Properties

Label 731.2.a.c.1.3
Level 731
Weight 2
Character 731.1
Self dual yes
Analytic conductor 5.837
Analytic rank 1
Dimension 6
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 731 = 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 731.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(5.83706438776\)
Analytic rank: \(1\)
Dimension: \(6\)
Coefficient field: 6.6.2460365.1
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(1.48737\)
Character \(\chi\) = 731.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.212277 q^{2} -2.83954 q^{3} -1.95494 q^{4} -1.65901 q^{5} +0.602769 q^{6} +2.53919 q^{7} +0.839542 q^{8} +5.06300 q^{9} +O(q^{10})\) \(q-0.212277 q^{2} -2.83954 q^{3} -1.95494 q^{4} -1.65901 q^{5} +0.602769 q^{6} +2.53919 q^{7} +0.839542 q^{8} +5.06300 q^{9} +0.352169 q^{10} +1.11540 q^{11} +5.55113 q^{12} +2.39509 q^{13} -0.539012 q^{14} +4.71083 q^{15} +3.73166 q^{16} -1.00000 q^{17} -1.07476 q^{18} -5.01350 q^{19} +3.24326 q^{20} -7.21014 q^{21} -0.236773 q^{22} +3.24795 q^{23} -2.38391 q^{24} -2.24769 q^{25} -0.508423 q^{26} -5.85797 q^{27} -4.96396 q^{28} -1.28054 q^{29} -1.00000 q^{30} +0.498801 q^{31} -2.47123 q^{32} -3.16722 q^{33} +0.212277 q^{34} -4.21254 q^{35} -9.89785 q^{36} -11.9871 q^{37} +1.06425 q^{38} -6.80097 q^{39} -1.39281 q^{40} +10.5784 q^{41} +1.53055 q^{42} -1.00000 q^{43} -2.18053 q^{44} -8.39957 q^{45} -0.689465 q^{46} +0.400325 q^{47} -10.5962 q^{48} -0.552508 q^{49} +0.477132 q^{50} +2.83954 q^{51} -4.68226 q^{52} -5.37685 q^{53} +1.24351 q^{54} -1.85045 q^{55} +2.13176 q^{56} +14.2360 q^{57} +0.271830 q^{58} +5.21308 q^{59} -9.20938 q^{60} +0.0130677 q^{61} -0.105884 q^{62} +12.8559 q^{63} -6.93874 q^{64} -3.97349 q^{65} +0.672327 q^{66} -8.24406 q^{67} +1.95494 q^{68} -9.22270 q^{69} +0.894226 q^{70} -8.15605 q^{71} +4.25060 q^{72} +5.99199 q^{73} +2.54459 q^{74} +6.38240 q^{75} +9.80108 q^{76} +2.83221 q^{77} +1.44369 q^{78} -1.43914 q^{79} -6.19086 q^{80} +1.44496 q^{81} -2.24555 q^{82} -1.09306 q^{83} +14.0954 q^{84} +1.65901 q^{85} +0.212277 q^{86} +3.63616 q^{87} +0.936422 q^{88} -10.7179 q^{89} +1.78303 q^{90} +6.08160 q^{91} -6.34955 q^{92} -1.41637 q^{93} -0.0849797 q^{94} +8.31744 q^{95} +7.01716 q^{96} -6.18621 q^{97} +0.117285 q^{98} +5.64725 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - q^{2} - 3q^{3} + 5q^{4} + 3q^{5} - 7q^{6} - 7q^{7} - 9q^{8} - 3q^{9} + O(q^{10}) \) \( 6q - q^{2} - 3q^{3} + 5q^{4} + 3q^{5} - 7q^{6} - 7q^{7} - 9q^{8} - 3q^{9} - 4q^{10} + 4q^{11} + 11q^{12} - 10q^{13} - 7q^{14} + q^{15} - q^{16} - 6q^{17} + q^{18} - 20q^{19} + q^{20} - 8q^{21} + 2q^{22} - 3q^{23} - 9q^{24} - 7q^{25} - 3q^{26} - 6q^{27} - 11q^{28} - 15q^{29} - 6q^{30} + 12q^{31} + q^{32} - 2q^{33} + q^{34} - 9q^{35} - 16q^{36} - 14q^{37} + 27q^{38} + 5q^{39} - 7q^{40} - 2q^{41} + 19q^{42} - 6q^{43} - 12q^{44} - 18q^{45} + 14q^{46} - 11q^{47} - 6q^{48} + 3q^{49} + 7q^{50} + 3q^{51} - 5q^{52} + 3q^{53} + 25q^{54} + 6q^{55} + 22q^{56} + 11q^{57} - 21q^{58} + 2q^{59} - q^{60} - 20q^{61} + 3q^{62} + 23q^{63} - 39q^{64} - 34q^{65} + 7q^{66} - 2q^{67} - 5q^{68} - 17q^{69} - q^{70} + q^{71} + 21q^{72} + 13q^{73} + 28q^{74} - 5q^{75} - 29q^{76} - 11q^{77} - 26q^{79} + 12q^{80} + 2q^{81} - 9q^{82} + 10q^{83} - 3q^{84} - 3q^{85} + q^{86} + 12q^{87} - 6q^{88} - 15q^{89} + 15q^{90} + 8q^{91} - 9q^{92} - 11q^{93} - 33q^{94} - 21q^{95} + 25q^{96} - 22q^{97} - 3q^{98} - 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.212277 −0.150102 −0.0750512 0.997180i \(-0.523912\pi\)
−0.0750512 + 0.997180i \(0.523912\pi\)
\(3\) −2.83954 −1.63941 −0.819705 0.572786i \(-0.805863\pi\)
−0.819705 + 0.572786i \(0.805863\pi\)
\(4\) −1.95494 −0.977469
\(5\) −1.65901 −0.741932 −0.370966 0.928646i \(-0.620973\pi\)
−0.370966 + 0.928646i \(0.620973\pi\)
\(6\) 0.602769 0.246079
\(7\) 2.53919 0.959724 0.479862 0.877344i \(-0.340687\pi\)
0.479862 + 0.877344i \(0.340687\pi\)
\(8\) 0.839542 0.296823
\(9\) 5.06300 1.68767
\(10\) 0.352169 0.111366
\(11\) 1.11540 0.336305 0.168152 0.985761i \(-0.446220\pi\)
0.168152 + 0.985761i \(0.446220\pi\)
\(12\) 5.55113 1.60247
\(13\) 2.39509 0.664280 0.332140 0.943230i \(-0.392229\pi\)
0.332140 + 0.943230i \(0.392229\pi\)
\(14\) −0.539012 −0.144057
\(15\) 4.71083 1.21633
\(16\) 3.73166 0.932915
\(17\) −1.00000 −0.242536
\(18\) −1.07476 −0.253323
\(19\) −5.01350 −1.15017 −0.575087 0.818092i \(-0.695032\pi\)
−0.575087 + 0.818092i \(0.695032\pi\)
\(20\) 3.24326 0.725216
\(21\) −7.21014 −1.57338
\(22\) −0.236773 −0.0504801
\(23\) 3.24795 0.677245 0.338622 0.940922i \(-0.390039\pi\)
0.338622 + 0.940922i \(0.390039\pi\)
\(24\) −2.38391 −0.486615
\(25\) −2.24769 −0.449537
\(26\) −0.508423 −0.0997100
\(27\) −5.85797 −1.12737
\(28\) −4.96396 −0.938101
\(29\) −1.28054 −0.237791 −0.118896 0.992907i \(-0.537935\pi\)
−0.118896 + 0.992907i \(0.537935\pi\)
\(30\) −1.00000 −0.182574
\(31\) 0.498801 0.0895873 0.0447936 0.998996i \(-0.485737\pi\)
0.0447936 + 0.998996i \(0.485737\pi\)
\(32\) −2.47123 −0.436856
\(33\) −3.16722 −0.551341
\(34\) 0.212277 0.0364052
\(35\) −4.21254 −0.712050
\(36\) −9.89785 −1.64964
\(37\) −11.9871 −1.97067 −0.985336 0.170625i \(-0.945421\pi\)
−0.985336 + 0.170625i \(0.945421\pi\)
\(38\) 1.06425 0.172644
\(39\) −6.80097 −1.08903
\(40\) −1.39281 −0.220222
\(41\) 10.5784 1.65207 0.826036 0.563617i \(-0.190591\pi\)
