Properties

Label 8007.2.a.f.1.8
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 1.8
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.17906 q^{2} -1.00000 q^{3} +2.74829 q^{4} -2.11197 q^{5} +2.17906 q^{6} +2.69680 q^{7} -1.63058 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.17906 q^{2} -1.00000 q^{3} +2.74829 q^{4} -2.11197 q^{5} +2.17906 q^{6} +2.69680 q^{7} -1.63058 q^{8} +1.00000 q^{9} +4.60211 q^{10} +3.86808 q^{11} -2.74829 q^{12} -2.95745 q^{13} -5.87648 q^{14} +2.11197 q^{15} -1.94347 q^{16} -1.00000 q^{17} -2.17906 q^{18} +2.38202 q^{19} -5.80432 q^{20} -2.69680 q^{21} -8.42877 q^{22} +6.54103 q^{23} +1.63058 q^{24} -0.539577 q^{25} +6.44446 q^{26} -1.00000 q^{27} +7.41160 q^{28} -0.373077 q^{29} -4.60211 q^{30} +0.0561826 q^{31} +7.49608 q^{32} -3.86808 q^{33} +2.17906 q^{34} -5.69556 q^{35} +2.74829 q^{36} +2.78351 q^{37} -5.19056 q^{38} +2.95745 q^{39} +3.44373 q^{40} -4.44920 q^{41} +5.87648 q^{42} -8.21989 q^{43} +10.6306 q^{44} -2.11197 q^{45} -14.2533 q^{46} +9.32591 q^{47} +1.94347 q^{48} +0.272727 q^{49} +1.17577 q^{50} +1.00000 q^{51} -8.12794 q^{52} +4.89515 q^{53} +2.17906 q^{54} -8.16927 q^{55} -4.39734 q^{56} -2.38202 q^{57} +0.812957 q^{58} +8.24937 q^{59} +5.80432 q^{60} -11.0605 q^{61} -0.122425 q^{62} +2.69680 q^{63} -12.4475 q^{64} +6.24605 q^{65} +8.42877 q^{66} -3.51722 q^{67} -2.74829 q^{68} -6.54103 q^{69} +12.4110 q^{70} -12.0755 q^{71} -1.63058 q^{72} -3.35786 q^{73} -6.06544 q^{74} +0.539577 q^{75} +6.54650 q^{76} +10.4314 q^{77} -6.44446 q^{78} -9.02614 q^{79} +4.10454 q^{80} +1.00000 q^{81} +9.69506 q^{82} -13.8275 q^{83} -7.41160 q^{84} +2.11197 q^{85} +17.9116 q^{86} +0.373077 q^{87} -6.30721 q^{88} +4.41269 q^{89} +4.60211 q^{90} -7.97565 q^{91} +17.9767 q^{92} -0.0561826 q^{93} -20.3217 q^{94} -5.03076 q^{95} -7.49608 q^{96} +17.3963 q^{97} -0.594287 q^{98} +3.86808 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} + O(q^{10}) \) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} - 20q^{10} + 5q^{11} - 45q^{12} - 8q^{13} + 4q^{14} - q^{15} + 39q^{16} - 48q^{17} - q^{18} - 6q^{19} + 6q^{20} + 13q^{21} - 35q^{22} - 8q^{23} + 6q^{24} + 13q^{25} + 17q^{26} - 48q^{27} - 38q^{28} + q^{29} + 20q^{30} - 21q^{31} - 3q^{32} - 5q^{33} + q^{34} + 19q^{35} + 45q^{36} - 58q^{37} - 14q^{38} + 8q^{39} - 54q^{40} - 3q^{41} - 4q^{42} - 33q^{43} + 2q^{44} + q^{45} - 26q^{46} + 9q^{47} - 39q^{48} + 11q^{49} + 4q^{50} + 48q^{51} - 31q^{52} - 33q^{53} + q^{54} - 21q^{55} + 6q^{57} - 55q^{58} + 77q^{59} - 6q^{60} - 29q^{61} - 46q^{62} - 13q^{63} + 24q^{64} - 49q^{65} + 35q^{66} - 44q^{67} - 45q^{68} + 8q^{69} + 4q^{70} + 22q^{71} - 6q^{72} - 63q^{73} - 16q^{74} - 13q^{75} - 46q^{76} - 30q^{77} - 17q^{78} - 46q^{79} - 14q^{80} + 48q^{81} - 75q^{82} + 11q^{83} + 38q^{84} - q^{85} + 8q^{86} - q^{87} - 116q^{88} + 10q^{89} - 20q^{90} - 67q^{91} - 64q^{92} + 21q^{93} - 16q^{94} - 8q^{95} + 3q^{96} - 96q^{97} - 46q^{98} + 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.17906 −1.54083 −0.770413 0.637545i \(-0.779950\pi\)
−0.770413 + 0.637545i \(0.779950\pi\)
\(3\) −1.00000 −0.577350
\(4\) 2.74829 1.37415
\(5\) −2.11197 −0.944502 −0.472251 0.881464i \(-0.656558\pi\)
−0.472251 + 0.881464i \(0.656558\pi\)
\(6\) 2.17906 0.889597
\(7\) 2.69680 1.01929 0.509647 0.860383i \(-0.329776\pi\)
0.509647 + 0.860383i \(0.329776\pi\)
\(8\) −1.63058 −0.576496
\(9\) 1.00000 0.333333
\(10\) 4.60211 1.45531
\(11\) 3.86808 1.16627 0.583135 0.812375i \(-0.301826\pi\)
0.583135 + 0.812375i \(0.301826\pi\)
\(12\) −2.74829 −0.793364
\(13\) −2.95745 −0.820249 −0.410125 0.912030i \(-0.634515\pi\)
−0.410125 + 0.912030i \(0.634515\pi\)
\(14\) −5.87648 −1.57056
\(15\) 2.11197 0.545309
\(16\) −1.94347 −0.485866
\(17\) −1.00000 −0.242536
\(18\) −2.17906 −0.513609
\(19\) 2.38202 0.546473 0.273237 0.961947i \(-0.411906\pi\)
0.273237 + 0.961947i \(0.411906\pi\)
\(20\) −5.80432 −1.29789
\(21\) −2.69680 −0.588490
\(22\) −8.42877 −1.79702
\(23\) 6.54103 1.36390 0.681949 0.731399i \(-0.261132\pi\)
0.681949 + 0.731399i \(0.261132\pi\)
\(24\) 1.63058 0.332840
\(25\) −0.539577 −0.107915
\(26\) 6.44446 1.26386
\(27\) −1.00000 −0.192450
\(28\) 7.41160 1.40066
\(29\) −0.373077 −0.0692787 −0.0346393 0.999400i \(-0.511028\pi\)
−0.0346393 + 0.999400i \(0.511028\pi\)
\(30\) −4.60211 −0.840226
\(31\) 0.0561826 0.0100907 0.00504535 0.999987i \(-0.498394\pi\)
0.00504535 + 0.999987i \(0.498394\pi\)
\(32\) 7.49608 1.32513
\(33\) −3.86808 −0.673346
\(34\) 2.17906 0.373705
\(35\) −5.69556 −0.962726
\(36\) 2.74829 0.458049
\(37\) 2.78351 0.457607 0.228803 0.973473i \(-0.426519\pi\)
0.228803 + 0.973473i \(0.426519\pi\)
\(38\) −5.19056 −0.842020
\(39\) 2.95745 0.473571
\(40\) 3.44373 0.544502
\(41\) −4.44920 −0.694848 −0.347424 0.937708i \(-0.612943\pi\)
−0.347424 + 0.937708i \(0.612943\pi\)
\(42\) 5.87648 0.906761
\(43\) −8.21989 −1.25352 −0.626761 0.779212i \(-0.715620\pi\)
−0.626761 + 0.779212i \(0.715620\pi\)
\(44\) 10.6306 1.60263
\(45\) −2.11197 −0.314834
\(46\) −14.2533 −2.10153
\(47\) 9.32591 1.36032 0.680162 0.733062i \(-0.261909\pi\)
0.680162 + 0.733062i \(0.261909\pi\)
\(48\) 1.94347 0.280515
\(49\) 0.272727 0.0389609
\(50\) 1.17577 0.166279
\(51\) 1.00000 0.140028
