Properties

Label 8015.2.a.l.1.28
Level 8015
Weight 2
Character 8015.1
Self dual yes
Analytic conductor 64.000
Analytic rank 0
Dimension 62
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8015 = 5 \cdot 7 \cdot 229 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8015.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(64.0000972201\)
Analytic rank: \(0\)
Dimension: \(62\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.28
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.431324 q^{2} +3.18734 q^{3} -1.81396 q^{4} -1.00000 q^{5} -1.37477 q^{6} -1.00000 q^{7} +1.64505 q^{8} +7.15913 q^{9} +O(q^{10})\) \(q-0.431324 q^{2} +3.18734 q^{3} -1.81396 q^{4} -1.00000 q^{5} -1.37477 q^{6} -1.00000 q^{7} +1.64505 q^{8} +7.15913 q^{9} +0.431324 q^{10} +3.80287 q^{11} -5.78170 q^{12} -2.66079 q^{13} +0.431324 q^{14} -3.18734 q^{15} +2.91837 q^{16} +4.14418 q^{17} -3.08790 q^{18} +0.188739 q^{19} +1.81396 q^{20} -3.18734 q^{21} -1.64027 q^{22} -5.11240 q^{23} +5.24334 q^{24} +1.00000 q^{25} +1.14766 q^{26} +13.2565 q^{27} +1.81396 q^{28} +6.66693 q^{29} +1.37477 q^{30} -3.15228 q^{31} -4.54887 q^{32} +12.1210 q^{33} -1.78748 q^{34} +1.00000 q^{35} -12.9864 q^{36} -5.04444 q^{37} -0.0814076 q^{38} -8.48084 q^{39} -1.64505 q^{40} +11.6032 q^{41} +1.37477 q^{42} +8.17712 q^{43} -6.89826 q^{44} -7.15913 q^{45} +2.20510 q^{46} -0.591708 q^{47} +9.30183 q^{48} +1.00000 q^{49} -0.431324 q^{50} +13.2089 q^{51} +4.82657 q^{52} -4.28908 q^{53} -5.71786 q^{54} -3.80287 q^{55} -1.64505 q^{56} +0.601575 q^{57} -2.87560 q^{58} +8.59415 q^{59} +5.78170 q^{60} -12.1270 q^{61} +1.35965 q^{62} -7.15913 q^{63} -3.87471 q^{64} +2.66079 q^{65} -5.22810 q^{66} -11.5559 q^{67} -7.51737 q^{68} -16.2949 q^{69} -0.431324 q^{70} +7.44658 q^{71} +11.7771 q^{72} +2.33383 q^{73} +2.17579 q^{74} +3.18734 q^{75} -0.342365 q^{76} -3.80287 q^{77} +3.65799 q^{78} +7.64931 q^{79} -2.91837 q^{80} +20.7757 q^{81} -5.00474 q^{82} +5.54696 q^{83} +5.78170 q^{84} -4.14418 q^{85} -3.52699 q^{86} +21.2498 q^{87} +6.25592 q^{88} -12.3112 q^{89} +3.08790 q^{90} +2.66079 q^{91} +9.27369 q^{92} -10.0474 q^{93} +0.255218 q^{94} -0.188739 q^{95} -14.4988 q^{96} -10.2903 q^{97} -0.431324 q^{98} +27.2253 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} + O(q^{10}) \) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} - 2q^{10} - 13q^{11} + 37q^{12} + 31q^{13} - 2q^{14} - 11q^{15} + 64q^{16} + 30q^{17} + 18q^{18} + 20q^{19} - 64q^{20} - 11q^{21} + 7q^{22} + 29q^{24} + 62q^{25} + 59q^{27} - 64q^{28} - 29q^{29} - 3q^{30} + 20q^{31} + 22q^{32} + 72q^{33} + 13q^{34} + 62q^{35} + 53q^{36} + 35q^{37} + 34q^{38} - 6q^{39} - 15q^{40} + 13q^{41} - 3q^{42} - 4q^{43} - 44q^{44} - 69q^{45} - 19q^{46} + 58q^{47} + 64q^{48} + 62q^{49} + 2q^{50} - 30q^{51} + 82q^{52} + 18q^{53} + 22q^{54} + 13q^{55} - 15q^{56} + 21q^{57} + 18q^{58} - 11q^{59} - 37q^{60} + 24q^{61} + 48q^{62} - 69q^{63} + 65q^{64} - 31q^{65} + 25q^{66} - 6q^{67} + 65q^{68} + 27q^{69} + 2q^{70} - 35q^{71} + 53q^{72} + 116q^{73} - 69q^{74} + 11q^{75} + 65q^{76} + 13q^{77} + 102q^{78} - 83q^{79} - 64q^{80} + 126q^{81} + 71q^{82} + 84q^{83} - 37q^{84} - 30q^{85} + 24q^{86} + 49q^{87} + 20q^{88} - 16q^{89} - 18q^{90} - 31q^{91} + 19q^{92} + 65q^{93} + 54q^{94} - 20q^{95} + 17q^{96} + 155q^{97} + 2q^{98} + 6q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.431324 −0.304992 −0.152496 0.988304i \(-0.548731\pi\)
−0.152496 + 0.988304i \(0.548731\pi\)
\(3\) 3.18734 1.84021 0.920105 0.391671i \(-0.128103\pi\)
0.920105 + 0.391671i \(0.128103\pi\)
\(4\) −1.81396 −0.906980
\(5\) −1.00000 −0.447214
\(6\) −1.37477 −0.561249
\(7\) −1.00000 −0.377964
\(8\) 1.64505 0.581614
\(9\) 7.15913 2.38638
\(10\) 0.431324 0.136397
\(11\) 3.80287 1.14661 0.573305 0.819342i \(-0.305661\pi\)
0.573305 + 0.819342i \(0.305661\pi\)
\(12\) −5.78170 −1.66903
\(13\) −2.66079 −0.737970 −0.368985 0.929435i \(-0.620295\pi\)
−0.368985 + 0.929435i \(0.620295\pi\)
\(14\) 0.431324 0.115276
\(15\) −3.18734 −0.822967
\(16\) 2.91837 0.729592
\(17\) 4.14418 1.00511 0.502555 0.864545i \(-0.332393\pi\)
0.502555 + 0.864545i \(0.332393\pi\)
\(18\) −3.08790 −0.727825
\(19\) 0.188739 0.0432997 0.0216498 0.999766i \(-0.493108\pi\)
0.0216498 + 0.999766i \(0.493108\pi\)
\(20\) 1.81396 0.405614
\(21\) −3.18734 −0.695534
\(22\) −1.64027 −0.349707
\(23\) −5.11240 −1.06601 −0.533004 0.846112i \(-0.678937\pi\)
−0.533004 + 0.846112i \(0.678937\pi\)
\(24\) 5.24334 1.07029
\(25\) 1.00000 0.200000
\(26\) 1.14766 0.225075
\(27\) 13.2565 2.55122
\(28\) 1.81396 0.342806
\(29\) 6.66693 1.23802 0.619009 0.785384i \(-0.287535\pi\)
0.619009 + 0.785384i \(0.287535\pi\)
\(30\) 1.37477 0.250998
\(31\) −3.15228 −0.566165 −0.283083 0.959096i \(-0.591357\pi\)
−0.283083 + 0.959096i \(0.591357\pi\)
\(32\) −4.54887 −0.804133
\(33\) 12.1210 2.11000
\(34\) −1.78748 −0.306551
\(35\) 1.00000 0.169031
\(36\) −12.9864 −2.16439
\(37\) −5.04444 −0.829300 −0.414650 0.909981i \(-0.636096\pi\)
−0.414650 + 0.909981i \(0.636096\pi\)
\(38\) −0.0814076 −0.0132061
\(39\) −8.48084 −1.35802
\(40\) −1.64505 −0.260105
\(41\) 11.6032 1.81212 0.906058 0.423154i \(-0.139077\pi\)
0.906058 + 0.423154i \(0.139077\pi\)
\(42\) 1.37477 0.212132
\(43\) 8.17712 1.24700 0.623500 0.781824i \(-0.285710\pi\)
