Properties

Label 6017.2.a.f.1.17
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 1.17
Character \(\chi\) = 6017.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.26471 q^{2} +2.40007 q^{3} +3.12892 q^{4} +2.90605 q^{5} -5.43547 q^{6} +2.22739 q^{7} -2.55669 q^{8} +2.76034 q^{9} +O(q^{10})\) \(q-2.26471 q^{2} +2.40007 q^{3} +3.12892 q^{4} +2.90605 q^{5} -5.43547 q^{6} +2.22739 q^{7} -2.55669 q^{8} +2.76034 q^{9} -6.58136 q^{10} -1.00000 q^{11} +7.50964 q^{12} +6.30048 q^{13} -5.04439 q^{14} +6.97472 q^{15} -0.467685 q^{16} -0.896955 q^{17} -6.25138 q^{18} -2.22648 q^{19} +9.09280 q^{20} +5.34589 q^{21} +2.26471 q^{22} +4.47739 q^{23} -6.13623 q^{24} +3.44511 q^{25} -14.2688 q^{26} -0.575194 q^{27} +6.96932 q^{28} -6.63826 q^{29} -15.7957 q^{30} +9.11413 q^{31} +6.17255 q^{32} -2.40007 q^{33} +2.03134 q^{34} +6.47289 q^{35} +8.63690 q^{36} +4.21519 q^{37} +5.04233 q^{38} +15.1216 q^{39} -7.42985 q^{40} -1.64037 q^{41} -12.1069 q^{42} -2.13008 q^{43} -3.12892 q^{44} +8.02169 q^{45} -10.1400 q^{46} -11.0526 q^{47} -1.12248 q^{48} -2.03875 q^{49} -7.80218 q^{50} -2.15276 q^{51} +19.7137 q^{52} +9.03466 q^{53} +1.30265 q^{54} -2.90605 q^{55} -5.69473 q^{56} -5.34370 q^{57} +15.0338 q^{58} +9.56003 q^{59} +21.8234 q^{60} -1.71805 q^{61} -20.6409 q^{62} +6.14835 q^{63} -13.0437 q^{64} +18.3095 q^{65} +5.43547 q^{66} +14.6108 q^{67} -2.80650 q^{68} +10.7461 q^{69} -14.6592 q^{70} -6.31978 q^{71} -7.05733 q^{72} -2.07545 q^{73} -9.54620 q^{74} +8.26851 q^{75} -6.96647 q^{76} -2.22739 q^{77} -34.2461 q^{78} +3.22444 q^{79} -1.35911 q^{80} -9.66154 q^{81} +3.71497 q^{82} -15.4616 q^{83} +16.7269 q^{84} -2.60659 q^{85} +4.82402 q^{86} -15.9323 q^{87} +2.55669 q^{88} +8.24373 q^{89} -18.1668 q^{90} +14.0336 q^{91} +14.0094 q^{92} +21.8746 q^{93} +25.0311 q^{94} -6.47024 q^{95} +14.8146 q^{96} -2.52172 q^{97} +4.61717 q^{98} -2.76034 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 121q + 2q^{2} + 18q^{3} + 138q^{4} + 13q^{5} + 10q^{6} + 56q^{7} + 12q^{8} + 143q^{9} + O(q^{10}) \) \( 121q + 2q^{2} + 18q^{3} + 138q^{4} + 13q^{5} + 10q^{6} + 56q^{7} + 12q^{8} + 143q^{9} + 20q^{10} - 121q^{11} + 40q^{12} + 31q^{13} + 7q^{14} + 53q^{15} + 164q^{16} - 23q^{17} + 14q^{18} + 62q^{19} + 53q^{20} + 19q^{21} - 2q^{22} + 34q^{23} + 34q^{24} + 172q^{25} + 34q^{26} + 87q^{27} + 91q^{28} - 30q^{29} + 2q^{30} + 102q^{31} + 31q^{32} - 18q^{33} + 30q^{34} + 20q^{35} + 164q^{36} + 58q^{37} + 35q^{38} + 42q^{39} + 52q^{40} - 12q^{41} + 56q^{42} + 96q^{43} - 138q^{44} + 72q^{45} + 48q^{46} + 136q^{47} + 99q^{48} + 199q^{49} - 7q^{50} + 22q^{51} + 81q^{52} + 24q^{53} + 37q^{54} - 13q^{55} + 28q^{56} + 25q^{57} + 76q^{58} + 58q^{59} + 81q^{60} + 14q^{61} - 2q^{62} + 152q^{63} + 236q^{64} - 29q^{65} - 10q^{66} + 112q^{67} - 61q^{68} + 41q^{69} + 105q^{70} + 56q^{71} + 71q^{72} + 113q^{73} - 23q^{74} + 111q^{75} + 144q^{76} - 56q^{77} + 59q^{78} + 80q^{79} + 100q^{80} + 177q^{81} + 123q^{82} + 6q^{83} + 79q^{84} + 26q^{85} + 14q^{86} + 180q^{87} - 12q^{88} + 26q^{89} + 75q^{90} + 72q^{91} + 58q^{92} + 139q^{93} + 37q^{94} + 39q^{95} + 66q^{96} + 136q^{97} + 7q^{98} - 143q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.26471 −1.60139 −0.800697 0.599070i \(-0.795537\pi\)
−0.800697 + 0.599070i \(0.795537\pi\)
\(3\) 2.40007 1.38568 0.692841 0.721090i \(-0.256359\pi\)
0.692841 + 0.721090i \(0.256359\pi\)
\(4\) 3.12892 1.56446
\(5\) 2.90605 1.29962 0.649812 0.760095i \(-0.274848\pi\)
0.649812 + 0.760095i \(0.274848\pi\)
\(6\) −5.43547 −2.21902
\(7\) 2.22739 0.841873 0.420937 0.907090i \(-0.361701\pi\)
0.420937 + 0.907090i \(0.361701\pi\)
\(8\) −2.55669 −0.903925
\(9\) 2.76034 0.920114
\(10\) −6.58136 −2.08121
\(11\) −1.00000 −0.301511
\(12\) 7.50964 2.16785
\(13\) 6.30048 1.74744 0.873720 0.486430i \(-0.161701\pi\)
0.873720 + 0.486430i \(0.161701\pi\)
\(14\) −5.04439 −1.34817
\(15\) 6.97472 1.80087
\(16\) −0.467685 −0.116921
\(17\) −0.896955 −0.217543 −0.108772 0.994067i \(-0.534692\pi\)
−0.108772 + 0.994067i \(0.534692\pi\)
\(18\) −6.25138 −1.47347
\(19\) −2.22648 −0.510789 −0.255394 0.966837i \(-0.582205\pi\)
−0.255394 + 0.966837i \(0.582205\pi\)
\(20\) 9.09280 2.03321
\(21\) 5.34589 1.16657
\(22\) 2.26471 0.482838
\(23\) 4.47739 0.933601 0.466800 0.884363i \(-0.345407\pi\)
0.466800 + 0.884363i \(0.345407\pi\)
\(24\) −6.13623 −1.25255
\(25\) 3.44511 0.689022
\(26\) −14.2688 −2.79834
\(27\) −0.575194 −0.110696
\(28\) 6.96932 1.31708
\(29\) −6.63826 −1.23269 −0.616347 0.787475i \(-0.711388\pi\)
−0.616347 + 0.787475i \(0.711388\pi\)
\(30\) −15.7957 −2.88389
\(31\) 9.11413 1.63695 0.818473 0.574545i \(-0.194821\pi\)
0.818473 + 0.574545i \(0.194821\pi\)
\(32\) 6.17255 1.09116
\(33\) −2.40007 −0.417799
\(34\) 2.03134 0.348373
\(35\) 6.47289 1.09412
\(36\) 8.63690 1.43948
\(37\) 4.21519 0.692974 0.346487 0.938055i \(-0.387375\pi\)
0.346487 + 0.938055i \(0.387375\pi\)
\(38\) 5.04233 0.817974
\(39\) 15.1216 2.42139
\(40\) −7.42985 −1.17476
\(41\) −1.64037 −0.256183 −0.128092 0.991762i \(-0.540885\pi\)
−0.128092 + 0.991762i \(0.540885\pi\)
\(42\) −12.1069 −1.86814
\(43\) −2.13008 −0.324834 −0.162417 0.986722i \(-0.551929\pi\)
−0.162417 + 0.986722i \(0.551929\pi\)
