Properties

Label 570.4.a.s.1.1
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 1.1
Root \(6.43713\) of defining polynomial
Character \(\chi\) \(=\) 570.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +5.00000 q^{5} +6.00000 q^{6} -15.8571 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +5.00000 q^{5} +6.00000 q^{6} -15.8571 q^{7} +8.00000 q^{8} +9.00000 q^{9} +10.0000 q^{10} +50.7314 q^{11} +12.0000 q^{12} +22.2003 q^{13} -31.7142 q^{14} +15.0000 q^{15} +16.0000 q^{16} -55.0234 q^{17} +18.0000 q^{18} +19.0000 q^{19} +20.0000 q^{20} -47.5714 q^{21} +101.463 q^{22} +148.394 q^{23} +24.0000 q^{24} +25.0000 q^{25} +44.4006 q^{26} +27.0000 q^{27} -63.4285 q^{28} +47.8615 q^{29} +30.0000 q^{30} -8.22219 q^{31} +32.0000 q^{32} +152.194 q^{33} -110.047 q^{34} -79.2856 q^{35} +36.0000 q^{36} -226.589 q^{37} +38.0000 q^{38} +66.6009 q^{39} +40.0000 q^{40} +284.264 q^{41} -95.1427 q^{42} +341.182 q^{43} +202.926 q^{44} +45.0000 q^{45} +296.789 q^{46} +561.047 q^{47} +48.0000 q^{48} -91.5518 q^{49} +50.0000 q^{50} -165.070 q^{51} +88.8012 q^{52} +430.176 q^{53} +54.0000 q^{54} +253.657 q^{55} -126.857 q^{56} +57.0000 q^{57} +95.7231 q^{58} -537.166 q^{59} +60.0000 q^{60} -767.733 q^{61} -16.4444 q^{62} -142.714 q^{63} +64.0000 q^{64} +111.002 q^{65} +304.388 q^{66} -457.125 q^{67} -220.094 q^{68} +445.183 q^{69} -158.571 q^{70} -28.3320 q^{71} +72.0000 q^{72} +663.799 q^{73} -453.177 q^{74} +75.0000 q^{75} +76.0000 q^{76} -804.454 q^{77} +133.202 q^{78} -220.526 q^{79} +80.0000 q^{80} +81.0000 q^{81} +568.527 q^{82} -316.427 q^{83} -190.285 q^{84} -275.117 q^{85} +682.363 q^{86} +143.585 q^{87} +405.851 q^{88} -1428.33 q^{89} +90.0000 q^{90} -352.033 q^{91} +593.578 q^{92} -24.6666 q^{93} +1122.09 q^{94} +95.0000 q^{95} +96.0000 q^{96} +1552.09 q^{97} -183.104 q^{98} +456.582 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 8q^{2} + 12q^{3} + 16q^{4} + 20q^{5} + 24q^{6} + 36q^{7} + 32q^{8} + 36q^{9} + O(q^{10}) \) \( 4q + 8q^{2} + 12q^{3} + 16q^{4} + 20q^{5} + 24q^{6} + 36q^{7} + 32q^{8} + 36q^{9} + 40q^{10} + 54q^{11} + 48q^{12} + 46q^{13} + 72q^{14} + 60q^{15} + 64q^{16} + 14q^{17} + 72q^{18} + 76q^{19} + 80q^{20} + 108q^{21} + 108q^{22} + 104q^{23} + 96q^{24} + 100q^{25} + 92q^{26} + 108q^{27} + 144q^{28} + 14q^{29} + 120q^{30} + 30q^{31} + 128q^{32} + 162q^{33} + 28q^{34} + 180q^{35} + 144q^{36} + 30q^{37} + 152q^{38} + 138q^{39} + 160q^{40} - 36q^{41} + 216q^{42} + 102q^{43} + 216q^{44} + 180q^{45} + 208q^{46} + 408q^{47} + 192q^{48} + 480q^{49} + 200q^{50} + 42q^{51} + 184q^{52} - 176q^{53} + 216q^{54} + 270q^{55} + 288q^{56} + 228q^{57} + 28q^{58} + 66q^{59} + 240q^{60} + 60q^{61} + 60q^{62} + 324q^{63} + 256q^{64} + 230q^{65} + 324q^{66} - 152q^{67} + 56q^{68} + 312q^{69} + 360q^{70} + 172q^{71} + 288q^{72} + 284q^{73} + 60q^{74} + 300q^{75} + 304q^{76} - 300q^{77} + 276q^{78} + 554q^{79} + 320q^{80} + 324q^{81} - 72q^{82} - 394q^{83} + 432q^{84} + 70q^{85} + 204q^{86} + 42q^{87} + 432q^{88} - 60q^{89} + 360q^{90} + 32q^{91} + 416q^{92} + 90q^{93} + 816q^{94} + 380q^{95} + 384q^{96} - 922q^{97} + 960q^{98} + 486q^{99} + O(q^{100}) \)

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
\(7\) −15.8571 −0.856204 −0.428102 0.903730i \(-0.640818\pi\)
−0.428102 + 0.903730i \(0.640818\pi\)
\(8\) 8.00000 0.353553
\(9\) 9.00000 0.333333
\(10\) 10.0000 0.316228
\(11\) 50.7314 1.39055 0.695277 0.718742i \(-0.255282\pi\)
0.695277 + 0.718742i \(0.255282\pi\)
\(12\) 12.0000 0.288675
\(13\) 22.2003 0.473635 0.236818 0.971554i \(-0.423896\pi\)
0.236818 + 0.971554i \(0.423896\pi\)
\(14\) −31.7142 −0.605428
\(15\) 15.0000 0.258199
\(16\) 16.0000 0.250000
\(17\) −55.0234 −0.785008 −0.392504 0.919750i \(-0.628391\pi\)
−0.392504 + 0.919750i \(0.628391\pi\)
\(18\) 18.0000 0.235702
\(19\) 19.0000 0.229416
\(20\) 20.0000 0.223607
\(21\) −47.5714 −0.494330
\(22\) 101.463 0.983270
\(23\) 148.394 1.34532 0.672661 0.739951i \(-0.265151\pi\)
0.672661 + 0.739951i \(0.265151\pi\)
\(24\) 24.0000 0.204124
\(25\) 25.0000 0.200000
\(26\) 44.4006 0.334911
\(27\) 27.0000 0.192450
\(28\) −63.4285 −0.428102
\(29\) 47.8615 0.306471 0.153236 0.988190i \(-0.451031\pi\)
0.153236 + 0.988190i \(0.451031\pi\)
\(30\) 30.0000 0.182574
\(31\) −8.22219 −0.0476371 −0.0238185 0.999716i \(-0.507582\pi\)
−0.0238185 + 0.999716i \(0.507582\pi\)
\(32\) 32.0000 0.176777
\(33\) 152.194 0.802836
\(34\) −110.047 −0.555085
\(35\) −79.2856 −0.382906
\(36\) 36.0000 0.166667
\(37\) −226.589 −1.00678 −0.503391 0.864059i \(-0.667914\pi\)
−0.503391 + 0.864059i \(0.667914\pi\)
\(38\) 38.0000 0.162221
\(39\) 66.6009 0.273453
\(40\) 40.0000 0.158114
\(41\) 284.264 1.08279 0.541396 0.840767i \(-0.317896\pi\)
0.541396 + 0.840767i \(0.317896\pi\)
\(42\) −95.1427 −0.349544
\(43\) 341.182 1.20999 0.604996 0.796228i \(-0.293175\pi\)
0.604996 + 0.796228i \(0.293175\pi\)
\(44\) 202.926 0.695277
\(45\) 45.0000 0.149071
\(46\) 296.789 0.951286
\(47\) 561.047 1.74122 0.870608 0.491977i \(-0.163726\pi\)
0.870608 + 0.491977i \(0.163726\pi\)
\(48\) 48.0000 0.144338
\(49\) −91.5518 −0.266915
\(50\) 50.0000 0.141421
\(51\) −165.070 −0.453225
\(52\) 88.8012 0.236818
\(53\) 430.176 1.11489 0.557446 0.830213i \(-0.311781\pi\)
