Properties

Label 354.4.a.b.1.1
Level 354
Weight 4
Character 354.1
Self dual yes
Analytic conductor 20.887
Analytic rank 0
Dimension 2
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 354 = 2 \cdot 3 \cdot 59 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 354.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(20.8866761420\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{51}) \)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-7.14143\)
Character \(\chi\) = 354.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +5.85857 q^{5} -6.00000 q^{6} +28.5657 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +5.85857 q^{5} -6.00000 q^{6} +28.5657 q^{7} -8.00000 q^{8} +9.00000 q^{9} -11.7171 q^{10} -2.56571 q^{11} +12.0000 q^{12} +82.9900 q^{13} -57.1314 q^{14} +17.5757 q^{15} +16.0000 q^{16} -74.8486 q^{17} -18.0000 q^{18} +34.0000 q^{19} +23.4343 q^{20} +85.6971 q^{21} +5.13143 q^{22} +15.1514 q^{23} -24.0000 q^{24} -90.6771 q^{25} -165.980 q^{26} +27.0000 q^{27} +114.263 q^{28} +239.273 q^{29} -35.1514 q^{30} -242.404 q^{31} -32.0000 q^{32} -7.69714 q^{33} +149.697 q^{34} +167.354 q^{35} +36.0000 q^{36} -269.010 q^{37} -68.0000 q^{38} +248.970 q^{39} -46.8686 q^{40} -179.454 q^{41} -171.394 q^{42} +441.131 q^{43} -10.2629 q^{44} +52.7271 q^{45} -30.3029 q^{46} -249.374 q^{47} +48.0000 q^{48} +473.000 q^{49} +181.354 q^{50} -224.546 q^{51} +331.960 q^{52} -19.2729 q^{53} -54.0000 q^{54} -15.0314 q^{55} -228.526 q^{56} +102.000 q^{57} -478.546 q^{58} +59.0000 q^{59} +70.3029 q^{60} +789.253 q^{61} +484.809 q^{62} +257.091 q^{63} +64.0000 q^{64} +486.203 q^{65} +15.3943 q^{66} +829.980 q^{67} -299.394 q^{68} +45.4543 q^{69} -334.709 q^{70} -825.961 q^{71} -72.0000 q^{72} +913.274 q^{73} +538.020 q^{74} -272.031 q^{75} +136.000 q^{76} -73.2914 q^{77} -497.940 q^{78} -1227.23 q^{79} +93.7371 q^{80} +81.0000 q^{81} +358.909 q^{82} +873.577 q^{83} +342.789 q^{84} -438.506 q^{85} -882.263 q^{86} +717.819 q^{87} +20.5257 q^{88} -888.729 q^{89} -105.454 q^{90} +2370.67 q^{91} +60.6057 q^{92} -727.213 q^{93} +498.749 q^{94} +199.191 q^{95} -96.0000 q^{96} +384.386 q^{97} -946.000 q^{98} -23.0914 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 4q^{2} + 6q^{3} + 8q^{4} + 26q^{5} - 12q^{6} - 16q^{8} + 18q^{9} + O(q^{10}) \) \( 2q - 4q^{2} + 6q^{3} + 8q^{4} + 26q^{5} - 12q^{6} - 16q^{8} + 18q^{9} - 52q^{10} + 52q^{11} + 24q^{12} + 66q^{13} + 78q^{15} + 32q^{16} - 64q^{17} - 36q^{18} + 68q^{19} + 104q^{20} - 104q^{22} + 116q^{23} - 48q^{24} + 190q^{25} - 132q^{26} + 54q^{27} + 350q^{29} - 156q^{30} - 242q^{31} - 64q^{32} + 156q^{33} + 128q^{34} - 408q^{35} + 72q^{36} - 638q^{37} - 136q^{38} + 198q^{39} - 208q^{40} - 616q^{41} + 768q^{43} + 208q^{44} + 234q^{45} - 232q^{46} + 44q^{47} + 96q^{48} + 946q^{49} - 380q^{50} - 192q^{51} + 264q^{52} + 90q^{53} - 108q^{54} + 1084q^{55} + 204q^{57} - 700q^{58} + 118q^{59} + 312q^{60} + 1250q^{61} + 484q^{62} + 128q^{64} + 144q^{65} - 312q^{66} + 1460q^{67} - 256q^{68} + 348q^{69} + 816q^{70} + 162q^{71} - 144q^{72} + 284q^{73} + 1276q^{74} + 570q^{75} + 272q^{76} - 1632q^{77} - 396q^{78} - 512q^{79} + 416q^{80} + 162q^{81} + 1232q^{82} + 376q^{83} - 220q^{85} - 1536q^{86} + 1050q^{87} - 416q^{88} - 492q^{89} - 468q^{90} + 2856q^{91} + 464q^{92} - 726q^{93} - 88q^{94} + 884q^{95} - 192q^{96} - 1088q^{97} - 1892q^{98} + 468q^{99} + O(q^{100}) \)

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
\(5\) 5.85857 0.524007 0.262003 0.965067i \(-0.415617\pi\)
0.262003 + 0.965067i \(0.415617\pi\)
\(6\) −6.00000 −0.408248
\(7\) 28.5657 1.54240 0.771202 0.636591i \(-0.219656\pi\)
0.771202 + 0.636591i \(0.219656\pi\)
\(8\) −8.00000 −0.353553
\(9\) 9.00000 0.333333
\(10\) −11.7171 −0.370529
\(11\) −2.56571 −0.0703265 −0.0351633 0.999382i \(-0.511195\pi\)
−0.0351633 + 0.999382i \(0.511195\pi\)
\(12\) 12.0000 0.288675
\(13\) 82.9900 1.77056 0.885280 0.465058i \(-0.153967\pi\)
0.885280 + 0.465058i \(0.153967\pi\)
\(14\) −57.1314 −1.09064
\(15\) 17.5757 0.302535
\(16\) 16.0000 0.250000
\(17\) −74.8486 −1.06785 −0.533925 0.845532i \(-0.679283\pi\)
−0.533925 + 0.845532i \(0.679283\pi\)
\(18\) −18.0000 −0.235702
\(19\) 34.0000 0.410533 0.205267 0.978706i \(-0.434194\pi\)
0.205267 + 0.978706i \(0.434194\pi\)
\(20\) 23.4343 0.262003
\(21\) 85.6971 0.890507
\(22\) 5.13143 0.0497284
\(23\) 15.1514 0.137360 0.0686802 0.997639i \(-0.478121\pi\)
0.0686802 + 0.997639i \(0.478121\pi\)
\(24\) −24.0000 −0.204124
\(25\) −90.6771 −0.725417
\(26\) −165.980 −1.25198
\(27\) 27.0000 0.192450
\(28\) 114.263 0.771202
\(29\) 239.273 1.53213 0.766066 0.642761i \(-0.222211\pi\)
0.766066 + 0.642761i \(0.222211\pi\)
\(30\) −35.1514 −0.213925
\(31\) −242.404 −1.40442 −0.702211 0.711969i \(-0.747804\pi\)
−0.702211 + 0.711969i \(0.747804\pi\)
\(32\) −32.0000 −0.176777
\(33\) −7.69714 −0.0406030
\(34\) 149.697 0.755084
\(35\) 167.354 0.808230
\(36\) 36.0000 0.166667
\(37\) −269.010 −1.19527 −0.597635 0.801768i \(-0.703893\pi\)
−0.597635 + 0.801768i \(0.703893\pi\)
\(38\) −68.0000 −0.290291
\(39\) 248.970 1.02223
\(40\) −46.8686 −0.185264
\(41\) −179.454 −0.683562 −0.341781 0.939780i \(-0.611030\pi\)
−0.341781 + 0.939780i \(0.611030\pi\)
\(42\) −171.394 −0.629684
\(43\) 441.131 1.56446 0.782232 0.622988i \(-0.214081\pi\)
