −36459.5 −1.39427 −0.697135 0.716940i \(-0.745542\pi\)
−0.697135 + 0.716940i \(0.745542\pi\)
\(882\) −859.470 −0.0328116
\(883\) −39492.5 −1.50513 −0.752565 0.658518i \(-0.771184\pi\)
−0.752565 + 0.658518i \(0.771184\pi\)
\(884\) −26455.8 −1.00657
\(885\) 3127.98 0.118809
\(886\) 17883.5 0.678113
\(887\) −11920.3 −0.451232 −0.225616 0.974216i \(-0.572439\pi\)
−0.225616 + 0.974216i \(0.572439\pi\)
\(888\) −131.704 −0.00497713
\(889\) −27858.9 −1.05102
\(890\) −11502.5 −0.433218
\(891\) 2368.03 0.0890370
\(892\) 5572.27 0.209163
\(893\) −125.280 −0.00469468
\(894\) −8326.39 −0.311495
\(895\) −14346.5 −0.535811
\(896\) 2199.41 0.0820057
\(897\) 1723.67 0.0641603
\(898\) 17540.6 0.651823
\(899\) −49171.1 −1.82419
\(900\) 900.000 0.0333333
\(901\) −19501.9 −0.721091
\(902\) −24745.3 −0.913444
\(903\) 13776.0 0.507681
\(904\) 4791.94 0.176303
\(905\) −12013.5 −0.441261
\(906\) 10125.8 0.371309
\(907\) −45690.1 −1.67267 −0.836337 0.548215i \(-0.815307\pi\)
−0.836337 + 0.548215i \(0.815307\pi\)
\(908\) −16716.7 −0.610974
\(909\) 17664.9 0.644564
\(910\) −12014.6 −0.437671
\(911\) −32444.3 −1.17994 −0.589971 0.807424i \(-0.700861\pi\)
−0.589971 + 0.807424i \(0.700861\pi\)
\(912\) 912.000 0.0331133
\(913\) −13983.5 −0.506884
\(914\) 28638.7 1.03641
\(915\) 7650.96 0.276429
\(916\) 11187.3 0.403537
\(917\) −36663.7 −1.32033
\(918\) 5107.88 0.183644
\(919\) −30990.9 −1.11240 −0.556201 0.831048i \(-0.687741\pi\)
−0.556201 + 0.831048i \(0.687741\pi\)
\(920\) −328.685 −0.0117787
\(921\) 17315.4 0.619502
\(922\) 5158.87 0.184272
\(923\) −23371.2 −0.833447
\(924\) 6028.09 0.214621
\(925\) −137.191 −0.00487657
\(926\) 38269.2 1.35810
\(927\) 13605.2 0.482041
\(928\) 6928.63 0.245090
\(929\) 18596.6 0.656766 0.328383 0.944545i \(-0.393496\pi\)
0.328383 + 0.944545i \(0.393496\pi\)
\(930\) −6812.92 −0.240220
\(931\) −907.218 −0.0319365
\(932\) −19870.4 −0.698365
\(933\) −18525.1 −0.650038
\(934\) 24560.1 0.860420
\(935\) 13826.7 0.483617
\(936\) −5034.38 −0.175805
\(937\) 38908.0 1.35653 0.678266 0.734816i \(-0.262732\pi\)
0.678266 + 0.734816i \(0.262732\pi\)
\(938\) 34725.5 1.20877
\(939\) 33121.0 1.15108
\(940\) −131.874 −0.00457581
\(941\) −30289.8 −1.04933 −0.524665 0.851309i \(-0.675809\pi\)
−0.524665 + 0.851309i \(0.675809\pi\)
\(942\) −11254.0 −0.389252
\(943\) 3477.60 0.120092
\(944\) 3336.52 0.115036
\(945\) 2319.69 0.0798513
\(946\) 15625.6 0.537033
\(947\) 5350.55 0.183600 0.0918002 0.995777i \(-0.470738\pi\)
0.0918002 + 0.995777i \(0.470738\pi\)
\(948\) 6030.46 0.206603
\(949\) 60600.8 2.07290
\(950\) 950.000 0.0324443
\(951\) −4279.55 −0.145924
\(952\) 13002.7 0.442668
\(953\) 18445.6 0.626978 0.313489 0.949592i \(-0.398502\pi\)
0.313489 + 0.949592i \(0.398502\pi\)
\(954\) −3711.10 −0.125945
\(955\) −3732.36 −0.126467
\(956\) 18794.5 0.635835
\(957\) 18989.8 0.641435
\(958\) 2854.85 0.0962799
\(959\) 14129.6 0.475776
\(960\) 960.000 0.0322749
\(961\) 21782.2 0.731167
\(962\) 767.415 0.0257198
\(963\) −9307.20 −0.311444
\(964\) −268.130 −0.00895840
\(965\) 3230.33 0.107760
\(966\) −847.164 −0.0282164
\(967\) 2251.28 0.0748670 0.0374335 0.999299i \(-0.488082\pi\)
0.0374335 + 0.999299i \(0.488082\pi\)
\(968\) −3810.55 −0.126525
\(969\) 5391.65 0.178746
\(970\) −13943.0 −0.461529
\(971\) −15117.4 −0.499630 −0.249815 0.968294i \(-0.580370\pi\)
−0.249815 + 0.968294i \(0.580370\pi\)
\(972\) 972.000 0.0320750
\(973\) 7272.35 0.239610
\(974\) 28514.4 0.938049
\(975\) −5244.14 −0.172253
\(976\) 8161.02 0.267652
\(977\) −52640.2 −1.72376 −0.861878 0.507116i \(-0.830712\pi\)
−0.861878 + 0.507116i \(0.830712\pi\)
\(978\) 5277.16 0.172541
\(979\) −33627.4 −1.09779
\(980\) −954.967 −0.0311279
\(981\) −4405.02 −0.143365
\(982\) −34858.5 −1.13277
\(983\) −3111.24 −0.100949 −0.0504746 0.998725i \(-0.516073\pi\)
−0.0504746 + 0.998725i \(0.516073\pi\)
\(984\) −10157.1 −0.329063
\(985\) 24532.3 0.793568
\(986\) 40961.4 1.32300
\(987\) −339.897 −0.0109615
\(988\) −5314.07 −0.171116
\(989\) −2195.97 −0.0706043
\(990\) 2631.14 0.0844679
\(991\) 20100.4 0.644308 0.322154 0.946687i \(-0.395593\pi\)
0.322154 + 0.946687i \(0.395593\pi\)
\(992\) −7267.11 −0.232592
\(993\) −2701.18 −0.0863236
\(994\) 11486.6 0.366534
\(995\) −5831.18 −0.185790
\(996\) −5739.76 −0.182602
\(997\) 53308.1 1.69337 0.846683 0.532098i \(-0.178596\pi\)
0.846683 + 0.532098i \(0.178596\pi\)
\(998\) −12561.5 −0.398423
\(999\) −148.167 −0.00469248
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.1.3 4
3.2 odd 2 1710.4.a.bc.1.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
570.4.a.s.1.3 4 1.1 even 1 trivial
1710.4.a.bc.1.3 4 3.2 odd 2