\(44\) −3.12892 −0.471703
\(45\) 8.02169 1.19580
\(46\) −10.1400 −1.49506
\(47\) −11.0526 −1.61219 −0.806097 0.591784i \(-0.798424\pi\)
−0.806097 + 0.591784i \(0.798424\pi\)
\(48\) −1.12248 −0.162016
\(49\) −2.03875 −0.291249
\(50\) −7.80218 −1.10340
\(51\) −2.15276 −0.301446
\(52\) 19.7137 2.73380
\(53\) 9.03466 1.24101 0.620503 0.784204i \(-0.286928\pi\)
0.620503 + 0.784204i \(0.286928\pi\)
\(54\) 1.30265 0.177268
\(55\) −2.90605 −0.391851
\(56\) −5.69473 −0.760991
\(57\) −5.34370 −0.707791
\(58\) 15.0338 1.97403
\(59\) 9.56003 1.24461 0.622305 0.782775i \(-0.286196\pi\)
0.622305 + 0.782775i \(0.286196\pi\)
\(60\) 21.8234 2.81738
\(61\) −1.71805 −0.219973 −0.109987 0.993933i \(-0.535081\pi\)
−0.109987 + 0.993933i \(0.535081\pi\)
\(62\) −20.6409 −2.62140
\(63\) 6.14835 0.774620
\(64\) −13.0437 −1.63046
\(65\) 18.3095 2.27101
\(66\) 5.43547 0.669060
\(67\) 14.6108 1.78499 0.892494 0.451058i \(-0.148953\pi\)
0.892494 + 0.451058i \(0.148953\pi\)
\(68\) −2.80650 −0.340338
\(69\) 10.7461 1.29367
\(70\) −14.6592 −1.75211
\(71\) −6.31978 −0.750020 −0.375010 0.927021i \(-0.622361\pi\)
−0.375010 + 0.927021i \(0.622361\pi\)
\(72\) −7.05733 −0.831715
\(73\) −2.07545 −0.242913 −0.121456 0.992597i \(-0.538756\pi\)
−0.121456 + 0.992597i \(0.538756\pi\)
\(74\) −9.54620 −1.10972
\(75\) 8.26851 0.954765
\(76\) −6.96647 −0.799109
\(77\) −2.22739 −0.253834
\(78\) −34.2461 −3.87761
\(79\) 3.22444 0.362778 0.181389 0.983411i \(-0.441941\pi\)
0.181389 + 0.983411i \(0.441941\pi\)
\(80\) −1.35911 −0.151954
\(81\) −9.66154 −1.07350
\(82\) 3.71497 0.410250
\(83\) −15.4616 −1.69713 −0.848566 0.529090i \(-0.822533\pi\)
−0.848566 + 0.529090i \(0.822533\pi\)
\(84\) 16.7269 1.82505
\(85\) −2.60659 −0.282725
\(86\) 4.82402 0.520188
\(87\) −15.9323 −1.70812
\(88\) 2.55669 0.272544
\(89\) 8.24373 0.873834 0.436917 0.899502i \(-0.356070\pi\)
0.436917 + 0.899502i \(0.356070\pi\)
\(90\) −18.1668 −1.91495
\(91\) 14.0336 1.47112
\(92\) 14.0094 1.46058
\(93\) 21.8746 2.26829
\(94\) 25.0311 2.58176
\(95\) −6.47024 −0.663833
\(96\) 14.8146 1.51200
\(97\) −2.52172 −0.256042 −0.128021 0.991771i \(-0.540863\pi\)
−0.128021 + 0.991771i \(0.540863\pi\)
\(98\) 4.61717 0.466405
\(99\) −2.76034 −0.277425
\(100\) 10.7795 1.07795
\(101\) 16.3208 1.62398 0.811992 0.583668i \(-0.198383\pi\)
0.811992 + 0.583668i \(0.198383\pi\)
\(102\) 4.87537 0.482734
\(103\) 12.2066 1.20275 0.601377 0.798966i \(-0.294619\pi\)
0.601377 + 0.798966i \(0.294619\pi\)
\(104\) −16.1084 −1.57955
\(105\) 15.5354 1.51610
\(106\) −20.4609 −1.98734
\(107\) −7.56420 −0.731259 −0.365630 0.930760i \(-0.619146\pi\)
−0.365630 + 0.930760i \(0.619146\pi\)
\(108\) −1.79974 −0.173180
\(109\) −9.82156 −0.940735 −0.470367 0.882471i \(-0.655879\pi\)
−0.470367 + 0.882471i \(0.655879\pi\)
\(110\) 6.58136 0.627508
\(111\) 10.1168 0.960241
\(112\) −1.04172 −0.0984328
\(113\) −13.2286 −1.24444 −0.622221 0.782842i \(-0.713769\pi\)
−0.622221 + 0.782842i \(0.713769\pi\)
\(114\) 12.1019 1.13345
\(115\) 13.0115 1.21333
\(116\) −20.7706 −1.92850
\(117\) 17.3915 1.60784
\(118\) −21.6507 −1.99311
\(119\) −1.99787 −0.183144
\(120\) −17.8322 −1.62785
\(121\) 1.00000 0.0909091
\(122\) 3.89088 0.352264
\(123\) −3.93701 −0.354989
\(124\) 28.5174 2.56094
\(125\) −4.51858 −0.404154
\(126\) −13.9243 −1.24047
\(127\) 8.52040 0.756063 0.378032 0.925793i \(-0.376601\pi\)
0.378032 + 0.925793i \(0.376601\pi\)
\(128\) 17.1951 1.51984
\(129\) −5.11235 −0.450117
\(130\) −41.4657 −3.63679
\(131\) 15.4050 1.34594 0.672970 0.739670i \(-0.265018\pi\)
0.672970 + 0.739670i \(0.265018\pi\)
\(132\) −7.50964 −0.653630
\(133\) −4.95922 −0.430019
\(134\) −33.0892 −2.85847
\(135\) −1.67154 −0.143863
\(136\) 2.29323 0.196643
\(137\) 6.97281 0.595727 0.297864 0.954608i \(-0.403726\pi\)
0.297864 + 0.954608i \(0.403726\pi\)
\(138\) −24.3367 −2.07168
\(139\) −10.2487 −0.869284 −0.434642 0.900603i \(-0.643125\pi\)
−0.434642 + 0.900603i \(0.643125\pi\)
\(140\) 20.2532 1.71171
\(141\) −26.5271 −2.23399
\(142\) 14.3125 1.20108
\(143\) −6.30048 −0.526873
\(144\) −1.29097 −0.107581
\(145\) −19.2911 −1.60204
\(146\) 4.70029 0.388999
\(147\) −4.89313 −0.403579
\(148\) 13.1890 1.08413
\(149\) 7.88191 0.645712 0.322856 0.946448i \(-0.395357\pi\)
0.322856 + 0.946448i \(0.395357\pi\)
\(150\) −18.7258 −1.52896
\(151\) −9.04358 −0.735956 −0.367978 0.929834i \(-0.619950\pi\)
−0.367978 + 0.929834i \(0.619950\pi\)
\(152\) 5.69240 0.461715
\(153\) −2.47590 −0.200165
\(154\) 5.04439 0.406489
\(155\) 26.4861 2.12741
\(156\) 47.3143 3.78818
\(157\) −0.826975 −0.0659998 −0.0329999 0.999455i \(-0.510506\pi\)
−0.0329999 + 0.999455i \(0.510506\pi\)
\(158\) −7.30244 −0.580951
\(159\) 21.6838 1.71964
\(160\) 17.9377 1.41810
\(161\) 9.97288 0.785973
\(162\) 21.8806 1.71910
\(163\) −3.68896 −0.288941 −0.144471 0.989509i \(-0.546148\pi\)
−0.144471 + 0.989509i \(0.546148\pi\)
\(164\) −5.13260 −0.400789
\(165\) −6.97472 −0.542981
\(166\) 35.0161 2.71778
\(167\) −12.3115 −0.952693 −0.476346 0.879258i \(-0.658039\pi\)
−0.476346 + 0.879258i \(0.658039\pi\)
\(168\) −13.6678 −1.05449
\(169\) 26.6961 2.05354
\(170\) 5.90318 0.452754
\(171\) −6.14584 −0.469984
\(172\) −6.66486 −0.508191
\(173\) −7.30289 −0.555229 −0.277614 0.960693i \(-0.589544\pi\)