0.782232 + 0.622988i \(0.214081\pi\)
\(44\) −10.2629 −0.0351633
\(45\) 52.7271 0.174669
\(46\) −30.3029 −0.0971285
\(47\) −249.374 −0.773936 −0.386968 0.922093i \(-0.626478\pi\)
−0.386968 + 0.922093i \(0.626478\pi\)
\(48\) 48.0000 0.144338
\(49\) 473.000 1.37901
\(50\) 181.354 0.512947
\(51\) −224.546 −0.616523
\(52\) 331.960 0.885280
\(53\) −19.2729 −0.0499496 −0.0249748 0.999688i \(-0.507951\pi\)
−0.0249748 + 0.999688i \(0.507951\pi\)
\(54\) −54.0000 −0.136083
\(55\) −15.0314 −0.0368516
\(56\) −228.526 −0.545322
\(57\) 102.000 0.237022
\(58\) −478.546 −1.08338
\(59\) 59.0000 0.130189
\(60\) 70.3029 0.151268
\(61\) 789.253 1.65661 0.828307 0.560274i \(-0.189304\pi\)
0.828307 + 0.560274i \(0.189304\pi\)
\(62\) 484.809 0.993077
\(63\) 257.091 0.514135
\(64\) 64.0000 0.125000
\(65\) 486.203 0.927785
\(66\) 15.3943 0.0287107
\(67\) 829.980 1.51341 0.756703 0.653759i \(-0.226809\pi\)
0.756703 + 0.653759i \(0.226809\pi\)
\(68\) −299.394 −0.533925
\(69\) 45.4543 0.0793051
\(70\) −334.709 −0.571505
\(71\) −825.961 −1.38061 −0.690307 0.723517i \(-0.742525\pi\)
−0.690307 + 0.723517i \(0.742525\pi\)
\(72\) −72.0000 −0.117851
\(73\) 913.274 1.46426 0.732128 0.681167i \(-0.238527\pi\)
0.732128 + 0.681167i \(0.238527\pi\)
\(74\) 538.020 0.845183
\(75\) −272.031 −0.418820
\(76\) 136.000 0.205267
\(77\) −73.2914 −0.108472
\(78\) −497.940 −0.722828
\(79\) −1227.23 −1.74778 −0.873890 0.486123i \(-0.838411\pi\)
−0.873890 + 0.486123i \(0.838411\pi\)
\(80\) 93.7371 0.131002
\(81\) 81.0000 0.111111
\(82\) 358.909 0.483351
\(83\) 873.577 1.15527 0.577636 0.816295i \(-0.303975\pi\)
0.577636 + 0.816295i \(0.303975\pi\)
\(84\) 342.789 0.445254
\(85\) −438.506 −0.559560
\(86\) −882.263 −1.10624
\(87\) 717.819 0.884577
\(88\) 20.5257 0.0248642
\(89\) −888.729 −1.05848 −0.529242 0.848471i \(-0.677524\pi\)
−0.529242 + 0.848471i \(0.677524\pi\)
\(90\) −105.454 −0.123510
\(91\) 2370.67 2.73092
\(92\) 60.6057 0.0686802
\(93\) −727.213 −0.810844
\(94\) 498.749 0.547255
\(95\) 199.191 0.215122
\(96\) −96.0000 −0.102062
\(97\) 384.386 0.402355 0.201178 0.979555i \(-0.435523\pi\)
0.201178 + 0.979555i \(0.435523\pi\)
\(98\) −946.000 −0.975106
\(99\) −23.0914 −0.0234422
\(100\) −362.709 −0.362709
\(101\) 1745.03 1.71918 0.859590 0.510985i \(-0.170719\pi\)
0.859590 + 0.510985i \(0.170719\pi\)
\(102\) 449.091 0.435948
\(103\) 500.221 0.478527 0.239264 0.970955i \(-0.423094\pi\)
0.239264 + 0.970955i \(0.423094\pi\)
\(104\) −663.920 −0.625988
\(105\) 502.063 0.466632
\(106\) 38.5457 0.0353197
\(107\) 1124.57 1.01604 0.508019 0.861346i \(-0.330378\pi\)
0.508019 + 0.861346i \(0.330378\pi\)
\(108\) 108.000 0.0962250
\(109\) −42.2614 −0.0371368 −0.0185684 0.999828i \(-0.505911\pi\)
−0.0185684 + 0.999828i \(0.505911\pi\)
\(110\) 30.0628 0.0260580
\(111\) −807.030 −0.690089
\(112\) 457.051 0.385601
\(113\) 1156.63 0.962889 0.481445 0.876477i \(-0.340112\pi\)
0.481445 + 0.876477i \(0.340112\pi\)
\(114\) −204.000 −0.167600
\(115\) 88.7657 0.0719778
\(116\) 957.091 0.766066
\(117\) 746.910 0.590187
\(118\) −118.000 −0.0920575
\(119\) −2138.10 −1.64706
\(120\) −140.606 −0.106962
\(121\) −1324.42 −0.995054
\(122\) −1578.51 −1.17140
\(123\) −538.363 −0.394655
\(124\) −969.617 −0.702211
\(125\) −1263.56 −0.904130
\(126\) −514.183 −0.363548
\(127\) −933.900 −0.652521 −0.326261 0.945280i \(-0.605789\pi\)
−0.326261 + 0.945280i \(0.605789\pi\)
\(128\) −128.000 −0.0883883
\(129\) 1323.39 0.903243
\(130\) −972.406 −0.656043
\(131\) −2424.02 −1.61670 −0.808351 0.588701i \(-0.799639\pi\)
−0.808351 + 0.588701i \(0.799639\pi\)
\(132\) −30.7886 −0.0203015
\(133\) 971.234 0.633208
\(134\) −1659.96 −1.07014
\(135\) 158.181 0.100845
\(136\) 598.789 0.377542
\(137\) −2958.20 −1.84479 −0.922395 0.386247i \(-0.873771\pi\)
−0.922395 + 0.386247i \(0.873771\pi\)
\(138\) −90.9086 −0.0560772
\(139\) −498.080 −0.303932 −0.151966 0.988386i \(-0.548560\pi\)
−0.151966 + 0.988386i \(0.548560\pi\)
\(140\) 669.417 0.404115
\(141\) −748.123 −0.446832
\(142\) 1651.92 0.976241
\(143\) −212.929 −0.124517
\(144\) 144.000 0.0833333
\(145\) 1401.80 0.802848
\(146\) −1826.55 −1.03539
\(147\) 1419.00 0.796171
\(148\) −1076.04 −0.597635
\(149\) −2904.35 −1.59687 −0.798435 0.602082i \(-0.794338\pi\)
−0.798435 + 0.602082i \(0.794338\pi\)
\(150\) 544.063 0.296150
\(151\) 536.064 0.288903 0.144451 0.989512i \(-0.453858\pi\)
0.144451 + 0.989512i \(0.453858\pi\)
\(152\) −272.000 −0.145145
\(153\) −673.637 −0.355950
\(154\) 146.583 0.0767012
\(155\) −1420.14 −0.735927
\(156\) 995.880 0.511117
\(157\) −1996.04 −1.01466 −0.507330 0.861752i \(-0.669368\pi\)
−0.507330 + 0.861752i \(0.669368\pi\)
\(158\) 2454.47 1.23587
\(159\) −57.8186 −0.0288384
\(160\) −187.474 −0.0926322
\(161\) 432.811 0.211865
\(162\) −162.000 −0.0785674
\(163\) −2393.15 −1.14998 −0.574989 0.818161i \(-0.694994\pi\)
−0.574989 + 0.818161i \(0.694994\pi\)
\(164\) −717.817 −0.341781
\(165\) −45.0943 −0.0212763
\(166\) −1747.15 −0.816900
\(167\) 61.2729 0.0283918 0.0141959 0.999899i \(-0.495481\pi\)
0.0141959 + 0.999899i \(0.495481\pi\)
\(168\) −685.577 −0.314842
\(169\) 4690.34 2.13488
\(170\) 877.011 0.395669
\(171\) 306.000 0.136844
\(172\) 1764.53 0.782232
\(173\) −3133.08 −1.37690 −0.688449 0.725285i \(-0.741708\pi\)
