Properties

Label 2166.4.a.j.1.2
Level $2166$
Weight $4$
Character 2166.1
Self dual yes
Analytic conductor $127.798$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2166 = 2 \cdot 3 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2166.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(127.798137072\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{10})^+\)
Defining polynomial: \(x^{2} - x - 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-0.618034\) of defining polynomial
Character \(\chi\) \(=\) 2166.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -0.909830 q^{5} +6.00000 q^{6} -16.3262 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -0.909830 q^{5} +6.00000 q^{6} -16.3262 q^{7} -8.00000 q^{8} +9.00000 q^{9} +1.81966 q^{10} -1.94427 q^{11} -12.0000 q^{12} -15.0902 q^{13} +32.6525 q^{14} +2.72949 q^{15} +16.0000 q^{16} +32.0132 q^{17} -18.0000 q^{18} -3.63932 q^{20} +48.9787 q^{21} +3.88854 q^{22} -44.8885 q^{23} +24.0000 q^{24} -124.172 q^{25} +30.1803 q^{26} -27.0000 q^{27} -65.3050 q^{28} -31.1509 q^{29} -5.45898 q^{30} +299.503 q^{31} -32.0000 q^{32} +5.83282 q^{33} -64.0263 q^{34} +14.8541 q^{35} +36.0000 q^{36} +252.885 q^{37} +45.2705 q^{39} +7.27864 q^{40} -81.6475 q^{41} -97.9574 q^{42} -217.095 q^{43} -7.77709 q^{44} -8.18847 q^{45} +89.7771 q^{46} +187.743 q^{47} -48.0000 q^{48} -76.4540 q^{49} +248.344 q^{50} -96.0395 q^{51} -60.3607 q^{52} +11.8127 q^{53} +54.0000 q^{54} +1.76896 q^{55} +130.610 q^{56} +62.3018 q^{58} -244.046 q^{59} +10.9180 q^{60} +526.508 q^{61} -599.007 q^{62} -146.936 q^{63} +64.0000 q^{64} +13.7295 q^{65} -11.6656 q^{66} +210.726 q^{67} +128.053 q^{68} +134.666 q^{69} -29.7082 q^{70} +503.418 q^{71} -72.0000 q^{72} +115.265 q^{73} -505.771 q^{74} +372.517 q^{75} +31.7426 q^{77} -90.5410 q^{78} -220.492 q^{79} -14.5573 q^{80} +81.0000 q^{81} +163.295 q^{82} +200.023 q^{83} +195.915 q^{84} -29.1265 q^{85} +434.190 q^{86} +93.4528 q^{87} +15.5542 q^{88} +174.091 q^{89} +16.3769 q^{90} +246.366 q^{91} -179.554 q^{92} -898.510 q^{93} -375.485 q^{94} +96.0000 q^{96} +1105.40 q^{97} +152.908 q^{98} -17.4984 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 4q^{2} - 6q^{3} + 8q^{4} - 13q^{5} + 12q^{6} - 17q^{7} - 16q^{8} + 18q^{9} + O(q^{10}) \) \( 2q - 4q^{2} - 6q^{3} + 8q^{4} - 13q^{5} + 12q^{6} - 17q^{7} - 16q^{8} + 18q^{9} + 26q^{10} + 14q^{11} - 24q^{12} - 19q^{13} + 34q^{14} + 39q^{15} + 32q^{16} - 12q^{17} - 36q^{18} - 52q^{20} + 51q^{21} - 28q^{22} - 54q^{23} + 48q^{24} - 103q^{25} + 38q^{26} - 54q^{27} - 68q^{28} + 130q^{29} - 78q^{30} + 239q^{31} - 64q^{32} - 42q^{33} + 24q^{34} + 23q^{35} + 72q^{36} + 148q^{37} + 57q^{39} + 104q^{40} - 331q^{41} - 102q^{42} - 224q^{43} + 56q^{44} - 117q^{45} + 108q^{46} + 333q^{47} - 96q^{48} - 419q^{49} + 206q^{50} + 36q^{51} - 76q^{52} + 766q^{53} + 108q^{54} - 191q^{55} + 136q^{56} - 260q^{58} + 460q^{59} + 156q^{60} + 494q^{61} - 478q^{62} - 153q^{63} + 128q^{64} + 61q^{65} + 84q^{66} + 133q^{67} - 48q^{68} + 162q^{69} - 46q^{70} + 459q^{71} - 144q^{72} + 396q^{73} - 296q^{74} + 309q^{75} + 21q^{77} - 114q^{78} - 1000q^{79} - 208q^{80} + 162q^{81} + 662q^{82} - 74q^{83} + 204q^{84} + 503q^{85} + 448q^{86} - 390q^{87} - 112q^{88} + 1180q^{89} + 234q^{90} + 249q^{91} - 216q^{92} - 717q^{93} - 666q^{94} + 192q^{96} + 1938q^{97} + 838q^{98} + 126q^{99} + O(q^{100}) \)

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
\(5\) −0.909830 −0.0813777 −0.0406888 0.999172i \(-0.512955\pi\)
−0.0406888 + 0.999172i \(0.512955\pi\)
\(6\) 6.00000 0.408248
\(7\) −16.3262 −0.881534 −0.440767 0.897622i \(-0.645293\pi\)
−0.440767 + 0.897622i \(0.645293\pi\)
\(8\) −8.00000 −0.353553
\(9\) 9.00000 0.333333
\(10\) 1.81966 0.0575427
\(11\) −1.94427 −0.0532927 −0.0266464 0.999645i \(-0.508483\pi\)
−0.0266464 + 0.999645i \(0.508483\pi\)
\(12\) −12.0000 −0.288675
\(13\) −15.0902 −0.321943 −0.160972 0.986959i \(-0.551463\pi\)
−0.160972 + 0.986959i \(0.551463\pi\)
\(14\) 32.6525 0.623339
\(15\) 2.72949 0.0469834
\(16\) 16.0000 0.250000
\(17\) 32.0132 0.456725 0.228363 0.973576i \(-0.426663\pi\)
0.228363 + 0.973576i \(0.426663\pi\)
\(18\) −18.0000 −0.235702
\(19\) 0 0
\(20\) −3.63932 −0.0406888
\(21\) 48.9787 0.508954
\(22\) 3.88854 0.0376837
\(23\) −44.8885 −0.406953 −0.203476 0.979080i \(-0.565224\pi\)
−0.203476 + 0.979080i \(0.565224\pi\)
\(24\) 24.0000 0.204124
\(25\) −124.172 −0.993378
\(26\) 30.1803 0.227648
\(27\) −27.0000 −0.192450
\(28\) −65.3050 −0.440767
\(29\) −31.1509 −0.199468 −0.0997342 0.995014i \(-0.531799\pi\)
−0.0997342 + 0.995014i \(0.531799\pi\)
\(30\) −5.45898 −0.0332223
\(31\) 299.503 1.73524 0.867620 0.497229i \(-0.165649\pi\)
0.867620 + 0.497229i \(0.165649\pi\)
\(32\) −32.0000 −0.176777
\(33\) 5.83282 0.0307686
\(34\) −64.0263 −0.322954
\(35\) 14.8541 0.0717372
\(36\) 36.0000 0.166667
\(37\) 252.885 1.12362 0.561812 0.827265i \(-0.310104\pi\)
0.561812 + 0.827265i \(0.310104\pi\)
\(38\) 0 0
\(39\) 45.2705 0.185874
\(40\) 7.27864 0.0287714
\(41\) −81.6475 −0.311005 −0.155502 0.987836i \(-0.549700\pi\)
−0.155502 + 0.987836i \(0.549700\pi\)
\(42\) −97.9574 −0.359885
\(43\) −217.095 −0.769923 −0.384962 0.922933i \(-0.625785\pi\)
−0.384962 + 0.922933i \(0.625785\pi\)
