Properties

Label 6017.2.a.f.1.12
Level 6017
Weight 2
Character 6017.1
Self dual yes
Analytic conductor 48.046
Analytic rank 0
Dimension 121
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6017 = 11 \cdot 547 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6017.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(48.0459868962\)
Analytic rank: \(0\)
Dimension: \(121\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) = 6017.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.37440 q^{2} -0.379878 q^{3} +3.63775 q^{4} -1.52566 q^{5} +0.901981 q^{6} +2.31296 q^{7} -3.88867 q^{8} -2.85569 q^{9} +O(q^{10})\) \(q-2.37440 q^{2} -0.379878 q^{3} +3.63775 q^{4} -1.52566 q^{5} +0.901981 q^{6} +2.31296 q^{7} -3.88867 q^{8} -2.85569 q^{9} +3.62251 q^{10} -1.00000 q^{11} -1.38190 q^{12} +1.64625 q^{13} -5.49189 q^{14} +0.579563 q^{15} +1.95774 q^{16} -7.33107 q^{17} +6.78054 q^{18} +0.596356 q^{19} -5.54996 q^{20} -0.878644 q^{21} +2.37440 q^{22} -4.14341 q^{23} +1.47722 q^{24} -2.67238 q^{25} -3.90884 q^{26} +2.22445 q^{27} +8.41398 q^{28} -1.76317 q^{29} -1.37611 q^{30} -1.69038 q^{31} +3.12890 q^{32} +0.379878 q^{33} +17.4069 q^{34} -3.52878 q^{35} -10.3883 q^{36} +3.15531 q^{37} -1.41598 q^{38} -0.625373 q^{39} +5.93277 q^{40} -11.5466 q^{41} +2.08625 q^{42} -0.926674 q^{43} -3.63775 q^{44} +4.35680 q^{45} +9.83809 q^{46} -7.87778 q^{47} -0.743702 q^{48} -1.65021 q^{49} +6.34528 q^{50} +2.78491 q^{51} +5.98863 q^{52} -2.09800 q^{53} -5.28172 q^{54} +1.52566 q^{55} -8.99435 q^{56} -0.226543 q^{57} +4.18645 q^{58} -6.92361 q^{59} +2.10831 q^{60} +7.40456 q^{61} +4.01364 q^{62} -6.60511 q^{63} -11.3447 q^{64} -2.51160 q^{65} -0.901981 q^{66} -5.55057 q^{67} -26.6686 q^{68} +1.57399 q^{69} +8.37872 q^{70} +14.5635 q^{71} +11.1048 q^{72} +2.39854 q^{73} -7.49195 q^{74} +1.01518 q^{75} +2.16939 q^{76} -2.31296 q^{77} +1.48488 q^{78} +3.21438 q^{79} -2.98683 q^{80} +7.72206 q^{81} +27.4162 q^{82} +6.04068 q^{83} -3.19629 q^{84} +11.1847 q^{85} +2.20029 q^{86} +0.669789 q^{87} +3.88867 q^{88} +11.7278 q^{89} -10.3448 q^{90} +3.80770 q^{91} -15.0727 q^{92} +0.642140 q^{93} +18.7050 q^{94} -0.909833 q^{95} -1.18860 q^{96} +0.507957 q^{97} +3.91825 q^{98} +2.85569 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 121q + 2q^{2} + 18q^{3} + 138q^{4} + 13q^{5} + 10q^{6} + 56q^{7} + 12q^{8} + 143q^{9} + O(q^{10}) \) \( 121q + 2q^{2} + 18q^{3} + 138q^{4} + 13q^{5} + 10q^{6} + 56q^{7} + 12q^{8} + 143q^{9} + 20q^{10} - 121q^{11} + 40q^{12} + 31q^{13} + 7q^{14} + 53q^{15} + 164q^{16} - 23q^{17} + 14q^{18} + 62q^{19} + 53q^{20} + 19q^{21} - 2q^{22} + 34q^{23} + 34q^{24} + 172q^{25} + 34q^{26} + 87q^{27} + 91q^{28} - 30q^{29} + 2q^{30} + 102q^{31} + 31q^{32} - 18q^{33} + 30q^{34} + 20q^{35} + 164q^{36} + 58q^{37} + 35q^{38} + 42q^{39} + 52q^{40} - 12q^{41} + 56q^{42} + 96q^{43} - 138q^{44} + 72q^{45} + 48q^{46} + 136q^{47} + 99q^{48} + 199q^{49} - 7q^{50} + 22q^{51} + 81q^{52} + 24q^{53} + 37q^{54} - 13q^{55} + 28q^{56} + 25q^{57} + 76q^{58} + 58q^{59} + 81q^{60} + 14q^{61} - 2q^{62} + 152q^{63} + 236q^{64} - 29q^{65} - 10q^{66} + 112q^{67} - 61q^{68} + 41q^{69} + 105q^{70} + 56q^{71} + 71q^{72} + 113q^{73} - 23q^{74} + 111q^{75} + 144q^{76} - 56q^{77} + 59q^{78} + 80q^{79} + 100q^{80} + 177q^{81} + 123q^{82} + 6q^{83} + 79q^{84} + 26q^{85} + 14q^{86} + 180q^{87} - 12q^{88} + 26q^{89} + 75q^{90} + 72q^{91} + 58q^{92} + 139q^{93} + 37q^{94} + 39q^{95} + 66q^{96} + 136q^{97} + 7q^{98} - 143q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.37440 −1.67895 −0.839475 0.543398i \(-0.817138\pi\)
−0.839475 + 0.543398i \(0.817138\pi\)
\(3\) −0.379878 −0.219323 −0.109661 0.993969i \(-0.534977\pi\)
−0.109661 + 0.993969i \(0.534977\pi\)
\(4\) 3.63775 1.81888
\(5\) −1.52566 −0.682294 −0.341147 0.940010i \(-0.610815\pi\)
−0.341147 + 0.940010i \(0.610815\pi\)
\(6\) 0.901981 0.368232
\(7\) 2.31296 0.874217 0.437109 0.899409i \(-0.356003\pi\)
0.437109 + 0.899409i \(0.356003\pi\)
\(8\) −3.88867 −1.37485
\(9\) −2.85569 −0.951897
\(10\) 3.62251 1.14554
\(11\) −1.00000 −0.301511
\(12\) −1.38190 −0.398921
\(13\) 1.64625 0.456586 0.228293 0.973592i \(-0.426686\pi\)
0.228293 + 0.973592i \(0.426686\pi\)
\(14\) −5.49189 −1.46777
\(15\) 0.579563 0.149643
\(16\) 1.95774 0.489434
\(17\) −7.33107 −1.77805 −0.889023 0.457863i \(-0.848615\pi\)
−0.889023 + 0.457863i \(0.848615\pi\)
\(18\) 6.78054 1.59819
\(19\) 0.596356 0.136813 0.0684067 0.997658i \(-0.478208\pi\)
0.0684067 + 0.997658i \(0.478208\pi\)
\(20\) −5.54996 −1.24101
\(21\) −0.878644 −0.191736
\(22\) 2.37440 0.506223
\(23\) −4.14341 −0.863960 −0.431980 0.901883i \(-0.642185\pi\)
−0.431980 + 0.901883i \(0.642185\pi\)
\(24\) 1.47722 0.301537
\(25\) −2.67238 −0.534475
\(26\) −3.90884 −0.766586
\(27\) 2.22445 0.428096
\(28\) 8.41398 1.59009
\(29\) −1.76317 −0.327412 −0.163706 0.986509i \(-0.552345\pi\)
−0.163706 + 0.986509i \(0.552345\pi\)
\(30\) −1.37611 −0.251243
\(31\) −1.69038 −0.303602 −0.151801 0.988411i \(-0.548507\pi\)
−0.151801 + 0.988411i \(0.548507\pi\)
\(32\) 3.12890 0.553117
\(33\) 0.379878 0.0661283
\(34\) 17.4069 2.98525
\(35\) −3.52878 −0.596473
\(36\) −10.3883 −1.73138
\(37\) 3.15531 0.518730 0.259365 0.965779i \(-0.416487\pi\)
0.259365 + 0.965779i \(0.416487\pi\)
\(38\) −1.41598 −0.229703