−0.688449 + 0.725285i \(0.741708\pi\)
\(174\) −1435.64 −0.625491
\(175\) −2590.26 −1.11889
\(176\) −41.0514 −0.0175816
\(177\) 177.000 0.0751646
\(178\) 1777.46 0.748461
\(179\) −85.9428 −0.0358864 −0.0179432 0.999839i \(-0.505712\pi\)
−0.0179432 + 0.999839i \(0.505712\pi\)
\(180\) 210.909 0.0873344
\(181\) −4292.06 −1.76258 −0.881289 0.472578i \(-0.843323\pi\)
−0.881289 + 0.472578i \(0.843323\pi\)
\(182\) −4741.34 −1.93105
\(183\) 2367.76 0.956447
\(184\) −121.211 −0.0485643
\(185\) −1576.01 −0.626329
\(186\) 1454.43 0.573353
\(187\) 192.040 0.0750982
\(188\) −997.497 −0.386968
\(189\) 771.274 0.296836
\(190\) −398.383 −0.152114
\(191\) 2606.47 0.987422 0.493711 0.869626i \(-0.335640\pi\)
0.493711 + 0.869626i \(0.335640\pi\)
\(192\) 192.000 0.0721688
\(193\) −2118.45 −0.790099 −0.395049 0.918660i \(-0.629273\pi\)
−0.395049 + 0.918660i \(0.629273\pi\)
\(194\) −768.771 −0.284508
\(195\) 1458.61 0.535657
\(196\) 1892.00 0.689504
\(197\) 3831.92 1.38585 0.692927 0.721008i \(-0.256321\pi\)
0.692927 + 0.721008i \(0.256321\pi\)
\(198\) 46.1828 0.0165761
\(199\) 415.837 0.148130 0.0740651 0.997253i \(-0.476403\pi\)
0.0740651 + 0.997253i \(0.476403\pi\)
\(200\) 725.417 0.256474
\(201\) 2489.94 0.873765
\(202\) −3490.06 −1.21564
\(203\) 6835.00 2.36317
\(204\) −898.183 −0.308262
\(205\) −1051.35 −0.358191
\(206\) −1000.44 −0.338370
\(207\) 136.363 0.0457868
\(208\) 1327.84 0.442640
\(209\) −87.2343 −0.0288714
\(210\) −1004.13 −0.329958
\(211\) 710.026 0.231660 0.115830 0.993269i \(-0.463047\pi\)
0.115830 + 0.993269i \(0.463047\pi\)
\(212\) −77.0914 −0.0249748
\(213\) −2477.88 −0.797098
\(214\) −2249.14 −0.718448
\(215\) 2584.40 0.819789
\(216\) −216.000 −0.0680414
\(217\) −6924.45 −2.16619
\(218\) 84.5229 0.0262597
\(219\) 2739.82 0.845388
\(220\) −60.1257 −0.0184258
\(221\) −6211.68 −1.89069
\(222\) 1614.06 0.487967
\(223\) 2339.69 0.702587 0.351294 0.936265i \(-0.385742\pi\)
0.351294 + 0.936265i \(0.385742\pi\)
\(224\) −914.103 −0.272661
\(225\) −816.094 −0.241806
\(226\) −2313.26 −0.680865
\(227\) −405.617 −0.118598 −0.0592990 0.998240i \(-0.518887\pi\)
−0.0592990 + 0.998240i \(0.518887\pi\)
\(228\) 408.000 0.118511
\(229\) 2445.74 0.705760 0.352880 0.935669i \(-0.385202\pi\)
0.352880 + 0.935669i \(0.385202\pi\)
\(230\) −177.531 −0.0508960
\(231\) −219.874 −0.0626263
\(232\) −1914.18 −0.541691
\(233\) −1010.14 −0.284019 −0.142010 0.989865i \(-0.545356\pi\)
−0.142010 + 0.989865i \(0.545356\pi\)
\(234\) −1493.82 −0.417325
\(235\) −1460.98 −0.405547
\(236\) 236.000 0.0650945
\(237\) −3681.70 −1.00908
\(238\) 4276.21 1.16464
\(239\) 4185.81 1.13288 0.566438 0.824104i \(-0.308321\pi\)
0.566438 + 0.824104i \(0.308321\pi\)
\(240\) 281.211 0.0756338
\(241\) 2986.14 0.798150 0.399075 0.916918i \(-0.369331\pi\)
0.399075 + 0.916918i \(0.369331\pi\)
\(242\) 2648.83 0.703610
\(243\) 243.000 0.0641500
\(244\) 3157.01 0.828307
\(245\) 2771.10 0.722610
\(246\) 1076.73 0.279063
\(247\) 2821.66 0.726874
\(248\) 1939.23 0.496538
\(249\) 2620.73 0.666996
\(250\) 2527.12 0.639316
\(251\) −2092.89 −0.526303 −0.263152 0.964754i \(-0.584762\pi\)
−0.263152 + 0.964754i \(0.584762\pi\)
\(252\) 1028.37 0.257067
\(253\) −38.8742 −0.00966009
\(254\) 1867.80 0.461402
\(255\) −1315.52 −0.323062
\(256\) 256.000 0.0625000
\(257\) −1619.57 −0.393098 −0.196549 0.980494i \(-0.562973\pi\)
−0.196549 + 0.980494i \(0.562973\pi\)
\(258\) −2646.79 −0.638689
\(259\) −7684.46 −1.84359
\(260\) 1944.81 0.463893
\(261\) 2153.46 0.510711
\(262\) 4848.05 1.14318
\(263\) 5558.30 1.30319 0.651595 0.758567i \(-0.274100\pi\)
0.651595 + 0.758567i \(0.274100\pi\)
\(264\) 61.5771 0.0143553
\(265\) −112.911 −0.0261739
\(266\) −1942.47 −0.447746
\(267\) −2666.19 −0.611116
\(268\) 3319.92 0.756703
\(269\) 297.389 0.0674056 0.0337028 0.999432i \(-0.489270\pi\)
0.0337028 + 0.999432i \(0.489270\pi\)
\(270\) −316.363 −0.0713083
\(271\) −2734.07 −0.612852 −0.306426 0.951895i \(-0.599133\pi\)
−0.306426 + 0.951895i \(0.599133\pi\)
\(272\) −1197.58 −0.266962
\(273\) 7112.01 1.57670
\(274\) 5916.41 1.30446
\(275\) 232.652 0.0510161
\(276\) 181.817 0.0396526
\(277\) 760.174 0.164890 0.0824449 0.996596i \(-0.473727\pi\)
0.0824449 + 0.996596i \(0.473727\pi\)
\(278\) 996.160 0.214913
\(279\) −2181.64 −0.468141
\(280\) −1338.83 −0.285752
\(281\) −2050.65 −0.435343 −0.217671 0.976022i \(-0.569846\pi\)
−0.217671 + 0.976022i \(0.569846\pi\)
\(282\) 1496.25 0.315958
\(283\) −4818.39 −1.01210 −0.506049 0.862505i \(-0.668894\pi\)
−0.506049 + 0.862505i \(0.668894\pi\)
\(284\) −3303.85 −0.690307
\(285\) 597.574 0.124201
\(286\) 425.857 0.0880471
\(287\) −5126.24 −1.05433
\(288\) −288.000 −0.0589256
\(289\) 689.309 0.140303
\(290\) −2803.59 −0.567699
\(291\) 1153.16 0.232300
\(292\) 3653.10 0.732128
\(293\) 1876.25 0.374102 0.187051 0.982350i \(-0.440107\pi\)
0.187051 + 0.982350i \(0.440107\pi\)
\(294\) −2838.00 −0.562978
\(295\) 345.656 0.0682198
\(296\) 2152.08 0.422592
\(297\) −69.2743 −0.0135343
\(298\) 5808.70 1.12916
\(299\) 1257.42 0.243205
\(300\) −1088.13 −0.209410
\(301\) 12601.2 2.41303
\(302\) −1072.13 −0.204285
\(303\) 5235.09 0.992569
\(304\) 544.000 0.102633
\(305\) 4623.89 0.868077
\(306\) 1347.27 0.251695
\(307\) 556.954 0.103541 0.0517705 0.998659i \(-0.483514\pi\)
0.0517705 + 0.998659i \(0.483514\pi\)
