Properties

Label 8007.2.a.f.1.41
Level 8007
Weight 2
Character 8007.1
Self dual yes
Analytic conductor 63.936
Analytic rank 1
Dimension 48
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8007 = 3 \cdot 17 \cdot 157 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8007.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(63.9362168984\)
Analytic rank: \(1\)
Dimension: \(48\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.41
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.99297 q^{2} -1.00000 q^{3} +1.97192 q^{4} +1.60110 q^{5} -1.99297 q^{6} -0.432857 q^{7} -0.0559561 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.99297 q^{2} -1.00000 q^{3} +1.97192 q^{4} +1.60110 q^{5} -1.99297 q^{6} -0.432857 q^{7} -0.0559561 q^{8} +1.00000 q^{9} +3.19095 q^{10} +1.01167 q^{11} -1.97192 q^{12} -6.62498 q^{13} -0.862669 q^{14} -1.60110 q^{15} -4.05537 q^{16} -1.00000 q^{17} +1.99297 q^{18} +1.52546 q^{19} +3.15726 q^{20} +0.432857 q^{21} +2.01622 q^{22} +4.61601 q^{23} +0.0559561 q^{24} -2.43646 q^{25} -13.2034 q^{26} -1.00000 q^{27} -0.853560 q^{28} +10.2590 q^{29} -3.19095 q^{30} +1.72586 q^{31} -7.97030 q^{32} -1.01167 q^{33} -1.99297 q^{34} -0.693049 q^{35} +1.97192 q^{36} -2.02527 q^{37} +3.04019 q^{38} +6.62498 q^{39} -0.0895916 q^{40} -0.00303029 q^{41} +0.862669 q^{42} +2.14892 q^{43} +1.99493 q^{44} +1.60110 q^{45} +9.19956 q^{46} -3.31533 q^{47} +4.05537 q^{48} -6.81264 q^{49} -4.85580 q^{50} +1.00000 q^{51} -13.0640 q^{52} -4.49136 q^{53} -1.99297 q^{54} +1.61979 q^{55} +0.0242210 q^{56} -1.52546 q^{57} +20.4460 q^{58} -12.6510 q^{59} -3.15726 q^{60} -1.11802 q^{61} +3.43959 q^{62} -0.432857 q^{63} -7.77383 q^{64} -10.6073 q^{65} -2.01622 q^{66} -13.6575 q^{67} -1.97192 q^{68} -4.61601 q^{69} -1.38122 q^{70} -7.62182 q^{71} -0.0559561 q^{72} +8.54418 q^{73} -4.03629 q^{74} +2.43646 q^{75} +3.00808 q^{76} -0.437907 q^{77} +13.2034 q^{78} +4.23499 q^{79} -6.49306 q^{80} +1.00000 q^{81} -0.00603926 q^{82} -11.5256 q^{83} +0.853560 q^{84} -1.60110 q^{85} +4.28272 q^{86} -10.2590 q^{87} -0.0566090 q^{88} +9.19145 q^{89} +3.19095 q^{90} +2.86767 q^{91} +9.10241 q^{92} -1.72586 q^{93} -6.60735 q^{94} +2.44242 q^{95} +7.97030 q^{96} +0.643877 q^{97} -13.5774 q^{98} +1.01167 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} + O(q^{10}) \) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} - 20q^{10} + 5q^{11} - 45q^{12} - 8q^{13} + 4q^{14} - q^{15} + 39q^{16} - 48q^{17} - q^{18} - 6q^{19} + 6q^{20} + 13q^{21} - 35q^{22} - 8q^{23} + 6q^{24} + 13q^{25} + 17q^{26} - 48q^{27} - 38q^{28} + q^{29} + 20q^{30} - 21q^{31} - 3q^{32} - 5q^{33} + q^{34} + 19q^{35} + 45q^{36} - 58q^{37} - 14q^{38} + 8q^{39} - 54q^{40} - 3q^{41} - 4q^{42} - 33q^{43} + 2q^{44} + q^{45} - 26q^{46} + 9q^{47} - 39q^{48} + 11q^{49} + 4q^{50} + 48q^{51} - 31q^{52} - 33q^{53} + q^{54} - 21q^{55} + 6q^{57} - 55q^{58} + 77q^{59} - 6q^{60} - 29q^{61} - 46q^{62} - 13q^{63} + 24q^{64} - 49q^{65} + 35q^{66} - 44q^{67} - 45q^{68} + 8q^{69} + 4q^{70} + 22q^{71} - 6q^{72} - 63q^{73} - 16q^{74} - 13q^{75} - 46q^{76} - 30q^{77} - 17q^{78} - 46q^{79} - 14q^{80} + 48q^{81} - 75q^{82} + 11q^{83} + 38q^{84} - q^{85} + 8q^{86} - q^{87} - 116q^{88} + 10q^{89} - 20q^{90} - 67q^{91} - 64q^{92} + 21q^{93} - 16q^{94} - 8q^{95} + 3q^{96} - 96q^{97} - 46q^{98} + 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.99297 1.40924 0.704621 0.709584i \(-0.251117\pi\)
0.704621 + 0.709584i \(0.251117\pi\)
\(3\) −1.00000 −0.577350
\(4\) 1.97192 0.985962
\(5\) 1.60110 0.716036 0.358018 0.933715i \(-0.383453\pi\)
0.358018 + 0.933715i \(0.383453\pi\)
\(6\) −1.99297 −0.813626
\(7\) −0.432857 −0.163604 −0.0818022 0.996649i \(-0.526068\pi\)
−0.0818022 + 0.996649i \(0.526068\pi\)
\(8\) −0.0559561 −0.0197835
\(9\) 1.00000 0.333333
\(10\) 3.19095 1.00907
\(11\) 1.01167 0.305029 0.152515 0.988301i \(-0.451263\pi\)
0.152515 + 0.988301i \(0.451263\pi\)
\(12\) −1.97192 −0.569245
\(13\) −6.62498 −1.83744 −0.918720 0.394910i \(-0.870776\pi\)
−0.918720 + 0.394910i \(0.870776\pi\)
\(14\) −0.862669 −0.230558
\(15\) −1.60110 −0.413403
\(16\) −4.05537 −1.01384
\(17\) −1.00000 −0.242536
\(18\) 1.99297 0.469747
\(19\) 1.52546 0.349964 0.174982 0.984572i \(-0.444013\pi\)
0.174982 + 0.984572i \(0.444013\pi\)
\(20\) 3.15726 0.705984
\(21\) 0.432857 0.0944570
\(22\) 2.01622 0.429860
\(23\) 4.61601 0.962504 0.481252 0.876582i \(-0.340182\pi\)
0.481252 + 0.876582i \(0.340182\pi\)
\(24\) 0.0559561 0.0114220
\(25\) −2.43646 −0.487293
\(26\) −13.2034 −2.58940
\(27\) −1.00000 −0.192450
\(28\) −0.853560 −0.161308
\(29\) 10.2590 1.90506 0.952529 0.304449i \(-0.0984723\pi\)
0.952529 + 0.304449i \(0.0984723\pi\)
\(30\) −3.19095 −0.582585
\(31\) 1.72586 0.309974 0.154987 0.987917i \(-0.450466\pi\)
0.154987 + 0.987917i \(0.450466\pi\)
\(32\) −7.97030 −1.40896
\(33\) −1.01167 −0.176109
\(34\) −1.99297 −0.341791
\(35\) −0.693049 −0.117147
\(36\) 1.97192 0.328654
\(37\) −2.02527 −0.332952 −0.166476 0.986046i \(-0.553239\pi\)
−0.166476 + 0.986046i \(0.553239\pi\)
\(38\) 3.04019 0.493183
\(39\) 6.62498 1.06085
\(40\) −0.0895916 −0.0141657
\(41\) −0.00303029 −0.000473251 0 −0.000236626 1.00000i \(-0.500075\pi\)
−0.000236626 1.00000i \(0.500075\pi\)
\(42\) 0.862669 0.133113
\(43\) 2.14892 0.327707 0.163853 0.986485i \(-0.447608\pi\)
