Properties

Label 4029.2.a.k.1.4
Level 4029
Weight 2
Character 4029.1
Self dual yes
Analytic conductor 32.172
Analytic rank 0
Dimension 31
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4029 = 3 \cdot 17 \cdot 79 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4029.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.1717269744\)
Analytic rank: \(0\)
Dimension: \(31\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) = 4029.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.28064 q^{2} +1.00000 q^{3} +3.20133 q^{4} +2.67486 q^{5} -2.28064 q^{6} -3.60745 q^{7} -2.73981 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.28064 q^{2} +1.00000 q^{3} +3.20133 q^{4} +2.67486 q^{5} -2.28064 q^{6} -3.60745 q^{7} -2.73981 q^{8} +1.00000 q^{9} -6.10039 q^{10} -4.75294 q^{11} +3.20133 q^{12} -2.82803 q^{13} +8.22732 q^{14} +2.67486 q^{15} -0.154140 q^{16} +1.00000 q^{17} -2.28064 q^{18} +7.19726 q^{19} +8.56310 q^{20} -3.60745 q^{21} +10.8398 q^{22} -7.90378 q^{23} -2.73981 q^{24} +2.15485 q^{25} +6.44974 q^{26} +1.00000 q^{27} -11.5487 q^{28} +3.76541 q^{29} -6.10039 q^{30} +10.2473 q^{31} +5.83115 q^{32} -4.75294 q^{33} -2.28064 q^{34} -9.64942 q^{35} +3.20133 q^{36} -11.2301 q^{37} -16.4144 q^{38} -2.82803 q^{39} -7.32859 q^{40} +3.99765 q^{41} +8.22732 q^{42} -2.71838 q^{43} -15.2158 q^{44} +2.67486 q^{45} +18.0257 q^{46} +7.28191 q^{47} -0.154140 q^{48} +6.01373 q^{49} -4.91444 q^{50} +1.00000 q^{51} -9.05348 q^{52} -10.1934 q^{53} -2.28064 q^{54} -12.7134 q^{55} +9.88373 q^{56} +7.19726 q^{57} -8.58756 q^{58} +1.09614 q^{59} +8.56310 q^{60} +8.22066 q^{61} -23.3703 q^{62} -3.60745 q^{63} -12.9905 q^{64} -7.56458 q^{65} +10.8398 q^{66} -1.58454 q^{67} +3.20133 q^{68} -7.90378 q^{69} +22.0069 q^{70} +12.1262 q^{71} -2.73981 q^{72} -11.5812 q^{73} +25.6118 q^{74} +2.15485 q^{75} +23.0408 q^{76} +17.1460 q^{77} +6.44974 q^{78} +1.00000 q^{79} -0.412301 q^{80} +1.00000 q^{81} -9.11721 q^{82} +14.9668 q^{83} -11.5487 q^{84} +2.67486 q^{85} +6.19965 q^{86} +3.76541 q^{87} +13.0222 q^{88} +5.52915 q^{89} -6.10039 q^{90} +10.2020 q^{91} -25.3026 q^{92} +10.2473 q^{93} -16.6074 q^{94} +19.2516 q^{95} +5.83115 q^{96} +9.40808 q^{97} -13.7152 q^{98} -4.75294 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 31q + 4q^{2} + 31q^{3} + 34q^{4} + 11q^{5} + 4q^{6} + 4q^{7} + 12q^{8} + 31q^{9} + O(q^{10}) \) \( 31q + 4q^{2} + 31q^{3} + 34q^{4} + 11q^{5} + 4q^{6} + 4q^{7} + 12q^{8} + 31q^{9} + 5q^{10} + 26q^{11} + 34q^{12} + 7q^{13} + 19q^{14} + 11q^{15} + 40q^{16} + 31q^{17} + 4q^{18} + 32q^{19} + 23q^{20} + 4q^{21} + 2q^{22} + 29q^{23} + 12q^{24} + 32q^{25} + 13q^{26} + 31q^{27} - 13q^{28} + 25q^{29} + 5q^{30} + 22q^{31} + 28q^{32} + 26q^{33} + 4q^{34} + 20q^{35} + 34q^{36} - 4q^{37} + 19q^{38} + 7q^{39} - 3q^{40} + 33q^{41} + 19q^{42} + 6q^{43} + 30q^{44} + 11q^{45} - 11q^{46} + 23q^{47} + 40q^{48} + 31q^{49} + 6q^{50} + 31q^{51} - 7q^{52} + 12q^{53} + 4q^{54} + 40q^{56} + 32q^{57} + 9q^{58} + 27q^{59} + 23q^{60} - 4q^{61} + 25q^{62} + 4q^{63} + 10q^{64} + 54q^{65} + 2q^{66} + 34q^{68} + 29q^{69} - 59q^{70} + 35q^{71} + 12q^{72} + 5q^{73} + 48q^{74} + 32q^{75} + 32q^{76} + 42q^{77} + 13q^{78} + 31q^{79} + 24q^{80} + 31q^{81} + 5q^{82} + 67q^{83} - 13q^{84} + 11q^{85} - 20q^{86} + 25q^{87} - 7q^{88} + 22q^{89} + 5q^{90} + 16q^{91} + 57q^{92} + 22q^{93} + 45q^{94} + 73q^{95} + 28q^{96} - 13q^{97} - 19q^{98} + 26q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.28064 −1.61266 −0.806329 0.591467i \(-0.798549\pi\)
−0.806329 + 0.591467i \(0.798549\pi\)
\(3\) 1.00000 0.577350
\(4\) 3.20133 1.60067
\(5\) 2.67486 1.19623 0.598116 0.801410i \(-0.295916\pi\)
0.598116 + 0.801410i \(0.295916\pi\)
\(6\) −2.28064 −0.931069
\(7\) −3.60745 −1.36349 −0.681745 0.731590i \(-0.738779\pi\)
−0.681745 + 0.731590i \(0.738779\pi\)
\(8\) −2.73981 −0.968668
\(9\) 1.00000 0.333333
\(10\) −6.10039 −1.92911
\(11\) −4.75294 −1.43307 −0.716533 0.697553i \(-0.754272\pi\)
−0.716533 + 0.697553i \(0.754272\pi\)
\(12\) 3.20133 0.924145
\(13\) −2.82803 −0.784356 −0.392178 0.919889i \(-0.628278\pi\)
−0.392178 + 0.919889i \(0.628278\pi\)
\(14\) 8.22732 2.19884
\(15\) 2.67486 0.690645
\(16\) −0.154140 −0.0385349
\(17\) 1.00000 0.242536
\(18\) −2.28064 −0.537553
\(19\) 7.19726 1.65117 0.825583 0.564281i \(-0.190846\pi\)
0.825583 + 0.564281i \(0.190846\pi\)
\(20\) 8.56310 1.91477
\(21\) −3.60745 −0.787211
\(22\) 10.8398 2.31105
\(23\) −7.90378 −1.64805 −0.824026 0.566552i \(-0.808277\pi\)
−0.824026 + 0.566552i \(0.808277\pi\)
\(24\) −2.73981 −0.559261
\(25\) 2.15485 0.430970
\(26\) 6.44974 1.26490
\(27\) 1.00000 0.192450
\(28\) −11.5487 −2.18249
\(29\) 3.76541 0.699220 0.349610 0.936895i \(-0.386314\pi\)
0.349610 + 0.936895i \(0.386314\pi\)
\(30\) −6.10039 −1.11377
\(31\) 10.2473 1.84046 0.920231 0.391376i \(-0.128001\pi\)
0.920231 + 0.391376i \(0.128001\pi\)
\(32\) 5.83115 1.03081
\(33\) −4.75294 −0.827381
\(34\) −2.28064 −0.391127
\(35\) −9.64942 −1.63105
\(36\) 3.20133 0.533555
\(37\) −11.2301 −1.84621 −0.923107 0.384543i \(-0.874359\pi\)
−0.923107 + 0.384543i \(0.874359\pi\)
\(38\) −16.4144 −2.66277
\(39\) −2.82803 −0.452848
\(40\) −7.32859 −1.15875
\(41\) 3.99765 0.624328 0.312164 0.950028i \(-0.398946\pi\)