0.826036 + 0.563617i \(0.190591\pi\)
\(42\) 1.53055 0.236168
\(43\) −1.00000 −0.152499
\(44\) −2.18053 −0.328728
\(45\) −8.39957 −1.25213
\(46\) −0.689465 −0.101656
\(47\) 0.400325 0.0583934 0.0291967 0.999574i \(-0.490705\pi\)
0.0291967 + 0.999574i \(0.490705\pi\)
\(48\) −10.5962 −1.52943
\(49\) −0.552508 −0.0789297
\(50\) 0.477132 0.0674766
\(51\) 2.83954 0.397615
\(52\) −4.68226 −0.649313
\(53\) −5.37685 −0.738566 −0.369283 0.929317i \(-0.620397\pi\)
−0.369283 + 0.929317i \(0.620397\pi\)
\(54\) 1.24351 0.169221
\(55\) −1.85045 −0.249515
\(56\) 2.13176 0.284868
\(57\) 14.2360 1.88561
\(58\) 0.271830 0.0356930
\(59\) 5.21308 0.678685 0.339342 0.940663i \(-0.389796\pi\)
0.339342 + 0.940663i \(0.389796\pi\)
\(60\) −9.20938 −1.18893
\(61\) 0.0130677 0.00167314 0.000836571 1.00000i \(-0.499734\pi\)
0.000836571 1.00000i \(0.499734\pi\)
\(62\) −0.105884 −0.0134473
\(63\) 12.8559 1.61969
\(64\) −6.93874 −0.867342
\(65\) −3.97349 −0.492850
\(66\) 0.672327 0.0827577
\(67\) −8.24406 −1.00717 −0.503586 0.863945i \(-0.667986\pi\)
−0.503586 + 0.863945i \(0.667986\pi\)
\(68\) 1.95494 0.237071
\(69\) −9.22270 −1.11028
\(70\) 0.894226 0.106880
\(71\) −8.15605 −0.967946 −0.483973 0.875083i \(-0.660807\pi\)
−0.483973 + 0.875083i \(0.660807\pi\)
\(72\) 4.25060 0.500938
\(73\) 5.99199 0.701310 0.350655 0.936505i \(-0.385959\pi\)
0.350655 + 0.936505i \(0.385959\pi\)
\(74\) 2.54459 0.295803
\(75\) 6.38240 0.736976
\(76\) 9.80108 1.12426
\(77\) 2.83221 0.322760
\(78\) 1.44369 0.163466
\(79\) −1.43914 −0.161916 −0.0809579 0.996718i \(-0.525798\pi\)
−0.0809579 + 0.996718i \(0.525798\pi\)
\(80\) −6.19086 −0.692160
\(81\) 1.44496 0.160551
\(82\) −2.24555 −0.247980
\(83\) −1.09306 −0.119978 −0.0599892 0.998199i \(-0.519107\pi\)
−0.0599892 + 0.998199i \(0.519107\pi\)
\(84\) 14.0954 1.53793
\(85\) 1.65901 0.179945
\(86\) 0.212277 0.0228904
\(87\) 3.63616 0.389837
\(88\) 0.936422 0.0998229
\(89\) −10.7179 −1.13610 −0.568048 0.822995i \(-0.692301\pi\)
−0.568048 + 0.822995i \(0.692301\pi\)
\(90\) 1.78303 0.187948
\(91\) 6.08160 0.637525
\(92\) −6.34955 −0.661986
\(93\) −1.41637 −0.146870
\(94\) −0.0849797 −0.00876499
\(95\) 8.31744 0.853351
\(96\) 7.01716 0.716186
\(97\) −6.18621 −0.628115 −0.314057 0.949404i \(-0.601688\pi\)
−0.314057 + 0.949404i \(0.601688\pi\)
\(98\) 0.117285 0.0118475
\(99\) 5.64725 0.567570
\(100\) 4.39409 0.439409
\(101\) −1.95718 −0.194747 −0.0973736 0.995248i \(-0.531044\pi\)
−0.0973736 + 0.995248i \(0.531044\pi\)
\(102\) −0.602769 −0.0596830
\(103\) 7.26547 0.715888 0.357944 0.933743i \(-0.383478\pi\)
0.357944 + 0.933743i \(0.383478\pi\)
\(104\) 2.01078 0.197173
\(105\) 11.9617 1.16734
\(106\) 1.14138 0.110861
\(107\) 8.14989 0.787880 0.393940 0.919136i \(-0.371112\pi\)
0.393940 + 0.919136i \(0.371112\pi\)
\(108\) 11.4520 1.10197
\(109\) −16.1863 −1.55036 −0.775181 0.631739i \(-0.782342\pi\)
−0.775181 + 0.631739i \(0.782342\pi\)
\(110\) 0.392809 0.0374528
\(111\) 34.0380 3.23074
\(112\) 9.47540 0.895341
\(113\) 4.46484 0.420017 0.210008 0.977700i \(-0.432651\pi\)
0.210008 + 0.977700i \(0.432651\pi\)
\(114\) −3.02198 −0.283034
\(115\) −5.38839 −0.502470
\(116\) 2.50339 0.232433
\(117\) 12.1264 1.12108
\(118\) −1.10662 −0.101872
\(119\) −2.53919 −0.232767
\(120\) 3.95494 0.361035
\(121\) −9.75589 −0.886899
\(122\) −0.00277396 −0.000251143 0
\(123\) −30.0379 −2.70842
\(124\) −0.975125 −0.0875688
\(125\) 12.0240 1.07546
\(126\) −2.72901 −0.243120
\(127\) −0.291837 −0.0258963 −0.0129482 0.999916i \(-0.504122\pi\)
−0.0129482 + 0.999916i \(0.504122\pi\)
\(128\) 6.41539 0.567046
\(129\) 2.83954 0.250008
\(130\) 0.843479 0.0739780
\(131\) 0.474123 0.0414243 0.0207122 0.999785i \(-0.493407\pi\)
0.0207122 + 0.999785i \(0.493407\pi\)
\(132\) 6.19171 0.538919
\(133\) −12.7302 −1.10385
\(134\) 1.75002 0.151179
\(135\) 9.71843 0.836430
\(136\) −0.839542 −0.0719901
\(137\) −19.1328 −1.63463 −0.817314 0.576192i \(-0.804538\pi\)
−0.817314 + 0.576192i \(0.804538\pi\)
\(138\) 1.95777 0.166656
\(139\) −9.70162 −0.822881 −0.411440 0.911437i \(-0.634974\pi\)
−0.411440 + 0.911437i \(0.634974\pi\)
\(140\) 8.23526 0.696007
\(141\) −1.13674 −0.0957307
\(142\) 1.73134 0.145291
\(143\) 2.67148 0.223400
\(144\) 18.8934 1.57445
\(145\) 2.12444 0.176425
\(146\) −1.27196 −0.105268
\(147\) 1.56887 0.129398
\(148\) 23.4341 1.92627
\(149\) −20.2460 −1.65861 −0.829307 0.558793i \(-0.811265\pi\)
−0.829307 + 0.558793i \(0.811265\pi\)
\(150\) −1.35484 −0.110622
\(151\) −5.52591 −0.449692 −0.224846 0.974394i \(-0.572188\pi\)
−0.224846 + 0.974394i \(0.572188\pi\)
\(152\) −4.20904 −0.341398
\(153\) −5.06300 −0.409319
\(154\) −0.601212 −0.0484470
\(155\) −0.827516 −0.0664677
\(156\) 13.2955 1.06449
\(157\) −8.65527 −0.690766 −0.345383 0.938462i \(-0.612251\pi\)
−0.345383 + 0.938462i \(0.612251\pi\)
\(158\) 0.305496 0.0243040
\(159\) 15.2678 1.21081
\(160\) 4.09979 0.324117
\(161\) 8.24717 0.649968
\(162\) −0.306731 −0.0240991
\(163\) 19.2922 1.51108 0.755541 0.655102i \(-0.227374\pi\)
0.755541 + 0.655102i \(0.227374\pi\)
\(164\) −20.6802 −1.61485
\(165\) 5.25444 0.409058
\(166\) 0.232030 0.0180091
\(167\) 2.26648 0.175385 0.0876926 0.996148i \(-0.472051\pi\)
0.0876926 + 0.996148i \(0.472051\pi\)
\(168\) −6.05322 −0.467016
\(169\) −7.26352 −0.558733
\(170\) −0.352169 −0.0270102
