Properties

Label 4730.2.a.bf.1.13
Level 4730
Weight 2
Character 4730.1
Self dual yes
Analytic conductor 37.769
Analytic rank 0
Dimension 13
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4730.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(37.7692401561\)
Analytic rank: \(0\)
Dimension: \(13\)
Coefficient field: \(\mathbb{Q}[x]/(x^{13} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Root \(-3.30461\)
Character \(\chi\) = 4730.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +3.30461 q^{3} +1.00000 q^{4} -1.00000 q^{5} +3.30461 q^{6} -0.676945 q^{7} +1.00000 q^{8} +7.92047 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +3.30461 q^{3} +1.00000 q^{4} -1.00000 q^{5} +3.30461 q^{6} -0.676945 q^{7} +1.00000 q^{8} +7.92047 q^{9} -1.00000 q^{10} +1.00000 q^{11} +3.30461 q^{12} -3.96088 q^{13} -0.676945 q^{14} -3.30461 q^{15} +1.00000 q^{16} -2.43964 q^{17} +7.92047 q^{18} +1.47849 q^{19} -1.00000 q^{20} -2.23704 q^{21} +1.00000 q^{22} +3.38657 q^{23} +3.30461 q^{24} +1.00000 q^{25} -3.96088 q^{26} +16.2602 q^{27} -0.676945 q^{28} +2.44967 q^{29} -3.30461 q^{30} +8.31634 q^{31} +1.00000 q^{32} +3.30461 q^{33} -2.43964 q^{34} +0.676945 q^{35} +7.92047 q^{36} +11.2005 q^{37} +1.47849 q^{38} -13.0892 q^{39} -1.00000 q^{40} -4.31368 q^{41} -2.23704 q^{42} +1.00000 q^{43} +1.00000 q^{44} -7.92047 q^{45} +3.38657 q^{46} +7.27516 q^{47} +3.30461 q^{48} -6.54175 q^{49} +1.00000 q^{50} -8.06207 q^{51} -3.96088 q^{52} +9.23964 q^{53} +16.2602 q^{54} -1.00000 q^{55} -0.676945 q^{56} +4.88583 q^{57} +2.44967 q^{58} +1.87853 q^{59} -3.30461 q^{60} -14.6864 q^{61} +8.31634 q^{62} -5.36172 q^{63} +1.00000 q^{64} +3.96088 q^{65} +3.30461 q^{66} -2.45232 q^{67} -2.43964 q^{68} +11.1913 q^{69} +0.676945 q^{70} +8.83857 q^{71} +7.92047 q^{72} +5.06238 q^{73} +11.2005 q^{74} +3.30461 q^{75} +1.47849 q^{76} -0.676945 q^{77} -13.0892 q^{78} +6.51534 q^{79} -1.00000 q^{80} +29.9724 q^{81} -4.31368 q^{82} -5.30438 q^{83} -2.23704 q^{84} +2.43964 q^{85} +1.00000 q^{86} +8.09520 q^{87} +1.00000 q^{88} -16.4475 q^{89} -7.92047 q^{90} +2.68130 q^{91} +3.38657 q^{92} +27.4823 q^{93} +7.27516 q^{94} -1.47849 q^{95} +3.30461 q^{96} -16.6841 q^{97} -6.54175 q^{98} +7.92047 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 13q + 13q^{2} + 13q^{4} - 13q^{5} + 7q^{7} + 13q^{8} + 25q^{9} + O(q^{10}) \) \( 13q + 13q^{2} + 13q^{4} - 13q^{5} + 7q^{7} + 13q^{8} + 25q^{9} - 13q^{10} + 13q^{11} + 11q^{13} + 7q^{14} + 13q^{16} - 2q^{17} + 25q^{18} + 7q^{19} - 13q^{20} + 12q^{21} + 13q^{22} + 12q^{23} + 13q^{25} + 11q^{26} - 15q^{27} + 7q^{28} + 14q^{29} + 20q^{31} + 13q^{32} - 2q^{34} - 7q^{35} + 25q^{36} + 17q^{37} + 7q^{38} - 4q^{39} - 13q^{40} + 9q^{41} + 12q^{42} + 13q^{43} + 13q^{44} - 25q^{45} + 12q^{46} - 9q^{47} + 30q^{49} + 13q^{50} - 3q^{51} + 11q^{52} + 22q^{53} - 15q^{54} - 13q^{55} + 7q^{56} + 17q^{57} + 14q^{58} + 19q^{59} + 2q^{61} + 20q^{62} + 12q^{63} + 13q^{64} - 11q^{65} + 9q^{67} - 2q^{68} - 6q^{69} - 7q^{70} + 6q^{71} + 25q^{72} + 7q^{73} + 17q^{74} + 7q^{76} + 7q^{77} - 4q^{78} + 50q^{79} - 13q^{80} + 85q^{81} + 9q^{82} + q^{83} + 12q^{84} + 2q^{85} + 13q^{86} - 21q^{87} + 13q^{88} + 5q^{89} - 25q^{90} + 5q^{91} + 12q^{92} + 3q^{93} - 9q^{94} - 7q^{95} + 20q^{97} + 30q^{98} + 25q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 3.30461 1.90792 0.953960 0.299935i \(-0.0969649\pi\)
0.953960 + 0.299935i \(0.0969649\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) 3.30461 1.34910
\(7\) −0.676945 −0.255861 −0.127931 0.991783i \(-0.540833\pi\)
−0.127931 + 0.991783i \(0.540833\pi\)
\(8\) 1.00000 0.353553
\(9\) 7.92047 2.64016
\(10\) −1.00000 −0.316228
\(11\) 1.00000 0.301511
\(12\) 3.30461 0.953960
\(13\) −3.96088 −1.09855 −0.549276 0.835641i \(-0.685096\pi\)
−0.549276 + 0.835641i \(0.685096\pi\)
\(14\) −0.676945 −0.180921
\(15\) −3.30461 −0.853248
\(16\) 1.00000 0.250000
\(17\) −2.43964 −0.591700 −0.295850 0.955234i \(-0.595603\pi\)
−0.295850 + 0.955234i \(0.595603\pi\)
\(18\) 7.92047 1.86687
\(19\) 1.47849 0.339189 0.169594 0.985514i \(-0.445754\pi\)
0.169594 + 0.985514i \(0.445754\pi\)
\(20\) −1.00000 −0.223607
\(21\) −2.23704 −0.488162
\(22\) 1.00000 0.213201
\(23\) 3.38657 0.706150 0.353075 0.935595i \(-0.385136\pi\)
0.353075 + 0.935595i \(0.385136\pi\)
\(24\) 3.30461 0.674551
\(25\) 1.00000 0.200000
\(26\) −3.96088 −0.776793
\(27\) 16.2602 3.12929
\(28\) −0.676945 −0.127931
\(29\) 2.44967 0.454892 0.227446 0.973791i \(-0.426963\pi\)
0.227446 + 0.973791i \(0.426963\pi\)
\(30\) −3.30461 −0.603337
\(31\) 8.31634 1.49366 0.746829 0.665016i \(-0.231575\pi\)
0.746829 + 0.665016i \(0.231575\pi\)
\(32\) 1.00000 0.176777
\(33\) 3.30461 0.575259
\(34\) −2.43964 −0.418395
\(35\) 0.676945 0.114425
\(36\) 7.92047 1.32008
\(37\) 11.2005 1.84135 0.920673 0.390334i \(-0.127640\pi\)
0.920673 + 0.390334i \(0.127640\pi\)
\(38\) 1.47849 0.239843
\(39\) −13.0892 −2.09595
\(40\) −1.00000 −0.158114
\(41\) −4.31368 −0.673684 −0.336842 0.941561i \(-0.609359\pi\)
−0.336842 + 0.941561i \(0.609359\pi\)
\(42\) −2.23704 −0.345183
\(43\) 1.00000 0.152499
\(44\) 1.00000 0.150756
\(45\) −7.92047 −1.18071
\(46\) 3.38657 0.499323
\(47\) 7.27516 1.06119 0.530596 0.847625i \(-0.321968\pi\)