0.312164 + 0.950028i \(0.398946\pi\)
\(42\) 8.22732 1.26950
\(43\) −2.71838 −0.414549 −0.207274 0.978283i \(-0.566459\pi\)
−0.207274 + 0.978283i \(0.566459\pi\)
\(44\) −15.2158 −2.29386
\(45\) 2.67486 0.398744
\(46\) 18.0257 2.65774
\(47\) 7.28191 1.06218 0.531088 0.847317i \(-0.321783\pi\)
0.531088 + 0.847317i \(0.321783\pi\)
\(48\) −0.154140 −0.0222481
\(49\) 6.01373 0.859104
\(50\) −4.91444 −0.695007
\(51\) 1.00000 0.140028
\(52\) −9.05348 −1.25549
\(53\) −10.1934 −1.40017 −0.700087 0.714057i \(-0.746856\pi\)
−0.700087 + 0.714057i \(0.746856\pi\)
\(54\) −2.28064 −0.310356
\(55\) −12.7134 −1.71428
\(56\) 9.88373 1.32077
\(57\) 7.19726 0.953301
\(58\) −8.58756 −1.12760
\(59\) 1.09614 0.142706 0.0713529 0.997451i \(-0.477268\pi\)
0.0713529 + 0.997451i \(0.477268\pi\)
\(60\) 8.56310 1.10549
\(61\) 8.22066 1.05255 0.526274 0.850315i \(-0.323589\pi\)
0.526274 + 0.850315i \(0.323589\pi\)
\(62\) −23.3703 −2.96803
\(63\) −3.60745 −0.454497
\(64\) −12.9905 −1.62381
\(65\) −7.56458 −0.938271
\(66\) 10.8398 1.33428
\(67\) −1.58454 −0.193582 −0.0967912 0.995305i \(-0.530858\pi\)
−0.0967912 + 0.995305i \(0.530858\pi\)
\(68\) 3.20133 0.388218
\(69\) −7.90378 −0.951503
\(70\) 22.0069 2.63032
\(71\) 12.1262 1.43912 0.719560 0.694430i \(-0.244343\pi\)
0.719560 + 0.694430i \(0.244343\pi\)
\(72\) −2.73981 −0.322889
\(73\) −11.5812 −1.35548 −0.677741 0.735301i \(-0.737041\pi\)
−0.677741 + 0.735301i \(0.737041\pi\)
\(74\) 25.6118 2.97731
\(75\) 2.15485 0.248821
\(76\) 23.0408 2.64296
\(77\) 17.1460 1.95397
\(78\) 6.44974 0.730289
\(79\) 1.00000 0.112509
\(80\) −0.412301 −0.0460967
\(81\) 1.00000 0.111111
\(82\) −9.11721 −1.00683
\(83\) 14.9668 1.64282 0.821412 0.570336i \(-0.193187\pi\)
0.821412 + 0.570336i \(0.193187\pi\)
\(84\) −11.5487 −1.26006
\(85\) 2.67486 0.290129
\(86\) 6.19965 0.668526
\(87\) 3.76541 0.403695
\(88\) 13.0222 1.38817
\(89\) 5.52915 0.586089 0.293045 0.956099i \(-0.405332\pi\)
0.293045 + 0.956099i \(0.405332\pi\)
\(90\) −6.10039 −0.643037
\(91\) 10.2020 1.06946
\(92\) −25.3026 −2.63798
\(93\) 10.2473 1.06259
\(94\) −16.6074 −1.71293
\(95\) 19.2516 1.97518
\(96\) 5.83115 0.595140
\(97\) 9.40808 0.955245 0.477623 0.878565i \(-0.341499\pi\)
0.477623 + 0.878565i \(0.341499\pi\)
\(98\) −13.7152 −1.38544
\(99\) −4.75294 −0.477689
\(100\) 6.89839 0.689839
\(101\) −1.63157 −0.162347 −0.0811735 0.996700i \(-0.525867\pi\)
−0.0811735 + 0.996700i \(0.525867\pi\)
\(102\) −2.28064 −0.225817
\(103\) 3.45584 0.340514 0.170257 0.985400i \(-0.445540\pi\)
0.170257 + 0.985400i \(0.445540\pi\)
\(104\) 7.74827 0.759781
\(105\) −9.64942 −0.941687
\(106\) 23.2476 2.25800
\(107\) 4.86976 0.470778 0.235389 0.971901i \(-0.424364\pi\)
0.235389 + 0.971901i \(0.424364\pi\)
\(108\) 3.20133 0.308048
\(109\) −4.34182 −0.415871 −0.207936 0.978143i \(-0.566674\pi\)
−0.207936 + 0.978143i \(0.566674\pi\)
\(110\) 28.9948 2.76455
\(111\) −11.2301 −1.06591
\(112\) 0.556052 0.0525420
\(113\) 14.8190 1.39405 0.697026 0.717046i \(-0.254506\pi\)
0.697026 + 0.717046i \(0.254506\pi\)
\(114\) −16.4144 −1.53735
\(115\) −21.1415 −1.97145
\(116\) 12.0543 1.11922
\(117\) −2.82803 −0.261452
\(118\) −2.49991 −0.230136
\(119\) −3.60745 −0.330695
\(120\) −7.32859 −0.669006
\(121\) 11.5905 1.05368
\(122\) −18.7484 −1.69740
\(123\) 3.99765 0.360456
\(124\) 32.8049 2.94596
\(125\) −7.61036 −0.680692
\(126\) 8.22732 0.732948
\(127\) 1.09995 0.0976048 0.0488024 0.998808i \(-0.484460\pi\)
0.0488024 + 0.998808i \(0.484460\pi\)
\(128\) 17.9644 1.58784
\(129\) −2.71838 −0.239340
\(130\) 17.2521 1.51311
\(131\) 18.1027 1.58164 0.790820 0.612049i \(-0.209655\pi\)
0.790820 + 0.612049i \(0.209655\pi\)
\(132\) −15.2158 −1.32436
\(133\) −25.9638 −2.25135
\(134\) 3.61377 0.312182
\(135\) 2.67486 0.230215
\(136\) −2.73981 −0.234937
\(137\) 2.48460 0.212273 0.106137 0.994352i \(-0.466152\pi\)
0.106137 + 0.994352i \(0.466152\pi\)
\(138\) 18.0257 1.53445
\(139\) 14.2415 1.20795 0.603973 0.797005i \(-0.293584\pi\)
0.603973 + 0.797005i \(0.293584\pi\)
\(140\) −30.8910 −2.61076
\(141\) 7.28191 0.613248
\(142\) −27.6556 −2.32081
\(143\) 13.4415 1.12403
\(144\) −0.154140 −0.0128450
\(145\) 10.0719 0.836429
\(146\) 26.4127 2.18593
\(147\) 6.01373 0.496004
\(148\) −35.9512 −2.95517
\(149\) −4.21059 −0.344945 −0.172472 0.985014i \(-0.555176\pi\)
−0.172472 + 0.985014i \(0.555176\pi\)
\(150\) −4.91444 −0.401263
\(151\) 4.14682 0.337464 0.168732 0.985662i \(-0.446033\pi\)
0.168732 + 0.985662i \(0.446033\pi\)
\(152\) −19.7191 −1.59943
\(153\) 1.00000 0.0808452
\(154\) −39.1040 −3.15109
\(155\) 27.4099 2.20162
\(156\) −9.05348 −0.724858
\(157\) 19.3117 1.54124 0.770620 0.637294i \(-0.219946\pi\)
0.770620 + 0.637294i \(0.219946\pi\)
\(158\) −2.28064 −0.181438
\(159\) −10.1934 −0.808391
\(160\) 15.5975 1.23309
\(161\) 28.5125 2.24710
\(162\) −2.28064 −0.179184
\(163\) −10.7248 −0.840031 −0.420016 0.907517i \(-0.637975\pi\)
−0.420016 + 0.907517i \(0.637975\pi\)
\(164\) 12.7978 0.999340
\(165\) −12.7134 −0.989740
\(166\) −34.1340 −2.64931
\(167\) 8.79439 0.680530 0.340265 0.940330i \(-0.389483\pi\)
0.340265 + 0.940330i \(0.389483\pi\)
\(168\) 9.88373 0.762547
\(169\) −5.00222 −0.384786
\(170\) −6.10039 −0.467878
\(171\) 7.19726 0.550389
\(172\) −8.70243 −0.663554