\(52\) −8.12794 −1.12714
\(53\) 4.89515 0.672400 0.336200 0.941791i \(-0.390858\pi\)
0.336200 + 0.941791i \(0.390858\pi\)
\(54\) 2.17906 0.296532
\(55\) −8.16927 −1.10154
\(56\) −4.39734 −0.587620
\(57\) −2.38202 −0.315506
\(58\) 0.812957 0.106746
\(59\) 8.24937 1.07398 0.536989 0.843590i \(-0.319562\pi\)
0.536989 + 0.843590i \(0.319562\pi\)
\(60\) 5.80432 0.749335
\(61\) −11.0605 −1.41615 −0.708077 0.706135i \(-0.750437\pi\)
−0.708077 + 0.706135i \(0.750437\pi\)
\(62\) −0.122425 −0.0155480
\(63\) 2.69680 0.339765
\(64\) −12.4475 −1.55593
\(65\) 6.24605 0.774727
\(66\) 8.42877 1.03751
\(67\) −3.51722 −0.429697 −0.214848 0.976647i \(-0.568926\pi\)
−0.214848 + 0.976647i \(0.568926\pi\)
\(68\) −2.74829 −0.333280
\(69\) −6.54103 −0.787447
\(70\) 12.4110 1.48339
\(71\) −12.0755 −1.43310 −0.716550 0.697536i \(-0.754280\pi\)
−0.716550 + 0.697536i \(0.754280\pi\)
\(72\) −1.63058 −0.192165
\(73\) −3.35786 −0.393008 −0.196504 0.980503i \(-0.562959\pi\)
−0.196504 + 0.980503i \(0.562959\pi\)
\(74\) −6.06544 −0.705093
\(75\) 0.539577 0.0623050
\(76\) 6.54650 0.750935
\(77\) 10.4314 1.18877
\(78\) −6.44446 −0.729691
\(79\) −9.02614 −1.01552 −0.507760 0.861499i \(-0.669526\pi\)
−0.507760 + 0.861499i \(0.669526\pi\)
\(80\) 4.10454 0.458902
\(81\) 1.00000 0.111111
\(82\) 9.69506 1.07064
\(83\) −13.8275 −1.51776 −0.758882 0.651229i \(-0.774254\pi\)
−0.758882 + 0.651229i \(0.774254\pi\)
\(84\) −7.41160 −0.808672
\(85\) 2.11197 0.229075
\(86\) 17.9116 1.93146
\(87\) 0.373077 0.0399981
\(88\) −6.30721 −0.672350
\(89\) 4.41269 0.467744 0.233872 0.972267i \(-0.424860\pi\)
0.233872 + 0.972267i \(0.424860\pi\)
\(90\) 4.60211 0.485105
\(91\) −7.97565 −0.836075
\(92\) 17.9767 1.87420
\(93\) −0.0561826 −0.00582587
\(94\) −20.3217 −2.09602
\(95\) −5.03076 −0.516145
\(96\) −7.49608 −0.765065
\(97\) 17.3963 1.76633 0.883164 0.469064i \(-0.155409\pi\)
0.883164 + 0.469064i \(0.155409\pi\)
\(98\) −0.594287 −0.0600321
\(99\) 3.86808 0.388757
\(100\) −1.48292 −0.148292
\(101\) −8.36277 −0.832126 −0.416063 0.909336i \(-0.636590\pi\)
−0.416063 + 0.909336i \(0.636590\pi\)
\(102\) −2.17906 −0.215759
\(103\) −14.3905 −1.41794 −0.708969 0.705239i \(-0.750839\pi\)
−0.708969 + 0.705239i \(0.750839\pi\)
\(104\) 4.82235 0.472871
\(105\) 5.69556 0.555830
\(106\) −10.6668 −1.03605
\(107\) 3.26151 0.315302 0.157651 0.987495i \(-0.449608\pi\)
0.157651 + 0.987495i \(0.449608\pi\)
\(108\) −2.74829 −0.264455
\(109\) −3.48691 −0.333985 −0.166992 0.985958i \(-0.553406\pi\)
−0.166992 + 0.985958i \(0.553406\pi\)
\(110\) 17.8013 1.69729
\(111\) −2.78351 −0.264200
\(112\) −5.24114 −0.495241
\(113\) −16.9344 −1.59306 −0.796529 0.604600i \(-0.793333\pi\)
−0.796529 + 0.604600i \(0.793333\pi\)
\(114\) 5.19056 0.486141
\(115\) −13.8145 −1.28821
\(116\) −1.02533 −0.0951991
\(117\) −2.95745 −0.273416
\(118\) −17.9759 −1.65481
\(119\) −2.69680 −0.247215
\(120\) −3.44373 −0.314368
\(121\) 3.96204 0.360185
\(122\) 24.1015 2.18205
\(123\) 4.44920 0.401170
\(124\) 0.154406 0.0138661
\(125\) 11.6994 1.04643
\(126\) −5.87648 −0.523519
\(127\) −14.9097 −1.32302 −0.661510 0.749936i \(-0.730084\pi\)
−0.661510 + 0.749936i \(0.730084\pi\)
\(128\) 12.1316 1.07229
\(129\) 8.21989 0.723721
\(130\) −13.6105 −1.19372
\(131\) 9.53654 0.833211 0.416606 0.909087i \(-0.363220\pi\)
0.416606 + 0.909087i \(0.363220\pi\)
\(132\) −10.6306 −0.925277
\(133\) 6.42383 0.557017
\(134\) 7.66423 0.662088
\(135\) 2.11197 0.181770
\(136\) 1.63058 0.139821
\(137\) −18.3801 −1.57032 −0.785159 0.619295i \(-0.787419\pi\)
−0.785159 + 0.619295i \(0.787419\pi\)
\(138\) 14.2533 1.21332
\(139\) 16.8849 1.43216 0.716078 0.698020i \(-0.245935\pi\)
0.716078 + 0.698020i \(0.245935\pi\)
\(140\) −15.6531 −1.32293
\(141\) −9.32591 −0.785384
\(142\) 26.3132 2.20816
\(143\) −11.4397 −0.956632
\(144\) −1.94347 −0.161955
\(145\) 0.787928 0.0654339
\(146\) 7.31698 0.605557
\(147\) −0.272727 −0.0224941
\(148\) 7.64992 0.628819
\(149\) −4.52276 −0.370519 −0.185259 0.982690i \(-0.559312\pi\)
−0.185259 + 0.982690i \(0.559312\pi\)
\(150\) −1.17577 −0.0960012
\(151\) −0.926814 −0.0754230 −0.0377115 0.999289i \(-0.512007\pi\)
−0.0377115 + 0.999289i \(0.512007\pi\)
\(152\) −3.88407 −0.315040
\(153\) −1.00000 −0.0808452
\(154\) −22.7307 −1.83169
\(155\) −0.118656 −0.00953068
\(156\) 8.12794 0.650756
\(157\) −1.00000 −0.0798087
\(158\) 19.6685 1.56474
\(159\) −4.89515 −0.388210
\(160\) −15.8315 −1.25159
\(161\) 17.6398 1.39021
\(162\) −2.17906 −0.171203
\(163\) −21.5271 −1.68613 −0.843066 0.537811i \(-0.819252\pi\)
−0.843066 + 0.537811i \(0.819252\pi\)
\(164\) −12.2277 −0.954823
\(165\) 8.16927 0.635977
\(166\) 30.1309 2.33861
\(167\) 6.11273 0.473017 0.236509 0.971629i \(-0.423997\pi\)
0.236509 + 0.971629i \(0.423997\pi\)
\(168\) 4.39734 0.339262
\(169\) −4.25349 −0.327192
\(170\) −4.60211 −0.352966
\(171\) 2.38202 0.182158
\(172\) −22.5907 −1.72252
\(173\) 23.4820 1.78530 0.892650 0.450750i \(-0.148843\pi\)
0.892650 + 0.450750i \(0.148843\pi\)
\(174\) −0.812957 −0.0616301
\(175\) −1.45513 −0.109998
\(176\) −7.51748 −0.566651
\(177\) −8.24937 −0.620061
\(178\) −9.61550 −0.720712
\(179\) 9.24636 0.691106 0.345553 0.938399i \(-0.387691\pi\)
0.345553 + 0.938399i \(0.387691\pi\)