\(44\) −7.77709 −0.0266464
\(45\) −8.18847 −0.0271259
\(46\) 89.7771 0.287759
\(47\) 187.743 0.582661 0.291331 0.956622i \(-0.405902\pi\)
0.291331 + 0.956622i \(0.405902\pi\)
\(48\) −48.0000 −0.144338
\(49\) −76.4540 −0.222898
\(50\) 248.344 0.702424
\(51\) −96.0395 −0.263690
\(52\) −60.3607 −0.160972
\(53\) 11.8127 0.0306151 0.0153076 0.999883i \(-0.495127\pi\)
0.0153076 + 0.999883i \(0.495127\pi\)
\(54\) 54.0000 0.136083
\(55\) 1.76896 0.00433684
\(56\) 130.610 0.311669
\(57\) 0 0
\(58\) 62.3018 0.141045
\(59\) −244.046 −0.538511 −0.269255 0.963069i \(-0.586778\pi\)
−0.269255 + 0.963069i \(0.586778\pi\)
\(60\) 10.9180 0.0234917
\(61\) 526.508 1.10512 0.552562 0.833472i \(-0.313650\pi\)
0.552562 + 0.833472i \(0.313650\pi\)
\(62\) −599.007 −1.22700
\(63\) −146.936 −0.293845
\(64\) 64.0000 0.125000
\(65\) 13.7295 0.0261990
\(66\) −11.6656 −0.0217567
\(67\) 210.726 0.384244 0.192122 0.981371i \(-0.438463\pi\)
0.192122 + 0.981371i \(0.438463\pi\)
\(68\) 128.053 0.228363
\(69\) 134.666 0.234954
\(70\) −29.7082 −0.0507259
\(71\) 503.418 0.841476 0.420738 0.907182i \(-0.361771\pi\)
0.420738 + 0.907182i \(0.361771\pi\)
\(72\) −72.0000 −0.117851
\(73\) 115.265 0.184806 0.0924028 0.995722i \(-0.470545\pi\)
0.0924028 + 0.995722i \(0.470545\pi\)
\(74\) −505.771 −0.794523
\(75\) 372.517 0.573527
\(76\) 0 0
\(77\) 31.7426 0.0469794
\(78\) −90.5410 −0.131433
\(79\) −220.492 −0.314016 −0.157008 0.987597i \(-0.550185\pi\)
−0.157008 + 0.987597i \(0.550185\pi\)
\(80\) −14.5573 −0.0203444
\(81\) 81.0000 0.111111
\(82\) 163.295 0.219913
\(83\) 200.023 0.264523 0.132261 0.991215i \(-0.457776\pi\)
0.132261 + 0.991215i \(0.457776\pi\)
\(84\) 195.915 0.254477
\(85\) −29.1265 −0.0371672
\(86\) 434.190 0.544418
\(87\) 93.4528 0.115163
\(88\) 15.5542 0.0188418
\(89\) 174.091 0.207344 0.103672 0.994612i \(-0.466941\pi\)
0.103672 + 0.994612i \(0.466941\pi\)
\(90\) 16.3769 0.0191809
\(91\) 246.366 0.283804
\(92\) −179.554 −0.203476
\(93\) −898.510 −1.00184
\(94\) −375.485 −0.412004
\(95\) 0 0
\(96\) 96.0000 0.102062
\(97\) 1105.40 1.15708 0.578538 0.815655i \(-0.303623\pi\)
0.578538 + 0.815655i \(0.303623\pi\)
\(98\) 152.908 0.157613
\(99\) −17.4984 −0.0177642
\(100\) −496.689 −0.496689
\(101\) −896.371 −0.883092 −0.441546 0.897239i \(-0.645570\pi\)
−0.441546 + 0.897239i \(0.645570\pi\)
\(102\) 192.079 0.186457
\(103\) −161.160 −0.154170 −0.0770852 0.997025i \(-0.524561\pi\)
−0.0770852 + 0.997025i \(0.524561\pi\)
\(104\) 120.721 0.113824
\(105\) −44.5623 −0.0414175
\(106\) −23.6254 −0.0216482
\(107\) 1121.56 1.01333 0.506663 0.862144i \(-0.330879\pi\)
0.506663 + 0.862144i \(0.330879\pi\)
\(108\) −108.000 −0.0962250
\(109\) −983.166 −0.863947 −0.431973 0.901886i \(-0.642183\pi\)
−0.431973 + 0.901886i \(0.642183\pi\)
\(110\) −3.53791 −0.00306661
\(111\) −758.656 −0.648725
\(112\) −261.220 −0.220383
\(113\) 500.349 0.416539 0.208270 0.978071i \(-0.433217\pi\)
0.208270 + 0.978071i \(0.433217\pi\)
\(114\) 0 0
\(115\) 40.8409 0.0331169
\(116\) −124.604 −0.0997342
\(117\) −135.812 −0.107314
\(118\) 488.093 0.380785
\(119\) −522.654 −0.402619
\(120\) −21.8359 −0.0166111
\(121\) −1327.22 −0.997160
\(122\) −1053.02 −0.781440
\(123\) 244.942 0.179559
\(124\) 1198.01 0.867620
\(125\) 226.704 0.162216
\(126\) 293.872 0.207780
\(127\) 865.459 0.604701 0.302351 0.953197i \(-0.402229\pi\)
0.302351 + 0.953197i \(0.402229\pi\)
\(128\) −128.000 −0.0883883
\(129\) 651.286 0.444515
\(130\) −27.4590 −0.0185255
\(131\) −2344.79 −1.56386 −0.781930 0.623366i \(-0.785765\pi\)
−0.781930 + 0.623366i \(0.785765\pi\)
\(132\) 23.3313 0.0153843
\(133\) 0 0
\(134\) −421.453 −0.271701
\(135\) 24.5654 0.0156611
\(136\) −256.105 −0.161477
\(137\) 2071.28 1.29169 0.645843 0.763470i \(-0.276506\pi\)
0.645843 + 0.763470i \(0.276506\pi\)
\(138\) −269.331 −0.166138
\(139\) −1467.54 −0.895507 −0.447753 0.894157i \(-0.647776\pi\)
−0.447753 + 0.894157i \(0.647776\pi\)
\(140\) 59.4164 0.0358686
\(141\) −563.228 −0.336400
\(142\) −1006.84 −0.595013
\(143\) 29.3394 0.0171572
\(144\) 144.000 0.0833333
\(145\) 28.3420 0.0162323
\(146\) −230.531 −0.130677
\(147\) 229.362 0.128690
\(148\) 1011.54 0.561812
\(149\) −176.948 −0.0972895 −0.0486447 0.998816i \(-0.515490\pi\)
−0.0486447 + 0.998816i \(0.515490\pi\)
\(150\) −745.033 −0.405545
\(151\) 1138.74 0.613706 0.306853 0.951757i \(-0.400724\pi\)
0.306853 + 0.951757i \(0.400724\pi\)
\(152\) 0 0
\(153\) 288.118 0.152242
\(154\) −63.4853 −0.0332194
\(155\) −272.497 −0.141210
\(156\) 181.082 0.0929370
\(157\) −1952.19 −0.992366 −0.496183 0.868218i \(-0.665266\pi\)
−0.496183 + 0.868218i \(0.665266\pi\)
\(158\) 440.983 0.222043
\(159\) −35.4381 −0.0176756
\(160\) 29.1146 0.0143857
\(161\) 732.861 0.358742
\(162\) −162.000 −0.0785674
\(163\) 385.974 0.185471 0.0927357 0.995691i \(-0.470439\pi\)
0.0927357 + 0.995691i \(0.470439\pi\)
\(164\) −326.590 −0.155502
\(165\) −5.30687 −0.00250387
\(166\) −400.046 −0.187046
\(167\) 3206.11 1.48561 0.742803 0.669510i \(-0.233496\pi\)
0.742803 + 0.669510i \(0.233496\pi\)
\(168\) −391.830 −0.179942
\(169\) −1969.29 −0.896353
\(170\) 58.2531 0.0262812
\(171\) 0 0
\(172\) −868.381 −0.384962
\(173\) 3194.72 1.40399 0.701993 0.712184i \(-0.252294\pi\)
