Properties

Label 8007.2.a.f.1.1
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 1.1
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.78117 q^{2} -1.00000 q^{3} +5.73492 q^{4} +2.04412 q^{5} +2.78117 q^{6} -0.793043 q^{7} -10.3875 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.78117 q^{2} -1.00000 q^{3} +5.73492 q^{4} +2.04412 q^{5} +2.78117 q^{6} -0.793043 q^{7} -10.3875 q^{8} +1.00000 q^{9} -5.68506 q^{10} +1.06235 q^{11} -5.73492 q^{12} +3.98874 q^{13} +2.20559 q^{14} -2.04412 q^{15} +17.4195 q^{16} -1.00000 q^{17} -2.78117 q^{18} -5.59005 q^{19} +11.7229 q^{20} +0.793043 q^{21} -2.95458 q^{22} +3.28010 q^{23} +10.3875 q^{24} -0.821567 q^{25} -11.0934 q^{26} -1.00000 q^{27} -4.54804 q^{28} +10.0517 q^{29} +5.68506 q^{30} +1.66926 q^{31} -27.6717 q^{32} -1.06235 q^{33} +2.78117 q^{34} -1.62108 q^{35} +5.73492 q^{36} -11.3116 q^{37} +15.5469 q^{38} -3.98874 q^{39} -21.2332 q^{40} +0.684806 q^{41} -2.20559 q^{42} -1.07901 q^{43} +6.09249 q^{44} +2.04412 q^{45} -9.12253 q^{46} +1.11157 q^{47} -17.4195 q^{48} -6.37108 q^{49} +2.28492 q^{50} +1.00000 q^{51} +22.8751 q^{52} -12.1494 q^{53} +2.78117 q^{54} +2.17157 q^{55} +8.23770 q^{56} +5.59005 q^{57} -27.9555 q^{58} +3.58942 q^{59} -11.7229 q^{60} -2.01522 q^{61} -4.64251 q^{62} -0.793043 q^{63} +42.1208 q^{64} +8.15347 q^{65} +2.95458 q^{66} -6.63755 q^{67} -5.73492 q^{68} -3.28010 q^{69} +4.50849 q^{70} +13.3868 q^{71} -10.3875 q^{72} -8.90585 q^{73} +31.4596 q^{74} +0.821567 q^{75} -32.0585 q^{76} -0.842488 q^{77} +11.0934 q^{78} -15.7566 q^{79} +35.6076 q^{80} +1.00000 q^{81} -1.90457 q^{82} +14.3787 q^{83} +4.54804 q^{84} -2.04412 q^{85} +3.00090 q^{86} -10.0517 q^{87} -11.0351 q^{88} -3.21069 q^{89} -5.68506 q^{90} -3.16324 q^{91} +18.8111 q^{92} -1.66926 q^{93} -3.09148 q^{94} -11.4267 q^{95} +27.6717 q^{96} +7.38175 q^{97} +17.7191 q^{98} +1.06235 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} + O(q^{10}) \) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} - 20q^{10} + 5q^{11} - 45q^{12} - 8q^{13} + 4q^{14} - q^{15} + 39q^{16} - 48q^{17} - q^{18} - 6q^{19} + 6q^{20} + 13q^{21} - 35q^{22} - 8q^{23} + 6q^{24} + 13q^{25} + 17q^{26} - 48q^{27} - 38q^{28} + q^{29} + 20q^{30} - 21q^{31} - 3q^{32} - 5q^{33} + q^{34} + 19q^{35} + 45q^{36} - 58q^{37} - 14q^{38} + 8q^{39} - 54q^{40} - 3q^{41} - 4q^{42} - 33q^{43} + 2q^{44} + q^{45} - 26q^{46} + 9q^{47} - 39q^{48} + 11q^{49} + 4q^{50} + 48q^{51} - 31q^{52} - 33q^{53} + q^{54} - 21q^{55} + 6q^{57} - 55q^{58} + 77q^{59} - 6q^{60} - 29q^{61} - 46q^{62} - 13q^{63} + 24q^{64} - 49q^{65} + 35q^{66} - 44q^{67} - 45q^{68} + 8q^{69} + 4q^{70} + 22q^{71} - 6q^{72} - 63q^{73} - 16q^{74} - 13q^{75} - 46q^{76} - 30q^{77} - 17q^{78} - 46q^{79} - 14q^{80} + 48q^{81} - 75q^{82} + 11q^{83} + 38q^{84} - q^{85} + 8q^{86} - q^{87} - 116q^{88} + 10q^{89} - 20q^{90} - 67q^{91} - 64q^{92} + 21q^{93} - 16q^{94} - 8q^{95} + 3q^{96} - 96q^{97} - 46q^{98} + 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.78117 −1.96659 −0.983293 0.182029i \(-0.941733\pi\)
−0.983293 + 0.182029i \(0.941733\pi\)
\(3\) −1.00000 −0.577350
\(4\) 5.73492 2.86746
\(5\) 2.04412 0.914159 0.457079 0.889426i \(-0.348896\pi\)
0.457079 + 0.889426i \(0.348896\pi\)
\(6\) 2.78117 1.13541
\(7\) −0.793043 −0.299742 −0.149871 0.988706i \(-0.547886\pi\)
−0.149871 + 0.988706i \(0.547886\pi\)
\(8\) −10.3875 −3.67252
\(9\) 1.00000 0.333333
\(10\) −5.68506 −1.79777
\(11\) 1.06235 0.320310 0.160155 0.987092i \(-0.448801\pi\)
0.160155 + 0.987092i \(0.448801\pi\)
\(12\) −5.73492 −1.65553
\(13\) 3.98874 1.10628 0.553139 0.833089i \(-0.313430\pi\)
0.553139 + 0.833089i \(0.313430\pi\)
\(14\) 2.20559 0.589468
\(15\) −2.04412 −0.527790
\(16\) 17.4195 4.35487
\(17\) −1.00000 −0.242536
\(18\) −2.78117 −0.655529
\(19\) −5.59005 −1.28244 −0.641222 0.767355i \(-0.721572\pi\)
−0.641222 + 0.767355i \(0.721572\pi\)
\(20\) 11.7229 2.62132
\(21\) 0.793043 0.173056
\(22\) −2.95458 −0.629918
\(23\) 3.28010 0.683948 0.341974 0.939709i \(-0.388904\pi\)
0.341974 + 0.939709i \(0.388904\pi\)
\(24\) 10.3875 2.12033
\(25\) −0.821567 −0.164313