0.557446 + 0.830213i \(0.311781\pi\)
\(54\) 54.0000 0.136083
\(55\) 253.657 0.621874
\(56\) −126.857 −0.302714
\(57\) 57.0000 0.132453
\(58\) 95.7231 0.216708
\(59\) −537.166 −1.18531 −0.592653 0.805458i \(-0.701919\pi\)
−0.592653 + 0.805458i \(0.701919\pi\)
\(60\) 60.0000 0.129099
\(61\) −767.733 −1.61144 −0.805722 0.592294i \(-0.798223\pi\)
−0.805722 + 0.592294i \(0.798223\pi\)
\(62\) −16.4444 −0.0336845
\(63\) −142.714 −0.285401
\(64\) 64.0000 0.125000
\(65\) 111.002 0.211816
\(66\) 304.388 0.567691
\(67\) −457.125 −0.833532 −0.416766 0.909014i \(-0.636837\pi\)
−0.416766 + 0.909014i \(0.636837\pi\)
\(68\) −220.094 −0.392504
\(69\) 445.183 0.776722
\(70\) −158.571 −0.270755
\(71\) −28.3320 −0.0473576 −0.0236788 0.999720i \(-0.507538\pi\)
−0.0236788 + 0.999720i \(0.507538\pi\)
\(72\) 72.0000 0.117851
\(73\) 663.799 1.06427 0.532135 0.846659i \(-0.321390\pi\)
0.532135 + 0.846659i \(0.321390\pi\)
\(74\) −453.177 −0.711903
\(75\) 75.0000 0.115470
\(76\) 76.0000 0.114708
\(77\) −804.454 −1.19060
\(78\) 133.202 0.193361
\(79\) −220.526 −0.314064 −0.157032 0.987593i \(-0.550193\pi\)
−0.157032 + 0.987593i \(0.550193\pi\)
\(80\) 80.0000 0.111803
\(81\) 81.0000 0.111111
\(82\) 568.527 0.765650
\(83\) −316.427 −0.418462 −0.209231 0.977866i \(-0.567096\pi\)
−0.209231 + 0.977866i \(0.567096\pi\)
\(84\) −190.285 −0.247165
\(85\) −275.117 −0.351066
\(86\) 682.363 0.855594
\(87\) 143.585 0.176941
\(88\) 405.851 0.491635
\(89\) −1428.33 −1.70115 −0.850574 0.525855i \(-0.823745\pi\)
−0.850574 + 0.525855i \(0.823745\pi\)
\(90\) 90.0000 0.105409
\(91\) −352.033 −0.405528
\(92\) 593.578 0.672661
\(93\) −24.6666 −0.0275033
\(94\) 1122.09 1.23123
\(95\) 95.0000 0.102598
\(96\) 96.0000 0.102062
\(97\) 1552.09 1.62465 0.812323 0.583208i \(-0.198203\pi\)
0.812323 + 0.583208i \(0.198203\pi\)
\(98\) −183.104 −0.188737
\(99\) 456.582 0.463518
\(100\) 100.000 0.100000
\(101\) 616.336 0.607205 0.303602 0.952799i \(-0.401811\pi\)
0.303602 + 0.952799i \(0.401811\pi\)
\(102\) −330.141 −0.320478
\(103\) −1795.44 −1.71757 −0.858784 0.512338i \(-0.828780\pi\)
−0.858784 + 0.512338i \(0.828780\pi\)
\(104\) 177.602 0.167455
\(105\) −237.857 −0.221071
\(106\) 860.353 0.788348
\(107\) 933.758 0.843643 0.421821 0.906679i \(-0.361391\pi\)
0.421821 + 0.906679i \(0.361391\pi\)
\(108\) 108.000 0.0962250
\(109\) 1867.99 1.64148 0.820738 0.571305i \(-0.193563\pi\)
0.820738 + 0.571305i \(0.193563\pi\)
\(110\) 507.314 0.439732
\(111\) −679.766 −0.581266
\(112\) −253.714 −0.214051
\(113\) −720.629 −0.599921 −0.299960 0.953952i \(-0.596973\pi\)
−0.299960 + 0.953952i \(0.596973\pi\)
\(114\) 114.000 0.0936586
\(115\) 741.972 0.601646
\(116\) 191.446 0.153236
\(117\) 199.803 0.157878
\(118\) −1074.33 −0.838138
\(119\) 872.513 0.672127
\(120\) 120.000 0.0912871
\(121\) 1242.67 0.933639
\(122\) −1535.47 −1.13946
\(123\) 852.791 0.625151
\(124\) −32.8888 −0.0238185
\(125\) 125.000 0.0894427
\(126\) −285.428 −0.201809
\(127\) −644.374 −0.450228 −0.225114 0.974332i \(-0.572275\pi\)
−0.225114 + 0.974332i \(0.572275\pi\)
\(128\) 128.000 0.0883883
\(129\) 1023.54 0.698590
\(130\) 222.003 0.149777
\(131\) −901.698 −0.601387 −0.300694 0.953721i \(-0.597218\pi\)
−0.300694 + 0.953721i \(0.597218\pi\)
\(132\) 608.777 0.401418
\(133\) −301.285 −0.196427
\(134\) −914.249 −0.589396
\(135\) 135.000 0.0860663
\(136\) −440.187 −0.277542
\(137\) −1839.55 −1.14718 −0.573588 0.819144i \(-0.694449\pi\)
−0.573588 + 0.819144i \(0.694449\pi\)
\(138\) 890.367 0.549225
\(139\) −3084.12 −1.88195 −0.940976 0.338474i \(-0.890089\pi\)
−0.940976 + 0.338474i \(0.890089\pi\)
\(140\) −317.142 −0.191453
\(141\) 1683.14 1.00529
\(142\) −56.6640 −0.0334869
\(143\) 1126.25 0.658615
\(144\) 144.000 0.0833333
\(145\) 239.308 0.137058
\(146\) 1327.60 0.752553
\(147\) −274.656 −0.154103
\(148\) −906.355 −0.503391
\(149\) 911.565 0.501197 0.250598 0.968091i \(-0.419373\pi\)
0.250598 + 0.968091i \(0.419373\pi\)
\(150\) 150.000 0.0816497
\(151\) −2771.47 −1.49364 −0.746818 0.665028i \(-0.768420\pi\)
−0.746818 + 0.665028i \(0.768420\pi\)
\(152\) 152.000 0.0811107
\(153\) −495.211 −0.261669
\(154\) −1608.91 −0.841879
\(155\) −41.1109 −0.0213039
\(156\) 266.404 0.136727
\(157\) 2546.36 1.29440 0.647202 0.762318i \(-0.275939\pi\)
0.647202 + 0.762318i \(0.275939\pi\)
\(158\) −441.051 −0.222077
\(159\) 1290.53 0.643683
\(160\) 160.000 0.0790569
\(161\) −2353.11 −1.15187
\(162\) 162.000 0.0785674
\(163\) 2765.37 1.32884 0.664418 0.747361i \(-0.268679\pi\)
0.664418 + 0.747361i \(0.268679\pi\)
\(164\) 1137.05 0.541396
\(165\) 760.971 0.359039
\(166\) −632.854 −0.295898
\(167\) −2551.63 −1.18234 −0.591170 0.806547i \(-0.701334\pi\)
−0.591170 + 0.806547i \(0.701334\pi\)
\(168\) −380.571 −0.174772
\(169\) −1704.15 −0.775670
\(170\) −550.234 −0.248241
\(171\) 171.000 0.0764719
\(172\) 1364.73 0.604996
\(173\) 530.424 0.233106 0.116553 0.993184i \(-0.462815\pi\)
0.116553 + 0.993184i \(0.462815\pi\)
\(174\) 287.169 0.125116
\(175\) −396.428 −0.171241
\(176\) 811.702 0.347638
\(177\) −1611.50 −0.684337
\(178\) −2856.65 −1.20289
\(179\) −304.410 −0.127110 −0.0635549 0.997978i \(-0.520244\pi\)
−0.0635549 + 0.997978i \(0.520244\pi\)
\(180\) 180.000 0.0745356
\(181\) −1211.98 −0.497710 −0.248855 0.968541i \(-0.580054\pi\)