\(39\) −0.625373 −0.100140
\(40\) 5.93277 0.938054
\(41\) −11.5466 −1.80328 −0.901639 0.432490i \(-0.857635\pi\)
−0.901639 + 0.432490i \(0.857635\pi\)
\(42\) 2.08625 0.321915
\(43\) −0.926674 −0.141316 −0.0706582 0.997501i \(-0.522510\pi\)
−0.0706582 + 0.997501i \(0.522510\pi\)
\(44\) −3.63775 −0.548412
\(45\) 4.35680 0.649474
\(46\) 9.83809 1.45055
\(47\) −7.87778 −1.14909 −0.574546 0.818472i \(-0.694822\pi\)
−0.574546 + 0.818472i \(0.694822\pi\)
\(48\) −0.743702 −0.107344
\(49\) −1.65021 −0.235744
\(50\) 6.34528 0.897358
\(51\) 2.78491 0.389966
\(52\) 5.98863 0.830474
\(53\) −2.09800 −0.288183 −0.144091 0.989564i \(-0.546026\pi\)
−0.144091 + 0.989564i \(0.546026\pi\)
\(54\) −5.28172 −0.718752
\(55\) 1.52566 0.205719
\(56\) −8.99435 −1.20192
\(57\) −0.226543 −0.0300063
\(58\) 4.18645 0.549708
\(59\) −6.92361 −0.901377 −0.450689 0.892681i \(-0.648821\pi\)
−0.450689 + 0.892681i \(0.648821\pi\)
\(60\) 2.10831 0.272181
\(61\) 7.40456 0.948057 0.474028 0.880510i \(-0.342799\pi\)
0.474028 + 0.880510i \(0.342799\pi\)
\(62\) 4.01364 0.509732
\(63\) −6.60511 −0.832165
\(64\) −11.3447 −1.41809
\(65\) −2.51160 −0.311526
\(66\) −0.901981 −0.111026
\(67\) −5.55057 −0.678110 −0.339055 0.940767i \(-0.610107\pi\)
−0.339055 + 0.940767i \(0.610107\pi\)
\(68\) −26.6686 −3.23404
\(69\) 1.57399 0.189486
\(70\) 8.37872 1.00145
\(71\) 14.5635 1.72837 0.864183 0.503177i \(-0.167836\pi\)
0.864183 + 0.503177i \(0.167836\pi\)
\(72\) 11.1048 1.30872
\(73\) 2.39854 0.280727 0.140364 0.990100i \(-0.455173\pi\)
0.140364 + 0.990100i \(0.455173\pi\)
\(74\) −7.49195 −0.870922
\(75\) 1.01518 0.117223
\(76\) 2.16939 0.248847
\(77\) −2.31296 −0.263586
\(78\) 1.48488 0.168130
\(79\) 3.21438 0.361646 0.180823 0.983516i \(-0.442124\pi\)
0.180823 + 0.983516i \(0.442124\pi\)
\(80\) −2.98683 −0.333938
\(81\) 7.72206 0.858006
\(82\) 27.4162 3.02761
\(83\) 6.04068 0.663051 0.331525 0.943446i \(-0.392437\pi\)
0.331525 + 0.943446i \(0.392437\pi\)
\(84\) −3.19629 −0.348744
\(85\) 11.1847 1.21315
\(86\) 2.20029 0.237263
\(87\) 0.669789 0.0718089
\(88\) 3.88867 0.414534
\(89\) 11.7278 1.24314 0.621572 0.783357i \(-0.286494\pi\)
0.621572 + 0.783357i \(0.286494\pi\)
\(90\) −10.3448 −1.09043
\(91\) 3.80770 0.399156
\(92\) −15.0727 −1.57144
\(93\) 0.642140 0.0665868
\(94\) 18.7050 1.92927
\(95\) −0.909833 −0.0933469
\(96\) −1.18860 −0.121311
\(97\) 0.507957 0.0515753 0.0257876 0.999667i \(-0.491791\pi\)
0.0257876 + 0.999667i \(0.491791\pi\)
\(98\) 3.91825 0.395803
\(99\) 2.85569 0.287008
\(100\) −9.72144 −0.972144
\(101\) 1.80900 0.180002 0.0900011 0.995942i \(-0.471313\pi\)
0.0900011 + 0.995942i \(0.471313\pi\)
\(102\) −6.61249 −0.654734
\(103\) −16.4299 −1.61889 −0.809444 0.587196i \(-0.800232\pi\)
−0.809444 + 0.587196i \(0.800232\pi\)
\(104\) −6.40171 −0.627739
\(105\) 1.34051 0.130820
\(106\) 4.98149 0.483845
\(107\) 0.129922 0.0125600 0.00628000 0.999980i \(-0.498001\pi\)
0.00628000 + 0.999980i \(0.498001\pi\)
\(108\) 8.09200 0.778653
\(109\) −7.00572 −0.671027 −0.335513 0.942035i \(-0.608910\pi\)
−0.335513 + 0.942035i \(0.608910\pi\)
\(110\) −3.62251 −0.345393
\(111\) −1.19863 −0.113769
\(112\) 4.52817 0.427872
\(113\) −11.3320 −1.06603 −0.533014 0.846107i \(-0.678941\pi\)
−0.533014 + 0.846107i \(0.678941\pi\)
\(114\) 0.537902 0.0503791
\(115\) 6.32141 0.589475
\(116\) −6.41396 −0.595521
\(117\) −4.70117 −0.434623
\(118\) 16.4394 1.51337
\(119\) −16.9565 −1.55440
\(120\) −2.25373 −0.205737
\(121\) 1.00000 0.0909091
\(122\) −17.5814 −1.59174
\(123\) 4.38631 0.395500
\(124\) −6.14919 −0.552214
\(125\) 11.7054 1.04696
\(126\) 15.6831 1.39716
\(127\) 14.8251 1.31551 0.657756 0.753231i \(-0.271506\pi\)
0.657756 + 0.753231i \(0.271506\pi\)
\(128\) 20.6790 1.82779
\(129\) 0.352023 0.0309939
\(130\) 5.96354 0.523037
\(131\) 3.08854 0.269847 0.134923 0.990856i \(-0.456921\pi\)
0.134923 + 0.990856i \(0.456921\pi\)
\(132\) 1.38190 0.120279
\(133\) 1.37935 0.119605
\(134\) 13.1792 1.13851
\(135\) −3.39374 −0.292087
\(136\) 28.5081 2.44455
\(137\) −20.1994 −1.72575 −0.862876 0.505416i \(-0.831339\pi\)
−0.862876 + 0.505416i \(0.831339\pi\)
\(138\) −3.73728 −0.318138
\(139\) 11.8822 1.00784 0.503918 0.863751i \(-0.331891\pi\)
0.503918 + 0.863751i \(0.331891\pi\)
\(140\) −12.8368 −1.08491
\(141\) 2.99260 0.252022
\(142\) −34.5794 −2.90184
\(143\) −1.64625 −0.137666
\(144\) −5.59070 −0.465891
\(145\) 2.68998 0.223391
\(146\) −5.69507 −0.471327
\(147\) 0.626878 0.0517041
\(148\) 11.4782 0.943505
\(149\) 2.83933 0.232607 0.116304 0.993214i \(-0.462895\pi\)
0.116304 + 0.993214i \(0.462895\pi\)
\(150\) −2.41043 −0.196811
\(151\) −17.8172 −1.44994 −0.724970 0.688780i \(-0.758146\pi\)
−0.724970 + 0.688780i \(0.758146\pi\)
\(152\) −2.31903 −0.188098
\(153\) 20.9353 1.69252
\(154\) 5.49189 0.442549
\(155\) 2.57894 0.207146
\(156\) −2.27495 −0.182142
\(157\) 11.7988 0.941643 0.470821 0.882229i \(-0.343958\pi\)
0.470821 + 0.882229i \(0.343958\pi\)
\(158\) −7.63222 −0.607187
\(159\) 0.796986 0.0632051
\(160\) −4.77362 −0.377388
\(161\) −9.58354 −0.755289
\(162\) −18.3352 −1.44055
\(163\) 3.20119 0.250737 0.125368 0.992110i \(-0.459989\pi\)
0.125368 + 0.992110i \(0.459989\pi\)
\(164\) −42.0037 −3.27994
\(165\) −0.579563 −0.0451189
\(166\) −14.3430 −1.11323
\(167\) −9.12246 −0.705917 −0.352959 0.935639i \(-0.614824\pi\)