\(26\) −11.0934 −2.17559
\(27\) −1.00000 −0.192450
\(28\) −4.54804 −0.859499
\(29\) 10.0517 1.86655 0.933276 0.359160i \(-0.116937\pi\)
0.933276 + 0.359160i \(0.116937\pi\)
\(30\) 5.68506 1.03794
\(31\) 1.66926 0.299809 0.149904 0.988701i \(-0.452103\pi\)
0.149904 + 0.988701i \(0.452103\pi\)
\(32\) −27.6717 −4.89171
\(33\) −1.06235 −0.184931
\(34\) 2.78117 0.476967
\(35\) −1.62108 −0.274012
\(36\) 5.73492 0.955820
\(37\) −11.3116 −1.85962 −0.929810 0.368041i \(-0.880029\pi\)
−0.929810 + 0.368041i \(0.880029\pi\)
\(38\) 15.5469 2.52204
\(39\) −3.98874 −0.638710
\(40\) −21.2332 −3.35727
\(41\) 0.684806 0.106949 0.0534744 0.998569i \(-0.482970\pi\)
0.0534744 + 0.998569i \(0.482970\pi\)
\(42\) −2.20559 −0.340330
\(43\) −1.07901 −0.164547 −0.0822735 0.996610i \(-0.526218\pi\)
−0.0822735 + 0.996610i \(0.526218\pi\)
\(44\) 6.09249 0.918477
\(45\) 2.04412 0.304720
\(46\) −9.12253 −1.34504
\(47\) 1.11157 0.162140 0.0810698 0.996708i \(-0.474166\pi\)
0.0810698 + 0.996708i \(0.474166\pi\)
\(48\) −17.4195 −2.51429
\(49\) −6.37108 −0.910155
\(50\) 2.28492 0.323137
\(51\) 1.00000 0.140028
\(52\) 22.8751 3.17221
\(53\) −12.1494 −1.66885 −0.834424 0.551123i \(-0.814199\pi\)
−0.834424 + 0.551123i \(0.814199\pi\)
\(54\) 2.78117 0.378470
\(55\) 2.17157 0.292814
\(56\) 8.23770 1.10081
\(57\) 5.59005 0.740420
\(58\) −27.9555 −3.67074
\(59\) 3.58942 0.467302 0.233651 0.972321i \(-0.424933\pi\)
0.233651 + 0.972321i \(0.424933\pi\)
\(60\) −11.7229 −1.51342
\(61\) −2.01522 −0.258022 −0.129011 0.991643i \(-0.541180\pi\)
−0.129011 + 0.991643i \(0.541180\pi\)
\(62\) −4.64251 −0.589599
\(63\) −0.793043 −0.0999140
\(64\) 42.1208 5.26510
\(65\) 8.15347 1.01131
\(66\) 2.95458 0.363683
\(67\) −6.63755 −0.810906 −0.405453 0.914116i \(-0.632886\pi\)
−0.405453 + 0.914116i \(0.632886\pi\)
\(68\) −5.73492 −0.695462
\(69\) −3.28010 −0.394878
\(70\) 4.50849 0.538868
\(71\) 13.3868 1.58873 0.794363 0.607443i \(-0.207805\pi\)
0.794363 + 0.607443i \(0.207805\pi\)
\(72\) −10.3875 −1.22417
\(73\) −8.90585 −1.04235 −0.521176 0.853449i \(-0.674506\pi\)
−0.521176 + 0.853449i \(0.674506\pi\)
\(74\) 31.4596 3.65710
\(75\) 0.821567 0.0948664
\(76\) −32.0585 −3.67736
\(77\) −0.842488 −0.0960104
\(78\) 11.0934 1.25608
\(79\) −15.7566 −1.77275 −0.886376 0.462967i \(-0.846785\pi\)
−0.886376 + 0.462967i \(0.846785\pi\)
\(80\) 35.6076 3.98105
\(81\) 1.00000 0.111111
\(82\) −1.90457 −0.210324
\(83\) 14.3787 1.57827 0.789134 0.614221i \(-0.210530\pi\)
0.789134 + 0.614221i \(0.210530\pi\)
\(84\) 4.54804 0.496232
\(85\) −2.04412 −0.221716
\(86\) 3.00090 0.323596
\(87\) −10.0517 −1.07765
\(88\) −11.0351 −1.17635
\(89\) −3.21069 −0.340332 −0.170166 0.985415i \(-0.554430\pi\)
−0.170166 + 0.985415i \(0.554430\pi\)
\(90\) −5.68506 −0.599257
\(91\) −3.16324 −0.331598
\(92\) 18.8111 1.96120
\(93\) −1.66926 −0.173095
\(94\) −3.09148 −0.318862
\(95\) −11.4267 −1.17236
\(96\) 27.6717 2.82423
\(97\) 7.38175 0.749504 0.374752 0.927125i \(-0.377728\pi\)
0.374752 + 0.927125i \(0.377728\pi\)
\(98\) 17.7191 1.78990
\(99\) 1.06235 0.106770
\(100\) −4.71163 −0.471163
\(101\) 1.14096 0.113529 0.0567647 0.998388i \(-0.481922\pi\)
0.0567647 + 0.998388i \(0.481922\pi\)
\(102\) −2.78117 −0.275377
\(103\) 8.05750 0.793929 0.396965 0.917834i \(-0.370064\pi\)
0.396965 + 0.917834i \(0.370064\pi\)
\(104\) −41.4329 −4.06283
\(105\) 1.62108 0.158201
\(106\) 33.7896 3.28193
\(107\) −2.63785 −0.255011 −0.127505 0.991838i \(-0.540697\pi\)
−0.127505 + 0.991838i \(0.540697\pi\)
\(108\) −5.73492 −0.551843
\(109\) 14.3300 1.37257 0.686285 0.727333i \(-0.259240\pi\)
0.686285 + 0.727333i \(0.259240\pi\)
\(110\) −6.03951 −0.575845
\(111\) 11.3116 1.07365
\(112\) −13.8144 −1.30534
\(113\) −11.8435 −1.11414 −0.557069 0.830466i \(-0.688074\pi\)
−0.557069 + 0.830466i \(0.688074\pi\)
\(114\) −15.5469 −1.45610
\(115\) 6.70493 0.625238
\(116\) 57.6457 5.35227
\(117\) 3.98874 0.368759
\(118\) −9.98278 −0.918990
\(119\) 0.793043 0.0726981
\(120\) 21.2332 1.93832
\(121\) −9.87142 −0.897401
\(122\) 5.60467 0.507423
\(123\) −0.684806 −0.0617469
\(124\) 9.57310 0.859689
\(125\) −11.9000 −1.06437