0.163853 + 0.986485i \(0.447608\pi\)
\(44\) 1.99493 0.300747
\(45\) 1.60110 0.238679
\(46\) 9.19956 1.35640
\(47\) −3.31533 −0.483591 −0.241795 0.970327i \(-0.577736\pi\)
−0.241795 + 0.970327i \(0.577736\pi\)
\(48\) 4.05537 0.585342
\(49\) −6.81264 −0.973234
\(50\) −4.85580 −0.686713
\(51\) 1.00000 0.140028
\(52\) −13.0640 −1.81165
\(53\) −4.49136 −0.616935 −0.308468 0.951235i \(-0.599816\pi\)
−0.308468 + 0.951235i \(0.599816\pi\)
\(54\) −1.99297 −0.271209
\(55\) 1.61979 0.218412
\(56\) 0.0242210 0.00323666
\(57\) −1.52546 −0.202052
\(58\) 20.4460 2.68469
\(59\) −12.6510 −1.64702 −0.823511 0.567300i \(-0.807988\pi\)
−0.823511 + 0.567300i \(0.807988\pi\)
\(60\) −3.15726 −0.407600
\(61\) −1.11802 −0.143148 −0.0715738 0.997435i \(-0.522802\pi\)
−0.0715738 + 0.997435i \(0.522802\pi\)
\(62\) 3.43959 0.436828
\(63\) −0.432857 −0.0545348
\(64\) −7.77383 −0.971729
\(65\) −10.6073 −1.31567
\(66\) −2.01622 −0.248180
\(67\) −13.6575 −1.66853 −0.834266 0.551362i \(-0.814108\pi\)
−0.834266 + 0.551362i \(0.814108\pi\)
\(68\) −1.97192 −0.239131
\(69\) −4.61601 −0.555702
\(70\) −1.38122 −0.165088
\(71\) −7.62182 −0.904544 −0.452272 0.891880i \(-0.649386\pi\)
−0.452272 + 0.891880i \(0.649386\pi\)
\(72\) −0.0559561 −0.00659449
\(73\) 8.54418 1.00002 0.500010 0.866019i \(-0.333330\pi\)
0.500010 + 0.866019i \(0.333330\pi\)
\(74\) −4.03629 −0.469209
\(75\) 2.43646 0.281339
\(76\) 3.00808 0.345051
\(77\) −0.437907 −0.0499041
\(78\) 13.2034 1.49499
\(79\) 4.23499 0.476474 0.238237 0.971207i \(-0.423431\pi\)
0.238237 + 0.971207i \(0.423431\pi\)
\(80\) −6.49306 −0.725947
\(81\) 1.00000 0.111111
\(82\) −0.00603926 −0.000666925 0
\(83\) −11.5256 −1.26510 −0.632552 0.774518i \(-0.717993\pi\)
−0.632552 + 0.774518i \(0.717993\pi\)
\(84\) 0.853560 0.0931310
\(85\) −1.60110 −0.173664
\(86\) 4.28272 0.461818
\(87\) −10.2590 −1.09989
\(88\) −0.0566090 −0.00603454
\(89\) 9.19145 0.974291 0.487146 0.873321i \(-0.338038\pi\)
0.487146 + 0.873321i \(0.338038\pi\)
\(90\) 3.19095 0.336356
\(91\) 2.86767 0.300613
\(92\) 9.10241 0.948992
\(93\) −1.72586 −0.178964
\(94\) −6.60735 −0.681496
\(95\) 2.44242 0.250587
\(96\) 7.97030 0.813466
\(97\) 0.643877 0.0653758 0.0326879 0.999466i \(-0.489593\pi\)
0.0326879 + 0.999466i \(0.489593\pi\)
\(98\) −13.5774 −1.37152
\(99\) 1.01167 0.101676
\(100\) −4.80452 −0.480452
\(101\) −16.9792 −1.68949 −0.844744 0.535170i \(-0.820248\pi\)
−0.844744 + 0.535170i \(0.820248\pi\)
\(102\) 1.99297 0.197333
\(103\) 0.0962444 0.00948325 0.00474162 0.999989i \(-0.498491\pi\)
0.00474162 + 0.999989i \(0.498491\pi\)
\(104\) 0.370708 0.0363509
\(105\) 0.693049 0.0676346
\(106\) −8.95113 −0.869411
\(107\) −19.1244 −1.84883 −0.924414 0.381390i \(-0.875445\pi\)
−0.924414 + 0.381390i \(0.875445\pi\)
\(108\) −1.97192 −0.189748
\(109\) 10.2719 0.983871 0.491935 0.870632i \(-0.336290\pi\)
0.491935 + 0.870632i \(0.336290\pi\)
\(110\) 3.22818 0.307795
\(111\) 2.02527 0.192230
\(112\) 1.75539 0.165869
\(113\) −14.4236 −1.35686 −0.678429 0.734666i \(-0.737339\pi\)
−0.678429 + 0.734666i \(0.737339\pi\)
\(114\) −3.04019 −0.284740
\(115\) 7.39071 0.689187
\(116\) 20.2301 1.87831
\(117\) −6.62498 −0.612480
\(118\) −25.2131 −2.32105
\(119\) 0.432857 0.0396799
\(120\) 0.0895916 0.00817855
\(121\) −9.97653 −0.906957
\(122\) −2.22818 −0.201730
\(123\) 0.00303029 0.000273232 0
\(124\) 3.40327 0.305623
\(125\) −11.9066 −1.06495
\(126\) −0.862669 −0.0768527
\(127\) −8.54721 −0.758442 −0.379221 0.925306i \(-0.623808\pi\)
−0.379221 + 0.925306i \(0.623808\pi\)
\(128\) 0.447605 0.0395630
\(129\) −2.14892 −0.189202
\(130\) −21.1400 −1.85410
\(131\) 8.69462 0.759653 0.379826 0.925058i \(-0.375984\pi\)
0.379826 + 0.925058i \(0.375984\pi\)
\(132\) −1.99493 −0.173636
\(133\) −0.660304 −0.0572556
\(134\) −27.2190 −2.35136
\(135\) −1.60110 −0.137801
\(136\) 0.0559561 0.00479820
\(137\) −8.40565 −0.718143 −0.359072 0.933310i \(-0.616907\pi\)
−0.359072 + 0.933310i \(0.616907\pi\)
\(138\) −9.19956 −0.783118
\(139\) 9.53648 0.808874 0.404437 0.914566i \(-0.367468\pi\)
0.404437 + 0.914566i \(0.367468\pi\)
\(140\) −1.36664 −0.115502
\(141\) 3.31533 0.279201
\(142\) −15.1900 −1.27472
\(143\) −6.70228 −0.560473
\(144\) −4.05537 −0.337947
\(145\) 16.4258 1.36409
\(146\) 17.0283 1.40927
\(147\) 6.81264 0.561897
\(148\) −3.99367 −0.328278
\(149\) 0.518737 0.0424966 0.0212483 0.999774i \(-0.493236\pi\)
0.0212483 + 0.999774i \(0.493236\pi\)
\(150\) 4.85580 0.396474
\(151\) −10.0706 −0.819532 −0.409766 0.912191i \(-0.634390\pi\)
−0.409766 + 0.912191i \(0.634390\pi\)
\(152\) −0.0853586 −0.00692350
\(153\) −1.00000 −0.0808452
\(154\) −0.872735 −0.0703270
\(155\) 2.76329 0.221953
\(156\) 13.0640 1.04595
\(157\) −1.00000 −0.0798087
\(158\) 8.44020 0.671467
\(159\) 4.49136 0.356188
\(160\) −12.7613 −1.00887
\(161\) −1.99807 −0.157470
\(162\) 1.99297 0.156582
\(163\) −19.6205 −1.53679 −0.768397 0.639973i \(-0.778946\pi\)
−0.768397 + 0.639973i \(0.778946\pi\)
\(164\) −0.00597549 −0.000466607 0
\(165\) −1.61979 −0.126100
\(166\) −22.9702 −1.78284
\(167\) −19.6883 −1.52353 −0.761763 0.647856i \(-0.775666\pi\)
−0.761763 + 0.647856i \(0.775666\pi\)
\(168\) −0.0242210 −0.00186869
\(169\) 30.8904 2.37619
\(170\) −3.19095 −0.244735
\(171\) 1.52546 0.116655
\(172\) 4.23750 0.323106
\(173\) 4.81636 0.366181 0.183090 0.983096i \(-0.441390\pi\)