−0.277614 + 0.960693i \(0.589544\pi\)
\(174\) 36.0821 2.73538
\(175\) 7.67359 0.580069
\(176\) 0.467685 0.0352531
\(177\) 22.9448 1.72463
\(178\) −18.6697 −1.39935
\(179\) 24.5936 1.83821 0.919107 0.394007i \(-0.128911\pi\)
0.919107 + 0.394007i \(0.128911\pi\)
\(180\) 25.0992 1.87079
\(181\) 22.4081 1.66558 0.832791 0.553588i \(-0.186742\pi\)
0.832791 + 0.553588i \(0.186742\pi\)
\(182\) −31.7821 −2.35585
\(183\) −4.12343 −0.304813
\(184\) −11.4473 −0.843905
\(185\) 12.2496 0.900605
\(186\) −49.5396 −3.63242
\(187\) 0.896955 0.0655918
\(188\) −34.5829 −2.52222
\(189\) −1.28118 −0.0931921
\(190\) 14.6532 1.06306
\(191\) 5.97476 0.432318 0.216159 0.976358i \(-0.430647\pi\)
0.216159 + 0.976358i \(0.430647\pi\)
\(192\) −31.3058 −2.25930
\(193\) 24.9862 1.79854 0.899272 0.437390i \(-0.144097\pi\)
0.899272 + 0.437390i \(0.144097\pi\)
\(194\) 5.71098 0.410024
\(195\) 43.9441 3.14690
\(196\) −6.37908 −0.455648
\(197\) −4.63803 −0.330446 −0.165223 0.986256i \(-0.552834\pi\)
−0.165223 + 0.986256i \(0.552834\pi\)
\(198\) 6.25138 0.444267
\(199\) −1.33297 −0.0944919 −0.0472459 0.998883i \(-0.515044\pi\)
−0.0472459 + 0.998883i \(0.515044\pi\)
\(200\) −8.80807 −0.622825
\(201\) 35.0669 2.47343
\(202\) −36.9620 −2.60064
\(203\) −14.7860 −1.03777
\(204\) −6.73581 −0.471601
\(205\) −4.76700 −0.332942
\(206\) −27.6445 −1.92608
\(207\) 12.3591 0.859019
\(208\) −2.94664 −0.204313
\(209\) 2.22648 0.154009
\(210\) −35.1832 −2.42787
\(211\) 17.6717 1.21657 0.608284 0.793719i \(-0.291858\pi\)
0.608284 + 0.793719i \(0.291858\pi\)
\(212\) 28.2688 1.94151
\(213\) −15.1679 −1.03929
\(214\) 17.1307 1.17103
\(215\) −6.19012 −0.422162
\(216\) 1.47059 0.100061
\(217\) 20.3007 1.37810
\(218\) 22.2430 1.50649
\(219\) −4.98123 −0.336600
\(220\) −9.09280 −0.613036
\(221\) −5.65125 −0.380144
\(222\) −22.9116 −1.53772
\(223\) 1.37143 0.0918378 0.0459189 0.998945i \(-0.485378\pi\)
0.0459189 + 0.998945i \(0.485378\pi\)
\(224\) 13.7487 0.918620
\(225\) 9.50969 0.633979
\(226\) 29.9590 1.99284
\(227\) 2.98940 0.198414 0.0992068 0.995067i \(-0.468369\pi\)
0.0992068 + 0.995067i \(0.468369\pi\)
\(228\) −16.7200 −1.10731
\(229\) −16.0462 −1.06036 −0.530180 0.847885i \(-0.677876\pi\)
−0.530180 + 0.847885i \(0.677876\pi\)
\(230\) −29.4673 −1.94302
\(231\) −5.34589 −0.351734
\(232\) 16.9720 1.11426
\(233\) −6.02108 −0.394454 −0.197227 0.980358i \(-0.563194\pi\)
−0.197227 + 0.980358i \(0.563194\pi\)
\(234\) −39.3867 −2.57479
\(235\) −32.1195 −2.09525
\(236\) 29.9126 1.94714
\(237\) 7.73889 0.502695
\(238\) 4.52459 0.293286
\(239\) −15.4681 −1.00055 −0.500274 0.865867i \(-0.666767\pi\)
−0.500274 + 0.865867i \(0.666767\pi\)
\(240\) −3.26197 −0.210559
\(241\) −12.8412 −0.827177 −0.413589 0.910464i \(-0.635725\pi\)
−0.413589 + 0.910464i \(0.635725\pi\)
\(242\) −2.26471 −0.145581
\(243\) −21.4628 −1.37684
\(244\) −5.37564 −0.344140
\(245\) −5.92469 −0.378515
\(246\) 8.91620 0.568476
\(247\) −14.0279 −0.892572
\(248\) −23.3020 −1.47968
\(249\) −37.1090 −2.35168
\(250\) 10.2333 0.647210
\(251\) 4.64066 0.292916 0.146458 0.989217i \(-0.453213\pi\)
0.146458 + 0.989217i \(0.453213\pi\)
\(252\) 19.2377 1.21186
\(253\) −4.47739 −0.281491
\(254\) −19.2963 −1.21075
\(255\) −6.25601 −0.391766
\(256\) −12.8546 −0.803411
\(257\) −16.8543 −1.05134 −0.525671 0.850688i \(-0.676186\pi\)
−0.525671 + 0.850688i \(0.676186\pi\)
\(258\) 11.5780 0.720815
\(259\) 9.38887 0.583396
\(260\) 57.2890 3.55291
\(261\) −18.3239 −1.13422
\(262\) −34.8879 −2.15538
\(263\) −11.0794 −0.683187 −0.341594 0.939848i \(-0.610967\pi\)
−0.341594 + 0.939848i \(0.610967\pi\)
\(264\) 6.13623 0.377659
\(265\) 26.2552 1.61284
\(266\) 11.2312 0.688630
\(267\) 19.7855 1.21086
\(268\) 45.7160 2.79255
\(269\) 14.9880 0.913837 0.456919 0.889508i \(-0.348953\pi\)
0.456919 + 0.889508i \(0.348953\pi\)
\(270\) 3.78556 0.230382
\(271\) −13.6067 −0.826546 −0.413273 0.910607i \(-0.635614\pi\)
−0.413273 + 0.910607i \(0.635614\pi\)
\(272\) 0.419492 0.0254354
\(273\) 33.6817 2.03851
\(274\) −15.7914 −0.953993
\(275\) −3.44511 −0.207748
\(276\) 33.6236 2.02390
\(277\) 14.7494 0.886205 0.443102 0.896471i \(-0.353878\pi\)
0.443102 + 0.896471i \(0.353878\pi\)
\(278\) 23.2104 1.39207
\(279\) 25.1581 1.50618
\(280\) −16.5492 −0.989002
\(281\) −29.4341 −1.75589 −0.877944 0.478763i \(-0.841085\pi\)
−0.877944 + 0.478763i \(0.841085\pi\)
\(282\) 60.0763 3.57749
\(283\) −21.7256 −1.29145 −0.645726 0.763569i \(-0.723445\pi\)
−0.645726 + 0.763569i \(0.723445\pi\)
\(284\) −19.7741 −1.17338
\(285\) −15.5290 −0.919861
\(286\) 14.2688 0.843731
\(287\) −3.65375 −0.215674
\(288\) 17.0383 1.00399
\(289\) −16.1955 −0.952675
\(290\) 43.6888 2.56549
\(291\) −6.05232 −0.354793
\(292\) −6.49392 −0.380028
\(293\) 14.5636 0.850813 0.425406 0.905002i \(-0.360131\pi\)
0.425406 + 0.905002i \(0.360131\pi\)
\(294\) 11.0815 0.646289
\(295\) 27.7819 1.61752
\(296\) −10.7769 −0.626396
\(297\) 0.575194 0.0333761
\(298\) −17.8503 −1.03404
\(299\) 28.2097 1.63141
\(300\) 25.8715 1.49369
\(301\) −4.74452 −0.273469
\(302\) 20.4811 1.17856
\(303\) 39.1712 2.25033
\(304\) 1.04129 0.0597220
\(305\) −4.99272 −0.285883
\(306\) 5.60721 0.320543