\(308\) −293.166 −0.0542359
\(309\) 1500.66 0.276278
\(310\) 2840.29 0.520379
\(311\) 3023.63 0.551300 0.275650 0.961258i \(-0.411107\pi\)
0.275650 + 0.961258i \(0.411107\pi\)
\(312\) −1991.76 −0.361414
\(313\) −467.129 −0.0843568 −0.0421784 0.999110i \(-0.513430\pi\)
−0.0421784 + 0.999110i \(0.513430\pi\)
\(314\) 3992.09 0.717473
\(315\) 1506.19 0.269410
\(316\) −4908.94 −0.873890
\(317\) −5033.09 −0.891756 −0.445878 0.895094i \(-0.647108\pi\)
−0.445878 + 0.895094i \(0.647108\pi\)
\(318\) 115.637 0.0203919
\(319\) −613.906 −0.107750
\(320\) 374.949 0.0655008
\(321\) 3373.71 0.586610
\(322\) −865.623 −0.149811
\(323\) −2544.85 −0.438388
\(324\) 324.000 0.0555556
\(325\) −7525.30 −1.28439
\(326\) 4786.31 0.813157
\(327\) −126.784 −0.0214409
\(328\) 1435.63 0.241676
\(329\) −7123.55 −1.19372
\(330\) 90.1885 0.0150446
\(331\) 5335.14 0.885939 0.442970 0.896537i \(-0.353925\pi\)
0.442970 + 0.896537i \(0.353925\pi\)
\(332\) 3494.31 0.577636
\(333\) −2421.09 −0.398423
\(334\) −122.546 −0.0200761
\(335\) 4862.50 0.793035
\(336\) 1371.15 0.222627
\(337\) −10352.7 −1.67343 −0.836715 0.547639i \(-0.815527\pi\)
−0.836715 + 0.547639i \(0.815527\pi\)
\(338\) −9380.68 −1.50959
\(339\) 3469.89 0.555924
\(340\) −1754.02 −0.279780
\(341\) 621.940 0.0987681
\(342\) −612.000 −0.0967637
\(343\) 3713.54 0.584584
\(344\) −3529.05 −0.553121
\(345\) 266.297 0.0415564
\(346\) 6266.15 0.973614
\(347\) 7113.77 1.10054 0.550269 0.834987i \(-0.314525\pi\)
0.550269 + 0.834987i \(0.314525\pi\)
\(348\) 2871.27 0.442289
\(349\) 3342.31 0.512635 0.256318 0.966593i \(-0.417491\pi\)
0.256318 + 0.966593i \(0.417491\pi\)
\(350\) 5180.51 0.791172
\(351\) 2240.73 0.340744
\(352\) 82.1028 0.0124321
\(353\) −12792.3 −1.92880 −0.964400 0.264447i \(-0.914810\pi\)
−0.964400 + 0.264447i \(0.914810\pi\)
\(354\) −354.000 −0.0531494
\(355\) −4838.95 −0.723451
\(356\) −3554.91 −0.529242
\(357\) −6414.31 −0.950928
\(358\) 171.886 0.0253755
\(359\) −5664.03 −0.832691 −0.416345 0.909207i \(-0.636689\pi\)
−0.416345 + 0.909207i \(0.636689\pi\)
\(360\) −421.817 −0.0617548
\(361\) −5703.00 −0.831462
\(362\) 8584.13 1.24633
\(363\) −3973.25 −0.574495
\(364\) 9482.67 1.36546
\(365\) 5350.48 0.767280
\(366\) −4735.52 −0.676310
\(367\) −7565.11 −1.07601 −0.538005 0.842942i \(-0.680822\pi\)
−0.538005 + 0.842942i \(0.680822\pi\)
\(368\) 242.423 0.0343401
\(369\) −1615.09 −0.227854
\(370\) 3152.03 0.442882
\(371\) −550.543 −0.0770425
\(372\) −2908.85 −0.405422
\(373\) −4152.32 −0.576405 −0.288202 0.957570i \(-0.593058\pi\)
−0.288202 + 0.957570i \(0.593058\pi\)
\(374\) −384.080 −0.0531024
\(375\) −3790.68 −0.522000
\(376\) 1994.99 0.273628
\(377\) 19857.3 2.71273
\(378\) −1542.55 −0.209895
\(379\) 2639.87 0.357787 0.178893 0.983868i \(-0.442748\pi\)
0.178893 + 0.983868i \(0.442748\pi\)
\(380\) 796.766 0.107561
\(381\) −2801.70 −0.376733
\(382\) −5212.94 −0.698213
\(383\) −7683.83 −1.02513 −0.512566 0.858648i \(-0.671305\pi\)
−0.512566 + 0.858648i \(0.671305\pi\)
\(384\) −384.000 −0.0510310
\(385\) −429.383 −0.0568400
\(386\) 4236.89 0.558684
\(387\) 3970.18 0.521488
\(388\) 1537.54 0.201178
\(389\) 206.350 0.0268955 0.0134478 0.999910i \(-0.495719\pi\)
0.0134478 + 0.999910i \(0.495719\pi\)
\(390\) −2917.22 −0.378767
\(391\) −1134.06 −0.146680
\(392\) −3784.00 −0.487553
\(393\) −7272.07 −0.933403
\(394\) −7663.85 −0.979947
\(395\) −7189.84 −0.915848
\(396\) −92.3657 −0.0117211
\(397\) −5677.30 −0.717722 −0.358861 0.933391i \(-0.616835\pi\)
−0.358861 + 0.933391i \(0.616835\pi\)
\(398\) −831.674 −0.104744
\(399\) 2913.70 0.365583
\(400\) −1450.83 −0.181354
\(401\) −2969.25 −0.369769 −0.184884 0.982760i \(-0.559191\pi\)
−0.184884 + 0.982760i \(0.559191\pi\)
\(402\) −4979.88 −0.617845
\(403\) −20117.1 −2.48661
\(404\) 6980.13 0.859590
\(405\) 474.544 0.0582230
\(406\) −13670.0 −1.67101
\(407\) 690.203 0.0840592
\(408\) 1796.37 0.217974
\(409\) 1198.04 0.144839 0.0724195 0.997374i \(-0.476928\pi\)
0.0724195 + 0.997374i \(0.476928\pi\)
\(410\) 2102.69 0.253279
\(411\) −8874.61 −1.06509
\(412\) 2000.89 0.239264
\(413\) 1685.38 0.200804
\(414\) −272.726 −0.0323762
\(415\) 5117.91 0.605370
\(416\) −2655.68 −0.312994
\(417\) −1494.24 −0.175475
\(418\) 174.469 0.0204152
\(419\) 11776.3 1.37305 0.686526 0.727105i \(-0.259135\pi\)
0.686526 + 0.727105i \(0.259135\pi\)
\(420\) 2008.25 0.233316
\(421\) −10303.0 −1.19272 −0.596362 0.802715i \(-0.703388\pi\)
−0.596362 + 0.802715i \(0.703388\pi\)
\(422\) −1420.05 −0.163808
\(423\) −2244.37 −0.257979
\(424\) 154.183 0.0176599
\(425\) 6787.05 0.774636
\(426\) 4955.77 0.563633
\(427\) 22545.6 2.55517
\(428\) 4498.27 0.508019
\(429\) −638.786 −0.0718901
\(430\) −5168.80 −0.579678
\(431\) 14017.8 1.56662 0.783310 0.621631i \(-0.213530\pi\)
0.783310 + 0.621631i \(0.213530\pi\)
\(432\) 432.000 0.0481125
\(433\) −6668.16 −0.740072 −0.370036 0.929017i \(-0.620655\pi\)
−0.370036 + 0.929017i \(0.620655\pi\)
\(434\) 13848.9 1.53172
\(435\) 4205.39 0.463524
\(436\) −169.046 −0.0185684
\(437\) 515.149 0.0563911
\(438\) −5479.65 −0.597780
\(439\) 11331.8 1.23198 0.615988 0.787756i \(-0.288757\pi\)
0.615988 + 0.787756i \(0.288757\pi\)
\(440\) 120.251 0.0130290
\(441\) 4257.00 0.459670
\(442\) 12423.4 1.33692
\(443\) 1013.77 0.108726 0.0543628 0.998521i \(-0.482687\pi\)