\(173\) 15.6994 1.19360 0.596802 0.802388i \(-0.296438\pi\)
0.596802 + 0.802388i \(0.296438\pi\)
\(174\) −8.58756 −0.651022
\(175\) −7.77352 −0.587623
\(176\) 0.732617 0.0552231
\(177\) 1.09614 0.0823912
\(178\) −12.6100 −0.945161
\(179\) 14.1097 1.05461 0.527305 0.849676i \(-0.323202\pi\)
0.527305 + 0.849676i \(0.323202\pi\)
\(180\) 8.56310 0.638256
\(181\) −9.59645 −0.713299 −0.356649 0.934238i \(-0.616081\pi\)
−0.356649 + 0.934238i \(0.616081\pi\)
\(182\) −23.2671 −1.72467
\(183\) 8.22066 0.607689
\(184\) 21.6548 1.59642
\(185\) −30.0388 −2.20850
\(186\) −23.3703 −1.71360
\(187\) −4.75294 −0.347570
\(188\) 23.3118 1.70019
\(189\) −3.60745 −0.262404
\(190\) −43.9061 −3.18528
\(191\) −16.8447 −1.21884 −0.609421 0.792847i \(-0.708598\pi\)
−0.609421 + 0.792847i \(0.708598\pi\)
\(192\) −12.9905 −0.937508
\(193\) −12.2947 −0.884995 −0.442497 0.896770i \(-0.645907\pi\)
−0.442497 + 0.896770i \(0.645907\pi\)
\(194\) −21.4565 −1.54048
\(195\) −7.56458 −0.541711
\(196\) 19.2519 1.37514
\(197\) 0.733843 0.0522841 0.0261421 0.999658i \(-0.491678\pi\)
0.0261421 + 0.999658i \(0.491678\pi\)
\(198\) 10.8398 0.770349
\(199\) 2.02286 0.143397 0.0716984 0.997426i \(-0.477158\pi\)
0.0716984 + 0.997426i \(0.477158\pi\)
\(200\) −5.90388 −0.417467
\(201\) −1.58454 −0.111765
\(202\) 3.72102 0.261810
\(203\) −13.5836 −0.953379
\(204\) 3.20133 0.224138
\(205\) 10.6931 0.746841
\(206\) −7.88155 −0.549133
\(207\) −7.90378 −0.549351
\(208\) 0.435912 0.0302251
\(209\) −34.2082 −2.36623
\(210\) 22.0069 1.51862
\(211\) −27.1196 −1.86699 −0.933496 0.358588i \(-0.883258\pi\)
−0.933496 + 0.358588i \(0.883258\pi\)
\(212\) −32.6325 −2.24121
\(213\) 12.1262 0.830877
\(214\) −11.1062 −0.759203
\(215\) −7.27127 −0.495896
\(216\) −2.73981 −0.186420
\(217\) −36.9665 −2.50945
\(218\) 9.90215 0.670658
\(219\) −11.5812 −0.782588
\(220\) −40.6999 −2.74399
\(221\) −2.82803 −0.190234
\(222\) 25.6118 1.71895
\(223\) −10.2494 −0.686351 −0.343175 0.939271i \(-0.611502\pi\)
−0.343175 + 0.939271i \(0.611502\pi\)
\(224\) −21.0356 −1.40550
\(225\) 2.15485 0.143657
\(226\) −33.7968 −2.24813
\(227\) 16.4170 1.08964 0.544819 0.838554i \(-0.316599\pi\)
0.544819 + 0.838554i \(0.316599\pi\)
\(228\) 23.0408 1.52592
\(229\) 10.9550 0.723927 0.361963 0.932192i \(-0.382107\pi\)
0.361963 + 0.932192i \(0.382107\pi\)
\(230\) 48.2161 3.17928
\(231\) 17.1460 1.12813
\(232\) −10.3165 −0.677312
\(233\) 27.2344 1.78419 0.892093 0.451852i \(-0.149237\pi\)
0.892093 + 0.451852i \(0.149237\pi\)
\(234\) 6.44974 0.421632
\(235\) 19.4781 1.27061
\(236\) 3.50912 0.228424
\(237\) 1.00000 0.0649570
\(238\) 8.22732 0.533298
\(239\) 11.1314 0.720031 0.360016 0.932946i \(-0.382771\pi\)
0.360016 + 0.932946i \(0.382771\pi\)
\(240\) −0.412301 −0.0266139
\(241\) −6.97632 −0.449384 −0.224692 0.974430i \(-0.572138\pi\)
−0.224692 + 0.974430i \(0.572138\pi\)
\(242\) −26.4338 −1.69923
\(243\) 1.00000 0.0641500
\(244\) 26.3171 1.68478
\(245\) 16.0859 1.02769
\(246\) −9.11721 −0.581292
\(247\) −20.3541 −1.29510
\(248\) −28.0755 −1.78280
\(249\) 14.9668 0.948485
\(250\) 17.3565 1.09772
\(251\) 12.5102 0.789638 0.394819 0.918759i \(-0.370807\pi\)
0.394819 + 0.918759i \(0.370807\pi\)
\(252\) −11.5487 −0.727497
\(253\) 37.5662 2.36177
\(254\) −2.50859 −0.157403
\(255\) 2.67486 0.167506
\(256\) −14.9893 −0.936834
\(257\) −19.8944 −1.24098 −0.620488 0.784216i \(-0.713065\pi\)
−0.620488 + 0.784216i \(0.713065\pi\)
\(258\) 6.19965 0.385973
\(259\) 40.5120 2.51729
\(260\) −24.2167 −1.50186
\(261\) 3.76541 0.233073
\(262\) −41.2858 −2.55064
\(263\) 5.61631 0.346316 0.173158 0.984894i \(-0.444603\pi\)
0.173158 + 0.984894i \(0.444603\pi\)
\(264\) 13.0222 0.801458
\(265\) −27.2659 −1.67493
\(266\) 59.2142 3.63065
\(267\) 5.52915 0.338379
\(268\) −5.07264 −0.309861
\(269\) −4.67648 −0.285130 −0.142565 0.989785i \(-0.545535\pi\)
−0.142565 + 0.989785i \(0.545535\pi\)
\(270\) −6.10039 −0.371258
\(271\) −5.49377 −0.333723 −0.166861 0.985980i \(-0.553363\pi\)
−0.166861 + 0.985980i \(0.553363\pi\)
\(272\) −0.154140 −0.00934609
\(273\) 10.2020 0.617454
\(274\) −5.66647 −0.342324
\(275\) −10.2419 −0.617609
\(276\) −25.3026 −1.52304
\(277\) −4.86185 −0.292120 −0.146060 0.989276i \(-0.546659\pi\)
−0.146060 + 0.989276i \(0.546659\pi\)
\(278\) −32.4797 −1.94800
\(279\) 10.2473 0.613487
\(280\) 26.4376 1.57995
\(281\) −19.5207 −1.16451 −0.582254 0.813007i \(-0.697829\pi\)
−0.582254 + 0.813007i \(0.697829\pi\)
\(282\) −16.6074 −0.988959
\(283\) 11.3990 0.677602 0.338801 0.940858i \(-0.389979\pi\)
0.338801 + 0.940858i \(0.389979\pi\)
\(284\) 38.8201 2.30355
\(285\) 19.2516 1.14037
\(286\) −30.6552 −1.81268
\(287\) −14.4213 −0.851265
\(288\) 5.83115 0.343604
\(289\) 1.00000 0.0588235
\(290\) −22.9705 −1.34887
\(291\) 9.40808 0.551511
\(292\) −37.0754 −2.16967
\(293\) 28.0156 1.63669 0.818343 0.574730i \(-0.194893\pi\)
0.818343 + 0.574730i \(0.194893\pi\)
\(294\) −13.7152 −0.799885
\(295\) 2.93203 0.170709
\(296\) 30.7683 1.78837
\(297\) −4.75294 −0.275794
\(298\) 9.60285 0.556278
\(299\) 22.3522 1.29266
\(300\) 6.89839 0.398279
\(301\) 9.80643 0.565233
\(302\) −9.45742 −0.544213
\(303\) −1.63157 −0.0937311
\(304\) −1.10938 −0.0636275
\(305\) 21.9891 1.25909
\(306\) −2.28064 −0.130376