−0.248855 + 0.968541i \(0.580054\pi\)
\(182\) −704.066 −0.286752
\(183\) −2303.20 −0.930368
\(184\) 1187.16 0.475643
\(185\) −1132.94 −0.450247
\(186\) −49.3331 −0.0194477
\(187\) −2791.41 −1.09160
\(188\) 2244.19 0.870608
\(189\) −428.142 −0.164777
\(190\) 190.000 0.0725476
\(191\) −213.308 −0.0808086 −0.0404043 0.999183i \(-0.512865\pi\)
−0.0404043 + 0.999183i \(0.512865\pi\)
\(192\) 192.000 0.0721688
\(193\) 86.5818 0.0322917 0.0161458 0.999870i \(-0.494860\pi\)
0.0161458 + 0.999870i \(0.494860\pi\)
\(194\) 3104.17 1.14880
\(195\) 333.005 0.122292
\(196\) −366.207 −0.133458
\(197\) −4694.88 −1.69795 −0.848976 0.528432i \(-0.822780\pi\)
−0.848976 + 0.528432i \(0.822780\pi\)
\(198\) 913.165 0.327757
\(199\) 4206.05 1.49829 0.749143 0.662408i \(-0.230466\pi\)
0.749143 + 0.662408i \(0.230466\pi\)
\(200\) 200.000 0.0707107
\(201\) −1371.37 −0.481240
\(202\) 1232.67 0.429359
\(203\) −758.946 −0.262402
\(204\) −660.281 −0.226612
\(205\) 1421.32 0.484240
\(206\) −3590.87 −1.21450
\(207\) 1335.55 0.448440
\(208\) 355.205 0.118409
\(209\) 963.896 0.319015
\(210\) −475.714 −0.156321
\(211\) 4148.47 1.35352 0.676759 0.736205i \(-0.263384\pi\)
0.676759 + 0.736205i \(0.263384\pi\)
\(212\) 1720.71 0.557446
\(213\) −84.9960 −0.0273419
\(214\) 1867.52 0.596545
\(215\) 1705.91 0.541125
\(216\) 216.000 0.0680414
\(217\) 130.380 0.0407870
\(218\) 3735.98 1.16070
\(219\) 1991.40 0.614457
\(220\) 1014.63 0.310937
\(221\) −1221.54 −0.371808
\(222\) −1359.53 −0.411017
\(223\) −4745.76 −1.42511 −0.712555 0.701616i \(-0.752462\pi\)
−0.712555 + 0.701616i \(0.752462\pi\)
\(224\) −507.428 −0.151357
\(225\) 225.000 0.0666667
\(226\) −1441.26 −0.424208
\(227\) −4213.15 −1.23188 −0.615940 0.787793i \(-0.711224\pi\)
−0.615940 + 0.787793i \(0.711224\pi\)
\(228\) 228.000 0.0662266
\(229\) −2596.66 −0.749310 −0.374655 0.927164i \(-0.622239\pi\)
−0.374655 + 0.927164i \(0.622239\pi\)
\(230\) 1483.94 0.425428
\(231\) −2413.36 −0.687392
\(232\) 382.892 0.108354
\(233\) −3787.12 −1.06482 −0.532408 0.846488i \(-0.678713\pi\)
−0.532408 + 0.846488i \(0.678713\pi\)
\(234\) 399.606 0.111637
\(235\) 2805.24 0.778696
\(236\) −2148.66 −0.592653
\(237\) −661.577 −0.181325
\(238\) 1745.03 0.475266
\(239\) 2701.41 0.731128 0.365564 0.930786i \(-0.380876\pi\)
0.365564 + 0.930786i \(0.380876\pi\)
\(240\) 240.000 0.0645497
\(241\) −5098.72 −1.36281 −0.681405 0.731906i \(-0.738631\pi\)
−0.681405 + 0.731906i \(0.738631\pi\)
\(242\) 2485.35 0.660182
\(243\) 243.000 0.0641500
\(244\) −3070.93 −0.805722
\(245\) −457.759 −0.119368
\(246\) 1705.58 0.442048
\(247\) 421.806 0.108659
\(248\) −65.7775 −0.0168422
\(249\) −949.281 −0.241599
\(250\) 250.000 0.0632456
\(251\) −5480.82 −1.37827 −0.689136 0.724632i \(-0.742010\pi\)
−0.689136 + 0.724632i \(0.742010\pi\)
\(252\) −570.856 −0.142701
\(253\) 7528.26 1.87074
\(254\) −1288.75 −0.318359
\(255\) −825.351 −0.202688
\(256\) 256.000 0.0625000
\(257\) −1287.94 −0.312605 −0.156303 0.987709i \(-0.549957\pi\)
−0.156303 + 0.987709i \(0.549957\pi\)
\(258\) 2047.09 0.493978
\(259\) 3593.04 0.862011
\(260\) 444.006 0.105908
\(261\) 430.754 0.102157
\(262\) −1803.40 −0.425245
\(263\) −4069.55 −0.954141 −0.477070 0.878865i \(-0.658301\pi\)
−0.477070 + 0.878865i \(0.658301\pi\)
\(264\) 1217.55 0.283846
\(265\) 2150.88 0.498595
\(266\) −602.570 −0.138895
\(267\) −4284.98 −0.982159
\(268\) −1828.50 −0.416766
\(269\) −2303.24 −0.522049 −0.261024 0.965332i \(-0.584060\pi\)
−0.261024 + 0.965332i \(0.584060\pi\)
\(270\) 270.000 0.0608581
\(271\) −4575.49 −1.02561 −0.512807 0.858504i \(-0.671394\pi\)
−0.512807 + 0.858504i \(0.671394\pi\)
\(272\) −880.375 −0.196252
\(273\) −1056.10 −0.234132
\(274\) −3679.10 −0.811176
\(275\) 1268.28 0.278111
\(276\) 1780.73 0.388361
\(277\) 2257.26 0.489623 0.244812 0.969571i \(-0.421274\pi\)
0.244812 + 0.969571i \(0.421274\pi\)
\(278\) −6168.23 −1.33074
\(279\) −73.9997 −0.0158790
\(280\) −634.285 −0.135378
\(281\) 4461.98 0.947257 0.473628 0.880725i \(-0.342944\pi\)
0.473628 + 0.880725i \(0.342944\pi\)
\(282\) 3366.28 0.710849
\(283\) 1315.17 0.276251 0.138125 0.990415i \(-0.455892\pi\)
0.138125 + 0.990415i \(0.455892\pi\)
\(284\) −113.328 −0.0236788
\(285\) 285.000 0.0592349
\(286\) 2252.51 0.465711
\(287\) −4507.60 −0.927091
\(288\) 288.000 0.0589256
\(289\) −1885.42 −0.383762
\(290\) 478.615 0.0969147
\(291\) 4656.26 0.937989
\(292\) 2655.19 0.532135
\(293\) 4905.15 0.978026 0.489013 0.872276i \(-0.337357\pi\)
0.489013 + 0.872276i \(0.337357\pi\)
\(294\) −549.311 −0.108968
\(295\) −2685.83 −0.530085
\(296\) −1812.71 −0.355951
\(297\) 1369.75 0.267612
\(298\) 1823.13 0.354400
\(299\) 3294.40 0.637191
\(300\) 300.000 0.0577350
\(301\) −5410.16 −1.03600
\(302\) −5542.94 −1.05616
\(303\) 1849.01 0.350570
\(304\) 304.000 0.0573539
\(305\) −3838.66 −0.720660
\(306\) −990.422 −0.185028
\(307\) −1871.47 −0.347917 −0.173958 0.984753i \(-0.555656\pi\)
−0.173958 + 0.984753i \(0.555656\pi\)
\(308\) −3217.81 −0.595299
\(309\) −5386.31 −0.991639
\(310\) −82.2219 −0.0150642
\(311\) −5183.32 −0.945077 −0.472539 0.881310i \(-0.656662\pi\)
−0.472539 + 0.881310i \(0.656662\pi\)
\(312\) 532.807 0.0966804
\(313\) 6174.73 1.11507 0.557534 0.830154i \(-0.311748\pi\)