\(126\) 2.20559 0.196489
\(127\) 3.46243 0.307241 0.153621 0.988130i \(-0.450907\pi\)
0.153621 + 0.988130i \(0.450907\pi\)
\(128\) −61.8018 −5.46256
\(129\) 1.07901 0.0950012
\(130\) −22.6762 −1.98883
\(131\) −7.37742 −0.644568 −0.322284 0.946643i \(-0.604451\pi\)
−0.322284 + 0.946643i \(0.604451\pi\)
\(132\) −6.09249 −0.530283
\(133\) 4.43315 0.384403
\(134\) 18.4602 1.59472
\(135\) −2.04412 −0.175930
\(136\) 10.3875 0.890718
\(137\) −18.2408 −1.55842 −0.779208 0.626765i \(-0.784378\pi\)
−0.779208 + 0.626765i \(0.784378\pi\)
\(138\) 9.12253 0.776561
\(139\) 5.90610 0.500949 0.250474 0.968123i \(-0.419413\pi\)
0.250474 + 0.968123i \(0.419413\pi\)
\(140\) −9.29674 −0.785718
\(141\) −1.11157 −0.0936114
\(142\) −37.2311 −3.12437
\(143\) 4.23743 0.354352
\(144\) 17.4195 1.45162
\(145\) 20.5469 1.70633
\(146\) 24.7687 2.04987
\(147\) 6.37108 0.525478
\(148\) −64.8713 −5.33239
\(149\) −17.0765 −1.39896 −0.699482 0.714650i \(-0.746586\pi\)
−0.699482 + 0.714650i \(0.746586\pi\)
\(150\) −2.28492 −0.186563
\(151\) −13.0331 −1.06062 −0.530310 0.847804i \(-0.677924\pi\)
−0.530310 + 0.847804i \(0.677924\pi\)
\(152\) 58.0664 4.70981
\(153\) −1.00000 −0.0808452
\(154\) 2.34310 0.188813
\(155\) 3.41218 0.274073
\(156\) −22.8751 −1.83147
\(157\) −1.00000 −0.0798087
\(158\) 43.8217 3.48627
\(159\) 12.1494 0.963510
\(160\) −56.5643 −4.47180
\(161\) −2.60126 −0.205008
\(162\) −2.78117 −0.218510
\(163\) −11.1265 −0.871495 −0.435748 0.900069i \(-0.643516\pi\)
−0.435748 + 0.900069i \(0.643516\pi\)
\(164\) 3.92731 0.306672
\(165\) −2.17157 −0.169056
\(166\) −39.9897 −3.10380
\(167\) −0.742955 −0.0574916 −0.0287458 0.999587i \(-0.509151\pi\)
−0.0287458 + 0.999587i \(0.509151\pi\)
\(168\) −8.23770 −0.635553
\(169\) 2.91004 0.223850
\(170\) 5.68506 0.436024
\(171\) −5.59005 −0.427482
\(172\) −6.18802 −0.471832
\(173\) −18.3969 −1.39869 −0.699346 0.714783i \(-0.746525\pi\)
−0.699346 + 0.714783i \(0.746525\pi\)
\(174\) 27.9555 2.11930
\(175\) 0.651538 0.0492517
\(176\) 18.5056 1.39491
\(177\) −3.58942 −0.269797
\(178\) 8.92947 0.669292
\(179\) −16.7600 −1.25270 −0.626352 0.779540i \(-0.715453\pi\)
−0.626352 + 0.779540i \(0.715453\pi\)
\(180\) 11.7229 0.873772
\(181\) 6.68478 0.496876 0.248438 0.968648i \(-0.420083\pi\)
0.248438 + 0.968648i \(0.420083\pi\)
\(182\) 8.79752 0.652116
\(183\) 2.01522 0.148969
\(184\) −34.0719 −2.51182
\(185\) −23.1223 −1.69999
\(186\) 4.64251 0.340405
\(187\) −1.06235 −0.0776866
\(188\) 6.37479 0.464929
\(189\) 0.793043 0.0576854
\(190\) 31.7797 2.30554
\(191\) 8.17962 0.591857 0.295928 0.955210i \(-0.404371\pi\)
0.295928 + 0.955210i \(0.404371\pi\)
\(192\) −42.1208 −3.03980
\(193\) 18.1913 1.30944 0.654720 0.755871i \(-0.272786\pi\)
0.654720 + 0.755871i \(0.272786\pi\)
\(194\) −20.5299 −1.47396
\(195\) −8.15347 −0.583882
\(196\) −36.5377 −2.60983
\(197\) −8.66866 −0.617617 −0.308808 0.951124i \(-0.599930\pi\)
−0.308808 + 0.951124i \(0.599930\pi\)
\(198\) −2.95458 −0.209973
\(199\) −11.7451 −0.832586 −0.416293 0.909231i \(-0.636671\pi\)
−0.416293 + 0.909231i \(0.636671\pi\)
\(200\) 8.53400 0.603445
\(201\) 6.63755 0.468177
\(202\) −3.17319 −0.223265
\(203\) −7.97142 −0.559484
\(204\) 5.73492 0.401525
\(205\) 1.39983 0.0977682
\(206\) −22.4093 −1.56133
\(207\) 3.28010 0.227983
\(208\) 69.4818 4.81770
\(209\) −5.93858 −0.410780
\(210\) −4.50849 −0.311116
\(211\) 15.0076 1.03316 0.516582 0.856238i \(-0.327204\pi\)
0.516582 + 0.856238i \(0.327204\pi\)
\(212\) −69.6758 −4.78536
\(213\) −13.3868 −0.917252
\(214\) 7.33632 0.501500
\(215\) −2.20562 −0.150422
\(216\) 10.3875 0.706778
\(217\) −1.32380 −0.0898652
\(218\) −39.8543 −2.69928
\(219\) 8.90585 0.601802
\(220\) 12.4538 0.839634
\(221\) −3.98874 −0.268312
\(222\) −31.4596 −2.11143
\(223\) 0.315330 0.0211161 0.0105580 0.999944i \(-0.496639\pi\)
0.0105580 + 0.999944i \(0.496639\pi\)
\(224\) 21.9448 1.46625
\(225\) −0.821567 −0.0547712
\(226\) 32.9387 2.19105
\(227\) 14.8865 0.988052 0.494026 0.869447i \(-0.335525\pi\)
0.494026 + 0.869447i \(0.335525\pi\)
\(228\) 32.0585 2.12313
\(229\) −25.6705 −1.69636 −0.848178 0.529711i \(-0.822300\pi\)