−0.352959 + 0.935639i \(0.614824\pi\)
\(168\) 3.41676 0.263609
\(169\) −10.2899 −0.791529
\(170\) −26.5569 −2.03682
\(171\) −1.70301 −0.130232
\(172\) −3.37101 −0.257037
\(173\) 21.7426 1.65306 0.826530 0.562893i \(-0.190312\pi\)
0.826530 + 0.562893i \(0.190312\pi\)
\(174\) −1.59034 −0.120564
\(175\) −6.18110 −0.467247
\(176\) −1.95774 −0.147570
\(177\) 2.63013 0.197693
\(178\) −27.8464 −2.08718
\(179\) 17.8020 1.33058 0.665291 0.746584i \(-0.268307\pi\)
0.665291 + 0.746584i \(0.268307\pi\)
\(180\) 15.8490 1.18131
\(181\) −7.42484 −0.551884 −0.275942 0.961174i \(-0.588990\pi\)
−0.275942 + 0.961174i \(0.588990\pi\)
\(182\) −9.04099 −0.670163
\(183\) −2.81283 −0.207931
\(184\) 16.1123 1.18782
\(185\) −4.81392 −0.353926
\(186\) −1.52469 −0.111796
\(187\) 7.33107 0.536101
\(188\) −28.6574 −2.09006
\(189\) 5.14507 0.374249
\(190\) 2.16030 0.156725
\(191\) −2.49913 −0.180831 −0.0904153 0.995904i \(-0.528819\pi\)
−0.0904153 + 0.995904i \(0.528819\pi\)
\(192\) 4.30961 0.311020
\(193\) 0.317512 0.0228550 0.0114275 0.999935i \(-0.496362\pi\)
0.0114275 + 0.999935i \(0.496362\pi\)
\(194\) −1.20609 −0.0865923
\(195\) 0.954103 0.0683248
\(196\) −6.00305 −0.428789
\(197\) 26.4283 1.88294 0.941470 0.337096i \(-0.109445\pi\)
0.941470 + 0.337096i \(0.109445\pi\)
\(198\) −6.78054 −0.481872
\(199\) −9.18108 −0.650829 −0.325415 0.945571i \(-0.605504\pi\)
−0.325415 + 0.945571i \(0.605504\pi\)
\(200\) 10.3920 0.734825
\(201\) 2.10854 0.148725
\(202\) −4.29528 −0.302215
\(203\) −4.07814 −0.286229
\(204\) 10.1308 0.709300
\(205\) 17.6161 1.23036
\(206\) 39.0111 2.71804
\(207\) 11.8323 0.822401
\(208\) 3.22292 0.223469
\(209\) −0.596356 −0.0412508
\(210\) −3.18290 −0.219641
\(211\) 10.2506 0.705677 0.352839 0.935684i \(-0.385216\pi\)
0.352839 + 0.935684i \(0.385216\pi\)
\(212\) −7.63202 −0.524169
\(213\) −5.53235 −0.379070
\(214\) −0.308485 −0.0210876
\(215\) 1.41378 0.0964193
\(216\) −8.65016 −0.588569
\(217\) −3.90979 −0.265414
\(218\) 16.6344 1.12662
\(219\) −0.911152 −0.0615699
\(220\) 5.54996 0.374178
\(221\) −12.0687 −0.811831
\(222\) 2.84603 0.191013
\(223\) −1.50988 −0.101109 −0.0505545 0.998721i \(-0.516099\pi\)
−0.0505545 + 0.998721i \(0.516099\pi\)
\(224\) 7.23702 0.483544
\(225\) 7.63148 0.508766
\(226\) 26.9067 1.78981
\(227\) 14.5784 0.967600 0.483800 0.875178i \(-0.339256\pi\)
0.483800 + 0.875178i \(0.339256\pi\)
\(228\) −0.824106 −0.0545777
\(229\) −6.95382 −0.459521 −0.229761 0.973247i \(-0.573794\pi\)
−0.229761 + 0.973247i \(0.573794\pi\)
\(230\) −15.0095 −0.989699
\(231\) 0.878644 0.0578105
\(232\) 6.85637 0.450143
\(233\) −11.6686 −0.764437 −0.382219 0.924072i \(-0.624840\pi\)
−0.382219 + 0.924072i \(0.624840\pi\)
\(234\) 11.1624 0.729711
\(235\) 12.0188 0.784019
\(236\) −25.1864 −1.63949
\(237\) −1.22107 −0.0793173
\(238\) 40.2614 2.60976
\(239\) −0.604201 −0.0390825 −0.0195413 0.999809i \(-0.506221\pi\)
−0.0195413 + 0.999809i \(0.506221\pi\)
\(240\) 1.13463 0.0732403
\(241\) −1.52378 −0.0981555 −0.0490777 0.998795i \(-0.515628\pi\)
−0.0490777 + 0.998795i \(0.515628\pi\)
\(242\) −2.37440 −0.152632
\(243\) −9.60679 −0.616276
\(244\) 26.9360 1.72440
\(245\) 2.51765 0.160847
\(246\) −10.4148 −0.664025
\(247\) 0.981748 0.0624671
\(248\) 6.57334 0.417408
\(249\) −2.29472 −0.145422
\(250\) −27.7932 −1.75780
\(251\) −13.3257 −0.841112 −0.420556 0.907267i \(-0.638165\pi\)
−0.420556 + 0.907267i \(0.638165\pi\)
\(252\) −24.0277 −1.51361
\(253\) 4.14341 0.260494
\(254\) −35.2006 −2.20868
\(255\) −4.24882 −0.266071
\(256\) −26.4108 −1.65067
\(257\) 30.6765 1.91355 0.956775 0.290831i \(-0.0939316\pi\)
0.956775 + 0.290831i \(0.0939316\pi\)
\(258\) −0.835842 −0.0520373
\(259\) 7.29811 0.453483
\(260\) −9.13659 −0.566627
\(261\) 5.03506 0.311662
\(262\) −7.33341 −0.453059
\(263\) −32.1757 −1.98404 −0.992019 0.126090i \(-0.959757\pi\)
−0.992019 + 0.126090i \(0.959757\pi\)
\(264\) −1.47722 −0.0909167
\(265\) 3.20083 0.196625
\(266\) −3.27512 −0.200810
\(267\) −4.45514 −0.272650
\(268\) −20.1916 −1.23340
\(269\) 4.26628 0.260120 0.130060 0.991506i \(-0.458483\pi\)
0.130060 + 0.991506i \(0.458483\pi\)
\(270\) 8.05809 0.490400
\(271\) −7.00480 −0.425511 −0.212756 0.977105i \(-0.568244\pi\)
−0.212756 + 0.977105i \(0.568244\pi\)
\(272\) −14.3523 −0.870237
\(273\) −1.44646 −0.0875440
\(274\) 47.9614 2.89745
\(275\) 2.67238 0.161150
\(276\) 5.72579 0.344652
\(277\) −32.0766 −1.92729 −0.963647 0.267179i \(-0.913908\pi\)
−0.963647 + 0.267179i \(0.913908\pi\)
\(278\) −28.2131 −1.69211
\(279\) 4.82721 0.288998
\(280\) 13.7223 0.820063
\(281\) −12.4777 −0.744358 −0.372179 0.928161i \(-0.621389\pi\)
−0.372179 + 0.928161i \(0.621389\pi\)
\(282\) −7.10561 −0.423133
\(283\) −17.9083 −1.06454 −0.532270 0.846575i \(-0.678661\pi\)
−0.532270 + 0.846575i \(0.678661\pi\)
\(284\) 52.9783 3.14368
\(285\) 0.345626 0.0204731
\(286\) 3.90884 0.231134
\(287\) −26.7069 −1.57646
\(288\) −8.93517 −0.526510
\(289\) 36.7446 2.16145
\(290\) −6.38708 −0.375062
\(291\) −0.192962 −0.0113116
\(292\) 8.72528 0.510608
\(293\) −16.2794 −0.951056 −0.475528 0.879701i \(-0.657743\pi\)
−0.475528 + 0.879701i \(0.657743\pi\)
\(294\) −1.48846 −0.0868086
\(295\) 10.5630 0.615004
\(296\) −12.2700 −0.713177
\(297\) −2.22445 −0.129076
\(298\) −6.74170 −0.390536
\(299\) −6.82106 −0.394472