0.0543628 + 0.998521i \(0.482687\pi\)
\(444\) −3228.12 −0.345045
\(445\) −5206.68 −0.554652
\(446\) −4679.37 −0.496804
\(447\) −8713.05 −0.921953
\(448\) 1828.21 0.192800
\(449\) 15549.2 1.63433 0.817163 0.576407i \(-0.195546\pi\)
0.817163 + 0.576407i \(0.195546\pi\)
\(450\) 1632.19 0.170982
\(451\) 460.428 0.0480726
\(452\) 4626.51 0.481445
\(453\) 1608.19 0.166798
\(454\) 811.234 0.0838615
\(455\) 13888.7 1.43102
\(456\) −816.000 −0.0837998
\(457\) −7003.64 −0.716885 −0.358442 0.933552i \(-0.616692\pi\)
−0.358442 + 0.933552i \(0.616692\pi\)
\(458\) −4891.48 −0.499047
\(459\) −2020.91 −0.205508
\(460\) 355.063 0.0359889
\(461\) −7990.32 −0.807258 −0.403629 0.914923i \(-0.632251\pi\)
−0.403629 + 0.914923i \(0.632251\pi\)
\(462\) 439.749 0.0442835
\(463\) −2385.84 −0.239480 −0.119740 0.992805i \(-0.538206\pi\)
−0.119740 + 0.992805i \(0.538206\pi\)
\(464\) 3828.37 0.383033
\(465\) −4260.43 −0.424887
\(466\) 2020.28 0.200832
\(467\) 5687.82 0.563599 0.281800 0.959473i \(-0.409069\pi\)
0.281800 + 0.959473i \(0.409069\pi\)
\(468\) 2987.64 0.295093
\(469\) 23709.0 2.33428
\(470\) 2921.95 0.286765
\(471\) −5988.13 −0.585814
\(472\) −472.000 −0.0460287
\(473\) −1131.82 −0.110023
\(474\) 7363.41 0.713528
\(475\) −3083.02 −0.297808
\(476\) −8552.41 −0.823528
\(477\) −173.456 −0.0166499
\(478\) −8371.61 −0.801064
\(479\) −13880.1 −1.32400 −0.662000 0.749504i \(-0.730292\pi\)
−0.662000 + 0.749504i \(0.730292\pi\)
\(480\) −562.423 −0.0534812
\(481\) −22325.1 −2.11630
\(482\) −5972.28 −0.564377
\(483\) 1298.43 0.122320
\(484\) −5297.67 −0.497527
\(485\) 2251.95 0.210837
\(486\) −486.000 −0.0453609
\(487\) 11256.2 1.04736 0.523681 0.851914i \(-0.324558\pi\)
0.523681 + 0.851914i \(0.324558\pi\)
\(488\) −6314.02 −0.585702
\(489\) −7179.46 −0.663940
\(490\) −5542.21 −0.510962
\(491\) −1621.08 −0.148999 −0.0744994 0.997221i \(-0.523736\pi\)
−0.0744994 + 0.997221i \(0.523736\pi\)
\(492\) −2153.45 −0.197327
\(493\) −17909.2 −1.63609
\(494\) −5643.32 −0.513978
\(495\) −135.283 −0.0122839
\(496\) −3878.47 −0.351106
\(497\) −23594.2 −2.12946
\(498\) −5241.46 −0.471638
\(499\) 17760.9 1.59337 0.796683 0.604398i \(-0.206586\pi\)
0.796683 + 0.604398i \(0.206586\pi\)
\(500\) −5054.24 −0.452065
\(501\) 183.819 0.0163920
\(502\) 4185.78 0.372153
\(503\) −19375.0 −1.71747 −0.858737 0.512416i \(-0.828751\pi\)
−0.858737 + 0.512416i \(0.828751\pi\)
\(504\) −2056.73 −0.181774
\(505\) 10223.4 0.900861
\(506\) 77.7485 0.00683071
\(507\) 14071.0 1.23258
\(508\) −3735.60 −0.326261
\(509\) −7180.52 −0.625287 −0.312643 0.949871i \(-0.601215\pi\)
−0.312643 + 0.949871i \(0.601215\pi\)
\(510\) 2631.03 0.228440
\(511\) 26088.3 2.25847
\(512\) −512.000 −0.0441942
\(513\) 918.000 0.0790072
\(514\) 3239.14 0.277962
\(515\) 2930.58 0.250751
\(516\) 5293.58 0.451622
\(517\) 639.823 0.0544282
\(518\) 15368.9 1.30361
\(519\) −9399.23 −0.794953
\(520\) −3889.62 −0.328022
\(521\) 8578.05 0.721327 0.360664 0.932696i \(-0.382550\pi\)
0.360664 + 0.932696i \(0.382550\pi\)
\(522\) −4306.91 −0.361127
\(523\) −5665.17 −0.473653 −0.236826 0.971552i \(-0.576107\pi\)
−0.236826 + 0.971552i \(0.576107\pi\)
\(524\) −9696.09 −0.808351
\(525\) −7770.77 −0.645989
\(526\) −11116.6 −0.921495
\(527\) 18143.6 1.49971
\(528\) −123.154 −0.0101508
\(529\) −11937.4 −0.981132
\(530\) 225.823 0.0185078
\(531\) 531.000 0.0433963
\(532\) 3884.94 0.316604
\(533\) −14892.9 −1.21029
\(534\) 5332.37 0.432124
\(535\) 6588.37 0.532411
\(536\) −6639.84 −0.535070
\(537\) −257.828 −0.0207190
\(538\) −594.777 −0.0476630
\(539\) −1213.58 −0.0969809
\(540\) 632.726 0.0504226
\(541\) −15726.2 −1.24976 −0.624881 0.780720i \(-0.714852\pi\)
−0.624881 + 0.780720i \(0.714852\pi\)
\(542\) 5468.14 0.433352
\(543\) −12876.2 −1.01762
\(544\) 2395.15 0.188771
\(545\) −247.592 −0.0194599
\(546\) −14224.0 −1.11489
\(547\) −12232.3 −0.956153 −0.478077 0.878318i \(-0.658666\pi\)
−0.478077 + 0.878318i \(0.658666\pi\)
\(548\) −11832.8 −0.922395
\(549\) 7103.28 0.552205
\(550\) −465.303 −0.0360738
\(551\) 8135.28 0.628992
\(552\) −363.634 −0.0280386
\(553\) −35056.8 −2.69578
\(554\) −1520.35 −0.116595
\(555\) −4728.04 −0.361611
\(556\) −1992.32 −0.151966
\(557\) 350.487 0.0266618 0.0133309 0.999911i \(-0.495757\pi\)
0.0133309 + 0.999911i \(0.495757\pi\)
\(558\) 4363.28 0.331026
\(559\) 36609.5 2.76998
\(560\) 2677.67 0.202057
\(561\) 576.120 0.0433579
\(562\) 4101.29 0.307834
\(563\) −2402.60 −0.179853 −0.0899267 0.995948i \(-0.528663\pi\)
−0.0899267 + 0.995948i \(0.528663\pi\)
\(564\) −2992.49 −0.223416
\(565\) 6776.19 0.504560
\(566\) 9636.78 0.715661
\(567\) 2313.82 0.171378
\(568\) 6607.69 0.488121
\(569\) −61.7656 −0.00455070 −0.00227535 0.999997i \(-0.500724\pi\)
−0.00227535 + 0.999997i \(0.500724\pi\)
\(570\) −1195.15 −0.0878233
\(571\) 22744.5 1.66695 0.833473 0.552561i \(-0.186349\pi\)
0.833473 + 0.552561i \(0.186349\pi\)
\(572\) −851.714 −0.0622587
\(573\) 7819.41 0.570088
\(574\) 10252.5 0.745523
\(575\) −1373.89 −0.0996437
\(576\) 576.000 0.0416667
\(577\) −23704.2 −1.71026 −0.855130 0.518413i \(-0.826523\pi\)
−0.855130 + 0.518413i \(0.826523\pi\)
\(578\) −1378.62 −0.0992092
\(579\) −6355.34 −0.456164
\(580\) 5607.19 0.401424
\(581\) 24954.4 1.78190
\(582\) −2306.31 −0.164261
\(583\) 49.4486 0.00351278