0.183090 + 0.983096i \(0.441390\pi\)
\(174\) −20.4460 −1.55000
\(175\) 1.05464 0.0797233
\(176\) −4.10268 −0.309251
\(177\) 12.6510 0.950909
\(178\) 18.3183 1.37301
\(179\) 15.0731 1.12662 0.563308 0.826247i \(-0.309529\pi\)
0.563308 + 0.826247i \(0.309529\pi\)
\(180\) 3.15726 0.235328
\(181\) 10.6825 0.794023 0.397012 0.917814i \(-0.370047\pi\)
0.397012 + 0.917814i \(0.370047\pi\)
\(182\) 5.71517 0.423637
\(183\) 1.11802 0.0826463
\(184\) −0.258294 −0.0190417
\(185\) −3.24266 −0.238405
\(186\) −3.43959 −0.252203
\(187\) −1.01167 −0.0739805
\(188\) −6.53758 −0.476802
\(189\) 0.432857 0.0314857
\(190\) 4.86766 0.353137
\(191\) −14.9692 −1.08314 −0.541568 0.840657i \(-0.682169\pi\)
−0.541568 + 0.840657i \(0.682169\pi\)
\(192\) 7.77383 0.561028
\(193\) −15.9861 −1.15070 −0.575352 0.817906i \(-0.695135\pi\)
−0.575352 + 0.817906i \(0.695135\pi\)
\(194\) 1.28323 0.0921303
\(195\) 10.6073 0.759604
\(196\) −13.4340 −0.959571
\(197\) −1.46441 −0.104335 −0.0521676 0.998638i \(-0.516613\pi\)
−0.0521676 + 0.998638i \(0.516613\pi\)
\(198\) 2.01622 0.143287
\(199\) 25.2045 1.78670 0.893350 0.449361i \(-0.148348\pi\)
0.893350 + 0.449361i \(0.148348\pi\)
\(200\) 0.136335 0.00964034
\(201\) 13.6575 0.963327
\(202\) −33.8389 −2.38090
\(203\) −4.44070 −0.311676
\(204\) 1.97192 0.138062
\(205\) −0.00485180 −0.000338865 0
\(206\) 0.191812 0.0133642
\(207\) 4.61601 0.320835
\(208\) 26.8667 1.86287
\(209\) 1.54326 0.106749
\(210\) 1.38122 0.0953135
\(211\) −16.0553 −1.10529 −0.552645 0.833416i \(-0.686382\pi\)
−0.552645 + 0.833416i \(0.686382\pi\)
\(212\) −8.85661 −0.608274
\(213\) 7.62182 0.522238
\(214\) −38.1144 −2.60545
\(215\) 3.44064 0.234650
\(216\) 0.0559561 0.00380733
\(217\) −0.747051 −0.0507131
\(218\) 20.4716 1.38651
\(219\) −8.54418 −0.577362
\(220\) 3.19409 0.215346
\(221\) 6.62498 0.445645
\(222\) 4.03629 0.270898
\(223\) 16.6067 1.11206 0.556032 0.831161i \(-0.312323\pi\)
0.556032 + 0.831161i \(0.312323\pi\)
\(224\) 3.45000 0.230513
\(225\) −2.43646 −0.162431
\(226\) −28.7458 −1.91214
\(227\) 13.4179 0.890575 0.445288 0.895388i \(-0.353101\pi\)
0.445288 + 0.895388i \(0.353101\pi\)
\(228\) −3.00808 −0.199215
\(229\) 13.1180 0.866862 0.433431 0.901187i \(-0.357303\pi\)
0.433431 + 0.901187i \(0.357303\pi\)
\(230\) 14.7295 0.971231
\(231\) 0.437907 0.0288122
\(232\) −0.574056 −0.0376886
\(233\) 3.59337 0.235409 0.117705 0.993049i \(-0.462446\pi\)
0.117705 + 0.993049i \(0.462446\pi\)
\(234\) −13.2034 −0.863132
\(235\) −5.30819 −0.346268
\(236\) −24.9468 −1.62390
\(237\) −4.23499 −0.275092
\(238\) 0.862669 0.0559186
\(239\) 1.63998 0.106081 0.0530407 0.998592i \(-0.483109\pi\)
0.0530407 + 0.998592i \(0.483109\pi\)
\(240\) 6.49306 0.419125
\(241\) −7.66528 −0.493764 −0.246882 0.969046i \(-0.579406\pi\)
−0.246882 + 0.969046i \(0.579406\pi\)
\(242\) −19.8829 −1.27812
\(243\) −1.00000 −0.0641500
\(244\) −2.20465 −0.141138
\(245\) −10.9077 −0.696870
\(246\) 0.00603926 0.000385049 0
\(247\) −10.1061 −0.643037
\(248\) −0.0965726 −0.00613236
\(249\) 11.5256 0.730408
\(250\) −23.7294 −1.50078
\(251\) 27.9627 1.76499 0.882496 0.470319i \(-0.155861\pi\)
0.882496 + 0.470319i \(0.155861\pi\)
\(252\) −0.853560 −0.0537692
\(253\) 4.66987 0.293592
\(254\) −17.0343 −1.06883
\(255\) 1.60110 0.100265
\(256\) 16.4397 1.02748
\(257\) −4.96860 −0.309933 −0.154966 0.987920i \(-0.549527\pi\)
−0.154966 + 0.987920i \(0.549527\pi\)
\(258\) −4.28272 −0.266631
\(259\) 0.876650 0.0544724
\(260\) −20.9168 −1.29720
\(261\) 10.2590 0.635019
\(262\) 17.3281 1.07053
\(263\) −28.1225 −1.73411 −0.867055 0.498213i \(-0.833990\pi\)
−0.867055 + 0.498213i \(0.833990\pi\)
\(264\) 0.0566090 0.00348404
\(265\) −7.19113 −0.441748
\(266\) −1.31596 −0.0806870
\(267\) −9.19145 −0.562507
\(268\) −26.9316 −1.64511
\(269\) −4.56721 −0.278468 −0.139234 0.990260i \(-0.544464\pi\)
−0.139234 + 0.990260i \(0.544464\pi\)
\(270\) −3.19095 −0.194195
\(271\) 7.03561 0.427383 0.213692 0.976901i \(-0.431451\pi\)
0.213692 + 0.976901i \(0.431451\pi\)
\(272\) 4.05537 0.245893
\(273\) −2.86767 −0.173559
\(274\) −16.7522 −1.01204
\(275\) −2.46489 −0.148639
\(276\) −9.10241 −0.547901
\(277\) −19.6517 −1.18075 −0.590377 0.807128i \(-0.701021\pi\)
−0.590377 + 0.807128i \(0.701021\pi\)
\(278\) 19.0059 1.13990
\(279\) 1.72586 0.103325
\(280\) 0.0387803 0.00231757
\(281\) −5.73467 −0.342101 −0.171051 0.985262i \(-0.554716\pi\)
−0.171051 + 0.985262i \(0.554716\pi\)
\(282\) 6.60735 0.393462
\(283\) 11.4583 0.681123 0.340561 0.940222i \(-0.389383\pi\)
0.340561 + 0.940222i \(0.389383\pi\)
\(284\) −15.0296 −0.891845
\(285\) −2.44242 −0.144676
\(286\) −13.3574 −0.789842
\(287\) 0.00131168 7.74260e−5 0
\(288\) −7.97030 −0.469655
\(289\) 1.00000 0.0588235
\(290\) 32.7361 1.92233
\(291\) −0.643877 −0.0377447
\(292\) 16.8485 0.985982
\(293\) 28.0591 1.63923 0.819616 0.572913i \(-0.194187\pi\)
0.819616 + 0.572913i \(0.194187\pi\)
\(294\) 13.5774 0.791848
\(295\) −20.2556 −1.17933
\(296\) 0.113326 0.00658694
\(297\) −1.01167 −0.0587029
\(298\) 1.03383 0.0598879
\(299\) −30.5810 −1.76854
\(300\) 4.80452 0.277389
\(301\) −0.930173 −0.0536143
\(302\) −20.0703 −1.15492
\(303\) 16.9792 0.975427
\(304\) −6.18628 −0.354808
\(305\) −1.79006 −0.102499
\(306\) −1.99297 −0.113930
\(307\) 25.2277 1.43982 0.719912 0.694066i \(-0.244182\pi\)