0.623500 + 0.781824i \(0.285710\pi\)
\(44\) −6.89826 −1.03995
\(45\) −7.15913 −1.06722
\(46\) 2.20510 0.325124
\(47\) −0.591708 −0.0863095 −0.0431548 0.999068i \(-0.513741\pi\)
−0.0431548 + 0.999068i \(0.513741\pi\)
\(48\) 9.30183 1.34260
\(49\) 1.00000 0.142857
\(50\) −0.431324 −0.0609984
\(51\) 13.2089 1.84961
\(52\) 4.82657 0.669324
\(53\) −4.28908 −0.589150 −0.294575 0.955628i \(-0.595178\pi\)
−0.294575 + 0.955628i \(0.595178\pi\)
\(54\) −5.71786 −0.778103
\(55\) −3.80287 −0.512780
\(56\) −1.64505 −0.219829
\(57\) 0.601575 0.0796806
\(58\) −2.87560 −0.377585
\(59\) 8.59415 1.11886 0.559432 0.828877i \(-0.311019\pi\)
0.559432 + 0.828877i \(0.311019\pi\)
\(60\) 5.78170 0.746415
\(61\) −12.1270 −1.55271 −0.776353 0.630299i \(-0.782932\pi\)
−0.776353 + 0.630299i \(0.782932\pi\)
\(62\) 1.35965 0.172676
\(63\) −7.15913 −0.901965
\(64\) −3.87471 −0.484338
\(65\) 2.66079 0.330030
\(66\) −5.22810 −0.643534
\(67\) −11.5559 −1.41178 −0.705890 0.708322i \(-0.749453\pi\)
−0.705890 + 0.708322i \(0.749453\pi\)
\(68\) −7.51737 −0.911615
\(69\) −16.2949 −1.96168
\(70\) −0.431324 −0.0515530
\(71\) 7.44658 0.883746 0.441873 0.897078i \(-0.354314\pi\)
0.441873 + 0.897078i \(0.354314\pi\)
\(72\) 11.7771 1.38795
\(73\) 2.33383 0.273154 0.136577 0.990629i \(-0.456390\pi\)
0.136577 + 0.990629i \(0.456390\pi\)
\(74\) 2.17579 0.252930
\(75\) 3.18734 0.368042
\(76\) −0.342365 −0.0392720
\(77\) −3.80287 −0.433378
\(78\) 3.65799 0.414185
\(79\) 7.64931 0.860615 0.430307 0.902682i \(-0.358405\pi\)
0.430307 + 0.902682i \(0.358405\pi\)
\(80\) −2.91837 −0.326284
\(81\) 20.7757 2.30841
\(82\) −5.00474 −0.552681
\(83\) 5.54696 0.608858 0.304429 0.952535i \(-0.401534\pi\)
0.304429 + 0.952535i \(0.401534\pi\)
\(84\) 5.78170 0.630836
\(85\) −4.14418 −0.449499
\(86\) −3.52699 −0.380325
\(87\) 21.2498 2.27821
\(88\) 6.25592 0.666884
\(89\) −12.3112 −1.30498 −0.652490 0.757798i \(-0.726275\pi\)
−0.652490 + 0.757798i \(0.726275\pi\)
\(90\) 3.08790 0.325493
\(91\) 2.66079 0.278927
\(92\) 9.27369 0.966849
\(93\) −10.0474 −1.04186
\(94\) 0.255218 0.0263237
\(95\) −0.188739 −0.0193642
\(96\) −14.4988 −1.47977
\(97\) −10.2903 −1.04483 −0.522413 0.852693i \(-0.674968\pi\)
−0.522413 + 0.852693i \(0.674968\pi\)
\(98\) −0.431324 −0.0435703
\(99\) 27.2253 2.73624
\(100\) −1.81396 −0.181396
\(101\) −4.91978 −0.489536 −0.244768 0.969582i \(-0.578712\pi\)
−0.244768 + 0.969582i \(0.578712\pi\)
\(102\) −5.69731 −0.564118
\(103\) 10.6717 1.05151 0.525757 0.850635i \(-0.323782\pi\)
0.525757 + 0.850635i \(0.323782\pi\)
\(104\) −4.37714 −0.429214
\(105\) 3.18734 0.311052
\(106\) 1.84998 0.179686
\(107\) 16.6958 1.61404 0.807020 0.590524i \(-0.201079\pi\)
0.807020 + 0.590524i \(0.201079\pi\)
\(108\) −24.0468 −2.31391
\(109\) −10.2366 −0.980488 −0.490244 0.871585i \(-0.663092\pi\)
−0.490244 + 0.871585i \(0.663092\pi\)
\(110\) 1.64027 0.156394
\(111\) −16.0783 −1.52609
\(112\) −2.91837 −0.275760
\(113\) 14.7513 1.38768 0.693841 0.720128i \(-0.255917\pi\)
0.693841 + 0.720128i \(0.255917\pi\)
\(114\) −0.259474 −0.0243019
\(115\) 5.11240 0.476734
\(116\) −12.0935 −1.12286
\(117\) −19.0489 −1.76107
\(118\) −3.70686 −0.341244
\(119\) −4.14418 −0.379896
\(120\) −5.24334 −0.478649
\(121\) 3.46186 0.314714
\(122\) 5.23067 0.473563
\(123\) 36.9833 3.33468
\(124\) 5.71810 0.513501
\(125\) −1.00000 −0.0894427
\(126\) 3.08790 0.275092
\(127\) −2.10873 −0.187120 −0.0935599 0.995614i \(-0.529825\pi\)
−0.0935599 + 0.995614i \(0.529825\pi\)
\(128\) 10.7690 0.951853
\(129\) 26.0633 2.29474
\(130\) −1.14766 −0.100657
\(131\) 17.5819 1.53614 0.768068 0.640368i \(-0.221218\pi\)
0.768068 + 0.640368i \(0.221218\pi\)
\(132\) −21.9871 −1.91373
\(133\) −0.188739 −0.0163657
\(134\) 4.98434 0.430581
\(135\) −13.2565 −1.14094
\(136\) 6.81738 0.584586
\(137\) −14.0926 −1.20402 −0.602008 0.798490i \(-0.705632\pi\)
−0.602008 + 0.798490i \(0.705632\pi\)
\(138\) 7.02840 0.598297
\(139\) −22.6086 −1.91764 −0.958820 0.284014i \(-0.908334\pi\)
−0.958820 + 0.284014i \(0.908334\pi\)
\(140\) −1.81396 −0.153308
\(141\) −1.88597 −0.158828
\(142\) −3.21189 −0.269535
\(143\) −10.1186 −0.846164
\(144\) 20.8930 1.74108
\(145\) −6.66693 −0.553658
\(146\) −1.00664 −0.0833097
\(147\) 3.18734 0.262887
\(148\) 9.15041 0.752159
\(149\) 17.8672 1.46374 0.731870 0.681444i \(-0.238648\pi\)
0.731870 + 0.681444i \(0.238648\pi\)
\(150\) −1.37477 −0.112250
\(151\) 10.5400 0.857732 0.428866 0.903368i \(-0.358913\pi\)
0.428866 + 0.903368i \(0.358913\pi\)
\(152\) 0.310485 0.0251837
\(153\) 29.6687 2.39857
\(154\) 1.64027 0.132177
\(155\) 3.15228 0.253197
\(156\) 15.3839 1.23170
\(157\) 18.3982 1.46834 0.734168 0.678968i \(-0.237573\pi\)
0.734168 + 0.678968i \(0.237573\pi\)
\(158\) −3.29933 −0.262481
\(159\) −13.6708 −1.08416
\(160\) 4.54887 0.359619
\(161\) 5.11240 0.402914
\(162\) −8.96106 −0.704048
\(163\) 23.9768 1.87801 0.939003 0.343909i \(-0.111751\pi\)
0.939003 + 0.343909i \(0.111751\pi\)
\(164\) −21.0477 −1.64355
\(165\) −12.1210 −0.943622
\(166\) −2.39253 −0.185697
\(167\) 23.7618 1.83875 0.919373 0.393387i \(-0.128697\pi\)
0.919373 + 0.393387i \(0.128697\pi\)
\(168\) −5.24334 −0.404532
\(169\) −5.92020 −0.455400
\(170\) 1.78748 0.137094
\(171\) 1.35121 0.103329
\(172\) −14.8330 −1.13100