\(171\) −25.3833 −1.94111
\(172\) 1.95494 0.149063
\(173\) −2.78795 −0.211964 −0.105982 0.994368i \(-0.533799\pi\)
−0.105982 + 0.994368i \(0.533799\pi\)
\(174\) −0.771872 −0.0585155
\(175\) −5.70730 −0.431432
\(176\) 4.16228 0.313744
\(177\) −14.8027 −1.11264
\(178\) 2.27517 0.170531
\(179\) −24.8463 −1.85710 −0.928549 0.371209i \(-0.878943\pi\)
−0.928549 + 0.371209i \(0.878943\pi\)
\(180\) 16.4206 1.22392
\(181\) −1.71039 −0.127132 −0.0635662 0.997978i \(-0.520247\pi\)
−0.0635662 + 0.997978i \(0.520247\pi\)
\(182\) −1.29098 −0.0956941
\(183\) −0.0371062 −0.00274297
\(184\) 2.72679 0.201022
\(185\) 19.8868 1.46210
\(186\) 0.300662 0.0220456
\(187\) −1.11540 −0.0815659
\(188\) −0.782611 −0.0570778
\(189\) −14.8745 −1.08196
\(190\) −1.76560 −0.128090
\(191\) 20.5373 1.48602 0.743012 0.669278i \(-0.233397\pi\)
0.743012 + 0.669278i \(0.233397\pi\)
\(192\) 19.7028 1.42193
\(193\) −13.1576 −0.947105 −0.473553 0.880766i \(-0.657029\pi\)
−0.473553 + 0.880766i \(0.657029\pi\)
\(194\) 1.31319 0.0942815
\(195\) 11.2829 0.807984
\(196\) 1.08012 0.0771513
\(197\) 15.4265 1.09909 0.549547 0.835463i \(-0.314800\pi\)
0.549547 + 0.835463i \(0.314800\pi\)
\(198\) −1.19878 −0.0851936
\(199\) 9.69335 0.687144 0.343572 0.939126i \(-0.388363\pi\)
0.343572 + 0.939126i \(0.388363\pi\)
\(200\) −1.88703 −0.133433
\(201\) 23.4094 1.65117
\(202\) 0.415465 0.0292320
\(203\) −3.25155 −0.228214
\(204\) −5.55113 −0.388657
\(205\) −17.5497 −1.22572
\(206\) −1.54229 −0.107457
\(207\) 16.4444 1.14296
\(208\) 8.93768 0.619717
\(209\) −5.59204 −0.386809
\(210\) −2.53919 −0.175221
\(211\) −20.9824 −1.44449 −0.722244 0.691639i \(-0.756889\pi\)
−0.722244 + 0.691639i \(0.756889\pi\)
\(212\) 10.5114 0.721926
\(213\) 23.1595 1.58686
\(214\) −1.73003 −0.118263
\(215\) 1.65901 0.113144
\(216\) −4.91801 −0.334628
\(217\) 1.26655 0.0859791
\(218\) 3.43597 0.232713
\(219\) −17.0145 −1.14973
\(220\) 3.61752 0.243893
\(221\) −2.39509 −0.161111
\(222\) −7.22547 −0.484942
\(223\) 14.4719 0.969109 0.484555 0.874761i \(-0.338982\pi\)
0.484555 + 0.874761i \(0.338982\pi\)
\(224\) −6.27492 −0.419261
\(225\) −11.3800 −0.758668
\(226\) −0.947783 −0.0630456
\(227\) 19.4270 1.28941 0.644706 0.764430i \(-0.276980\pi\)
0.644706 + 0.764430i \(0.276980\pi\)
\(228\) −27.8306 −1.84312
\(229\) −17.1473 −1.13312 −0.566562 0.824019i \(-0.691727\pi\)
−0.566562 + 0.824019i \(0.691727\pi\)
\(230\) 1.14383 0.0754219
\(231\) −8.04217 −0.529136
\(232\) −1.07507 −0.0705818
\(233\) −1.27543 −0.0835559 −0.0417780 0.999127i \(-0.513302\pi\)
−0.0417780 + 0.999127i \(0.513302\pi\)
\(234\) −2.57415 −0.168277
\(235\) −0.664143 −0.0433239
\(236\) −10.1912 −0.663393
\(237\) 4.08650 0.265446
\(238\) 0.539012 0.0349389
\(239\) −9.91245 −0.641183 −0.320592 0.947218i \(-0.603882\pi\)
−0.320592 + 0.947218i \(0.603882\pi\)
\(240\) 17.5792 1.13473
\(241\) −29.4709 −1.89839 −0.949193 0.314694i \(-0.898098\pi\)
−0.949193 + 0.314694i \(0.898098\pi\)
\(242\) 2.07095 0.133126
\(243\) 13.4709 0.864158
\(244\) −0.0255465 −0.00163544
\(245\) 0.916616 0.0585604
\(246\) 6.37635 0.406541
\(247\) −12.0078 −0.764038
\(248\) 0.418764 0.0265916
\(249\) 3.10378 0.196694
\(250\) −2.55241 −0.161429
\(251\) 16.6596 1.05155 0.525774 0.850624i \(-0.323776\pi\)
0.525774 + 0.850624i \(0.323776\pi\)
\(252\) −25.1325 −1.58320
\(253\) 3.62276 0.227761
\(254\) 0.0619502 0.00388710
\(255\) −4.71083 −0.295004
\(256\) 12.5156 0.782227
\(257\) −13.6655 −0.852434 −0.426217 0.904621i \(-0.640154\pi\)
−0.426217 + 0.904621i \(0.640154\pi\)
\(258\) −0.602769 −0.0375268
\(259\) −30.4376 −1.89130
\(260\) 7.76792 0.481746
\(261\) −6.48339 −0.401312
\(262\) −0.100645 −0.00621789
\(263\) −13.8793 −0.855835 −0.427917 0.903818i \(-0.640753\pi\)
−0.427917 + 0.903818i \(0.640753\pi\)
\(264\) −2.65901 −0.163651
\(265\) 8.92024 0.547966
\(266\) 2.70233 0.165691
\(267\) 30.4340 1.86253
\(268\) 16.1166 0.984480
\(269\) −1.13342 −0.0691057 −0.0345528 0.999403i \(-0.511001\pi\)
−0.0345528 + 0.999403i \(0.511001\pi\)
\(270\) −2.06300 −0.125550
\(271\) 15.3569 0.932868 0.466434 0.884556i \(-0.345538\pi\)
0.466434 + 0.884556i \(0.345538\pi\)
\(272\) −3.73166 −0.226265
\(273\) −17.2690 −1.04517
\(274\) 4.06146 0.245362
\(275\) −2.50706 −0.151181
\(276\) 18.0298 1.08527
\(277\) 24.7714 1.48837 0.744183 0.667975i \(-0.232839\pi\)
0.744183 + 0.667975i \(0.232839\pi\)
\(278\) 2.05943 0.123516
\(279\) 2.52543 0.151193
\(280\) −3.53661 −0.211353
\(281\) −0.0469321 −0.00279973 −0.00139987 0.999999i \(-0.500446\pi\)
−0.00139987 + 0.999999i \(0.500446\pi\)
\(282\) 0.241304 0.0143694
\(283\) −16.9012 −1.00467 −0.502335 0.864673i \(-0.667526\pi\)
−0.502335 + 0.864673i \(0.667526\pi\)
\(284\) 15.9446 0.946137
\(285\) −23.6177 −1.39899
\(286\) −0.567093 −0.0335329
\(287\) 26.8606 1.58553
\(288\) −12.5118 −0.737267
\(289\) 1.00000 0.0588235
\(290\) −0.450969 −0.0264818
\(291\) 17.5660 1.02974
\(292\) −11.7140 −0.685509
\(293\) 30.8356 1.80143 0.900717 0.434407i \(-0.143042\pi\)
0.900717 + 0.434407i \(0.143042\pi\)
\(294\) −0.333035 −0.0194230
\(295\) −8.64854 −0.503538
\(296\) −10.0637 −0.584941
\(297\) −6.53396 −0.379139
\(298\) 4.29775 0.248962
\(299\) 7.77915 0.449880
\(300\) −12.4772 −0.720371
\(301\) −2.53919 −0.146357
\(302\) 1.17302 0.0674999
\(303\) 5.55751 0.319271
\(304\) −18.7087 −1.07302
\(305\) −0.0216794 −0.00124136