0.557534 + 0.830154i \(0.311748\pi\)
\(314\) 5092.72 0.915282
\(315\) −713.570 −0.127635
\(316\) −882.103 −0.157032
\(317\) 60.0596 0.0106413 0.00532064 0.999986i \(-0.498306\pi\)
0.00532064 + 0.999986i \(0.498306\pi\)
\(318\) 2581.06 0.455153
\(319\) 2428.08 0.426165
\(320\) 320.000 0.0559017
\(321\) 2801.27 0.487077
\(322\) −4706.22 −0.814494
\(323\) −1045.45 −0.180093
\(324\) 324.000 0.0555556
\(325\) 555.008 0.0947270
\(326\) 5530.74 0.939629
\(327\) 5603.96 0.947706
\(328\) 2274.11 0.382825
\(329\) −8896.59 −1.49084
\(330\) 1521.94 0.253879
\(331\) −5472.36 −0.908726 −0.454363 0.890817i \(-0.650133\pi\)
−0.454363 + 0.890817i \(0.650133\pi\)
\(332\) −1265.71 −0.209231
\(333\) −2039.30 −0.335594
\(334\) −5103.26 −0.836041
\(335\) −2285.62 −0.372767
\(336\) −761.142 −0.123582
\(337\) −5752.93 −0.929917 −0.464959 0.885332i \(-0.653931\pi\)
−0.464959 + 0.885332i \(0.653931\pi\)
\(338\) −3408.29 −0.548481
\(339\) −2161.89 −0.346364
\(340\) −1100.47 −0.175533
\(341\) −417.123 −0.0662419
\(342\) 342.000 0.0540738
\(343\) 6890.74 1.08474
\(344\) 2729.45 0.427797
\(345\) 2225.92 0.347360
\(346\) 1060.85 0.164831
\(347\) −1904.93 −0.294704 −0.147352 0.989084i \(-0.547075\pi\)
−0.147352 + 0.989084i \(0.547075\pi\)
\(348\) 574.338 0.0884706
\(349\) 6389.95 0.980075 0.490038 0.871701i \(-0.336983\pi\)
0.490038 + 0.871701i \(0.336983\pi\)
\(350\) −792.856 −0.121086
\(351\) 599.408 0.0911511
\(352\) 1623.40 0.245817
\(353\) −10230.2 −1.54249 −0.771246 0.636537i \(-0.780366\pi\)
−0.771246 + 0.636537i \(0.780366\pi\)
\(354\) −3223.00 −0.483899
\(355\) −141.660 −0.0211790
\(356\) −5713.30 −0.850574
\(357\) 2617.54 0.388053
\(358\) −608.819 −0.0898802
\(359\) −581.945 −0.0855540 −0.0427770 0.999085i \(-0.513620\pi\)
−0.0427770 + 0.999085i \(0.513620\pi\)
\(360\) 360.000 0.0527046
\(361\) 361.000 0.0526316
\(362\) −2423.95 −0.351934
\(363\) 3728.02 0.539037
\(364\) −1408.13 −0.202764
\(365\) 3318.99 0.475956
\(366\) −4606.40 −0.657869
\(367\) 10047.4 1.42907 0.714535 0.699599i \(-0.246638\pi\)
0.714535 + 0.699599i \(0.246638\pi\)
\(368\) 2374.31 0.336330
\(369\) 2558.37 0.360931
\(370\) −2265.89 −0.318372
\(371\) −6821.36 −0.954575
\(372\) −98.6663 −0.0137516
\(373\) 14080.4 1.95457 0.977285 0.211927i \(-0.0679741\pi\)
0.977285 + 0.211927i \(0.0679741\pi\)
\(374\) −5582.83 −0.771875
\(375\) 375.000 0.0516398
\(376\) 4488.38 0.615613
\(377\) 1062.54 0.145156
\(378\) −856.284 −0.116515
\(379\) 5515.37 0.747507 0.373754 0.927528i \(-0.378071\pi\)
0.373754 + 0.927528i \(0.378071\pi\)
\(380\) 380.000 0.0512989
\(381\) −1933.12 −0.259939
\(382\) −426.616 −0.0571403
\(383\) 3365.31 0.448980 0.224490 0.974476i \(-0.427928\pi\)
0.224490 + 0.974476i \(0.427928\pi\)
\(384\) 384.000 0.0510310
\(385\) −4022.27 −0.532451
\(386\) 173.164 0.0228337
\(387\) 3070.63 0.403331
\(388\) 6208.35 0.812323
\(389\) 5391.60 0.702737 0.351369 0.936237i \(-0.385716\pi\)
0.351369 + 0.936237i \(0.385716\pi\)
\(390\) 666.009 0.0864736
\(391\) −8165.17 −1.05609
\(392\) −732.415 −0.0943687
\(393\) −2705.10 −0.347211
\(394\) −9389.76 −1.20063
\(395\) −1102.63 −0.140454
\(396\) 1826.33 0.231759
\(397\) 4380.78 0.553816 0.276908 0.960896i \(-0.410690\pi\)
0.276908 + 0.960896i \(0.410690\pi\)
\(398\) 8412.10 1.05945
\(399\) −903.856 −0.113407
\(400\) 400.000 0.0500000
\(401\) −9635.17 −1.19989 −0.599947 0.800040i \(-0.704812\pi\)
−0.599947 + 0.800040i \(0.704812\pi\)
\(402\) −2742.75 −0.340288
\(403\) −182.535 −0.0225626
\(404\) 2465.34 0.303602
\(405\) 405.000 0.0496904
\(406\) −1517.89 −0.185546
\(407\) −11495.2 −1.39998
\(408\) −1320.56 −0.160239
\(409\) −1837.81 −0.222186 −0.111093 0.993810i \(-0.535435\pi\)
−0.111093 + 0.993810i \(0.535435\pi\)
\(410\) 2842.64 0.342409
\(411\) −5518.64 −0.662323
\(412\) −7181.74 −0.858784
\(413\) 8517.91 1.01486
\(414\) 2671.10 0.317095
\(415\) −1582.14 −0.187142
\(416\) 710.410 0.0837277
\(417\) −9252.35 −1.08655
\(418\) 1927.79 0.225578
\(419\) 5812.61 0.677720 0.338860 0.940837i \(-0.389959\pi\)
0.338860 + 0.940837i \(0.389959\pi\)
\(420\) −951.427 −0.110535
\(421\) 8992.63 1.04103 0.520516 0.853852i \(-0.325740\pi\)
0.520516 + 0.853852i \(0.325740\pi\)
\(422\) 8296.94 0.957082
\(423\) 5049.43 0.580406
\(424\) 3441.41 0.394174
\(425\) −1375.59 −0.157002
\(426\) −169.992 −0.0193337
\(427\) 12174.0 1.37972
\(428\) 3735.03 0.421821
\(429\) 3378.76 0.380252
\(430\) 3411.82 0.382633
\(431\) 147.925 0.0165320 0.00826601 0.999966i \(-0.497369\pi\)
0.00826601 + 0.999966i \(0.497369\pi\)
\(432\) 432.000 0.0481125
\(433\) 9308.09 1.03307 0.516534 0.856267i \(-0.327222\pi\)
0.516534 + 0.856267i \(0.327222\pi\)
\(434\) 260.760 0.0288408
\(435\) 717.923 0.0791305
\(436\) 7471.95 0.820738
\(437\) 2819.49 0.308638
\(438\) 3982.79 0.434487
\(439\) −832.727 −0.0905327 −0.0452664 0.998975i \(-0.514414\pi\)
−0.0452664 + 0.998975i \(0.514414\pi\)
\(440\) 2029.26 0.219866
\(441\) −823.967 −0.0889717
\(442\) −2443.07 −0.262908
\(443\) −156.708 −0.0168068 −0.00840339 0.999965i \(-0.502675\pi\)
−0.00840339 + 0.999965i \(0.502675\pi\)
\(444\) −2719.06 −0.290633
\(445\) −7141.63 −0.760777
\(446\) −9491.52 −1.00771
\(447\) 2734.70 0.289366
\(448\) −1014.86 −0.107025