−0.848178 + 0.529711i \(0.822300\pi\)
\(230\) −18.6476 −1.22958
\(231\) 0.842488 0.0554316
\(232\) −104.412 −6.85496
\(233\) 4.96647 0.325364 0.162682 0.986679i \(-0.447985\pi\)
0.162682 + 0.986679i \(0.447985\pi\)
\(234\) −11.0934 −0.725197
\(235\) 2.27219 0.148221
\(236\) 20.5850 1.33997
\(237\) 15.7566 1.02350
\(238\) −2.20559 −0.142967
\(239\) 1.02229 0.0661264 0.0330632 0.999453i \(-0.489474\pi\)
0.0330632 + 0.999453i \(0.489474\pi\)
\(240\) −35.6076 −2.29846
\(241\) −12.2771 −0.790836 −0.395418 0.918501i \(-0.629400\pi\)
−0.395418 + 0.918501i \(0.629400\pi\)
\(242\) 27.4541 1.76482
\(243\) −1.00000 −0.0641500
\(244\) −11.5571 −0.739869
\(245\) −13.0233 −0.832026
\(246\) 1.90457 0.121431
\(247\) −22.2972 −1.41874
\(248\) −17.3394 −1.10105
\(249\) −14.3787 −0.911214
\(250\) 33.0959 2.09317
\(251\) 1.05288 0.0664575 0.0332287 0.999448i \(-0.489421\pi\)
0.0332287 + 0.999448i \(0.489421\pi\)
\(252\) −4.54804 −0.286500
\(253\) 3.48461 0.219076
\(254\) −9.62963 −0.604216
\(255\) 2.04412 0.128008
\(256\) 87.6398 5.47749
\(257\) −13.0568 −0.814461 −0.407230 0.913325i \(-0.633505\pi\)
−0.407230 + 0.913325i \(0.633505\pi\)
\(258\) −3.00090 −0.186828
\(259\) 8.97060 0.557406
\(260\) 46.7595 2.89990
\(261\) 10.0517 0.622184
\(262\) 20.5179 1.26760
\(263\) 16.2349 1.00109 0.500544 0.865711i \(-0.333133\pi\)
0.500544 + 0.865711i \(0.333133\pi\)
\(264\) 11.0351 0.679164
\(265\) −24.8348 −1.52559
\(266\) −12.3293 −0.755961
\(267\) 3.21069 0.196491
\(268\) −38.0659 −2.32524
\(269\) 9.51640 0.580225 0.290112 0.956993i \(-0.406307\pi\)
0.290112 + 0.956993i \(0.406307\pi\)
\(270\) 5.68506 0.345981
\(271\) 1.55394 0.0943954 0.0471977 0.998886i \(-0.484971\pi\)
0.0471977 + 0.998886i \(0.484971\pi\)
\(272\) −17.4195 −1.05621
\(273\) 3.16324 0.191448
\(274\) 50.7308 3.06476
\(275\) −0.872791 −0.0526313
\(276\) −18.8111 −1.13230
\(277\) −17.9592 −1.07907 −0.539533 0.841965i \(-0.681399\pi\)
−0.539533 + 0.841965i \(0.681399\pi\)
\(278\) −16.4259 −0.985159
\(279\) 1.66926 0.0999362
\(280\) 16.8389 1.00631
\(281\) 29.8844 1.78275 0.891376 0.453264i \(-0.149741\pi\)
0.891376 + 0.453264i \(0.149741\pi\)
\(282\) 3.09148 0.184095
\(283\) −7.24127 −0.430449 −0.215225 0.976565i \(-0.569048\pi\)
−0.215225 + 0.976565i \(0.569048\pi\)
\(284\) 76.7725 4.55561
\(285\) 11.4267 0.676861
\(286\) −11.7850 −0.696864
\(287\) −0.543081 −0.0320570
\(288\) −27.6717 −1.63057
\(289\) 1.00000 0.0588235
\(290\) −57.1444 −3.35564
\(291\) −7.38175 −0.432726
\(292\) −51.0744 −2.98890
\(293\) 15.2781 0.892556 0.446278 0.894894i \(-0.352749\pi\)
0.446278 + 0.894894i \(0.352749\pi\)
\(294\) −17.7191 −1.03340
\(295\) 7.33720 0.427188
\(296\) 117.499 6.82950
\(297\) −1.06235 −0.0616437
\(298\) 47.4928 2.75118
\(299\) 13.0835 0.756637
\(300\) 4.71163 0.272026
\(301\) 0.855698 0.0493216
\(302\) 36.2473 2.08580
\(303\) −1.14096 −0.0655462
\(304\) −97.3758 −5.58488
\(305\) −4.11935 −0.235874
\(306\) 2.78117 0.158989
\(307\) −30.5663 −1.74451 −0.872257 0.489049i \(-0.837344\pi\)
−0.872257 + 0.489049i \(0.837344\pi\)
\(308\) −4.83160 −0.275306
\(309\) −8.05750 −0.458375
\(310\) −9.48985 −0.538987
\(311\) 8.61773 0.488667 0.244333 0.969691i \(-0.421431\pi\)
0.244333 + 0.969691i \(0.421431\pi\)
\(312\) 41.4329 2.34568
\(313\) −27.7786 −1.57014 −0.785069 0.619408i \(-0.787373\pi\)
−0.785069 + 0.619408i \(0.787373\pi\)
\(314\) 2.78117 0.156951
\(315\) −1.62108 −0.0913373
\(316\) −90.3626 −5.08330
\(317\) 13.5481 0.760935 0.380467 0.924794i \(-0.375763\pi\)
0.380467 + 0.924794i \(0.375763\pi\)
\(318\) −33.7896 −1.89482
\(319\) 10.6784 0.597876
\(320\) 86.1000 4.81313
\(321\) 2.63785 0.147230
\(322\) 7.23456 0.403166
\(323\) 5.59005 0.311039
\(324\) 5.73492 0.318607
\(325\) −3.27702 −0.181776
\(326\) 30.9447 1.71387
\(327\) −14.3300 −0.792453
\(328\) −7.11340 −0.392772
\(329\) −0.881526 −0.0486001
\(330\) 6.03951 0.332464
\(331\) 21.0128 1.15497 0.577484 0.816402i \(-0.304035\pi\)
0.577484 + 0.816402i \(0.304035\pi\)
\(332\) 82.4608 4.52562
\(333\) −11.3116 −0.619873
\(334\) 2.06629 0.113062
\(335\) −13.5680 −0.741297
\(336\) 13.8144 0.753637