\(180\) −5.80432 −0.432628
\(181\) 25.9507 1.92890 0.964451 0.264261i \(-0.0851281\pi\)
0.964451 + 0.264261i \(0.0851281\pi\)
\(182\) 17.3794 1.28825
\(183\) 11.0605 0.817617
\(184\) −10.6657 −0.786283
\(185\) −5.87870 −0.432211
\(186\) 0.122425 0.00897665
\(187\) −3.86808 −0.282862
\(188\) 25.6304 1.86929
\(189\) −2.69680 −0.196163
\(190\) 10.9623 0.795290
\(191\) 7.58483 0.548819 0.274410 0.961613i \(-0.411518\pi\)
0.274410 + 0.961613i \(0.411518\pi\)
\(192\) 12.4475 0.898318
\(193\) −9.64509 −0.694269 −0.347134 0.937815i \(-0.612845\pi\)
−0.347134 + 0.937815i \(0.612845\pi\)
\(194\) −37.9076 −2.72161
\(195\) −6.24605 −0.447289
\(196\) 0.749533 0.0535381
\(197\) −18.5587 −1.32225 −0.661126 0.750275i \(-0.729921\pi\)
−0.661126 + 0.750275i \(0.729921\pi\)
\(198\) −8.42877 −0.599007
\(199\) −10.6954 −0.758180 −0.379090 0.925360i \(-0.623763\pi\)
−0.379090 + 0.925360i \(0.623763\pi\)
\(200\) 0.879822 0.0622128
\(201\) 3.51722 0.248086
\(202\) 18.2230 1.28216
\(203\) −1.00611 −0.0706153
\(204\) 2.74829 0.192419
\(205\) 9.39657 0.656285
\(206\) 31.3577 2.18480
\(207\) 6.54103 0.454633
\(208\) 5.74770 0.398531
\(209\) 9.21385 0.637335
\(210\) −12.4110 −0.856438
\(211\) 22.3890 1.54132 0.770662 0.637245i \(-0.219926\pi\)
0.770662 + 0.637245i \(0.219926\pi\)
\(212\) 13.4533 0.923977
\(213\) 12.0755 0.827401
\(214\) −7.10702 −0.485826
\(215\) 17.3602 1.18395
\(216\) 1.63058 0.110947
\(217\) 0.151513 0.0102854
\(218\) 7.59817 0.514613
\(219\) 3.35786 0.226903
\(220\) −22.4516 −1.51368
\(221\) 2.95745 0.198940
\(222\) 6.06544 0.407086
\(223\) −14.6092 −0.978302 −0.489151 0.872199i \(-0.662693\pi\)
−0.489151 + 0.872199i \(0.662693\pi\)
\(224\) 20.2154 1.35070
\(225\) −0.539577 −0.0359718
\(226\) 36.9011 2.45463
\(227\) −3.22125 −0.213802 −0.106901 0.994270i \(-0.534093\pi\)
−0.106901 + 0.994270i \(0.534093\pi\)
\(228\) −6.54650 −0.433552
\(229\) 3.84496 0.254082 0.127041 0.991897i \(-0.459452\pi\)
0.127041 + 0.991897i \(0.459452\pi\)
\(230\) 30.1025 1.98490
\(231\) −10.4314 −0.686338
\(232\) 0.608331 0.0399389
\(233\) 9.64403 0.631801 0.315901 0.948792i \(-0.397693\pi\)
0.315901 + 0.948792i \(0.397693\pi\)
\(234\) 6.44446 0.421287
\(235\) −19.6961 −1.28483
\(236\) 22.6717 1.47580
\(237\) 9.02614 0.586311
\(238\) 5.87648 0.380916
\(239\) 21.5983 1.39708 0.698540 0.715571i \(-0.253833\pi\)
0.698540 + 0.715571i \(0.253833\pi\)
\(240\) −4.10454 −0.264947
\(241\) −0.331039 −0.0213241 −0.0106620 0.999943i \(-0.503394\pi\)
−0.0106620 + 0.999943i \(0.503394\pi\)
\(242\) −8.63351 −0.554983
\(243\) −1.00000 −0.0641500
\(244\) −30.3976 −1.94600
\(245\) −0.575991 −0.0367987
\(246\) −9.69506 −0.618134
\(247\) −7.04471 −0.448244
\(248\) −0.0916101 −0.00581725
\(249\) 13.8275 0.876281
\(250\) −25.4937 −1.61237
\(251\) −16.3893 −1.03448 −0.517242 0.855839i \(-0.673041\pi\)
−0.517242 + 0.855839i \(0.673041\pi\)
\(252\) 7.41160 0.466887
\(253\) 25.3012 1.59067
\(254\) 32.4891 2.03855
\(255\) −2.11197 −0.132257
\(256\) −1.54051 −0.0962821
\(257\) 7.34696 0.458291 0.229145 0.973392i \(-0.426407\pi\)
0.229145 + 0.973392i \(0.426407\pi\)
\(258\) −17.9116 −1.11513
\(259\) 7.50658 0.466436
\(260\) 17.1660 1.06459
\(261\) −0.373077 −0.0230929
\(262\) −20.7807 −1.28383
\(263\) 10.9172 0.673185 0.336593 0.941650i \(-0.390726\pi\)
0.336593 + 0.941650i \(0.390726\pi\)
\(264\) 6.30721 0.388182
\(265\) −10.3384 −0.635083
\(266\) −13.9979 −0.858267
\(267\) −4.41269 −0.270052
\(268\) −9.66636 −0.590467
\(269\) −26.3169 −1.60457 −0.802285 0.596942i \(-0.796382\pi\)
−0.802285 + 0.596942i \(0.796382\pi\)
\(270\) −4.60211 −0.280075
\(271\) 15.7062 0.954081 0.477041 0.878881i \(-0.341709\pi\)
0.477041 + 0.878881i \(0.341709\pi\)
\(272\) 1.94347 0.117840
\(273\) 7.97565 0.482708
\(274\) 40.0513 2.41959
\(275\) −2.08713 −0.125858
\(276\) −17.9767 −1.08207
\(277\) 21.1409 1.27023 0.635116 0.772416i \(-0.280952\pi\)
0.635116 + 0.772416i \(0.280952\pi\)
\(278\) −36.7931 −2.20671
\(279\) 0.0561826 0.00336356
\(280\) 9.28706 0.555008
\(281\) 25.1756 1.50185 0.750926 0.660387i \(-0.229608\pi\)
0.750926 + 0.660387i \(0.229608\pi\)
\(282\) 20.3217 1.21014
\(283\) 10.0335 0.596427 0.298214 0.954499i \(-0.403609\pi\)
0.298214 + 0.954499i \(0.403609\pi\)
\(284\) −33.1871 −1.96929
\(285\) 5.03076 0.297997
\(286\) 24.9277 1.47400
\(287\) −11.9986 −0.708254
\(288\) 7.49608 0.441711
\(289\) 1.00000 0.0588235
\(290\) −1.71694 −0.100822
\(291\) −17.3963 −1.01979
\(292\) −9.22839 −0.540051
\(293\) −17.1601 −1.00251 −0.501253 0.865301i \(-0.667127\pi\)
−0.501253 + 0.865301i \(0.667127\pi\)
\(294\) 0.594287 0.0346595
\(295\) −17.4224 −1.01437
\(296\) −4.53874 −0.263809
\(297\) −3.86808 −0.224449
\(298\) 9.85535 0.570905
\(299\) −19.3448 −1.11874
\(300\) 1.48292 0.0856162
\(301\) −22.1674 −1.27771
\(302\) 2.01958 0.116214
\(303\) 8.36277 0.480428
\(304\) −4.62937 −0.265513
\(305\) 23.3595 1.33756
\(306\) 2.17906 0.124568
\(307\) −12.3845 −0.706820 −0.353410 0.935468i \(-0.614978\pi\)
−0.353410 + 0.935468i \(0.614978\pi\)
\(308\) 28.6687 1.63355
\(309\) 14.3905 0.818647
\(310\) 0.258558 0.0146851
\(311\) 0.513125 0.0290966 0.0145483 0.999894i \(-0.495369\pi\)
0.0145483 + 0.999894i \(0.495369\pi\)
\(312\) −4.82235 −0.273012