0.530596 + 0.847625i \(0.321968\pi\)
\(48\) 3.30461 0.476980
\(49\) −6.54175 −0.934535
\(50\) 1.00000 0.141421
\(51\) −8.06207 −1.12892
\(52\) −3.96088 −0.549276
\(53\) 9.23964 1.26916 0.634581 0.772857i \(-0.281173\pi\)
0.634581 + 0.772857i \(0.281173\pi\)
\(54\) 16.2602 2.21274
\(55\) −1.00000 −0.134840
\(56\) −0.676945 −0.0904606
\(57\) 4.88583 0.647145
\(58\) 2.44967 0.321657
\(59\) 1.87853 0.244563 0.122282 0.992495i \(-0.460979\pi\)
0.122282 + 0.992495i \(0.460979\pi\)
\(60\) −3.30461 −0.426624
\(61\) −14.6864 −1.88040 −0.940198 0.340630i \(-0.889360\pi\)
−0.940198 + 0.340630i \(0.889360\pi\)
\(62\) 8.31634 1.05618
\(63\) −5.36172 −0.675513
\(64\) 1.00000 0.125000
\(65\) 3.96088 0.491287
\(66\) 3.30461 0.406770
\(67\) −2.45232 −0.299599 −0.149799 0.988716i \(-0.547863\pi\)
−0.149799 + 0.988716i \(0.547863\pi\)
\(68\) −2.43964 −0.295850
\(69\) 11.1913 1.34728
\(70\) 0.676945 0.0809104
\(71\) 8.83857 1.04895 0.524473 0.851427i \(-0.324262\pi\)
0.524473 + 0.851427i \(0.324262\pi\)
\(72\) 7.92047 0.933436
\(73\) 5.06238 0.592507 0.296253 0.955109i \(-0.404263\pi\)
0.296253 + 0.955109i \(0.404263\pi\)
\(74\) 11.2005 1.30203
\(75\) 3.30461 0.381584
\(76\) 1.47849 0.169594
\(77\) −0.676945 −0.0771450
\(78\) −13.0892 −1.48206
\(79\) 6.51534 0.733033 0.366517 0.930411i \(-0.380550\pi\)
0.366517 + 0.930411i \(0.380550\pi\)
\(80\) −1.00000 −0.111803
\(81\) 29.9724 3.33027
\(82\) −4.31368 −0.476366
\(83\) −5.30438 −0.582231 −0.291116 0.956688i \(-0.594026\pi\)
−0.291116 + 0.956688i \(0.594026\pi\)
\(84\) −2.23704 −0.244081
\(85\) 2.43964 0.264616
\(86\) 1.00000 0.107833
\(87\) 8.09520 0.867897
\(88\) 1.00000 0.106600
\(89\) −16.4475 −1.74343 −0.871716 0.490011i \(-0.836993\pi\)
−0.871716 + 0.490011i \(0.836993\pi\)
\(90\) −7.92047 −0.834891
\(91\) 2.68130 0.281077
\(92\) 3.38657 0.353075
\(93\) 27.4823 2.84978
\(94\) 7.27516 0.750376
\(95\) −1.47849 −0.151690
\(96\) 3.30461 0.337276
\(97\) −16.6841 −1.69401 −0.847004 0.531586i \(-0.821596\pi\)
−0.847004 + 0.531586i \(0.821596\pi\)
\(98\) −6.54175 −0.660816
\(99\) 7.92047 0.796037
\(100\) 1.00000 0.100000
\(101\) 9.00199 0.895732 0.447866 0.894101i \(-0.352184\pi\)
0.447866 + 0.894101i \(0.352184\pi\)
\(102\) −8.06207 −0.798264
\(103\) 4.73558 0.466610 0.233305 0.972404i \(-0.425046\pi\)
0.233305 + 0.972404i \(0.425046\pi\)
\(104\) −3.96088 −0.388397
\(105\) 2.23704 0.218313
\(106\) 9.23964 0.897433
\(107\) 7.25685 0.701546 0.350773 0.936460i \(-0.385919\pi\)
0.350773 + 0.936460i \(0.385919\pi\)
\(108\) 16.2602 1.56464
\(109\) −9.44895 −0.905045 −0.452523 0.891753i \(-0.649476\pi\)
−0.452523 + 0.891753i \(0.649476\pi\)
\(110\) −1.00000 −0.0953463
\(111\) 37.0132 3.51314
\(112\) −0.676945 −0.0639653
\(113\) −16.2365 −1.52741 −0.763703 0.645568i \(-0.776621\pi\)
−0.763703 + 0.645568i \(0.776621\pi\)
\(114\) 4.88583 0.457600
\(115\) −3.38657 −0.315800
\(116\) 2.44967 0.227446
\(117\) −31.3721 −2.90035
\(118\) 1.87853 0.172932
\(119\) 1.65150 0.151393
\(120\) −3.30461 −0.301669
\(121\) 1.00000 0.0909091
\(122\) −14.6864 −1.32964
\(123\) −14.2550 −1.28533
\(124\) 8.31634 0.746829
\(125\) −1.00000 −0.0894427
\(126\) −5.36172 −0.477660
\(127\) 9.05438 0.803446 0.401723 0.915761i \(-0.368411\pi\)
0.401723 + 0.915761i \(0.368411\pi\)
\(128\) 1.00000 0.0883883
\(129\) 3.30461 0.290955
\(130\) 3.96088 0.347393
\(131\) −10.2913 −0.899154 −0.449577 0.893242i \(-0.648425\pi\)
−0.449577 + 0.893242i \(0.648425\pi\)
\(132\) 3.30461 0.287630
\(133\) −1.00086 −0.0867852
\(134\) −2.45232 −0.211848
\(135\) −16.2602 −1.39946
\(136\) −2.43964 −0.209197
\(137\) −16.2179 −1.38559 −0.692794 0.721135i \(-0.743621\pi\)
−0.692794 + 0.721135i \(0.743621\pi\)
\(138\) 11.1913 0.952668
\(139\) −17.3571 −1.47221 −0.736104 0.676868i \(-0.763337\pi\)
−0.736104 + 0.676868i \(0.763337\pi\)
\(140\) 0.676945 0.0572123
\(141\) 24.0416 2.02467
\(142\) 8.83857 0.741716
\(143\) −3.96088 −0.331226
\(144\) 7.92047 0.660039
\(145\) −2.44967 −0.203434
\(146\) 5.06238 0.418965
\(147\) −21.6179 −1.78302
\(148\) 11.2005 0.920673
\(149\) −9.35161 −0.766114 −0.383057 0.923725i \(-0.625129\pi\)
−0.383057 + 0.923725i \(0.625129\pi\)
\(150\) 3.30461 0.269821
\(151\) −2.95411 −0.240402 −0.120201 0.992750i \(-0.538354\pi\)
−0.120201 + 0.992750i \(0.538354\pi\)
\(152\) 1.47849 0.119921
\(153\) −19.3231 −1.56218
\(154\) −0.676945 −0.0545498
\(155\) −8.31634 −0.667984
\(156\) −13.0892 −1.04797
\(157\) −5.28247 −0.421587 −0.210794 0.977531i \(-0.567605\pi\)
−0.210794 + 0.977531i \(0.567605\pi\)
\(158\) 6.51534 0.518333
\(159\) 30.5334 2.42146
\(160\) −1.00000 −0.0790569
\(161\) −2.29252 −0.180676
\(162\) 29.9724 2.35486
\(163\) −0.152295 −0.0119287 −0.00596433 0.999982i \(-0.501899\pi\)
−0.00596433 + 0.999982i \(0.501899\pi\)
\(164\) −4.31368 −0.336842
\(165\) −3.30461 −0.257264
\(166\) −5.30438 −0.411700
\(167\) −15.9649 −1.23540 −0.617699 0.786415i \(-0.711935\pi\)
−0.617699 + 0.786415i \(0.711935\pi\)
\(168\) −2.23704 −0.172591
\(169\) 2.68861 0.206816
\(170\) 2.43964 0.187112
\(171\) 11.7103 0.895511
\(172\) 1.00000 0.0762493
\(173\) −12.2545 −0.931692 −0.465846 0.884866i \(-0.654250\pi\)
−0.465846 + 0.884866i \(0.654250\pi\)
\(174\) 8.09520 0.613696
\(175\) −0.676945 −0.0511722