\(337\) 2.23255 0.121615 0.0608073 0.998150i \(-0.480632\pi\)
0.0608073 + 0.998150i \(0.480632\pi\)
\(338\) −8.09334 −0.440220
\(339\) 11.8435 0.643248
\(340\) −11.7229 −0.635762
\(341\) 1.77334 0.0960317
\(342\) 15.5469 0.840679
\(343\) 10.6038 0.572554
\(344\) 11.2081 0.604302
\(345\) −6.70493 −0.360981
\(346\) 51.1650 2.75065
\(347\) 20.8091 1.11709 0.558545 0.829474i \(-0.311360\pi\)
0.558545 + 0.829474i \(0.311360\pi\)
\(348\) −57.6457 −3.09013
\(349\) 15.1545 0.811200 0.405600 0.914051i \(-0.367063\pi\)
0.405600 + 0.914051i \(0.367063\pi\)
\(350\) −1.81204 −0.0968576
\(351\) −3.98874 −0.212903
\(352\) −29.3970 −1.56686
\(353\) −27.9906 −1.48979 −0.744895 0.667182i \(-0.767500\pi\)
−0.744895 + 0.667182i \(0.767500\pi\)
\(354\) 9.98278 0.530579
\(355\) 27.3643 1.45235
\(356\) −18.4130 −0.975889
\(357\) −0.793043 −0.0419723
\(358\) 46.6126 2.46355
\(359\) −12.6783 −0.669134 −0.334567 0.942372i \(-0.608590\pi\)
−0.334567 + 0.942372i \(0.608590\pi\)
\(360\) −21.2332 −1.11909
\(361\) 12.2486 0.644665
\(362\) −18.5915 −0.977149
\(363\) 9.87142 0.518115
\(364\) −18.1409 −0.950844
\(365\) −18.2046 −0.952875
\(366\) −5.60467 −0.292961
\(367\) −30.4634 −1.59018 −0.795088 0.606494i \(-0.792575\pi\)
−0.795088 + 0.606494i \(0.792575\pi\)
\(368\) 57.1377 2.97851
\(369\) 0.684806 0.0356496
\(370\) 64.3072 3.34317
\(371\) 9.63499 0.500224
\(372\) −9.57310 −0.496342
\(373\) −9.54066 −0.493997 −0.246998 0.969016i \(-0.579444\pi\)
−0.246998 + 0.969016i \(0.579444\pi\)
\(374\) 2.95458 0.152777
\(375\) 11.9000 0.614513
\(376\) −11.5464 −0.595462
\(377\) 40.0936 2.06492
\(378\) −2.20559 −0.113443
\(379\) 0.0855176 0.00439275 0.00219637 0.999998i \(-0.499301\pi\)
0.00219637 + 0.999998i \(0.499301\pi\)
\(380\) −65.5314 −3.36169
\(381\) −3.46243 −0.177386
\(382\) −22.7489 −1.16394
\(383\) 24.9754 1.27618 0.638091 0.769961i \(-0.279724\pi\)
0.638091 + 0.769961i \(0.279724\pi\)
\(384\) 61.8018 3.15381
\(385\) −1.72215 −0.0877688
\(386\) −50.5932 −2.57513
\(387\) −1.07901 −0.0548490
\(388\) 42.3338 2.14917
\(389\) 23.2810 1.18039 0.590196 0.807260i \(-0.299051\pi\)
0.590196 + 0.807260i \(0.299051\pi\)
\(390\) 22.6762 1.14825
\(391\) −3.28010 −0.165882
\(392\) 66.1794 3.34256
\(393\) 7.37742 0.372142
\(394\) 24.1090 1.21460
\(395\) −32.2083 −1.62058
\(396\) 6.09249 0.306159
\(397\) −10.1432 −0.509071 −0.254535 0.967063i \(-0.581922\pi\)
−0.254535 + 0.967063i \(0.581922\pi\)
\(398\) 32.6651 1.63735
\(399\) −4.43315 −0.221935
\(400\) −14.3113 −0.715564
\(401\) −9.78510 −0.488644 −0.244322 0.969694i \(-0.578565\pi\)
−0.244322 + 0.969694i \(0.578565\pi\)
\(402\) −18.4602 −0.920710
\(403\) 6.65826 0.331671
\(404\) 6.54329 0.325541
\(405\) 2.04412 0.101573
\(406\) 22.1699 1.10027
\(407\) −12.0169 −0.595655
\(408\) −10.3875 −0.514256
\(409\) −34.5835 −1.71005 −0.855023 0.518591i \(-0.826457\pi\)
−0.855023 + 0.518591i \(0.826457\pi\)
\(410\) −3.89316 −0.192270
\(411\) 18.2408 0.899752
\(412\) 46.2091 2.27656
\(413\) −2.84656 −0.140070
\(414\) −9.12253 −0.448348
\(415\) 29.3918 1.44279
\(416\) −110.375 −5.41159
\(417\) −5.90610 −0.289223
\(418\) 16.5162 0.807835
\(419\) 0.911116 0.0445109 0.0222555 0.999752i \(-0.492915\pi\)
0.0222555 + 0.999752i \(0.492915\pi\)
\(420\) 9.29674 0.453635
\(421\) 23.1251 1.12705 0.563524 0.826100i \(-0.309445\pi\)
0.563524 + 0.826100i \(0.309445\pi\)
\(422\) −41.7387 −2.03181
\(423\) 1.11157 0.0540466
\(424\) 126.201 6.12888
\(425\) 0.821567 0.0398519
\(426\) 37.2311 1.80385
\(427\) 1.59816 0.0773402
\(428\) −15.1279 −0.731233
\(429\) −4.23743 −0.204585
\(430\) 6.13421 0.295818
\(431\) 13.5066 0.650589 0.325294 0.945613i \(-0.394537\pi\)
0.325294 + 0.945613i \(0.394537\pi\)
\(432\) −17.4195 −0.838096
\(433\) −26.0792 −1.25328 −0.626642 0.779307i \(-0.715571\pi\)
−0.626642 + 0.779307i \(0.715571\pi\)
\(434\) 3.68171 0.176728
\(435\) −20.5469 −0.985147
\(436\) 82.1817 3.93579
\(437\) −18.3359 −0.877126
\(438\) −24.7687 −1.18350
\(439\) −4.76967 −0.227644 −0.113822 0.993501i \(-0.536309\pi\)
−0.113822 + 0.993501i \(0.536309\pi\)
\(440\) −22.5571 −1.07537
\(441\) −6.37108 −0.303385