\(173\) 21.0548 1.60077 0.800385 0.599487i \(-0.204629\pi\)
0.800385 + 0.599487i \(0.204629\pi\)
\(174\) −9.16553 −0.694837
\(175\) −1.00000 −0.0755929
\(176\) 11.0982 0.836558
\(177\) 27.3925 2.05894
\(178\) 5.31009 0.398008
\(179\) −17.6887 −1.32211 −0.661057 0.750336i \(-0.729892\pi\)
−0.661057 + 0.750336i \(0.729892\pi\)
\(180\) 12.9864 0.967947
\(181\) −11.7329 −0.872099 −0.436049 0.899923i \(-0.643623\pi\)
−0.436049 + 0.899923i \(0.643623\pi\)
\(182\) −1.14766 −0.0850704
\(183\) −38.6529 −2.85730
\(184\) −8.41016 −0.620005
\(185\) 5.04444 0.370874
\(186\) 4.33367 0.317760
\(187\) 15.7598 1.15247
\(188\) 1.07334 0.0782810
\(189\) −13.2565 −0.964272
\(190\) 0.0814076 0.00590593
\(191\) −13.0233 −0.942331 −0.471165 0.882045i \(-0.656166\pi\)
−0.471165 + 0.882045i \(0.656166\pi\)
\(192\) −12.3500 −0.891284
\(193\) 18.0577 1.29982 0.649912 0.760009i \(-0.274806\pi\)
0.649912 + 0.760009i \(0.274806\pi\)
\(194\) 4.43847 0.318663
\(195\) 8.48084 0.607325
\(196\) −1.81396 −0.129569
\(197\) 9.89014 0.704644 0.352322 0.935879i \(-0.385392\pi\)
0.352322 + 0.935879i \(0.385392\pi\)
\(198\) −11.7429 −0.834532
\(199\) −1.37522 −0.0974868 −0.0487434 0.998811i \(-0.515522\pi\)
−0.0487434 + 0.998811i \(0.515522\pi\)
\(200\) 1.64505 0.116323
\(201\) −36.8326 −2.59797
\(202\) 2.12202 0.149305
\(203\) −6.66693 −0.467927
\(204\) −23.9604 −1.67756
\(205\) −11.6032 −0.810403
\(206\) −4.60295 −0.320703
\(207\) −36.6003 −2.54390
\(208\) −7.76517 −0.538418
\(209\) 0.717751 0.0496479
\(210\) −1.37477 −0.0948685
\(211\) −11.3366 −0.780443 −0.390222 0.920721i \(-0.627602\pi\)
−0.390222 + 0.920721i \(0.627602\pi\)
\(212\) 7.78022 0.534348
\(213\) 23.7348 1.62628
\(214\) −7.20128 −0.492269
\(215\) −8.17712 −0.557675
\(216\) 21.8077 1.48383
\(217\) 3.15228 0.213990
\(218\) 4.41529 0.299041
\(219\) 7.43870 0.502661
\(220\) 6.89826 0.465081
\(221\) −11.0268 −0.741741
\(222\) 6.93497 0.465444
\(223\) 24.8557 1.66446 0.832230 0.554430i \(-0.187064\pi\)
0.832230 + 0.554430i \(0.187064\pi\)
\(224\) 4.54887 0.303934
\(225\) 7.15913 0.477275
\(226\) −6.36257 −0.423232
\(227\) −16.4839 −1.09407 −0.547036 0.837109i \(-0.684244\pi\)
−0.547036 + 0.837109i \(0.684244\pi\)
\(228\) −1.09123 −0.0722687
\(229\) 1.00000 0.0660819
\(230\) −2.20510 −0.145400
\(231\) −12.1210 −0.797506
\(232\) 10.9674 0.720048
\(233\) 14.6913 0.962461 0.481231 0.876594i \(-0.340190\pi\)
0.481231 + 0.876594i \(0.340190\pi\)
\(234\) 8.21626 0.537114
\(235\) 0.591708 0.0385988
\(236\) −15.5894 −1.01479
\(237\) 24.3810 1.58371
\(238\) 1.78748 0.115865
\(239\) −3.65923 −0.236696 −0.118348 0.992972i \(-0.537760\pi\)
−0.118348 + 0.992972i \(0.537760\pi\)
\(240\) −9.30183 −0.600431
\(241\) −15.3783 −0.990606 −0.495303 0.868720i \(-0.664943\pi\)
−0.495303 + 0.868720i \(0.664943\pi\)
\(242\) −1.49318 −0.0959853
\(243\) 26.4496 1.69674
\(244\) 21.9979 1.40827
\(245\) −1.00000 −0.0638877
\(246\) −15.9518 −1.01705
\(247\) −0.502195 −0.0319539
\(248\) −5.18566 −0.329289
\(249\) 17.6800 1.12043
\(250\) 0.431324 0.0272793
\(251\) 18.6118 1.17477 0.587383 0.809309i \(-0.300158\pi\)
0.587383 + 0.809309i \(0.300158\pi\)
\(252\) 12.9864 0.818064
\(253\) −19.4418 −1.22230
\(254\) 0.909547 0.0570700
\(255\) −13.2089 −0.827173
\(256\) 3.10449 0.194031
\(257\) 11.4758 0.715839 0.357919 0.933753i \(-0.383486\pi\)
0.357919 + 0.933753i \(0.383486\pi\)
\(258\) −11.2417 −0.699878
\(259\) 5.04444 0.313446
\(260\) −4.82657 −0.299331
\(261\) 47.7294 2.95438
\(262\) −7.58349 −0.468509
\(263\) −19.2988 −1.19002 −0.595008 0.803720i \(-0.702851\pi\)
−0.595008 + 0.803720i \(0.702851\pi\)
\(264\) 19.9398 1.22721
\(265\) 4.28908 0.263476
\(266\) 0.0814076 0.00499142
\(267\) −39.2398 −2.40144
\(268\) 20.9620 1.28046
\(269\) −14.8908 −0.907907 −0.453953 0.891025i \(-0.649987\pi\)
−0.453953 + 0.891025i \(0.649987\pi\)
\(270\) 5.71786 0.347978
\(271\) 13.9433 0.846993 0.423496 0.905898i \(-0.360803\pi\)
0.423496 + 0.905898i \(0.360803\pi\)
\(272\) 12.0942 0.733321
\(273\) 8.48084 0.513284
\(274\) 6.07849 0.367215
\(275\) 3.80287 0.229322
\(276\) 29.5584 1.77921
\(277\) −17.9895 −1.08089 −0.540444 0.841380i \(-0.681744\pi\)
−0.540444 + 0.841380i \(0.681744\pi\)
\(278\) 9.75165 0.584865
\(279\) −22.5675 −1.35108
\(280\) 1.64505 0.0983106
\(281\) 22.1310 1.32023 0.660113 0.751166i \(-0.270508\pi\)
0.660113 + 0.751166i \(0.270508\pi\)
\(282\) 0.813466 0.0484412
\(283\) −30.3258 −1.80268 −0.901341 0.433109i \(-0.857416\pi\)
−0.901341 + 0.433109i \(0.857416\pi\)
\(284\) −13.5078 −0.801540
\(285\) −0.601575 −0.0356342
\(286\) 4.36441 0.258073
\(287\) −11.6032 −0.684915
\(288\) −32.5659 −1.91896
\(289\) 0.174190 0.0102465
\(290\) 2.87560 0.168861
\(291\) −32.7988 −1.92270
\(292\) −4.23347 −0.247745
\(293\) 19.3863 1.13256 0.566280 0.824213i \(-0.308382\pi\)
0.566280 + 0.824213i \(0.308382\pi\)
\(294\) −1.37477 −0.0801785
\(295\) −8.59415 −0.500371
\(296\) −8.29836 −0.482332
\(297\) 50.4130 2.92526
\(298\) −7.70656 −0.446429
\(299\) 13.6030 0.786683
\(300\) −5.78170 −0.333807
\(301\) −8.17712 −0.471321
\(302\) −4.54615 −0.261602
\(303\) −15.6810 −0.900850
\(304\) 0.550810 0.0315911
\(305\) 12.1270 0.694391
\(306\) −12.7968 −0.731545
\(307\) 28.8830 1.64844 0.824219 0.566271i \(-0.191615\pi\)
0.824219 + 0.566271i \(0.191615\pi\)