\(307\) 24.2347 1.38315 0.691573 0.722306i \(-0.256918\pi\)
0.691573 + 0.722306i \(0.256918\pi\)
\(308\) 54.8901 3.12766
\(309\) 3.45584 0.196596
\(310\) −62.5122 −3.55046
\(311\) 7.00815 0.397396 0.198698 0.980061i \(-0.436329\pi\)
0.198698 + 0.980061i \(0.436329\pi\)
\(312\) 7.74827 0.438659
\(313\) 9.00979 0.509263 0.254632 0.967038i \(-0.418046\pi\)
0.254632 + 0.967038i \(0.418046\pi\)
\(314\) −44.0431 −2.48549
\(315\) −9.64942 −0.543683
\(316\) 3.20133 0.180089
\(317\) −7.95241 −0.446652 −0.223326 0.974744i \(-0.571691\pi\)
−0.223326 + 0.974744i \(0.571691\pi\)
\(318\) 23.2476 1.30366
\(319\) −17.8968 −1.00203
\(320\) −34.7477 −1.94246
\(321\) 4.86976 0.271804
\(322\) −65.0269 −3.62381
\(323\) 7.19726 0.400467
\(324\) 3.20133 0.177852
\(325\) −6.09399 −0.338034
\(326\) 24.4594 1.35468
\(327\) −4.34182 −0.240103
\(328\) −10.9528 −0.604767
\(329\) −26.2692 −1.44827
\(330\) 28.9948 1.59611
\(331\) −31.3687 −1.72418 −0.862091 0.506754i \(-0.830845\pi\)
−0.862091 + 0.506754i \(0.830845\pi\)
\(332\) 47.9138 2.62961
\(333\) −11.2301 −0.615405
\(334\) −20.0569 −1.09746
\(335\) −4.23841 −0.231569
\(336\) 0.556052 0.0303351
\(337\) 0.391866 0.0213463 0.0106731 0.999943i \(-0.496603\pi\)
0.0106731 + 0.999943i \(0.496603\pi\)
\(338\) 11.4083 0.620529
\(339\) 14.8190 0.804856
\(340\) 8.56310 0.464399
\(341\) −48.7046 −2.63750
\(342\) −16.4144 −0.887589
\(343\) 3.55793 0.192110
\(344\) 7.44784 0.401560
\(345\) −21.1415 −1.13822
\(346\) −35.8048 −1.92488
\(347\) 31.2815 1.67928 0.839639 0.543145i \(-0.182767\pi\)
0.839639 + 0.543145i \(0.182767\pi\)
\(348\) 12.0543 0.646180
\(349\) 34.3713 1.83985 0.919927 0.392091i \(-0.128248\pi\)
0.919927 + 0.392091i \(0.128248\pi\)
\(350\) 17.7286 0.947635
\(351\) −2.82803 −0.150949
\(352\) −27.7151 −1.47722
\(353\) 5.00856 0.266579 0.133289 0.991077i \(-0.457446\pi\)
0.133289 + 0.991077i \(0.457446\pi\)
\(354\) −2.49991 −0.132869
\(355\) 32.4359 1.72152
\(356\) 17.7007 0.938133
\(357\) −3.60745 −0.190927
\(358\) −32.1793 −1.70073
\(359\) −17.6801 −0.933119 −0.466560 0.884490i \(-0.654507\pi\)
−0.466560 + 0.884490i \(0.654507\pi\)
\(360\) −7.32859 −0.386251
\(361\) 32.8006 1.72635
\(362\) 21.8861 1.15031
\(363\) 11.5905 0.608343
\(364\) 32.6600 1.71185
\(365\) −30.9782 −1.62147
\(366\) −18.7484 −0.979994
\(367\) 0.783792 0.0409136 0.0204568 0.999791i \(-0.493488\pi\)
0.0204568 + 0.999791i \(0.493488\pi\)
\(368\) 1.21829 0.0635075
\(369\) 3.99765 0.208109
\(370\) 68.5079 3.56155
\(371\) 36.7723 1.90912
\(372\) 32.8049 1.70085
\(373\) −12.0319 −0.622986 −0.311493 0.950248i \(-0.600829\pi\)
−0.311493 + 0.950248i \(0.600829\pi\)
\(374\) 10.8398 0.560511
\(375\) −7.61036 −0.392998
\(376\) −19.9510 −1.02890
\(377\) −10.6487 −0.548437
\(378\) 8.22732 0.423167
\(379\) −11.2666 −0.578725 −0.289362 0.957220i \(-0.593443\pi\)
−0.289362 + 0.957220i \(0.593443\pi\)
\(380\) 61.6309 3.16160
\(381\) 1.09995 0.0563522
\(382\) 38.4168 1.96558
\(383\) −24.0861 −1.23074 −0.615370 0.788238i \(-0.710993\pi\)
−0.615370 + 0.788238i \(0.710993\pi\)
\(384\) 17.9644 0.916741
\(385\) 45.8632 2.33740
\(386\) 28.0399 1.42719
\(387\) −2.71838 −0.138183
\(388\) 30.1184 1.52903
\(389\) −19.6932 −0.998486 −0.499243 0.866462i \(-0.666389\pi\)
−0.499243 + 0.866462i \(0.666389\pi\)
\(390\) 17.2521 0.873595
\(391\) −7.90378 −0.399711
\(392\) −16.4765 −0.832187
\(393\) 18.1027 0.913160
\(394\) −1.67363 −0.0843164
\(395\) 2.67486 0.134587
\(396\) −15.2158 −0.764620
\(397\) −24.9800 −1.25371 −0.626854 0.779137i \(-0.715658\pi\)
−0.626854 + 0.779137i \(0.715658\pi\)
\(398\) −4.61342 −0.231250
\(399\) −25.9638 −1.29982
\(400\) −0.332148 −0.0166074
\(401\) 22.8544 1.14129 0.570646 0.821196i \(-0.306693\pi\)
0.570646 + 0.821196i \(0.306693\pi\)
\(402\) 3.61377 0.180238
\(403\) −28.9796 −1.44358
\(404\) −5.22319 −0.259863
\(405\) 2.67486 0.132915
\(406\) 30.9793 1.53747
\(407\) 53.3760 2.64575
\(408\) −2.73981 −0.135641
\(409\) −10.5353 −0.520939 −0.260470 0.965482i \(-0.583877\pi\)
−0.260470 + 0.965482i \(0.583877\pi\)
\(410\) −24.3872 −1.20440
\(411\) 2.48460 0.122556
\(412\) 11.0633 0.545050
\(413\) −3.95429 −0.194578
\(414\) 18.0257 0.885915
\(415\) 40.0341 1.96520
\(416\) −16.4907 −0.808523
\(417\) 14.2415 0.697407
\(418\) 78.0167 3.81592
\(419\) 19.7915 0.966878 0.483439 0.875378i \(-0.339387\pi\)
0.483439 + 0.875378i \(0.339387\pi\)
\(420\) −30.8910 −1.50733
\(421\) 4.49625 0.219134 0.109567 0.993979i \(-0.465054\pi\)
0.109567 + 0.993979i \(0.465054\pi\)
\(422\) 61.8502 3.01082
\(423\) 7.28191 0.354059
\(424\) 27.9280 1.35631
\(425\) 2.15485 0.104526
\(426\) −27.6556 −1.33992
\(427\) −29.6557 −1.43514
\(428\) 15.5897 0.753558
\(429\) 13.4415 0.648961
\(430\) 16.5832 0.799711
\(431\) 20.0253 0.964585 0.482292 0.876010i \(-0.339804\pi\)
0.482292 + 0.876010i \(0.339804\pi\)
\(432\) −0.154140 −0.00741605
\(433\) −15.5180 −0.745746 −0.372873 0.927882i \(-0.621627\pi\)
−0.372873 + 0.927882i \(0.621627\pi\)
\(434\) 84.3074 4.04689
\(435\) 10.0719 0.482912
\(436\) −13.8996 −0.665671
\(437\) −56.8856 −2.72121
\(438\) 26.4127 1.26205
\(439\) −10.3652 −0.494703 −0.247351 0.968926i \(-0.579560\pi\)
−0.247351 + 0.968926i \(0.579560\pi\)
\(440\) 34.8324 1.66057
\(441\) 6.01373 0.286368
\(442\) 6.44974 0.306783