\(442\) 11.0934 0.527658
\(443\) 31.2293 1.48375 0.741875 0.670538i \(-0.233937\pi\)
0.741875 + 0.670538i \(0.233937\pi\)
\(444\) 64.8713 3.07865
\(445\) −6.56303 −0.311118
\(446\) −0.876988 −0.0415266
\(447\) 17.0765 0.807692
\(448\) −33.4036 −1.57817
\(449\) 14.0429 0.662726 0.331363 0.943503i \(-0.392492\pi\)
0.331363 + 0.943503i \(0.392492\pi\)
\(450\) 2.28492 0.107712
\(451\) 0.727503 0.0342568
\(452\) −67.9213 −3.19475
\(453\) 13.0331 0.612349
\(454\) −41.4019 −1.94309
\(455\) −6.46605 −0.303133
\(456\) −58.0664 −2.71921
\(457\) 3.64033 0.170287 0.0851437 0.996369i \(-0.472865\pi\)
0.0851437 + 0.996369i \(0.472865\pi\)
\(458\) 71.3942 3.33603
\(459\) 1.00000 0.0466760
\(460\) 38.4522 1.79284
\(461\) 11.5650 0.538638 0.269319 0.963051i \(-0.413201\pi\)
0.269319 + 0.963051i \(0.413201\pi\)
\(462\) −2.34310 −0.109011
\(463\) 35.3593 1.64329 0.821644 0.570002i \(-0.193057\pi\)
0.821644 + 0.570002i \(0.193057\pi\)
\(464\) 175.095 8.12860
\(465\) −3.41218 −0.158236
\(466\) −13.8126 −0.639857
\(467\) −31.2182 −1.44461 −0.722304 0.691576i \(-0.756917\pi\)
−0.722304 + 0.691576i \(0.756917\pi\)
\(468\) 22.8751 1.05740
\(469\) 5.26386 0.243063
\(470\) −6.31936 −0.291490
\(471\) 1.00000 0.0460776
\(472\) −37.2849 −1.71618
\(473\) −1.14628 −0.0527061
\(474\) −43.8217 −2.01280
\(475\) 4.59260 0.210723
\(476\) 4.54804 0.208459
\(477\) −12.1494 −0.556283
\(478\) −2.84316 −0.130043
\(479\) 33.7519 1.54216 0.771081 0.636737i \(-0.219716\pi\)
0.771081 + 0.636737i \(0.219716\pi\)
\(480\) 56.5643 2.58179
\(481\) −45.1191 −2.05725
\(482\) 34.1447 1.55525
\(483\) 2.60126 0.118361
\(484\) −56.6118 −2.57326
\(485\) 15.0892 0.685165
\(486\) 2.78117 0.126157
\(487\) 34.3433 1.55624 0.778122 0.628113i \(-0.216173\pi\)
0.778122 + 0.628113i \(0.216173\pi\)
\(488\) 20.9330 0.947594
\(489\) 11.1265 0.503158
\(490\) 36.2200 1.63625
\(491\) −33.5486 −1.51403 −0.757013 0.653400i \(-0.773342\pi\)
−0.757013 + 0.653400i \(0.773342\pi\)
\(492\) −3.92731 −0.177057
\(493\) −10.0517 −0.452705
\(494\) 62.0125 2.79007
\(495\) 2.17157 0.0976048
\(496\) 29.0777 1.30563
\(497\) −10.6163 −0.476208
\(498\) 39.9897 1.79198
\(499\) 27.3326 1.22357 0.611787 0.791022i \(-0.290451\pi\)
0.611787 + 0.791022i \(0.290451\pi\)
\(500\) −68.2455 −3.05203
\(501\) 0.742955 0.0331928
\(502\) −2.92825 −0.130694
\(503\) −7.72050 −0.344240 −0.172120 0.985076i \(-0.555062\pi\)
−0.172120 + 0.985076i \(0.555062\pi\)
\(504\) 8.23770 0.366937
\(505\) 2.33225 0.103784
\(506\) −9.69131 −0.430831
\(507\) −2.91004 −0.129240
\(508\) 19.8568 0.881003
\(509\) −15.7002 −0.695900 −0.347950 0.937513i \(-0.613122\pi\)
−0.347950 + 0.937513i \(0.613122\pi\)
\(510\) −5.68506 −0.251738
\(511\) 7.06272 0.312437
\(512\) −120.138 −5.30940
\(513\) 5.59005 0.246807
\(514\) 36.3132 1.60171
\(515\) 16.4705 0.725777
\(516\) 6.18802 0.272412
\(517\) 1.18088 0.0519350
\(518\) −24.9488 −1.09619
\(519\) 18.3969 0.807535
\(520\) −84.6939 −3.71407
\(521\) 8.39486 0.367785 0.183893 0.982946i \(-0.441130\pi\)
0.183893 + 0.982946i \(0.441130\pi\)
\(522\) −27.9555 −1.22358
\(523\) 2.31624 0.101282 0.0506410 0.998717i \(-0.483874\pi\)
0.0506410 + 0.998717i \(0.483874\pi\)
\(524\) −42.3089 −1.84827
\(525\) −0.651538 −0.0284355
\(526\) −45.1522 −1.96873
\(527\) −1.66926 −0.0727143
\(528\) −18.5056 −0.805352
\(529\) −12.2409 −0.532214
\(530\) 69.0700 3.00021
\(531\) 3.58942 0.155767
\(532\) 25.4238 1.10226
\(533\) 2.73151 0.118315
\(534\) −8.92947 −0.386416
\(535\) −5.39209 −0.233120
\(536\) 68.9474 2.97807
\(537\) 16.7600 0.723249
\(538\) −26.4667 −1.14106
\(539\) −6.76831 −0.291532
\(540\) −11.7229 −0.504472
\(541\) 39.0012 1.67679 0.838395 0.545062i \(-0.183494\pi\)
0.838395 + 0.545062i \(0.183494\pi\)
\(542\) −4.32179 −0.185637
\(543\) −6.68478 −0.286871
\(544\) 27.6717 1.18641
\(545\) 29.2924 1.25475
\(546\) −8.79752 −0.376499
\(547\) 2.68725 0.114899 0.0574493 0.998348i \(-0.481703\pi\)
0.0574493 + 0.998348i \(0.481703\pi\)
\(548\) −104.610 −4.46870
\(549\) −2.01522 −0.0860075
\(550\) 2.42738 0.103504
\(551\) −56.1894 −2.39375
\(552\) 34.0719 1.45020
\(553\) 12.4956 0.531368