\(449\) −4607.38 −0.484266 −0.242133 0.970243i \(-0.577847\pi\)
−0.242133 + 0.970243i \(0.577847\pi\)
\(450\) 450.000 0.0471405
\(451\) 14421.1 1.50568
\(452\) −2882.51 −0.299960
\(453\) −8314.41 −0.862351
\(454\) −8426.30 −0.871070
\(455\) −1760.16 −0.181358
\(456\) 456.000 0.0468293
\(457\) 7656.99 0.783762 0.391881 0.920016i \(-0.371825\pi\)
0.391881 + 0.920016i \(0.371825\pi\)
\(458\) −5193.32 −0.529842
\(459\) −1485.63 −0.151075
\(460\) 2967.89 0.300823
\(461\) −12317.8 −1.24447 −0.622234 0.782832i \(-0.713775\pi\)
−0.622234 + 0.782832i \(0.713775\pi\)
\(462\) −4826.72 −0.486059
\(463\) 10751.8 1.07922 0.539608 0.841916i \(-0.318572\pi\)
0.539608 + 0.841916i \(0.318572\pi\)
\(464\) 765.785 0.0766178
\(465\) −123.333 −0.0122998
\(466\) −7574.23 −0.752939
\(467\) −11618.8 −1.15129 −0.575647 0.817699i \(-0.695250\pi\)
−0.575647 + 0.817699i \(0.695250\pi\)
\(468\) 799.211 0.0789392
\(469\) 7248.68 0.713674
\(470\) 5610.47 0.550621
\(471\) 7639.08 0.747325
\(472\) −4297.33 −0.419069
\(473\) 17308.6 1.68256
\(474\) −1323.15 −0.128216
\(475\) 475.000 0.0458831
\(476\) 3490.05 0.336064
\(477\) 3871.59 0.371631
\(478\) 5402.82 0.516986
\(479\) 2195.73 0.209448 0.104724 0.994501i \(-0.466604\pi\)
0.104724 + 0.994501i \(0.466604\pi\)
\(480\) 480.000 0.0456435
\(481\) −5030.34 −0.476848
\(482\) −10197.4 −0.963653
\(483\) −7059.33 −0.665032
\(484\) 4970.69 0.466820
\(485\) 7760.44 0.726563
\(486\) 486.000 0.0453609
\(487\) −1633.07 −0.151954 −0.0759769 0.997110i \(-0.524208\pi\)
−0.0759769 + 0.997110i \(0.524208\pi\)
\(488\) −6141.86 −0.569732
\(489\) 8296.10 0.767204
\(490\) −915.518 −0.0844059
\(491\) −8508.71 −0.782063 −0.391031 0.920377i \(-0.627882\pi\)
−0.391031 + 0.920377i \(0.627882\pi\)
\(492\) 3411.16 0.312575
\(493\) −2633.51 −0.240582
\(494\) 843.612 0.0768338
\(495\) 2282.91 0.207291
\(496\) −131.555 −0.0119093
\(497\) 449.264 0.0405478
\(498\) −1898.56 −0.170837
\(499\) −5631.15 −0.505181 −0.252590 0.967573i \(-0.581282\pi\)
−0.252590 + 0.967573i \(0.581282\pi\)
\(500\) 500.000 0.0447214
\(501\) −7654.88 −0.682625
\(502\) −10961.6 −0.974585
\(503\) 14035.5 1.24416 0.622078 0.782955i \(-0.286289\pi\)
0.622078 + 0.782955i \(0.286289\pi\)
\(504\) −1141.71 −0.100905
\(505\) 3081.68 0.271550
\(506\) 15056.5 1.32281
\(507\) −5112.44 −0.447833
\(508\) −2577.49 −0.225114
\(509\) 16758.0 1.45930 0.729650 0.683821i \(-0.239683\pi\)
0.729650 + 0.683821i \(0.239683\pi\)
\(510\) −1650.70 −0.143322
\(511\) −10525.9 −0.911233
\(512\) 512.000 0.0441942
\(513\) 513.000 0.0441511
\(514\) −2575.88 −0.221045
\(515\) −8977.18 −0.768120
\(516\) 4094.18 0.349295
\(517\) 28462.7 2.42125
\(518\) 7186.08 0.609534
\(519\) 1591.27 0.134584
\(520\) 888.012 0.0748883
\(521\) 1472.09 0.123787 0.0618937 0.998083i \(-0.480286\pi\)
0.0618937 + 0.998083i \(0.480286\pi\)
\(522\) 861.508 0.0722359
\(523\) −10915.9 −0.912656 −0.456328 0.889812i \(-0.650836\pi\)
−0.456328 + 0.889812i \(0.650836\pi\)
\(524\) −3606.79 −0.300694
\(525\) −1189.28 −0.0988659
\(526\) −8139.09 −0.674679
\(527\) 452.413 0.0373955
\(528\) 2435.11 0.200709
\(529\) 9853.92 0.809889
\(530\) 4301.76 0.352560
\(531\) −4834.49 −0.395102
\(532\) −1205.14 −0.0982133
\(533\) 6310.74 0.512849
\(534\) −8569.95 −0.694491
\(535\) 4668.79 0.377288
\(536\) −3657.00 −0.294698
\(537\) −913.229 −0.0733869
\(538\) −4606.49 −0.369144
\(539\) −4644.55 −0.371160
\(540\) 540.000 0.0430331
\(541\) 195.388 0.0155275 0.00776377 0.999970i \(-0.497529\pi\)
0.00776377 + 0.999970i \(0.497529\pi\)
\(542\) −9150.98 −0.725218
\(543\) −3635.93 −0.287353
\(544\) −1760.75 −0.138771
\(545\) 9339.94 0.734090
\(546\) −2112.20 −0.165556
\(547\) −12927.8 −1.01052 −0.505259 0.862968i \(-0.668603\pi\)
−0.505259 + 0.862968i \(0.668603\pi\)
\(548\) −7358.19 −0.573588
\(549\) −6909.60 −0.537148
\(550\) 2536.57 0.196654
\(551\) 909.369 0.0703093
\(552\) 3561.47 0.274613
\(553\) 3496.90 0.268903
\(554\) 4514.52 0.346216
\(555\) −3398.83 −0.259950
\(556\) −12336.5 −0.940976
\(557\) 17152.6 1.30481 0.652407 0.757869i \(-0.273759\pi\)
0.652407 + 0.757869i \(0.273759\pi\)
\(558\) −147.999 −0.0112282
\(559\) 7574.34 0.573095
\(560\) −1268.57 −0.0957265
\(561\) −8374.24 −0.630233
\(562\) 8923.95 0.669812
\(563\) 19714.9 1.47582 0.737909 0.674901i \(-0.235814\pi\)
0.737909 + 0.674901i \(0.235814\pi\)
\(564\) 6732.57 0.502646
\(565\) −3603.14 −0.268293
\(566\) 2630.35 0.195339
\(567\) −1284.43 −0.0951338
\(568\) −226.656 −0.0167434
\(569\) 16286.4 1.19993 0.599964 0.800027i \(-0.295181\pi\)
0.599964 + 0.800027i \(0.295181\pi\)
\(570\) 570.000 0.0418854
\(571\) −19645.3 −1.43981 −0.719903 0.694075i \(-0.755814\pi\)
−0.719903 + 0.694075i \(0.755814\pi\)
\(572\) 4505.01 0.329308
\(573\) −639.925 −0.0466549
\(574\) −9015.20 −0.655553
\(575\) 3709.86 0.269064
\(576\) 576.000 0.0416667
\(577\) 5176.59 0.373491 0.186745 0.982408i \(-0.440206\pi\)
0.186745 + 0.982408i \(0.440206\pi\)
\(578\) −3770.84 −0.271361
\(579\) 259.745 0.0186436
\(580\) 957.231 0.0685290
\(581\) 5017.62 0.358289
\(582\) 9312.52 0.663259
\(583\) 21823.4 1.55032
\(584\) 5310.39 0.376277
\(585\) 999.014 0.0706054
\(586\) 9810.29 0.691569
\(587\) 18538.7 1.30353 0.651766 0.758420i \(-0.274028\pi\)
0.651766 + 0.758420i \(0.274028\pi\)
\(588\) −1098.62 −0.0770517