\(306\) 1.07476 0.0614398
\(307\) 3.07155 0.175303 0.0876513 0.996151i \(-0.472064\pi\)
0.0876513 + 0.996151i \(0.472064\pi\)
\(308\) −5.53679 −0.315488
\(309\) −20.6306 −1.17363
\(310\) 0.175662 0.00997696
\(311\) −32.2382 −1.82806 −0.914030 0.405646i \(-0.867047\pi\)
−0.914030 + 0.405646i \(0.867047\pi\)
\(312\) −5.70970 −0.323248
\(313\) 0.706328 0.0399240 0.0199620 0.999801i \(-0.493645\pi\)
0.0199620 + 0.999801i \(0.493645\pi\)
\(314\) 1.83731 0.103686
\(315\) −21.3281 −1.20170
\(316\) 2.81343 0.158268
\(317\) 11.8604 0.666148 0.333074 0.942901i \(-0.391914\pi\)
0.333074 + 0.942901i \(0.391914\pi\)
\(318\) −3.24100 −0.181746
\(319\) −1.42831 −0.0799703
\(320\) 11.5114 0.643509
\(321\) −23.1420 −1.29166
\(322\) −1.75068 −0.0975618
\(323\) 5.01350 0.278958
\(324\) −2.82480 −0.156934
\(325\) −5.38342 −0.298618
\(326\) −4.09529 −0.226817
\(327\) 45.9616 2.54168
\(328\) 8.88103 0.490373
\(329\) 1.01650 0.0560416
\(330\) −1.11540 −0.0614006
\(331\) −24.7566 −1.36075 −0.680373 0.732866i \(-0.738182\pi\)
−0.680373 + 0.732866i \(0.738182\pi\)
\(332\) 2.13686 0.117275
\(333\) −60.6908 −3.32584
\(334\) −0.481120 −0.0263257
\(335\) 13.6770 0.747253
\(336\) −26.9058 −1.46783
\(337\) 13.2780 0.723296 0.361648 0.932315i \(-0.382214\pi\)
0.361648 + 0.932315i \(0.382214\pi\)
\(338\) 1.54188 0.0838671
\(339\) −12.6781 −0.688580
\(340\) −3.24326 −0.175891
\(341\) 0.556361 0.0301286
\(342\) 5.38829 0.291365
\(343\) −19.1773 −1.03547
\(344\) −0.839542 −0.0452651
\(345\) 15.3005 0.823754
\(346\) 0.591818 0.0318163
\(347\) 0.888881 0.0477177 0.0238588 0.999715i \(-0.492405\pi\)
0.0238588 + 0.999715i \(0.492405\pi\)
\(348\) −7.10847 −0.381054
\(349\) 26.9773 1.44406 0.722030 0.691862i \(-0.243209\pi\)
0.722030 + 0.691862i \(0.243209\pi\)
\(350\) 1.21153 0.0647589
\(351\) −14.0304 −0.748887
\(352\) −2.75640 −0.146917
\(353\) 22.5168 1.19845 0.599224 0.800581i \(-0.295476\pi\)
0.599224 + 0.800581i \(0.295476\pi\)
\(354\) 3.14228 0.167010
\(355\) 13.5310 0.718150
\(356\) 20.9529 1.11050
\(357\) 7.21014 0.381601
\(358\) 5.27429 0.278755
\(359\) 19.5922 1.03404 0.517018 0.855975i \(-0.327042\pi\)
0.517018 + 0.855975i \(0.327042\pi\)
\(360\) −7.05179 −0.371662
\(361\) 6.13514 0.322902
\(362\) 0.363077 0.0190829
\(363\) 27.7023 1.45399
\(364\) −11.8892 −0.623161
\(365\) −9.94078 −0.520324
\(366\) 0.00787678 0.000411726 0
\(367\) −8.26173 −0.431259 −0.215630 0.976475i \(-0.569180\pi\)
−0.215630 + 0.976475i \(0.569180\pi\)
\(368\) 12.1203 0.631812
\(369\) 53.5585 2.78815
\(370\) −4.22150 −0.219465
\(371\) −13.6528 −0.708820
\(372\) 2.76891 0.143561
\(373\) −18.9938 −0.983462 −0.491731 0.870747i \(-0.663636\pi\)
−0.491731 + 0.870747i \(0.663636\pi\)
\(374\) 0.236773 0.0122432
\(375\) −34.1426 −1.76312
\(376\) 0.336090 0.0173325
\(377\) −3.06702 −0.157960
\(378\) 3.15751 0.162405
\(379\) 22.6083 1.16131 0.580654 0.814150i \(-0.302797\pi\)
0.580654 + 0.814150i \(0.302797\pi\)
\(380\) −16.2601 −0.834125
\(381\) 0.828682 0.0424547
\(382\) −4.35958 −0.223056
\(383\) −16.3572 −0.835814 −0.417907 0.908490i \(-0.637236\pi\)
−0.417907 + 0.908490i \(0.637236\pi\)
\(384\) −18.2168 −0.929621
\(385\) −4.69866 −0.239466
\(386\) 2.79306 0.142163
\(387\) −5.06300 −0.257367
\(388\) 12.0937 0.613963
\(389\) −31.5393 −1.59911 −0.799554 0.600594i \(-0.794931\pi\)
−0.799554 + 0.600594i \(0.794931\pi\)
\(390\) −2.39509 −0.121280
\(391\) −3.24795 −0.164256
\(392\) −0.463853 −0.0234281
\(393\) −1.34629 −0.0679114
\(394\) −3.27469 −0.164977
\(395\) 2.38755 0.120131
\(396\) −11.0400 −0.554782
\(397\) −22.6234 −1.13543 −0.567717 0.823224i \(-0.692173\pi\)
−0.567717 + 0.823224i \(0.692173\pi\)
\(398\) −2.05767 −0.103142
\(399\) 36.1480 1.80966
\(400\) −8.38760 −0.419380
\(401\) 17.2056 0.859205 0.429603 0.903018i \(-0.358654\pi\)
0.429603 + 0.903018i \(0.358654\pi\)
\(402\) −4.96927 −0.247844
\(403\) 1.19468 0.0595110
\(404\) 3.82618 0.190359
\(405\) −2.39720 −0.119118
\(406\) 0.690228 0.0342554
\(407\) −13.3704 −0.662746
\(408\) 2.38391 0.118021
\(409\) −0.928413 −0.0459071 −0.0229535 0.999737i \(-0.507307\pi\)
−0.0229535 + 0.999737i \(0.507307\pi\)
\(410\) 3.72540 0.183984
\(411\) 54.3285 2.67983
\(412\) −14.2036 −0.699759
\(413\) 13.2370 0.651350
\(414\) −3.49076 −0.171562
\(415\) 1.81339 0.0890159
\(416\) −5.91883 −0.290194
\(417\) 27.5482 1.34904
\(418\) 1.18706 0.0580610
\(419\) −20.6047 −1.00660 −0.503302 0.864111i \(-0.667882\pi\)
−0.503302 + 0.864111i \(0.667882\pi\)
\(420\) −23.3844 −1.14104
\(421\) −25.6177 −1.24853 −0.624265 0.781213i \(-0.714601\pi\)
−0.624265 + 0.781213i \(0.714601\pi\)
\(422\) 4.45408 0.216821
\(423\) 2.02684 0.0985486
\(424\) −4.51409 −0.219223
\(425\) 2.24769 0.109029
\(426\) −4.91622 −0.238192
\(427\) 0.0331813 0.00160575
\(428\) −15.9325 −0.770129
\(429\) −7.58578 −0.366245
\(430\) −0.352169 −0.0169831
\(431\) 31.2758 1.50650 0.753250 0.657734i \(-0.228485\pi\)
0.753250 + 0.657734i \(0.228485\pi\)
\(432\) −21.8600 −1.05174
\(433\) −30.1102 −1.44700 −0.723502 0.690322i \(-0.757469\pi\)
−0.723502 + 0.690322i \(0.757469\pi\)
\(434\) −0.268859 −0.0129057
\(435\) −6.03243 −0.289233
\(436\) 31.6431 1.51543
\(437\) −16.2836 −0.778950
\(438\) 3.61179 0.172578
\(439\) 7.51969 0.358895 0.179448 0.983768i \(-0.442569\pi\)
0.179448 + 0.983768i \(0.442569\pi\)
\(440\) −1.55353 −0.0740618