0.719912 + 0.694066i \(0.244182\pi\)
\(308\) −0.863519 −0.0492036
\(309\) −0.0962444 −0.00547515
\(310\) 5.50714 0.312785
\(311\) −30.4752 −1.72809 −0.864044 0.503417i \(-0.832076\pi\)
−0.864044 + 0.503417i \(0.832076\pi\)
\(312\) −0.370708 −0.0209872
\(313\) −8.90078 −0.503102 −0.251551 0.967844i \(-0.580941\pi\)
−0.251551 + 0.967844i \(0.580941\pi\)
\(314\) −1.99297 −0.112470
\(315\) −0.693049 −0.0390489
\(316\) 8.35108 0.469785
\(317\) 21.2670 1.19447 0.597237 0.802065i \(-0.296265\pi\)
0.597237 + 0.802065i \(0.296265\pi\)
\(318\) 8.95113 0.501954
\(319\) 10.3787 0.581098
\(320\) −12.4467 −0.695793
\(321\) 19.1244 1.06742
\(322\) −3.98209 −0.221913
\(323\) −1.52546 −0.0848787
\(324\) 1.97192 0.109551
\(325\) 16.1415 0.895371
\(326\) −39.1030 −2.16571
\(327\) −10.2719 −0.568038
\(328\) 0.000169563 0 9.36255e−6 0
\(329\) 1.43506 0.0791175
\(330\) −3.22818 −0.177706
\(331\) 26.6616 1.46546 0.732728 0.680522i \(-0.238247\pi\)
0.732728 + 0.680522i \(0.238247\pi\)
\(332\) −22.7277 −1.24734
\(333\) −2.02527 −0.110984
\(334\) −39.2381 −2.14702
\(335\) −21.8671 −1.19473
\(336\) −1.75539 −0.0957644
\(337\) 23.3113 1.26985 0.634925 0.772574i \(-0.281031\pi\)
0.634925 + 0.772574i \(0.281031\pi\)
\(338\) 61.5636 3.34862
\(339\) 14.4236 0.783382
\(340\) −3.15726 −0.171226
\(341\) 1.74600 0.0945512
\(342\) 3.04019 0.164394
\(343\) 5.97889 0.322830
\(344\) −0.120245 −0.00648318
\(345\) −7.39071 −0.397902
\(346\) 9.59885 0.516037
\(347\) 24.8691 1.33504 0.667521 0.744591i \(-0.267356\pi\)
0.667521 + 0.744591i \(0.267356\pi\)
\(348\) −20.2301 −1.08444
\(349\) −24.0955 −1.28980 −0.644901 0.764266i \(-0.723101\pi\)
−0.644901 + 0.764266i \(0.723101\pi\)
\(350\) 2.10186 0.112349
\(351\) 6.62498 0.353615
\(352\) −8.06330 −0.429775
\(353\) 8.21102 0.437029 0.218514 0.975834i \(-0.429879\pi\)
0.218514 + 0.975834i \(0.429879\pi\)
\(354\) 25.2131 1.34006
\(355\) −12.2033 −0.647686
\(356\) 18.1248 0.960614
\(357\) −0.432857 −0.0229092
\(358\) 30.0402 1.58767
\(359\) 0.725163 0.0382727 0.0191363 0.999817i \(-0.493908\pi\)
0.0191363 + 0.999817i \(0.493908\pi\)
\(360\) −0.0895916 −0.00472189
\(361\) −16.6730 −0.877525
\(362\) 21.2899 1.11897
\(363\) 9.97653 0.523632
\(364\) 5.65482 0.296393
\(365\) 13.6801 0.716050
\(366\) 2.22818 0.116469
\(367\) 11.9680 0.624723 0.312362 0.949963i \(-0.398880\pi\)
0.312362 + 0.949963i \(0.398880\pi\)
\(368\) −18.7196 −0.975826
\(369\) −0.00303029 −0.000157750 0
\(370\) −6.46252 −0.335971
\(371\) 1.94411 0.100933
\(372\) −3.40327 −0.176451
\(373\) −24.0803 −1.24683 −0.623415 0.781891i \(-0.714255\pi\)
−0.623415 + 0.781891i \(0.714255\pi\)
\(374\) −2.01622 −0.104256
\(375\) 11.9066 0.614852
\(376\) 0.185513 0.00956710
\(377\) −67.9660 −3.50043
\(378\) 0.862669 0.0443709
\(379\) 8.38669 0.430795 0.215398 0.976526i \(-0.430895\pi\)
0.215398 + 0.976526i \(0.430895\pi\)
\(380\) 4.81626 0.247069
\(381\) 8.54721 0.437887
\(382\) −29.8332 −1.52640
\(383\) 32.2643 1.64863 0.824314 0.566133i \(-0.191561\pi\)
0.824314 + 0.566133i \(0.191561\pi\)
\(384\) −0.447605 −0.0228417
\(385\) −0.701135 −0.0357331
\(386\) −31.8597 −1.62162
\(387\) 2.14892 0.109236
\(388\) 1.26968 0.0644580
\(389\) 7.64544 0.387639 0.193820 0.981037i \(-0.437912\pi\)
0.193820 + 0.981037i \(0.437912\pi\)
\(390\) 21.1400 1.07047
\(391\) −4.61601 −0.233442
\(392\) 0.381209 0.0192539
\(393\) −8.69462 −0.438586
\(394\) −2.91853 −0.147034
\(395\) 6.78066 0.341172
\(396\) 1.99493 0.100249
\(397\) 12.7191 0.638354 0.319177 0.947695i \(-0.396594\pi\)
0.319177 + 0.947695i \(0.396594\pi\)
\(398\) 50.2318 2.51789
\(399\) 0.660304 0.0330565
\(400\) 9.88075 0.494038
\(401\) 36.2024 1.80786 0.903930 0.427680i \(-0.140669\pi\)
0.903930 + 0.427680i \(0.140669\pi\)
\(402\) 27.2190 1.35756
\(403\) −11.4338 −0.569559
\(404\) −33.4816 −1.66577
\(405\) 1.60110 0.0795595
\(406\) −8.85017 −0.439226
\(407\) −2.04890 −0.101560
\(408\) −0.0559561 −0.00277024
\(409\) −38.0524 −1.88157 −0.940785 0.339004i \(-0.889910\pi\)
−0.940785 + 0.339004i \(0.889910\pi\)
\(410\) −0.00966949 −0.000477542 0
\(411\) 8.40565 0.414620
\(412\) 0.189787 0.00935012
\(413\) 5.47608 0.269460
\(414\) 9.19956 0.452134
\(415\) −18.4538 −0.905860
\(416\) 52.8031 2.58889
\(417\) −9.53648 −0.467004
\(418\) 3.07566 0.150435
\(419\) 17.6411 0.861824 0.430912 0.902394i \(-0.358192\pi\)
0.430912 + 0.902394i \(0.358192\pi\)
\(420\) 1.36664 0.0666851
\(421\) −24.1281 −1.17593 −0.587967 0.808885i \(-0.700071\pi\)
−0.587967 + 0.808885i \(0.700071\pi\)
\(422\) −31.9977 −1.55762
\(423\) −3.31533 −0.161197
\(424\) 0.251319 0.0122051
\(425\) 2.43646 0.118186
\(426\) 15.1900 0.735960
\(427\) 0.483942 0.0234196
\(428\) −37.7119 −1.82287
\(429\) 6.70228 0.323589
\(430\) 6.85709 0.330678
\(431\) −26.7262 −1.28736 −0.643678 0.765296i \(-0.722592\pi\)
−0.643678 + 0.765296i \(0.722592\pi\)
\(432\) 4.05537 0.195114
\(433\) 8.13961 0.391165 0.195582 0.980687i \(-0.437340\pi\)
0.195582 + 0.980687i \(0.437340\pi\)
\(434\) −1.48885 −0.0714670
\(435\) −16.4258 −0.787557
\(436\) 20.2554 0.970059
\(437\) 7.04152 0.336841
\(438\) −17.0283 −0.813643
\(439\) 7.27620 0.347274 0.173637 0.984810i \(-0.444448\pi\)
0.173637 + 0.984810i \(0.444448\pi\)
\(440\) −0.0906369 −0.00432095
\(441\) −6.81264 −0.324411
\(442\) 13.2034 0.628021
\(443\) 5.49941 0.261285 0.130642 0.991430i \(-0.458296\pi\)