\(307\) −31.3585 −1.78972 −0.894861 0.446345i \(-0.852725\pi\)
−0.894861 + 0.446345i \(0.852725\pi\)
\(308\) −6.96932 −0.397114
\(309\) 29.2967 1.66663
\(310\) −59.9834 −3.40683
\(311\) −21.7027 −1.23065 −0.615323 0.788275i \(-0.710974\pi\)
−0.615323 + 0.788275i \(0.710974\pi\)
\(312\) −38.6612 −2.18876
\(313\) 13.6646 0.772366 0.386183 0.922422i \(-0.373793\pi\)
0.386183 + 0.922422i \(0.373793\pi\)
\(314\) 1.87286 0.105692
\(315\) 17.8674 1.00671
\(316\) 10.0890 0.567553
\(317\) 14.8044 0.831496 0.415748 0.909480i \(-0.363520\pi\)
0.415748 + 0.909480i \(0.363520\pi\)
\(318\) −49.1076 −2.75382
\(319\) 6.63826 0.371671
\(320\) −37.9055 −2.11898
\(321\) −18.1546 −1.01329
\(322\) −22.5857 −1.25865
\(323\) 1.99705 0.111119
\(324\) −30.2302 −1.67946
\(325\) 21.7059 1.20402
\(326\) 8.35443 0.462709
\(327\) −23.5724 −1.30356
\(328\) 4.19392 0.231571
\(329\) −24.6185 −1.35726
\(330\) 15.7957 0.869527
\(331\) 11.8365 0.650592 0.325296 0.945612i \(-0.394536\pi\)
0.325296 + 0.945612i \(0.394536\pi\)
\(332\) −48.3782 −2.65510
\(333\) 11.6354 0.637615
\(334\) 27.8820 1.52564
\(335\) 42.4596 2.31981
\(336\) −2.50019 −0.136397
\(337\) 7.30611 0.397989 0.198995 0.980001i \(-0.436232\pi\)
0.198995 + 0.980001i \(0.436232\pi\)
\(338\) −60.4589 −3.28853
\(339\) −31.7496 −1.72440
\(340\) −8.15583 −0.442312
\(341\) −9.11413 −0.493558
\(342\) 13.9186 0.752629
\(343\) −20.1328 −1.08707
\(344\) 5.44595 0.293626
\(345\) 31.2286 1.68129
\(346\) 16.5390 0.889140
\(347\) −0.414264 −0.0222389 −0.0111194 0.999938i \(-0.503539\pi\)
−0.0111194 + 0.999938i \(0.503539\pi\)
\(348\) −49.8510 −2.67229
\(349\) 3.23929 0.173395 0.0866976 0.996235i \(-0.472369\pi\)
0.0866976 + 0.996235i \(0.472369\pi\)
\(350\) −17.3785 −0.928919
\(351\) −3.62400 −0.193435
\(352\) −6.17255 −0.328998
\(353\) −28.3935 −1.51124 −0.755618 0.655013i \(-0.772663\pi\)
−0.755618 + 0.655013i \(0.772663\pi\)
\(354\) −51.9633 −2.76182
\(355\) −18.3656 −0.974744
\(356\) 25.7940 1.36708
\(357\) −4.79502 −0.253779
\(358\) −55.6975 −2.94371
\(359\) 13.3128 0.702622 0.351311 0.936259i \(-0.385736\pi\)
0.351311 + 0.936259i \(0.385736\pi\)
\(360\) −20.5089 −1.08092
\(361\) −14.0428 −0.739095
\(362\) −50.7479 −2.66725
\(363\) 2.40007 0.125971
\(364\) 43.9101 2.30151
\(365\) −6.03135 −0.315695
\(366\) 9.33840 0.488126
\(367\) −11.5594 −0.603394 −0.301697 0.953404i \(-0.597553\pi\)
−0.301697 + 0.953404i \(0.597553\pi\)
\(368\) −2.09401 −0.109158
\(369\) −4.52799 −0.235718
\(370\) −27.7417 −1.44222
\(371\) 20.1237 1.04477
\(372\) 68.4439 3.54865
\(373\) −5.23621 −0.271121 −0.135560 0.990769i \(-0.543283\pi\)
−0.135560 + 0.990769i \(0.543283\pi\)
\(374\) −2.03134 −0.105038
\(375\) −10.8449 −0.560029
\(376\) 28.2582 1.45730
\(377\) −41.8242 −2.15406
\(378\) 2.90150 0.149237
\(379\) 19.4471 0.998933 0.499466 0.866333i \(-0.333529\pi\)
0.499466 + 0.866333i \(0.333529\pi\)
\(380\) −20.2449 −1.03854
\(381\) 20.4496 1.04766
\(382\) −13.5311 −0.692312
\(383\) −16.0024 −0.817682 −0.408841 0.912606i \(-0.634067\pi\)
−0.408841 + 0.912606i \(0.634067\pi\)
\(384\) 41.2694 2.10602
\(385\) −6.47289 −0.329889
\(386\) −56.5865 −2.88018
\(387\) −5.87975 −0.298885
\(388\) −7.89028 −0.400568
\(389\) −29.8579 −1.51386 −0.756929 0.653497i \(-0.773301\pi\)
−0.756929 + 0.653497i \(0.773301\pi\)
\(390\) −99.5208 −5.03943
\(391\) −4.01602 −0.203099
\(392\) 5.21243 0.263268
\(393\) 36.9730 1.86504
\(394\) 10.5038 0.529174
\(395\) 9.37038 0.471475
\(396\) −8.63690 −0.434021
\(397\) 26.2568 1.31779 0.658896 0.752234i \(-0.271024\pi\)
0.658896 + 0.752234i \(0.271024\pi\)
\(398\) 3.01880 0.151319
\(399\) −11.9025 −0.595870
\(400\) −1.61123 −0.0805613
\(401\) −27.4785 −1.37221 −0.686107 0.727501i \(-0.740682\pi\)
−0.686107 + 0.727501i \(0.740682\pi\)
\(402\) −79.4164 −3.96093
\(403\) 57.4234 2.86046
\(404\) 51.0667 2.54066
\(405\) −28.0769 −1.39515
\(406\) 33.4860 1.66188
\(407\) −4.21519 −0.208939
\(408\) 5.50392 0.272485
\(409\) 26.8563 1.32796 0.663978 0.747752i \(-0.268867\pi\)
0.663978 + 0.747752i \(0.268867\pi\)
\(410\) 10.7959 0.533171
\(411\) 16.7352 0.825488
\(412\) 38.1936 1.88166
\(413\) 21.2939 1.04780
\(414\) −27.9899 −1.37563
\(415\) −44.9322 −2.20563
\(416\) 38.8900 1.90674
\(417\) −24.5976 −1.20455
\(418\) −5.04233 −0.246628
\(419\) −0.383344 −0.0187276 −0.00936378 0.999956i \(-0.502981\pi\)
−0.00936378 + 0.999956i \(0.502981\pi\)
\(420\) 48.6091 2.37188
\(421\) −6.13651 −0.299075 −0.149538 0.988756i \(-0.547778\pi\)
−0.149538 + 0.988756i \(0.547778\pi\)
\(422\) −40.0213 −1.94821
\(423\) −30.5091 −1.48340
\(424\) −23.0988 −1.12178
\(425\) −3.09011 −0.149892
\(426\) 34.3510 1.66431
\(427\) −3.82676 −0.185190
\(428\) −23.6678 −1.14403
\(429\) −15.1216 −0.730078
\(430\) 14.0188 0.676048
\(431\) −13.5160 −0.651042 −0.325521 0.945535i \(-0.605540\pi\)
−0.325521 + 0.945535i \(0.605540\pi\)
\(432\) 0.269009 0.0129427
\(433\) −31.2874 −1.50358 −0.751788 0.659405i \(-0.770808\pi\)
−0.751788 + 0.659405i \(0.770808\pi\)
\(434\) −45.9753 −2.20688
\(435\) −46.3000 −2.21992
\(436\) −30.7309 −1.47174
\(437\) −9.96880 −0.476873
\(438\) 11.2810 0.539029
\(439\) 14.3302 0.683944 0.341972 0.939710i \(-0.388905\pi\)
0.341972 + 0.939710i \(0.388905\pi\)
\(440\) 7.42985 0.354204