\(300\) 3.69296 0.213213
\(301\) −2.14336 −0.123541
\(302\) 42.3050 2.43438
\(303\) −0.687200 −0.0394786
\(304\) 1.16751 0.0669612
\(305\) −11.2968 −0.646853
\(306\) −49.7086 −2.84165
\(307\) −19.3620 −1.10505 −0.552524 0.833497i \(-0.686335\pi\)
−0.552524 + 0.833497i \(0.686335\pi\)
\(308\) −8.41398 −0.479431
\(309\) 6.24137 0.355059
\(310\) −6.12343 −0.347787
\(311\) −32.2489 −1.82867 −0.914335 0.404959i \(-0.867286\pi\)
−0.914335 + 0.404959i \(0.867286\pi\)
\(312\) 2.43187 0.137678
\(313\) 27.9487 1.57975 0.789877 0.613266i \(-0.210144\pi\)
0.789877 + 0.613266i \(0.210144\pi\)
\(314\) −28.0149 −1.58097
\(315\) 10.0771 0.567781
\(316\) 11.6931 0.657790
\(317\) 15.0173 0.843458 0.421729 0.906722i \(-0.361423\pi\)
0.421729 + 0.906722i \(0.361423\pi\)
\(318\) −1.89236 −0.106118
\(319\) 1.76317 0.0987183
\(320\) 17.3081 0.967554
\(321\) −0.0493544 −0.00275469
\(322\) 22.7551 1.26809
\(323\) −4.37193 −0.243260
\(324\) 28.0909 1.56061
\(325\) −4.39939 −0.244034
\(326\) −7.60089 −0.420975
\(327\) 2.66132 0.147171
\(328\) 44.9010 2.47924
\(329\) −18.2210 −1.00456
\(330\) 1.37611 0.0757525
\(331\) 18.8230 1.03461 0.517303 0.855802i \(-0.326936\pi\)
0.517303 + 0.855802i \(0.326936\pi\)
\(332\) 21.9745 1.20601
\(333\) −9.01060 −0.493778
\(334\) 21.6603 1.18520
\(335\) 8.46825 0.462670
\(336\) −1.72015 −0.0938421
\(337\) 24.9740 1.36042 0.680211 0.733017i \(-0.261888\pi\)
0.680211 + 0.733017i \(0.261888\pi\)
\(338\) 24.4322 1.32894
\(339\) 4.30479 0.233804
\(340\) 40.6871 2.20657
\(341\) 1.69038 0.0915394
\(342\) 4.04362 0.218654
\(343\) −20.0076 −1.08031
\(344\) 3.60353 0.194289
\(345\) −2.40137 −0.129285
\(346\) −51.6255 −2.77541
\(347\) 1.78528 0.0958390 0.0479195 0.998851i \(-0.484741\pi\)
0.0479195 + 0.998851i \(0.484741\pi\)
\(348\) 2.43652 0.130611
\(349\) −28.2923 −1.51445 −0.757226 0.653153i \(-0.773446\pi\)
−0.757226 + 0.653153i \(0.773446\pi\)
\(350\) 14.6764 0.784486
\(351\) 3.66199 0.195463
\(352\) −3.12890 −0.166771
\(353\) 0.673531 0.0358484 0.0179242 0.999839i \(-0.494294\pi\)
0.0179242 + 0.999839i \(0.494294\pi\)
\(354\) −6.24496 −0.331916
\(355\) −22.2188 −1.17925
\(356\) 42.6629 2.26113
\(357\) 6.44140 0.340915
\(358\) −42.2689 −2.23398
\(359\) −21.2194 −1.11992 −0.559958 0.828521i \(-0.689183\pi\)
−0.559958 + 0.828521i \(0.689183\pi\)
\(360\) −16.9422 −0.892931
\(361\) −18.6444 −0.981282
\(362\) 17.6295 0.926586
\(363\) −0.379878 −0.0199384
\(364\) 13.8515 0.726015
\(365\) −3.65934 −0.191539
\(366\) 6.67877 0.349105
\(367\) 11.7727 0.614528 0.307264 0.951624i \(-0.400587\pi\)
0.307264 + 0.951624i \(0.400587\pi\)
\(368\) −8.11170 −0.422852
\(369\) 32.9736 1.71654
\(370\) 11.4301 0.594225
\(371\) −4.85260 −0.251934
\(372\) 2.33595 0.121113
\(373\) 34.7053 1.79697 0.898485 0.439003i \(-0.144668\pi\)
0.898485 + 0.439003i \(0.144668\pi\)
\(374\) −17.4069 −0.900087
\(375\) −4.44663 −0.229623
\(376\) 30.6341 1.57983
\(377\) −2.90260 −0.149492
\(378\) −12.2164 −0.628345
\(379\) 11.8470 0.608542 0.304271 0.952586i \(-0.401587\pi\)
0.304271 + 0.952586i \(0.401587\pi\)
\(380\) −3.30975 −0.169787
\(381\) −5.63172 −0.288522
\(382\) 5.93392 0.303606
\(383\) 2.81172 0.143672 0.0718360 0.997416i \(-0.477114\pi\)
0.0718360 + 0.997416i \(0.477114\pi\)
\(384\) −7.85552 −0.400875
\(385\) 3.52878 0.179843
\(386\) −0.753900 −0.0383725
\(387\) 2.64630 0.134519
\(388\) 1.84782 0.0938090
\(389\) 29.2873 1.48493 0.742464 0.669886i \(-0.233657\pi\)
0.742464 + 0.669886i \(0.233657\pi\)
\(390\) −2.26542 −0.114714
\(391\) 30.3756 1.53616
\(392\) 6.41712 0.324113
\(393\) −1.17327 −0.0591835
\(394\) −62.7513 −3.16136
\(395\) −4.90404 −0.246749
\(396\) 10.3883 0.522032
\(397\) 12.9833 0.651613 0.325806 0.945437i \(-0.394364\pi\)
0.325806 + 0.945437i \(0.394364\pi\)
\(398\) 21.7995 1.09271
\(399\) −0.523984 −0.0262320
\(400\) −5.23181 −0.261591
\(401\) 19.2524 0.961419 0.480709 0.876880i \(-0.340379\pi\)
0.480709 + 0.876880i \(0.340379\pi\)
\(402\) −5.00651 −0.249702
\(403\) −2.78279 −0.138620
\(404\) 6.58069 0.327402
\(405\) −11.7812 −0.585412
\(406\) 9.68311 0.480564
\(407\) −3.15531 −0.156403
\(408\) −10.8296 −0.536146
\(409\) −34.0648 −1.68440 −0.842199 0.539167i \(-0.818739\pi\)
−0.842199 + 0.539167i \(0.818739\pi\)
\(410\) −41.8277 −2.06572
\(411\) 7.67331 0.378497
\(412\) −59.7680 −2.94456
\(413\) −16.0140 −0.787999
\(414\) −28.0945 −1.38077
\(415\) −9.21600 −0.452396
\(416\) 5.15094 0.252545
\(417\) −4.51380 −0.221042
\(418\) 1.41598 0.0692581
\(419\) −26.3897 −1.28922 −0.644610 0.764512i \(-0.722980\pi\)
−0.644610 + 0.764512i \(0.722980\pi\)
\(420\) 4.87644 0.237946
\(421\) −4.56363 −0.222418 −0.111209 0.993797i \(-0.535472\pi\)
−0.111209 + 0.993797i \(0.535472\pi\)
\(422\) −24.3389 −1.18480
\(423\) 22.4965 1.09382
\(424\) 8.15844 0.396209
\(425\) 19.5914 0.950321
\(426\) 13.1360 0.636440
\(427\) 17.1265 0.828808
\(428\) 0.472623 0.0228451
\(429\) 0.625373 0.0301933
\(430\) −3.35688 −0.161883
\(431\) −4.27167 −0.205759 −0.102880 0.994694i \(-0.532806\pi\)
−0.102880 + 0.994694i \(0.532806\pi\)
\(432\) 4.35489 0.209525
\(433\) 31.0919 1.49418 0.747090 0.664723i \(-0.231450\pi\)
0.747090 + 0.664723i \(0.231450\pi\)
\(434\) 9.28339 0.445617
\(435\) −1.02187 −0.0489947
\(436\) −25.4851 −1.22051
\(437\) −2.47094 −0.118201