\(308\) 6.89826 0.393065
\(309\) 34.0143 1.93501
\(310\) −1.35965 −0.0772230
\(311\) 0.982883 0.0557342 0.0278671 0.999612i \(-0.491128\pi\)
0.0278671 + 0.999612i \(0.491128\pi\)
\(312\) −13.9514 −0.789843
\(313\) 3.23297 0.182738 0.0913692 0.995817i \(-0.470876\pi\)
0.0913692 + 0.995817i \(0.470876\pi\)
\(314\) −7.93557 −0.447830
\(315\) 7.15913 0.403371
\(316\) −13.8755 −0.780560
\(317\) 14.4678 0.812592 0.406296 0.913741i \(-0.366820\pi\)
0.406296 + 0.913741i \(0.366820\pi\)
\(318\) 5.89652 0.330660
\(319\) 25.3535 1.41952
\(320\) 3.87471 0.216603
\(321\) 53.2150 2.97017
\(322\) −2.20510 −0.122885
\(323\) 0.782167 0.0435210
\(324\) −37.6863 −2.09369
\(325\) −2.66079 −0.147594
\(326\) −10.3418 −0.572777
\(327\) −32.6275 −1.80430
\(328\) 19.0879 1.05395
\(329\) 0.591708 0.0326219
\(330\) 5.22810 0.287797
\(331\) −30.5538 −1.67939 −0.839693 0.543061i \(-0.817265\pi\)
−0.839693 + 0.543061i \(0.817265\pi\)
\(332\) −10.0620 −0.552222
\(333\) −36.1138 −1.97902
\(334\) −10.2490 −0.560803
\(335\) 11.5559 0.631367
\(336\) −9.30183 −0.507457
\(337\) −31.4380 −1.71254 −0.856268 0.516533i \(-0.827222\pi\)
−0.856268 + 0.516533i \(0.827222\pi\)
\(338\) 2.55352 0.138893
\(339\) 47.0173 2.55363
\(340\) 7.51737 0.407687
\(341\) −11.9877 −0.649171
\(342\) −0.582807 −0.0315146
\(343\) −1.00000 −0.0539949
\(344\) 13.4518 0.725272
\(345\) 16.2949 0.877291
\(346\) −9.08145 −0.488222
\(347\) 6.81509 0.365853 0.182927 0.983127i \(-0.441443\pi\)
0.182927 + 0.983127i \(0.441443\pi\)
\(348\) −38.5462 −2.06629
\(349\) −1.51865 −0.0812914 −0.0406457 0.999174i \(-0.512941\pi\)
−0.0406457 + 0.999174i \(0.512941\pi\)
\(350\) 0.431324 0.0230552
\(351\) −35.2729 −1.88273
\(352\) −17.2988 −0.922027
\(353\) 19.4322 1.03427 0.517136 0.855903i \(-0.326998\pi\)
0.517136 + 0.855903i \(0.326998\pi\)
\(354\) −11.8150 −0.627961
\(355\) −7.44658 −0.395223
\(356\) 22.3319 1.18359
\(357\) −13.2089 −0.699089
\(358\) 7.62955 0.403234
\(359\) 16.9024 0.892074 0.446037 0.895015i \(-0.352835\pi\)
0.446037 + 0.895015i \(0.352835\pi\)
\(360\) −11.7771 −0.620709
\(361\) −18.9644 −0.998125
\(362\) 5.06067 0.265983
\(363\) 11.0341 0.579140
\(364\) −4.82657 −0.252981
\(365\) −2.33383 −0.122158
\(366\) 16.6719 0.871455
\(367\) −17.8773 −0.933186 −0.466593 0.884472i \(-0.654519\pi\)
−0.466593 + 0.884472i \(0.654519\pi\)
\(368\) −14.9199 −0.777752
\(369\) 83.0688 4.32439
\(370\) −2.17579 −0.113114
\(371\) 4.28908 0.222678
\(372\) 18.2255 0.944949
\(373\) 0.860712 0.0445660 0.0222830 0.999752i \(-0.492907\pi\)
0.0222830 + 0.999752i \(0.492907\pi\)
\(374\) −6.79757 −0.351494
\(375\) −3.18734 −0.164593
\(376\) −0.973391 −0.0501988
\(377\) −17.7393 −0.913620
\(378\) 5.71786 0.294095
\(379\) 7.68378 0.394689 0.197345 0.980334i \(-0.436768\pi\)
0.197345 + 0.980334i \(0.436768\pi\)
\(380\) 0.342365 0.0175630
\(381\) −6.72125 −0.344340
\(382\) 5.61724 0.287403
\(383\) −2.46551 −0.125982 −0.0629909 0.998014i \(-0.520064\pi\)
−0.0629909 + 0.998014i \(0.520064\pi\)
\(384\) 34.3244 1.75161
\(385\) 3.80287 0.193812
\(386\) −7.78873 −0.396436
\(387\) 58.5411 2.97581
\(388\) 18.6663 0.947636
\(389\) 23.8264 1.20805 0.604023 0.796967i \(-0.293563\pi\)
0.604023 + 0.796967i \(0.293563\pi\)
\(390\) −3.65799 −0.185229
\(391\) −21.1867 −1.07146
\(392\) 1.64505 0.0830876
\(393\) 56.0394 2.82682
\(394\) −4.26585 −0.214911
\(395\) −7.64931 −0.384879
\(396\) −49.3855 −2.48172
\(397\) 9.21387 0.462431 0.231215 0.972903i \(-0.425730\pi\)
0.231215 + 0.972903i \(0.425730\pi\)
\(398\) 0.593165 0.0297327
\(399\) −0.601575 −0.0301164
\(400\) 2.91837 0.145918
\(401\) −8.71805 −0.435359 −0.217679 0.976020i \(-0.569849\pi\)
−0.217679 + 0.976020i \(0.569849\pi\)
\(402\) 15.8868 0.792361
\(403\) 8.38754 0.417813
\(404\) 8.92428 0.444000
\(405\) −20.7757 −1.03235
\(406\) 2.87560 0.142714
\(407\) −19.1834 −0.950884
\(408\) 21.7293 1.07576
\(409\) −0.578684 −0.0286141 −0.0143070 0.999898i \(-0.504554\pi\)
−0.0143070 + 0.999898i \(0.504554\pi\)
\(410\) 5.00474 0.247166
\(411\) −44.9180 −2.21564
\(412\) −19.3580 −0.953701
\(413\) −8.59415 −0.422890
\(414\) 15.7866 0.775868
\(415\) −5.54696 −0.272289
\(416\) 12.1036 0.593427
\(417\) −72.0614 −3.52886
\(418\) −0.309583 −0.0151422
\(419\) 17.2738 0.843880 0.421940 0.906624i \(-0.361349\pi\)
0.421940 + 0.906624i \(0.361349\pi\)
\(420\) −5.78170 −0.282118
\(421\) −15.7648 −0.768329 −0.384165 0.923265i \(-0.625511\pi\)
−0.384165 + 0.923265i \(0.625511\pi\)
\(422\) 4.88974 0.238029
\(423\) −4.23612 −0.205967
\(424\) −7.05576 −0.342658
\(425\) 4.14418 0.201022
\(426\) −10.2374 −0.496002
\(427\) 12.1270 0.586867
\(428\) −30.2854 −1.46390
\(429\) −32.2516 −1.55712
\(430\) 3.52699 0.170086
\(431\) 15.6648 0.754549 0.377275 0.926101i \(-0.376861\pi\)
0.377275 + 0.926101i \(0.376861\pi\)
\(432\) 38.6875 1.86135
\(433\) 21.7596 1.04570 0.522850 0.852425i \(-0.324869\pi\)
0.522850 + 0.852425i \(0.324869\pi\)
\(434\) −1.35965 −0.0652653
\(435\) −21.2498 −1.01885
\(436\) 18.5688 0.889283
\(437\) −0.964909 −0.0461579
\(438\) −3.20849 −0.153307
\(439\) 12.3074 0.587399 0.293700 0.955898i \(-0.405113\pi\)
0.293700 + 0.955898i \(0.405113\pi\)
\(440\) −6.25592 −0.298240
\(441\) 7.15913 0.340911
\(442\) 4.75611 0.226225
\(443\) 19.7789 0.939722 0.469861 0.882740i \(-0.344304\pi\)