\(441\) −5.62764 −0.267983
\(442\) 12.7984 0.608760
\(443\) −15.3750 −0.730490 −0.365245 0.930911i \(-0.619015\pi\)
−0.365245 + 0.930911i \(0.619015\pi\)
\(444\) 31.6546 1.50226
\(445\) 23.9567 1.13566
\(446\) −3.10590 −0.147068
\(447\) 18.9172 0.894751
\(448\) −29.0533 −1.37264
\(449\) 26.4079 1.24627 0.623133 0.782116i \(-0.285860\pi\)
0.623133 + 0.782116i \(0.285860\pi\)
\(450\) −21.5367 −1.01525
\(451\) 1.64037 0.0772422
\(452\) −41.3913 −1.94688
\(453\) −21.7052 −1.01980
\(454\) −6.77014 −0.317738
\(455\) 40.7823 1.91191
\(456\) 13.6622 0.639790
\(457\) −32.2906 −1.51049 −0.755246 0.655441i \(-0.772483\pi\)
−0.755246 + 0.655441i \(0.772483\pi\)
\(458\) 36.3400 1.69805
\(459\) 0.515923 0.0240812
\(460\) 40.7120 1.89821
\(461\) −41.2060 −1.91915 −0.959576 0.281448i \(-0.909185\pi\)
−0.959576 + 0.281448i \(0.909185\pi\)
\(462\) 12.1069 0.563264
\(463\) −24.3427 −1.13130 −0.565652 0.824644i \(-0.691375\pi\)
−0.565652 + 0.824644i \(0.691375\pi\)
\(464\) 3.10461 0.144128
\(465\) 63.5685 2.94792
\(466\) 13.6360 0.631677
\(467\) 19.4190 0.898603 0.449302 0.893380i \(-0.351673\pi\)
0.449302 + 0.893380i \(0.351673\pi\)
\(468\) 54.4166 2.51541
\(469\) 32.5438 1.50273
\(470\) 72.7414 3.35531
\(471\) −1.98480 −0.0914547
\(472\) −24.4420 −1.12503
\(473\) 2.13008 0.0979412
\(474\) −17.5264 −0.805013
\(475\) −7.67045 −0.351945
\(476\) −6.25117 −0.286522
\(477\) 24.9388 1.14187
\(478\) 35.0308 1.60227
\(479\) −5.25923 −0.240300 −0.120150 0.992756i \(-0.538338\pi\)
−0.120150 + 0.992756i \(0.538338\pi\)
\(480\) 43.0518 1.96504
\(481\) 26.5577 1.21093
\(482\) 29.0817 1.32464
\(483\) 23.9356 1.08911
\(484\) 3.12892 0.142224
\(485\) −7.32825 −0.332759
\(486\) 48.6071 2.20486
\(487\) −25.9349 −1.17522 −0.587610 0.809144i \(-0.699931\pi\)
−0.587610 + 0.809144i \(0.699931\pi\)
\(488\) 4.39251 0.198840
\(489\) −8.85376 −0.400381
\(490\) 13.4177 0.606151
\(491\) −33.9538 −1.53231 −0.766157 0.642654i \(-0.777833\pi\)
−0.766157 + 0.642654i \(0.777833\pi\)
\(492\) −12.3186 −0.555366
\(493\) 5.95422 0.268165
\(494\) 31.7691 1.42936
\(495\) −8.02169 −0.360548
\(496\) −4.26254 −0.191394
\(497\) −14.0766 −0.631422
\(498\) 84.0411 3.76597
\(499\) 27.8017 1.24457 0.622287 0.782789i \(-0.286204\pi\)
0.622287 + 0.782789i \(0.286204\pi\)
\(500\) −14.1383 −0.632284
\(501\) −29.5485 −1.32013
\(502\) −10.5098 −0.469074
\(503\) 9.76960 0.435605 0.217802 0.975993i \(-0.430111\pi\)
0.217802 + 0.975993i \(0.430111\pi\)
\(504\) −15.7194 −0.700198
\(505\) 47.4291 2.11057
\(506\) 10.1400 0.450778
\(507\) 64.0725 2.84556
\(508\) 26.6597 1.18283
\(509\) 12.8454 0.569364 0.284682 0.958622i \(-0.408112\pi\)
0.284682 + 0.958622i \(0.408112\pi\)
\(510\) 14.1681 0.627372
\(511\) −4.62283 −0.204502
\(512\) −5.27825 −0.233268
\(513\) 1.28065 0.0565423
\(514\) 38.1701 1.68361
\(515\) 35.4730 1.56313
\(516\) −15.9961 −0.704191
\(517\) 11.0526 0.486095
\(518\) −21.2631 −0.934247
\(519\) −17.5275 −0.769370
\(520\) −46.8117 −2.05283
\(521\) −8.90370 −0.390078 −0.195039 0.980795i \(-0.562483\pi\)
−0.195039 + 0.980795i \(0.562483\pi\)
\(522\) 41.4983 1.81633
\(523\) −8.33103 −0.364290 −0.182145 0.983272i \(-0.558304\pi\)
−0.182145 + 0.983272i \(0.558304\pi\)
\(524\) 48.2010 2.10567
\(525\) 18.4172 0.803791
\(526\) 25.0917 1.09405
\(527\) −8.17497 −0.356107
\(528\) 1.12248 0.0488495
\(529\) −2.95297 −0.128390
\(530\) −59.4604 −2.58279
\(531\) 26.3890 1.14518
\(532\) −15.5170 −0.672749
\(533\) −10.3351 −0.447665
\(534\) −44.8086 −1.93906
\(535\) −21.9819 −0.950362
\(536\) −37.3552 −1.61350
\(537\) 59.0265 2.54718
\(538\) −33.9436 −1.46341
\(539\) 2.03875 0.0878150
\(540\) −5.23012 −0.225069
\(541\) −33.1038 −1.42324 −0.711621 0.702563i \(-0.752039\pi\)
−0.711621 + 0.702563i \(0.752039\pi\)
\(542\) 30.8152 1.32363
\(543\) 53.7811 2.30797
\(544\) −5.53649 −0.237375
\(545\) −28.5419 −1.22260
\(546\) −76.2793 −3.26445
\(547\) 1.00000 0.0427569
\(548\) 21.8174 0.931992
\(549\) −4.74240 −0.202401
\(550\) 7.80218 0.332686
\(551\) 14.7799 0.629646
\(552\) −27.4743 −1.16938
\(553\) 7.18208 0.305413
\(554\) −33.4031 −1.41916
\(555\) 29.3998 1.24795
\(556\) −32.0674 −1.35996
\(557\) −28.0960 −1.19047 −0.595233 0.803553i \(-0.702940\pi\)
−0.595233 + 0.803553i \(0.702940\pi\)
\(558\) −56.9759 −2.41198
\(559\) −13.4205 −0.567628
\(560\) −3.02727 −0.127926
\(561\) 2.15276 0.0908894
\(562\) 66.6597 2.81187
\(563\) 44.8284 1.88929 0.944646 0.328091i \(-0.106405\pi\)
0.944646 + 0.328091i \(0.106405\pi\)
\(564\) −83.0014 −3.49499
\(565\) −38.4429 −1.61731
\(566\) 49.2022 2.06812
\(567\) −21.5200 −0.903754
\(568\) 16.1577 0.677963
\(569\) −3.73399 −0.156537 −0.0782684 0.996932i \(-0.524939\pi\)
−0.0782684 + 0.996932i \(0.524939\pi\)
\(570\) 35.1688 1.47306
\(571\) 43.8805 1.83634 0.918171 0.396185i \(-0.129666\pi\)
0.918171 + 0.396185i \(0.129666\pi\)
\(572\) −19.7137 −0.824272
\(573\) 14.3398 0.599056
\(574\) 8.27469 0.345379
\(575\) 15.4251 0.643271
\(576\) −36.0050 −1.50021
\(577\) −4.34050 −0.180697 −0.0903486 0.995910i \(-0.528798\pi\)
−0.0903486 + 0.995910i \(0.528798\pi\)
\(578\) 36.6781 1.52561
\(579\) 59.9686 2.49221
\(580\) −60.3604 −2.50633
\(581\) −34.4390 −1.42877
\(582\) 13.7068 0.568163
\(583\) −9.03466 −0.374177