0.701993 + 0.712184i \(0.252294\pi\)
\(174\) −186.906 −0.0814326
\(175\) 2027.27 0.875696
\(176\) −31.1084 −0.0133232
\(177\) 732.139 0.310909
\(178\) −348.183 −0.146615
\(179\) −2449.26 −1.02272 −0.511358 0.859368i \(-0.670858\pi\)
−0.511358 + 0.859368i \(0.670858\pi\)
\(180\) −32.7539 −0.0135629
\(181\) 2002.67 0.822415 0.411207 0.911542i \(-0.365107\pi\)
0.411207 + 0.911542i \(0.365107\pi\)
\(182\) −492.731 −0.200680
\(183\) −1579.53 −0.638043
\(184\) 359.108 0.143879
\(185\) −230.083 −0.0914380
\(186\) 1797.02 0.708408
\(187\) −62.2423 −0.0243401
\(188\) 750.971 0.291331
\(189\) 440.808 0.169651
\(190\) 0 0
\(191\) 4101.97 1.55397 0.776984 0.629520i \(-0.216749\pi\)
0.776984 + 0.629520i \(0.216749\pi\)
\(192\) −192.000 −0.0721688
\(193\) −1756.55 −0.655126 −0.327563 0.944829i \(-0.606227\pi\)
−0.327563 + 0.944829i \(0.606227\pi\)
\(194\) −2210.80 −0.818176
\(195\) −41.1885 −0.0151260
\(196\) −305.816 −0.111449
\(197\) 3670.57 1.32750 0.663750 0.747955i \(-0.268964\pi\)
0.663750 + 0.747955i \(0.268964\pi\)
\(198\) 34.9969 0.0125612
\(199\) −2610.75 −0.930007 −0.465004 0.885309i \(-0.653947\pi\)
−0.465004 + 0.885309i \(0.653947\pi\)
\(200\) 993.378 0.351212
\(201\) −632.179 −0.221843
\(202\) 1792.74 0.624440
\(203\) 508.577 0.175838
\(204\) −384.158 −0.131845
\(205\) 74.2853 0.0253088
\(206\) 322.320 0.109015
\(207\) −403.997 −0.135651
\(208\) −241.443 −0.0804858
\(209\) 0 0
\(210\) 89.1246 0.0292866
\(211\) 3473.35 1.13325 0.566624 0.823976i \(-0.308249\pi\)
0.566624 + 0.823976i \(0.308249\pi\)
\(212\) 47.2509 0.0153076
\(213\) −1510.25 −0.485826
\(214\) −2243.13 −0.716529
\(215\) 197.520 0.0626546
\(216\) 216.000 0.0680414
\(217\) −4889.76 −1.52967
\(218\) 1966.33 0.610903
\(219\) −345.796 −0.106698
\(220\) 7.07583 0.00216842
\(221\) −483.084 −0.147040
\(222\) 1517.31 0.458718
\(223\) −2530.49 −0.759885 −0.379942 0.925010i \(-0.624056\pi\)
−0.379942 + 0.925010i \(0.624056\pi\)
\(224\) 522.440 0.155835
\(225\) −1117.55 −0.331126
\(226\) −1000.70 −0.294538
\(227\) 6734.59 1.96912 0.984560 0.175046i \(-0.0560074\pi\)
0.984560 + 0.175046i \(0.0560074\pi\)
\(228\) 0 0
\(229\) −337.719 −0.0974546 −0.0487273 0.998812i \(-0.515517\pi\)
−0.0487273 + 0.998812i \(0.515517\pi\)
\(230\) −81.6819 −0.0234172
\(231\) −95.2279 −0.0271235
\(232\) 249.207 0.0705227
\(233\) −6311.26 −1.77452 −0.887262 0.461265i \(-0.847396\pi\)
−0.887262 + 0.461265i \(0.847396\pi\)
\(234\) 271.623 0.0758827
\(235\) −170.814 −0.0474156
\(236\) −976.186 −0.269255
\(237\) 661.475 0.181297
\(238\) 1045.31 0.284695
\(239\) −3275.56 −0.886519 −0.443260 0.896393i \(-0.646178\pi\)
−0.443260 + 0.896393i \(0.646178\pi\)
\(240\) 43.6718 0.0117459
\(241\) −1668.27 −0.445904 −0.222952 0.974829i \(-0.571569\pi\)
−0.222952 + 0.974829i \(0.571569\pi\)
\(242\) 2654.44 0.705099
\(243\) −243.000 −0.0641500
\(244\) 2106.03 0.552562
\(245\) 69.5601 0.0181389
\(246\) −489.885 −0.126967
\(247\) 0 0
\(248\) −2396.03 −0.613500
\(249\) −600.070 −0.152722
\(250\) −453.409 −0.114704
\(251\) −2044.39 −0.514106 −0.257053 0.966397i \(-0.582751\pi\)
−0.257053 + 0.966397i \(0.582751\pi\)
\(252\) −587.745 −0.146922
\(253\) 87.2755 0.0216876
\(254\) −1730.92 −0.427588
\(255\) 87.3796 0.0214585
\(256\) 256.000 0.0625000
\(257\) −5181.31 −1.25759 −0.628797 0.777570i \(-0.716452\pi\)
−0.628797 + 0.777570i \(0.716452\pi\)
\(258\) −1302.57 −0.314320
\(259\) −4128.67 −0.990513
\(260\) 54.9180 0.0130995
\(261\) −280.358 −0.0664894
\(262\) 4689.59 1.10582
\(263\) 7137.93 1.67355 0.836774 0.547548i \(-0.184439\pi\)
0.836774 + 0.547548i \(0.184439\pi\)
\(264\) −46.6625 −0.0108783
\(265\) −10.7476 −0.00249139
\(266\) 0 0
\(267\) −522.274 −0.119710
\(268\) 842.906 0.192122
\(269\) −6395.52 −1.44960 −0.724798 0.688961i \(-0.758067\pi\)
−0.724798 + 0.688961i \(0.758067\pi\)
\(270\) −49.1308 −0.0110741
\(271\) −6478.86 −1.45226 −0.726131 0.687556i \(-0.758683\pi\)
−0.726131 + 0.687556i \(0.758683\pi\)
\(272\) 512.210 0.114181
\(273\) −739.097 −0.163854
\(274\) −4142.55 −0.913360
\(275\) 241.425 0.0529398
\(276\) 538.663 0.117477
\(277\) 3501.93 0.759606 0.379803 0.925067i \(-0.375992\pi\)
0.379803 + 0.925067i \(0.375992\pi\)
\(278\) 2935.09 0.633219
\(279\) 2695.53 0.578413
\(280\) −118.833 −0.0253629
\(281\) −1722.75 −0.365731 −0.182865 0.983138i \(-0.558537\pi\)
−0.182865 + 0.983138i \(0.558537\pi\)
\(282\) 1126.46 0.237870
\(283\) −905.945 −0.190293 −0.0951464 0.995463i \(-0.530332\pi\)
−0.0951464 + 0.995463i \(0.530332\pi\)
\(284\) 2013.67 0.420738
\(285\) 0 0
\(286\) −58.6788 −0.0121320
\(287\) 1333.00 0.274161
\(288\) −288.000 −0.0589256
\(289\) −3888.16 −0.791402
\(290\) −56.6841 −0.0114779
\(291\) −3316.20 −0.668038
\(292\) 461.062 0.0924028
\(293\) −6570.56 −1.31009 −0.655045 0.755590i \(-0.727350\pi\)
−0.655045 + 0.755590i \(0.727350\pi\)
\(294\) −458.724 −0.0909977
\(295\) 222.041 0.0438228
\(296\) −2023.08 −0.397261
\(297\) 52.4953 0.0102562
\(298\) 353.896 0.0687940
\(299\) 677.376 0.131016
\(300\) 1490.07 0.286763
\(301\) 3544.35 0.678714
\(302\) −2277.49 −0.433956
\(303\) 2689.11 0.509853
\(304\) 0 0
\(305\) −479.033 −0.0899323
\(306\) −576.237 −0.107651
\(307\) −566.581 −0.105331 −0.0526653 0.998612i \(-0.516772\pi\)