0.130642 + 0.991430i \(0.458296\pi\)
\(444\) 3.99367 0.189531
\(445\) 14.7165 0.697627
\(446\) 33.0966 1.56717
\(447\) −0.518737 −0.0245354
\(448\) 3.36495 0.158979
\(449\) −5.84793 −0.275981 −0.137990 0.990434i \(-0.544064\pi\)
−0.137990 + 0.990434i \(0.544064\pi\)
\(450\) −4.85580 −0.228904
\(451\) −0.00306564 −0.000144355 0
\(452\) −28.4422 −1.33781
\(453\) 10.0706 0.473157
\(454\) 26.7414 1.25504
\(455\) 4.59144 0.215250
\(456\) 0.0853586 0.00399728
\(457\) −21.2467 −0.993877 −0.496939 0.867786i \(-0.665543\pi\)
−0.496939 + 0.867786i \(0.665543\pi\)
\(458\) 26.1438 1.22162
\(459\) 1.00000 0.0466760
\(460\) 14.5739 0.679512
\(461\) −3.33124 −0.155151 −0.0775756 0.996986i \(-0.524718\pi\)
−0.0775756 + 0.996986i \(0.524718\pi\)
\(462\) 0.872735 0.0406033
\(463\) −36.8487 −1.71251 −0.856253 0.516557i \(-0.827213\pi\)
−0.856253 + 0.516557i \(0.827213\pi\)
\(464\) −41.6042 −1.93143
\(465\) −2.76329 −0.128144
\(466\) 7.16147 0.331749
\(467\) −26.9362 −1.24646 −0.623229 0.782040i \(-0.714179\pi\)
−0.623229 + 0.782040i \(0.714179\pi\)
\(468\) −13.0640 −0.603882
\(469\) 5.91175 0.272979
\(470\) −10.5791 −0.487975
\(471\) 1.00000 0.0460776
\(472\) 0.707902 0.0325838
\(473\) 2.17399 0.0999602
\(474\) −8.44020 −0.387671
\(475\) −3.71672 −0.170535
\(476\) 0.853560 0.0391229
\(477\) −4.49136 −0.205645
\(478\) 3.26843 0.149494
\(479\) −19.7511 −0.902450 −0.451225 0.892410i \(-0.649013\pi\)
−0.451225 + 0.892410i \(0.649013\pi\)
\(480\) 12.7613 0.582470
\(481\) 13.4174 0.611779
\(482\) −15.2767 −0.695832
\(483\) 1.99807 0.0909153
\(484\) −19.6729 −0.894225
\(485\) 1.03091 0.0468114
\(486\) −1.99297 −0.0904029
\(487\) 22.2900 1.01006 0.505028 0.863103i \(-0.331482\pi\)
0.505028 + 0.863103i \(0.331482\pi\)
\(488\) 0.0625600 0.00283196
\(489\) 19.6205 0.887269
\(490\) −21.7388 −0.982058
\(491\) 5.41662 0.244449 0.122224 0.992502i \(-0.460997\pi\)
0.122224 + 0.992502i \(0.460997\pi\)
\(492\) 0.00597549 0.000269396 0
\(493\) −10.2590 −0.462044
\(494\) −20.1412 −0.906195
\(495\) 1.61979 0.0728040
\(496\) −6.99900 −0.314265
\(497\) 3.29915 0.147987
\(498\) 22.9702 1.02932
\(499\) −29.6564 −1.32760 −0.663801 0.747910i \(-0.731058\pi\)
−0.663801 + 0.747910i \(0.731058\pi\)
\(500\) −23.4788 −1.05000
\(501\) 19.6883 0.879608
\(502\) 55.7289 2.48730
\(503\) −16.8329 −0.750542 −0.375271 0.926915i \(-0.622450\pi\)
−0.375271 + 0.926915i \(0.622450\pi\)
\(504\) 0.0242210 0.00107889
\(505\) −27.1854 −1.20973
\(506\) 9.30690 0.413742
\(507\) −30.8904 −1.37189
\(508\) −16.8544 −0.747795
\(509\) −34.0036 −1.50718 −0.753592 0.657342i \(-0.771681\pi\)
−0.753592 + 0.657342i \(0.771681\pi\)
\(510\) 3.19095 0.141298
\(511\) −3.69840 −0.163608
\(512\) 31.8686 1.40841
\(513\) −1.52546 −0.0673505
\(514\) −9.90226 −0.436770
\(515\) 0.154097 0.00679034
\(516\) −4.23750 −0.186546
\(517\) −3.35401 −0.147509
\(518\) 1.74714 0.0767647
\(519\) −4.81636 −0.211415
\(520\) 0.593543 0.0260286
\(521\) 24.7635 1.08491 0.542454 0.840086i \(-0.317495\pi\)
0.542454 + 0.840086i \(0.317495\pi\)
\(522\) 20.4460 0.894895
\(523\) 24.0515 1.05170 0.525849 0.850578i \(-0.323748\pi\)
0.525849 + 0.850578i \(0.323748\pi\)
\(524\) 17.1451 0.748988
\(525\) −1.05464 −0.0460282
\(526\) −56.0473 −2.44378
\(527\) −1.72586 −0.0751798
\(528\) 4.10268 0.178546
\(529\) −1.69248 −0.0735861
\(530\) −14.3317 −0.622529
\(531\) −12.6510 −0.549008
\(532\) −1.30207 −0.0564518
\(533\) 0.0200756 0.000869571 0
\(534\) −18.3183 −0.792709
\(535\) −30.6202 −1.32383
\(536\) 0.764222 0.0330093
\(537\) −15.0731 −0.650452
\(538\) −9.10231 −0.392429
\(539\) −6.89212 −0.296865
\(540\) −3.15726 −0.135867
\(541\) −39.8999 −1.71543 −0.857715 0.514125i \(-0.828117\pi\)
−0.857715 + 0.514125i \(0.828117\pi\)
\(542\) 14.0218 0.602286
\(543\) −10.6825 −0.458430
\(544\) 7.97030 0.341724
\(545\) 16.4464 0.704486
\(546\) −5.71517 −0.244587
\(547\) 19.2275 0.822110 0.411055 0.911611i \(-0.365160\pi\)
0.411055 + 0.911611i \(0.365160\pi\)
\(548\) −16.5753 −0.708062
\(549\) −1.11802 −0.0477159
\(550\) −4.91245 −0.209468
\(551\) 15.6497 0.666701
\(552\) 0.258294 0.0109937
\(553\) −1.83314 −0.0779532
\(554\) −39.1651 −1.66397
\(555\) 3.24266 0.137643
\(556\) 18.8052 0.797519
\(557\) 42.0447 1.78149 0.890745 0.454503i \(-0.150183\pi\)
0.890745 + 0.454503i \(0.150183\pi\)
\(558\) 3.43959 0.145609
\(559\) −14.2365 −0.602142
\(560\) 2.81056 0.118768
\(561\) 1.01167 0.0427127
\(562\) −11.4290 −0.482104
\(563\) −36.1407 −1.52315 −0.761574 0.648078i \(-0.775573\pi\)
−0.761574 + 0.648078i \(0.775573\pi\)
\(564\) 6.53758 0.275282
\(565\) −23.0937 −0.971559
\(566\) 22.8359 0.959866
\(567\) −0.432857 −0.0181783
\(568\) 0.426487 0.0178950
\(569\) 12.3688 0.518529 0.259264 0.965806i \(-0.416520\pi\)
0.259264 + 0.965806i \(0.416520\pi\)
\(570\) −4.86766 −0.203884
\(571\) 26.1997 1.09642 0.548212 0.836340i \(-0.315309\pi\)
0.548212 + 0.836340i \(0.315309\pi\)
\(572\) −13.2164 −0.552605
\(573\) 14.9692 0.625349
\(574\) 0.00261413 0.000109112 0
\(575\) −11.2467 −0.469021
\(576\) −7.77383 −0.323910
\(577\) 14.0642 0.585500 0.292750 0.956189i \(-0.405430\pi\)
0.292750 + 0.956189i \(0.405430\pi\)
\(578\) 1.99297 0.0828966
\(579\) 15.9861 0.664359
\(580\) 32.3904 1.34494
\(581\) 4.98895 0.206977
\(582\) −1.28323 −0.0531914
\(583\) −4.54376 −0.188183