\(441\) −2.79735 −0.133207
\(442\) 0.508423 0.0241832
\(443\) −4.83603 −0.229767 −0.114883 0.993379i \(-0.536649\pi\)
−0.114883 + 0.993379i \(0.536649\pi\)
\(444\) −66.5421 −3.15795
\(445\) 17.7811 0.842907
\(446\) −3.07205 −0.145466
\(447\) 57.4893 2.71915
\(448\) −17.6188 −0.832409
\(449\) 24.1377 1.13913 0.569565 0.821947i \(-0.307112\pi\)
0.569565 + 0.821947i \(0.307112\pi\)
\(450\) 2.41572 0.113878
\(451\) 11.7991 0.555600
\(452\) −8.72849 −0.410554
\(453\) 15.6911 0.737230
\(454\) −4.12389 −0.193544
\(455\) −10.0894 −0.473000
\(456\) 11.9517 0.559692
\(457\) −0.253686 −0.0118669 −0.00593347 0.999982i \(-0.501889\pi\)
−0.00593347 + 0.999982i \(0.501889\pi\)
\(458\) 3.63997 0.170085
\(459\) 5.85797 0.273427
\(460\) 10.5340 0.491149
\(461\) −24.3643 −1.13476 −0.567379 0.823457i \(-0.692042\pi\)
−0.567379 + 0.823457i \(0.692042\pi\)
\(462\) 1.70717 0.0794245
\(463\) −3.20234 −0.148825 −0.0744127 0.997228i \(-0.523708\pi\)
−0.0744127 + 0.997228i \(0.523708\pi\)
\(464\) −4.77856 −0.221839
\(465\) 2.34977 0.108968
\(466\) 0.270743 0.0125419
\(467\) 3.56529 0.164982 0.0824909 0.996592i \(-0.473712\pi\)
0.0824909 + 0.996592i \(0.473712\pi\)
\(468\) −23.7063 −1.09582
\(469\) −20.9332 −0.966608
\(470\) 0.140982 0.00650303
\(471\) 24.5770 1.13245
\(472\) 4.37660 0.201449
\(473\) −1.11540 −0.0512860
\(474\) −0.867469 −0.0398442
\(475\) 11.2688 0.517046
\(476\) 4.96396 0.227523
\(477\) −27.2230 −1.24645
\(478\) 2.10418 0.0962431
\(479\) −6.80763 −0.311048 −0.155524 0.987832i \(-0.549707\pi\)
−0.155524 + 0.987832i \(0.549707\pi\)
\(480\) −11.6415 −0.531361
\(481\) −28.7103 −1.30908
\(482\) 6.25599 0.284952
\(483\) −23.4182 −1.06556
\(484\) 19.0722 0.866917
\(485\) 10.2630 0.466018
\(486\) −2.85956 −0.129712
\(487\) 2.20169 0.0997679 0.0498840 0.998755i \(-0.484115\pi\)
0.0498840 + 0.998755i \(0.484115\pi\)
\(488\) 0.0109708 0.000496627 0
\(489\) −54.7810 −2.47728
\(490\) −0.194576 −0.00879006
\(491\) 24.9880 1.12769 0.563847 0.825879i \(-0.309321\pi\)
0.563847 + 0.825879i \(0.309321\pi\)
\(492\) 58.7222 2.64740
\(493\) 1.28054 0.0576728
\(494\) 2.54898 0.114684
\(495\) −9.36885 −0.421098
\(496\) 1.86136 0.0835774
\(497\) −20.7098 −0.928961
\(498\) −0.658860 −0.0295242
\(499\) 5.04332 0.225770 0.112885 0.993608i \(-0.463991\pi\)
0.112885 + 0.993608i \(0.463991\pi\)
\(500\) −23.5061 −1.05123
\(501\) −6.43575 −0.287528
\(502\) −3.53646 −0.157840
\(503\) −20.4975 −0.913938 −0.456969 0.889483i \(-0.651065\pi\)
−0.456969 + 0.889483i \(0.651065\pi\)
\(504\) 10.7931 0.480762
\(505\) 3.24699 0.144489
\(506\) −0.769027 −0.0341874
\(507\) 20.6251 0.915992
\(508\) 0.570523 0.0253129
\(509\) −27.7373 −1.22944 −0.614718 0.788747i \(-0.710730\pi\)
−0.614718 + 0.788747i \(0.710730\pi\)
\(510\) 1.00000 0.0442807
\(511\) 15.2148 0.673064
\(512\) −15.4876 −0.684460
\(513\) 29.3689 1.29667
\(514\) 2.90088 0.127952
\(515\) −12.0535 −0.531140
\(516\) −5.55113 −0.244375
\(517\) 0.446521 0.0196380
\(518\) 6.46120 0.283889
\(519\) 7.91651 0.347496
\(520\) −3.33591 −0.146289
\(521\) −9.37969 −0.410932 −0.205466 0.978664i \(-0.565871\pi\)
−0.205466 + 0.978664i \(0.565871\pi\)
\(522\) 1.37627 0.0602379
\(523\) −36.4986 −1.59597 −0.797986 0.602675i \(-0.794101\pi\)
−0.797986 + 0.602675i \(0.794101\pi\)
\(524\) −0.926881 −0.0404910
\(525\) 16.2061 0.707293
\(526\) 2.94626 0.128463
\(527\) −0.498801 −0.0217281
\(528\) −11.8190 −0.514355
\(529\) −12.4508 −0.541339
\(530\) −1.89356 −0.0822510
\(531\) 26.3938 1.14539
\(532\) 24.8868 1.07898
\(533\) 25.3363 1.09744
\(534\) −6.46043 −0.279570
\(535\) −13.5208 −0.584553
\(536\) −6.92124 −0.298952
\(537\) 70.5521 3.04455
\(538\) 0.240598 0.0103729
\(539\) −0.616265 −0.0265444
\(540\) −18.9989 −0.817584
\(541\) −21.2609 −0.914075 −0.457038 0.889447i \(-0.651090\pi\)
−0.457038 + 0.889447i \(0.651090\pi\)
\(542\) −3.25992 −0.140026
\(543\) 4.85673 0.208422
\(544\) 2.47123 0.105953
\(545\) 26.8532 1.15026
\(546\) 3.66580 0.156882
\(547\) 14.5000 0.619976 0.309988 0.950740i \(-0.399675\pi\)
0.309988 + 0.950740i \(0.399675\pi\)
\(548\) 37.4035 1.59780
\(549\) 0.0661615 0.00282371
\(550\) 0.532191 0.0226927
\(551\) 6.42000 0.273501
\(552\) −7.74284 −0.329557
\(553\) −3.65425 −0.155395
\(554\) −5.25839 −0.223407
\(555\) −56.4693 −2.39699
\(556\) 18.9661 0.804341
\(557\) 41.8703 1.77410 0.887052 0.461670i \(-0.152750\pi\)
0.887052 + 0.461670i \(0.152750\pi\)
\(558\) −0.536090 −0.0226945
\(559\) −2.39509 −0.101302
\(560\) −15.7198 −0.664282
\(561\) 3.16722 0.133720
\(562\) 0.00996259 0.000420247 0
\(563\) 30.3605 1.27954 0.639772 0.768565i \(-0.279029\pi\)
0.639772 + 0.768565i \(0.279029\pi\)
\(564\) 2.22226 0.0935739
\(565\) −7.40722 −0.311624
\(566\) 3.58773 0.150803
\(567\) 3.66902 0.154085
\(568\) −6.84735 −0.287308
\(569\) −1.79244 −0.0751431 −0.0375716 0.999294i \(-0.511962\pi\)
−0.0375716 + 0.999294i \(0.511962\pi\)
\(570\) 5.01350 0.209992
\(571\) 18.7085 0.782926 0.391463 0.920194i \(-0.371969\pi\)
0.391463 + 0.920194i \(0.371969\pi\)
\(572\) −5.22258 −0.218367
\(573\) −58.3164 −2.43620
\(574\) −5.70189 −0.237992
\(575\) −7.30037 −0.304447
\(576\) −35.1308 −1.46378
\(577\) 0.286316 0.0119195 0.00595975 0.999982i \(-0.498103\pi\)
0.00595975 + 0.999982i \(0.498103\pi\)
\(578\) −0.212277 −0.00882955
\(579\) 37.3616 1.55269
\(580\) −4.15314 −0.172450