\(313\) 12.5013 0.706617 0.353309 0.935507i \(-0.385057\pi\)
0.353309 + 0.935507i \(0.385057\pi\)
\(314\) 2.17906 0.122971
\(315\) −5.69556 −0.320909
\(316\) −24.8065 −1.39547
\(317\) 8.32697 0.467689 0.233845 0.972274i \(-0.424869\pi\)
0.233845 + 0.972274i \(0.424869\pi\)
\(318\) 10.6668 0.598165
\(319\) −1.44309 −0.0807976
\(320\) 26.2887 1.46958
\(321\) −3.26151 −0.182040
\(322\) −38.4382 −2.14208
\(323\) −2.38202 −0.132539
\(324\) 2.74829 0.152683
\(325\) 1.59577 0.0885175
\(326\) 46.9088 2.59804
\(327\) 3.48691 0.192826
\(328\) 7.25476 0.400577
\(329\) 25.1501 1.38657
\(330\) −17.8013 −0.979930
\(331\) −11.5544 −0.635089 −0.317545 0.948243i \(-0.602858\pi\)
−0.317545 + 0.948243i \(0.602858\pi\)
\(332\) −38.0020 −2.08563
\(333\) 2.78351 0.152536
\(334\) −13.3200 −0.728837
\(335\) 7.42827 0.405850
\(336\) 5.24114 0.285927
\(337\) 19.0497 1.03771 0.518853 0.854864i \(-0.326359\pi\)
0.518853 + 0.854864i \(0.326359\pi\)
\(338\) 9.26860 0.504145
\(339\) 16.9344 0.919753
\(340\) 5.80432 0.314783
\(341\) 0.217319 0.0117685
\(342\) −5.19056 −0.280673
\(343\) −18.1421 −0.979582
\(344\) 13.4032 0.722651
\(345\) 13.8145 0.743746
\(346\) −51.1686 −2.75084
\(347\) −18.0836 −0.970778 −0.485389 0.874298i \(-0.661322\pi\)
−0.485389 + 0.874298i \(0.661322\pi\)
\(348\) 1.02533 0.0549632
\(349\) 36.4607 1.95170 0.975848 0.218452i \(-0.0701007\pi\)
0.975848 + 0.218452i \(0.0701007\pi\)
\(350\) 3.17081 0.169487
\(351\) 2.95745 0.157857
\(352\) 28.9954 1.54546
\(353\) −28.3352 −1.50813 −0.754066 0.656798i \(-0.771910\pi\)
−0.754066 + 0.656798i \(0.771910\pi\)
\(354\) 17.9759 0.955407
\(355\) 25.5031 1.35357
\(356\) 12.1274 0.642749
\(357\) 2.69680 0.142730
\(358\) −20.1484 −1.06487
\(359\) −34.3831 −1.81467 −0.907336 0.420407i \(-0.861887\pi\)
−0.907336 + 0.420407i \(0.861887\pi\)
\(360\) 3.44373 0.181501
\(361\) −13.3260 −0.701367
\(362\) −56.5481 −2.97210
\(363\) −3.96204 −0.207953
\(364\) −21.9194 −1.14889
\(365\) 7.09171 0.371197
\(366\) −24.1015 −1.25981
\(367\) −5.82738 −0.304187 −0.152093 0.988366i \(-0.548601\pi\)
−0.152093 + 0.988366i \(0.548601\pi\)
\(368\) −12.7123 −0.662672
\(369\) −4.44920 −0.231616
\(370\) 12.8100 0.665962
\(371\) 13.2012 0.685373
\(372\) −0.154406 −0.00800560
\(373\) 4.44885 0.230353 0.115176 0.993345i \(-0.463257\pi\)
0.115176 + 0.993345i \(0.463257\pi\)
\(374\) 8.42877 0.435841
\(375\) −11.6994 −0.604156
\(376\) −15.2066 −0.784222
\(377\) 1.10336 0.0568258
\(378\) 5.87648 0.302254
\(379\) −19.1773 −0.985073 −0.492537 0.870292i \(-0.663930\pi\)
−0.492537 + 0.870292i \(0.663930\pi\)
\(380\) −13.8260 −0.709259
\(381\) 14.9097 0.763846
\(382\) −16.5278 −0.845636
\(383\) −31.8856 −1.62928 −0.814638 0.579970i \(-0.803064\pi\)
−0.814638 + 0.579970i \(0.803064\pi\)
\(384\) −12.1316 −0.619088
\(385\) −22.0309 −1.12280
\(386\) 21.0172 1.06975
\(387\) −8.21989 −0.417841
\(388\) 47.8102 2.42719
\(389\) 31.0338 1.57348 0.786738 0.617287i \(-0.211768\pi\)
0.786738 + 0.617287i \(0.211768\pi\)
\(390\) 13.6105 0.689195
\(391\) −6.54103 −0.330794
\(392\) −0.444702 −0.0224608
\(393\) −9.53654 −0.481055
\(394\) 40.4405 2.03736
\(395\) 19.0629 0.959161
\(396\) 10.6306 0.534209
\(397\) −22.2317 −1.11578 −0.557888 0.829916i \(-0.688388\pi\)
−0.557888 + 0.829916i \(0.688388\pi\)
\(398\) 23.3060 1.16822
\(399\) −6.42383 −0.321594
\(400\) 1.04865 0.0524324
\(401\) 34.7042 1.73304 0.866521 0.499140i \(-0.166351\pi\)
0.866521 + 0.499140i \(0.166351\pi\)
\(402\) −7.66423 −0.382257
\(403\) −0.166157 −0.00827688
\(404\) −22.9833 −1.14346
\(405\) −2.11197 −0.104945
\(406\) 2.19238 0.108806
\(407\) 10.7669 0.533693
\(408\) −1.63058 −0.0807256
\(409\) −14.3081 −0.707492 −0.353746 0.935342i \(-0.615092\pi\)
−0.353746 + 0.935342i \(0.615092\pi\)
\(410\) −20.4757 −1.01122
\(411\) 18.3801 0.906623
\(412\) −39.5493 −1.94846
\(413\) 22.2469 1.09470
\(414\) −14.2533 −0.700511
\(415\) 29.2032 1.43353
\(416\) −22.1693 −1.08694
\(417\) −16.8849 −0.826856
\(418\) −20.0775 −0.982023
\(419\) −17.4127 −0.850668 −0.425334 0.905036i \(-0.639843\pi\)
−0.425334 + 0.905036i \(0.639843\pi\)
\(420\) 15.6531 0.763792
\(421\) −19.8586 −0.967848 −0.483924 0.875110i \(-0.660789\pi\)
−0.483924 + 0.875110i \(0.660789\pi\)
\(422\) −48.7870 −2.37491
\(423\) 9.32591 0.453441
\(424\) −7.98192 −0.387636
\(425\) 0.539577 0.0261733
\(426\) −26.3132 −1.27488
\(427\) −29.8280 −1.44348
\(428\) 8.96360 0.433272
\(429\) 11.4397 0.552312
\(430\) −37.8288 −1.82427
\(431\) −25.2344 −1.21550 −0.607750 0.794128i \(-0.707928\pi\)
−0.607750 + 0.794128i \(0.707928\pi\)
\(432\) 1.94347 0.0935050
\(433\) −19.8315 −0.953043 −0.476521 0.879163i \(-0.658103\pi\)
−0.476521 + 0.879163i \(0.658103\pi\)
\(434\) −0.330156 −0.0158480
\(435\) −0.787928 −0.0377783
\(436\) −9.58304 −0.458945
\(437\) 15.5809 0.745334
\(438\) −7.31698 −0.349619
\(439\) −10.0525 −0.479779 −0.239889 0.970800i \(-0.577111\pi\)
−0.239889 + 0.970800i \(0.577111\pi\)
\(440\) 13.3206 0.635036
\(441\) 0.272727 0.0129870
\(442\) −6.44446 −0.306532
\(443\) 31.3857 1.49118 0.745591 0.666404i \(-0.232167\pi\)
0.745591 + 0.666404i \(0.232167\pi\)
\(444\) −7.64992 −0.363049
\(445\) −9.31946 −0.441785
\(446\) 31.8342 1.50739
\(447\) 4.52276 0.213919
\(448\) −33.5683 −1.58595