\(584\) −0.478099 −0.0197839
\(585\) −10.6073 −0.438558
\(586\) 55.9210 2.31007
\(587\) −24.1041 −0.994884 −0.497442 0.867497i \(-0.665727\pi\)
−0.497442 + 0.867497i \(0.665727\pi\)
\(588\) 13.4340 0.554009
\(589\) 2.63273 0.108480
\(590\) −40.3688 −1.66196
\(591\) 1.46441 0.0602380
\(592\) 8.21319 0.337560
\(593\) −18.0093 −0.739552 −0.369776 0.929121i \(-0.620566\pi\)
−0.369776 + 0.929121i \(0.620566\pi\)
\(594\) −2.01622 −0.0827266
\(595\) 0.693049 0.0284122
\(596\) 1.02291 0.0419000
\(597\) −25.2045 −1.03155
\(598\) −60.9469 −2.49230
\(599\) −4.37223 −0.178645 −0.0893223 0.996003i \(-0.528470\pi\)
−0.0893223 + 0.996003i \(0.528470\pi\)
\(600\) −0.136335 −0.00556586
\(601\) 26.2338 1.07010 0.535049 0.844821i \(-0.320293\pi\)
0.535049 + 0.844821i \(0.320293\pi\)
\(602\) −1.85380 −0.0755554
\(603\) −13.6575 −0.556177
\(604\) −19.8584 −0.808027
\(605\) −15.9735 −0.649414
\(606\) 33.8389 1.37461
\(607\) −20.8752 −0.847297 −0.423649 0.905827i \(-0.639251\pi\)
−0.423649 + 0.905827i \(0.639251\pi\)
\(608\) −12.1583 −0.493086
\(609\) 4.44070 0.179946
\(610\) −3.56754 −0.144446
\(611\) 21.9640 0.888569
\(612\) −1.97192 −0.0797103
\(613\) −29.3060 −1.18366 −0.591829 0.806064i \(-0.701594\pi\)
−0.591829 + 0.806064i \(0.701594\pi\)
\(614\) 50.2781 2.02906
\(615\) 0.00485180 0.000195644 0
\(616\) 0.0245036 0.000987277 0
\(617\) −0.294244 −0.0118458 −0.00592291 0.999982i \(-0.501885\pi\)
−0.00592291 + 0.999982i \(0.501885\pi\)
\(618\) −0.191812 −0.00771581
\(619\) −26.2966 −1.05695 −0.528476 0.848948i \(-0.677236\pi\)
−0.528476 + 0.848948i \(0.677236\pi\)
\(620\) 5.44899 0.218837
\(621\) −4.61601 −0.185234
\(622\) −60.7360 −2.43529
\(623\) −3.97858 −0.159398
\(624\) −26.8667 −1.07553
\(625\) −6.88132 −0.275253
\(626\) −17.7390 −0.708992
\(627\) −1.54326 −0.0616317
\(628\) −1.97192 −0.0786883
\(629\) 2.02527 0.0807526
\(630\) −1.38122 −0.0550293
\(631\) 31.8860 1.26936 0.634681 0.772774i \(-0.281132\pi\)
0.634681 + 0.772774i \(0.281132\pi\)
\(632\) −0.236974 −0.00942630
\(633\) 16.0553 0.638140
\(634\) 42.3845 1.68330
\(635\) −13.6850 −0.543072
\(636\) 8.85661 0.351187
\(637\) 45.1336 1.78826
\(638\) 20.6845 0.818908
\(639\) −7.62182 −0.301515
\(640\) 0.716662 0.0283286
\(641\) 24.5313 0.968929 0.484465 0.874811i \(-0.339014\pi\)
0.484465 + 0.874811i \(0.339014\pi\)
\(642\) 38.1144 1.50425
\(643\) 37.7961 1.49053 0.745267 0.666766i \(-0.232322\pi\)
0.745267 + 0.666766i \(0.232322\pi\)
\(644\) −3.94004 −0.155259
\(645\) −3.44064 −0.135475
\(646\) −3.04019 −0.119615
\(647\) −26.1212 −1.02693 −0.513465 0.858111i \(-0.671638\pi\)
−0.513465 + 0.858111i \(0.671638\pi\)
\(648\) −0.0559561 −0.00219816
\(649\) −12.7986 −0.502390
\(650\) 32.1696 1.26179
\(651\) 0.747051 0.0292792
\(652\) −38.6901 −1.51522
\(653\) −34.4860 −1.34954 −0.674772 0.738027i \(-0.735758\pi\)
−0.674772 + 0.738027i \(0.735758\pi\)
\(654\) −20.4716 −0.800503
\(655\) 13.9210 0.543938
\(656\) 0.0122889 0.000479802 0
\(657\) 8.54418 0.333340
\(658\) 2.86003 0.111496
\(659\) −26.2577 −1.02285 −0.511427 0.859327i \(-0.670883\pi\)
−0.511427 + 0.859327i \(0.670883\pi\)
\(660\) −3.19409 −0.124330
\(661\) −26.2617 −1.02146 −0.510731 0.859741i \(-0.670625\pi\)
−0.510731 + 0.859741i \(0.670625\pi\)
\(662\) 53.1358 2.06518
\(663\) −6.62498 −0.257293
\(664\) 0.644930 0.0250281
\(665\) −1.05722 −0.0409971
\(666\) −4.03629 −0.156403
\(667\) 47.3558 1.83363
\(668\) −38.8238 −1.50214
\(669\) −16.6067 −0.642051
\(670\) −43.5805 −1.68366
\(671\) −1.13106 −0.0436642
\(672\) −3.45000 −0.133087
\(673\) −12.2140 −0.470816 −0.235408 0.971897i \(-0.575643\pi\)
−0.235408 + 0.971897i \(0.575643\pi\)
\(674\) 46.4588 1.78952
\(675\) 2.43646 0.0937796
\(676\) 60.9135 2.34283
\(677\) −29.4272 −1.13098 −0.565490 0.824755i \(-0.691313\pi\)
−0.565490 + 0.824755i \(0.691313\pi\)
\(678\) 28.7458 1.10397
\(679\) −0.278706 −0.0106958
\(680\) 0.0895916 0.00343568
\(681\) −13.4179 −0.514174
\(682\) 3.47972 0.133245
\(683\) 39.4492 1.50948 0.754741 0.656023i \(-0.227762\pi\)
0.754741 + 0.656023i \(0.227762\pi\)
\(684\) 3.00808 0.115017
\(685\) −13.4583 −0.514216
\(686\) 11.9157 0.454945
\(687\) −13.1180 −0.500483
\(688\) −8.71464 −0.332243
\(689\) 29.7552 1.13358
\(690\) −14.7295 −0.560741
\(691\) 12.5047 0.475702 0.237851 0.971302i \(-0.423557\pi\)
0.237851 + 0.971302i \(0.423557\pi\)
\(692\) 9.49749 0.361040
\(693\) −0.437907 −0.0166347
\(694\) 49.5633 1.88140
\(695\) 15.2689 0.579183
\(696\) 0.574056 0.0217596
\(697\) 0.00303029 0.000114780 0
\(698\) −48.0215 −1.81764
\(699\) −3.59337 −0.135914
\(700\) 2.07967 0.0786041
\(701\) −4.30313 −0.162527 −0.0812636 0.996693i \(-0.525896\pi\)
−0.0812636 + 0.996693i \(0.525896\pi\)
\(702\) 13.2034 0.498330
\(703\) −3.08946 −0.116521
\(704\) −7.86454 −0.296406
\(705\) 5.30819 0.199918
\(706\) 16.3643 0.615879
\(707\) 7.34954 0.276408
\(708\) 24.9468 0.937560
\(709\) −40.0643 −1.50465 −0.752323 0.658794i \(-0.771067\pi\)
−0.752323 + 0.658794i \(0.771067\pi\)
\(710\) −24.3209 −0.912745
\(711\) 4.23499 0.158825
\(712\) −0.514318 −0.0192749
\(713\) 7.96659 0.298351
\(714\) −0.862669 −0.0322846
\(715\) −10.7311 −0.401319
\(716\) 29.7230 1.11080
\(717\) −1.63998 −0.0612462
\(718\) 1.44523 0.0539354
\(719\) 35.2408 1.31426 0.657129 0.753778i \(-0.271771\pi\)
0.657129 + 0.753778i \(0.271771\pi\)