0.469861 + 0.882740i \(0.344304\pi\)
\(444\) 29.1654 1.38413
\(445\) 12.3112 0.583604
\(446\) −10.7209 −0.507647
\(447\) 56.9489 2.69359
\(448\) 3.87471 0.183063
\(449\) 0.916740 0.0432636 0.0216318 0.999766i \(-0.493114\pi\)
0.0216318 + 0.999766i \(0.493114\pi\)
\(450\) −3.08790 −0.145565
\(451\) 44.1255 2.07779
\(452\) −26.7582 −1.25860
\(453\) 33.5945 1.57841
\(454\) 7.10988 0.333683
\(455\) −2.66079 −0.124740
\(456\) 0.989622 0.0463433
\(457\) 39.4881 1.84718 0.923588 0.383386i \(-0.125242\pi\)
0.923588 + 0.383386i \(0.125242\pi\)
\(458\) −0.431324 −0.0201544
\(459\) 54.9375 2.56426
\(460\) −9.27369 −0.432388
\(461\) −15.2780 −0.711566 −0.355783 0.934569i \(-0.615786\pi\)
−0.355783 + 0.934569i \(0.615786\pi\)
\(462\) 5.22810 0.243233
\(463\) 41.0319 1.90691 0.953456 0.301531i \(-0.0974978\pi\)
0.953456 + 0.301531i \(0.0974978\pi\)
\(464\) 19.4566 0.903248
\(465\) 10.0474 0.465936
\(466\) −6.33672 −0.293543
\(467\) −11.5529 −0.534603 −0.267302 0.963613i \(-0.586132\pi\)
−0.267302 + 0.963613i \(0.586132\pi\)
\(468\) 34.5540 1.59726
\(469\) 11.5559 0.533603
\(470\) −0.255218 −0.0117723
\(471\) 58.6412 2.70205
\(472\) 14.1378 0.650746
\(473\) 31.0966 1.42982
\(474\) −10.5161 −0.483020
\(475\) 0.188739 0.00865994
\(476\) 7.51737 0.344558
\(477\) −30.7061 −1.40593
\(478\) 1.57831 0.0721904
\(479\) 23.1406 1.05732 0.528661 0.848833i \(-0.322694\pi\)
0.528661 + 0.848833i \(0.322694\pi\)
\(480\) 14.4988 0.661775
\(481\) 13.4222 0.611999
\(482\) 6.63304 0.302127
\(483\) 16.2949 0.741446
\(484\) −6.27967 −0.285439
\(485\) 10.2903 0.467260
\(486\) −11.4084 −0.517493
\(487\) −12.3142 −0.558009 −0.279005 0.960290i \(-0.590005\pi\)
−0.279005 + 0.960290i \(0.590005\pi\)
\(488\) −19.9496 −0.903074
\(489\) 76.4221 3.45593
\(490\) 0.431324 0.0194852
\(491\) 6.07097 0.273979 0.136989 0.990573i \(-0.456257\pi\)
0.136989 + 0.990573i \(0.456257\pi\)
\(492\) −67.0863 −3.02448
\(493\) 27.6289 1.24434
\(494\) 0.216609 0.00974568
\(495\) −27.2253 −1.22368
\(496\) −9.19951 −0.413070
\(497\) −7.44658 −0.334025
\(498\) −7.62582 −0.341721
\(499\) 1.10464 0.0494504 0.0247252 0.999694i \(-0.492129\pi\)
0.0247252 + 0.999694i \(0.492129\pi\)
\(500\) 1.81396 0.0811227
\(501\) 75.7370 3.38368
\(502\) −8.02770 −0.358294
\(503\) −25.8473 −1.15248 −0.576238 0.817282i \(-0.695480\pi\)
−0.576238 + 0.817282i \(0.695480\pi\)
\(504\) −11.7771 −0.524595
\(505\) 4.91978 0.218927
\(506\) 8.38572 0.372791
\(507\) −18.8697 −0.838032
\(508\) 3.82516 0.169714
\(509\) 16.9051 0.749306 0.374653 0.927165i \(-0.377762\pi\)
0.374653 + 0.927165i \(0.377762\pi\)
\(510\) 5.69731 0.252281
\(511\) −2.33383 −0.103242
\(512\) −22.8770 −1.01103
\(513\) 2.50203 0.110467
\(514\) −4.94977 −0.218325
\(515\) −10.6717 −0.470251
\(516\) −47.2777 −2.08128
\(517\) −2.25019 −0.0989633
\(518\) −2.17579 −0.0955985
\(519\) 67.1089 2.94575
\(520\) 4.37714 0.191950
\(521\) −3.68794 −0.161571 −0.0807857 0.996731i \(-0.525743\pi\)
−0.0807857 + 0.996731i \(0.525743\pi\)
\(522\) −20.5868 −0.901061
\(523\) 26.3095 1.15043 0.575216 0.818001i \(-0.304918\pi\)
0.575216 + 0.818001i \(0.304918\pi\)
\(524\) −31.8928 −1.39324
\(525\) −3.18734 −0.139107
\(526\) 8.32404 0.362945
\(527\) −13.0636 −0.569059
\(528\) 35.3737 1.53944
\(529\) 3.13663 0.136375
\(530\) −1.84998 −0.0803581
\(531\) 61.5266 2.67003
\(532\) 0.342365 0.0148434
\(533\) −30.8737 −1.33729
\(534\) 16.9251 0.732419
\(535\) −16.6958 −0.721821
\(536\) −19.0101 −0.821110
\(537\) −56.3798 −2.43297
\(538\) 6.42275 0.276904
\(539\) 3.80287 0.163801
\(540\) 24.0468 1.03481
\(541\) −29.9342 −1.28697 −0.643486 0.765458i \(-0.722513\pi\)
−0.643486 + 0.765458i \(0.722513\pi\)
\(542\) −6.01406 −0.258326
\(543\) −37.3967 −1.60485
\(544\) −18.8513 −0.808243
\(545\) 10.2366 0.438488
\(546\) −3.65799 −0.156547
\(547\) −25.5394 −1.09199 −0.545993 0.837790i \(-0.683847\pi\)
−0.545993 + 0.837790i \(0.683847\pi\)
\(548\) 25.5635 1.09202
\(549\) −86.8188 −3.70534
\(550\) −1.64027 −0.0699414
\(551\) 1.25831 0.0536058
\(552\) −26.8060 −1.14094
\(553\) −7.64931 −0.325282
\(554\) 7.75932 0.329662
\(555\) 16.0783 0.682487
\(556\) 41.0112 1.73926
\(557\) 2.12199 0.0899116 0.0449558 0.998989i \(-0.485685\pi\)
0.0449558 + 0.998989i \(0.485685\pi\)
\(558\) 9.73392 0.412070
\(559\) −21.7576 −0.920248
\(560\) 2.91837 0.123324
\(561\) 50.2318 2.12079
\(562\) −9.54564 −0.402658
\(563\) 25.4240 1.07149 0.535747 0.844379i \(-0.320030\pi\)
0.535747 + 0.844379i \(0.320030\pi\)
\(564\) 3.42108 0.144054
\(565\) −14.7513 −0.620590
\(566\) 13.0802 0.549804
\(567\) −20.7757 −0.872498
\(568\) 12.2500 0.513999
\(569\) 34.2223 1.43467 0.717337 0.696726i \(-0.245361\pi\)
0.717337 + 0.696726i \(0.245361\pi\)
\(570\) 0.259474 0.0108682
\(571\) −37.6687 −1.57638 −0.788192 0.615429i \(-0.788983\pi\)
−0.788192 + 0.615429i \(0.788983\pi\)
\(572\) 18.3548 0.767454
\(573\) −41.5096 −1.73409
\(574\) 5.00474 0.208894
\(575\) −5.11240 −0.213202
\(576\) −27.7395 −1.15581
\(577\) −32.1430 −1.33813 −0.669066 0.743203i \(-0.733306\pi\)
−0.669066 + 0.743203i \(0.733306\pi\)
\(578\) −0.0751323 −0.00312509
\(579\) 57.5561 2.39195
\(580\) 12.0935 0.502157
\(581\) −5.54696 −0.230127
\(582\) 14.1469 0.586408
\(583\) −16.3108 −0.675526
\(584\) 3.83927 0.158870
\(585\) 19.0489 0.787576