\(438\) 2.16343 0.103373
\(439\) 32.6791 1.55969 0.779844 0.625974i \(-0.215298\pi\)
0.779844 + 0.625974i \(0.215298\pi\)
\(440\) −5.93277 −0.282834
\(441\) 4.71249 0.224404
\(442\) 28.6560 1.36302
\(443\) 18.8986 0.897897 0.448949 0.893558i \(-0.351799\pi\)
0.448949 + 0.893558i \(0.351799\pi\)
\(444\) −4.36033 −0.206932
\(445\) −17.8926 −0.848190
\(446\) 3.58505 0.169757
\(447\) −1.07860 −0.0510161
\(448\) −26.2399 −1.23972
\(449\) −7.56865 −0.357187 −0.178593 0.983923i \(-0.557155\pi\)
−0.178593 + 0.983923i \(0.557155\pi\)
\(450\) −18.1202 −0.854192
\(451\) 11.5466 0.543709
\(452\) −41.2231 −1.93897
\(453\) 6.76835 0.318005
\(454\) −34.6148 −1.62455
\(455\) −5.80924 −0.272341
\(456\) 0.880950 0.0412543
\(457\) 11.6773 0.546242 0.273121 0.961980i \(-0.411944\pi\)
0.273121 + 0.961980i \(0.411944\pi\)
\(458\) 16.5111 0.771514
\(459\) −16.3076 −0.761174
\(460\) 22.9957 1.07218
\(461\) −4.24332 −0.197631 −0.0988157 0.995106i \(-0.531505\pi\)
−0.0988157 + 0.995106i \(0.531505\pi\)
\(462\) −2.08625 −0.0970610
\(463\) 14.9966 0.696949 0.348474 0.937318i \(-0.386700\pi\)
0.348474 + 0.937318i \(0.386700\pi\)
\(464\) −3.45182 −0.160247
\(465\) −0.979684 −0.0454318
\(466\) 27.7059 1.28345
\(467\) 34.3602 1.59000 0.795001 0.606608i \(-0.207470\pi\)
0.795001 + 0.606608i \(0.207470\pi\)
\(468\) −17.1017 −0.790526
\(469\) −12.8383 −0.592815
\(470\) −28.5373 −1.31633
\(471\) −4.48209 −0.206524
\(472\) 26.9236 1.23926
\(473\) 0.926674 0.0426085
\(474\) 2.89931 0.133170
\(475\) −1.59369 −0.0731234
\(476\) −61.6835 −2.82726
\(477\) 5.99125 0.274321
\(478\) 1.43461 0.0656176
\(479\) 24.6064 1.12429 0.562147 0.827037i \(-0.309975\pi\)
0.562147 + 0.827037i \(0.309975\pi\)
\(480\) 1.81340 0.0827698
\(481\) 5.19441 0.236845
\(482\) 3.61806 0.164798
\(483\) 3.64058 0.165652
\(484\) 3.63775 0.165352
\(485\) −0.774968 −0.0351895
\(486\) 22.8103 1.03470
\(487\) 0.127499 0.00577752 0.00288876 0.999996i \(-0.499080\pi\)
0.00288876 + 0.999996i \(0.499080\pi\)
\(488\) −28.7939 −1.30344
\(489\) −1.21606 −0.0549923
\(490\) −5.97789 −0.270054
\(491\) −36.3290 −1.63951 −0.819753 0.572717i \(-0.805889\pi\)
−0.819753 + 0.572717i \(0.805889\pi\)
\(492\) 15.9563 0.719365
\(493\) 12.9259 0.582153
\(494\) −2.33106 −0.104879
\(495\) −4.35680 −0.195824
\(496\) −3.30933 −0.148593
\(497\) 33.6848 1.51097
\(498\) 5.44858 0.244157
\(499\) −16.1578 −0.723324 −0.361662 0.932309i \(-0.617791\pi\)
−0.361662 + 0.932309i \(0.617791\pi\)
\(500\) 42.5814 1.90430
\(501\) 3.46542 0.154824
\(502\) 31.6405 1.41219
\(503\) −23.5017 −1.04789 −0.523943 0.851753i \(-0.675540\pi\)
−0.523943 + 0.851753i \(0.675540\pi\)
\(504\) 25.6851 1.14410
\(505\) −2.75991 −0.122814
\(506\) −9.83809 −0.437356
\(507\) 3.90890 0.173600
\(508\) 53.9299 2.39275
\(509\) 39.0973 1.73296 0.866478 0.499216i \(-0.166378\pi\)
0.866478 + 0.499216i \(0.166378\pi\)
\(510\) 10.0884 0.446721
\(511\) 5.54772 0.245417
\(512\) 21.3516 0.943615
\(513\) 1.32656 0.0585692
\(514\) −72.8382 −3.21276
\(515\) 25.0664 1.10456
\(516\) 1.28057 0.0563741
\(517\) 7.87778 0.346465
\(518\) −17.3286 −0.761375
\(519\) −8.25954 −0.362554
\(520\) 9.76680 0.428302
\(521\) 28.1116 1.23159 0.615796 0.787906i \(-0.288835\pi\)
0.615796 + 0.787906i \(0.288835\pi\)
\(522\) −11.9552 −0.523266
\(523\) −32.9979 −1.44290 −0.721448 0.692468i \(-0.756523\pi\)
−0.721448 + 0.692468i \(0.756523\pi\)
\(524\) 11.2353 0.490818
\(525\) 2.34807 0.102478
\(526\) 76.3978 3.33110
\(527\) 12.3923 0.539818
\(528\) 0.743702 0.0323655
\(529\) −5.83218 −0.253573
\(530\) −7.60003 −0.330124
\(531\) 19.7717 0.858019
\(532\) 5.01773 0.217546
\(533\) −19.0085 −0.823352
\(534\) 10.5783 0.457766
\(535\) −0.198216 −0.00856961
\(536\) 21.5843 0.932301
\(537\) −6.76259 −0.291827
\(538\) −10.1298 −0.436728
\(539\) 1.65021 0.0710795
\(540\) −12.3456 −0.531270
\(541\) −5.22353 −0.224577 −0.112289 0.993676i \(-0.535818\pi\)
−0.112289 + 0.993676i \(0.535818\pi\)
\(542\) 16.6322 0.714413
\(543\) 2.82053 0.121041
\(544\) −22.9382 −0.983466
\(545\) 10.6883 0.457837
\(546\) 3.43448 0.146982
\(547\) 1.00000 0.0427569
\(548\) −73.4804 −3.13893
\(549\) −21.1451 −0.902453
\(550\) −6.34528 −0.270563
\(551\) −1.05147 −0.0447943
\(552\) −6.12073 −0.260516
\(553\) 7.43475 0.316158
\(554\) 76.1624 3.23583
\(555\) 1.82870 0.0776241
\(556\) 43.2246 1.83313
\(557\) −28.2444 −1.19675 −0.598377 0.801215i \(-0.704187\pi\)
−0.598377 + 0.801215i \(0.704187\pi\)
\(558\) −11.4617 −0.485213
\(559\) −1.52553 −0.0645231
\(560\) −6.90843 −0.291934
\(561\) −2.78491 −0.117579
\(562\) 29.6270 1.24974
\(563\) 32.5021 1.36980 0.684900 0.728637i \(-0.259846\pi\)
0.684900 + 0.728637i \(0.259846\pi\)
\(564\) 10.8863 0.458397
\(565\) 17.2888 0.727344
\(566\) 42.5214 1.78731
\(567\) 17.8608 0.750084
\(568\) −56.6326 −2.37625
\(569\) −4.88569 −0.204819 −0.102409 0.994742i \(-0.532655\pi\)
−0.102409 + 0.994742i \(0.532655\pi\)
\(570\) −0.820653 −0.0343734
\(571\) 10.1483 0.424692 0.212346 0.977195i \(-0.431890\pi\)
0.212346 + 0.977195i \(0.431890\pi\)
\(572\) −5.98863 −0.250397
\(573\) 0.949364 0.0396603
\(574\) 63.4126 2.64679
\(575\) 11.0727 0.461765
\(576\) 32.3970 1.34988
\(577\) 18.4933 0.769888 0.384944 0.922940i \(-0.374221\pi\)
0.384944 + 0.922940i \(0.374221\pi\)
\(578\) −87.2461 −3.62896
\(579\) −0.120616 −0.00501263