\(584\) 5.30627 0.219575
\(585\) 50.5405 2.08959
\(586\) −32.9823 −1.36249
\(587\) −14.8076 −0.611174 −0.305587 0.952164i \(-0.598853\pi\)
−0.305587 + 0.952164i \(0.598853\pi\)
\(588\) −15.3102 −0.631384
\(589\) −20.2924 −0.836134
\(590\) −62.9180 −2.59029
\(591\) −11.1316 −0.457893
\(592\) −1.97138 −0.0810233
\(593\) −3.58712 −0.147305 −0.0736526 0.997284i \(-0.523466\pi\)
−0.0736526 + 0.997284i \(0.523466\pi\)
\(594\) −1.30265 −0.0534483
\(595\) −5.80589 −0.238018
\(596\) 24.6619 1.01019
\(597\) −3.19923 −0.130936
\(598\) −63.8869 −2.61253
\(599\) 26.3718 1.07752 0.538762 0.842458i \(-0.318892\pi\)
0.538762 + 0.842458i \(0.318892\pi\)
\(600\) −21.1400 −0.863037
\(601\) 40.6923 1.65987 0.829936 0.557858i \(-0.188377\pi\)
0.829936 + 0.557858i \(0.188377\pi\)
\(602\) 10.7450 0.437932
\(603\) 40.3307 1.64239
\(604\) −28.2967 −1.15138
\(605\) 2.90605 0.118148
\(606\) −88.7115 −3.60366
\(607\) 10.2238 0.414971 0.207486 0.978238i \(-0.433472\pi\)
0.207486 + 0.978238i \(0.433472\pi\)
\(608\) −13.7430 −0.557353
\(609\) −35.4874 −1.43802
\(610\) 11.3071 0.457811
\(611\) −69.6370 −2.81721
\(612\) −7.74691 −0.313150
\(613\) −13.5400 −0.546876 −0.273438 0.961890i \(-0.588161\pi\)
−0.273438 + 0.961890i \(0.588161\pi\)
\(614\) 71.0179 2.86605
\(615\) −11.4411 −0.461352
\(616\) 5.69473 0.229447
\(617\) 33.2214 1.33744 0.668722 0.743513i \(-0.266842\pi\)
0.668722 + 0.743513i \(0.266842\pi\)
\(618\) −66.3487 −2.66894
\(619\) 9.04033 0.363362 0.181681 0.983358i \(-0.441846\pi\)
0.181681 + 0.983358i \(0.441846\pi\)
\(620\) 82.8730 3.32826
\(621\) −2.57537 −0.103346
\(622\) 49.1503 1.97075
\(623\) 18.3620 0.735657
\(624\) −7.07215 −0.283112
\(625\) −30.3568 −1.21427
\(626\) −30.9463 −1.23686
\(627\) 5.34370 0.213407
\(628\) −2.58754 −0.103254
\(629\) −3.78084 −0.150752
\(630\) −40.4645 −1.61215
\(631\) −17.5309 −0.697893 −0.348946 0.937143i \(-0.613460\pi\)
−0.348946 + 0.937143i \(0.613460\pi\)
\(632\) −8.24389 −0.327924
\(633\) 42.4133 1.68578
\(634\) −33.5276 −1.33155
\(635\) 24.7607 0.982598
\(636\) 67.8471 2.69031
\(637\) −12.8451 −0.508941
\(638\) −15.0338 −0.595192
\(639\) −17.4448 −0.690105
\(640\) 49.9697 1.97523
\(641\) −14.0223 −0.553846 −0.276923 0.960892i \(-0.589315\pi\)
−0.276923 + 0.960892i \(0.589315\pi\)
\(642\) 41.1150 1.62268
\(643\) 26.3216 1.03802 0.519011 0.854767i \(-0.326300\pi\)
0.519011 + 0.854767i \(0.326300\pi\)
\(644\) 31.2044 1.22963
\(645\) −14.8567 −0.584983
\(646\) −4.52274 −0.177945
\(647\) −1.17257 −0.0460984 −0.0230492 0.999734i \(-0.507337\pi\)
−0.0230492 + 0.999734i \(0.507337\pi\)
\(648\) 24.7015 0.970368
\(649\) −9.56003 −0.375264
\(650\) −49.1575 −1.92812
\(651\) 48.7231 1.90961
\(652\) −11.5425 −0.452038
\(653\) −27.8465 −1.08972 −0.544860 0.838527i \(-0.683417\pi\)
−0.544860 + 0.838527i \(0.683417\pi\)
\(654\) 53.3848 2.08751
\(655\) 44.7676 1.74921
\(656\) 0.767178 0.0299533
\(657\) −5.72895 −0.223508
\(658\) 55.7539 2.17351
\(659\) 31.4448 1.22492 0.612458 0.790503i \(-0.290181\pi\)
0.612458 + 0.790503i \(0.290181\pi\)
\(660\) −21.8234 −0.849473
\(661\) −10.3826 −0.403838 −0.201919 0.979402i \(-0.564718\pi\)
−0.201919 + 0.979402i \(0.564718\pi\)
\(662\) −26.8062 −1.04185
\(663\) −13.5634 −0.526759
\(664\) 39.5305 1.53408
\(665\) −14.4117 −0.558863
\(666\) −26.3508 −1.02107
\(667\) −29.7221 −1.15084
\(668\) −38.5217 −1.49045
\(669\) 3.29153 0.127258
\(670\) −96.1587 −3.71494
\(671\) 1.71805 0.0663245
\(672\) 32.9977 1.27292
\(673\) 24.5829 0.947599 0.473800 0.880633i \(-0.342882\pi\)
0.473800 + 0.880633i \(0.342882\pi\)
\(674\) −16.5462 −0.637337
\(675\) −1.98161 −0.0762720
\(676\) 83.5299 3.21269
\(677\) −18.7401 −0.720241 −0.360121 0.932906i \(-0.617264\pi\)
−0.360121 + 0.932906i \(0.617264\pi\)
\(678\) 71.9037 2.76144
\(679\) −5.61685 −0.215555
\(680\) 6.66424 0.255562
\(681\) 7.17478 0.274938
\(682\) 20.6409 0.790381
\(683\) 28.4579 1.08891 0.544456 0.838790i \(-0.316736\pi\)
0.544456 + 0.838790i \(0.316736\pi\)
\(684\) −19.2299 −0.735272
\(685\) 20.2633 0.774221
\(686\) 45.5950 1.74082
\(687\) −38.5119 −1.46932
\(688\) 0.996206 0.0379800
\(689\) 56.9227 2.16858
\(690\) −70.7237 −2.69241
\(691\) 35.1906 1.33871 0.669356 0.742942i \(-0.266570\pi\)
0.669356 + 0.742942i \(0.266570\pi\)
\(692\) −22.8502 −0.868634
\(693\) −6.14835 −0.233557
\(694\) 0.938189 0.0356132
\(695\) −29.7832 −1.12974
\(696\) 40.7339 1.54402
\(697\) 1.47134 0.0557310
\(698\) −7.33606 −0.277674
\(699\) −14.4510 −0.546588
\(700\) 24.0101 0.907496
\(701\) −44.1461 −1.66738 −0.833688 0.552235i \(-0.813775\pi\)
−0.833688 + 0.552235i \(0.813775\pi\)
\(702\) 8.20731 0.309765
\(703\) −9.38503 −0.353963
\(704\) 13.0437 0.491602
\(705\) −77.0891 −2.90334
\(706\) 64.3032 2.42008
\(707\) 36.3528 1.36719
\(708\) 71.7924 2.69812
\(709\) −1.70949 −0.0642014 −0.0321007 0.999485i \(-0.510220\pi\)
−0.0321007 + 0.999485i \(0.510220\pi\)
\(710\) 41.5928 1.56095
\(711\) 8.90057 0.333797
\(712\) −21.0766 −0.789881
\(713\) 40.8075 1.52825
\(714\) 10.8593 0.406401
\(715\) −18.3095 −0.684736
\(716\) 76.9516 2.87582
\(717\) −37.1245 −1.38644
\(718\) −30.1496 −1.12517
\(719\) −7.86550 −0.293334 −0.146667 0.989186i \(-0.546855\pi\)
−0.146667 + 0.989186i \(0.546855\pi\)