−0.0526653 + 0.998612i \(0.516772\pi\)
\(308\) 126.971 0.0234897
\(309\) 483.479 0.0890103
\(310\) 544.995 0.0998504
\(311\) 3507.55 0.639534 0.319767 0.947496i \(-0.396395\pi\)
0.319767 + 0.947496i \(0.396395\pi\)
\(312\) −362.164 −0.0657164
\(313\) −321.768 −0.0581067 −0.0290534 0.999578i \(-0.509249\pi\)
−0.0290534 + 0.999578i \(0.509249\pi\)
\(314\) 3904.37 0.701709
\(315\) 133.687 0.0239124
\(316\) −881.966 −0.157008
\(317\) 3797.03 0.672752 0.336376 0.941728i \(-0.390799\pi\)
0.336376 + 0.941728i \(0.390799\pi\)
\(318\) 70.8763 0.0124986
\(319\) 60.5659 0.0106302
\(320\) −58.2291 −0.0101722
\(321\) −3364.69 −0.585043
\(322\) −1465.72 −0.253669
\(323\) 0 0
\(324\) 324.000 0.0555556
\(325\) 1873.78 0.319811
\(326\) −771.948 −0.131148
\(327\) 2949.50 0.498800
\(328\) 653.180 0.109957
\(329\) −3065.13 −0.513636
\(330\) 10.6137 0.00177051
\(331\) −9588.45 −1.59223 −0.796116 0.605144i \(-0.793115\pi\)
−0.796116 + 0.605144i \(0.793115\pi\)
\(332\) 800.093 0.132261
\(333\) 2275.97 0.374542
\(334\) −6412.22 −1.05048
\(335\) −191.725 −0.0312689
\(336\) 783.659 0.127238
\(337\) −9263.59 −1.49739 −0.748694 0.662916i \(-0.769319\pi\)
−0.748694 + 0.662916i \(0.769319\pi\)
\(338\) 3938.57 0.633817
\(339\) −1501.05 −0.240489
\(340\) −116.506 −0.0185836
\(341\) −582.316 −0.0924756
\(342\) 0 0
\(343\) 6848.11 1.07803
\(344\) 1736.76 0.272209
\(345\) −122.523 −0.0191200
\(346\) −6389.43 −0.992768
\(347\) −3603.50 −0.557481 −0.278740 0.960367i \(-0.589917\pi\)
−0.278740 + 0.960367i \(0.589917\pi\)
\(348\) 373.811 0.0575815
\(349\) 3751.60 0.575411 0.287706 0.957719i \(-0.407108\pi\)
0.287706 + 0.957719i \(0.407108\pi\)
\(350\) −4054.53 −0.619211
\(351\) 407.435 0.0619580
\(352\) 62.2167 0.00942091
\(353\) −8836.39 −1.33233 −0.666166 0.745803i \(-0.732066\pi\)
−0.666166 + 0.745803i \(0.732066\pi\)
\(354\) −1464.28 −0.219846
\(355\) −458.025 −0.0684773
\(356\) 696.365 0.103672
\(357\) 1567.96 0.232452
\(358\) 4898.52 0.723170
\(359\) 7348.14 1.08028 0.540139 0.841576i \(-0.318371\pi\)
0.540139 + 0.841576i \(0.318371\pi\)
\(360\) 65.5078 0.00959045
\(361\) 0 0
\(362\) −4005.33 −0.581535
\(363\) 3981.66 0.575711
\(364\) 985.463 0.141902
\(365\) −104.872 −0.0150390
\(366\) 3159.05 0.451165
\(367\) −10829.4 −1.54030 −0.770150 0.637862i \(-0.779819\pi\)
−0.770150 + 0.637862i \(0.779819\pi\)
\(368\) −718.217 −0.101738
\(369\) −734.827 −0.103668
\(370\) 460.166 0.0646564
\(371\) −192.857 −0.0269883
\(372\) −3594.04 −0.500920
\(373\) −10614.6 −1.47347 −0.736734 0.676183i \(-0.763633\pi\)
−0.736734 + 0.676183i \(0.763633\pi\)
\(374\) 124.485 0.0172111
\(375\) −680.113 −0.0936557
\(376\) −1501.94 −0.206002
\(377\) 470.073 0.0642174
\(378\) −881.617 −0.119962
\(379\) −3538.17 −0.479535 −0.239767 0.970830i \(-0.577071\pi\)
−0.239767 + 0.970830i \(0.577071\pi\)
\(380\) 0 0
\(381\) −2596.38 −0.349124
\(382\) −8203.93 −1.09882
\(383\) −13138.1 −1.75280 −0.876402 0.481581i \(-0.840063\pi\)
−0.876402 + 0.481581i \(0.840063\pi\)
\(384\) 384.000 0.0510310
\(385\) −28.8804 −0.00382307
\(386\) 3513.10 0.463244
\(387\) −1953.86 −0.256641
\(388\) 4421.60 0.578538
\(389\) 1058.46 0.137958 0.0689792 0.997618i \(-0.478026\pi\)
0.0689792 + 0.997618i \(0.478026\pi\)
\(390\) 82.3769 0.0106957
\(391\) −1437.02 −0.185866
\(392\) 611.632 0.0788063
\(393\) 7034.38 0.902895
\(394\) −7341.14 −0.938684
\(395\) 200.610 0.0255539
\(396\) −69.9938 −0.00888212
\(397\) −15180.8 −1.91915 −0.959573 0.281461i \(-0.909181\pi\)
−0.959573 + 0.281461i \(0.909181\pi\)
\(398\) 5221.51 0.657615
\(399\) 0 0
\(400\) −1986.76 −0.248344
\(401\) 1336.20 0.166400 0.0832002 0.996533i \(-0.473486\pi\)
0.0832002 + 0.996533i \(0.473486\pi\)
\(402\) 1264.36 0.156867
\(403\) −4519.56 −0.558648
\(404\) −3585.49 −0.441546
\(405\) −73.6962 −0.00904196
\(406\) −1017.15 −0.124336
\(407\) −491.678 −0.0598810
\(408\) 768.316 0.0932287
\(409\) 1976.03 0.238896 0.119448 0.992840i \(-0.461888\pi\)
0.119448 + 0.992840i \(0.461888\pi\)
\(410\) −148.571 −0.0178960
\(411\) −6213.83 −0.745755
\(412\) −644.639 −0.0770852
\(413\) 3984.36 0.474716
\(414\) 807.994 0.0959196
\(415\) −181.987 −0.0215263
\(416\) 482.885 0.0569120
\(417\) 4402.63 0.517021
\(418\) 0 0
\(419\) 3242.90 0.378105 0.189052 0.981967i \(-0.439458\pi\)
0.189052 + 0.981967i \(0.439458\pi\)
\(420\) −178.249 −0.0207087
\(421\) −11959.4 −1.38448 −0.692241 0.721667i \(-0.743376\pi\)
−0.692241 + 0.721667i \(0.743376\pi\)
\(422\) −6946.71 −0.801328
\(423\) 1689.68 0.194220
\(424\) −94.5017 −0.0108241
\(425\) −3975.14 −0.453701
\(426\) 3020.51 0.343531
\(427\) −8595.90 −0.974204
\(428\) 4486.26 0.506663
\(429\) −88.0182 −0.00990573
\(430\) −395.039 −0.0443035
\(431\) 7226.13 0.807589 0.403794 0.914850i \(-0.367691\pi\)
0.403794 + 0.914850i \(0.367691\pi\)
\(432\) −432.000 −0.0481125
\(433\) −9903.01 −1.09909 −0.549547 0.835462i \(-0.685200\pi\)
−0.549547 + 0.835462i \(0.685200\pi\)
\(434\) 9779.53 1.08164
\(435\) −85.0261 −0.00937170
\(436\) −3932.66 −0.431973
\(437\) 0 0
\(438\) 691.593 0.0754465
\(439\) −7077.97 −0.769506 −0.384753 0.923020i \(-0.625713\pi\)
−0.384753 + 0.923020i \(0.625713\pi\)
\(440\) −14.1517 −0.00153330
\(441\) −688.086 −0.0742993
\(442\) 966.168 0.103973