\(443\) 17.7311 0.842428 0.421214 0.906961i \(-0.361604\pi\)
0.421214 + 0.906961i \(0.361604\pi\)
\(444\) −35.9512 −1.70617
\(445\) 14.7897 0.701098
\(446\) 23.3752 1.10685
\(447\) −4.21059 −0.199154
\(448\) 46.8626 2.21405
\(449\) 7.17495 0.338607 0.169303 0.985564i \(-0.445848\pi\)
0.169303 + 0.985564i \(0.445848\pi\)
\(450\) −4.91444 −0.231669
\(451\) −19.0006 −0.894704
\(452\) 47.4404 2.23141
\(453\) 4.14682 0.194835
\(454\) −37.4414 −1.75721
\(455\) 27.2889 1.27932
\(456\) −19.7191 −0.923433
\(457\) 23.3766 1.09351 0.546756 0.837292i \(-0.315863\pi\)
0.546756 + 0.837292i \(0.315863\pi\)
\(458\) −24.9844 −1.16745
\(459\) 1.00000 0.0466760
\(460\) −67.6808 −3.15564
\(461\) −20.8454 −0.970866 −0.485433 0.874274i \(-0.661338\pi\)
−0.485433 + 0.874274i \(0.661338\pi\)
\(462\) −39.1040 −1.81928
\(463\) 19.5630 0.909168 0.454584 0.890704i \(-0.349788\pi\)
0.454584 + 0.890704i \(0.349788\pi\)
\(464\) −0.580400 −0.0269444
\(465\) 27.4099 1.27110
\(466\) −62.1120 −2.87728
\(467\) −32.1144 −1.48608 −0.743038 0.669250i \(-0.766616\pi\)
−0.743038 + 0.669250i \(0.766616\pi\)
\(468\) −9.05348 −0.418497
\(469\) 5.71616 0.263948
\(470\) −44.4225 −2.04906
\(471\) 19.3117 0.889836
\(472\) −3.00322 −0.138235
\(473\) 12.9203 0.594076
\(474\) −2.28064 −0.104753
\(475\) 15.5090 0.711603
\(476\) −11.5487 −0.529332
\(477\) −10.1934 −0.466725
\(478\) −25.3868 −1.16116
\(479\) 28.6345 1.30834 0.654172 0.756346i \(-0.273017\pi\)
0.654172 + 0.756346i \(0.273017\pi\)
\(480\) 15.5975 0.711925
\(481\) 31.7591 1.44809
\(482\) 15.9105 0.724703
\(483\) 28.5125 1.29737
\(484\) 37.1050 1.68659
\(485\) 25.1652 1.14269
\(486\) −2.28064 −0.103452
\(487\) 11.3785 0.515609 0.257804 0.966197i \(-0.417001\pi\)
0.257804 + 0.966197i \(0.417001\pi\)
\(488\) −22.5230 −1.01957
\(489\) −10.7248 −0.484992
\(490\) −36.6861 −1.65731
\(491\) −1.47855 −0.0667258 −0.0333629 0.999443i \(-0.510622\pi\)
−0.0333629 + 0.999443i \(0.510622\pi\)
\(492\) 12.7978 0.576969
\(493\) 3.76541 0.169586
\(494\) 46.4205 2.08856
\(495\) −12.7134 −0.571427
\(496\) −1.57951 −0.0709220
\(497\) −43.7449 −1.96223
\(498\) −34.1340 −1.52958
\(499\) 10.6851 0.478332 0.239166 0.970979i \(-0.423126\pi\)
0.239166 + 0.970979i \(0.423126\pi\)
\(500\) −24.3633 −1.08956
\(501\) 8.79439 0.392904
\(502\) −28.5314 −1.27342
\(503\) 15.3226 0.683200 0.341600 0.939845i \(-0.389031\pi\)
0.341600 + 0.939845i \(0.389031\pi\)
\(504\) 9.88373 0.440256
\(505\) −4.36421 −0.194205
\(506\) −85.6752 −3.80873
\(507\) −5.00222 −0.222156
\(508\) 3.52131 0.156233
\(509\) −9.58075 −0.424659 −0.212330 0.977198i \(-0.568105\pi\)
−0.212330 + 0.977198i \(0.568105\pi\)
\(510\) −6.10039 −0.270130
\(511\) 41.7788 1.84819
\(512\) −1.74344 −0.0770498
\(513\) 7.19726 0.317767
\(514\) 45.3719 2.00127
\(515\) 9.24388 0.407334
\(516\) −8.70243 −0.383103
\(517\) −34.6105 −1.52217
\(518\) −92.3934 −4.05953
\(519\) 15.6994 0.689128
\(520\) 20.7255 0.908873
\(521\) −25.6248 −1.12264 −0.561322 0.827597i \(-0.689707\pi\)
−0.561322 + 0.827597i \(0.689707\pi\)
\(522\) −8.58756 −0.375868
\(523\) 19.2731 0.842755 0.421377 0.906885i \(-0.361547\pi\)
0.421377 + 0.906885i \(0.361547\pi\)
\(524\) 57.9527 2.53168
\(525\) −7.77352 −0.339264
\(526\) −12.8088 −0.558490
\(527\) 10.2473 0.446377
\(528\) 0.732617 0.0318831
\(529\) 39.4697 1.71608
\(530\) 62.1839 2.70109
\(531\) 1.09614 0.0475686
\(532\) −83.1188 −3.60365
\(533\) −11.3055 −0.489695
\(534\) −12.6100 −0.545689
\(535\) 13.0259 0.563159
\(536\) 4.34133 0.187517
\(537\) 14.1097 0.608880
\(538\) 10.6654 0.459817
\(539\) −28.5829 −1.23115
\(540\) 8.56310 0.368497
\(541\) 34.2905 1.47426 0.737131 0.675750i \(-0.236180\pi\)
0.737131 + 0.675750i \(0.236180\pi\)
\(542\) 12.5293 0.538181
\(543\) −9.59645 −0.411823
\(544\) 5.83115 0.250009
\(545\) −11.6138 −0.497478
\(546\) −23.2671 −0.995741
\(547\) 23.4414 1.00228 0.501142 0.865365i \(-0.332914\pi\)
0.501142 + 0.865365i \(0.332914\pi\)
\(548\) 7.95401 0.339779
\(549\) 8.22066 0.350849
\(550\) 23.3581 0.995992
\(551\) 27.1007 1.15453
\(552\) 21.6548 0.921691
\(553\) −3.60745 −0.153405
\(554\) 11.0881 0.471090
\(555\) −30.0388 −1.27508
\(556\) 45.5916 1.93352
\(557\) −13.8969 −0.588829 −0.294414 0.955678i \(-0.595125\pi\)
−0.294414 + 0.955678i \(0.595125\pi\)
\(558\) −23.3703 −0.989345
\(559\) 7.68767 0.325154
\(560\) 1.48736 0.0628523
\(561\) −4.75294 −0.200669
\(562\) 44.5198 1.87795
\(563\) 37.6222 1.58559 0.792794 0.609489i \(-0.208626\pi\)
0.792794 + 0.609489i \(0.208626\pi\)
\(564\) 23.3118 0.981604
\(565\) 39.6386 1.66761
\(566\) −25.9971 −1.09274
\(567\) −3.60745 −0.151499
\(568\) −33.2236 −1.39403
\(569\) 17.1420 0.718631 0.359316 0.933216i \(-0.383010\pi\)
0.359316 + 0.933216i \(0.383010\pi\)
\(570\) −43.9061 −1.83902
\(571\) −22.0795 −0.923999 −0.461999 0.886880i \(-0.652868\pi\)
−0.461999 + 0.886880i \(0.652868\pi\)
\(572\) 43.0307 1.79920
\(573\) −16.8447 −0.703699
\(574\) 32.8899 1.37280
\(575\) −17.0315 −0.710261
\(576\) −12.9905 −0.541271
\(577\) 7.95890 0.331333 0.165667 0.986182i \(-0.447022\pi\)
0.165667 + 0.986182i \(0.447022\pi\)
\(578\) −2.28064 −0.0948622
\(579\) −12.2947 −0.510952
\(580\) 32.2436 1.33884
\(581\) −53.9922 −2.23997
\(582\) −21.4565 −0.889399
\(583\) 48.4488 2.00654