\(720\) −3.75162 −0.139815
\(721\) 27.1889 1.01257
\(722\) 31.8029 1.18358
\(723\) −30.8199 −1.14620
\(724\) 70.1133 2.60574
\(725\) −22.8695 −0.849354
\(726\) −5.43547 −0.201729
\(727\) 9.50640 0.352573 0.176286 0.984339i \(-0.443591\pi\)
0.176286 + 0.984339i \(0.443591\pi\)
\(728\) −35.8796 −1.32978
\(729\) −22.5276 −0.834357
\(730\) 13.6593 0.505553
\(731\) 1.91059 0.0706656
\(732\) −12.9019 −0.476868
\(733\) 42.4248 1.56699 0.783497 0.621395i \(-0.213434\pi\)
0.783497 + 0.621395i \(0.213434\pi\)
\(734\) 26.1786 0.966271
\(735\) −14.2197 −0.524501
\(736\) 27.6369 1.01871
\(737\) −14.6108 −0.538194
\(738\) 10.2546 0.377477
\(739\) 31.0873 1.14357 0.571783 0.820405i \(-0.306252\pi\)
0.571783 + 0.820405i \(0.306252\pi\)
\(740\) 38.3279 1.40896
\(741\) −33.6679 −1.23682
\(742\) −45.5744 −1.67309
\(743\) 11.8372 0.434265 0.217133 0.976142i \(-0.430330\pi\)
0.217133 + 0.976142i \(0.430330\pi\)
\(744\) −55.9264 −2.05036
\(745\) 22.9052 0.839182
\(746\) 11.8585 0.434171
\(747\) −42.6793 −1.56156
\(748\) 2.80650 0.102616
\(749\) −16.8484 −0.615627
\(750\) 24.5606 0.896828
\(751\) −35.0759 −1.27994 −0.639969 0.768400i \(-0.721053\pi\)
−0.639969 + 0.768400i \(0.721053\pi\)
\(752\) 5.16915 0.188500
\(753\) 11.1379 0.405888
\(754\) 94.7199 3.44950
\(755\) −26.2811 −0.956466
\(756\) −4.00871 −0.145795
\(757\) −36.0009 −1.30847 −0.654237 0.756289i \(-0.727010\pi\)
−0.654237 + 0.756289i \(0.727010\pi\)
\(758\) −44.0422 −1.59968
\(759\) −10.7461 −0.390057
\(760\) 16.5424 0.600056
\(761\) −3.27360 −0.118668 −0.0593340 0.998238i \(-0.518898\pi\)
−0.0593340 + 0.998238i \(0.518898\pi\)
\(762\) −46.3124 −1.67772
\(763\) −21.8764 −0.791979
\(764\) 18.6946 0.676345
\(765\) −7.19509 −0.260139
\(766\) 36.2407 1.30943
\(767\) 60.2328 2.17488
\(768\) −30.8519 −1.11327
\(769\) 43.8610 1.58167 0.790835 0.612030i \(-0.209647\pi\)
0.790835 + 0.612030i \(0.209647\pi\)
\(770\) 14.6592 0.528282
\(771\) −40.4515 −1.45683
\(772\) 78.1798 2.81375
\(773\) −55.1511 −1.98365 −0.991823 0.127619i \(-0.959267\pi\)
−0.991823 + 0.127619i \(0.959267\pi\)
\(774\) 13.3160 0.478632
\(775\) 31.3992 1.12789
\(776\) 6.44726 0.231443
\(777\) 22.5340 0.808401
\(778\) 67.6197 2.42428
\(779\) 3.65225 0.130856
\(780\) 137.498 4.92321
\(781\) 6.31978 0.226140
\(782\) 9.09513 0.325241
\(783\) 3.81829 0.136454
\(784\) 0.953490 0.0340532
\(785\) −2.40323 −0.0857749
\(786\) −83.7333 −2.98667
\(787\) −15.2864 −0.544900 −0.272450 0.962170i \(-0.587834\pi\)
−0.272450 + 0.962170i \(0.587834\pi\)
\(788\) −14.5120 −0.516970
\(789\) −26.5914 −0.946680
\(790\) −21.2212 −0.755017
\(791\) −29.4652 −1.04766
\(792\) 7.05733 0.250771
\(793\) −10.8245 −0.384390
\(794\) −59.4642 −2.11030
\(795\) 63.0142 2.23488
\(796\) −4.17077 −0.147829
\(797\) 9.23811 0.327231 0.163615 0.986524i \(-0.447684\pi\)
0.163615 + 0.986524i \(0.447684\pi\)
\(798\) 26.9557 0.954222
\(799\) 9.91372 0.350722
\(800\) 21.2651 0.751835
\(801\) 22.7555 0.804027
\(802\) 62.2310 2.19745
\(803\) 2.07545 0.0732410
\(804\) 109.722 3.86958
\(805\) 28.9817 1.02147
\(806\) −130.048 −4.58073
\(807\) 35.9724 1.26629
\(808\) −41.7273 −1.46796
\(809\) 38.7649 1.36290 0.681450 0.731865i \(-0.261350\pi\)
0.681450 + 0.731865i \(0.261350\pi\)
\(810\) 63.5861 2.23419
\(811\) 20.3474 0.714493 0.357247 0.934010i \(-0.383716\pi\)
0.357247 + 0.934010i \(0.383716\pi\)
\(812\) −46.2642 −1.62356
\(813\) −32.6570 −1.14533
\(814\) 9.54620 0.334594
\(815\) −10.7203 −0.375515
\(816\) 1.00681 0.0352454
\(817\) 4.74257 0.165922
\(818\) −60.8217 −2.12658
\(819\) 38.7376 1.35360
\(820\) −14.9156 −0.520875
\(821\) 33.9620 1.18528 0.592641 0.805466i \(-0.298085\pi\)
0.592641 + 0.805466i \(0.298085\pi\)
\(822\) −37.9005 −1.32193
\(823\) 46.6641 1.62661 0.813304 0.581840i \(-0.197667\pi\)
0.813304 + 0.581840i \(0.197667\pi\)
\(824\) −31.2085 −1.08720
\(825\) −8.26851 −0.287873
\(826\) −48.2245 −1.67795
\(827\) 30.8221 1.07179 0.535895 0.844285i \(-0.319974\pi\)
0.535895 + 0.844285i \(0.319974\pi\)
\(828\) 38.6708 1.34390
\(829\) −14.4517 −0.501927 −0.250963 0.967997i \(-0.580747\pi\)
−0.250963 + 0.967997i \(0.580747\pi\)
\(830\) 101.758 3.53209
\(831\) 35.3996 1.22800
\(832\) −82.1814 −2.84913
\(833\) 1.82866 0.0633594
\(834\) 55.7065 1.92896
\(835\) −35.7778 −1.23814
\(836\) 6.96647 0.240941
\(837\) −5.24239 −0.181204
\(838\) 0.868164 0.0299902
\(839\) 19.3792 0.669045 0.334522 0.942388i \(-0.391425\pi\)
0.334522 + 0.942388i \(0.391425\pi\)
\(840\) −39.7192 −1.37044
\(841\) 15.0665 0.519535
\(842\) 13.8974 0.478937
\(843\) −70.6438 −2.43310
\(844\) 55.2933 1.90328
\(845\) 77.5800 2.66883
\(846\) 69.0943 2.37551
\(847\) 2.22739 0.0765339
\(848\) −4.22537 −0.145100
\(849\) −52.1430 −1.78954
\(850\) 6.99821 0.240036
\(851\) 18.8731 0.646960
\(852\) −47.4593 −1.62593
\(853\) 13.7587 0.471090 0.235545 0.971863i \(-0.424313\pi\)
0.235545 + 0.971863i \(0.424313\pi\)
\(854\) 8.66650 0.296562
\(855\) −17.8601 −0.610802
\(856\) 19.3393 0.661004
\(857\) 9.26259 0.316404 0.158202 0.987407i \(-0.449430\pi\)
0.158202 + 0.987407i \(0.449430\pi\)
\(858\) 34.2461 1.16914
\(859\) −33.7390 −1.15116 −0.575580 0.817746i \(-0.695224\pi\)
−0.575580 + 0.817746i \(0.695224\pi\)
\(860\) −19.3684 −0.660457