\(443\) −7730.58 −0.829099 −0.414550 0.910027i \(-0.636061\pi\)
−0.414550 + 0.910027i \(0.636061\pi\)
\(444\) −3034.63 −0.324362
\(445\) −158.394 −0.0168732
\(446\) 5060.98 0.537320
\(447\) 530.843 0.0561701
\(448\) −1044.88 −0.110192
\(449\) −2353.41 −0.247359 −0.123679 0.992322i \(-0.539469\pi\)
−0.123679 + 0.992322i \(0.539469\pi\)
\(450\) 2235.10 0.234141
\(451\) 158.745 0.0165743
\(452\) 2001.40 0.208270
\(453\) −3416.23 −0.354323
\(454\) −13469.2 −1.39238
\(455\) −224.151 −0.0230953
\(456\) 0 0
\(457\) 8420.95 0.861959 0.430980 0.902362i \(-0.358168\pi\)
0.430980 + 0.902362i \(0.358168\pi\)
\(458\) 675.438 0.0689108
\(459\) −864.355 −0.0878968
\(460\) 163.364 0.0165584
\(461\) −669.622 −0.0676517 −0.0338258 0.999428i \(-0.510769\pi\)
−0.0338258 + 0.999428i \(0.510769\pi\)
\(462\) 190.456 0.0191792
\(463\) 5570.89 0.559182 0.279591 0.960119i \(-0.409801\pi\)
0.279591 + 0.960119i \(0.409801\pi\)
\(464\) −498.415 −0.0498671
\(465\) 817.492 0.0815275
\(466\) 12622.5 1.25478
\(467\) −10869.8 −1.07707 −0.538537 0.842602i \(-0.681023\pi\)
−0.538537 + 0.842602i \(0.681023\pi\)
\(468\) −543.246 −0.0536572
\(469\) −3440.37 −0.338724
\(470\) 341.628 0.0335279
\(471\) 5856.56 0.572943
\(472\) 1952.37 0.190392
\(473\) 422.092 0.0410313
\(474\) −1322.95 −0.128196
\(475\) 0 0
\(476\) −2090.62 −0.201309
\(477\) 106.314 0.0102050
\(478\) 6551.11 0.626864
\(479\) −2435.33 −0.232303 −0.116151 0.993232i \(-0.537056\pi\)
−0.116151 + 0.993232i \(0.537056\pi\)
\(480\) −87.3437 −0.00830557
\(481\) −3816.08 −0.361743
\(482\) 3336.55 0.315302
\(483\) −2198.58 −0.207120
\(484\) −5308.88 −0.498580
\(485\) −1005.73 −0.0941602
\(486\) 486.000 0.0453609
\(487\) −10685.2 −0.994233 −0.497116 0.867684i \(-0.665608\pi\)
−0.497116 + 0.867684i \(0.665608\pi\)
\(488\) −4212.07 −0.390720
\(489\) −1157.92 −0.107082
\(490\) −139.120 −0.0128261
\(491\) −9068.91 −0.833552 −0.416776 0.909009i \(-0.636840\pi\)
−0.416776 + 0.909009i \(0.636840\pi\)
\(492\) 979.769 0.0897793
\(493\) −997.239 −0.0911022
\(494\) 0 0
\(495\) 15.9206 0.00144561
\(496\) 4792.06 0.433810
\(497\) −8218.93 −0.741789
\(498\) 1200.14 0.107991
\(499\) −9085.54 −0.815080 −0.407540 0.913187i \(-0.633613\pi\)
−0.407540 + 0.913187i \(0.633613\pi\)
\(500\) 906.817 0.0811082
\(501\) −9618.33 −0.857716
\(502\) 4088.77 0.363528
\(503\) −229.914 −0.0203804 −0.0101902 0.999948i \(-0.503244\pi\)
−0.0101902 + 0.999948i \(0.503244\pi\)
\(504\) 1175.49 0.103890
\(505\) 815.546 0.0718640
\(506\) −174.551 −0.0153355
\(507\) 5907.86 0.517509
\(508\) 3461.84 0.302351
\(509\) −9812.78 −0.854507 −0.427253 0.904132i \(-0.640519\pi\)
−0.427253 + 0.904132i \(0.640519\pi\)
\(510\) −174.759 −0.0151735
\(511\) −1881.85 −0.162912
\(512\) −512.000 −0.0441942
\(513\) 0 0
\(514\) 10362.6 0.889253
\(515\) 146.628 0.0125460
\(516\) 2605.14 0.222258
\(517\) −365.023 −0.0310516
\(518\) 8257.34 0.700399
\(519\) −9584.15 −0.810592
\(520\) −109.836 −0.00926274
\(521\) −8772.27 −0.737658 −0.368829 0.929497i \(-0.620241\pi\)
−0.368829 + 0.929497i \(0.620241\pi\)
\(522\) 560.717 0.0470151
\(523\) 4563.38 0.381535 0.190767 0.981635i \(-0.438902\pi\)
0.190767 + 0.981635i \(0.438902\pi\)
\(524\) −9379.18 −0.781930
\(525\) −6081.80 −0.505583
\(526\) −14275.9 −1.18338
\(527\) 9588.05 0.792528
\(528\) 93.3251 0.00769214
\(529\) −10152.0 −0.834390
\(530\) 21.4951 0.00176168
\(531\) −2196.42 −0.179504
\(532\) 0 0
\(533\) 1232.07 0.100126
\(534\) 1044.55 0.0846480
\(535\) −1020.43 −0.0824620
\(536\) −1685.81 −0.135851
\(537\) 7347.78 0.590466
\(538\) 12791.0 1.02502
\(539\) 148.647 0.0118788
\(540\) 98.2616 0.00783057
\(541\) −5541.69 −0.440399 −0.220200 0.975455i \(-0.570671\pi\)
−0.220200 + 0.975455i \(0.570671\pi\)
\(542\) 12957.7 1.02690
\(543\) −6008.00 −0.474821
\(544\) −1024.42 −0.0807384
\(545\) 894.514 0.0703060
\(546\) 1478.19 0.115862
\(547\) −482.902 −0.0377466 −0.0188733 0.999822i \(-0.506008\pi\)
−0.0188733 + 0.999822i \(0.506008\pi\)
\(548\) 8285.10 0.645843
\(549\) 4738.58 0.368374
\(550\) −482.849 −0.0374341
\(551\) 0 0
\(552\) −1077.33 −0.0830688
\(553\) 3599.80 0.276815
\(554\) −7003.87 −0.537123
\(555\) 690.248 0.0527917
\(556\) −5870.18 −0.447753
\(557\) −9850.15 −0.749308 −0.374654 0.927165i \(-0.622238\pi\)
−0.374654 + 0.927165i \(0.622238\pi\)
\(558\) −5391.06 −0.409000
\(559\) 3276.00 0.247872
\(560\) 237.666 0.0179343
\(561\) 186.727 0.0140528
\(562\) 3445.49 0.258611
\(563\) 15083.7 1.12913 0.564567 0.825387i \(-0.309043\pi\)
0.564567 + 0.825387i \(0.309043\pi\)
\(564\) −2252.91 −0.168200
\(565\) −455.233 −0.0338970
\(566\) 1811.89 0.134557
\(567\) −1322.43 −0.0979482
\(568\) −4027.35 −0.297507
\(569\) −354.846 −0.0261439 −0.0130720 0.999915i \(-0.504161\pi\)
−0.0130720 + 0.999915i \(0.504161\pi\)
\(570\) 0 0
\(571\) 10394.6 0.761821 0.380910 0.924612i \(-0.375611\pi\)
0.380910 + 0.924612i \(0.375611\pi\)
\(572\) 117.358 0.00857861
\(573\) −12305.9 −0.897184
\(574\) −2665.99 −0.193861
\(575\) 5573.91 0.404258
\(576\) 576.000 0.0416667
\(577\) 1289.40 0.0930303 0.0465151 0.998918i \(-0.485188\pi\)
0.0465151 + 0.998918i \(0.485188\pi\)
\(578\) 7776.32 0.559606
\(579\) 5269.65 0.378237
\(580\) 113.368 0.00811613
\(581\) −3265.63 −0.233186
\(582\) 6632.40 0.472374