\(554\) 49.9477 2.12208
\(555\) 23.1223 0.981488
\(556\) 33.8710 1.43645
\(557\) −7.49146 −0.317423 −0.158712 0.987325i \(-0.550734\pi\)
−0.158712 + 0.987325i \(0.550734\pi\)
\(558\) −4.64251 −0.196533
\(559\) −4.30388 −0.182035
\(560\) −28.2383 −1.19329
\(561\) 1.06235 0.0448524
\(562\) −83.1136 −3.50594
\(563\) 39.6264 1.67005 0.835027 0.550210i \(-0.185452\pi\)
0.835027 + 0.550210i \(0.185452\pi\)
\(564\) −6.37479 −0.268427
\(565\) −24.2095 −1.01850
\(566\) 20.1392 0.846515
\(567\) −0.793043 −0.0333047
\(568\) −139.055 −5.83464
\(569\) −31.3757 −1.31534 −0.657669 0.753307i \(-0.728457\pi\)
−0.657669 + 0.753307i \(0.728457\pi\)
\(570\) −31.7797 −1.33111
\(571\) −3.97999 −0.166557 −0.0832786 0.996526i \(-0.526539\pi\)
−0.0832786 + 0.996526i \(0.526539\pi\)
\(572\) 24.3013 1.01609
\(573\) −8.17962 −0.341709
\(574\) 1.51040 0.0630429
\(575\) −2.69482 −0.112382
\(576\) 42.1208 1.75503
\(577\) 19.3682 0.806311 0.403155 0.915132i \(-0.367913\pi\)
0.403155 + 0.915132i \(0.367913\pi\)
\(578\) −2.78117 −0.115682
\(579\) −18.1913 −0.756006
\(580\) 117.835 4.89282
\(581\) −11.4029 −0.473073
\(582\) 20.5299 0.850993
\(583\) −12.9069 −0.534549
\(584\) 92.5093 3.82806
\(585\) 8.15347 0.337104
\(586\) −42.4910 −1.75529
\(587\) −0.435759 −0.0179857 −0.00899285 0.999960i \(-0.502863\pi\)
−0.00899285 + 0.999960i \(0.502863\pi\)
\(588\) 36.5377 1.50679
\(589\) −9.33126 −0.384488
\(590\) −20.4060 −0.840103
\(591\) 8.66866 0.356581
\(592\) −197.043 −8.09841
\(593\) 35.2992 1.44956 0.724781 0.688979i \(-0.241941\pi\)
0.724781 + 0.688979i \(0.241941\pi\)
\(594\) 2.95458 0.121228
\(595\) 1.62108 0.0664576
\(596\) −97.9326 −4.01148
\(597\) 11.7451 0.480694
\(598\) −36.3874 −1.48799
\(599\) 0.630423 0.0257584 0.0128792 0.999917i \(-0.495900\pi\)
0.0128792 + 0.999917i \(0.495900\pi\)
\(600\) −8.53400 −0.348399
\(601\) 39.1641 1.59754 0.798768 0.601639i \(-0.205485\pi\)
0.798768 + 0.601639i \(0.205485\pi\)
\(602\) −2.37984 −0.0969952
\(603\) −6.63755 −0.270302
\(604\) −74.7439 −3.04129
\(605\) −20.1784 −0.820367
\(606\) 3.17319 0.128902
\(607\) 29.2631 1.18775 0.593876 0.804557i \(-0.297597\pi\)
0.593876 + 0.804557i \(0.297597\pi\)
\(608\) 154.686 6.27335
\(609\) 7.97142 0.323018
\(610\) 11.4566 0.463866
\(611\) 4.43378 0.179371
\(612\) −5.73492 −0.231821
\(613\) −15.1074 −0.610180 −0.305090 0.952323i \(-0.598687\pi\)
−0.305090 + 0.952323i \(0.598687\pi\)
\(614\) 85.0103 3.43074
\(615\) −1.39983 −0.0564465
\(616\) 8.75131 0.352601
\(617\) −24.2197 −0.975050 −0.487525 0.873109i \(-0.662100\pi\)
−0.487525 + 0.873109i \(0.662100\pi\)
\(618\) 22.4093 0.901434
\(619\) −2.12188 −0.0852854 −0.0426427 0.999090i \(-0.513578\pi\)
−0.0426427 + 0.999090i \(0.513578\pi\)
\(620\) 19.5686 0.785893
\(621\) −3.28010 −0.131626
\(622\) −23.9674 −0.961005
\(623\) 2.54621 0.102012
\(624\) −69.4818 −2.78150
\(625\) −20.2172 −0.808688
\(626\) 77.2571 3.08781
\(627\) 5.93858 0.237164
\(628\) −5.73492 −0.228848
\(629\) 11.3116 0.451024
\(630\) 4.50849 0.179623
\(631\) −5.30104 −0.211031 −0.105516 0.994418i \(-0.533649\pi\)
−0.105516 + 0.994418i \(0.533649\pi\)
\(632\) 163.671 6.51047
\(633\) −15.0076 −0.596498
\(634\) −37.6795 −1.49644
\(635\) 7.07763 0.280867
\(636\) 69.6758 2.76283
\(637\) −25.4126 −1.00688
\(638\) −29.6985 −1.17577
\(639\) 13.3868 0.529575
\(640\) −126.330 −4.99364
\(641\) −15.8826 −0.627323 −0.313662 0.949535i \(-0.601556\pi\)
−0.313662 + 0.949535i \(0.601556\pi\)
\(642\) −7.33632 −0.289541
\(643\) −9.03438 −0.356281 −0.178141 0.984005i \(-0.557008\pi\)
−0.178141 + 0.984005i \(0.557008\pi\)
\(644\) −14.9180 −0.587853
\(645\) 2.20562 0.0868462
\(646\) −15.5469 −0.611684
\(647\) −45.6949 −1.79645 −0.898227 0.439533i \(-0.855144\pi\)
−0.898227 + 0.439533i \(0.855144\pi\)
\(648\) −10.3875 −0.408058
\(649\) 3.81321 0.149682
\(650\) 9.11396 0.357479
\(651\) 1.32380 0.0518837
\(652\) −63.8097 −2.49898
\(653\) −43.4820 −1.70158 −0.850791 0.525504i \(-0.823877\pi\)
−0.850791 + 0.525504i \(0.823877\pi\)
\(654\) 39.8543 1.55843
\(655\) −15.0803 −0.589238
\(656\) 11.9290 0.465748
\(657\) −8.90585 −0.347450
\(658\) 2.45167 0.0955762