\(861\) −8.76925 −0.298855
\(862\) 30.6098 1.04257
\(863\) 30.2815 1.03079 0.515397 0.856952i \(-0.327645\pi\)
0.515397 + 0.856952i \(0.327645\pi\)
\(864\) −3.55041 −0.120787
\(865\) −21.2225 −0.721588
\(866\) 70.8569 2.40782
\(867\) −38.8703 −1.32010
\(868\) 63.5194 2.15599
\(869\) −3.22444 −0.109382
\(870\) 104.856 3.55496
\(871\) 92.0548 3.11916
\(872\) 25.1107 0.850354
\(873\) −6.96082 −0.235588
\(874\) 22.5765 0.763661
\(875\) −10.0646 −0.340247
\(876\) −15.5859 −0.526598
\(877\) 7.39214 0.249615 0.124807 0.992181i \(-0.460169\pi\)
0.124807 + 0.992181i \(0.460169\pi\)
\(878\) −32.4538 −1.09526
\(879\) 34.9536 1.17896
\(880\) 1.35911 0.0458157
\(881\) −50.0138 −1.68501 −0.842504 0.538691i \(-0.818919\pi\)
−0.842504 + 0.538691i \(0.818919\pi\)
\(882\) 12.7450 0.429146
\(883\) 28.2190 0.949645 0.474823 0.880082i \(-0.342512\pi\)
0.474823 + 0.880082i \(0.342512\pi\)
\(884\) −17.6823 −0.594721
\(885\) 66.6785 2.24137
\(886\) 34.8200 1.16980
\(887\) −28.8518 −0.968748 −0.484374 0.874861i \(-0.660953\pi\)
−0.484374 + 0.874861i \(0.660953\pi\)
\(888\) −25.8654 −0.867986
\(889\) 18.9782 0.636509
\(890\) −54.2550 −1.81863
\(891\) 9.66154 0.323674
\(892\) 4.29110 0.143677
\(893\) 24.6084 0.823490
\(894\) −42.8419 −1.43285
\(895\) 71.4703 2.38899
\(896\) 38.3001 1.27952
\(897\) 67.7053 2.26062
\(898\) −59.8063 −1.99576
\(899\) −60.5020 −2.01785
\(900\) 29.7551 0.991836
\(901\) −8.10368 −0.269973
\(902\) −3.71497 −0.123695
\(903\) −11.3872 −0.378941
\(904\) 33.8214 1.12488
\(905\) 65.1190 2.16463
\(906\) 49.1561 1.63310
\(907\) −28.4396 −0.944320 −0.472160 0.881513i \(-0.656526\pi\)
−0.472160 + 0.881513i \(0.656526\pi\)
\(908\) 9.35361 0.310411
\(909\) 45.0511 1.49425
\(910\) −92.3603 −3.06171
\(911\) −53.4627 −1.77130 −0.885649 0.464356i \(-0.846286\pi\)
−0.885649 + 0.464356i \(0.846286\pi\)
\(912\) 2.49917 0.0827557
\(913\) 15.4616 0.511704
\(914\) 73.1290 2.41889
\(915\) −11.9829 −0.396142
\(916\) −50.2072 −1.65889
\(917\) 34.3129 1.13311
\(918\) −1.16842 −0.0385635
\(919\) 16.4426 0.542392 0.271196 0.962524i \(-0.412581\pi\)
0.271196 + 0.962524i \(0.412581\pi\)
\(920\) −33.2664 −1.09676
\(921\) −75.2626 −2.47999
\(922\) 93.3197 3.07332
\(923\) −39.8177 −1.31061
\(924\) −16.7269 −0.550274
\(925\) 14.5218 0.477474
\(926\) 55.1293 1.81166
\(927\) 33.6944 1.10667
\(928\) −40.9750 −1.34507
\(929\) 25.9956 0.852888 0.426444 0.904514i \(-0.359766\pi\)
0.426444 + 0.904514i \(0.359766\pi\)
\(930\) −143.964 −4.72078
\(931\) 4.53922 0.148767
\(932\) −18.8395 −0.617109
\(933\) −52.0880 −1.70528
\(934\) −43.9784 −1.43902
\(935\) 2.60659 0.0852447
\(936\) −44.4646 −1.45337
\(937\) 7.09486 0.231779 0.115889 0.993262i \(-0.463028\pi\)
0.115889 + 0.993262i \(0.463028\pi\)
\(938\) −73.7024 −2.40647
\(939\) 32.7959 1.07025
\(940\) −100.499 −3.27793
\(941\) 14.7845 0.481960 0.240980 0.970530i \(-0.422531\pi\)
0.240980 + 0.970530i \(0.422531\pi\)
\(942\) 4.49500 0.146455
\(943\) −7.34459 −0.239173
\(944\) −4.47108 −0.145521
\(945\) −3.72317 −0.121115
\(946\) −4.82402 −0.156842
\(947\) −21.9232 −0.712408 −0.356204 0.934408i \(-0.615929\pi\)
−0.356204 + 0.934408i \(0.615929\pi\)
\(948\) 24.2144 0.786447
\(949\) −13.0763 −0.424475
\(950\) 17.3714 0.563602
\(951\) 35.5315 1.15219
\(952\) 5.10792 0.165549
\(953\) −21.2598 −0.688671 −0.344336 0.938847i \(-0.611896\pi\)
−0.344336 + 0.938847i \(0.611896\pi\)
\(954\) −56.4791 −1.82858
\(955\) 17.3629 0.561851
\(956\) −48.3985 −1.56532
\(957\) 15.9323 0.515018
\(958\) 11.9106 0.384815
\(959\) 15.5311 0.501527
\(960\) −90.9760 −2.93624
\(961\) 52.0674 1.67959
\(962\) −60.1457 −1.93917
\(963\) −20.8798 −0.672842
\(964\) −40.1793 −1.29409
\(965\) 72.6110 2.33743
\(966\) −54.2073 −1.74409
\(967\) −5.99138 −0.192670 −0.0963349 0.995349i \(-0.530712\pi\)
−0.0963349 + 0.995349i \(0.530712\pi\)
\(968\) −2.55669 −0.0821750
\(969\) 4.79306 0.153975
\(970\) 16.5964 0.532877
\(971\) −28.8081 −0.924495 −0.462248 0.886751i \(-0.652957\pi\)
−0.462248 + 0.886751i \(0.652957\pi\)
\(972\) −67.1554 −2.15401
\(973\) −22.8278 −0.731827
\(974\) 58.7350 1.88199
\(975\) 52.0956 1.66839
\(976\) 0.803504 0.0257195
\(977\) −39.6943 −1.26993 −0.634967 0.772539i \(-0.718986\pi\)
−0.634967 + 0.772539i \(0.718986\pi\)
\(978\) 20.0512 0.641168
\(979\) −8.24373 −0.263471
\(980\) −18.5379 −0.592172
\(981\) −27.1109 −0.865583
\(982\) 76.8956 2.45384
\(983\) 46.8682 1.49486 0.747431 0.664339i \(-0.231287\pi\)
0.747431 + 0.664339i \(0.231287\pi\)
\(984\) 10.0657 0.320883
\(985\) −13.4783 −0.429455
\(986\) −13.4846 −0.429437
\(987\) −59.0862 −1.88073
\(988\) −43.8921 −1.39639
\(989\) −9.53721 −0.303265
\(990\) 18.1668 0.577379
\(991\) 35.6494 1.13244 0.566220 0.824254i \(-0.308405\pi\)
0.566220 + 0.824254i \(0.308405\pi\)
\(992\) 56.2574 1.78617
\(993\) 28.4084 0.901513
\(994\) 31.8795 1.01116
\(995\) −3.87368 −0.122804
\(996\) −116.111 −3.67912
\(997\) −38.4897 −1.21898 −0.609490 0.792794i \(-0.708626\pi\)
−0.609490 + 0.792794i \(0.708626\pi\)
\(998\) −62.9629 −1.99305
\(999\) −2.42455 −0.0767094
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.1.17 121
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6017.2.a.f.1.17 121 1.1 even 1 trivial