\(584\) 31.7304 1.31301
\(585\) −7.56458 −0.312757
\(586\) −63.8935 −2.63942
\(587\) −41.2626 −1.70309 −0.851545 0.524282i \(-0.824334\pi\)
−0.851545 + 0.524282i \(0.824334\pi\)
\(588\) 19.2519 0.793937
\(589\) 73.7522 3.03891
\(590\) −6.68691 −0.275296
\(591\) 0.733843 0.0301863
\(592\) 1.73100 0.0711437
\(593\) −1.56993 −0.0644692 −0.0322346 0.999480i \(-0.510262\pi\)
−0.0322346 + 0.999480i \(0.510262\pi\)
\(594\) 10.8398 0.444761
\(595\) −9.64942 −0.395588
\(596\) −13.4795 −0.552141
\(597\) 2.02286 0.0827902
\(598\) −50.9773 −2.08462
\(599\) −4.24121 −0.173291 −0.0866455 0.996239i \(-0.527615\pi\)
−0.0866455 + 0.996239i \(0.527615\pi\)
\(600\) −5.90388 −0.241025
\(601\) 1.90328 0.0776363 0.0388182 0.999246i \(-0.487641\pi\)
0.0388182 + 0.999246i \(0.487641\pi\)
\(602\) −22.3650 −0.911528
\(603\) −1.58454 −0.0645274
\(604\) 13.2754 0.540166
\(605\) 31.0029 1.26045
\(606\) 3.72102 0.151156
\(607\) −11.0660 −0.449154 −0.224577 0.974456i \(-0.572100\pi\)
−0.224577 + 0.974456i \(0.572100\pi\)
\(608\) 41.9684 1.70204
\(609\) −13.5836 −0.550434
\(610\) −50.1492 −2.03048
\(611\) −20.5935 −0.833124
\(612\) 3.20133 0.129406
\(613\) −22.9468 −0.926812 −0.463406 0.886146i \(-0.653373\pi\)
−0.463406 + 0.886146i \(0.653373\pi\)
\(614\) −55.2707 −2.23054
\(615\) 10.6931 0.431189
\(616\) −46.9768 −1.89275
\(617\) 16.6111 0.668736 0.334368 0.942443i \(-0.391477\pi\)
0.334368 + 0.942443i \(0.391477\pi\)
\(618\) −7.88155 −0.317042
\(619\) 36.1536 1.45314 0.726568 0.687095i \(-0.241114\pi\)
0.726568 + 0.687095i \(0.241114\pi\)
\(620\) 87.7483 3.52405
\(621\) −7.90378 −0.317168
\(622\) −15.9831 −0.640863
\(623\) −19.9462 −0.799126
\(624\) 0.435912 0.0174505
\(625\) −31.1309 −1.24523
\(626\) −20.5481 −0.821268
\(627\) −34.2082 −1.36614
\(628\) 61.8231 2.46701
\(629\) −11.2301 −0.447773
\(630\) 22.0069 0.876775
\(631\) 19.5470 0.778154 0.389077 0.921205i \(-0.372794\pi\)
0.389077 + 0.921205i \(0.372794\pi\)
\(632\) −2.73981 −0.108984
\(633\) −27.1196 −1.07791
\(634\) 18.1366 0.720297
\(635\) 2.94221 0.116758
\(636\) −32.6325 −1.29396
\(637\) −17.0070 −0.673843
\(638\) 40.8162 1.61593
\(639\) 12.1262 0.479707
\(640\) 48.0521 1.89943
\(641\) −3.41916 −0.135049 −0.0675243 0.997718i \(-0.521510\pi\)
−0.0675243 + 0.997718i \(0.521510\pi\)
\(642\) −11.1062 −0.438326
\(643\) −6.95943 −0.274453 −0.137227 0.990540i \(-0.543819\pi\)
−0.137227 + 0.990540i \(0.543819\pi\)
\(644\) 91.2781 3.59686
\(645\) −7.27127 −0.286306
\(646\) −16.4144 −0.645816
\(647\) 36.9986 1.45456 0.727282 0.686338i \(-0.240783\pi\)
0.727282 + 0.686338i \(0.240783\pi\)
\(648\) −2.73981 −0.107630
\(649\) −5.20991 −0.204507
\(650\) 13.8982 0.545133
\(651\) −36.9665 −1.44883
\(652\) −34.3336 −1.34461
\(653\) −2.59348 −0.101491 −0.0507454 0.998712i \(-0.516160\pi\)
−0.0507454 + 0.998712i \(0.516160\pi\)
\(654\) 9.90215 0.387205
\(655\) 48.4221 1.89201
\(656\) −0.616196 −0.0240584
\(657\) −11.5812 −0.451827
\(658\) 59.9106 2.33556
\(659\) −8.26032 −0.321776 −0.160888 0.986973i \(-0.551436\pi\)
−0.160888 + 0.986973i \(0.551436\pi\)
\(660\) −40.6999 −1.58424
\(661\) −15.3132 −0.595613 −0.297807 0.954626i \(-0.596255\pi\)
−0.297807 + 0.954626i \(0.596255\pi\)
\(662\) 71.5409 2.78051
\(663\) −2.82803 −0.109832
\(664\) −41.0063 −1.59135
\(665\) −69.4494 −2.69313
\(666\) 25.6118 0.992437
\(667\) −29.7610 −1.15235
\(668\) 28.1537 1.08930
\(669\) −10.2494 −0.396265
\(670\) 9.66631 0.373442
\(671\) −39.0723 −1.50837
\(672\) −21.0356 −0.811467
\(673\) −46.0965 −1.77689 −0.888444 0.458985i \(-0.848213\pi\)
−0.888444 + 0.458985i \(0.848213\pi\)
\(674\) −0.893706 −0.0344243
\(675\) 2.15485 0.0829402
\(676\) −16.0138 −0.615914
\(677\) 8.43950 0.324356 0.162178 0.986761i \(-0.448148\pi\)
0.162178 + 0.986761i \(0.448148\pi\)
\(678\) −33.7968 −1.29796
\(679\) −33.9392 −1.30247
\(680\) −7.32859 −0.281039
\(681\) 16.4170 0.629102
\(682\) 111.078 4.25339
\(683\) 18.2588 0.698652 0.349326 0.937001i \(-0.386411\pi\)
0.349326 + 0.937001i \(0.386411\pi\)
\(684\) 23.0408 0.880988
\(685\) 6.64593 0.253928
\(686\) −8.11436 −0.309808
\(687\) 10.9550 0.417959
\(688\) 0.419010 0.0159746
\(689\) 28.8274 1.09823
\(690\) 48.2161 1.83556
\(691\) 22.9533 0.873184 0.436592 0.899660i \(-0.356185\pi\)
0.436592 + 0.899660i \(0.356185\pi\)
\(692\) 50.2590 1.91056
\(693\) 17.1460 0.651324
\(694\) −71.3419 −2.70810
\(695\) 38.0938 1.44498
\(696\) −10.3165 −0.391046
\(697\) 3.99765 0.151422
\(698\) −78.3886 −2.96705
\(699\) 27.2344 1.03010
\(700\) −24.8856 −0.940588
\(701\) 1.00287 0.0378780 0.0189390 0.999821i \(-0.493971\pi\)
0.0189390 + 0.999821i \(0.493971\pi\)
\(702\) 6.44974 0.243430
\(703\) −80.8259 −3.04841
\(704\) 61.7431 2.32703
\(705\) 19.4781 0.733586
\(706\) −11.4227 −0.429900
\(707\) 5.88580 0.221358
\(708\) 3.50912 0.131881
\(709\) 35.9356 1.34959 0.674795 0.738005i \(-0.264232\pi\)
0.674795 + 0.738005i \(0.264232\pi\)
\(710\) −73.9748 −2.77623
\(711\) 1.00000 0.0375029
\(712\) −15.1488 −0.567726
\(713\) −80.9921 −3.03318
\(714\) 8.22732 0.307900
\(715\) 35.9540 1.34460
\(716\) 45.1699 1.68808
\(717\) 11.1314 0.415710
\(718\) 40.3220 1.50480
\(719\) −52.1302 −1.94413 −0.972065 0.234713i \(-0.924585\pi\)
−0.972065 + 0.234713i \(0.924585\pi\)
\(720\) −0.412301 −0.0153656