\(580\) 9.78549 0.406321
\(581\) 13.9719 0.579651
\(582\) 0.458168 0.0189917
\(583\) 2.09800 0.0868904
\(584\) −9.32712 −0.385959
\(585\) 7.17237 0.296541
\(586\) 38.6538 1.59678
\(587\) −33.4541 −1.38080 −0.690400 0.723428i \(-0.742565\pi\)
−0.690400 + 0.723428i \(0.742565\pi\)
\(588\) 2.28043 0.0940433
\(589\) −1.00807 −0.0415368
\(590\) −25.0808 −1.03256
\(591\) −10.0395 −0.412972
\(592\) 6.17727 0.253884
\(593\) 20.0698 0.824168 0.412084 0.911146i \(-0.364801\pi\)
0.412084 + 0.911146i \(0.364801\pi\)
\(594\) 5.28172 0.216712
\(595\) 25.8697 1.06056
\(596\) 10.3288 0.423084
\(597\) 3.48769 0.142742
\(598\) 16.1959 0.662300
\(599\) −2.26682 −0.0926197 −0.0463098 0.998927i \(-0.514746\pi\)
−0.0463098 + 0.998927i \(0.514746\pi\)
\(600\) −3.94769 −0.161164
\(601\) 21.4662 0.875626 0.437813 0.899066i \(-0.355753\pi\)
0.437813 + 0.899066i \(0.355753\pi\)
\(602\) 5.08919 0.207420
\(603\) 15.8507 0.645491
\(604\) −64.8144 −2.63726
\(605\) −1.52566 −0.0620267
\(606\) 1.63168 0.0662826
\(607\) −10.0336 −0.407252 −0.203626 0.979049i \(-0.565273\pi\)
−0.203626 + 0.979049i \(0.565273\pi\)
\(608\) 1.86594 0.0756738
\(609\) 1.54920 0.0627766
\(610\) 26.8231 1.08604
\(611\) −12.9688 −0.524660
\(612\) 76.1574 3.07848
\(613\) −5.97121 −0.241175 −0.120587 0.992703i \(-0.538478\pi\)
−0.120587 + 0.992703i \(0.538478\pi\)
\(614\) 45.9730 1.85532
\(615\) −6.69199 −0.269847
\(616\) 8.99435 0.362393
\(617\) −11.7149 −0.471622 −0.235811 0.971799i \(-0.575775\pi\)
−0.235811 + 0.971799i \(0.575775\pi\)
\(618\) −14.8195 −0.596127
\(619\) 33.8837 1.36190 0.680950 0.732330i \(-0.261567\pi\)
0.680950 + 0.732330i \(0.261567\pi\)
\(620\) 9.38155 0.376772
\(621\) −9.21680 −0.369858
\(622\) 76.5717 3.07025
\(623\) 27.1260 1.08678
\(624\) −1.22432 −0.0490119
\(625\) −4.49653 −0.179861
\(626\) −66.3612 −2.65233
\(627\) 0.226543 0.00904724
\(628\) 42.9209 1.71273
\(629\) −23.1318 −0.922325
\(630\) −23.9271 −0.953277
\(631\) 35.4607 1.41167 0.705835 0.708376i \(-0.250572\pi\)
0.705835 + 0.708376i \(0.250572\pi\)
\(632\) −12.4997 −0.497211
\(633\) −3.89396 −0.154771
\(634\) −35.6571 −1.41612
\(635\) −22.6179 −0.897566
\(636\) 2.89924 0.114962
\(637\) −2.71665 −0.107637
\(638\) −4.18645 −0.165743
\(639\) −41.5888 −1.64523
\(640\) −31.5491 −1.24709
\(641\) 5.77380 0.228051 0.114026 0.993478i \(-0.463625\pi\)
0.114026 + 0.993478i \(0.463625\pi\)
\(642\) 0.117187 0.00462500
\(643\) 20.6036 0.812528 0.406264 0.913756i \(-0.366831\pi\)
0.406264 + 0.913756i \(0.366831\pi\)
\(644\) −34.8626 −1.37378
\(645\) −0.537066 −0.0211470
\(646\) 10.3807 0.408422
\(647\) −3.12303 −0.122779 −0.0613895 0.998114i \(-0.519553\pi\)
−0.0613895 + 0.998114i \(0.519553\pi\)
\(648\) −30.0285 −1.17963
\(649\) 6.92361 0.271775
\(650\) 10.4459 0.409721
\(651\) 1.48524 0.0582113
\(652\) 11.6451 0.456059
\(653\) 23.5311 0.920845 0.460422 0.887700i \(-0.347698\pi\)
0.460422 + 0.887700i \(0.347698\pi\)
\(654\) −6.31903 −0.247094
\(655\) −4.71204 −0.184115
\(656\) −22.6052 −0.882586
\(657\) −6.84948 −0.267224
\(658\) 43.2639 1.68660
\(659\) 44.6544 1.73949 0.869744 0.493503i \(-0.164284\pi\)
0.869744 + 0.493503i \(0.164284\pi\)
\(660\) −2.10831 −0.0820658
\(661\) −13.6967 −0.532741 −0.266371 0.963871i \(-0.585825\pi\)
−0.266371 + 0.963871i \(0.585825\pi\)
\(662\) −44.6933 −1.73705
\(663\) 4.58465 0.178053
\(664\) −23.4902 −0.911598
\(665\) −2.10441 −0.0816055
\(666\) 21.3947 0.829028
\(667\) 7.30551 0.282871
\(668\) −33.1853 −1.28398
\(669\) 0.573570 0.0221755
\(670\) −20.1070 −0.776800
\(671\) −7.40456 −0.285850
\(672\) −2.74919 −0.106052
\(673\) 28.3961 1.09459 0.547294 0.836940i \(-0.315658\pi\)
0.547294 + 0.836940i \(0.315658\pi\)
\(674\) −59.2982 −2.28408
\(675\) −5.94457 −0.228807
\(676\) −37.4320 −1.43969
\(677\) 21.7804 0.837088 0.418544 0.908197i \(-0.362541\pi\)
0.418544 + 0.908197i \(0.362541\pi\)
\(678\) −10.2213 −0.392546
\(679\) 1.17489 0.0450880
\(680\) −43.4936 −1.66790
\(681\) −5.53801 −0.212217
\(682\) −4.01364 −0.153690
\(683\) 47.0415 1.79999 0.899997 0.435896i \(-0.143568\pi\)
0.899997 + 0.435896i \(0.143568\pi\)
\(684\) −6.19512 −0.236876
\(685\) 30.8173 1.17747
\(686\) 47.5059 1.81379
\(687\) 2.64160 0.100783
\(688\) −1.81418 −0.0691651
\(689\) −3.45383 −0.131580
\(690\) 5.70179 0.217064
\(691\) −45.6569 −1.73687 −0.868435 0.495804i \(-0.834874\pi\)
−0.868435 + 0.495804i \(0.834874\pi\)
\(692\) 79.0942 3.00671
\(693\) 6.60511 0.250907
\(694\) −4.23897 −0.160909
\(695\) −18.1282 −0.687641
\(696\) −2.60459 −0.0987266
\(697\) 84.6490 3.20631
\(698\) 67.1771 2.54269
\(699\) 4.43266 0.167659
\(700\) −22.4853 −0.849865
\(701\) 1.01791 0.0384460 0.0192230 0.999815i \(-0.493881\pi\)
0.0192230 + 0.999815i \(0.493881\pi\)
\(702\) −8.69501 −0.328172
\(703\) 1.88169 0.0709692
\(704\) 11.3447 0.427570
\(705\) −4.56567 −0.171953
\(706\) −1.59923 −0.0601878
\(707\) 4.18415 0.157361
\(708\) 9.56776 0.359578
\(709\) 37.3897 1.40420 0.702099 0.712079i \(-0.252246\pi\)
0.702099 + 0.712079i \(0.252246\pi\)
\(710\) 52.7563 1.97991
\(711\) −9.17929 −0.344250
\(712\) −45.6056 −1.70914
\(713\) 7.00394 0.262300
\(714\) −15.2944 −0.572380
\(715\) 2.51160 0.0939286
\(716\) 64.7592 2.42016
\(717\) 0.229523 0.00857169
\(718\) 50.3832 1.88028
\(719\) −38.6234 −1.44041 −0.720205 0.693761i \(-0.755952\pi\)