\(586\) −8.36177 −0.345421
\(587\) −28.5355 −1.17779 −0.588893 0.808211i \(-0.700436\pi\)
−0.588893 + 0.808211i \(0.700436\pi\)
\(588\) −5.78170 −0.238433
\(589\) −0.594957 −0.0245148
\(590\) 3.70686 0.152609
\(591\) 31.5232 1.29669
\(592\) −14.7215 −0.605051
\(593\) 37.2555 1.52990 0.764951 0.644089i \(-0.222763\pi\)
0.764951 + 0.644089i \(0.222763\pi\)
\(594\) −21.7443 −0.892180
\(595\) 4.14418 0.169895
\(596\) −32.4104 −1.32758
\(597\) −4.38329 −0.179396
\(598\) −5.86731 −0.239932
\(599\) −10.5346 −0.430432 −0.215216 0.976566i \(-0.569046\pi\)
−0.215216 + 0.976566i \(0.569046\pi\)
\(600\) 5.24334 0.214058
\(601\) −8.77443 −0.357916 −0.178958 0.983857i \(-0.557273\pi\)
−0.178958 + 0.983857i \(0.557273\pi\)
\(602\) 3.52699 0.143749
\(603\) −82.7303 −3.36904
\(604\) −19.1191 −0.777946
\(605\) −3.46186 −0.140744
\(606\) 6.76359 0.274752
\(607\) 36.5587 1.48387 0.741935 0.670471i \(-0.233908\pi\)
0.741935 + 0.670471i \(0.233908\pi\)
\(608\) −0.858548 −0.0348187
\(609\) −21.2498 −0.861084
\(610\) −5.23067 −0.211784
\(611\) 1.57441 0.0636939
\(612\) −53.8178 −2.17546
\(613\) −43.1191 −1.74156 −0.870781 0.491670i \(-0.836386\pi\)
−0.870781 + 0.491670i \(0.836386\pi\)
\(614\) −12.4579 −0.502760
\(615\) −36.9833 −1.49131
\(616\) −6.25592 −0.252058
\(617\) 29.9756 1.20677 0.603386 0.797449i \(-0.293818\pi\)
0.603386 + 0.797449i \(0.293818\pi\)
\(618\) −14.6712 −0.590161
\(619\) −46.9897 −1.88868 −0.944339 0.328975i \(-0.893297\pi\)
−0.944339 + 0.328975i \(0.893297\pi\)
\(620\) −5.71810 −0.229644
\(621\) −67.7728 −2.71963
\(622\) −0.423941 −0.0169985
\(623\) 12.3112 0.493236
\(624\) −24.7502 −0.990802
\(625\) 1.00000 0.0400000
\(626\) −1.39446 −0.0557337
\(627\) 2.28771 0.0913625
\(628\) −33.3736 −1.33175
\(629\) −20.9050 −0.833538
\(630\) −3.08790 −0.123025
\(631\) −4.43882 −0.176707 −0.0883534 0.996089i \(-0.528160\pi\)
−0.0883534 + 0.996089i \(0.528160\pi\)
\(632\) 12.5835 0.500545
\(633\) −36.1336 −1.43618
\(634\) −6.24030 −0.247834
\(635\) 2.10873 0.0836825
\(636\) 24.7982 0.983312
\(637\) −2.66079 −0.105424
\(638\) −10.9356 −0.432943
\(639\) 53.3110 2.10895
\(640\) −10.7690 −0.425681
\(641\) −2.17254 −0.0858104 −0.0429052 0.999079i \(-0.513661\pi\)
−0.0429052 + 0.999079i \(0.513661\pi\)
\(642\) −22.9529 −0.905879
\(643\) 13.2621 0.523004 0.261502 0.965203i \(-0.415782\pi\)
0.261502 + 0.965203i \(0.415782\pi\)
\(644\) −9.27369 −0.365434
\(645\) −26.0633 −1.02624
\(646\) −0.337367 −0.0132735
\(647\) 2.15262 0.0846283 0.0423141 0.999104i \(-0.486527\pi\)
0.0423141 + 0.999104i \(0.486527\pi\)
\(648\) 34.1771 1.34260
\(649\) 32.6825 1.28290
\(650\) 1.14766 0.0450150
\(651\) 10.0474 0.393787
\(652\) −43.4929 −1.70331
\(653\) −8.59362 −0.336294 −0.168147 0.985762i \(-0.553778\pi\)
−0.168147 + 0.985762i \(0.553778\pi\)
\(654\) 14.0730 0.550298
\(655\) −17.5819 −0.686981
\(656\) 33.8624 1.32211
\(657\) 16.7082 0.651848
\(658\) −0.255218 −0.00994943
\(659\) −0.271480 −0.0105753 −0.00528767 0.999986i \(-0.501683\pi\)
−0.00528767 + 0.999986i \(0.501683\pi\)
\(660\) 21.9871 0.855847
\(661\) 36.6340 1.42490 0.712449 0.701724i \(-0.247586\pi\)
0.712449 + 0.701724i \(0.247586\pi\)
\(662\) 13.1786 0.512199
\(663\) −35.1461 −1.36496
\(664\) 9.12503 0.354120
\(665\) 0.188739 0.00731898
\(666\) 15.5767 0.603586
\(667\) −34.0840 −1.31974
\(668\) −43.1030 −1.66771
\(669\) 79.2235 3.06296
\(670\) −4.98434 −0.192562
\(671\) −46.1175 −1.78035
\(672\) 14.4988 0.559302
\(673\) −25.2255 −0.972372 −0.486186 0.873855i \(-0.661612\pi\)
−0.486186 + 0.873855i \(0.661612\pi\)
\(674\) 13.5599 0.522309
\(675\) 13.2565 0.510245
\(676\) 10.7390 0.413039
\(677\) −39.5064 −1.51835 −0.759177 0.650884i \(-0.774398\pi\)
−0.759177 + 0.650884i \(0.774398\pi\)
\(678\) −20.2797 −0.778836
\(679\) 10.2903 0.394907
\(680\) −6.81738 −0.261435
\(681\) −52.5396 −2.01332
\(682\) 5.17058 0.197992
\(683\) 4.74035 0.181385 0.0906923 0.995879i \(-0.471092\pi\)
0.0906923 + 0.995879i \(0.471092\pi\)
\(684\) −2.45103 −0.0937176
\(685\) 14.0926 0.538452
\(686\) 0.431324 0.0164680
\(687\) 3.18734 0.121605
\(688\) 23.8639 0.909801
\(689\) 11.4123 0.434776
\(690\) −7.02840 −0.267567
\(691\) −3.87633 −0.147463 −0.0737313 0.997278i \(-0.523491\pi\)
−0.0737313 + 0.997278i \(0.523491\pi\)
\(692\) −38.1926 −1.45187
\(693\) −27.2253 −1.03420
\(694\) −2.93951 −0.111582
\(695\) 22.6086 0.857595
\(696\) 34.9569 1.32504
\(697\) 48.0857 1.82138
\(698\) 0.655029 0.0247932
\(699\) 46.8262 1.77113
\(700\) 1.81396 0.0685612
\(701\) −40.6005 −1.53346 −0.766729 0.641971i \(-0.778117\pi\)
−0.766729 + 0.641971i \(0.778117\pi\)
\(702\) 15.2140 0.574217
\(703\) −0.952082 −0.0359085
\(704\) −14.7350 −0.555347
\(705\) 1.88597 0.0710299
\(706\) −8.38157 −0.315444
\(707\) 4.91978 0.185027
\(708\) −49.6888 −1.86742
\(709\) −5.15024 −0.193421 −0.0967107 0.995313i \(-0.530832\pi\)
−0.0967107 + 0.995313i \(0.530832\pi\)
\(710\) 3.21189 0.120540
\(711\) 54.7624 2.05375
\(712\) −20.2525 −0.758994
\(713\) 16.1157 0.603537
\(714\) 5.69731 0.213216
\(715\) 10.1186 0.378416
\(716\) 32.0865 1.19913
\(717\) −11.6632 −0.435571
\(718\) −7.29040 −0.272075
\(719\) −12.2737 −0.457730 −0.228865 0.973458i \(-0.573501\pi\)
−0.228865 + 0.973458i \(0.573501\pi\)
\(720\) −20.8930 −0.778635
\(721\) −10.6717 −0.397435