\(584\) −7306.19 −0.517693
\(585\) 4375.83 0.309262
\(586\) −3752.51 −0.264530
\(587\) 26918.0 1.89271 0.946357 0.323122i \(-0.104733\pi\)
0.946357 + 0.323122i \(0.104733\pi\)
\(588\) 5676.00 0.398086
\(589\) −8241.75 −0.576562
\(590\) −691.311 −0.0482387
\(591\) 11495.8 0.800123
\(592\) −4304.16 −0.298817
\(593\) 16937.8 1.17294 0.586468 0.809973i \(-0.300518\pi\)
0.586468 + 0.809973i \(0.300518\pi\)
\(594\) 138.549 0.00957023
\(595\) −12526.2 −0.863068
\(596\) −11617.4 −0.798435
\(597\) 1247.51 0.0855230
\(598\) −2514.83 −0.171972
\(599\) 4012.73 0.273716 0.136858 0.990591i \(-0.456300\pi\)
0.136858 + 0.990591i \(0.456300\pi\)
\(600\) 2176.25 0.148075
\(601\) −18843.7 −1.27895 −0.639477 0.768810i \(-0.720849\pi\)
−0.639477 + 0.768810i \(0.720849\pi\)
\(602\) −25202.5 −1.70627
\(603\) 7469.82 0.504469
\(604\) 2144.26 0.144451
\(605\) −7759.19 −0.521415
\(606\) −10470.2 −0.701852
\(607\) 22926.5 1.53305 0.766523 0.642217i \(-0.221985\pi\)
0.766523 + 0.642217i \(0.221985\pi\)
\(608\) −1088.00 −0.0725727
\(609\) 20505.0 1.36438
\(610\) −9247.79 −0.613823
\(611\) −20695.6 −1.37030
\(612\) −2694.55 −0.177975
\(613\) 4307.74 0.283830 0.141915 0.989879i \(-0.454674\pi\)
0.141915 + 0.989879i \(0.454674\pi\)
\(614\) −1113.91 −0.0732145
\(615\) −3154.04 −0.206802
\(616\) 586.332 0.0383506
\(617\) −2484.00 −0.162078 −0.0810390 0.996711i \(-0.525824\pi\)
−0.0810390 + 0.996711i \(0.525824\pi\)
\(618\) −3001.33 −0.195358
\(619\) −6644.09 −0.431419 −0.215709 0.976458i \(-0.569206\pi\)
−0.215709 + 0.976458i \(0.569206\pi\)
\(620\) −5680.57 −0.367963
\(621\) 409.089 0.0264350
\(622\) −6047.25 −0.389828
\(623\) −25387.2 −1.63261
\(624\) 3983.52 0.255558
\(625\) 3931.99 0.251647
\(626\) 934.257 0.0596492
\(627\) −261.703 −0.0166689
\(628\) −7984.18 −0.507330
\(629\) 20135.0 1.27637
\(630\) −3012.38 −0.190502
\(631\) 4264.63 0.269053 0.134526 0.990910i \(-0.457049\pi\)
0.134526 + 0.990910i \(0.457049\pi\)
\(632\) 9817.87 0.617934
\(633\) 2130.08 0.133749
\(634\) 10066.2 0.630566
\(635\) −5471.32 −0.341926
\(636\) −231.274 −0.0144192
\(637\) 39254.3 2.44162
\(638\) 1227.81 0.0761905
\(639\) −7433.65 −0.460205
\(640\) −749.897 −0.0463161
\(641\) −11537.6 −0.710931 −0.355466 0.934689i \(-0.615678\pi\)
−0.355466 + 0.934689i \(0.615678\pi\)
\(642\) −6747.41 −0.414796
\(643\) 10699.0 0.656188 0.328094 0.944645i \(-0.393594\pi\)
0.328094 + 0.944645i \(0.393594\pi\)
\(644\) 1731.25 0.105933
\(645\) 7753.20 0.473305
\(646\) 5089.70 0.309987
\(647\) 1499.52 0.0911163 0.0455582 0.998962i \(-0.485493\pi\)
0.0455582 + 0.998962i \(0.485493\pi\)
\(648\) −648.000 −0.0392837
\(649\) −151.377 −0.00915573
\(650\) 15050.6 0.908204
\(651\) −20773.4 −1.25065
\(652\) −9572.62 −0.574989
\(653\) 26399.4 1.58207 0.791033 0.611774i \(-0.209544\pi\)
0.791033 + 0.611774i \(0.209544\pi\)
\(654\) 253.569 0.0151610
\(655\) −14201.3 −0.847162
\(656\) −2871.27 −0.170891
\(657\) 8219.47 0.488085
\(658\) 14247.1 0.844088
\(659\) −9799.08 −0.579238 −0.289619 0.957142i \(-0.593529\pi\)
−0.289619 + 0.957142i \(0.593529\pi\)
\(660\) −180.377 −0.0106381
\(661\) −17044.3 −1.00294 −0.501471 0.865174i \(-0.667208\pi\)
−0.501471 + 0.865174i \(0.667208\pi\)
\(662\) −10670.3 −0.626454
\(663\) −18635.0 −1.09159
\(664\) −6988.62 −0.408450
\(665\) 5690.05 0.331805
\(666\) 4842.18 0.281728
\(667\) 3625.33 0.210455
\(668\) 245.091 0.0141959
\(669\) 7019.06 0.405639
\(670\) −9724.99 −0.560760
\(671\) −2025.00 −0.116504
\(672\) −2742.31 −0.157421
\(673\) −3868.05 −0.221549 −0.110775 0.993846i \(-0.535333\pi\)
−0.110775 + 0.993846i \(0.535333\pi\)
\(674\) 20705.3 1.18329
\(675\) −2448.28 −0.139607
\(676\) 18761.4 1.06744
\(677\) 20146.7 1.14372 0.571861 0.820351i \(-0.306222\pi\)
0.571861 + 0.820351i \(0.306222\pi\)
\(678\) −6939.77 −0.393098
\(679\) 10980.3 0.620594
\(680\) 3508.05 0.197834
\(681\) −1216.85 −0.0684726
\(682\) −1243.88 −0.0698396
\(683\) 20028.9 1.12209 0.561044 0.827786i \(-0.310400\pi\)
0.561044 + 0.827786i \(0.310400\pi\)
\(684\) 1224.00 0.0684222
\(685\) −17330.8 −0.966682
\(686\) −7427.09 −0.413364
\(687\) 7337.22 0.407471
\(688\) 7058.10 0.391116
\(689\) −1599.45 −0.0884388
\(690\) −532.594 −0.0293848
\(691\) −24354.1 −1.34077 −0.670385 0.742013i \(-0.733871\pi\)
−0.670385 + 0.742013i \(0.733871\pi\)
\(692\) −12532.3 −0.688449
\(693\) −659.623 −0.0361573
\(694\) −14227.5 −0.778198
\(695\) −2918.04 −0.159263
\(696\) −5742.55 −0.312745
\(697\) 13431.9 0.729942
\(698\) −6684.62 −0.362488
\(699\) −3030.42 −0.163979
\(700\) −10361.0 −0.559443
\(701\) −12776.4 −0.688386 −0.344193 0.938899i \(-0.611847\pi\)
−0.344193 + 0.938899i \(0.611847\pi\)
\(702\) −4481.46 −0.240943
\(703\) −9146.34 −0.490698
\(704\) −164.206 −0.00879082
\(705\) −4382.93 −0.234143
\(706\) 25584.6 1.36387
\(707\) 49848.1 2.65167
\(708\) 708.000 0.0375823
\(709\) −26252.7 −1.39061 −0.695305 0.718715i \(-0.744731\pi\)
−0.695305 + 0.718715i \(0.744731\pi\)
\(710\) 9677.91 0.511557
\(711\) −11045.1 −0.582593
\(712\) 7109.83 0.374230
\(713\) −3672.77 −0.192912
\(714\) 12828.6 0.672407
\(715\) −1247.46 −0.0652479
\(716\) −343.771 −0.0179432
\(717\) 12557.4 0.654066
\(718\) 11328.1 0.588801
\(719\) −2432.80 −0.126187 −0.0630934 0.998008i \(-0.520097\pi\)
−0.0630934 + 0.998008i \(0.520097\pi\)
\(720\) 843.634 0.0436672