\(589\) −156.222 −0.0109287
\(590\) −5371.66 −0.374827
\(591\) −14084.6 −0.980313
\(592\) −3625.42 −0.251696
\(593\) 16412.2 1.13654 0.568270 0.822842i \(-0.307613\pi\)
0.568270 + 0.822842i \(0.307613\pi\)
\(594\) 2739.49 0.189230
\(595\) 4362.56 0.300584
\(596\) 3646.26 0.250598
\(597\) 12618.1 0.865036
\(598\) 6588.81 0.450562
\(599\) −24397.0 −1.66416 −0.832082 0.554653i \(-0.812851\pi\)
−0.832082 + 0.554653i \(0.812851\pi\)
\(600\) 600.000 0.0408248
\(601\) 26547.9 1.80185 0.900926 0.433973i \(-0.142889\pi\)
0.900926 + 0.433973i \(0.142889\pi\)
\(602\) −10820.3 −0.732563
\(603\) −4114.12 −0.277844
\(604\) −11085.9 −0.746818
\(605\) 6213.37 0.417536
\(606\) 3698.01 0.247890
\(607\) 3740.95 0.250149 0.125075 0.992147i \(-0.460083\pi\)
0.125075 + 0.992147i \(0.460083\pi\)
\(608\) 608.000 0.0405554
\(609\) −2276.84 −0.151498
\(610\) −7677.33 −0.509583
\(611\) 12455.4 0.824702
\(612\) −1980.84 −0.130835
\(613\) 13449.2 0.886144 0.443072 0.896486i \(-0.353889\pi\)
0.443072 + 0.896486i \(0.353889\pi\)
\(614\) −3742.94 −0.246014
\(615\) 4263.95 0.279576
\(616\) −6435.63 −0.420940
\(617\) 13438.8 0.876866 0.438433 0.898764i \(-0.355534\pi\)
0.438433 + 0.898764i \(0.355534\pi\)
\(618\) −10772.6 −0.701194
\(619\) −18146.7 −1.17832 −0.589159 0.808017i \(-0.700541\pi\)
−0.589159 + 0.808017i \(0.700541\pi\)
\(620\) −164.444 −0.0106520
\(621\) 4006.65 0.258907
\(622\) −10366.6 −0.668271
\(623\) 22649.1 1.45653
\(624\) 1065.61 0.0683634
\(625\) 625.000 0.0400000
\(626\) 12349.5 0.788472
\(627\) 2891.69 0.184183
\(628\) 10185.4 0.647202
\(629\) 12467.7 0.790332
\(630\) −1427.14 −0.0902518
\(631\) −5015.02 −0.316394 −0.158197 0.987408i \(-0.550568\pi\)
−0.158197 + 0.987408i \(0.550568\pi\)
\(632\) −1764.21 −0.111038
\(633\) 12445.4 0.781454
\(634\) 120.119 0.00752452
\(635\) −3221.87 −0.201348
\(636\) 5162.12 0.321842
\(637\) −2032.48 −0.126420
\(638\) 4856.16 0.301344
\(639\) −254.988 −0.0157859
\(640\) 640.000 0.0395285
\(641\) −17869.0 −1.10107 −0.550534 0.834813i \(-0.685576\pi\)
−0.550534 + 0.834813i \(0.685576\pi\)
\(642\) 5602.55 0.344416
\(643\) −10833.2 −0.664419 −0.332209 0.943206i \(-0.607794\pi\)
−0.332209 + 0.943206i \(0.607794\pi\)
\(644\) −9412.43 −0.575935
\(645\) 5117.72 0.312419
\(646\) −2090.89 −0.127345
\(647\) 2378.25 0.144511 0.0722555 0.997386i \(-0.476980\pi\)
0.0722555 + 0.997386i \(0.476980\pi\)
\(648\) 648.000 0.0392837
\(649\) −27251.2 −1.64823
\(650\) 1110.02 0.0669821
\(651\) 391.141 0.0235484
\(652\) 11061.5 0.664418
\(653\) −12759.1 −0.764627 −0.382314 0.924033i \(-0.624873\pi\)
−0.382314 + 0.924033i \(0.624873\pi\)
\(654\) 11207.9 0.670130
\(655\) −4508.49 −0.268949
\(656\) 4548.22 0.270698
\(657\) 5974.19 0.354757
\(658\) −17793.2 −1.05418
\(659\) 15189.7 0.897883 0.448942 0.893561i \(-0.351801\pi\)
0.448942 + 0.893561i \(0.351801\pi\)
\(660\) 3043.88 0.179520
\(661\) 4398.55 0.258826 0.129413 0.991591i \(-0.458691\pi\)
0.129413 + 0.991591i \(0.458691\pi\)
\(662\) −10944.7 −0.642566
\(663\) −3664.61 −0.214663
\(664\) −2531.42 −0.147949
\(665\) −1506.43 −0.0878447
\(666\) −4078.60 −0.237301
\(667\) 7102.39 0.412302
\(668\) −10206.5 −0.591170
\(669\) −14237.3 −0.822788
\(670\) −4571.25 −0.263586
\(671\) −38948.2 −2.24080
\(672\) −1522.28 −0.0873859
\(673\) 16170.9 0.926215 0.463108 0.886302i \(-0.346734\pi\)
0.463108 + 0.886302i \(0.346734\pi\)
\(674\) −11505.9 −0.657551
\(675\) 675.000 0.0384900
\(676\) −6816.58 −0.387835
\(677\) 17812.2 1.01120 0.505598 0.862769i \(-0.331272\pi\)
0.505598 + 0.862769i \(0.331272\pi\)
\(678\) −4323.77 −0.244917
\(679\) −24611.6 −1.39103
\(680\) −2200.94 −0.124121
\(681\) −12639.5 −0.711226
\(682\) −834.246 −0.0468401
\(683\) 25203.8 1.41200 0.705999 0.708213i \(-0.250498\pi\)
0.705999 + 0.708213i \(0.250498\pi\)
\(684\) 684.000 0.0382360
\(685\) −9197.74 −0.513033
\(686\) 13781.5 0.767025
\(687\) −7789.98 −0.432615
\(688\) 5458.90 0.302498
\(689\) 9550.05 0.528052
\(690\) 4451.83 0.245621
\(691\) 10306.9 0.567430 0.283715 0.958909i \(-0.408433\pi\)
0.283715 + 0.958909i \(0.408433\pi\)
\(692\) 2121.70 0.116553
\(693\) −7240.08 −0.396866
\(694\) −3809.87 −0.208387
\(695\) −15420.6 −0.841634
\(696\) 1148.68 0.0625582
\(697\) −15641.2 −0.850001
\(698\) 12779.9 0.693018
\(699\) −11361.4 −0.614772
\(700\) −1585.71 −0.0856204
\(701\) 22781.9 1.22747 0.613737 0.789510i \(-0.289665\pi\)
0.613737 + 0.789510i \(0.289665\pi\)
\(702\) 1198.82 0.0644536
\(703\) −4305.18 −0.230972
\(704\) 3246.81 0.173819
\(705\) 8415.71 0.449580
\(706\) −20460.5 −1.09071
\(707\) −9773.31 −0.519891
\(708\) −6445.99 −0.342168
\(709\) −16970.4 −0.898924 −0.449462 0.893299i \(-0.648384\pi\)
−0.449462 + 0.893299i \(0.648384\pi\)
\(710\) −283.320 −0.0149758
\(711\) −1984.73 −0.104688
\(712\) −11426.6 −0.601447
\(713\) −1220.13 −0.0640871
\(714\) 5235.08 0.274395
\(715\) 5631.26 0.294542
\(716\) −1217.64 −0.0635549
\(717\) 8104.23 0.422117
\(718\) −1163.89 −0.0604958
\(719\) −7479.87 −0.387972 −0.193986 0.981004i \(-0.562142\pi\)
−0.193986 + 0.981004i \(0.562142\pi\)
\(720\) 720.000 0.0372678
\(721\) 28470.4 1.47059
\(722\) 722.000 0.0372161
\(723\) −15296.2 −0.786819
\(724\) −4847.90 −0.248855
\(725\) 1196.54 0.0612942
\(726\) 7456.04 0.381157