\(176\) 1.00000 0.0753778
\(177\) 6.20780 0.466607
\(178\) −16.4475 −1.23279
\(179\) 8.15698 0.609681 0.304841 0.952403i \(-0.401397\pi\)
0.304841 + 0.952403i \(0.401397\pi\)
\(180\) −7.92047 −0.590357
\(181\) −13.5358 −1.00611 −0.503055 0.864254i \(-0.667791\pi\)
−0.503055 + 0.864254i \(0.667791\pi\)
\(182\) 2.68130 0.198751
\(183\) −48.5327 −3.58764
\(184\) 3.38657 0.249662
\(185\) −11.2005 −0.823475
\(186\) 27.4823 2.01510
\(187\) −2.43964 −0.178404
\(188\) 7.27516 0.530596
\(189\) −11.0073 −0.800663
\(190\) −1.47849 −0.107261
\(191\) −19.3235 −1.39820 −0.699098 0.715026i \(-0.746415\pi\)
−0.699098 + 0.715026i \(0.746415\pi\)
\(192\) 3.30461 0.238490
\(193\) 18.0569 1.29977 0.649883 0.760035i \(-0.274818\pi\)
0.649883 + 0.760035i \(0.274818\pi\)
\(194\) −16.6841 −1.19785
\(195\) 13.0892 0.937337
\(196\) −6.54175 −0.467268
\(197\) −8.44971 −0.602017 −0.301008 0.953621i \(-0.597323\pi\)
−0.301008 + 0.953621i \(0.597323\pi\)
\(198\) 7.92047 0.562883
\(199\) −11.9972 −0.850456 −0.425228 0.905086i \(-0.639806\pi\)
−0.425228 + 0.905086i \(0.639806\pi\)
\(200\) 1.00000 0.0707107
\(201\) −8.10398 −0.571611
\(202\) 9.00199 0.633378
\(203\) −1.65829 −0.116389
\(204\) −8.06207 −0.564458
\(205\) 4.31368 0.301280
\(206\) 4.73558 0.329943
\(207\) 26.8233 1.86435
\(208\) −3.96088 −0.274638
\(209\) 1.47849 0.102269
\(210\) 2.23704 0.154371
\(211\) 22.8792 1.57507 0.787535 0.616270i \(-0.211357\pi\)
0.787535 + 0.616270i \(0.211357\pi\)
\(212\) 9.23964 0.634581
\(213\) 29.2081 2.00130
\(214\) 7.25685 0.496068
\(215\) −1.00000 −0.0681994
\(216\) 16.2602 1.10637
\(217\) −5.62970 −0.382169
\(218\) −9.44895 −0.639964
\(219\) 16.7292 1.13045
\(220\) −1.00000 −0.0674200
\(221\) 9.66314 0.650013
\(222\) 37.0132 2.48417
\(223\) −19.3913 −1.29854 −0.649269 0.760559i \(-0.724925\pi\)
−0.649269 + 0.760559i \(0.724925\pi\)
\(224\) −0.676945 −0.0452303
\(225\) 7.92047 0.528031
\(226\) −16.2365 −1.08004
\(227\) −26.9170 −1.78654 −0.893271 0.449519i \(-0.851595\pi\)
−0.893271 + 0.449519i \(0.851595\pi\)
\(228\) 4.88583 0.323572
\(229\) 9.32600 0.616280 0.308140 0.951341i \(-0.400294\pi\)
0.308140 + 0.951341i \(0.400294\pi\)
\(230\) −3.38657 −0.223304
\(231\) −2.23704 −0.147187
\(232\) 2.44967 0.160828
\(233\) −4.22910 −0.277057 −0.138529 0.990358i \(-0.544237\pi\)
−0.138529 + 0.990358i \(0.544237\pi\)
\(234\) −31.3721 −2.05086
\(235\) −7.27516 −0.474579
\(236\) 1.87853 0.122282
\(237\) 21.5307 1.39857
\(238\) 1.65150 0.107051
\(239\) 27.1055 1.75331 0.876656 0.481118i \(-0.159769\pi\)
0.876656 + 0.481118i \(0.159769\pi\)
\(240\) −3.30461 −0.213312
\(241\) −3.64322 −0.234681 −0.117340 0.993092i \(-0.537437\pi\)
−0.117340 + 0.993092i \(0.537437\pi\)
\(242\) 1.00000 0.0642824
\(243\) 50.2665 3.22460
\(244\) −14.6864 −0.940198
\(245\) 6.54175 0.417937
\(246\) −14.2550 −0.908868
\(247\) −5.85612 −0.372616
\(248\) 8.31634 0.528088
\(249\) −17.5289 −1.11085
\(250\) −1.00000 −0.0632456
\(251\) 28.9498 1.82730 0.913648 0.406506i \(-0.133253\pi\)
0.913648 + 0.406506i \(0.133253\pi\)
\(252\) −5.36172 −0.337757
\(253\) 3.38657 0.212912
\(254\) 9.05438 0.568122
\(255\) 8.06207 0.504866
\(256\) 1.00000 0.0625000
\(257\) 9.62097 0.600140 0.300070 0.953917i \(-0.402990\pi\)
0.300070 + 0.953917i \(0.402990\pi\)
\(258\) 3.30461 0.205736
\(259\) −7.58211 −0.471129
\(260\) 3.96088 0.245644
\(261\) 19.4025 1.20099
\(262\) −10.2913 −0.635798
\(263\) −29.6602 −1.82892 −0.914462 0.404671i \(-0.867386\pi\)
−0.914462 + 0.404671i \(0.867386\pi\)
\(264\) 3.30461 0.203385
\(265\) −9.23964 −0.567586
\(266\) −1.00086 −0.0613664
\(267\) −54.3527 −3.32633
\(268\) −2.45232 −0.149799
\(269\) −15.7263 −0.958852 −0.479426 0.877582i \(-0.659155\pi\)
−0.479426 + 0.877582i \(0.659155\pi\)
\(270\) −16.2602 −0.989567
\(271\) 2.41395 0.146637 0.0733185 0.997309i \(-0.476641\pi\)
0.0733185 + 0.997309i \(0.476641\pi\)
\(272\) −2.43964 −0.147925
\(273\) 8.86066 0.536272
\(274\) −16.2179 −0.979759
\(275\) 1.00000 0.0603023
\(276\) 11.1913 0.673638
\(277\) −3.14074 −0.188709 −0.0943544 0.995539i \(-0.530079\pi\)
−0.0943544 + 0.995539i \(0.530079\pi\)
\(278\) −17.3571 −1.04101
\(279\) 65.8693 3.94349
\(280\) 0.676945 0.0404552
\(281\) 8.06027 0.480835 0.240418 0.970670i \(-0.422716\pi\)
0.240418 + 0.970670i \(0.422716\pi\)
\(282\) 24.0416 1.43166
\(283\) 32.6449 1.94054 0.970268 0.242032i \(-0.0778140\pi\)
0.970268 + 0.242032i \(0.0778140\pi\)
\(284\) 8.83857 0.524473
\(285\) −4.88583 −0.289412
\(286\) −3.96088 −0.234212
\(287\) 2.92012 0.172369
\(288\) 7.92047 0.466718
\(289\) −11.0482 −0.649891
\(290\) −2.44967 −0.143849
\(291\) −55.1343 −3.23203
\(292\) 5.06238 0.296253
\(293\) 23.9367 1.39839 0.699197 0.714929i \(-0.253541\pi\)
0.699197 + 0.714929i \(0.253541\pi\)
\(294\) −21.6179 −1.26078
\(295\) −1.87853 −0.109372
\(296\) 11.2005 0.651014
\(297\) 16.2602 0.943515
\(298\) −9.35161 −0.541724
\(299\) −13.4138 −0.775742
\(300\) 3.30461 0.190792
\(301\) −0.676945 −0.0390185
\(302\) −2.95411 −0.169990
\(303\) 29.7481 1.70898
\(304\) 1.47849 0.0847972
\(305\) 14.6864 0.840938
\(306\) −19.3231 −1.10463
\(307\) −24.8926 −1.42069 −0.710347 0.703851i \(-0.751462\pi\)
−0.710347 + 0.703851i \(0.751462\pi\)
\(308\) −0.676945 −0.0385725
\(309\) 15.6492 0.890255