\(721\) 14289.2 0.738082
\(722\) 11406.0 0.587933
\(723\) 8958.42 0.460812
\(724\) −17168.3 −0.881289
\(725\) −21696.6 −1.11144
\(726\) 7946.50 0.406229
\(727\) −28792.5 −1.46885 −0.734426 0.678689i \(-0.762548\pi\)
−0.734426 + 0.678689i \(0.762548\pi\)
\(728\) −18965.3 −0.965526
\(729\) 729.000 0.0370370
\(730\) −10701.0 −0.542549
\(731\) −33018.1 −1.67061
\(732\) 9471.03 0.478223
\(733\) −2585.38 −0.130277 −0.0651386 0.997876i \(-0.520749\pi\)
−0.0651386 + 0.997876i \(0.520749\pi\)
\(734\) 15130.2 0.760854
\(735\) 8313.31 0.417199
\(736\) −484.846 −0.0242821
\(737\) −2129.49 −0.106433
\(738\) 3230.18 0.161117
\(739\) 20270.7 1.00902 0.504511 0.863405i \(-0.331673\pi\)
0.504511 + 0.863405i \(0.331673\pi\)
\(740\) −6304.06 −0.313165
\(741\) 8464.98 0.419661
\(742\) 1101.09 0.0544773
\(743\) −16354.8 −0.807538 −0.403769 0.914861i \(-0.632300\pi\)
−0.403769 + 0.914861i \(0.632300\pi\)
\(744\) 5817.70 0.286677
\(745\) −17015.3 −0.836770
\(746\) 8304.64 0.407580
\(747\) 7862.19 0.385091
\(748\) 768.160 0.0375491
\(749\) 32124.1 1.56714
\(750\) 7581.36 0.369109
\(751\) 15766.0 0.766059 0.383030 0.923736i \(-0.374881\pi\)
0.383030 + 0.923736i \(0.374881\pi\)
\(752\) −3989.99 −0.193484
\(753\) −6278.67 −0.303861
\(754\) −39714.5 −1.91819
\(755\) 3140.57 0.151387
\(756\) 3085.10 0.148418
\(757\) −3767.14 −0.180871 −0.0904354 0.995902i \(-0.528826\pi\)
−0.0904354 + 0.995902i \(0.528826\pi\)
\(758\) −5279.75 −0.252994
\(759\) −116.623 −0.00557725
\(760\) −1593.53 −0.0760572
\(761\) −24685.2 −1.17587 −0.587936 0.808907i \(-0.700059\pi\)
−0.587936 + 0.808907i \(0.700059\pi\)
\(762\) 5603.40 0.266391
\(763\) −1207.23 −0.0572799
\(764\) 10425.9 0.493711
\(765\) −3946.55 −0.186520
\(766\) 15367.7 0.724878
\(767\) 4896.41 0.230507
\(768\) 768.000 0.0360844
\(769\) 36694.2 1.72071 0.860356 0.509694i \(-0.170241\pi\)
0.860356 + 0.509694i \(0.170241\pi\)
\(770\) 858.766 0.0401919
\(771\) −4858.71 −0.226955
\(772\) −8473.78 −0.395049
\(773\) 14539.4 0.676514 0.338257 0.941054i \(-0.390163\pi\)
0.338257 + 0.941054i \(0.390163\pi\)
\(774\) −7940.37 −0.368747
\(775\) 21980.5 1.01879
\(776\) −3075.09 −0.142254
\(777\) −23053.4 −1.06440
\(778\) −412.700 −0.0190180
\(779\) −6101.45 −0.280625
\(780\) 5834.43 0.267829
\(781\) 2119.18 0.0970938
\(782\) 2268.13 0.103719
\(783\) 6460.37 0.294859
\(784\) 7568.00 0.344752
\(785\) −11694.0 −0.531689
\(786\) 14544.1 0.660016
\(787\) −21340.0 −0.966567 −0.483283 0.875464i \(-0.660556\pi\)
−0.483283 + 0.875464i \(0.660556\pi\)
\(788\) 15327.7 0.692927
\(789\) 16674.9 0.752398
\(790\) 14379.7 0.647603
\(791\) 33039.9 1.48516
\(792\) 184.731 0.00828806
\(793\) 65500.1 2.93314
\(794\) 11354.6 0.507506
\(795\) −338.734 −0.0151115
\(796\) 1663.35 0.0740651
\(797\) 20967.1 0.931861 0.465930 0.884821i \(-0.345720\pi\)
0.465930 + 0.884821i \(0.345720\pi\)
\(798\) −5827.41 −0.258506
\(799\) 18665.3 0.826447
\(800\) 2901.67 0.128237
\(801\) −7998.56 −0.352828
\(802\) 5938.50 0.261466
\(803\) −2343.20 −0.102976
\(804\) 9959.76 0.436883
\(805\) 2535.66 0.111019
\(806\) 40234.3 1.75830
\(807\) 892.166 0.0389166
\(808\) −13960.3 −0.607822
\(809\) −4118.53 −0.178986 −0.0894931 0.995987i \(-0.528525\pi\)
−0.0894931 + 0.995987i \(0.528525\pi\)
\(810\) −949.089 −0.0411698
\(811\) 11302.8 0.489389 0.244695 0.969600i \(-0.421312\pi\)
0.244695 + 0.969600i \(0.421312\pi\)
\(812\) 27340.0 1.18158
\(813\) −8202.21 −0.353830
\(814\) −1380.41 −0.0594388
\(815\) −14020.5 −0.602596
\(816\) −3592.73 −0.154131
\(817\) 14998.5 0.642264
\(818\) −2396.07 −0.102417
\(819\) 21336.0 0.910306
\(820\) −4205.38 −0.179096
\(821\) 34915.8 1.48425 0.742125 0.670261i \(-0.233818\pi\)
0.742125 + 0.670261i \(0.233818\pi\)
\(822\) 17749.2 0.753133
\(823\) −4155.81 −0.176018 −0.0880088 0.996120i \(-0.528050\pi\)
−0.0880088 + 0.996120i \(0.528050\pi\)
\(824\) −4001.77 −0.169185
\(825\) 697.955 0.0294541
\(826\) −3370.75 −0.141990
\(827\) 29006.5 1.21965 0.609827 0.792535i \(-0.291239\pi\)
0.609827 + 0.792535i \(0.291239\pi\)
\(828\) 545.451 0.0228934
\(829\) 23464.3 0.983052 0.491526 0.870863i \(-0.336439\pi\)
0.491526 + 0.870863i \(0.336439\pi\)
\(830\) −10235.8 −0.428061
\(831\) 2280.52 0.0951991
\(832\) 5311.36 0.221320
\(833\) −35403.4 −1.47257
\(834\) 2988.48 0.124080
\(835\) 358.971 0.0148775
\(836\) −348.937 −0.0144357
\(837\) −6544.92 −0.270281
\(838\) −23552.6 −0.970895
\(839\) 24537.3 1.00968 0.504840 0.863213i \(-0.331552\pi\)
0.504840 + 0.863213i \(0.331552\pi\)
\(840\) −4016.50 −0.164979
\(841\) 32862.5 1.34743
\(842\) 20606.0 0.843384
\(843\) −6151.94 −0.251345
\(844\) 2840.10 0.115830
\(845\) 27478.7 1.11869
\(846\) 4488.74 0.182418
\(847\) −37832.9 −1.53478
\(848\) −308.366 −0.0124874
\(849\) −14455.2 −0.584335
\(850\) −13574.1 −0.547751
\(851\) −4075.89 −0.164183
\(852\) −9911.54 −0.398549
\(853\) −19684.4 −0.790130 −0.395065 0.918653i \(-0.629278\pi\)
−0.395065 + 0.918653i \(0.629278\pi\)
\(854\) −45091.1 −1.80678
\(855\) 1792.72 0.0717074
\(856\) −8996.55 −0.359224
\(857\) −33312.2 −1.32780 −0.663898 0.747823i \(-0.731099\pi\)
−0.663898 + 0.747823i \(0.731099\pi\)
\(858\) 1277.57 0.0508340
\(859\) −11928.6 −0.473805 −0.236902 0.971533i \(-0.576132\pi\)
−0.236902 + 0.971533i \(0.576132\pi\)
\(860\) 10337.6 0.409894
\(861\) −15378.7 −0.608717