\(720\) −6.49306 −0.241982
\(721\) −0.0416600 −0.00155150
\(722\) −33.2287 −1.23665
\(723\) 7.66528 0.285075
\(724\) 21.0651 0.782876
\(725\) −24.9958 −0.928321
\(726\) 19.8829 0.737924
\(727\) 0.701989 0.0260353 0.0130177 0.999915i \(-0.495856\pi\)
0.0130177 + 0.999915i \(0.495856\pi\)
\(728\) −0.160464 −0.00594717
\(729\) 1.00000 0.0370370
\(730\) 27.2641 1.00909
\(731\) −2.14892 −0.0794806
\(732\) 2.20465 0.0814861
\(733\) −16.8186 −0.621208 −0.310604 0.950539i \(-0.600531\pi\)
−0.310604 + 0.950539i \(0.600531\pi\)
\(734\) 23.8518 0.880386
\(735\) 10.9077 0.402338
\(736\) −36.7910 −1.35613
\(737\) −13.8169 −0.508951
\(738\) −0.00603926 −0.000222308 0
\(739\) 45.2138 1.66322 0.831609 0.555361i \(-0.187420\pi\)
0.831609 + 0.555361i \(0.187420\pi\)
\(740\) −6.39428 −0.235058
\(741\) 10.1061 0.371258
\(742\) 3.87455 0.142239
\(743\) 25.6625 0.941466 0.470733 0.882276i \(-0.343989\pi\)
0.470733 + 0.882276i \(0.343989\pi\)
\(744\) 0.0965726 0.00354052
\(745\) 0.830552 0.0304291
\(746\) −47.9913 −1.75709
\(747\) −11.5256 −0.421701
\(748\) −1.99493 −0.0729419
\(749\) 8.27813 0.302476
\(750\) 23.7294 0.866475
\(751\) 14.2218 0.518961 0.259481 0.965748i \(-0.416449\pi\)
0.259481 + 0.965748i \(0.416449\pi\)
\(752\) 13.4449 0.490284
\(753\) −27.9627 −1.01902
\(754\) −135.454 −4.93295
\(755\) −16.1240 −0.586814
\(756\) 0.853560 0.0310437
\(757\) −11.8283 −0.429906 −0.214953 0.976624i \(-0.568960\pi\)
−0.214953 + 0.976624i \(0.568960\pi\)
\(758\) 16.7144 0.607094
\(759\) −4.66987 −0.169505
\(760\) −0.136668 −0.00495747
\(761\) 8.85396 0.320956 0.160478 0.987039i \(-0.448696\pi\)
0.160478 + 0.987039i \(0.448696\pi\)
\(762\) 17.0343 0.617088
\(763\) −4.44626 −0.160966
\(764\) −29.5182 −1.06793
\(765\) −1.60110 −0.0578881
\(766\) 64.3017 2.32331
\(767\) 83.8128 3.02631
\(768\) −16.4397 −0.593217
\(769\) 13.8857 0.500731 0.250365 0.968151i \(-0.419449\pi\)
0.250365 + 0.968151i \(0.419449\pi\)
\(770\) −1.39734 −0.0503566
\(771\) 4.96860 0.178940
\(772\) −31.5233 −1.13455
\(773\) −4.70018 −0.169054 −0.0845268 0.996421i \(-0.526938\pi\)
−0.0845268 + 0.996421i \(0.526938\pi\)
\(774\) 4.28272 0.153939
\(775\) −4.20500 −0.151048
\(776\) −0.0360288 −0.00129336
\(777\) −0.876650 −0.0314496
\(778\) 15.2371 0.546277
\(779\) −0.00462257 −0.000165621 0
\(780\) 20.9168 0.748940
\(781\) −7.71075 −0.275912
\(782\) −9.19956 −0.328975
\(783\) −10.2590 −0.366628
\(784\) 27.6277 0.986704
\(785\) −1.60110 −0.0571459
\(786\) −17.3281 −0.618073
\(787\) −24.1514 −0.860903 −0.430451 0.902614i \(-0.641646\pi\)
−0.430451 + 0.902614i \(0.641646\pi\)
\(788\) −2.88771 −0.102871
\(789\) 28.1225 1.00119
\(790\) 13.5136 0.480794
\(791\) 6.24335 0.221988
\(792\) −0.0566090 −0.00201151
\(793\) 7.40686 0.263025
\(794\) 25.3488 0.899595
\(795\) 7.19113 0.255043
\(796\) 49.7014 1.76162
\(797\) −6.01909 −0.213207 −0.106604 0.994302i \(-0.533998\pi\)
−0.106604 + 0.994302i \(0.533998\pi\)
\(798\) 1.31596 0.0465846
\(799\) 3.31533 0.117288
\(800\) 19.4194 0.686578
\(801\) 9.19145 0.324764
\(802\) 72.1502 2.54771
\(803\) 8.64387 0.305036
\(804\) 26.9316 0.949804
\(805\) −3.19912 −0.112754
\(806\) −22.7872 −0.802646
\(807\) 4.56721 0.160774
\(808\) 0.950087 0.0334240
\(809\) 29.4135 1.03412 0.517062 0.855948i \(-0.327026\pi\)
0.517062 + 0.855948i \(0.327026\pi\)
\(810\) 3.19095 0.112119
\(811\) 49.2940 1.73095 0.865473 0.500956i \(-0.167018\pi\)
0.865473 + 0.500956i \(0.167018\pi\)
\(812\) −8.75671 −0.307300
\(813\) −7.03561 −0.246750
\(814\) −4.08339 −0.143123
\(815\) −31.4144 −1.10040
\(816\) −4.05537 −0.141966
\(817\) 3.27808 0.114685
\(818\) −75.8372 −2.65159
\(819\) 2.86767 0.100204
\(820\) −0.00956739 −0.000334108 0
\(821\) 40.0959 1.39936 0.699678 0.714458i \(-0.253327\pi\)
0.699678 + 0.714458i \(0.253327\pi\)
\(822\) 16.7522 0.584300
\(823\) 37.8978 1.32103 0.660517 0.750811i \(-0.270337\pi\)
0.660517 + 0.750811i \(0.270337\pi\)
\(824\) −0.00538546 −0.000187612 0
\(825\) 2.46489 0.0858165
\(826\) 10.9137 0.379734
\(827\) 25.3479 0.881432 0.440716 0.897647i \(-0.354725\pi\)
0.440716 + 0.897647i \(0.354725\pi\)
\(828\) 9.10241 0.316331
\(829\) −2.63384 −0.0914772 −0.0457386 0.998953i \(-0.514564\pi\)
−0.0457386 + 0.998953i \(0.514564\pi\)
\(830\) −36.7778 −1.27657
\(831\) 19.6517 0.681708
\(832\) 51.5015 1.78549
\(833\) 6.81264 0.236044
\(834\) −19.0059 −0.658121
\(835\) −31.5230 −1.09090
\(836\) 3.04318 0.105251
\(837\) −1.72586 −0.0596545
\(838\) 35.1581 1.21452
\(839\) 16.2186 0.559929 0.279964 0.960010i \(-0.409677\pi\)
0.279964 + 0.960010i \(0.409677\pi\)
\(840\) −0.0387803 −0.00133805
\(841\) 76.2481 2.62924
\(842\) −48.0866 −1.65717
\(843\) 5.73467 0.197512
\(844\) −31.6598 −1.08977
\(845\) 49.4588 1.70143
\(846\) −6.60735 −0.227165
\(847\) 4.31841 0.148382
\(848\) 18.2141 0.625474
\(849\) −11.4583 −0.393246
\(850\) 4.85580 0.166552
\(851\) −9.34864 −0.320467
\(852\) 15.0296 0.514907
\(853\) −8.32339 −0.284988 −0.142494 0.989796i \(-0.545512\pi\)
−0.142494 + 0.989796i \(0.545512\pi\)
\(854\) 0.964480 0.0330038
\(855\) 2.44242 0.0835288
\(856\) 1.07013 0.0365762
\(857\) −6.64789 −0.227088 −0.113544 0.993533i \(-0.536220\pi\)
−0.113544 + 0.993533i \(0.536220\pi\)
\(858\) 13.3574 0.456015
\(859\) 48.1724 1.64362 0.821811 0.569760i \(-0.192964\pi\)
0.821811 + 0.569760i \(0.192964\pi\)
\(860\) 6.78468 0.231356