\(310\) −8.31634 −0.472336
\(311\) 15.6134 0.885357 0.442678 0.896680i \(-0.354028\pi\)
0.442678 + 0.896680i \(0.354028\pi\)
\(312\) −13.0892 −0.741030
\(313\) −12.0771 −0.682640 −0.341320 0.939947i \(-0.610874\pi\)
−0.341320 + 0.939947i \(0.610874\pi\)
\(314\) −5.28247 −0.298107
\(315\) 5.36172 0.302099
\(316\) 6.51534 0.366517
\(317\) −3.32552 −0.186780 −0.0933899 0.995630i \(-0.529770\pi\)
−0.0933899 + 0.995630i \(0.529770\pi\)
\(318\) 30.5334 1.71223
\(319\) 2.44967 0.137155
\(320\) −1.00000 −0.0559017
\(321\) 23.9811 1.33849
\(322\) −2.29252 −0.127757
\(323\) −3.60698 −0.200698
\(324\) 29.9724 1.66513
\(325\) −3.96088 −0.219710
\(326\) −0.152295 −0.00843484
\(327\) −31.2251 −1.72675
\(328\) −4.31368 −0.238183
\(329\) −4.92489 −0.271518
\(330\) −3.30461 −0.181913
\(331\) −5.98882 −0.329175 −0.164588 0.986362i \(-0.552629\pi\)
−0.164588 + 0.986362i \(0.552629\pi\)
\(332\) −5.30438 −0.291116
\(333\) 88.7130 4.86144
\(334\) −15.9649 −0.873558
\(335\) 2.45232 0.133985
\(336\) −2.23704 −0.122041
\(337\) −1.92465 −0.104842 −0.0524212 0.998625i \(-0.516694\pi\)
−0.0524212 + 0.998625i \(0.516694\pi\)
\(338\) 2.68861 0.146241
\(339\) −53.6555 −2.91417
\(340\) 2.43964 0.132308
\(341\) 8.31634 0.450355
\(342\) 11.7103 0.633222
\(343\) 9.16702 0.494972
\(344\) 1.00000 0.0539164
\(345\) −11.1913 −0.602520
\(346\) −12.2545 −0.658806
\(347\) −14.2654 −0.765809 −0.382905 0.923788i \(-0.625076\pi\)
−0.382905 + 0.923788i \(0.625076\pi\)
\(348\) 8.09520 0.433948
\(349\) 12.5777 0.673267 0.336634 0.941636i \(-0.390712\pi\)
0.336634 + 0.941636i \(0.390712\pi\)
\(350\) −0.676945 −0.0361842
\(351\) −64.4050 −3.43768
\(352\) 1.00000 0.0533002
\(353\) −12.9817 −0.690949 −0.345474 0.938428i \(-0.612282\pi\)
−0.345474 + 0.938428i \(0.612282\pi\)
\(354\) 6.20780 0.329941
\(355\) −8.83857 −0.469103
\(356\) −16.4475 −0.871716
\(357\) 5.45758 0.288846
\(358\) 8.15698 0.431110
\(359\) 14.4988 0.765219 0.382609 0.923910i \(-0.375026\pi\)
0.382609 + 0.923910i \(0.375026\pi\)
\(360\) −7.92047 −0.417445
\(361\) −16.8141 −0.884951
\(362\) −13.5358 −0.711428
\(363\) 3.30461 0.173447
\(364\) 2.68130 0.140538
\(365\) −5.06238 −0.264977
\(366\) −48.5327 −2.53685
\(367\) −4.16242 −0.217276 −0.108638 0.994081i \(-0.534649\pi\)
−0.108638 + 0.994081i \(0.534649\pi\)
\(368\) 3.38657 0.176537
\(369\) −34.1664 −1.77863
\(370\) −11.2005 −0.582285
\(371\) −6.25472 −0.324729
\(372\) 27.4823 1.42489
\(373\) 31.7738 1.64519 0.822593 0.568631i \(-0.192527\pi\)
0.822593 + 0.568631i \(0.192527\pi\)
\(374\) −2.43964 −0.126151
\(375\) −3.30461 −0.170650
\(376\) 7.27516 0.375188
\(377\) −9.70285 −0.499722
\(378\) −11.0073 −0.566154
\(379\) 26.8216 1.37773 0.688867 0.724888i \(-0.258108\pi\)
0.688867 + 0.724888i \(0.258108\pi\)
\(380\) −1.47849 −0.0758449
\(381\) 29.9212 1.53291
\(382\) −19.3235 −0.988674
\(383\) 34.1094 1.74291 0.871454 0.490477i \(-0.163178\pi\)
0.871454 + 0.490477i \(0.163178\pi\)
\(384\) 3.30461 0.168638
\(385\) 0.676945 0.0345003
\(386\) 18.0569 0.919073
\(387\) 7.92047 0.402620
\(388\) −16.6841 −0.847004
\(389\) −0.877885 −0.0445105 −0.0222553 0.999752i \(-0.507085\pi\)
−0.0222553 + 0.999752i \(0.507085\pi\)
\(390\) 13.0892 0.662797
\(391\) −8.26202 −0.417829
\(392\) −6.54175 −0.330408
\(393\) −34.0087 −1.71551
\(394\) −8.44971 −0.425690
\(395\) −6.51534 −0.327822
\(396\) 7.92047 0.398019
\(397\) −25.4297 −1.27628 −0.638140 0.769920i \(-0.720296\pi\)
−0.638140 + 0.769920i \(0.720296\pi\)
\(398\) −11.9972 −0.601363
\(399\) −3.30744 −0.165579
\(400\) 1.00000 0.0500000
\(401\) 15.5181 0.774937 0.387468 0.921883i \(-0.373350\pi\)
0.387468 + 0.921883i \(0.373350\pi\)
\(402\) −8.10398 −0.404190
\(403\) −32.9401 −1.64086
\(404\) 9.00199 0.447866
\(405\) −29.9724 −1.48934
\(406\) −1.65829 −0.0822995
\(407\) 11.2005 0.555187
\(408\) −8.06207 −0.399132
\(409\) 23.6642 1.17012 0.585059 0.810991i \(-0.301071\pi\)
0.585059 + 0.810991i \(0.301071\pi\)
\(410\) 4.31368 0.213037
\(411\) −53.5939 −2.64359
\(412\) 4.73558 0.233305
\(413\) −1.27166 −0.0625742
\(414\) 26.8233 1.31829
\(415\) 5.30438 0.260382
\(416\) −3.96088 −0.194198
\(417\) −57.3584 −2.80886
\(418\) 1.47849 0.0723153
\(419\) −16.0191 −0.782582 −0.391291 0.920267i \(-0.627971\pi\)
−0.391291 + 0.920267i \(0.627971\pi\)
\(420\) 2.23704 0.109156
\(421\) 2.89947 0.141312 0.0706558 0.997501i \(-0.477491\pi\)
0.0706558 + 0.997501i \(0.477491\pi\)
\(422\) 22.8792 1.11374
\(423\) 57.6227 2.80171
\(424\) 9.23964 0.448716
\(425\) −2.43964 −0.118340
\(426\) 29.2081 1.41514
\(427\) 9.94185 0.481120
\(428\) 7.25685 0.350773
\(429\) −13.0892 −0.631952
\(430\) −1.00000 −0.0482243
\(431\) 36.0935 1.73856 0.869280 0.494319i \(-0.164583\pi\)
0.869280 + 0.494319i \(0.164583\pi\)
\(432\) 16.2602 0.782322
\(433\) −28.4339 −1.36645 −0.683223 0.730210i \(-0.739422\pi\)
−0.683223 + 0.730210i \(0.739422\pi\)
\(434\) −5.62970 −0.270234
\(435\) −8.09520 −0.388135
\(436\) −9.44895 −0.452523
\(437\) 5.00701 0.239518
\(438\) 16.7292 0.799352
\(439\) 17.4292 0.831850 0.415925 0.909399i \(-0.363458\pi\)
0.415925 + 0.909399i \(0.363458\pi\)
\(440\) −1.00000 −0.0476731
\(441\) −51.8137 −2.46732
\(442\) 9.66314 0.459629
\(443\) −19.2963 −0.916796 −0.458398 0.888747i \(-0.651577\pi\)