\(581\) −2.77548 −0.115146
\(582\) −3.72886 −0.154566
\(583\) −5.99731 −0.248383
\(584\) 5.03053 0.208165
\(585\) −20.1178 −0.831767
\(586\) −6.54568 −0.270399
\(587\) −23.7797 −0.981495 −0.490748 0.871302i \(-0.663276\pi\)
−0.490748 + 0.871302i \(0.663276\pi\)
\(588\) −3.06704 −0.126483
\(589\) −2.50074 −0.103041
\(590\) 1.83589 0.0755822
\(591\) −43.8043 −1.80187
\(592\) −44.7319 −1.83847
\(593\) 16.1975 0.665152 0.332576 0.943076i \(-0.392082\pi\)
0.332576 + 0.943076i \(0.392082\pi\)
\(594\) 1.38701 0.0569097
\(595\) 4.21254 0.172697
\(596\) 39.5796 1.62124
\(597\) −27.5247 −1.12651
\(598\) −1.65133 −0.0675281
\(599\) 8.90490 0.363844 0.181922 0.983313i \(-0.441768\pi\)
0.181922 + 0.983313i \(0.441768\pi\)
\(600\) 5.35829 0.218751
\(601\) −5.00807 −0.204283 −0.102142 0.994770i \(-0.532569\pi\)
−0.102142 + 0.994770i \(0.532569\pi\)
\(602\) 0.539012 0.0219685
\(603\) −41.7397 −1.69977
\(604\) 10.8028 0.439561
\(605\) 16.1851 0.658019
\(606\) −1.17973 −0.0479233
\(607\) 35.2057 1.42895 0.714477 0.699659i \(-0.246665\pi\)
0.714477 + 0.699659i \(0.246665\pi\)
\(608\) 12.3895 0.502461
\(609\) 9.23290 0.374136
\(610\) 0.00460203 0.000186331 0
\(611\) 0.958816 0.0387895
\(612\) 9.89785 0.400097
\(613\) 23.4816 0.948411 0.474205 0.880414i \(-0.342735\pi\)
0.474205 + 0.880414i \(0.342735\pi\)
\(614\) −0.652019 −0.0263134
\(615\) 49.8331 2.00947
\(616\) 2.37776 0.0958025
\(617\) 8.17066 0.328939 0.164469 0.986382i \(-0.447409\pi\)
0.164469 + 0.986382i \(0.447409\pi\)
\(618\) 4.37940 0.176165
\(619\) 19.2859 0.775166 0.387583 0.921835i \(-0.373310\pi\)
0.387583 + 0.921835i \(0.373310\pi\)
\(620\) 1.61774 0.0649701
\(621\) −19.0264 −0.763504
\(622\) 6.84342 0.274396
\(623\) −27.2148 −1.09034
\(624\) −25.3789 −1.01597
\(625\) −8.70948 −0.348379
\(626\) −0.149937 −0.00599269
\(627\) 15.8788 0.634139
\(628\) 16.9205 0.675203
\(629\) 11.9871 0.477958
\(630\) 4.52746 0.180378
\(631\) 18.3501 0.730508 0.365254 0.930908i \(-0.380982\pi\)
0.365254 + 0.930908i \(0.380982\pi\)
\(632\) −1.20822 −0.0480603
\(633\) 59.5804 2.36811
\(634\) −2.51770 −0.0999905
\(635\) 0.484160 0.0192133
\(636\) −29.8476 −1.18353
\(637\) −1.32331 −0.0524314
\(638\) 0.303198 0.0120037
\(639\) −41.2941 −1.63357
\(640\) −10.6432 −0.420709
\(641\) 40.9509 1.61746 0.808732 0.588177i \(-0.200154\pi\)
0.808732 + 0.588177i \(0.200154\pi\)
\(642\) 4.91250 0.193881
\(643\) −29.1707 −1.15038 −0.575191 0.818019i \(-0.695072\pi\)
−0.575191 + 0.818019i \(0.695072\pi\)
\(644\) −16.1227 −0.635324
\(645\) −4.71083 −0.185489
\(646\) −1.06425 −0.0418723
\(647\) 33.5423 1.31868 0.659341 0.751844i \(-0.270835\pi\)
0.659341 + 0.751844i \(0.270835\pi\)
\(648\) 1.21310 0.0476552
\(649\) 5.81465 0.228245
\(650\) 1.14278 0.0448233
\(651\) −3.59642 −0.140955
\(652\) −37.7151 −1.47704
\(653\) −1.36258 −0.0533218 −0.0266609 0.999645i \(-0.508487\pi\)
−0.0266609 + 0.999645i \(0.508487\pi\)
\(654\) −9.75658 −0.381512
\(655\) −0.786575 −0.0307340
\(656\) 39.4751 1.54124
\(657\) 30.3374 1.18358
\(658\) −0.215780 −0.00841197
\(659\) −3.00400 −0.117019 −0.0585097 0.998287i \(-0.518635\pi\)
−0.0585097 + 0.998287i \(0.518635\pi\)
\(660\) −10.2721 −0.399841
\(661\) −45.7661 −1.78010 −0.890048 0.455868i \(-0.849329\pi\)
−0.890048 + 0.455868i \(0.849329\pi\)
\(662\) 5.25525 0.204251
\(663\) 6.80097 0.264128
\(664\) −0.917666 −0.0356124
\(665\) 21.1196 0.818982
\(666\) 12.8833 0.499216
\(667\) −4.15915 −0.161043
\(668\) −4.43082 −0.171434
\(669\) −41.0935 −1.58877
\(670\) −2.90331 −0.112165
\(671\) 0.0145756 0.000562686 0
\(672\) 17.8179 0.687341
\(673\) −18.0592 −0.696130 −0.348065 0.937470i \(-0.613161\pi\)
−0.348065 + 0.937470i \(0.613161\pi\)
\(674\) −2.81860 −0.108568
\(675\) 13.1669 0.506793
\(676\) 14.1997 0.546144
\(677\) 21.1629 0.813355 0.406677 0.913572i \(-0.366687\pi\)
0.406677 + 0.913572i \(0.366687\pi\)
\(678\) 2.69127 0.103358
\(679\) −15.7080 −0.602817
\(680\) 1.39281 0.0534118
\(681\) −55.1637 −2.11388
\(682\) −0.118103 −0.00452238
\(683\) 5.23314 0.200241 0.100120 0.994975i \(-0.468077\pi\)
0.100120 + 0.994975i \(0.468077\pi\)
\(684\) 49.6228 1.89738
\(685\) 31.7416 1.21278
\(686\) 4.07089 0.155427
\(687\) 48.6904 1.85766
\(688\) −3.73166 −0.142268
\(689\) −12.8781 −0.490615
\(690\) −3.24795 −0.123647
\(691\) −18.4677 −0.702543 −0.351272 0.936274i \(-0.614251\pi\)
−0.351272 + 0.936274i \(0.614251\pi\)
\(692\) 5.45028 0.207188
\(693\) 14.3395 0.544711
\(694\) −0.188689 −0.00716253
\(695\) 16.0951 0.610522
\(696\) 3.05271 0.115713
\(697\) −10.5784 −0.400686
\(698\) −5.72665 −0.216757
\(699\) 3.62163 0.136982
\(700\) 11.1574 0.421711
\(701\) −31.0116 −1.17129 −0.585645 0.810567i \(-0.699159\pi\)
−0.585645 + 0.810567i \(0.699159\pi\)
\(702\) 2.97833 0.112410
\(703\) 60.0974 2.26662
\(704\) −7.73945 −0.291691
\(705\) 1.88586 0.0710257
\(706\) −4.77980 −0.179890
\(707\) −4.96967 −0.186904
\(708\) 28.9385 1.08757
\(709\) 39.7743 1.49376 0.746878 0.664961i \(-0.231552\pi\)
0.746878 + 0.664961i \(0.231552\pi\)
\(710\) −2.87231 −0.107796
\(711\) −7.28636 −0.273260
\(712\) −8.99814 −0.337220
\(713\) 1.62008 0.0606725
\(714\) −1.53055 −0.0572792
\(715\) −4.43201 −0.165748
\(716\) 48.5730 1.81526
\(717\) 28.1468 1.05116
\(718\) −4.15897 −0.155211
\(719\) 27.8343 1.03804 0.519022 0.854761i \(-0.326296\pi\)
0.519022 + 0.854761i \(0.326296\pi\)