\(727\) −15908.9 −0.811595 −0.405797 0.913963i \(-0.633006\pi\)
−0.405797 + 0.913963i \(0.633006\pi\)
\(728\) −2816.26 −0.143376
\(729\) 729.000 0.0370370
\(730\) 6637.99 0.336552
\(731\) −18773.0 −0.949855
\(732\) −9212.79 −0.465184
\(733\) 1892.84 0.0953804 0.0476902 0.998862i \(-0.484814\pi\)
0.0476902 + 0.998862i \(0.484814\pi\)
\(734\) 20094.8 1.01051
\(735\) −1373.28 −0.0689172
\(736\) 4748.62 0.237821
\(737\) −23190.6 −1.15907
\(738\) 5116.74 0.255217
\(739\) −1412.05 −0.0702886 −0.0351443 0.999382i \(-0.511189\pi\)
−0.0351443 + 0.999382i \(0.511189\pi\)
\(740\) −4531.77 −0.225123
\(741\) 1265.42 0.0627345
\(742\) −13642.7 −0.674986
\(743\) −29072.8 −1.43550 −0.717751 0.696300i \(-0.754828\pi\)
−0.717751 + 0.696300i \(0.754828\pi\)
\(744\) −197.333 −0.00972387
\(745\) 4557.83 0.224142
\(746\) 28160.8 1.38209
\(747\) −2847.84 −0.139487
\(748\) −11165.7 −0.545798
\(749\) −14806.7 −0.722330
\(750\) 750.000 0.0365148
\(751\) 12794.4 0.621668 0.310834 0.950464i \(-0.399392\pi\)
0.310834 + 0.950464i \(0.399392\pi\)
\(752\) 8976.76 0.435304
\(753\) −16442.5 −0.795746
\(754\) 2125.08 0.102640
\(755\) −13857.4 −0.667975
\(756\) −1712.57 −0.0823883
\(757\) 3334.12 0.160080 0.0800401 0.996792i \(-0.474495\pi\)
0.0800401 + 0.996792i \(0.474495\pi\)
\(758\) 11030.7 0.528568
\(759\) 22584.8 1.08007
\(760\) 760.000 0.0362738
\(761\) 37410.1 1.78202 0.891009 0.453985i \(-0.149998\pi\)
0.891009 + 0.453985i \(0.149998\pi\)
\(762\) −3866.24 −0.183805
\(763\) −29620.9 −1.40544
\(764\) −853.233 −0.0404043
\(765\) −2476.05 −0.117022
\(766\) 6730.61 0.317476
\(767\) −11925.3 −0.561403
\(768\) 768.000 0.0360844
\(769\) 15438.0 0.723941 0.361970 0.932190i \(-0.382104\pi\)
0.361970 + 0.932190i \(0.382104\pi\)
\(770\) −8044.54 −0.376500
\(771\) −3863.82 −0.180483
\(772\) 346.327 0.0161458
\(773\) −24903.7 −1.15876 −0.579381 0.815057i \(-0.696706\pi\)
−0.579381 + 0.815057i \(0.696706\pi\)
\(774\) 6141.27 0.285198
\(775\) −205.555 −0.00952741
\(776\) 12416.7 0.574399
\(777\) 10779.1 0.497682
\(778\) 10783.2 0.496910
\(779\) 5401.01 0.248410
\(780\) 1332.02 0.0611460
\(781\) −1437.32 −0.0658533
\(782\) −16330.3 −0.746767
\(783\) 1292.26 0.0589804
\(784\) −1464.83 −0.0667288
\(785\) 12731.8 0.578875
\(786\) −5410.19 −0.245515
\(787\) −2237.73 −0.101355 −0.0506775 0.998715i \(-0.516138\pi\)
−0.0506775 + 0.998715i \(0.516138\pi\)
\(788\) −18779.5 −0.848976
\(789\) −12208.6 −0.550873
\(790\) −2205.26 −0.0993158
\(791\) 11427.1 0.513654
\(792\) 3652.66 0.163878
\(793\) −17043.9 −0.763237
\(794\) 8761.55 0.391607
\(795\) 6452.64 0.287864
\(796\) 16824.2 0.749143
\(797\) −9047.59 −0.402111 −0.201055 0.979580i \(-0.564437\pi\)
−0.201055 + 0.979580i \(0.564437\pi\)
\(798\) −1807.71 −0.0801908
\(799\) −30870.8 −1.36687
\(800\) 800.000 0.0353553
\(801\) −12854.9 −0.567050
\(802\) −19270.3 −0.848453
\(803\) 33675.4 1.47993
\(804\) −5485.50 −0.240620
\(805\) −11765.5 −0.515132
\(806\) −365.070 −0.0159542
\(807\) −6909.73 −0.301405
\(808\) 4930.69 0.214679
\(809\) −6467.14 −0.281054 −0.140527 0.990077i \(-0.544880\pi\)
−0.140527 + 0.990077i \(0.544880\pi\)
\(810\) 810.000 0.0351364
\(811\) −10840.0 −0.469352 −0.234676 0.972074i \(-0.575403\pi\)
−0.234676 + 0.972074i \(0.575403\pi\)
\(812\) −3035.78 −0.131201
\(813\) −13726.5 −0.592138
\(814\) −22990.3 −0.989939
\(815\) 13826.8 0.594274
\(816\) −2641.12 −0.113306
\(817\) 6482.45 0.277591
\(818\) −3675.62 −0.157109
\(819\) −3168.30 −0.135176
\(820\) 5685.27 0.242120
\(821\) −3920.48 −0.166657 −0.0833286 0.996522i \(-0.526555\pi\)
−0.0833286 + 0.996522i \(0.526555\pi\)
\(822\) −11037.3 −0.468333
\(823\) 138.929 0.00588427 0.00294214 0.999996i \(-0.499063\pi\)
0.00294214 + 0.999996i \(0.499063\pi\)
\(824\) −14363.5 −0.607252
\(825\) 3804.85 0.160567
\(826\) 17035.8 0.717617
\(827\) −23967.6 −1.00778 −0.503890 0.863768i \(-0.668098\pi\)
−0.503890 + 0.863768i \(0.668098\pi\)
\(828\) 5342.20 0.224220
\(829\) −26196.6 −1.09752 −0.548760 0.835980i \(-0.684900\pi\)
−0.548760 + 0.835980i \(0.684900\pi\)
\(830\) −3164.27 −0.132329
\(831\) 6771.78 0.282684
\(832\) 1420.82 0.0592044
\(833\) 5037.50 0.209531
\(834\) −18504.7 −0.768304
\(835\) −12758.1 −0.528759
\(836\) 3855.59 0.159507
\(837\) −221.999 −0.00916775
\(838\) 11625.2 0.479220
\(839\) 3239.87 0.133317 0.0666583 0.997776i \(-0.478766\pi\)
0.0666583 + 0.997776i \(0.478766\pi\)
\(840\) −1902.85 −0.0781604
\(841\) −22098.3 −0.906075
\(842\) 17985.3 0.736120
\(843\) 13385.9 0.546899
\(844\) 16593.9 0.676759
\(845\) −8520.73 −0.346890
\(846\) 10098.9 0.410409
\(847\) −19705.2 −0.799385
\(848\) 6882.82 0.278723
\(849\) 3945.52 0.159493
\(850\) −2751.17 −0.111017
\(851\) −33624.5 −1.35445
\(852\) −339.984 −0.0136710
\(853\) −34062.5 −1.36726 −0.683632 0.729827i \(-0.739601\pi\)
−0.683632 + 0.729827i \(0.739601\pi\)
\(854\) 24348.1 0.975613
\(855\) 855.000 0.0341993
\(856\) 7470.06 0.298273
\(857\) 7779.69 0.310092 0.155046 0.987907i \(-0.450447\pi\)
0.155046 + 0.987907i \(0.450447\pi\)
\(858\) 6757.52 0.268879
\(859\) −17297.7 −0.687068 −0.343534 0.939140i \(-0.611624\pi\)
−0.343534 + 0.939140i \(0.611624\pi\)
\(860\) 6823.63 0.270563
\(861\) −13522.8 −0.535256
\(862\) 295.850 0.0116899