−0.458398 + 0.888747i \(0.651577\pi\)
\(444\) 37.0132 1.75657
\(445\) 16.4475 0.779687
\(446\) −19.3913 −0.918205
\(447\) −30.9035 −1.46168
\(448\) −0.676945 −0.0319826
\(449\) −23.6300 −1.11517 −0.557585 0.830120i \(-0.688272\pi\)
−0.557585 + 0.830120i \(0.688272\pi\)
\(450\) 7.92047 0.373375
\(451\) −4.31368 −0.203123
\(452\) −16.2365 −0.763703
\(453\) −9.76218 −0.458667
\(454\) −26.9170 −1.26328
\(455\) −2.68130 −0.125701
\(456\) 4.88583 0.228800
\(457\) −9.26335 −0.433321 −0.216661 0.976247i \(-0.569516\pi\)
−0.216661 + 0.976247i \(0.569516\pi\)
\(458\) 9.32600 0.435775
\(459\) −39.6692 −1.85160
\(460\) −3.38657 −0.157900
\(461\) 22.8018 1.06199 0.530993 0.847376i \(-0.321819\pi\)
0.530993 + 0.847376i \(0.321819\pi\)
\(462\) −2.23704 −0.104077
\(463\) 28.3243 1.31634 0.658172 0.752868i \(-0.271330\pi\)
0.658172 + 0.752868i \(0.271330\pi\)
\(464\) 2.44967 0.113723
\(465\) −27.4823 −1.27446
\(466\) −4.22910 −0.195909
\(467\) 22.8550 1.05760 0.528801 0.848746i \(-0.322642\pi\)
0.528801 + 0.848746i \(0.322642\pi\)
\(468\) −31.3721 −1.45017
\(469\) 1.66009 0.0766557
\(470\) −7.27516 −0.335578
\(471\) −17.4565 −0.804354
\(472\) 1.87853 0.0864661
\(473\) 1.00000 0.0459800
\(474\) 21.5307 0.988937
\(475\) 1.47849 0.0678377
\(476\) 1.65150 0.0756965
\(477\) 73.1822 3.35078
\(478\) 27.1055 1.23978
\(479\) 33.3747 1.52493 0.762465 0.647029i \(-0.223989\pi\)
0.762465 + 0.647029i \(0.223989\pi\)
\(480\) −3.30461 −0.150834
\(481\) −44.3638 −2.02281
\(482\) −3.64322 −0.165944
\(483\) −7.57591 −0.344716
\(484\) 1.00000 0.0454545
\(485\) 16.6841 0.757584
\(486\) 50.2665 2.28014
\(487\) −35.4355 −1.60574 −0.802868 0.596157i \(-0.796694\pi\)
−0.802868 + 0.596157i \(0.796694\pi\)
\(488\) −14.6864 −0.664820
\(489\) −0.503276 −0.0227589
\(490\) 6.54175 0.295526
\(491\) 10.2100 0.460769 0.230384 0.973100i \(-0.426002\pi\)
0.230384 + 0.973100i \(0.426002\pi\)
\(492\) −14.2550 −0.642667
\(493\) −5.97631 −0.269159
\(494\) −5.85612 −0.263479
\(495\) −7.92047 −0.355999
\(496\) 8.31634 0.373415
\(497\) −5.98323 −0.268384
\(498\) −17.5289 −0.785490
\(499\) 18.9638 0.848937 0.424469 0.905443i \(-0.360461\pi\)
0.424469 + 0.905443i \(0.360461\pi\)
\(500\) −1.00000 −0.0447214
\(501\) −52.7577 −2.35704
\(502\) 28.9498 1.29209
\(503\) 3.80534 0.169672 0.0848359 0.996395i \(-0.472963\pi\)
0.0848359 + 0.996395i \(0.472963\pi\)
\(504\) −5.36172 −0.238830
\(505\) −9.00199 −0.400583
\(506\) 3.38657 0.150552
\(507\) 8.88481 0.394588
\(508\) 9.05438 0.401723
\(509\) −41.5482 −1.84159 −0.920796 0.390045i \(-0.872460\pi\)
−0.920796 + 0.390045i \(0.872460\pi\)
\(510\) 8.06207 0.356994
\(511\) −3.42695 −0.151599
\(512\) 1.00000 0.0441942
\(513\) 24.0406 1.06142
\(514\) 9.62097 0.424363
\(515\) −4.73558 −0.208674
\(516\) 3.30461 0.145477
\(517\) 7.27516 0.319961
\(518\) −7.58211 −0.333139
\(519\) −40.4964 −1.77759
\(520\) 3.96088 0.173696
\(521\) −27.0241 −1.18395 −0.591974 0.805957i \(-0.701651\pi\)
−0.591974 + 0.805957i \(0.701651\pi\)
\(522\) 19.4025 0.849225
\(523\) 17.1384 0.749410 0.374705 0.927144i \(-0.377744\pi\)
0.374705 + 0.927144i \(0.377744\pi\)
\(524\) −10.2913 −0.449577
\(525\) −2.23704 −0.0976325
\(526\) −29.6602 −1.29324
\(527\) −20.2889 −0.883797
\(528\) 3.30461 0.143815
\(529\) −11.5311 −0.501353
\(530\) −9.23964 −0.401344
\(531\) 14.8788 0.645685
\(532\) −1.00086 −0.0433926
\(533\) 17.0860 0.740076
\(534\) −54.3527 −2.35207
\(535\) −7.25685 −0.313741
\(536\) −2.45232 −0.105924
\(537\) 26.9557 1.16322
\(538\) −15.7263 −0.678010
\(539\) −6.54175 −0.281773
\(540\) −16.2602 −0.699730
\(541\) 17.2997 0.743772 0.371886 0.928278i \(-0.378711\pi\)
0.371886 + 0.928278i \(0.378711\pi\)
\(542\) 2.41395 0.103688
\(543\) −44.7307 −1.91958
\(544\) −2.43964 −0.104599
\(545\) 9.44895 0.404749
\(546\) 8.86066 0.379201
\(547\) 19.7981 0.846504 0.423252 0.906012i \(-0.360888\pi\)
0.423252 + 0.906012i \(0.360888\pi\)
\(548\) −16.2179 −0.692794
\(549\) −116.323 −4.96454
\(550\) 1.00000 0.0426401
\(551\) 3.62180 0.154294
\(552\) 11.1913 0.476334
\(553\) −4.41053 −0.187555
\(554\) −3.14074 −0.133437
\(555\) −37.0132 −1.57112
\(556\) −17.3571 −0.736104
\(557\) −43.5172 −1.84388 −0.921942 0.387328i \(-0.873398\pi\)
−0.921942 + 0.387328i \(0.873398\pi\)
\(558\) 65.8693 2.78847
\(559\) −3.96088 −0.167528
\(560\) 0.676945 0.0286061
\(561\) −8.06207 −0.340381
\(562\) 8.06027 0.340002
\(563\) −21.4447 −0.903787 −0.451893 0.892072i \(-0.649251\pi\)
−0.451893 + 0.892072i \(0.649251\pi\)
\(564\) 24.0416 1.01233
\(565\) 16.2365 0.683076
\(566\) 32.6449 1.37217
\(567\) −20.2897 −0.852087
\(568\) 8.83857 0.370858
\(569\) 9.22680 0.386808 0.193404 0.981119i \(-0.438047\pi\)
0.193404 + 0.981119i \(0.438047\pi\)
\(570\) −4.88583 −0.204645
\(571\) −19.9634 −0.835443 −0.417722 0.908575i \(-0.637171\pi\)
−0.417722 + 0.908575i \(0.637171\pi\)
\(572\) −3.96088 −0.165613
\(573\) −63.8565 −2.66765
\(574\) 2.92012 0.121884
\(575\) 3.38657 0.141230
\(576\) 7.92047 0.330020
\(577\) 1.20303 0.0500828 0.0250414 0.999686i \(-0.492028\pi\)
0.0250414 + 0.999686i \(0.492028\pi\)
\(578\) −11.0482 −0.459543
\(579\) 59.6711 2.47985
\(580\) −2.44967 −0.101717
\(581\) 3.59077 0.148970
\(582\) −55.1343 −2.28539
\(583\) 9.23964 0.382667
\(584\) 5.06238 0.209483