\(449\) 33.3758 1.57510 0.787551 0.616249i \(-0.211349\pi\)
0.787551 + 0.616249i \(0.211349\pi\)
\(450\) 1.17577 0.0554263
\(451\) −17.2098 −0.810380
\(452\) −46.5408 −2.18910
\(453\) 0.926814 0.0435455
\(454\) 7.01929 0.329432
\(455\) 16.8443 0.789675
\(456\) 3.88407 0.181888
\(457\) 4.89199 0.228838 0.114419 0.993433i \(-0.463499\pi\)
0.114419 + 0.993433i \(0.463499\pi\)
\(458\) −8.37839 −0.391496
\(459\) 1.00000 0.0466760
\(460\) −37.9662 −1.77018
\(461\) 18.3178 0.853145 0.426572 0.904453i \(-0.359721\pi\)
0.426572 + 0.904453i \(0.359721\pi\)
\(462\) 22.7307 1.05753
\(463\) −13.7118 −0.637240 −0.318620 0.947882i \(-0.603219\pi\)
−0.318620 + 0.947882i \(0.603219\pi\)
\(464\) 0.725062 0.0336602
\(465\) 0.118656 0.00550254
\(466\) −21.0149 −0.973497
\(467\) −3.37767 −0.156300 −0.0781501 0.996942i \(-0.524901\pi\)
−0.0781501 + 0.996942i \(0.524901\pi\)
\(468\) −8.12794 −0.375714
\(469\) −9.48524 −0.437988
\(470\) 42.9189 1.97970
\(471\) 1.00000 0.0460776
\(472\) −13.4512 −0.619144
\(473\) −31.7952 −1.46194
\(474\) −19.6685 −0.903403
\(475\) −1.28528 −0.0589728
\(476\) −7.41160 −0.339710
\(477\) 4.89515 0.224133
\(478\) −47.0640 −2.15266
\(479\) 20.2762 0.926445 0.463222 0.886242i \(-0.346693\pi\)
0.463222 + 0.886242i \(0.346693\pi\)
\(480\) 15.8315 0.722606
\(481\) −8.23210 −0.375352
\(482\) 0.721353 0.0328567
\(483\) −17.6398 −0.802641
\(484\) 10.8888 0.494948
\(485\) −36.7405 −1.66830
\(486\) 2.17906 0.0988441
\(487\) −19.4435 −0.881069 −0.440534 0.897736i \(-0.645211\pi\)
−0.440534 + 0.897736i \(0.645211\pi\)
\(488\) 18.0350 0.816408
\(489\) 21.5271 0.973488
\(490\) 1.25512 0.0567004
\(491\) −31.0238 −1.40008 −0.700042 0.714102i \(-0.746835\pi\)
−0.700042 + 0.714102i \(0.746835\pi\)
\(492\) 12.2277 0.551267
\(493\) 0.373077 0.0168025
\(494\) 15.3508 0.690666
\(495\) −8.16927 −0.367182
\(496\) −0.109189 −0.00490273
\(497\) −32.5652 −1.46075
\(498\) −30.1309 −1.35020
\(499\) 20.7560 0.929165 0.464582 0.885530i \(-0.346204\pi\)
0.464582 + 0.885530i \(0.346204\pi\)
\(500\) 32.1535 1.43795
\(501\) −6.11273 −0.273097
\(502\) 35.7133 1.59396
\(503\) −12.9342 −0.576708 −0.288354 0.957524i \(-0.593108\pi\)
−0.288354 + 0.957524i \(0.593108\pi\)
\(504\) −4.39734 −0.195873
\(505\) 17.6619 0.785945
\(506\) −55.1328 −2.45095
\(507\) 4.25349 0.188904
\(508\) −40.9762 −1.81802
\(509\) −10.3352 −0.458102 −0.229051 0.973414i \(-0.573562\pi\)
−0.229051 + 0.973414i \(0.573562\pi\)
\(510\) 4.60211 0.203785
\(511\) −9.05548 −0.400591
\(512\) −20.9063 −0.923937
\(513\) −2.38202 −0.105169
\(514\) −16.0095 −0.706147
\(515\) 30.3923 1.33925
\(516\) 22.5907 0.994499
\(517\) 36.0734 1.58651
\(518\) −16.3573 −0.718697
\(519\) −23.4820 −1.03074
\(520\) −10.1847 −0.446627
\(521\) 14.8498 0.650584 0.325292 0.945614i \(-0.394537\pi\)
0.325292 + 0.945614i \(0.394537\pi\)
\(522\) 0.812957 0.0355821
\(523\) 0.00955388 0.000417762 0 0.000208881 1.00000i \(-0.499934\pi\)
0.000208881 1.00000i \(0.499934\pi\)
\(524\) 26.2092 1.14496
\(525\) 1.45513 0.0635071
\(526\) −23.7893 −1.03726
\(527\) −0.0561826 −0.00244735
\(528\) 7.51748 0.327156
\(529\) 19.7851 0.860220
\(530\) 22.5280 0.978553
\(531\) 8.24937 0.357992
\(532\) 17.6546 0.765423
\(533\) 13.1583 0.569948
\(534\) 9.61550 0.416103
\(535\) −6.88822 −0.297804
\(536\) 5.73510 0.247719
\(537\) −9.24636 −0.399010
\(538\) 57.3460 2.47236
\(539\) 1.05493 0.0454390
\(540\) 5.80432 0.249778
\(541\) −38.4825 −1.65449 −0.827247 0.561839i \(-0.810094\pi\)
−0.827247 + 0.561839i \(0.810094\pi\)
\(542\) −34.2246 −1.47007
\(543\) −25.9507 −1.11365
\(544\) −7.49608 −0.321392
\(545\) 7.36424 0.315450
\(546\) −17.3794 −0.743770
\(547\) 3.96629 0.169586 0.0847931 0.996399i \(-0.472977\pi\)
0.0847931 + 0.996399i \(0.472977\pi\)
\(548\) −50.5139 −2.15785
\(549\) −11.0605 −0.472051
\(550\) 4.54797 0.193926
\(551\) −0.888677 −0.0378589
\(552\) 10.6657 0.453961
\(553\) −24.3417 −1.03511
\(554\) −46.0672 −1.95721
\(555\) 5.87870 0.249537
\(556\) 46.4046 1.96799
\(557\) 40.3010 1.70761 0.853805 0.520593i \(-0.174289\pi\)
0.853805 + 0.520593i \(0.174289\pi\)
\(558\) −0.122425 −0.00518267
\(559\) 24.3099 1.02820
\(560\) 11.0691 0.467756
\(561\) 3.86808 0.163310
\(562\) −54.8591 −2.31409
\(563\) 3.76673 0.158749 0.0793744 0.996845i \(-0.474708\pi\)
0.0793744 + 0.996845i \(0.474708\pi\)
\(564\) −25.6304 −1.07923
\(565\) 35.7651 1.50465
\(566\) −21.8635 −0.918991
\(567\) 2.69680 0.113255
\(568\) 19.6901 0.826177
\(569\) −4.76646 −0.199820 −0.0999102 0.994996i \(-0.531856\pi\)
−0.0999102 + 0.994996i \(0.531856\pi\)
\(570\) −10.9623 −0.459161
\(571\) −31.0140 −1.29790 −0.648949 0.760832i \(-0.724791\pi\)
−0.648949 + 0.760832i \(0.724791\pi\)
\(572\) −31.4395 −1.31455
\(573\) −7.58483 −0.316861
\(574\) 26.1456 1.09130
\(575\) −3.52939 −0.147186
\(576\) −12.4475 −0.518644
\(577\) −25.9928 −1.08210 −0.541048 0.840992i \(-0.681972\pi\)
−0.541048 + 0.840992i \(0.681972\pi\)
\(578\) −2.17906 −0.0906369
\(579\) 9.64509 0.400836
\(580\) 2.16546 0.0899158
\(581\) −37.2899 −1.54705
\(582\) 37.9076 1.57132
\(583\) 18.9348 0.784200
\(584\) 5.47526 0.226568
\(585\) 6.24605 0.258242
\(586\) 37.3929 1.54469
\(587\) 9.46799 0.390786 0.195393 0.980725i \(-0.437402\pi\)