−0.720205 + 0.693761i \(0.755952\pi\)
\(720\) 8.52948 0.317875
\(721\) −38.0018 −1.41526
\(722\) 44.2691 1.64752
\(723\) 0.578852 0.0215277
\(724\) −27.0097 −1.00381
\(725\) 4.71184 0.174993
\(726\) 0.901981 0.0334757
\(727\) 20.6368 0.765378 0.382689 0.923877i \(-0.374998\pi\)
0.382689 + 0.923877i \(0.374998\pi\)
\(728\) −14.8069 −0.548780
\(729\) −19.5168 −0.722843
\(730\) 8.68872 0.321584
\(731\) 6.79351 0.251267
\(732\) −10.2324 −0.378200
\(733\) −29.8075 −1.10097 −0.550483 0.834846i \(-0.685556\pi\)
−0.550483 + 0.834846i \(0.685556\pi\)
\(734\) −27.9529 −1.03176
\(735\) −0.956400 −0.0352774
\(736\) −12.9643 −0.477871
\(737\) 5.55057 0.204458
\(738\) −78.2923 −2.88198
\(739\) −4.96854 −0.182771 −0.0913853 0.995816i \(-0.529129\pi\)
−0.0913853 + 0.995816i \(0.529129\pi\)
\(740\) −17.5118 −0.643748
\(741\) −0.372945 −0.0137005
\(742\) 11.5220 0.422986
\(743\) 8.27933 0.303739 0.151870 0.988401i \(-0.451471\pi\)
0.151870 + 0.988401i \(0.451471\pi\)
\(744\) −2.49707 −0.0915471
\(745\) −4.33184 −0.158706
\(746\) −82.4040 −3.01703
\(747\) −17.2503 −0.631157
\(748\) 26.6686 0.975101
\(749\) 0.300504 0.0109802
\(750\) 10.5581 0.385526
\(751\) 46.2989 1.68947 0.844735 0.535185i \(-0.179758\pi\)
0.844735 + 0.535185i \(0.179758\pi\)
\(752\) −15.4226 −0.562406
\(753\) 5.06215 0.184475
\(754\) 6.89193 0.250989
\(755\) 27.1828 0.989285
\(756\) 18.7165 0.680712
\(757\) −18.3597 −0.667295 −0.333647 0.942698i \(-0.608279\pi\)
−0.333647 + 0.942698i \(0.608279\pi\)
\(758\) −28.1296 −1.02171
\(759\) −1.57399 −0.0571322
\(760\) 3.53804 0.128338
\(761\) 48.2636 1.74955 0.874777 0.484526i \(-0.161008\pi\)
0.874777 + 0.484526i \(0.161008\pi\)
\(762\) 13.3719 0.484414
\(763\) −16.2040 −0.586623
\(764\) −9.09121 −0.328908
\(765\) −31.9400 −1.15479
\(766\) −6.67613 −0.241218
\(767\) −11.3980 −0.411556
\(768\) 10.0329 0.362031
\(769\) −21.0854 −0.760358 −0.380179 0.924913i \(-0.624138\pi\)
−0.380179 + 0.924913i \(0.624138\pi\)
\(770\) −8.37872 −0.301948
\(771\) −11.6533 −0.419685
\(772\) 1.15503 0.0415705
\(773\) 35.3472 1.27135 0.635674 0.771957i \(-0.280722\pi\)
0.635674 + 0.771957i \(0.280722\pi\)
\(774\) −6.28335 −0.225850
\(775\) 4.51734 0.162268
\(776\) −1.97528 −0.0709084
\(777\) −2.77239 −0.0994591
\(778\) −69.5397 −2.49312
\(779\) −6.88589 −0.246712
\(780\) 3.47079 0.124274
\(781\) −14.5635 −0.521122
\(782\) −72.1237 −2.57914
\(783\) −3.92208 −0.140164
\(784\) −3.23068 −0.115381
\(785\) −18.0008 −0.642477
\(786\) 2.78580 0.0993663
\(787\) 31.7552 1.13195 0.565976 0.824422i \(-0.308500\pi\)
0.565976 + 0.824422i \(0.308500\pi\)
\(788\) 96.1397 3.42484
\(789\) 12.2228 0.435145
\(790\) 11.6441 0.414280
\(791\) −26.2105 −0.931940
\(792\) −11.1048 −0.394594
\(793\) 12.1897 0.432870
\(794\) −30.8275 −1.09403
\(795\) −1.21593 −0.0431244
\(796\) −33.3985 −1.18378
\(797\) −18.6362 −0.660129 −0.330064 0.943958i \(-0.607070\pi\)
−0.330064 + 0.943958i \(0.607070\pi\)
\(798\) 1.24415 0.0440423
\(799\) 57.7526 2.04314
\(800\) −8.36160 −0.295627
\(801\) −33.4910 −1.18335
\(802\) −45.7128 −1.61417
\(803\) −2.39854 −0.0846425
\(804\) 7.67035 0.270512
\(805\) 14.6212 0.515329
\(806\) 6.60743 0.232737
\(807\) −1.62067 −0.0570502
\(808\) −7.03461 −0.247477
\(809\) 18.7206 0.658182 0.329091 0.944298i \(-0.393258\pi\)
0.329091 + 0.944298i \(0.393258\pi\)
\(810\) 27.9732 0.982879
\(811\) 33.9505 1.19216 0.596082 0.802923i \(-0.296723\pi\)
0.596082 + 0.802923i \(0.296723\pi\)
\(812\) −14.8352 −0.520615
\(813\) 2.66097 0.0933244
\(814\) 7.49195 0.262593
\(815\) −4.88391 −0.171076
\(816\) 5.45213 0.190863
\(817\) −0.552627 −0.0193340
\(818\) 80.8834 2.82802
\(819\) −10.8736 −0.379955
\(820\) 64.0832 2.23788
\(821\) 0.942862 0.0329061 0.0164530 0.999865i \(-0.494763\pi\)
0.0164530 + 0.999865i \(0.494763\pi\)
\(822\) −18.2195 −0.635477
\(823\) 19.9823 0.696540 0.348270 0.937394i \(-0.386769\pi\)
0.348270 + 0.937394i \(0.386769\pi\)
\(824\) 63.8906 2.22573
\(825\) −1.01518 −0.0353439
\(826\) 38.0237 1.32301
\(827\) 49.3839 1.71725 0.858624 0.512606i \(-0.171320\pi\)
0.858624 + 0.512606i \(0.171320\pi\)
\(828\) 43.0430 1.49585
\(829\) 31.0129 1.07712 0.538561 0.842587i \(-0.318968\pi\)
0.538561 + 0.842587i \(0.318968\pi\)
\(830\) 21.8824 0.759550
\(831\) 12.1852 0.422700
\(832\) −18.6762 −0.647480
\(833\) 12.0978 0.419164
\(834\) 10.7175 0.371118
\(835\) 13.9177 0.481643
\(836\) −2.16939 −0.0750301
\(837\) −3.76017 −0.129971
\(838\) 62.6595 2.16454
\(839\) 44.5836 1.53920 0.769598 0.638529i \(-0.220457\pi\)
0.769598 + 0.638529i \(0.220457\pi\)
\(840\) −5.21279 −0.179858
\(841\) −25.8912 −0.892802
\(842\) 10.8359 0.373428
\(843\) 4.74001 0.163255
\(844\) 37.2890 1.28354
\(845\) 15.6988 0.540055
\(846\) −53.4156 −1.83647
\(847\) 2.31296 0.0794743
\(848\) −4.10734 −0.141047
\(849\) 6.80298 0.233478
\(850\) −46.5177 −1.59554
\(851\) −13.0737 −0.448162
\(852\) −20.1253 −0.689482
\(853\) 19.1985 0.657345 0.328672 0.944444i \(-0.393399\pi\)
0.328672 + 0.944444i \(0.393399\pi\)
\(854\) −40.6650 −1.39153
\(855\) 2.59820 0.0888567
\(856\) −0.505223 −0.0172682
\(857\) −27.0414 −0.923716 −0.461858 0.886954i \(-0.652817\pi\)
−0.461858 + 0.886954i \(0.652817\pi\)
\(858\) −1.48488 −0.0506930
\(859\) −28.9901 −0.989130 −0.494565 0.869141i \(-0.664673\pi\)
−0.494565 + 0.869141i \(0.664673\pi\)