\(585\) 31.3721 1.29708
\(586\) 23.9367 0.988814
\(587\) 17.4649 0.720852 0.360426 0.932788i \(-0.382631\pi\)
0.360426 + 0.932788i \(0.382631\pi\)
\(588\) −21.6179 −0.891509
\(589\) 12.2956 0.506632
\(590\) −1.87853 −0.0773377
\(591\) −27.9230 −1.14860
\(592\) 11.2005 0.460337
\(593\) −9.04775 −0.371547 −0.185773 0.982593i \(-0.559479\pi\)
−0.185773 + 0.982593i \(0.559479\pi\)
\(594\) 16.2602 0.667166
\(595\) −1.65150 −0.0677050
\(596\) −9.35161 −0.383057
\(597\) −39.6460 −1.62260
\(598\) −13.4138 −0.548532
\(599\) −17.1612 −0.701187 −0.350594 0.936528i \(-0.614020\pi\)
−0.350594 + 0.936528i \(0.614020\pi\)
\(600\) 3.30461 0.134910
\(601\) −19.3655 −0.789937 −0.394968 0.918695i \(-0.629244\pi\)
−0.394968 + 0.918695i \(0.629244\pi\)
\(602\) −0.676945 −0.0275902
\(603\) −19.4235 −0.790988
\(604\) −2.95411 −0.120201
\(605\) −1.00000 −0.0406558
\(606\) 29.7481 1.20843
\(607\) 9.69049 0.393325 0.196662 0.980471i \(-0.436990\pi\)
0.196662 + 0.980471i \(0.436990\pi\)
\(608\) 1.47849 0.0599606
\(609\) −5.48001 −0.222061
\(610\) 14.6864 0.594633
\(611\) −28.8161 −1.16577
\(612\) −19.3231 −0.781090
\(613\) −10.2335 −0.413325 −0.206663 0.978412i \(-0.566260\pi\)
−0.206663 + 0.978412i \(0.566260\pi\)
\(614\) −24.8926 −1.00458
\(615\) 14.2550 0.574819
\(616\) −0.676945 −0.0272749
\(617\) 27.5357 1.10855 0.554273 0.832335i \(-0.312996\pi\)
0.554273 + 0.832335i \(0.312996\pi\)
\(618\) 15.6492 0.629505
\(619\) 32.7425 1.31603 0.658016 0.753004i \(-0.271396\pi\)
0.658016 + 0.753004i \(0.271396\pi\)
\(620\) −8.31634 −0.333992
\(621\) 55.0665 2.20974
\(622\) 15.6134 0.626042
\(623\) 11.1341 0.446077
\(624\) −13.0892 −0.523987
\(625\) 1.00000 0.0400000
\(626\) −12.0771 −0.482699
\(627\) 4.88583 0.195121
\(628\) −5.28247 −0.210794
\(629\) −27.3251 −1.08952
\(630\) 5.36172 0.213616
\(631\) 1.26167 0.0502261 0.0251131 0.999685i \(-0.492005\pi\)
0.0251131 + 0.999685i \(0.492005\pi\)
\(632\) 6.51534 0.259166
\(633\) 75.6070 3.00511
\(634\) −3.32552 −0.132073
\(635\) −9.05438 −0.359312
\(636\) 30.5334 1.21073
\(637\) 25.9111 1.02664
\(638\) 2.44967 0.0969832
\(639\) 70.0056 2.76938
\(640\) −1.00000 −0.0395285
\(641\) −10.6406 −0.420279 −0.210139 0.977671i \(-0.567392\pi\)
−0.210139 + 0.977671i \(0.567392\pi\)
\(642\) 23.9811 0.946458
\(643\) 15.9591 0.629365 0.314683 0.949197i \(-0.398102\pi\)
0.314683 + 0.949197i \(0.398102\pi\)
\(644\) −2.29252 −0.0903381
\(645\) −3.30461 −0.130119
\(646\) −3.60698 −0.141915
\(647\) 25.7481 1.01226 0.506132 0.862456i \(-0.331075\pi\)
0.506132 + 0.862456i \(0.331075\pi\)
\(648\) 29.9724 1.17743
\(649\) 1.87853 0.0737386
\(650\) −3.96088 −0.155359
\(651\) −18.6040 −0.729148
\(652\) −0.152295 −0.00596433
\(653\) 20.5634 0.804710 0.402355 0.915484i \(-0.368192\pi\)
0.402355 + 0.915484i \(0.368192\pi\)
\(654\) −31.2251 −1.22100
\(655\) 10.2913 0.402114
\(656\) −4.31368 −0.168421
\(657\) 40.0964 1.56431
\(658\) −4.92489 −0.191992
\(659\) −25.7968 −1.00490 −0.502451 0.864606i \(-0.667568\pi\)
−0.502451 + 0.864606i \(0.667568\pi\)
\(660\) −3.30461 −0.128632
\(661\) 4.79294 0.186424 0.0932120 0.995646i \(-0.470287\pi\)
0.0932120 + 0.995646i \(0.470287\pi\)
\(662\) −5.98882 −0.232762
\(663\) 31.9329 1.24017
\(664\) −5.30438 −0.205850
\(665\) 1.00086 0.0388115
\(666\) 88.7130 3.43756
\(667\) 8.29598 0.321222
\(668\) −15.9649 −0.617699
\(669\) −64.0808 −2.47751
\(670\) 2.45232 0.0947415
\(671\) −14.6864 −0.566960
\(672\) −2.23704 −0.0862957
\(673\) 39.4943 1.52239 0.761196 0.648522i \(-0.224613\pi\)
0.761196 + 0.648522i \(0.224613\pi\)
\(674\) −1.92465 −0.0741348
\(675\) 16.2602 0.625857
\(676\) 2.68861 0.103408
\(677\) −38.2045 −1.46832 −0.734159 0.678977i \(-0.762423\pi\)
−0.734159 + 0.678977i \(0.762423\pi\)
\(678\) −53.6555 −2.06063
\(679\) 11.2942 0.433431
\(680\) 2.43964 0.0935559
\(681\) −88.9502 −3.40858
\(682\) 8.31634 0.318449
\(683\) −29.5186 −1.12950 −0.564749 0.825263i \(-0.691027\pi\)
−0.564749 + 0.825263i \(0.691027\pi\)
\(684\) 11.7103 0.447756
\(685\) 16.2179 0.619654
\(686\) 9.16702 0.349998
\(687\) 30.8188 1.17581
\(688\) 1.00000 0.0381246
\(689\) −36.5971 −1.39424
\(690\) −11.1913 −0.426046
\(691\) 29.2300 1.11196 0.555981 0.831195i \(-0.312343\pi\)
0.555981 + 0.831195i \(0.312343\pi\)
\(692\) −12.2545 −0.465846
\(693\) −5.36172 −0.203675
\(694\) −14.2654 −0.541509
\(695\) 17.3571 0.658392
\(696\) 8.09520 0.306848
\(697\) 10.5238 0.398618
\(698\) 12.5777 0.476072
\(699\) −13.9755 −0.528603
\(700\) −0.676945 −0.0255861
\(701\) 7.25187 0.273899 0.136950 0.990578i \(-0.456270\pi\)
0.136950 + 0.990578i \(0.456270\pi\)
\(702\) −64.4050 −2.43081
\(703\) 16.5598 0.624564
\(704\) 1.00000 0.0376889
\(705\) −24.0416 −0.905459
\(706\) −12.9817 −0.488575
\(707\) −6.09385 −0.229183
\(708\) 6.20780 0.233303
\(709\) −34.1209 −1.28144 −0.640719 0.767775i \(-0.721364\pi\)
−0.640719 + 0.767775i \(0.721364\pi\)
\(710\) −8.83857 −0.331706
\(711\) 51.6046 1.93532
\(712\) −16.4475 −0.616396
\(713\) 28.1639 1.05475
\(714\) 5.45758 0.204245
\(715\) 3.96088 0.148129
\(716\) 8.15698 0.304841
\(717\) 89.5734 3.34518
\(718\) 14.4988 0.541091
\(719\) 34.0289 1.26906 0.634531 0.772897i \(-0.281193\pi\)
0.634531 + 0.772897i \(0.281193\pi\)
\(720\) −7.92047 −0.295178
\(721\) −3.20572 −0.119387