\(583\) −22.9671 −0.00163156
\(584\) −922.124 −0.0653386
\(585\) 123.565 0.00873299
\(586\) 13141.1 0.926373
\(587\) 19612.9 1.37906 0.689531 0.724256i \(-0.257817\pi\)
0.689531 + 0.724256i \(0.257817\pi\)
\(588\) 917.447 0.0643451
\(589\) 0 0
\(590\) −444.082 −0.0309874
\(591\) −11011.7 −0.766432
\(592\) 4046.17 0.280906
\(593\) 7358.41 0.509568 0.254784 0.966998i \(-0.417996\pi\)
0.254784 + 0.966998i \(0.417996\pi\)
\(594\) −104.991 −0.00725222
\(595\) 475.527 0.0327642
\(596\) −707.791 −0.0486447
\(597\) 7832.26 0.536940
\(598\) −1354.75 −0.0926420
\(599\) −16712.6 −1.13999 −0.569997 0.821647i \(-0.693056\pi\)
−0.569997 + 0.821647i \(0.693056\pi\)
\(600\) −2980.13 −0.202772
\(601\) −8181.83 −0.555314 −0.277657 0.960680i \(-0.589558\pi\)
−0.277657 + 0.960680i \(0.589558\pi\)
\(602\) −7088.70 −0.479923
\(603\) 1896.54 0.128081
\(604\) 4554.97 0.306853
\(605\) 1207.54 0.0811466
\(606\) −5378.23 −0.360521
\(607\) −19171.1 −1.28193 −0.640966 0.767569i \(-0.721466\pi\)
−0.640966 + 0.767569i \(0.721466\pi\)
\(608\) 0 0
\(609\) −1525.73 −0.101520
\(610\) 958.067 0.0635918
\(611\) −2833.07 −0.187584
\(612\) 1152.47 0.0761209
\(613\) −23387.4 −1.54096 −0.770481 0.637463i \(-0.779984\pi\)
−0.770481 + 0.637463i \(0.779984\pi\)
\(614\) 1133.16 0.0744800
\(615\) −222.856 −0.0146121
\(616\) −253.941 −0.0166097
\(617\) 29646.2 1.93438 0.967189 0.254056i \(-0.0817649\pi\)
0.967189 + 0.254056i \(0.0817649\pi\)
\(618\) −966.959 −0.0629398
\(619\) 17042.8 1.10663 0.553317 0.832971i \(-0.313362\pi\)
0.553317 + 0.832971i \(0.313362\pi\)
\(620\) −1089.99 −0.0706049
\(621\) 1211.99 0.0783181
\(622\) −7015.11 −0.452219
\(623\) −2842.26 −0.182781
\(624\) 724.328 0.0464685
\(625\) 15315.3 0.980177
\(626\) 643.536 0.0410876
\(627\) 0 0
\(628\) −7808.75 −0.496183
\(629\) 8095.66 0.513188
\(630\) −267.374 −0.0169086
\(631\) −12936.7 −0.816170 −0.408085 0.912944i \(-0.633803\pi\)
−0.408085 + 0.912944i \(0.633803\pi\)
\(632\) 1763.93 0.111021
\(633\) −10420.1 −0.654282
\(634\) −7594.05 −0.475707
\(635\) −787.421 −0.0492092
\(636\) −141.753 −0.00883782
\(637\) 1153.70 0.0717604
\(638\) −121.132 −0.00751669
\(639\) 4530.76 0.280492
\(640\) 116.458 0.00719284
\(641\) 30925.1 1.90557 0.952783 0.303650i \(-0.0982055\pi\)
0.952783 + 0.303650i \(0.0982055\pi\)
\(642\) 6729.39 0.413688
\(643\) −2848.23 −0.174686 −0.0873430 0.996178i \(-0.527838\pi\)
−0.0873430 + 0.996178i \(0.527838\pi\)
\(644\) 2931.44 0.179371
\(645\) −592.559 −0.0361736
\(646\) 0 0
\(647\) 14856.5 0.902733 0.451367 0.892339i \(-0.350937\pi\)
0.451367 + 0.892339i \(0.350937\pi\)
\(648\) −648.000 −0.0392837
\(649\) 474.493 0.0286987
\(650\) −3747.56 −0.226141
\(651\) 14669.3 0.883157
\(652\) 1543.90 0.0927357
\(653\) −697.326 −0.0417894 −0.0208947 0.999782i \(-0.506651\pi\)
−0.0208947 + 0.999782i \(0.506651\pi\)
\(654\) −5898.99 −0.352705
\(655\) 2133.36 0.127263
\(656\) −1306.36 −0.0777512
\(657\) 1037.39 0.0616018
\(658\) 6130.26 0.363195
\(659\) 2792.41 0.165064 0.0825319 0.996588i \(-0.473699\pi\)
0.0825319 + 0.996588i \(0.473699\pi\)
\(660\) −21.2275 −0.00125194
\(661\) −28297.2 −1.66510 −0.832551 0.553949i \(-0.813120\pi\)
−0.832551 + 0.553949i \(0.813120\pi\)
\(662\) 19176.9 1.12588
\(663\) 1449.25 0.0848933
\(664\) −1600.19 −0.0935230
\(665\) 0 0
\(666\) −4551.94 −0.264841
\(667\) 1398.32 0.0811741
\(668\) 12824.4 0.742803
\(669\) 7591.48 0.438720
\(670\) 383.450 0.0221104
\(671\) −1023.68 −0.0588950
\(672\) −1567.32 −0.0899712
\(673\) 19162.8 1.09758 0.548790 0.835960i \(-0.315089\pi\)
0.548790 + 0.835960i \(0.315089\pi\)
\(674\) 18527.2 1.05881
\(675\) 3352.65 0.191176
\(676\) −7877.15 −0.448176
\(677\) 14029.7 0.796463 0.398232 0.917285i \(-0.369624\pi\)
0.398232 + 0.917285i \(0.369624\pi\)
\(678\) 3002.10 0.170051
\(679\) −18047.0 −1.02000
\(680\) 233.012 0.0131406
\(681\) −20203.8 −1.13687
\(682\) 1164.63 0.0653901
\(683\) 6578.33 0.368540 0.184270 0.982876i \(-0.441008\pi\)
0.184270 + 0.982876i \(0.441008\pi\)
\(684\) 0 0
\(685\) −1884.51 −0.105114
\(686\) −13696.2 −0.762279
\(687\) 1013.16 0.0562654
\(688\) −3473.52 −0.192481
\(689\) −178.256 −0.00985633
\(690\) 245.046 0.0135199
\(691\) 28001.9 1.54159 0.770797 0.637080i \(-0.219858\pi\)
0.770797 + 0.637080i \(0.219858\pi\)
\(692\) 12778.9 0.701993
\(693\) 285.684 0.0156598
\(694\) 7206.99 0.394198
\(695\) 1335.22 0.0728743
\(696\) −747.622 −0.0407163
\(697\) −2613.79 −0.142044
\(698\) −7503.20 −0.406877
\(699\) 18933.8 1.02452
\(700\) 8109.06 0.437848
\(701\) 1649.54 0.0888762 0.0444381 0.999012i \(-0.485850\pi\)
0.0444381 + 0.999012i \(0.485850\pi\)
\(702\) −814.869 −0.0438109
\(703\) 0 0
\(704\) −124.433 −0.00666159
\(705\) 512.442 0.0273754
\(706\) 17672.8 0.942102
\(707\) 14634.4 0.778476
\(708\) 2928.56 0.155455
\(709\) 12138.8 0.642993 0.321496 0.946911i \(-0.395814\pi\)
0.321496 + 0.946911i \(0.395814\pi\)
\(710\) 916.050 0.0484208
\(711\) −1984.42 −0.104672
\(712\) −1392.73 −0.0733073
\(713\) −13444.3 −0.706160
\(714\) −3135.93 −0.164368
\(715\) −26.6939 −0.00139622
\(716\) −9797.04 −0.511358
\(717\) 9826.67 0.511832
\(718\) −14696.3 −0.763872
\(719\) −17081.4 −0.885994 −0.442997 0.896523i \(-0.646085\pi\)
−0.442997 + 0.896523i \(0.646085\pi\)
\(720\) −131.016 −0.00678147