\(721\) −12.4668 −0.464288
\(722\) −74.8065 −2.78401
\(723\) −6.97632 −0.259452
\(724\) −30.7214 −1.14175
\(725\) 8.11390 0.301343
\(726\) −26.4338 −0.981049
\(727\) 29.6731 1.10052 0.550258 0.834995i \(-0.314530\pi\)
0.550258 + 0.834995i \(0.314530\pi\)
\(728\) −27.9515 −1.03595
\(729\) 1.00000 0.0370370
\(730\) 70.6501 2.61488
\(731\) −2.71838 −0.100543
\(732\) 26.3171 0.972706
\(733\) 34.1023 1.25960 0.629798 0.776759i \(-0.283138\pi\)
0.629798 + 0.776759i \(0.283138\pi\)
\(734\) −1.78755 −0.0659796
\(735\) 16.0859 0.593336
\(736\) −46.0882 −1.69883
\(737\) 7.53123 0.277416
\(738\) −9.11721 −0.335609
\(739\) −47.1048 −1.73278 −0.866389 0.499369i \(-0.833565\pi\)
−0.866389 + 0.499369i \(0.833565\pi\)
\(740\) −96.1643 −3.53507
\(741\) −20.3541 −0.747727
\(742\) −83.8645 −3.07876
\(743\) −18.7353 −0.687333 −0.343666 0.939092i \(-0.611669\pi\)
−0.343666 + 0.939092i \(0.611669\pi\)
\(744\) −28.0755 −1.02930
\(745\) −11.2627 −0.412634
\(746\) 27.4404 1.00466
\(747\) 14.9668 0.547608
\(748\) −15.2158 −0.556343
\(749\) −17.5674 −0.641901
\(750\) 17.3565 0.633771
\(751\) 29.1066 1.06211 0.531057 0.847336i \(-0.321795\pi\)
0.531057 + 0.847336i \(0.321795\pi\)
\(752\) −1.12243 −0.0409309
\(753\) 12.5102 0.455898
\(754\) 24.2859 0.884441
\(755\) 11.0921 0.403685
\(756\) −11.5487 −0.420021
\(757\) −38.3125 −1.39249 −0.696245 0.717804i \(-0.745147\pi\)
−0.696245 + 0.717804i \(0.745147\pi\)
\(758\) 25.6950 0.933285
\(759\) 37.5662 1.36357
\(760\) −52.7458 −1.91329
\(761\) −15.3461 −0.556295 −0.278147 0.960538i \(-0.589720\pi\)
−0.278147 + 0.960538i \(0.589720\pi\)
\(762\) −2.50859 −0.0908768
\(763\) 15.6629 0.567036
\(764\) −53.9256 −1.95096
\(765\) 2.67486 0.0967096
\(766\) 54.9317 1.98476
\(767\) −3.09993 −0.111932
\(768\) −14.9893 −0.540881
\(769\) −34.5021 −1.24418 −0.622089 0.782946i \(-0.713716\pi\)
−0.622089 + 0.782946i \(0.713716\pi\)
\(770\) −104.597 −3.76943
\(771\) −19.8944 −0.716478
\(772\) −39.3595 −1.41658
\(773\) −30.9623 −1.11364 −0.556819 0.830634i \(-0.687978\pi\)
−0.556819 + 0.830634i \(0.687978\pi\)
\(774\) 6.19965 0.222842
\(775\) 22.0813 0.793184
\(776\) −25.7763 −0.925316
\(777\) 40.5120 1.45336
\(778\) 44.9132 1.61022
\(779\) 28.7721 1.03087
\(780\) −24.2167 −0.867098
\(781\) −57.6354 −2.06236
\(782\) 18.0257 0.644598
\(783\) 3.76541 0.134565
\(784\) −0.926954 −0.0331055
\(785\) 51.6560 1.84368
\(786\) −41.2858 −1.47261
\(787\) −5.77261 −0.205771 −0.102886 0.994693i \(-0.532808\pi\)
−0.102886 + 0.994693i \(0.532808\pi\)
\(788\) 2.34927 0.0836894
\(789\) 5.61631 0.199946
\(790\) −6.10039 −0.217042
\(791\) −53.4587 −1.90077
\(792\) 13.0222 0.462722
\(793\) −23.2483 −0.825572
\(794\) 56.9704 2.02180
\(795\) −27.2659 −0.967023
\(796\) 6.47585 0.229530
\(797\) −27.9204 −0.988992 −0.494496 0.869180i \(-0.664647\pi\)
−0.494496 + 0.869180i \(0.664647\pi\)
\(798\) 59.2142 2.09616
\(799\) 7.28191 0.257616
\(800\) 12.5653 0.444249
\(801\) 5.52915 0.195363
\(802\) −52.1226 −1.84051
\(803\) 55.0450 1.94250
\(804\) −5.07264 −0.178898
\(805\) 76.2669 2.68805
\(806\) 66.0921 2.32799
\(807\) −4.67648 −0.164620
\(808\) 4.47018 0.157260
\(809\) −5.24753 −0.184493 −0.0922466 0.995736i \(-0.529405\pi\)
−0.0922466 + 0.995736i \(0.529405\pi\)
\(810\) −6.10039 −0.214346
\(811\) 17.8684 0.627444 0.313722 0.949515i \(-0.398424\pi\)
0.313722 + 0.949515i \(0.398424\pi\)
\(812\) −43.4855 −1.52604
\(813\) −5.49377 −0.192675
\(814\) −121.731 −4.26669
\(815\) −28.6873 −1.00487
\(816\) −0.154140 −0.00539597
\(817\) −19.5649 −0.684489
\(818\) 24.0274 0.840097
\(819\) 10.2020 0.356487
\(820\) 34.2323 1.19544
\(821\) −17.9143 −0.625214 −0.312607 0.949883i \(-0.601202\pi\)
−0.312607 + 0.949883i \(0.601202\pi\)
\(822\) −5.66647 −0.197641
\(823\) −34.9092 −1.21686 −0.608428 0.793609i \(-0.708200\pi\)
−0.608428 + 0.793609i \(0.708200\pi\)
\(824\) −9.46835 −0.329846
\(825\) −10.2419 −0.356577
\(826\) 9.01832 0.313788
\(827\) −8.52974 −0.296608 −0.148304 0.988942i \(-0.547381\pi\)
−0.148304 + 0.988942i \(0.547381\pi\)
\(828\) −25.3026 −0.879327
\(829\) −44.8678 −1.55832 −0.779161 0.626823i \(-0.784355\pi\)
−0.779161 + 0.626823i \(0.784355\pi\)
\(830\) −91.3035 −3.16919
\(831\) −4.86185 −0.168656
\(832\) 36.7376 1.27365
\(833\) 6.01373 0.208363
\(834\) −32.4797 −1.12468
\(835\) 23.5237 0.814072
\(836\) −109.512 −3.78754
\(837\) 10.2473 0.354197
\(838\) −45.1373 −1.55924
\(839\) −36.0127 −1.24330 −0.621649 0.783296i \(-0.713537\pi\)
−0.621649 + 0.783296i \(0.713537\pi\)
\(840\) 26.4376 0.912182
\(841\) −14.8217 −0.511092
\(842\) −10.2543 −0.353388
\(843\) −19.5207 −0.672329
\(844\) −86.8189 −2.98843
\(845\) −13.3802 −0.460293
\(846\) −16.6074 −0.570976
\(847\) −41.8121 −1.43668
\(848\) 1.57121 0.0539556
\(849\) 11.3990 0.391214
\(850\) −4.91444 −0.168564
\(851\) 88.7601 3.04266
\(852\) 38.8201 1.32996
\(853\) −25.4854 −0.872603 −0.436302 0.899800i \(-0.643712\pi\)
−0.436302 + 0.899800i \(0.643712\pi\)
\(854\) 67.6339 2.31439
\(855\) 19.2516 0.658392
\(856\) −13.3422 −0.456027
\(857\) −1.34025 −0.0457819 −0.0228910 0.999738i \(-0.507287\pi\)
−0.0228910 + 0.999738i \(0.507287\pi\)
\(858\) −30.6552 −1.04655
\(859\) −0.493425 −0.0168355 −0.00841773 0.999965i \(-0.502679\pi\)
−0.00841773 + 0.999965i \(0.502679\pi\)