\(722\) −16.8141 −0.625755
\(723\) −12.0394 −0.447752
\(724\) −13.5358 −0.503055
\(725\) 2.44967 0.0909783
\(726\) 3.30461 0.122646
\(727\) 21.9246 0.813138 0.406569 0.913620i \(-0.366725\pi\)
0.406569 + 0.913620i \(0.366725\pi\)
\(728\) 2.68130 0.0993756
\(729\) 76.1942 2.82201
\(730\) −5.06238 −0.187367
\(731\) −2.43964 −0.0902334
\(732\) −48.5327 −1.79382
\(733\) −26.8182 −0.990552 −0.495276 0.868736i \(-0.664933\pi\)
−0.495276 + 0.868736i \(0.664933\pi\)
\(734\) −4.16242 −0.153638
\(735\) 21.6179 0.797390
\(736\) 3.38657 0.124831
\(737\) −2.45232 −0.0903325
\(738\) −34.1664 −1.25768
\(739\) 15.8968 0.584772 0.292386 0.956300i \(-0.405551\pi\)
0.292386 + 0.956300i \(0.405551\pi\)
\(740\) −11.2005 −0.411738
\(741\) −19.3522 −0.710922
\(742\) −6.25472 −0.229618
\(743\) 26.6094 0.976204 0.488102 0.872787i \(-0.337689\pi\)
0.488102 + 0.872787i \(0.337689\pi\)
\(744\) 27.4823 1.00755
\(745\) 9.35161 0.342617
\(746\) 31.7738 1.16332
\(747\) −42.0132 −1.53718
\(748\) −2.43964 −0.0892021
\(749\) −4.91249 −0.179498
\(750\) −3.30461 −0.120667
\(751\) 9.86322 0.359914 0.179957 0.983674i \(-0.442404\pi\)
0.179957 + 0.983674i \(0.442404\pi\)
\(752\) 7.27516 0.265298
\(753\) 95.6680 3.48633
\(754\) −9.70285 −0.353357
\(755\) 2.95411 0.107511
\(756\) −11.0073 −0.400331
\(757\) 20.6951 0.752176 0.376088 0.926584i \(-0.377269\pi\)
0.376088 + 0.926584i \(0.377269\pi\)
\(758\) 26.8216 0.974205
\(759\) 11.1913 0.406219
\(760\) −1.47849 −0.0536304
\(761\) 27.8460 1.00942 0.504708 0.863290i \(-0.331600\pi\)
0.504708 + 0.863290i \(0.331600\pi\)
\(762\) 29.9212 1.08393
\(763\) 6.39642 0.231566
\(764\) −19.3235 −0.699098
\(765\) 19.3231 0.698628
\(766\) 34.1094 1.23242
\(767\) −7.44062 −0.268665
\(768\) 3.30461 0.119245
\(769\) 11.7386 0.423304 0.211652 0.977345i \(-0.432116\pi\)
0.211652 + 0.977345i \(0.432116\pi\)
\(770\) 0.676945 0.0243954
\(771\) 31.7936 1.14502
\(772\) 18.0569 0.649883
\(773\) 11.9546 0.429976 0.214988 0.976617i \(-0.431029\pi\)
0.214988 + 0.976617i \(0.431029\pi\)
\(774\) 7.92047 0.284695
\(775\) 8.31634 0.298732
\(776\) −16.6841 −0.598923
\(777\) −25.0559 −0.898876
\(778\) −0.877885 −0.0314737
\(779\) −6.37773 −0.228506
\(780\) 13.0892 0.468668
\(781\) 8.83857 0.316269
\(782\) −8.26202 −0.295449
\(783\) 39.8322 1.42349
\(784\) −6.54175 −0.233634
\(785\) 5.28247 0.188539
\(786\) −34.0087 −1.21305
\(787\) −19.1096 −0.681183 −0.340592 0.940211i \(-0.610627\pi\)
−0.340592 + 0.940211i \(0.610627\pi\)
\(788\) −8.44971 −0.301008
\(789\) −98.0154 −3.48944
\(790\) −6.51534 −0.231806
\(791\) 10.9912 0.390804
\(792\) 7.92047 0.281442
\(793\) 58.1710 2.06571
\(794\) −25.4297 −0.902466
\(795\) −30.5334 −1.08291
\(796\) −11.9972 −0.425228
\(797\) −0.297496 −0.0105378 −0.00526892 0.999986i \(-0.501677\pi\)
−0.00526892 + 0.999986i \(0.501677\pi\)
\(798\) −3.30744 −0.117082
\(799\) −17.7488 −0.627907
\(800\) 1.00000 0.0353553
\(801\) −130.272 −4.60293
\(802\) 15.5181 0.547963
\(803\) 5.06238 0.178647
\(804\) −8.10398 −0.285805
\(805\) 2.29252 0.0808009
\(806\) −32.9401 −1.16026
\(807\) −51.9695 −1.82941
\(808\) 9.00199 0.316689
\(809\) 11.2834 0.396705 0.198352 0.980131i \(-0.436441\pi\)
0.198352 + 0.980131i \(0.436441\pi\)
\(810\) −29.9724 −1.05312
\(811\) −35.8029 −1.25721 −0.628605 0.777725i \(-0.716374\pi\)
−0.628605 + 0.777725i \(0.716374\pi\)
\(812\) −1.65829 −0.0581946
\(813\) 7.97717 0.279771
\(814\) 11.2005 0.392576
\(815\) 0.152295 0.00533466
\(816\) −8.06207 −0.282229
\(817\) 1.47849 0.0517258
\(818\) 23.6642 0.827399
\(819\) 21.2372 0.742087
\(820\) 4.31368 0.150640
\(821\) −8.80261 −0.307213 −0.153607 0.988132i \(-0.549089\pi\)
−0.153607 + 0.988132i \(0.549089\pi\)
\(822\) −53.5939 −1.86930
\(823\) −4.94921 −0.172519 −0.0862593 0.996273i \(-0.527491\pi\)
−0.0862593 + 0.996273i \(0.527491\pi\)
\(824\) 4.73558 0.164972
\(825\) 3.30461 0.115052
\(826\) −1.27166 −0.0442467
\(827\) −19.5859 −0.681070 −0.340535 0.940232i \(-0.610608\pi\)
−0.340535 + 0.940232i \(0.610608\pi\)
\(828\) 26.8233 0.932173
\(829\) 23.8513 0.828389 0.414194 0.910188i \(-0.364063\pi\)
0.414194 + 0.910188i \(0.364063\pi\)
\(830\) 5.30438 0.184118
\(831\) −10.3789 −0.360041
\(832\) −3.96088 −0.137319
\(833\) 15.9595 0.552964
\(834\) −57.3584 −1.98616
\(835\) 15.9649 0.552487
\(836\) 1.47849 0.0511346
\(837\) 135.226 4.67408
\(838\) −16.0191 −0.553369
\(839\) 16.0606 0.554474 0.277237 0.960802i \(-0.410581\pi\)
0.277237 + 0.960802i \(0.410581\pi\)
\(840\) 2.23704 0.0771853
\(841\) −22.9991 −0.793074
\(842\) 2.89947 0.0999224
\(843\) 26.6361 0.917395
\(844\) 22.8792 0.787535
\(845\) −2.68861 −0.0924910
\(846\) 57.6227 1.98111
\(847\) −0.676945 −0.0232601
\(848\) 9.23964 0.317290
\(849\) 107.879 3.70239
\(850\) −2.43964 −0.0836790
\(851\) 37.9312 1.30027
\(852\) 29.2081 1.00065
\(853\) 14.9965 0.513469 0.256735 0.966482i \(-0.417353\pi\)
0.256735 + 0.966482i \(0.417353\pi\)
\(854\) 9.94185 0.340203
\(855\) −11.7103 −0.400485
\(856\) 7.25685 0.248034
\(857\) −21.9522 −0.749873 −0.374936 0.927051i \(-0.622335\pi\)
−0.374936 + 0.927051i \(0.622335\pi\)
\(858\) −13.0892 −0.446858
\(859\) 6.73823 0.229906 0.114953 0.993371i \(-0.463328\pi\)
0.114953 + 0.993371i \(0.463328\pi\)
\(860\) −1.00000 −0.0340997