0.195393 + 0.980725i \(0.437402\pi\)
\(588\) −0.749533 −0.0309102
\(589\) 0.133828 0.00551429
\(590\) 37.9645 1.56297
\(591\) 18.5587 0.763403
\(592\) −5.40966 −0.222336
\(593\) −0.566854 −0.0232779 −0.0116389 0.999932i \(-0.503705\pi\)
−0.0116389 + 0.999932i \(0.503705\pi\)
\(594\) 8.42877 0.345837
\(595\) 5.69556 0.233495
\(596\) −12.4299 −0.509147
\(597\) 10.6954 0.437735
\(598\) 42.1534 1.72378
\(599\) 7.16888 0.292912 0.146456 0.989217i \(-0.453213\pi\)
0.146456 + 0.989217i \(0.453213\pi\)
\(600\) −0.879822 −0.0359186
\(601\) 5.03026 0.205189 0.102594 0.994723i \(-0.467286\pi\)
0.102594 + 0.994723i \(0.467286\pi\)
\(602\) 48.3040 1.96873
\(603\) −3.51722 −0.143232
\(604\) −2.54716 −0.103642
\(605\) −8.36771 −0.340196
\(606\) −18.2230 −0.740257
\(607\) −0.718841 −0.0291768 −0.0145884 0.999894i \(-0.504644\pi\)
−0.0145884 + 0.999894i \(0.504644\pi\)
\(608\) 17.8558 0.724149
\(609\) 1.00611 0.0407698
\(610\) −50.9017 −2.06095
\(611\) −27.5809 −1.11580
\(612\) −2.74829 −0.111093
\(613\) −9.89319 −0.399582 −0.199791 0.979839i \(-0.564026\pi\)
−0.199791 + 0.979839i \(0.564026\pi\)
\(614\) 26.9865 1.08909
\(615\) −9.39657 −0.378906
\(616\) −17.0093 −0.685323
\(617\) −26.8405 −1.08056 −0.540280 0.841486i \(-0.681682\pi\)
−0.540280 + 0.841486i \(0.681682\pi\)
\(618\) −31.3577 −1.26139
\(619\) 38.1813 1.53464 0.767318 0.641266i \(-0.221591\pi\)
0.767318 + 0.641266i \(0.221591\pi\)
\(620\) −0.326102 −0.0130966
\(621\) −6.54103 −0.262482
\(622\) −1.11813 −0.0448329
\(623\) 11.9001 0.476769
\(624\) −5.74770 −0.230092
\(625\) −22.0110 −0.880439
\(626\) −27.2411 −1.08877
\(627\) −9.21385 −0.367966
\(628\) −2.74829 −0.109669
\(629\) −2.78351 −0.110986
\(630\) 12.4110 0.494465
\(631\) 26.6293 1.06009 0.530047 0.847968i \(-0.322174\pi\)
0.530047 + 0.847968i \(0.322174\pi\)
\(632\) 14.7178 0.585443
\(633\) −22.3890 −0.889883
\(634\) −18.1450 −0.720628
\(635\) 31.4888 1.24960
\(636\) −13.4533 −0.533458
\(637\) −0.806575 −0.0319577
\(638\) 3.14458 0.124495
\(639\) −12.0755 −0.477700
\(640\) −25.6216 −1.01278
\(641\) −6.95415 −0.274673 −0.137336 0.990524i \(-0.543854\pi\)
−0.137336 + 0.990524i \(0.543854\pi\)
\(642\) 7.10702 0.280492
\(643\) −0.313263 −0.0123539 −0.00617695 0.999981i \(-0.501966\pi\)
−0.00617695 + 0.999981i \(0.501966\pi\)
\(644\) 48.4795 1.91036
\(645\) −17.3602 −0.683556
\(646\) 5.19056 0.204220
\(647\) −19.8133 −0.778943 −0.389471 0.921039i \(-0.627342\pi\)
−0.389471 + 0.921039i \(0.627342\pi\)
\(648\) −1.63058 −0.0640552
\(649\) 31.9092 1.25255
\(650\) −3.47728 −0.136390
\(651\) −0.151513 −0.00593827
\(652\) −59.1628 −2.31699
\(653\) −39.9324 −1.56268 −0.781338 0.624108i \(-0.785463\pi\)
−0.781338 + 0.624108i \(0.785463\pi\)
\(654\) −7.59817 −0.297112
\(655\) −20.1409 −0.786970
\(656\) 8.64686 0.337603
\(657\) −3.35786 −0.131003
\(658\) −54.8036 −2.13647
\(659\) 26.8018 1.04405 0.522025 0.852930i \(-0.325177\pi\)
0.522025 + 0.852930i \(0.325177\pi\)
\(660\) 22.4516 0.873926
\(661\) 15.5641 0.605373 0.302686 0.953090i \(-0.402117\pi\)
0.302686 + 0.953090i \(0.402117\pi\)
\(662\) 25.1778 0.978562
\(663\) −2.95745 −0.114858
\(664\) 22.5468 0.874985
\(665\) −13.5670 −0.526104
\(666\) −6.06544 −0.235031
\(667\) −2.44031 −0.0944891
\(668\) 16.7996 0.649995
\(669\) 14.6092 0.564823
\(670\) −16.1866 −0.625344
\(671\) −42.7830 −1.65162
\(672\) −20.2154 −0.779827
\(673\) 7.90781 0.304824 0.152412 0.988317i \(-0.451296\pi\)
0.152412 + 0.988317i \(0.451296\pi\)
\(674\) −41.5105 −1.59893
\(675\) 0.539577 0.0207683
\(676\) −11.6898 −0.449609
\(677\) −21.3072 −0.818902 −0.409451 0.912332i \(-0.634280\pi\)
−0.409451 + 0.912332i \(0.634280\pi\)
\(678\) −36.9011 −1.41718
\(679\) 46.9144 1.80041
\(680\) −3.44373 −0.132061
\(681\) 3.22125 0.123439
\(682\) −0.473550 −0.0181332
\(683\) 1.16602 0.0446163 0.0223082 0.999751i \(-0.492899\pi\)
0.0223082 + 0.999751i \(0.492899\pi\)
\(684\) 6.54650 0.250312
\(685\) 38.8182 1.48317
\(686\) 39.5327 1.50937
\(687\) −3.84496 −0.146694
\(688\) 15.9751 0.609044
\(689\) −14.4771 −0.551535
\(690\) −30.1025 −1.14598
\(691\) 0.680408 0.0258839 0.0129420 0.999916i \(-0.495880\pi\)
0.0129420 + 0.999916i \(0.495880\pi\)
\(692\) 64.5354 2.45327
\(693\) 10.4314 0.396257
\(694\) 39.4052 1.49580
\(695\) −35.6604 −1.35268
\(696\) −0.608331 −0.0230587
\(697\) 4.44920 0.168525
\(698\) −79.4499 −3.00722
\(699\) −9.64403 −0.364771
\(700\) −3.99913 −0.151153
\(701\) 26.9917 1.01946 0.509732 0.860333i \(-0.329745\pi\)
0.509732 + 0.860333i \(0.329745\pi\)
\(702\) −6.44446 −0.243230
\(703\) 6.63039 0.250070
\(704\) −48.1478 −1.81464
\(705\) 19.6961 0.741797
\(706\) 61.7441 2.32377
\(707\) −22.5527 −0.848182
\(708\) −22.6717 −0.852055
\(709\) −2.54356 −0.0955253 −0.0477626 0.998859i \(-0.515209\pi\)
−0.0477626 + 0.998859i \(0.515209\pi\)
\(710\) −55.5728 −2.08561
\(711\) −9.02614 −0.338507
\(712\) −7.19523 −0.269653
\(713\) 0.367492 0.0137627
\(714\) −5.87648 −0.219922
\(715\) 24.1602 0.903541
\(716\) 25.4117 0.949681
\(717\) −21.5983 −0.806604
\(718\) 74.9228 2.79609
\(719\) −0.366136 −0.0136546 −0.00682728 0.999977i \(-0.502173\pi\)
−0.00682728 + 0.999977i \(0.502173\pi\)
\(720\) 4.10454 0.152967
\(721\) −38.8083 −1.44530
\(722\) 29.0381 1.08069
\(723\) 0.331039 0.0123115