\(721\) 2631.13 0.135906
\(722\) 0 0
\(723\) 5004.82 0.257443
\(724\) 8010.67 0.411207
\(725\) 3868.08 0.198147
\(726\) −7963.32 −0.407089
\(727\) −8523.48 −0.434826 −0.217413 0.976080i \(-0.569762\pi\)
−0.217413 + 0.976080i \(0.569762\pi\)
\(728\) −1970.93 −0.100340
\(729\) 729.000 0.0370370
\(730\) 209.744 0.0106342
\(731\) −6949.90 −0.351644
\(732\) −6318.10 −0.319022
\(733\) 19655.2 0.990425 0.495212 0.868772i \(-0.335090\pi\)
0.495212 + 0.868772i \(0.335090\pi\)
\(734\) 21658.8 1.08916
\(735\) −208.680 −0.0104725
\(736\) 1436.43 0.0719397
\(737\) −409.709 −0.0204774
\(738\) 1469.65 0.0733045
\(739\) −844.721 −0.0420481 −0.0210241 0.999779i \(-0.506693\pi\)
−0.0210241 + 0.999779i \(0.506693\pi\)
\(740\) −920.331 −0.0457190
\(741\) 0 0
\(742\) 385.714 0.0190836
\(743\) 23692.3 1.16983 0.584916 0.811094i \(-0.301127\pi\)
0.584916 + 0.811094i \(0.301127\pi\)
\(744\) 7188.08 0.354204
\(745\) 160.992 0.00791719
\(746\) 21229.2 1.04190
\(747\) 1800.21 0.0881743
\(748\) −248.969 −0.0121701
\(749\) −18310.9 −0.893280
\(750\) 1360.23 0.0662246
\(751\) 8581.33 0.416960 0.208480 0.978027i \(-0.433148\pi\)
0.208480 + 0.978027i \(0.433148\pi\)
\(752\) 3003.88 0.145665
\(753\) 6133.16 0.296819
\(754\) −940.145 −0.0454086
\(755\) −1036.06 −0.0499420
\(756\) 1763.23 0.0848256
\(757\) −19326.7 −0.927926 −0.463963 0.885855i \(-0.653573\pi\)
−0.463963 + 0.885855i \(0.653573\pi\)
\(758\) 7076.34 0.339082
\(759\) −261.827 −0.0125213
\(760\) 0 0
\(761\) −26601.6 −1.26716 −0.633580 0.773677i \(-0.718415\pi\)
−0.633580 + 0.773677i \(0.718415\pi\)
\(762\) 5192.75 0.246868
\(763\) 16051.4 0.761598
\(764\) 16407.9 0.776984
\(765\) −262.139 −0.0123891
\(766\) 26276.1 1.23942
\(767\) 3682.70 0.173370
\(768\) −768.000 −0.0360844
\(769\) −24235.8 −1.13650 −0.568248 0.822857i \(-0.692379\pi\)
−0.568248 + 0.822857i \(0.692379\pi\)
\(770\) 57.7608 0.00270332
\(771\) 15543.9 0.726072
\(772\) −7026.20 −0.327563
\(773\) 11054.8 0.514377 0.257188 0.966361i \(-0.417204\pi\)
0.257188 + 0.966361i \(0.417204\pi\)
\(774\) 3907.71 0.181473
\(775\) −37190.0 −1.72375
\(776\) −8843.20 −0.409088
\(777\) 12386.0 0.571873
\(778\) −2116.91 −0.0975514
\(779\) 0 0
\(780\) −164.754 −0.00756299
\(781\) −978.782 −0.0448445
\(782\) 2874.05 0.131427
\(783\) 841.075 0.0383877
\(784\) −1223.26 −0.0557245
\(785\) 1776.16 0.0807565
\(786\) −14068.8 −0.638443
\(787\) 34632.5 1.56863 0.784316 0.620361i \(-0.213014\pi\)
0.784316 + 0.620361i \(0.213014\pi\)
\(788\) 14682.3 0.663750
\(789\) −21413.8 −0.966224
\(790\) −401.220 −0.0180693
\(791\) −8168.82 −0.367193
\(792\) 139.988 0.00628061
\(793\) −7945.10 −0.355787
\(794\) 30361.5 1.35704
\(795\) 32.2427 0.00143840
\(796\) −10443.0 −0.465004
\(797\) −21904.6 −0.973526 −0.486763 0.873534i \(-0.661822\pi\)
−0.486763 + 0.873534i \(0.661822\pi\)
\(798\) 0 0
\(799\) 6010.23 0.266116
\(800\) 3973.51 0.175606
\(801\) 1566.82 0.0691148
\(802\) −2672.40 −0.117663
\(803\) −224.107 −0.00984879
\(804\) −2528.72 −0.110922
\(805\) −666.779 −0.0291936
\(806\) 9039.12 0.395024
\(807\) 19186.6 0.836925
\(808\) 7170.97 0.312220
\(809\) 33327.8 1.44838 0.724192 0.689598i \(-0.242213\pi\)
0.724192 + 0.689598i \(0.242213\pi\)
\(810\) 147.392 0.00639363
\(811\) −1389.76 −0.0601738 −0.0300869 0.999547i \(-0.509578\pi\)
−0.0300869 + 0.999547i \(0.509578\pi\)
\(812\) 2034.31 0.0879191
\(813\) 19436.6 0.838464
\(814\) 983.356 0.0423423
\(815\) −351.171 −0.0150932
\(816\) −1536.63 −0.0659226
\(817\) 0 0
\(818\) −3952.06 −0.168925
\(819\) 2217.29 0.0946013
\(820\) 297.141 0.0126544
\(821\) −11572.6 −0.491943 −0.245972 0.969277i \(-0.579107\pi\)
−0.245972 + 0.969277i \(0.579107\pi\)
\(822\) 12427.7 0.527329
\(823\) 26073.3 1.10432 0.552162 0.833737i \(-0.313803\pi\)
0.552162 + 0.833737i \(0.313803\pi\)
\(824\) 1289.28 0.0545074
\(825\) −724.274 −0.0305648
\(826\) −7968.72 −0.335675
\(827\) −44795.6 −1.88355 −0.941775 0.336245i \(-0.890843\pi\)
−0.941775 + 0.336245i \(0.890843\pi\)
\(828\) −1615.99 −0.0678254
\(829\) −12346.2 −0.517250 −0.258625 0.965978i \(-0.583269\pi\)
−0.258625 + 0.965978i \(0.583269\pi\)
\(830\) 363.974 0.0152214
\(831\) −10505.8 −0.438559
\(832\) −965.771 −0.0402429
\(833\) −2447.53 −0.101803
\(834\) −8805.26 −0.365589
\(835\) −2917.02 −0.120895
\(836\) 0 0
\(837\) −8086.59 −0.333947
\(838\) −6485.79 −0.267360
\(839\) 7050.38 0.290115 0.145057 0.989423i \(-0.453663\pi\)
0.145057 + 0.989423i \(0.453663\pi\)
\(840\) 356.498 0.0146433
\(841\) −23418.6 −0.960212
\(842\) 23918.8 0.978976
\(843\) 5168.24 0.211155
\(844\) 13893.4 0.566624
\(845\) 1791.72 0.0729431
\(846\) −3379.37 −0.137335
\(847\) 21668.5 0.879030
\(848\) 189.003 0.00765378
\(849\) 2717.84 0.109866
\(850\) 7950.29 0.320815
\(851\) −11351.7 −0.457262
\(852\) −6041.02 −0.242913
\(853\) 6590.63 0.264547 0.132274 0.991213i \(-0.457772\pi\)
0.132274 + 0.991213i \(0.457772\pi\)
\(854\) 17191.8 0.688866
\(855\) 0 0
\(856\) −8972.52 −0.358264
\(857\) −41470.4 −1.65298 −0.826489 0.562954i \(-0.809665\pi\)
−0.826489 + 0.562954i \(0.809665\pi\)
\(858\) 176.036 0.00700441
\(859\) 33928.2 1.34763 0.673816 0.738899i \(-0.264654\pi\)
0.673816 + 0.738899i \(0.264654\pi\)
\(860\) 790.079 0.0313273
\(861\) −3998.99 −0.158287