\(860\) −23.2777 −0.793764
\(861\) −14.4213 −0.491478
\(862\) −45.6706 −1.55555
\(863\) −26.2936 −0.895044 −0.447522 0.894273i \(-0.647693\pi\)
−0.447522 + 0.894273i \(0.647693\pi\)
\(864\) 5.83115 0.198380
\(865\) 41.9937 1.42783
\(866\) 35.3909 1.20263
\(867\) 1.00000 0.0339618
\(868\) −118.342 −4.01679
\(869\) −4.75294 −0.161233
\(870\) −22.9705 −0.778773
\(871\) 4.48113 0.151837
\(872\) 11.8958 0.402841
\(873\) 9.40808 0.318415
\(874\) 129.736 4.38838
\(875\) 27.4540 0.928116
\(876\) −37.0754 −1.25266
\(877\) 37.1018 1.25284 0.626420 0.779486i \(-0.284519\pi\)
0.626420 + 0.779486i \(0.284519\pi\)
\(878\) 23.6393 0.797787
\(879\) 28.0156 0.944941
\(880\) 1.95964 0.0660596
\(881\) 23.6374 0.796365 0.398183 0.917306i \(-0.369641\pi\)
0.398183 + 0.917306i \(0.369641\pi\)
\(882\) −13.7152 −0.461814
\(883\) 23.3225 0.784865 0.392433 0.919781i \(-0.371634\pi\)
0.392433 + 0.919781i \(0.371634\pi\)
\(884\) −9.05348 −0.304501
\(885\) 2.93203 0.0985590
\(886\) −40.4382 −1.35855
\(887\) 39.9203 1.34039 0.670196 0.742184i \(-0.266210\pi\)
0.670196 + 0.742184i \(0.266210\pi\)
\(888\) 30.7683 1.03252
\(889\) −3.96802 −0.133083
\(890\) −33.7300 −1.13063
\(891\) −4.75294 −0.159230
\(892\) −32.8117 −1.09862
\(893\) 52.4099 1.75383
\(894\) 9.60285 0.321167
\(895\) 37.7415 1.26156
\(896\) −64.8057 −2.16501
\(897\) 22.3522 0.746317
\(898\) −16.3635 −0.546057
\(899\) 38.5852 1.28689
\(900\) 6.89839 0.229946
\(901\) −10.1934 −0.339592
\(902\) 43.3336 1.44285
\(903\) 9.80643 0.326338
\(904\) −40.6011 −1.35037
\(905\) −25.6691 −0.853270
\(906\) −9.45742 −0.314202
\(907\) 51.1793 1.69938 0.849691 0.527281i \(-0.176789\pi\)
0.849691 + 0.527281i \(0.176789\pi\)
\(908\) 52.5564 1.74414
\(909\) −1.63157 −0.0541157
\(910\) −62.2362 −2.06311
\(911\) 8.16327 0.270461 0.135231 0.990814i \(-0.456822\pi\)
0.135231 + 0.990814i \(0.456822\pi\)
\(912\) −1.10938 −0.0367354
\(913\) −71.1365 −2.35428
\(914\) −53.3137 −1.76346
\(915\) 21.9891 0.726936
\(916\) 35.0706 1.15877
\(917\) −65.3046 −2.15655
\(918\) −2.28064 −0.0752724
\(919\) −39.4561 −1.30154 −0.650768 0.759277i \(-0.725553\pi\)
−0.650768 + 0.759277i \(0.725553\pi\)
\(920\) 57.9236 1.90968
\(921\) 24.2347 0.798560
\(922\) 47.5409 1.56568
\(923\) −34.2934 −1.12878
\(924\) 54.8901 1.80575
\(925\) −24.1991 −0.795663
\(926\) −44.6161 −1.46618
\(927\) 3.45584 0.113505
\(928\) 21.9567 0.720764
\(929\) −2.23502 −0.0733287 −0.0366643 0.999328i \(-0.511673\pi\)
−0.0366643 + 0.999328i \(0.511673\pi\)
\(930\) −62.5122 −2.04986
\(931\) 43.2824 1.41852
\(932\) 87.1864 2.85588
\(933\) 7.00815 0.229437
\(934\) 73.2414 2.39653
\(935\) −12.7134 −0.415774
\(936\) 7.74827 0.253260
\(937\) −2.39393 −0.0782064 −0.0391032 0.999235i \(-0.512450\pi\)
−0.0391032 + 0.999235i \(0.512450\pi\)
\(938\) −13.0365 −0.425657
\(939\) 9.00979 0.294023
\(940\) 62.3557 2.03382
\(941\) 34.1571 1.11349 0.556745 0.830683i \(-0.312050\pi\)
0.556745 + 0.830683i \(0.312050\pi\)
\(942\) −44.0431 −1.43500
\(943\) −31.5965 −1.02892
\(944\) −0.168959 −0.00549916
\(945\) −9.64942 −0.313896
\(946\) −29.4666 −0.958042
\(947\) 3.25604 0.105807 0.0529036 0.998600i \(-0.483152\pi\)
0.0529036 + 0.998600i \(0.483152\pi\)
\(948\) 3.20133 0.103974
\(949\) 32.7522 1.06318
\(950\) −35.3705 −1.14757
\(951\) −7.95241 −0.257875
\(952\) 9.88373 0.320334
\(953\) 47.3449 1.53365 0.766825 0.641856i \(-0.221835\pi\)
0.766825 + 0.641856i \(0.221835\pi\)
\(954\) 23.2476 0.752668
\(955\) −45.0572 −1.45802
\(956\) 35.6353 1.15253
\(957\) −17.8968 −0.578522
\(958\) −65.3051 −2.10991
\(959\) −8.96306 −0.289432
\(960\) −34.7477 −1.12148
\(961\) 74.0063 2.38730
\(962\) −72.4311 −2.33527
\(963\) 4.86976 0.156926
\(964\) −22.3335 −0.719314
\(965\) −32.8867 −1.05866
\(966\) −65.0269 −2.09221
\(967\) −18.8957 −0.607646 −0.303823 0.952729i \(-0.598263\pi\)
−0.303823 + 0.952729i \(0.598263\pi\)
\(968\) −31.7557 −1.02067
\(969\) 7.19726 0.231209
\(970\) −57.3929 −1.84278
\(971\) 59.1280 1.89751 0.948755 0.316014i \(-0.102345\pi\)
0.948755 + 0.316014i \(0.102345\pi\)
\(972\) 3.20133 0.102683
\(973\) −51.3754 −1.64702
\(974\) −25.9503 −0.831501
\(975\) −6.09399 −0.195164
\(976\) −1.26713 −0.0405598
\(977\) −18.3485 −0.587021 −0.293510 0.955956i \(-0.594823\pi\)
−0.293510 + 0.955956i \(0.594823\pi\)
\(978\) 24.4594 0.782127
\(979\) −26.2798 −0.839905
\(980\) 51.4962 1.64498
\(981\) −4.34182 −0.138624
\(982\) 3.37203 0.107606
\(983\) −40.5263 −1.29259 −0.646294 0.763088i \(-0.723682\pi\)
−0.646294 + 0.763088i \(0.723682\pi\)
\(984\) −10.9528 −0.349162
\(985\) 1.96292 0.0625439
\(986\) −8.58756 −0.273484
\(987\) −26.2692 −0.836157
\(988\) −65.1603 −2.07302
\(989\) 21.4855 0.683198
\(990\) 28.9948 0.921516
\(991\) 4.68239 0.148741 0.0743706 0.997231i \(-0.476305\pi\)
0.0743706 + 0.997231i \(0.476305\pi\)
\(992\) 59.7533 1.89717
\(993\) −31.3687 −0.995456
\(994\) 99.7664 3.16440
\(995\) 5.41086 0.171536
\(996\) 47.9138 1.51821
\(997\) 45.3096 1.43497 0.717485 0.696574i \(-0.245293\pi\)
0.717485 + 0.696574i \(0.245293\pi\)
\(998\) −24.3690 −0.771386
\(999\) −11.2301 −0.355304
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 4029.2.a.k.1.4 31
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4029.2.a.k.1.4 31 1.1 even 1 trivial