\(724\) 71.3203 2.65060
\(725\) 0.201304 0.00747623
\(726\) 8.63351 0.320420
\(727\) −30.4594 −1.12968 −0.564839 0.825201i \(-0.691062\pi\)
−0.564839 + 0.825201i \(0.691062\pi\)
\(728\) 13.0049 0.481994
\(729\) 1.00000 0.0370370
\(730\) −15.4532 −0.571950
\(731\) 8.21989 0.304024
\(732\) 30.3976 1.12353
\(733\) 34.1123 1.25997 0.629984 0.776608i \(-0.283061\pi\)
0.629984 + 0.776608i \(0.283061\pi\)
\(734\) 12.6982 0.468699
\(735\) 0.575991 0.0212457
\(736\) 49.0321 1.80735
\(737\) −13.6049 −0.501142
\(738\) 9.69506 0.356880
\(739\) 34.7478 1.27822 0.639108 0.769117i \(-0.279303\pi\)
0.639108 + 0.769117i \(0.279303\pi\)
\(740\) −16.1564 −0.593921
\(741\) 7.04471 0.258794
\(742\) −28.7662 −1.05604
\(743\) 13.4799 0.494530 0.247265 0.968948i \(-0.420468\pi\)
0.247265 + 0.968948i \(0.420468\pi\)
\(744\) 0.0916101 0.00335859
\(745\) 9.55193 0.349956
\(746\) −9.69429 −0.354933
\(747\) −13.8275 −0.505921
\(748\) −10.6306 −0.388694
\(749\) 8.79564 0.321386
\(750\) 25.4937 0.930900
\(751\) 40.7030 1.48527 0.742636 0.669695i \(-0.233575\pi\)
0.742636 + 0.669695i \(0.233575\pi\)
\(752\) −18.1246 −0.660936
\(753\) 16.3893 0.597260
\(754\) −2.40428 −0.0875587
\(755\) 1.95740 0.0712372
\(756\) −7.41160 −0.269557
\(757\) −14.6769 −0.533440 −0.266720 0.963774i \(-0.585940\pi\)
−0.266720 + 0.963774i \(0.585940\pi\)
\(758\) 41.7885 1.51783
\(759\) −25.3012 −0.918376
\(760\) 8.20305 0.297556
\(761\) −20.1385 −0.730019 −0.365009 0.931004i \(-0.618934\pi\)
−0.365009 + 0.931004i \(0.618934\pi\)
\(762\) −32.4891 −1.17695
\(763\) −9.40348 −0.340429
\(764\) 20.8454 0.754159
\(765\) 2.11197 0.0763585
\(766\) 69.4805 2.51043
\(767\) −24.3971 −0.880929
\(768\) 1.54051 0.0555885
\(769\) 17.8489 0.643649 0.321825 0.946799i \(-0.395704\pi\)
0.321825 + 0.946799i \(0.395704\pi\)
\(770\) 48.0066 1.73004
\(771\) −7.34696 −0.264594
\(772\) −26.5075 −0.954027
\(773\) −15.7529 −0.566593 −0.283296 0.959032i \(-0.591428\pi\)
−0.283296 + 0.959032i \(0.591428\pi\)
\(774\) 17.9116 0.643820
\(775\) −0.0303148 −0.00108894
\(776\) −28.3660 −1.01828
\(777\) −7.50658 −0.269297
\(778\) −67.6245 −2.42445
\(779\) −10.5981 −0.379716
\(780\) −17.1660 −0.614641
\(781\) −46.7090 −1.67138
\(782\) 14.2533 0.509696
\(783\) 0.373077 0.0133327
\(784\) −0.530035 −0.0189298
\(785\) 2.11197 0.0753795
\(786\) 20.7807 0.741222
\(787\) 3.85152 0.137292 0.0686459 0.997641i \(-0.478132\pi\)
0.0686459 + 0.997641i \(0.478132\pi\)
\(788\) −51.0048 −1.81697
\(789\) −10.9172 −0.388664
\(790\) −41.5393 −1.47790
\(791\) −45.6688 −1.62380
\(792\) −6.30721 −0.224117
\(793\) 32.7109 1.16160
\(794\) 48.4441 1.71922
\(795\) 10.3384 0.366666
\(796\) −29.3942 −1.04185
\(797\) −29.9733 −1.06171 −0.530854 0.847463i \(-0.678129\pi\)
−0.530854 + 0.847463i \(0.678129\pi\)
\(798\) 13.9979 0.495520
\(799\) −9.32591 −0.329927
\(800\) −4.04471 −0.143002
\(801\) 4.41269 0.155915
\(802\) −75.6224 −2.67032
\(803\) −12.9885 −0.458353
\(804\) 9.66636 0.340906
\(805\) −37.2548 −1.31306
\(806\) 0.362066 0.0127532
\(807\) 26.3169 0.926399
\(808\) 13.6361 0.479718
\(809\) 0.559803 0.0196816 0.00984080 0.999952i \(-0.496868\pi\)
0.00984080 + 0.999952i \(0.496868\pi\)
\(810\) 4.60211 0.161702
\(811\) −31.0479 −1.09024 −0.545120 0.838358i \(-0.683516\pi\)
−0.545120 + 0.838358i \(0.683516\pi\)
\(812\) −2.76510 −0.0970359
\(813\) −15.7062 −0.550839
\(814\) −23.4616 −0.822329
\(815\) 45.4646 1.59256
\(816\) −1.94347 −0.0680349
\(817\) −19.5800 −0.685016
\(818\) 31.1783 1.09012
\(819\) −7.97565 −0.278692
\(820\) 25.8246 0.901833
\(821\) −34.5665 −1.20638 −0.603189 0.797598i \(-0.706104\pi\)
−0.603189 + 0.797598i \(0.706104\pi\)
\(822\) −40.0513 −1.39695
\(823\) 27.4537 0.956977 0.478489 0.878094i \(-0.341185\pi\)
0.478489 + 0.878094i \(0.341185\pi\)
\(824\) 23.4648 0.817436
\(825\) 2.08713 0.0726644
\(826\) −48.4773 −1.68674
\(827\) −36.4227 −1.26654 −0.633271 0.773930i \(-0.718288\pi\)
−0.633271 + 0.773930i \(0.718288\pi\)
\(828\) 17.9767 0.624733
\(829\) −6.58206 −0.228604 −0.114302 0.993446i \(-0.536463\pi\)
−0.114302 + 0.993446i \(0.536463\pi\)
\(830\) −63.6356 −2.20882
\(831\) −21.1409 −0.733369
\(832\) 36.8128 1.27625
\(833\) −0.272727 −0.00944942
\(834\) 36.7931 1.27404
\(835\) −12.9099 −0.446766
\(836\) 25.3224 0.875792
\(837\) −0.0561826 −0.00194196
\(838\) 37.9434 1.31073
\(839\) −49.4206 −1.70619 −0.853094 0.521758i \(-0.825276\pi\)
−0.853094 + 0.521758i \(0.825276\pi\)
\(840\) −9.28706 −0.320434
\(841\) −28.8608 −0.995200
\(842\) 43.2730 1.49129
\(843\) −25.1756 −0.867094
\(844\) 61.5316 2.11801
\(845\) 8.98325 0.309033
\(846\) −20.3217 −0.698675
\(847\) 10.6848 0.367135
\(848\) −9.51354 −0.326696
\(849\) −10.0335 −0.344347
\(850\) −1.17577 −0.0403286
\(851\) 18.2070 0.624130
\(852\) 33.1871 1.13697
\(853\) 0.889324 0.0304499 0.0152249 0.999884i \(-0.495154\pi\)
0.0152249 + 0.999884i \(0.495154\pi\)
\(854\) 64.9969 2.22415
\(855\) −5.03076 −0.172048
\(856\) −5.31815 −0.181771
\(857\) 27.6391 0.944135 0.472067 0.881562i \(-0.343508\pi\)
0.472067 + 0.881562i \(0.343508\pi\)
\(858\) −24.9277 −0.851016
\(859\) 44.6674 1.52403 0.762016 0.647558i \(-0.224210\pi\)
0.762016 + 0.647558i \(0.224210\pi\)
\(860\) 47.7109 1.62693
\(861\) 11.9986 0.408911