\(720\) −31.3443 −1.16813
\(721\) 18.4484 0.687055
\(722\) −1.30235 −0.0484684
\(723\) 83.6838 3.11223
\(724\) 3.34371 0.124268
\(725\) 2.87826 0.106896
\(726\) −5.88055 −0.218248
\(727\) 20.7165 0.768332 0.384166 0.923264i \(-0.374489\pi\)
0.384166 + 0.923264i \(0.374489\pi\)
\(728\) 5.10576 0.189232
\(729\) −42.5860 −1.57726
\(730\) 2.11020 0.0781019
\(731\) 1.00000 0.0369863
\(732\) 0.0725403 0.00268117
\(733\) 33.5896 1.24066 0.620330 0.784341i \(-0.286999\pi\)
0.620330 + 0.784341i \(0.286999\pi\)
\(734\) 1.75378 0.0647330
\(735\) −2.60277 −0.0960046
\(736\) −8.02644 −0.295858
\(737\) −9.19540 −0.338717
\(738\) −11.3692 −0.418507
\(739\) 24.8390 0.913716 0.456858 0.889540i \(-0.348975\pi\)
0.456858 + 0.889540i \(0.348975\pi\)
\(740\) −38.8774 −1.42916
\(741\) 34.0966 1.25257
\(742\) 2.89818 0.106396
\(743\) 3.14892 0.115523 0.0577614 0.998330i \(-0.481604\pi\)
0.0577614 + 0.998330i \(0.481604\pi\)
\(744\) −1.18910 −0.0435945
\(745\) 33.5883 1.23058
\(746\) 4.03194 0.147620
\(747\) −5.53414 −0.202484
\(748\) 2.18053 0.0797281
\(749\) 20.6941 0.756147
\(750\) 7.24769 0.264648
\(751\) 50.6694 1.84895 0.924476 0.381240i \(-0.124503\pi\)
0.924476 + 0.381240i \(0.124503\pi\)
\(752\) 1.49388 0.0544761
\(753\) −47.3058 −1.72392
\(754\) 0.651058 0.0237101
\(755\) 9.16755 0.333641
\(756\) 29.0787 1.05758
\(757\) −33.9812 −1.23507 −0.617534 0.786544i \(-0.711868\pi\)
−0.617534 + 0.786544i \(0.711868\pi\)
\(758\) −4.79921 −0.174315
\(759\) −10.2870 −0.373393
\(760\) 6.98284 0.253294
\(761\) 20.2111 0.732652 0.366326 0.930487i \(-0.380616\pi\)
0.366326 + 0.930487i \(0.380616\pi\)
\(762\) −0.175910 −0.00637255
\(763\) −41.1000 −1.48792
\(764\) −40.1491 −1.45254
\(765\) 8.39957 0.303687
\(766\) 3.47225 0.125458
\(767\) 12.4858 0.450836
\(768\) −35.5387 −1.28239
\(769\) 54.2117 1.95492 0.977461 0.211114i \(-0.0677091\pi\)
0.977461 + 0.211114i \(0.0677091\pi\)
\(770\) 0.997416 0.0359444
\(771\) 38.8039 1.39749
\(772\) 25.7223 0.925766
\(773\) −6.03236 −0.216969 −0.108485 0.994098i \(-0.534600\pi\)
−0.108485 + 0.994098i \(0.534600\pi\)
\(774\) 1.07476 0.0386314
\(775\) −1.12115 −0.0402728
\(776\) −5.19359 −0.186439
\(777\) 86.4289 3.10062
\(778\) 6.69507 0.240030
\(779\) −53.0349 −1.90017
\(780\) −22.0573 −0.789779
\(781\) −9.09724 −0.325525
\(782\) 0.689465 0.0246552
\(783\) 7.50139 0.268078
\(784\) −2.06177 −0.0736347
\(785\) 14.3592 0.512501
\(786\) 0.285787 0.0101937
\(787\) −42.1924 −1.50400 −0.751998 0.659165i \(-0.770910\pi\)
−0.751998 + 0.659165i \(0.770910\pi\)
\(788\) −30.1579 −1.07433
\(789\) 39.4109 1.40306
\(790\) −0.506821 −0.0180319
\(791\) 11.3371 0.403100
\(792\) 4.74110 0.168468
\(793\) 0.0312983 0.00111143
\(794\) 4.80242 0.170431
\(795\) −25.3294 −0.898341
\(796\) −18.9499 −0.671662
\(797\) 7.85342 0.278182 0.139091 0.990280i \(-0.455582\pi\)
0.139091 + 0.990280i \(0.455582\pi\)
\(798\) −7.67339 −0.271635
\(799\) −0.400325 −0.0141625
\(800\) 5.55455 0.196383
\(801\) −54.2648 −1.91735
\(802\) −3.65234 −0.128969
\(803\) 6.68345 0.235854
\(804\) −45.7639 −1.61397
\(805\) −13.6821 −0.482232
\(806\) −0.253602 −0.00893274
\(807\) 3.21839 0.113293
\(808\) −1.64314 −0.0578054
\(809\) 33.1598 1.16584 0.582919 0.812531i \(-0.301911\pi\)
0.582919 + 0.812531i \(0.301911\pi\)
\(810\) 0.508870 0.0178799
\(811\) −17.7207 −0.622259 −0.311130 0.950367i \(-0.600707\pi\)
−0.311130 + 0.950367i \(0.600707\pi\)
\(812\) 6.35657 0.223072
\(813\) −43.6067 −1.52935
\(814\) 2.83823 0.0994798
\(815\) −32.0059 −1.12112
\(816\) 10.5962 0.370942
\(817\) 5.01350 0.175400
\(818\) 0.197081 0.00689076
\(819\) 30.7911 1.07593
\(820\) 34.3086 1.19811
\(821\) −46.1710 −1.61138 −0.805689 0.592339i \(-0.798205\pi\)
−0.805689 + 0.592339i \(0.798205\pi\)
\(822\) −11.5327 −0.402249
\(823\) 29.8326 1.03990 0.519949 0.854197i \(-0.325951\pi\)
0.519949 + 0.854197i \(0.325951\pi\)
\(824\) 6.09967 0.212492
\(825\) 7.11890 0.247848
\(826\) −2.80991 −0.0977692
\(827\) −32.2143 −1.12020 −0.560101 0.828424i \(-0.689238\pi\)
−0.560101 + 0.828424i \(0.689238\pi\)
\(828\) −32.1477 −1.11721
\(829\) 29.4265 1.02203 0.511013 0.859573i \(-0.329270\pi\)
0.511013 + 0.859573i \(0.329270\pi\)
\(830\) −0.384941 −0.0133615
\(831\) −70.3393 −2.44004
\(832\) −16.6189 −0.576158
\(833\) 0.552508 0.0191433
\(834\) −5.84784 −0.202494
\(835\) −3.76011 −0.130124
\(836\) 10.9321 0.378094
\(837\) −2.92196 −0.100998
\(838\) 4.37389 0.151094
\(839\) −35.6961 −1.23237 −0.616183 0.787603i \(-0.711322\pi\)
−0.616183 + 0.787603i \(0.711322\pi\)
\(840\) 10.0423 0.346494
\(841\) −27.3602 −0.943455
\(842\) 5.43804 0.187407
\(843\) 0.133266 0.00458991
\(844\) 41.0193 1.41194
\(845\) 12.0503 0.414542
\(846\) −0.430252 −0.0147924
\(847\) −24.7721 −0.851178
\(848\) −20.0646 −0.689020
\(849\) 47.9916 1.64707
\(850\) −0.477132 −0.0163655
\(851\) −38.9336 −1.33463
\(852\) −45.2753 −1.55111
\(853\) 44.7203 1.53120 0.765598 0.643320i \(-0.222443\pi\)
0.765598 + 0.643320i \(0.222443\pi\)
\(854\) −0.00704362 −0.000241028 0
\(855\) 42.1112 1.44017
\(856\) 6.84218 0.233861
\(857\) −45.1768 −1.54321 −0.771605 0.636102i \(-0.780546\pi\)
−0.771605 + 0.636102i \(0.780546\pi\)
\(858\) 1.61029 0.0549742
\(859\) 39.5488 1.34939 0.674694 0.738098i \(-0.264276\pi\)
0.674694 + 0.738098i \(0.264276\pi\)
\(860\) −3.24326 −0.110594
\(861\) −76.2719 −2.59934