\(722\) 8.17979 0.304420
\(723\) −49.0160 −1.82292
\(724\) 21.2830 0.790976
\(725\) 6.66693 0.247604
\(726\) −4.75927 −0.176633
\(727\) 22.5932 0.837936 0.418968 0.908001i \(-0.362392\pi\)
0.418968 + 0.908001i \(0.362392\pi\)
\(728\) 4.37714 0.162227
\(729\) 21.9767 0.813954
\(730\) 1.00664 0.0372572
\(731\) 33.8874 1.25337
\(732\) 70.1148 2.59152
\(733\) −41.6416 −1.53807 −0.769034 0.639208i \(-0.779262\pi\)
−0.769034 + 0.639208i \(0.779262\pi\)
\(734\) 7.71090 0.284614
\(735\) −3.18734 −0.117567
\(736\) 23.2556 0.857213
\(737\) −43.9457 −1.61876
\(738\) −35.8296 −1.31890
\(739\) 13.0710 0.480826 0.240413 0.970671i \(-0.422717\pi\)
0.240413 + 0.970671i \(0.422717\pi\)
\(740\) −9.15041 −0.336376
\(741\) −1.60066 −0.0588019
\(742\) −1.84998 −0.0679150
\(743\) −50.9362 −1.86867 −0.934335 0.356397i \(-0.884005\pi\)
−0.934335 + 0.356397i \(0.884005\pi\)
\(744\) −16.5284 −0.605962
\(745\) −17.8672 −0.654604
\(746\) −0.371246 −0.0135923
\(747\) 39.7114 1.45296
\(748\) −28.5876 −1.04527
\(749\) −16.6958 −0.610050
\(750\) 1.37477 0.0501997
\(751\) −44.5613 −1.62607 −0.813033 0.582218i \(-0.802185\pi\)
−0.813033 + 0.582218i \(0.802185\pi\)
\(752\) −1.72682 −0.0629708
\(753\) 59.3221 2.16182
\(754\) 7.65138 0.278647
\(755\) −10.5400 −0.383590
\(756\) 24.0468 0.874575
\(757\) −1.26477 −0.0459689 −0.0229844 0.999736i \(-0.507317\pi\)
−0.0229844 + 0.999736i \(0.507317\pi\)
\(758\) −3.31420 −0.120377
\(759\) −61.9676 −2.24928
\(760\) −0.310485 −0.0112625
\(761\) −50.3101 −1.82374 −0.911870 0.410478i \(-0.865362\pi\)
−0.911870 + 0.410478i \(0.865362\pi\)
\(762\) 2.89903 0.105021
\(763\) 10.2366 0.370590
\(764\) 23.6237 0.854675
\(765\) −29.6687 −1.07267
\(766\) 1.06343 0.0384234
\(767\) −22.8672 −0.825688
\(768\) 9.89507 0.357058
\(769\) −1.10149 −0.0397208 −0.0198604 0.999803i \(-0.506322\pi\)
−0.0198604 + 0.999803i \(0.506322\pi\)
\(770\) −1.64027 −0.0591112
\(771\) 36.5772 1.31729
\(772\) −32.7560 −1.17891
\(773\) −0.461182 −0.0165876 −0.00829378 0.999966i \(-0.502640\pi\)
−0.00829378 + 0.999966i \(0.502640\pi\)
\(774\) −25.2501 −0.907598
\(775\) −3.15228 −0.113233
\(776\) −16.9281 −0.607685
\(777\) 16.0783 0.576807
\(778\) −10.2769 −0.368444
\(779\) 2.18998 0.0784641
\(780\) −15.3839 −0.550832
\(781\) 28.3184 1.01331
\(782\) 9.13832 0.326786
\(783\) 88.3805 3.15846
\(784\) 2.91837 0.104227
\(785\) −18.3982 −0.656659
\(786\) −24.1711 −0.862156
\(787\) 10.8517 0.386820 0.193410 0.981118i \(-0.438045\pi\)
0.193410 + 0.981118i \(0.438045\pi\)
\(788\) −17.9403 −0.639098
\(789\) −61.5119 −2.18988
\(790\) 3.29933 0.117385
\(791\) −14.7513 −0.524495
\(792\) 44.7870 1.59144
\(793\) 32.2674 1.14585
\(794\) −3.97416 −0.141038
\(795\) 13.6708 0.484852
\(796\) 2.49460 0.0884186
\(797\) 15.2348 0.539644 0.269822 0.962910i \(-0.413035\pi\)
0.269822 + 0.962910i \(0.413035\pi\)
\(798\) 0.259474 0.00918527
\(799\) −2.45214 −0.0867506
\(800\) −4.54887 −0.160827
\(801\) −88.1371 −3.11417
\(802\) 3.76030 0.132781
\(803\) 8.87525 0.313201
\(804\) 66.8129 2.35631
\(805\) −5.11240 −0.180188
\(806\) −3.61775 −0.127430
\(807\) −47.4619 −1.67074
\(808\) −8.09329 −0.284721
\(809\) −7.09334 −0.249389 −0.124694 0.992195i \(-0.539795\pi\)
−0.124694 + 0.992195i \(0.539795\pi\)
\(810\) 8.96106 0.314860
\(811\) −11.1450 −0.391354 −0.195677 0.980668i \(-0.562690\pi\)
−0.195677 + 0.980668i \(0.562690\pi\)
\(812\) 12.0935 0.424400
\(813\) 44.4419 1.55864
\(814\) 8.27424 0.290012
\(815\) −23.9768 −0.839870
\(816\) 38.5484 1.34946
\(817\) 1.54334 0.0539947
\(818\) 0.249600 0.00872707
\(819\) 19.0489 0.665624
\(820\) 21.0477 0.735019
\(821\) −8.02219 −0.279976 −0.139988 0.990153i \(-0.544706\pi\)
−0.139988 + 0.990153i \(0.544706\pi\)
\(822\) 19.3742 0.675753
\(823\) 28.3107 0.986850 0.493425 0.869788i \(-0.335745\pi\)
0.493425 + 0.869788i \(0.335745\pi\)
\(824\) 17.5555 0.611574
\(825\) 12.1210 0.422001
\(826\) 3.70686 0.128978
\(827\) 52.5170 1.82620 0.913098 0.407739i \(-0.133683\pi\)
0.913098 + 0.407739i \(0.133683\pi\)
\(828\) 66.3915 2.30726
\(829\) 0.127034 0.00441208 0.00220604 0.999998i \(-0.499298\pi\)
0.00220604 + 0.999998i \(0.499298\pi\)
\(830\) 2.39253 0.0830461
\(831\) −57.3388 −1.98906
\(832\) 10.3098 0.357427
\(833\) 4.14418 0.143587
\(834\) 31.0818 1.07627
\(835\) −23.7618 −0.822312
\(836\) −1.30197 −0.0450296
\(837\) −41.7883 −1.44441
\(838\) −7.45060 −0.257377
\(839\) −37.2003 −1.28430 −0.642148 0.766580i \(-0.721957\pi\)
−0.642148 + 0.766580i \(0.721957\pi\)
\(840\) 5.24334 0.180912
\(841\) 15.4479 0.532688
\(842\) 6.79973 0.234334
\(843\) 70.5391 2.42950
\(844\) 20.5641 0.707847
\(845\) 5.92020 0.203661
\(846\) 1.82714 0.0628183
\(847\) −3.46186 −0.118951
\(848\) −12.5171 −0.429840
\(849\) −96.6587 −3.31732
\(850\) −1.78748 −0.0613101
\(851\) 25.7892 0.884042
\(852\) −43.0539 −1.47500
\(853\) 28.5784 0.978505 0.489253 0.872142i \(-0.337270\pi\)
0.489253 + 0.872142i \(0.337270\pi\)
\(854\) −5.23067 −0.178990
\(855\) −1.35121 −0.0462103
\(856\) 27.4654 0.938748
\(857\) −49.2472 −1.68225 −0.841127 0.540838i \(-0.818107\pi\)
−0.841127 + 0.540838i \(0.818107\pi\)
\(858\) 13.9109 0.474909
\(859\) −45.0012 −1.53542 −0.767711 0.640796i \(-0.778604\pi\)
−0.767711 + 0.640796i \(0.778604\pi\)
\(860\) 14.8330 0.505800