\(862\) −28035.6 −1.10777
\(863\) −42805.1 −1.68842 −0.844208 0.536015i \(-0.819929\pi\)
−0.844208 + 0.536015i \(0.819929\pi\)
\(864\) −864.000 −0.0340207
\(865\) −18355.4 −0.721504
\(866\) 13336.3 0.523310
\(867\) 2067.93 0.0810040
\(868\) −27697.8 −1.08309
\(869\) 3148.73 0.122915
\(870\) −8410.78 −0.327761
\(871\) 68880.0 2.67958
\(872\) 338.092 0.0131298
\(873\) 3459.47 0.134118
\(874\) −1030.30 −0.0398745
\(875\) −36094.5 −1.39453
\(876\) 10959.3 0.422694
\(877\) 11297.7 0.435002 0.217501 0.976060i \(-0.430209\pi\)
0.217501 + 0.976060i \(0.430209\pi\)
\(878\) −22663.6 −0.871139
\(879\) 5628.76 0.215988
\(880\) −240.503 −0.00921289
\(881\) 44382.1 1.69724 0.848622 0.529000i \(-0.177433\pi\)
0.848622 + 0.529000i \(0.177433\pi\)
\(882\) −8514.00 −0.325035
\(883\) −16656.6 −0.634813 −0.317407 0.948290i \(-0.602812\pi\)
−0.317407 + 0.948290i \(0.602812\pi\)
\(884\) −24846.7 −0.945346
\(885\) 1036.97 0.0393867
\(886\) −2027.53 −0.0768807
\(887\) 15233.9 0.576669 0.288334 0.957530i \(-0.406899\pi\)
0.288334 + 0.957530i \(0.406899\pi\)
\(888\) 6456.24 0.243983
\(889\) −26677.5 −1.00645
\(890\) 10413.4 0.392198
\(891\) −207.823 −0.00781406
\(892\) 9358.74 0.351294
\(893\) −8478.73 −0.317726
\(894\) 17426.1 0.651919
\(895\) −503.502 −0.0188047
\(896\) −3656.41 −0.136331
\(897\) 3772.25 0.140414
\(898\) −31098.4 −1.15564
\(899\) −58000.8 −2.15176
\(900\) −3264.38 −0.120903
\(901\) 1442.55 0.0533387
\(902\) −920.857 −0.0339924
\(903\) 37803.7 1.39317
\(904\) −9253.03 −0.340433
\(905\) −25145.4 −0.923602
\(906\) −3216.39 −0.117944
\(907\) 7813.26 0.286037 0.143018 0.989720i \(-0.454319\pi\)
0.143018 + 0.989720i \(0.454319\pi\)
\(908\) −1622.47 −0.0592990
\(909\) 15705.3 0.573060
\(910\) −27777.5 −1.01188
\(911\) −10661.5 −0.387739 −0.193869 0.981027i \(-0.562104\pi\)
−0.193869 + 0.981027i \(0.562104\pi\)
\(912\) 1632.00 0.0592554
\(913\) −2241.35 −0.0812462
\(914\) 14007.3 0.506914
\(915\) 13871.7 0.501184
\(916\) 9782.95 0.352880
\(917\) −69243.9 −2.49361
\(918\) 4041.82 0.145316
\(919\) −30469.0 −1.09367 −0.546834 0.837241i \(-0.684167\pi\)
−0.546834 + 0.837241i \(0.684167\pi\)
\(920\) −710.126 −0.0254480
\(921\) 1670.86 0.0597794
\(922\) 15980.6 0.570818
\(923\) −68546.5 −2.44446
\(924\) −879.497 −0.0313131
\(925\) 24393.1 0.867069
\(926\) 4771.68 0.169338
\(927\) 4501.99 0.159509
\(928\) −7656.73 −0.270845
\(929\) −4514.41 −0.159433 −0.0797164 0.996818i \(-0.525401\pi\)
−0.0797164 + 0.996818i \(0.525401\pi\)
\(930\) 8520.86 0.300441
\(931\) 16082.0 0.566129
\(932\) −4040.56 −0.142010
\(933\) 9070.88 0.318293
\(934\) −11375.6 −0.398525
\(935\) 1125.08 0.0393519
\(936\) −5975.28 −0.208663
\(937\) −20904.5 −0.728837 −0.364418 0.931235i \(-0.618732\pi\)
−0.364418 + 0.931235i \(0.618732\pi\)
\(938\) −47417.9 −1.65059
\(939\) −1401.39 −0.0487034
\(940\) −5843.91 −0.202774
\(941\) 22393.3 0.775771 0.387886 0.921708i \(-0.373206\pi\)
0.387886 + 0.921708i \(0.373206\pi\)
\(942\) 11976.3 0.414233
\(943\) −2718.99 −0.0938944
\(944\) 944.000 0.0325472
\(945\) 4518.57 0.155544
\(946\) 2263.63 0.0777982
\(947\) −52752.3 −1.81016 −0.905079 0.425243i \(-0.860189\pi\)
−0.905079 + 0.425243i \(0.860189\pi\)
\(948\) −14726.8 −0.504541
\(949\) 75792.6 2.59255
\(950\) 6166.05 0.210582
\(951\) −15099.3 −0.514855
\(952\) 17104.8 0.582322
\(953\) 19837.4 0.674287 0.337144 0.941453i \(-0.390539\pi\)
0.337144 + 0.941453i \(0.390539\pi\)
\(954\) 346.911 0.0117732
\(955\) 15270.2 0.517416
\(956\) 16743.2 0.566438
\(957\) −1841.72 −0.0622093
\(958\) 27760.1 0.936210
\(959\) −84503.2 −2.84541
\(960\) 1124.85 0.0378169
\(961\) 28968.8 0.972402
\(962\) 44650.3 1.49645
\(963\) 10121.1 0.338680
\(964\) 11944.6 0.399075
\(965\) −12411.1 −0.414017
\(966\) −2596.87 −0.0864937
\(967\) 35535.4 1.18174 0.590870 0.806767i \(-0.298785\pi\)
0.590870 + 0.806767i \(0.298785\pi\)
\(968\) 10595.3 0.351805
\(969\) −7634.55 −0.253103
\(970\) −4503.90 −0.149084
\(971\) −6393.93 −0.211319 −0.105660 0.994402i \(-0.533695\pi\)
−0.105660 + 0.994402i \(0.533695\pi\)
\(972\) 972.000 0.0320750
\(973\) −14228.0 −0.468786
\(974\) −22512.3 −0.740597
\(975\) −22575.9 −0.741546
\(976\) 12628.0 0.414154
\(977\) 900.777 0.0294968 0.0147484 0.999891i \(-0.495305\pi\)
0.0147484 + 0.999891i \(0.495305\pi\)
\(978\) 14358.9 0.469476
\(979\) 2280.22 0.0744395
\(980\) 11084.4 0.361305
\(981\) −380.353 −0.0123789
\(982\) 3242.17 0.105358
\(983\) −56145.1 −1.82172 −0.910860 0.412716i \(-0.864580\pi\)
−0.910860 + 0.412716i \(0.864580\pi\)
\(984\) 4306.90 0.139532
\(985\) 22449.6 0.726197
\(986\) 35818.5 1.15689
\(987\) −21370.7 −0.689195
\(988\) 11286.6 0.363437
\(989\) 6683.77 0.214895
\(990\) 270.566 0.00868600
\(991\) 4295.90 0.137703 0.0688515 0.997627i \(-0.478067\pi\)
0.0688515 + 0.997627i \(0.478067\pi\)
\(992\) 7756.94 0.248269
\(993\) 16005.4 0.511497
\(994\) 47188.4 1.50576
\(995\) 2436.21 0.0776212
\(996\) 10482.9 0.333498
\(997\) −36710.7 −1.16614 −0.583070 0.812422i \(-0.698149\pi\)
−0.583070 + 0.812422i \(0.698149\pi\)
\(998\) −35521.9 −1.12668
\(999\) −7263.27 −0.230030
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 354.4.a.b.1.1 2
3.2 odd 2 1062.4.a.g.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
354.4.a.b.1.1 2 1.1 even 1 trivial
1062.4.a.g.1.2 2 3.2 odd 2