\(862\) −6.63912 −0.226129
\(863\) −47.9021 −1.63061 −0.815303 0.579034i \(-0.803430\pi\)
−0.815303 + 0.579034i \(0.803430\pi\)
\(864\) 14.4764 0.492497
\(865\) 4.62524 0.157263
\(866\) 6.39170 0.217199
\(867\) −2.83954 −0.0964359
\(868\) −2.47603 −0.0840419
\(869\) −1.60521 −0.0544531
\(870\) 1.28054 0.0434145
\(871\) −19.7453 −0.669044
\(872\) −13.5890 −0.460183
\(873\) −31.3208 −1.06005
\(874\) 3.45663 0.116922
\(875\) 30.5312 1.03214
\(876\) 33.2623 1.12383
\(877\) 33.5981 1.13453 0.567264 0.823536i \(-0.308002\pi\)
0.567264 + 0.823536i \(0.308002\pi\)
\(878\) −1.59626 −0.0538710
\(879\) −87.5589 −2.95329
\(880\) −6.90527 −0.232777
\(881\) 5.00316 0.168561 0.0842804 0.996442i \(-0.473141\pi\)
0.0842804 + 0.996442i \(0.473141\pi\)
\(882\) 0.593812 0.0199947
\(883\) −18.9288 −0.637005 −0.318503 0.947922i \(-0.603180\pi\)
−0.318503 + 0.947922i \(0.603180\pi\)
\(884\) 4.68226 0.157482
\(885\) 24.5579 0.825505
\(886\) 1.02658 0.0344885
\(887\) 22.5167 0.756037 0.378019 0.925798i \(-0.376606\pi\)
0.378019 + 0.925798i \(0.376606\pi\)
\(888\) 28.5763 0.958958
\(889\) −0.741029 −0.0248533
\(890\) −3.77452 −0.126522
\(891\) 1.61170 0.0539940
\(892\) −28.2916 −0.947274
\(893\) −2.00703 −0.0671626
\(894\) −12.2036 −0.408151
\(895\) 41.2202 1.37784
\(896\) 16.2899 0.544208
\(897\) −22.0892 −0.737538
\(898\) −5.12388 −0.170986
\(899\) −0.638737 −0.0213031
\(900\) 22.2473 0.741575
\(901\) 5.37685 0.179129
\(902\) −2.50468 −0.0833968
\(903\) 7.21014 0.239938
\(904\) 3.74842 0.124671
\(905\) 2.83756 0.0943236
\(906\) −3.33085 −0.110660
\(907\) −19.7476 −0.655709 −0.327855 0.944728i \(-0.606326\pi\)
−0.327855 + 0.944728i \(0.606326\pi\)
\(908\) −37.9785 −1.26036
\(909\) −9.90922 −0.328668
\(910\) 2.14175 0.0709985
\(911\) −45.3377 −1.50210 −0.751052 0.660243i \(-0.770453\pi\)
−0.751052 + 0.660243i \(0.770453\pi\)
\(912\) 53.1241 1.75911
\(913\) −1.21919 −0.0403493
\(914\) 0.0538517 0.00178126
\(915\) 0.0615595 0.00203509
\(916\) 33.5219 1.10759
\(917\) 1.20389 0.0397559
\(918\) −1.24351 −0.0410420
\(919\) −51.7641 −1.70754 −0.853771 0.520649i \(-0.825690\pi\)
−0.853771 + 0.520649i \(0.825690\pi\)
\(920\) −4.52378 −0.149144
\(921\) −8.72180 −0.287393
\(922\) 5.17197 0.170330
\(923\) −19.5345 −0.642987
\(924\) 15.7219 0.517214
\(925\) 26.9433 0.885890
\(926\) 0.679783 0.0223391
\(927\) 36.7851 1.20818
\(928\) 3.16452 0.103880
\(929\) −55.7602 −1.82943 −0.914716 0.404098i \(-0.867585\pi\)
−0.914716 + 0.404098i \(0.867585\pi\)
\(930\) −0.498801 −0.0163563
\(931\) 2.76999 0.0907829
\(932\) 2.49338 0.0816734
\(933\) 91.5417 2.99694
\(934\) −0.756828 −0.0247642
\(935\) 1.85045 0.0605163
\(936\) 10.1806 0.332763
\(937\) −3.30658 −0.108021 −0.0540106 0.998540i \(-0.517200\pi\)
−0.0540106 + 0.998540i \(0.517200\pi\)
\(938\) 4.44364 0.145090
\(939\) −2.00565 −0.0654518
\(940\) 1.29836 0.0423478
\(941\) −13.2953 −0.433415 −0.216708 0.976237i \(-0.569532\pi\)
−0.216708 + 0.976237i \(0.569532\pi\)
\(942\) −5.21713 −0.169983
\(943\) 34.3582 1.11886
\(944\) 19.4534 0.633155
\(945\) 24.6770 0.802742
\(946\) 0.236773 0.00769815
\(947\) −7.42234 −0.241194 −0.120597 0.992702i \(-0.538481\pi\)
−0.120597 + 0.992702i \(0.538481\pi\)
\(948\) −7.98885 −0.259466
\(949\) 14.3514 0.465866
\(950\) −2.39210 −0.0776099
\(951\) −33.6782 −1.09209
\(952\) −2.13176 −0.0690907
\(953\) −13.2058 −0.427777 −0.213888 0.976858i \(-0.568613\pi\)
−0.213888 + 0.976858i \(0.568613\pi\)
\(954\) 5.77880 0.187096
\(955\) −34.0715 −1.10253
\(956\) 19.3782 0.626737
\(957\) 4.05576 0.131104
\(958\) 1.44510 0.0466891
\(959\) −48.5819 −1.56879
\(960\) −32.6872 −1.05498
\(961\) −30.7512 −0.991974
\(962\) 6.09453 0.196496
\(963\) 41.2629 1.32968
\(964\) 57.6138 1.85561
\(965\) 21.8286 0.702688
\(966\) 4.97114 0.159944
\(967\) −16.1744 −0.520135 −0.260067 0.965591i \(-0.583745\pi\)
−0.260067 + 0.965591i \(0.583745\pi\)
\(968\) −8.19048 −0.263252
\(969\) −14.2360 −0.457327
\(970\) −2.17860 −0.0699505
\(971\) 51.3760 1.64873 0.824367 0.566056i \(-0.191531\pi\)
0.824367 + 0.566056i \(0.191531\pi\)
\(972\) −26.3348 −0.844688
\(973\) −24.6343 −0.789739
\(974\) −0.467367 −0.0149754
\(975\) 15.2864 0.489558
\(976\) 0.0487641 0.00156090
\(977\) 9.39621 0.300611 0.150306 0.988640i \(-0.451974\pi\)
0.150306 + 0.988640i \(0.451974\pi\)
\(978\) 11.6287 0.371846
\(979\) −11.9547 −0.382075
\(980\) −1.79193 −0.0572410
\(981\) −81.9510 −2.61649
\(982\) −5.30438 −0.169270
\(983\) −17.8674 −0.569883 −0.284942 0.958545i \(-0.591974\pi\)
−0.284942 + 0.958545i \(0.591974\pi\)
\(984\) −25.2181 −0.803922
\(985\) −25.5928 −0.815453
\(986\) −0.271830 −0.00865683
\(987\) −2.88640 −0.0918751
\(988\) 23.4745 0.746823
\(989\) −3.24795 −0.103279
\(990\) 1.98879 0.0632079
\(991\) −29.1968 −0.927467 −0.463733 0.885975i \(-0.653490\pi\)
−0.463733 + 0.885975i \(0.653490\pi\)
\(992\) −1.23265 −0.0391367
\(993\) 70.2974 2.23082
\(994\) 4.39621 0.139439
\(995\) −16.0814 −0.509814
\(996\) −6.06770 −0.192262
\(997\) −40.5691 −1.28484 −0.642419 0.766354i \(-0.722069\pi\)
−0.642419 + 0.766354i \(0.722069\pi\)
\(998\) −1.07058 −0.0338886
\(999\) 70.2203 2.22167
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 731.2.a.c.1.3 6
3.2 odd 2 6579.2.a.j.1.4 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
731.2.a.c.1.3 6 1.1 even 1 trivial
6579.2.a.j.1.4 6 3.2 odd 2