\(861\) −0.00131168 −4.47019e−5 0
\(862\) −53.2645 −1.81420
\(863\) −48.0557 −1.63583 −0.817917 0.575336i \(-0.804871\pi\)
−0.817917 + 0.575336i \(0.804871\pi\)
\(864\) 7.97030 0.271155
\(865\) 7.71149 0.262199
\(866\) 16.2220 0.551245
\(867\) −1.00000 −0.0339618
\(868\) −1.47313 −0.0500012
\(869\) 4.28440 0.145338
\(870\) −32.7361 −1.10986
\(871\) 90.4809 3.06583
\(872\) −0.574776 −0.0194644
\(873\) 0.643877 0.0217919
\(874\) 14.0335 0.474691
\(875\) 5.15383 0.174231
\(876\) −16.8485 −0.569257
\(877\) −3.43556 −0.116011 −0.0580053 0.998316i \(-0.518474\pi\)
−0.0580053 + 0.998316i \(0.518474\pi\)
\(878\) 14.5012 0.489393
\(879\) −28.0591 −0.946412
\(880\) −6.56882 −0.221435
\(881\) 51.0698 1.72058 0.860292 0.509802i \(-0.170281\pi\)
0.860292 + 0.509802i \(0.170281\pi\)
\(882\) −13.5774 −0.457174
\(883\) −35.5021 −1.19474 −0.597371 0.801965i \(-0.703788\pi\)
−0.597371 + 0.801965i \(0.703788\pi\)
\(884\) 13.0640 0.439389
\(885\) 20.2556 0.680885
\(886\) 10.9602 0.368214
\(887\) 37.8314 1.27025 0.635126 0.772408i \(-0.280948\pi\)
0.635126 + 0.772408i \(0.280948\pi\)
\(888\) −0.113326 −0.00380297
\(889\) 3.69971 0.124084
\(890\) 29.3295 0.983126
\(891\) 1.01167 0.0338921
\(892\) 32.7471 1.09645
\(893\) −5.05739 −0.169239
\(894\) −1.03383 −0.0345763
\(895\) 24.1336 0.806697
\(896\) −0.193749 −0.00647269
\(897\) 30.5810 1.02107
\(898\) −11.6547 −0.388924
\(899\) 17.7057 0.590518
\(900\) −4.80452 −0.160151
\(901\) 4.49136 0.149629
\(902\) −0.00610973 −0.000203432 0
\(903\) 0.930173 0.0309542
\(904\) 0.807088 0.0268434
\(905\) 17.1038 0.568549
\(906\) 20.0703 0.666792
\(907\) 0.918220 0.0304890 0.0152445 0.999884i \(-0.495147\pi\)
0.0152445 + 0.999884i \(0.495147\pi\)
\(908\) 26.4590 0.878073
\(909\) −16.9792 −0.563163
\(910\) 9.15059 0.303339
\(911\) −38.2580 −1.26754 −0.633772 0.773520i \(-0.718494\pi\)
−0.633772 + 0.773520i \(0.718494\pi\)
\(912\) 6.18628 0.204848
\(913\) −11.6601 −0.385894
\(914\) −42.3439 −1.40061
\(915\) 1.79006 0.0591777
\(916\) 25.8677 0.854692
\(917\) −3.76352 −0.124282
\(918\) 1.99297 0.0657778
\(919\) 19.5757 0.645743 0.322871 0.946443i \(-0.395352\pi\)
0.322871 + 0.946443i \(0.395352\pi\)
\(920\) −0.413555 −0.0136345
\(921\) −25.2277 −0.831282
\(922\) −6.63905 −0.218645
\(923\) 50.4944 1.66204
\(924\) 0.863519 0.0284077
\(925\) 4.93449 0.162245
\(926\) −73.4383 −2.41333
\(927\) 0.0962444 0.00316108
\(928\) −81.7677 −2.68416
\(929\) −17.2376 −0.565548 −0.282774 0.959187i \(-0.591255\pi\)
−0.282774 + 0.959187i \(0.591255\pi\)
\(930\) −5.50714 −0.180586
\(931\) −10.3924 −0.340596
\(932\) 7.08585 0.232105
\(933\) 30.4752 0.997712
\(934\) −53.6829 −1.75656
\(935\) −1.61979 −0.0529727
\(936\) 0.370708 0.0121170
\(937\) 48.9576 1.59938 0.799688 0.600416i \(-0.204998\pi\)
0.799688 + 0.600416i \(0.204998\pi\)
\(938\) 11.7819 0.384693
\(939\) 8.90078 0.290466
\(940\) −10.4673 −0.341407
\(941\) −14.1271 −0.460532 −0.230266 0.973128i \(-0.573960\pi\)
−0.230266 + 0.973128i \(0.573960\pi\)
\(942\) 1.99297 0.0649344
\(943\) −0.0139878 −0.000455506 0
\(944\) 51.3045 1.66982
\(945\) 0.693049 0.0225449
\(946\) 4.33269 0.140868
\(947\) −22.5368 −0.732347 −0.366173 0.930547i \(-0.619332\pi\)
−0.366173 + 0.930547i \(0.619332\pi\)
\(948\) −8.35108 −0.271230
\(949\) −56.6050 −1.83748
\(950\) −7.40731 −0.240325
\(951\) −21.2670 −0.689630
\(952\) −0.0242210 −0.000785006 0
\(953\) −16.0109 −0.518644 −0.259322 0.965791i \(-0.583499\pi\)
−0.259322 + 0.965791i \(0.583499\pi\)
\(954\) −8.95113 −0.289804
\(955\) −23.9673 −0.775564
\(956\) 3.23391 0.104592
\(957\) −10.3787 −0.335497
\(958\) −39.3633 −1.27177
\(959\) 3.63844 0.117491
\(960\) 12.4467 0.401716
\(961\) −28.0214 −0.903916
\(962\) 26.7404 0.862144
\(963\) −19.1244 −0.616276
\(964\) −15.1153 −0.486832
\(965\) −25.5954 −0.823944
\(966\) 3.98209 0.128122
\(967\) 43.0782 1.38530 0.692651 0.721273i \(-0.256443\pi\)
0.692651 + 0.721273i \(0.256443\pi\)
\(968\) 0.558248 0.0179428
\(969\) 1.52546 0.0490047
\(970\) 2.05458 0.0659686
\(971\) 48.0368 1.54157 0.770787 0.637093i \(-0.219863\pi\)
0.770787 + 0.637093i \(0.219863\pi\)
\(972\) −1.97192 −0.0632495
\(973\) −4.12793 −0.132335
\(974\) 44.4233 1.42341
\(975\) −16.1415 −0.516943
\(976\) 4.53397 0.145129
\(977\) −10.8729 −0.347856 −0.173928 0.984758i \(-0.555646\pi\)
−0.173928 + 0.984758i \(0.555646\pi\)
\(978\) 39.1030 1.25038
\(979\) 9.29869 0.297187
\(980\) −21.5092 −0.687087
\(981\) 10.2719 0.327957
\(982\) 10.7952 0.344487
\(983\) −26.8200 −0.855425 −0.427712 0.903915i \(-0.640680\pi\)
−0.427712 + 0.903915i \(0.640680\pi\)
\(984\) −0.000169563 0 −5.40547e−6 0
\(985\) −2.34468 −0.0747078
\(986\) −20.4460 −0.651132
\(987\) −1.43506 −0.0456785
\(988\) −19.9285 −0.634010
\(989\) 9.91942 0.315419
\(990\) 3.22818 0.102598
\(991\) 7.75001 0.246187 0.123094 0.992395i \(-0.460718\pi\)
0.123094 + 0.992395i \(0.460718\pi\)
\(992\) −13.7556 −0.436742
\(993\) −26.6616 −0.846081
\(994\) 6.57511 0.208550
\(995\) 40.3550 1.27934
\(996\) 22.7277 0.720154
\(997\) 37.1197 1.17559 0.587797 0.809009i \(-0.299996\pi\)
0.587797 + 0.809009i \(0.299996\pi\)
\(998\) −59.1042 −1.87091
\(999\) 2.02527 0.0640766
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 8007.2.a.f.1.41 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8007.2.a.f.1.41 48 1.1 even 1 trivial