\(863\) −14014.6 −0.552796 −0.276398 0.961043i \(-0.589141\pi\)
−0.276398 + 0.961043i \(0.589141\pi\)
\(864\) 864.000 0.0340207
\(865\) 2652.12 0.104248
\(866\) 18616.2 0.730489
\(867\) −5656.27 −0.221565
\(868\) 521.521 0.0203935
\(869\) −11187.6 −0.436723
\(870\) 1435.85 0.0559537
\(871\) −10148.3 −0.394790
\(872\) 14943.9 0.580349
\(873\) 13968.8 0.541548
\(874\) 5638.99 0.218240
\(875\) −1982.14 −0.0765812
\(876\) 7965.58 0.307229
\(877\) 34301.0 1.32071 0.660355 0.750954i \(-0.270406\pi\)
0.660355 + 0.750954i \(0.270406\pi\)
\(878\) −1665.45 −0.0640163
\(879\) 14715.4 0.564664
\(880\) 4058.51 0.155469
\(881\) 4025.57 0.153944 0.0769721 0.997033i \(-0.475475\pi\)
0.0769721 + 0.997033i \(0.475475\pi\)
\(882\) −1647.93 −0.0629125
\(883\) 12216.0 0.465573 0.232786 0.972528i \(-0.425216\pi\)
0.232786 + 0.972528i \(0.425216\pi\)
\(884\) −4886.15 −0.185904
\(885\) −8057.49 −0.306045
\(886\) −313.415 −0.0118842
\(887\) 14443.0 0.546728 0.273364 0.961911i \(-0.411864\pi\)
0.273364 + 0.961911i \(0.411864\pi\)
\(888\) −5438.13 −0.205509
\(889\) 10217.9 0.385487
\(890\) −14283.3 −0.537950
\(891\) 4109.24 0.154506
\(892\) −18983.0 −0.712555
\(893\) 10659.9 0.399462
\(894\) 5469.39 0.204613
\(895\) −1522.05 −0.0568452
\(896\) −2029.71 −0.0756784
\(897\) 9883.21 0.367883
\(898\) −9214.75 −0.342428
\(899\) −393.527 −0.0145994
\(900\) 900.000 0.0333333
\(901\) −23669.8 −0.875199
\(902\) 28842.2 1.06468
\(903\) −16230.5 −0.598135
\(904\) −5765.03 −0.212104
\(905\) −6059.88 −0.222583
\(906\) −16628.8 −0.609775
\(907\) 16427.3 0.601387 0.300693 0.953721i \(-0.402782\pi\)
0.300693 + 0.953721i \(0.402782\pi\)
\(908\) −16852.6 −0.615940
\(909\) 5547.02 0.202402
\(910\) −3520.33 −0.128239
\(911\) 7719.97 0.280762 0.140381 0.990098i \(-0.455167\pi\)
0.140381 + 0.990098i \(0.455167\pi\)
\(912\) 912.000 0.0331133
\(913\) −16052.8 −0.581894
\(914\) 15314.0 0.554203
\(915\) −11516.0 −0.416073
\(916\) −10386.6 −0.374655
\(917\) 14298.3 0.514910
\(918\) −2971.27 −0.106826
\(919\) −36761.3 −1.31953 −0.659763 0.751474i \(-0.729343\pi\)
−0.659763 + 0.751474i \(0.729343\pi\)
\(920\) 5935.78 0.212714
\(921\) −5614.41 −0.200870
\(922\) −24635.7 −0.879971
\(923\) −628.979 −0.0224302
\(924\) −9653.44 −0.343696
\(925\) −5664.72 −0.201356
\(926\) 21503.5 0.763121
\(927\) −16158.9 −0.572523
\(928\) 1531.57 0.0541770
\(929\) 7843.88 0.277018 0.138509 0.990361i \(-0.455769\pi\)
0.138509 + 0.990361i \(0.455769\pi\)
\(930\) −246.666 −0.00869730
\(931\) −1739.49 −0.0612345
\(932\) −15148.5 −0.532408
\(933\) −15550.0 −0.545641
\(934\) −23237.6 −0.814087
\(935\) −13957.1 −0.488177
\(936\) 1598.42 0.0558184
\(937\) −49214.3 −1.71586 −0.857930 0.513767i \(-0.828250\pi\)
−0.857930 + 0.513767i \(0.828250\pi\)
\(938\) 14497.4 0.504643
\(939\) 18524.2 0.643785
\(940\) 11220.9 0.389348
\(941\) 8370.20 0.289969 0.144984 0.989434i \(-0.453687\pi\)
0.144984 + 0.989434i \(0.453687\pi\)
\(942\) 15278.2 0.528439
\(943\) 42183.1 1.45670
\(944\) −8594.66 −0.296327
\(945\) −2140.71 −0.0736903
\(946\) 34617.2 1.18975
\(947\) −31820.3 −1.09189 −0.545945 0.837821i \(-0.683829\pi\)
−0.545945 + 0.837821i \(0.683829\pi\)
\(948\) −2646.31 −0.0906625
\(949\) 14736.5 0.504076
\(950\) 950.000 0.0324443
\(951\) 180.179 0.00614374
\(952\) 6980.10 0.237633
\(953\) −53391.9 −1.81483 −0.907415 0.420235i \(-0.861948\pi\)
−0.907415 + 0.420235i \(0.861948\pi\)
\(954\) 7743.17 0.262783
\(955\) −1066.54 −0.0361387
\(956\) 10805.6 0.365564
\(957\) 7284.25 0.246046
\(958\) 4391.47 0.148102
\(959\) 29169.9 0.982217
\(960\) 960.000 0.0322749
\(961\) −29723.4 −0.997731
\(962\) −10060.7 −0.337182
\(963\) 8403.82 0.281214
\(964\) −20394.9 −0.681405
\(965\) 432.909 0.0144413
\(966\) −14118.7 −0.470249
\(967\) 12889.7 0.428650 0.214325 0.976762i \(-0.431245\pi\)
0.214325 + 0.976762i \(0.431245\pi\)
\(968\) 9941.39 0.330091
\(969\) −3136.34 −0.103977
\(970\) 15520.9 0.513758
\(971\) −51052.1 −1.68727 −0.843636 0.536916i \(-0.819589\pi\)
−0.843636 + 0.536916i \(0.819589\pi\)
\(972\) 972.000 0.0320750
\(973\) 48905.2 1.61133
\(974\) −3266.14 −0.107448
\(975\) 1665.02 0.0546907
\(976\) −12283.7 −0.402861
\(977\) −26920.8 −0.881548 −0.440774 0.897618i \(-0.645296\pi\)
−0.440774 + 0.897618i \(0.645296\pi\)
\(978\) 16592.2 0.542495
\(979\) −72460.9 −2.36554
\(980\) −1831.04 −0.0596840
\(981\) 16811.9 0.547158
\(982\) −17017.4 −0.553002
\(983\) 10536.9 0.341886 0.170943 0.985281i \(-0.445319\pi\)
0.170943 + 0.985281i \(0.445319\pi\)
\(984\) 6822.32 0.221024
\(985\) −23474.4 −0.759347
\(986\) −5267.01 −0.170117
\(987\) −26689.8 −0.860735
\(988\) 1687.22 0.0543297
\(989\) 50629.5 1.62783
\(990\) 4565.82 0.146577
\(991\) −14974.1 −0.479987 −0.239994 0.970774i \(-0.577145\pi\)
−0.239994 + 0.970774i \(0.577145\pi\)
\(992\) −263.110 −0.00842112
\(993\) −16417.1 −0.524653
\(994\) 898.528 0.0286716
\(995\) 21030.2 0.670054
\(996\) −3797.12 −0.120800
\(997\) −26765.1 −0.850210 −0.425105 0.905144i \(-0.639763\pi\)
−0.425105 + 0.905144i \(0.639763\pi\)
\(998\) −11262.3 −0.357217
\(999\) −6117.89 −0.193755
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.1.1 4
3.2 odd 2 1710.4.a.bc.1.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
570.4.a.s.1.1 4 1.1 even 1 trivial
1710.4.a.bc.1.1 4 3.2 odd 2