\(862\) 54.9873 1.87287
\(863\) −48.8577 −1.66313 −0.831567 0.555424i \(-0.812556\pi\)
−0.831567 + 0.555424i \(0.812556\pi\)
\(864\) −7.49608 −0.255022
\(865\) −49.5932 −1.68622
\(866\) 43.2141 1.46847
\(867\) −1.00000 −0.0339618
\(868\) 0.416403 0.0141336
\(869\) −34.9138 −1.18437
\(870\) 1.71694 0.0582098
\(871\) 10.4020 0.352458
\(872\) 5.68567 0.192541
\(873\) 17.3963 0.588776
\(874\) −33.9516 −1.14843
\(875\) 31.5510 1.06662
\(876\) 9.22839 0.311799
\(877\) −31.1375 −1.05144 −0.525719 0.850659i \(-0.676204\pi\)
−0.525719 + 0.850659i \(0.676204\pi\)
\(878\) 21.9049 0.739256
\(879\) 17.1601 0.578797
\(880\) 15.8767 0.535203
\(881\) −20.5395 −0.691993 −0.345996 0.938236i \(-0.612459\pi\)
−0.345996 + 0.938236i \(0.612459\pi\)
\(882\) −0.594287 −0.0200107
\(883\) −22.9662 −0.772874 −0.386437 0.922316i \(-0.626294\pi\)
−0.386437 + 0.922316i \(0.626294\pi\)
\(884\) 8.12794 0.273372
\(885\) 17.4224 0.585649
\(886\) −68.3914 −2.29765
\(887\) −15.9416 −0.535267 −0.267634 0.963521i \(-0.586242\pi\)
−0.267634 + 0.963521i \(0.586242\pi\)
\(888\) 4.53874 0.152310
\(889\) −40.2084 −1.34855
\(890\) 20.3077 0.680714
\(891\) 3.86808 0.129586
\(892\) −40.1503 −1.34433
\(893\) 22.2145 0.743381
\(894\) −9.85535 −0.329612
\(895\) −19.5281 −0.652751
\(896\) 32.7165 1.09298
\(897\) 19.3448 0.645903
\(898\) −72.7279 −2.42696
\(899\) −0.0209604 −0.000699070 0
\(900\) −1.48292 −0.0494305
\(901\) −4.89515 −0.163081
\(902\) 37.5012 1.24865
\(903\) 22.1674 0.737685
\(904\) 27.6129 0.918392
\(905\) −54.8072 −1.82185
\(906\) −2.01958 −0.0670961
\(907\) −46.6453 −1.54883 −0.774416 0.632676i \(-0.781956\pi\)
−0.774416 + 0.632676i \(0.781956\pi\)
\(908\) −8.85295 −0.293795
\(909\) −8.36277 −0.277375
\(910\) −36.7048 −1.21675
\(911\) 31.6895 1.04992 0.524960 0.851127i \(-0.324080\pi\)
0.524960 + 0.851127i \(0.324080\pi\)
\(912\) 4.62937 0.153294
\(913\) −53.4858 −1.77012
\(914\) −10.6599 −0.352600
\(915\) −23.3595 −0.772241
\(916\) 10.5671 0.349146
\(917\) 25.7181 0.849287
\(918\) −2.17906 −0.0719196
\(919\) −48.2394 −1.59127 −0.795636 0.605775i \(-0.792863\pi\)
−0.795636 + 0.605775i \(0.792863\pi\)
\(920\) 22.5256 0.742646
\(921\) 12.3845 0.408083
\(922\) −39.9155 −1.31455
\(923\) 35.7127 1.17550
\(924\) −28.6687 −0.943130
\(925\) −1.50192 −0.0493828
\(926\) 29.8788 0.981877
\(927\) −14.3905 −0.472646
\(928\) −2.79662 −0.0918034
\(929\) −42.5217 −1.39509 −0.697546 0.716540i \(-0.745725\pi\)
−0.697546 + 0.716540i \(0.745725\pi\)
\(930\) −0.258558 −0.00847847
\(931\) 0.649641 0.0212911
\(932\) 26.5046 0.868188
\(933\) −0.513125 −0.0167990
\(934\) 7.36015 0.240831
\(935\) 8.16927 0.267164
\(936\) 4.82235 0.157624
\(937\) −25.2527 −0.824971 −0.412485 0.910964i \(-0.635339\pi\)
−0.412485 + 0.910964i \(0.635339\pi\)
\(938\) 20.6689 0.674863
\(939\) −12.5013 −0.407966
\(940\) −54.1306 −1.76555
\(941\) 15.0814 0.491640 0.245820 0.969315i \(-0.420943\pi\)
0.245820 + 0.969315i \(0.420943\pi\)
\(942\) −2.17906 −0.0709976
\(943\) −29.1023 −0.947702
\(944\) −16.0324 −0.521809
\(945\) 5.69556 0.185277
\(946\) 69.2836 2.25260
\(947\) 45.3069 1.47228 0.736139 0.676831i \(-0.236647\pi\)
0.736139 + 0.676831i \(0.236647\pi\)
\(948\) 24.8065 0.805677
\(949\) 9.93071 0.322364
\(950\) 2.80071 0.0908669
\(951\) −8.32697 −0.270021
\(952\) 4.39734 0.142519
\(953\) −41.7836 −1.35350 −0.676751 0.736212i \(-0.736613\pi\)
−0.676751 + 0.736212i \(0.736613\pi\)
\(954\) −10.6668 −0.345351
\(955\) −16.0190 −0.518361
\(956\) 59.3586 1.91979
\(957\) 1.44309 0.0466485
\(958\) −44.1831 −1.42749
\(959\) −49.5674 −1.60062
\(960\) −26.2887 −0.848464
\(961\) −30.9968 −0.999898
\(962\) 17.9382 0.578352
\(963\) 3.26151 0.105101
\(964\) −0.909793 −0.0293025
\(965\) 20.3701 0.655738
\(966\) 38.4382 1.23673
\(967\) −43.7585 −1.40718 −0.703589 0.710607i \(-0.748420\pi\)
−0.703589 + 0.710607i \(0.748420\pi\)
\(968\) −6.46041 −0.207645
\(969\) 2.38202 0.0765215
\(970\) 80.0597 2.57056
\(971\) 49.8280 1.59906 0.799528 0.600629i \(-0.205083\pi\)
0.799528 + 0.600629i \(0.205083\pi\)
\(972\) −2.74829 −0.0881516
\(973\) 45.5351 1.45979
\(974\) 42.3685 1.35757
\(975\) −1.59577 −0.0511056
\(976\) 21.4957 0.688062
\(977\) −54.2989 −1.73718 −0.868588 0.495536i \(-0.834972\pi\)
−0.868588 + 0.495536i \(0.834972\pi\)
\(978\) −46.9088 −1.49998
\(979\) 17.0686 0.545515
\(980\) −1.58299 −0.0505668
\(981\) −3.48691 −0.111328
\(982\) 67.6026 2.15729
\(983\) −38.3446 −1.22300 −0.611502 0.791243i \(-0.709434\pi\)
−0.611502 + 0.791243i \(0.709434\pi\)
\(984\) −7.25476 −0.231273
\(985\) 39.1954 1.24887
\(986\) −0.812957 −0.0258898
\(987\) −25.1501 −0.800537
\(988\) −19.3609 −0.615953
\(989\) −53.7665 −1.70968
\(990\) 17.8013 0.565763
\(991\) −48.3036 −1.53442 −0.767208 0.641399i \(-0.778354\pi\)
−0.767208 + 0.641399i \(0.778354\pi\)
\(992\) 0.421149 0.0133715
\(993\) 11.5544 0.366669
\(994\) 70.9616 2.25076
\(995\) 22.5885 0.716102
\(996\) 38.0020 1.20414
\(997\) −9.66132 −0.305977 −0.152989 0.988228i \(-0.548890\pi\)
−0.152989 + 0.988228i \(0.548890\pi\)
\(998\) −45.2285 −1.43168
\(999\) −2.78351 −0.0880665
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.1.8 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8007.2.a.f.1.8 48 1.1 even 1 trivial