\(860\) 5.14300 0.175375
\(861\) 10.1454 0.345753
\(862\) 10.1426 0.345460
\(863\) −52.5172 −1.78771 −0.893853 0.448361i \(-0.852008\pi\)
−0.893853 + 0.448361i \(0.852008\pi\)
\(864\) 6.96008 0.236787
\(865\) −33.1717 −1.12787
\(866\) −73.8244 −2.50865
\(867\) −13.9585 −0.474054
\(868\) −14.2229 −0.482755
\(869\) −3.21438 −0.109041
\(870\) 2.42631 0.0822598
\(871\) −9.13760 −0.309616
\(872\) 27.2430 0.922563
\(873\) −1.45057 −0.0490944
\(874\) 5.86700 0.198454
\(875\) 27.0741 0.915273
\(876\) −3.31454 −0.111988
\(877\) −17.3204 −0.584867 −0.292434 0.956286i \(-0.594465\pi\)
−0.292434 + 0.956286i \(0.594465\pi\)
\(878\) −77.5931 −2.61864
\(879\) 6.18421 0.208588
\(880\) 2.98683 0.100686
\(881\) −17.9414 −0.604462 −0.302231 0.953235i \(-0.597731\pi\)
−0.302231 + 0.953235i \(0.597731\pi\)
\(882\) −11.1893 −0.376764
\(883\) −7.93763 −0.267123 −0.133561 0.991041i \(-0.542641\pi\)
−0.133561 + 0.991041i \(0.542641\pi\)
\(884\) −43.9031 −1.47662
\(885\) −4.01267 −0.134884
\(886\) −44.8726 −1.50753
\(887\) 45.4386 1.52568 0.762840 0.646587i \(-0.223804\pi\)
0.762840 + 0.646587i \(0.223804\pi\)
\(888\) 4.66109 0.156416
\(889\) 34.2898 1.15004
\(890\) 42.4841 1.42407
\(891\) −7.72206 −0.258699
\(892\) −5.49257 −0.183905
\(893\) −4.69796 −0.157211
\(894\) 2.56102 0.0856535
\(895\) −27.1597 −0.907848
\(896\) 47.8298 1.59788
\(897\) 2.59117 0.0865168
\(898\) 17.9710 0.599699
\(899\) 2.98043 0.0994028
\(900\) 27.7614 0.925382
\(901\) 15.3806 0.512402
\(902\) −27.4162 −0.912860
\(903\) 0.814216 0.0270954
\(904\) 44.0665 1.46563
\(905\) 11.3277 0.376547
\(906\) −16.0707 −0.533915
\(907\) 31.2975 1.03922 0.519609 0.854404i \(-0.326078\pi\)
0.519609 + 0.854404i \(0.326078\pi\)
\(908\) 53.0325 1.75995
\(909\) −5.16595 −0.171344
\(910\) 13.7934 0.457248
\(911\) −51.8452 −1.71771 −0.858855 0.512219i \(-0.828824\pi\)
−0.858855 + 0.512219i \(0.828824\pi\)
\(912\) −0.443511 −0.0146861
\(913\) −6.04068 −0.199917
\(914\) −27.7266 −0.917114
\(915\) 4.29141 0.141870
\(916\) −25.2963 −0.835812
\(917\) 7.14367 0.235905
\(918\) 38.7207 1.27797
\(919\) −22.2196 −0.732958 −0.366479 0.930426i \(-0.619437\pi\)
−0.366479 + 0.930426i \(0.619437\pi\)
\(920\) −24.5819 −0.810441
\(921\) 7.35520 0.242362
\(922\) 10.0753 0.331813
\(923\) 23.9750 0.789148
\(924\) 3.19629 0.105150
\(925\) −8.43217 −0.277248
\(926\) −35.6077 −1.17014
\(927\) 46.9188 1.54102
\(928\) −5.51677 −0.181097
\(929\) −13.1563 −0.431643 −0.215822 0.976433i \(-0.569243\pi\)
−0.215822 + 0.976433i \(0.569243\pi\)
\(930\) 2.32616 0.0762777
\(931\) −0.984111 −0.0322529
\(932\) −42.4476 −1.39042
\(933\) 12.2507 0.401069
\(934\) −81.5847 −2.66953
\(935\) −11.1847 −0.365778
\(936\) 18.2813 0.597543
\(937\) 34.2681 1.11949 0.559744 0.828665i \(-0.310899\pi\)
0.559744 + 0.828665i \(0.310899\pi\)
\(938\) 30.4831 0.995308
\(939\) −10.6171 −0.346476
\(940\) 43.7214 1.42603
\(941\) −34.9287 −1.13864 −0.569321 0.822115i \(-0.692794\pi\)
−0.569321 + 0.822115i \(0.692794\pi\)
\(942\) 10.6423 0.346743
\(943\) 47.8423 1.55796
\(944\) −13.5546 −0.441165
\(945\) −7.84960 −0.255348
\(946\) −2.20029 −0.0715376
\(947\) 18.7070 0.607894 0.303947 0.952689i \(-0.401695\pi\)
0.303947 + 0.952689i \(0.401695\pi\)
\(948\) −4.44197 −0.144268
\(949\) 3.94858 0.128176
\(950\) 3.78404 0.122771
\(951\) −5.70476 −0.184989
\(952\) 65.9382 2.13707
\(953\) 1.52844 0.0495109 0.0247555 0.999694i \(-0.492119\pi\)
0.0247555 + 0.999694i \(0.492119\pi\)
\(954\) −14.2256 −0.460571
\(955\) 3.81281 0.123380
\(956\) −2.19793 −0.0710863
\(957\) −0.669789 −0.0216512
\(958\) −58.4253 −1.88764
\(959\) −46.7204 −1.50868
\(960\) −6.57498 −0.212207
\(961\) −28.1426 −0.907826
\(962\) −12.3336 −0.397651
\(963\) −0.371016 −0.0119558
\(964\) −5.54315 −0.178533
\(965\) −0.484414 −0.0155939
\(966\) −8.64417 −0.278122
\(967\) 39.8422 1.28124 0.640619 0.767859i \(-0.278678\pi\)
0.640619 + 0.767859i \(0.278678\pi\)
\(968\) −3.88867 −0.124987
\(969\) 1.66080 0.0533526
\(970\) 1.84008 0.0590814
\(971\) 7.42297 0.238214 0.119107 0.992881i \(-0.461997\pi\)
0.119107 + 0.992881i \(0.461997\pi\)
\(972\) −34.9471 −1.12093
\(973\) 27.4831 0.881068
\(974\) −0.302732 −0.00970017
\(975\) 1.67123 0.0535222
\(976\) 14.4962 0.464012
\(977\) 11.9392 0.381970 0.190985 0.981593i \(-0.438832\pi\)
0.190985 + 0.981593i \(0.438832\pi\)
\(978\) 2.88741 0.0923293
\(979\) −11.7278 −0.374822
\(980\) 9.15858 0.292560
\(981\) 20.0062 0.638749
\(982\) 86.2595 2.75265
\(983\) −18.7762 −0.598869 −0.299434 0.954117i \(-0.596798\pi\)
−0.299434 + 0.954117i \(0.596798\pi\)
\(984\) −17.0569 −0.543754
\(985\) −40.3205 −1.28472
\(986\) −30.6912 −0.977406
\(987\) 6.92177 0.220322
\(988\) 3.57136 0.113620
\(989\) 3.83959 0.122092
\(990\) 10.3448 0.328778
\(991\) 44.9718 1.42858 0.714289 0.699851i \(-0.246750\pi\)
0.714289 + 0.699851i \(0.246750\pi\)
\(992\) −5.28904 −0.167927
\(993\) −7.15046 −0.226913
\(994\) −79.9809 −2.53684
\(995\) 14.0072 0.444057
\(996\) −8.34764 −0.264505
\(997\) 0.591835 0.0187436 0.00937181 0.999956i \(-0.497017\pi\)
0.00937181 + 0.999956i \(0.497017\pi\)
\(998\) 38.3651 1.21443
\(999\) 7.01883 0.222066
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 6017.2.a.f.1.12 121
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6017.2.a.f.1.12 121 1.1 even 1 trivial