\(861\) 9.64988 0.328867
\(862\) 36.0935 1.22935
\(863\) −40.6180 −1.38265 −0.691326 0.722543i \(-0.742973\pi\)
−0.691326 + 0.722543i \(0.742973\pi\)
\(864\) 16.2602 0.553185
\(865\) 12.2545 0.416666
\(866\) −28.4339 −0.966223
\(867\) −36.5099 −1.23994
\(868\) −5.62970 −0.191085
\(869\) 6.51534 0.221018
\(870\) −8.09520 −0.274453
\(871\) 9.71337 0.329125
\(872\) −9.44895 −0.319982
\(873\) −132.146 −4.47245
\(874\) 5.00701 0.169365
\(875\) 0.676945 0.0228849
\(876\) 16.7292 0.565227
\(877\) −23.7664 −0.802533 −0.401266 0.915961i \(-0.631430\pi\)
−0.401266 + 0.915961i \(0.631430\pi\)
\(878\) 17.4292 0.588207
\(879\) 79.1014 2.66802
\(880\) −1.00000 −0.0337100
\(881\) −11.1950 −0.377168 −0.188584 0.982057i \(-0.560390\pi\)
−0.188584 + 0.982057i \(0.560390\pi\)
\(882\) −51.8137 −1.74466
\(883\) 42.1459 1.41832 0.709161 0.705046i \(-0.249074\pi\)
0.709161 + 0.705046i \(0.249074\pi\)
\(884\) 9.66314 0.325006
\(885\) −6.20780 −0.208673
\(886\) −19.2963 −0.648273
\(887\) −55.0513 −1.84844 −0.924221 0.381857i \(-0.875285\pi\)
−0.924221 + 0.381857i \(0.875285\pi\)
\(888\) 37.0132 1.24208
\(889\) −6.12932 −0.205571
\(890\) 16.4475 0.551322
\(891\) 29.9724 1.00411
\(892\) −19.3913 −0.649269
\(893\) 10.7562 0.359944
\(894\) −30.9035 −1.03357
\(895\) −8.15698 −0.272658
\(896\) −0.676945 −0.0226151
\(897\) −44.3275 −1.48005
\(898\) −23.6300 −0.788545
\(899\) 20.3723 0.679453
\(900\) 7.92047 0.264016
\(901\) −22.5414 −0.750963
\(902\) −4.31368 −0.143630
\(903\) −2.23704 −0.0744441
\(904\) −16.2365 −0.540019
\(905\) 13.5358 0.449946
\(906\) −9.76218 −0.324327
\(907\) 6.60026 0.219158 0.109579 0.993978i \(-0.465050\pi\)
0.109579 + 0.993978i \(0.465050\pi\)
\(908\) −26.9170 −0.893271
\(909\) 71.3000 2.36487
\(910\) −2.68130 −0.0888843
\(911\) 32.7077 1.08365 0.541827 0.840490i \(-0.317733\pi\)
0.541827 + 0.840490i \(0.317733\pi\)
\(912\) 4.88583 0.161786
\(913\) −5.30438 −0.175549
\(914\) −9.26335 −0.306404
\(915\) 48.5327 1.60444
\(916\) 9.32600 0.308140
\(917\) 6.96663 0.230059
\(918\) −39.6692 −1.30928
\(919\) 11.2922 0.372496 0.186248 0.982503i \(-0.440367\pi\)
0.186248 + 0.982503i \(0.440367\pi\)
\(920\) −3.38657 −0.111652
\(921\) −82.2604 −2.71057
\(922\) 22.8018 0.750937
\(923\) −35.0086 −1.15232
\(924\) −2.23704 −0.0735933
\(925\) 11.2005 0.368269
\(926\) 28.3243 0.930795
\(927\) 37.5080 1.23192
\(928\) 2.44967 0.0804142
\(929\) 32.9114 1.07979 0.539893 0.841734i \(-0.318465\pi\)
0.539893 + 0.841734i \(0.318465\pi\)
\(930\) −27.4823 −0.901179
\(931\) −9.67190 −0.316984
\(932\) −4.22910 −0.138529
\(933\) 51.5964 1.68919
\(934\) 22.8550 0.747837
\(935\) 2.43964 0.0797848
\(936\) −31.3721 −1.02543
\(937\) −15.6220 −0.510350 −0.255175 0.966895i \(-0.582133\pi\)
−0.255175 + 0.966895i \(0.582133\pi\)
\(938\) 1.66009 0.0542038
\(939\) −39.9103 −1.30242
\(940\) −7.27516 −0.237290
\(941\) −3.79032 −0.123561 −0.0617804 0.998090i \(-0.519678\pi\)
−0.0617804 + 0.998090i \(0.519678\pi\)
\(942\) −17.4565 −0.568764
\(943\) −14.6086 −0.475721
\(944\) 1.87853 0.0611408
\(945\) 11.0073 0.358067
\(946\) 1.00000 0.0325128
\(947\) 14.2981 0.464625 0.232312 0.972641i \(-0.425371\pi\)
0.232312 + 0.972641i \(0.425371\pi\)
\(948\) 21.5307 0.699284
\(949\) −20.0515 −0.650899
\(950\) 1.47849 0.0479685
\(951\) −10.9896 −0.356361
\(952\) 1.65150 0.0535255
\(953\) −34.1947 −1.10768 −0.553838 0.832625i \(-0.686837\pi\)
−0.553838 + 0.832625i \(0.686837\pi\)
\(954\) 73.1822 2.36936
\(955\) 19.3235 0.625292
\(956\) 27.1055 0.876656
\(957\) 8.09520 0.261681
\(958\) 33.3747 1.07829
\(959\) 10.9786 0.354518
\(960\) −3.30461 −0.106656
\(961\) 38.1614 1.23101
\(962\) −44.3638 −1.43035
\(963\) 57.4777 1.85219
\(964\) −3.64322 −0.117340
\(965\) −18.0569 −0.581273
\(966\) −7.57591 −0.243751
\(967\) 17.3858 0.559090 0.279545 0.960133i \(-0.409816\pi\)
0.279545 + 0.960133i \(0.409816\pi\)
\(968\) 1.00000 0.0321412
\(969\) −11.9197 −0.382915
\(970\) 16.6841 0.535693
\(971\) −40.3039 −1.29341 −0.646706 0.762739i \(-0.723854\pi\)
−0.646706 + 0.762739i \(0.723854\pi\)
\(972\) 50.2665 1.61230
\(973\) 11.7498 0.376681
\(974\) −35.4355 −1.13543
\(975\) −13.0892 −0.419190
\(976\) −14.6864 −0.470099
\(977\) −18.3480 −0.587004 −0.293502 0.955958i \(-0.594821\pi\)
−0.293502 + 0.955958i \(0.594821\pi\)
\(978\) −0.503276 −0.0160930
\(979\) −16.4475 −0.525665
\(980\) 6.54175 0.208968
\(981\) −74.8401 −2.38946
\(982\) 10.2100 0.325813
\(983\) 16.4070 0.523301 0.261650 0.965163i \(-0.415733\pi\)
0.261650 + 0.965163i \(0.415733\pi\)
\(984\) −14.2550 −0.454434
\(985\) 8.44971 0.269230
\(986\) −5.97631 −0.190324
\(987\) −16.2748 −0.518034
\(988\) −5.85612 −0.186308
\(989\) 3.38657 0.107687
\(990\) −7.92047 −0.251729
\(991\) 9.64013 0.306229 0.153114 0.988208i \(-0.451070\pi\)
0.153114 + 0.988208i \(0.451070\pi\)
\(992\) 8.31634 0.264044
\(993\) −19.7907 −0.628040
\(994\) −5.98323 −0.189776
\(995\) 11.9972 0.380335
\(996\) −17.5289 −0.555425
\(997\) −54.1525 −1.71503 −0.857514 0.514461i \(-0.827992\pi\)
−0.857514 + 0.514461i \(0.827992\pi\)
\(998\) 18.9638 0.600289
\(999\) 182.123 5.76210
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 4730.2.a.bf.1.13 13
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4730.2.a.bf.1.13 13 1.1 even 1 trivial