\(862\) −14452.3 −0.571051
\(863\) 6042.42 0.238339 0.119169 0.992874i \(-0.461977\pi\)
0.119169 + 0.992874i \(0.461977\pi\)
\(864\) 864.000 0.0340207
\(865\) −2906.65 −0.114253
\(866\) 19806.0 0.777177
\(867\) 11664.5 0.456916
\(868\) −19559.1 −0.764836
\(869\) 428.695 0.0167347
\(870\) 170.052 0.00662680
\(871\) −3179.90 −0.123705
\(872\) 7865.32 0.305451
\(873\) 9948.60 0.385692
\(874\) 0 0
\(875\) −3701.23 −0.142999
\(876\) −1383.19 −0.0533488
\(877\) 23546.2 0.906611 0.453306 0.891355i \(-0.350245\pi\)
0.453306 + 0.891355i \(0.350245\pi\)
\(878\) 14155.9 0.544123
\(879\) 19711.7 0.756381
\(880\) 28.3033 0.00108421
\(881\) −39700.3 −1.51820 −0.759101 0.650973i \(-0.774361\pi\)
−0.759101 + 0.650973i \(0.774361\pi\)
\(882\) 1376.17 0.0525375
\(883\) −41792.3 −1.59278 −0.796389 0.604785i \(-0.793259\pi\)
−0.796389 + 0.604785i \(0.793259\pi\)
\(884\) −1932.34 −0.0735198
\(885\) −666.122 −0.0253011
\(886\) 15461.2 0.586262
\(887\) 3207.98 0.121435 0.0607177 0.998155i \(-0.480661\pi\)
0.0607177 + 0.998155i \(0.480661\pi\)
\(888\) 6069.25 0.229359
\(889\) −14129.7 −0.533065
\(890\) 316.787 0.0119312
\(891\) −157.486 −0.00592141
\(892\) −10122.0 −0.379942
\(893\) 0 0
\(894\) −1061.69 −0.0397183
\(895\) 2228.41 0.0832263
\(896\) 2089.76 0.0779173
\(897\) −2032.13 −0.0756419
\(898\) 4706.81 0.174909
\(899\) −9329.81 −0.346125
\(900\) −4470.20 −0.165563
\(901\) 378.162 0.0139827
\(902\) −317.490 −0.0117198
\(903\) −10633.0 −0.391856
\(904\) −4002.80 −0.147269
\(905\) −1822.09 −0.0669262
\(906\) 6832.46 0.250544
\(907\) −51184.8 −1.87383 −0.936915 0.349558i \(-0.886332\pi\)
−0.936915 + 0.349558i \(0.886332\pi\)
\(908\) 26938.4 0.984560
\(909\) −8067.34 −0.294364
\(910\) 448.302 0.0163308
\(911\) −15160.8 −0.551372 −0.275686 0.961248i \(-0.588905\pi\)
−0.275686 + 0.961248i \(0.588905\pi\)
\(912\) 0 0
\(913\) −388.900 −0.0140971
\(914\) −16841.9 −0.609497
\(915\) 1437.10 0.0519225
\(916\) −1350.88 −0.0487273
\(917\) 38281.7 1.37860
\(918\) 1728.71 0.0621524
\(919\) 33318.2 1.19594 0.597969 0.801519i \(-0.295974\pi\)
0.597969 + 0.801519i \(0.295974\pi\)
\(920\) −326.728 −0.0117086
\(921\) 1699.74 0.0608127
\(922\) 1339.24 0.0478369
\(923\) −7596.67 −0.270907
\(924\) −380.912 −0.0135618
\(925\) −31401.3 −1.11618
\(926\) −11141.8 −0.395401
\(927\) −1450.44 −0.0513901
\(928\) 996.830 0.0352613
\(929\) 14464.8 0.510843 0.255421 0.966830i \(-0.417786\pi\)
0.255421 + 0.966830i \(0.417786\pi\)
\(930\) −1634.98 −0.0576486
\(931\) 0 0
\(932\) −25245.0 −0.887262
\(933\) −10522.7 −0.369235
\(934\) 21739.6 0.761606
\(935\) 56.6299 0.00198074
\(936\) 1086.49 0.0379414
\(937\) 16046.8 0.559475 0.279737 0.960077i \(-0.409753\pi\)
0.279737 + 0.960077i \(0.409753\pi\)
\(938\) 6880.74 0.239514
\(939\) 965.304 0.0335479
\(940\) −683.256 −0.0237078
\(941\) −19129.4 −0.662700 −0.331350 0.943508i \(-0.607504\pi\)
−0.331350 + 0.943508i \(0.607504\pi\)
\(942\) −11713.1 −0.405132
\(943\) 3665.04 0.126564
\(944\) −3904.74 −0.134628
\(945\) −401.061 −0.0138058
\(946\) −844.184 −0.0290135
\(947\) −41617.7 −1.42808 −0.714041 0.700104i \(-0.753137\pi\)
−0.714041 + 0.700104i \(0.753137\pi\)
\(948\) 2645.90 0.0906485
\(949\) −1739.38 −0.0594969
\(950\) 0 0
\(951\) −11391.1 −0.388413
\(952\) 4181.24 0.142347
\(953\) 36269.8 1.23284 0.616419 0.787419i \(-0.288583\pi\)
0.616419 + 0.787419i \(0.288583\pi\)
\(954\) −212.629 −0.00721605
\(955\) −3732.09 −0.126458
\(956\) −13102.2 −0.443260
\(957\) −181.698 −0.00613736
\(958\) 4870.66 0.164263
\(959\) −33816.1 −1.13867
\(960\) 174.687 0.00587293
\(961\) 59911.3 2.01105
\(962\) 7632.17 0.255791
\(963\) 10094.1 0.337775
\(964\) −6673.09 −0.222952
\(965\) 1598.16 0.0533126
\(966\) 4397.17 0.146456
\(967\) 28249.4 0.939442 0.469721 0.882815i \(-0.344354\pi\)
0.469721 + 0.882815i \(0.344354\pi\)
\(968\) 10617.8 0.352549
\(969\) 0 0
\(970\) 2011.45 0.0665813
\(971\) 11234.1 0.371285 0.185643 0.982617i \(-0.440563\pi\)
0.185643 + 0.982617i \(0.440563\pi\)
\(972\) −972.000 −0.0320750
\(973\) 23959.5 0.789420
\(974\) 21370.3 0.703029
\(975\) −5621.34 −0.184643
\(976\) 8424.14 0.276281
\(977\) 10338.6 0.338547 0.169273 0.985569i \(-0.445858\pi\)
0.169273 + 0.985569i \(0.445858\pi\)
\(978\) 2315.84 0.0757184
\(979\) −338.481 −0.0110499
\(980\) 278.240 0.00906945
\(981\) −8848.49 −0.287982
\(982\) 18137.8 0.589410
\(983\) 35054.0 1.13739 0.568693 0.822550i \(-0.307449\pi\)
0.568693 + 0.822550i \(0.307449\pi\)
\(984\) −1959.54 −0.0634836
\(985\) −3339.60 −0.108029
\(986\) 1994.48 0.0644190
\(987\) 9195.39 0.296548
\(988\) 0 0
\(989\) 9745.09 0.313322
\(990\) −31.8412 −0.00102220
\(991\) 25256.8 0.809595 0.404798 0.914406i \(-0.367342\pi\)
0.404798 + 0.914406i \(0.367342\pi\)
\(992\) −9584.11 −0.306750
\(993\) 28765.3 0.919275
\(994\) 16437.9 0.524524
\(995\) 2375.34 0.0756818
\(996\) −2400.28 −0.0763612
\(997\) −39035.2 −1.23998 −0.619989 0.784611i \(-0.712863\pi\)
−0.619989 + 0.784611i \(0.712863\pi\)
\(998\) 18171.1 0.576348
\(999\) −6827.91 −0.216242
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 2166.4.a.j.1.2 2
19.18 odd 2 2166.4.a.p.1.2 yes 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2166.4.a.j.1.2 2 1.1 even 1 trivial
2166.4.a.p.1.2 yes 2 19.18 odd 2