\(861\) −36.9833 −1.26039
\(862\) −6.75662 −0.230131
\(863\) −5.75485 −0.195897 −0.0979486 0.995191i \(-0.531228\pi\)
−0.0979486 + 0.995191i \(0.531228\pi\)
\(864\) −60.3023 −2.05152
\(865\) −21.0548 −0.715886
\(866\) −9.38543 −0.318930
\(867\) 0.555203 0.0188557
\(868\) −5.71810 −0.194085
\(869\) 29.0894 0.986790
\(870\) 9.16553 0.310740
\(871\) 30.7479 1.04185
\(872\) −16.8397 −0.570265
\(873\) −73.6699 −2.49335
\(874\) 0.416188 0.0140778
\(875\) 1.00000 0.0338062
\(876\) −13.4935 −0.455903
\(877\) 26.8334 0.906101 0.453051 0.891485i \(-0.350336\pi\)
0.453051 + 0.891485i \(0.350336\pi\)
\(878\) −5.30846 −0.179152
\(879\) 61.7907 2.08415
\(880\) −11.0982 −0.374120
\(881\) −37.0951 −1.24977 −0.624883 0.780718i \(-0.714853\pi\)
−0.624883 + 0.780718i \(0.714853\pi\)
\(882\) −3.08790 −0.103975
\(883\) −48.8596 −1.64426 −0.822129 0.569301i \(-0.807214\pi\)
−0.822129 + 0.569301i \(0.807214\pi\)
\(884\) 20.0021 0.672745
\(885\) −27.3925 −0.920788
\(886\) −8.53110 −0.286608
\(887\) −16.8207 −0.564783 −0.282392 0.959299i \(-0.591128\pi\)
−0.282392 + 0.959299i \(0.591128\pi\)
\(888\) −26.4497 −0.887593
\(889\) 2.10873 0.0707247
\(890\) −5.31009 −0.177995
\(891\) 79.0075 2.64685
\(892\) −45.0872 −1.50963
\(893\) −0.111678 −0.00373718
\(894\) −24.5634 −0.821523
\(895\) 17.6887 0.591267
\(896\) −10.7690 −0.359766
\(897\) 43.3574 1.44766
\(898\) −0.395412 −0.0131951
\(899\) −21.0160 −0.700923
\(900\) −12.9864 −0.432879
\(901\) −17.7747 −0.592161
\(902\) −19.0324 −0.633709
\(903\) −26.0633 −0.867331
\(904\) 24.2666 0.807095
\(905\) 11.7329 0.390014
\(906\) −14.4901 −0.481402
\(907\) −34.1951 −1.13543 −0.567715 0.823225i \(-0.692172\pi\)
−0.567715 + 0.823225i \(0.692172\pi\)
\(908\) 29.9010 0.992301
\(909\) −35.2213 −1.16822
\(910\) 1.14766 0.0380446
\(911\) 52.0548 1.72465 0.862327 0.506352i \(-0.169006\pi\)
0.862327 + 0.506352i \(0.169006\pi\)
\(912\) 1.75562 0.0581343
\(913\) 21.0944 0.698122
\(914\) −17.0322 −0.563374
\(915\) 38.6529 1.27783
\(916\) −1.81396 −0.0599349
\(917\) −17.5819 −0.580605
\(918\) −23.6958 −0.782079
\(919\) −31.3659 −1.03467 −0.517333 0.855784i \(-0.673075\pi\)
−0.517333 + 0.855784i \(0.673075\pi\)
\(920\) 8.41016 0.277275
\(921\) 92.0598 3.03347
\(922\) 6.58976 0.217022
\(923\) −19.8138 −0.652178
\(924\) 21.9871 0.723322
\(925\) −5.04444 −0.165860
\(926\) −17.6980 −0.581593
\(927\) 76.4000 2.50931
\(928\) −30.3270 −0.995531
\(929\) −11.4975 −0.377220 −0.188610 0.982052i \(-0.560398\pi\)
−0.188610 + 0.982052i \(0.560398\pi\)
\(930\) −4.33367 −0.142107
\(931\) 0.188739 0.00618567
\(932\) −26.6495 −0.872933
\(933\) 3.13278 0.102563
\(934\) 4.98303 0.163050
\(935\) −15.7598 −0.515400
\(936\) −31.3365 −1.02426
\(937\) 23.7500 0.775879 0.387939 0.921685i \(-0.373187\pi\)
0.387939 + 0.921685i \(0.373187\pi\)
\(938\) −4.98434 −0.162745
\(939\) 10.3046 0.336277
\(940\) −1.07334 −0.0350083
\(941\) 27.0664 0.882339 0.441170 0.897424i \(-0.354564\pi\)
0.441170 + 0.897424i \(0.354564\pi\)
\(942\) −25.2934 −0.824102
\(943\) −59.3202 −1.93173
\(944\) 25.0809 0.816314
\(945\) 13.2565 0.431236
\(946\) −13.4127 −0.436084
\(947\) −56.4179 −1.83334 −0.916668 0.399651i \(-0.869131\pi\)
−0.916668 + 0.399651i \(0.869131\pi\)
\(948\) −44.2261 −1.43640
\(949\) −6.20982 −0.201579
\(950\) −0.0814076 −0.00264121
\(951\) 46.1138 1.49534
\(952\) −6.81738 −0.220953
\(953\) 18.1390 0.587580 0.293790 0.955870i \(-0.405083\pi\)
0.293790 + 0.955870i \(0.405083\pi\)
\(954\) 13.2443 0.428799
\(955\) 13.0233 0.421423
\(956\) 6.63770 0.214679
\(957\) 80.8102 2.61222
\(958\) −9.98110 −0.322475
\(959\) 14.0926 0.455075
\(960\) 12.3500 0.398595
\(961\) −21.0632 −0.679457
\(962\) −5.78931 −0.186655
\(963\) 119.527 3.85171
\(964\) 27.8957 0.898460
\(965\) −18.0577 −0.581299
\(966\) −7.02840 −0.226135
\(967\) 56.4223 1.81442 0.907209 0.420681i \(-0.138209\pi\)
0.907209 + 0.420681i \(0.138209\pi\)
\(968\) 5.69493 0.183042
\(969\) 2.49303 0.0800877
\(970\) −4.43847 −0.142511
\(971\) −17.5102 −0.561929 −0.280965 0.959718i \(-0.590654\pi\)
−0.280965 + 0.959718i \(0.590654\pi\)
\(972\) −47.9786 −1.53891
\(973\) 22.6086 0.724800
\(974\) 5.31141 0.170188
\(975\) −8.48084 −0.271604
\(976\) −35.3911 −1.13284
\(977\) 16.3052 0.521650 0.260825 0.965386i \(-0.416005\pi\)
0.260825 + 0.965386i \(0.416005\pi\)
\(978\) −32.9627 −1.05403
\(979\) −46.8178 −1.49630
\(980\) 1.81396 0.0579448
\(981\) −73.2851 −2.33981
\(982\) −2.61855 −0.0835613
\(983\) −38.7562 −1.23613 −0.618066 0.786127i \(-0.712083\pi\)
−0.618066 + 0.786127i \(0.712083\pi\)
\(984\) 60.8395 1.93949
\(985\) −9.89014 −0.315126
\(986\) −11.9170 −0.379515
\(987\) 1.88597 0.0600312
\(988\) 0.910961 0.0289815
\(989\) −41.8047 −1.32931
\(990\) 11.7429 0.373214
\(991\) −29.2154 −0.928057 −0.464028 0.885820i \(-0.653596\pi\)
−0.464028 + 0.885820i \(0.653596\pi\)
\(992\) 14.3393 0.455272
\(993\) −97.3852 −3.09042
\(994\) 3.21189 0.101875
\(995\) 1.37522 0.0435974
\(996\) −32.0709 −1.01620
\(997\) −25.9415 −0.821574 −0.410787 0.911731i \(-0.634746\pi\)
−0.410787 + 0.911731i \(0.634746\pi\)
\(998\) −0.476456 −0.0150820
\(999\) −66.8718 −2.11573
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 8015.2.a.l.1.28 62
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8015.2.a.l.1.28 62 1.1 even 1 trivial