\(659\) −28.0538 −1.09282 −0.546410 0.837518i \(-0.684006\pi\)
−0.546410 + 0.837518i \(0.684006\pi\)
\(660\) −12.4538 −0.484763
\(661\) −30.1890 −1.17422 −0.587108 0.809508i \(-0.699734\pi\)
−0.587108 + 0.809508i \(0.699734\pi\)
\(662\) −58.4402 −2.27134
\(663\) 3.98874 0.154910
\(664\) −149.358 −5.79623
\(665\) 9.06189 0.351405
\(666\) 31.4596 1.21903
\(667\) 32.9706 1.27663
\(668\) −4.26079 −0.164855
\(669\) −0.315330 −0.0121914
\(670\) 37.7349 1.45782
\(671\) −2.14087 −0.0826472
\(672\) −21.9448 −0.846540
\(673\) 32.6659 1.25918 0.629589 0.776928i \(-0.283223\pi\)
0.629589 + 0.776928i \(0.283223\pi\)
\(674\) −6.20910 −0.239166
\(675\) 0.821567 0.0316221
\(676\) 16.6889 0.641880
\(677\) 1.01583 0.0390415 0.0195207 0.999809i \(-0.493786\pi\)
0.0195207 + 0.999809i \(0.493786\pi\)
\(678\) −32.9387 −1.26500
\(679\) −5.85405 −0.224658
\(680\) 21.2332 0.814258
\(681\) −14.8865 −0.570452
\(682\) −4.93196 −0.188855
\(683\) 25.5372 0.977154 0.488577 0.872521i \(-0.337516\pi\)
0.488577 + 0.872521i \(0.337516\pi\)
\(684\) −32.0585 −1.22579
\(685\) −37.2864 −1.42464
\(686\) −29.4911 −1.12598
\(687\) 25.6705 0.979391
\(688\) −18.7957 −0.716581
\(689\) −48.4608 −1.84621
\(690\) 18.6476 0.709900
\(691\) 20.2036 0.768582 0.384291 0.923212i \(-0.374446\pi\)
0.384291 + 0.923212i \(0.374446\pi\)
\(692\) −105.505 −4.01070
\(693\) −0.842488 −0.0320035
\(694\) −57.8736 −2.19685
\(695\) 12.0728 0.457947
\(696\) 104.412 3.95771
\(697\) −0.684806 −0.0259389
\(698\) −42.1472 −1.59529
\(699\) −4.96647 −0.187849
\(700\) 3.73652 0.141227
\(701\) −47.4558 −1.79238 −0.896190 0.443671i \(-0.853676\pi\)
−0.896190 + 0.443671i \(0.853676\pi\)
\(702\) 11.0934 0.418692
\(703\) 63.2325 2.38486
\(704\) 44.7469 1.68646
\(705\) −2.27219 −0.0855757
\(706\) 77.8467 2.92980
\(707\) −0.904827 −0.0340295
\(708\) −20.5850 −0.773632
\(709\) 21.2865 0.799431 0.399716 0.916639i \(-0.369109\pi\)
0.399716 + 0.916639i \(0.369109\pi\)
\(710\) −76.1050 −2.85617
\(711\) −15.7566 −0.590917
\(712\) 33.3509 1.24988
\(713\) 5.47535 0.205054
\(714\) 2.20559 0.0825421
\(715\) 8.66183 0.323934
\(716\) −96.1175 −3.59208
\(717\) −1.02229 −0.0381781
\(718\) 35.2605 1.31591
\(719\) −36.7495 −1.37053 −0.685263 0.728296i \(-0.740313\pi\)
−0.685263 + 0.728296i \(0.740313\pi\)
\(720\) 35.6076 1.32702
\(721\) −6.38994 −0.237974
\(722\) −34.0656 −1.26779
\(723\) 12.2771 0.456589
\(724\) 38.3367 1.42477
\(725\) −8.25814 −0.306700
\(726\) −27.4541 −1.01892
\(727\) −20.0426 −0.743339 −0.371669 0.928365i \(-0.621215\pi\)
−0.371669 + 0.928365i \(0.621215\pi\)
\(728\) 32.8581 1.21780
\(729\) 1.00000 0.0370370
\(730\) 50.6303 1.87391
\(731\) 1.07901 0.0399085
\(732\) 11.5571 0.427164
\(733\) −25.1311 −0.928239 −0.464119 0.885773i \(-0.653629\pi\)
−0.464119 + 0.885773i \(0.653629\pi\)
\(734\) 84.7239 3.12722
\(735\) 13.0233 0.480370
\(736\) −90.7660 −3.34568
\(737\) −7.05140 −0.259741
\(738\) −1.90457 −0.0701080
\(739\) 0.219901 0.00808918 0.00404459 0.999992i \(-0.498713\pi\)
0.00404459 + 0.999992i \(0.498713\pi\)
\(740\) −132.605 −4.87465
\(741\) 22.2972 0.819110
\(742\) −26.7966 −0.983733
\(743\) −50.4513 −1.85088 −0.925439 0.378896i \(-0.876304\pi\)
−0.925439 + 0.378896i \(0.876304\pi\)
\(744\) 17.3394 0.635694
\(745\) −34.9065 −1.27888
\(746\) 26.5342 0.971487
\(747\) 14.3787 0.526089
\(748\) −6.09249 −0.222763
\(749\) 2.09193 0.0764374
\(750\) −33.0959 −1.20849
\(751\) 8.74882 0.319249 0.159625 0.987178i \(-0.448972\pi\)
0.159625 + 0.987178i \(0.448972\pi\)
\(752\) 19.3631 0.706098
\(753\) −1.05288 −0.0383693
\(754\) −111.507 −4.06085
\(755\) −26.6413 −0.969575
\(756\) 4.54804 0.165411
\(757\) −35.1530 −1.27766 −0.638828 0.769350i \(-0.720580\pi\)
−0.638828 + 0.769350i \(0.720580\pi\)
\(758\) −0.237839 −0.00863871
\(759\) −3.48461 −0.126483
\(760\) 118.695 4.30551
\(761\) −36.6628 −1.32903 −0.664513 0.747276i \(-0.731361\pi\)
−0.664513 + 0.747276i \(0.731361\pi\)
\(762\) 9.62963 0.348845
\(763\) −11.3643 −0.411417
\(764\) 46.9095 1.69713
\(765\) −2.04412 −0.0739054
\(766\) −69.4608 −2.50972
\(767\) 14.3172 0.516966
\(768\) −87.6398 −3.16243
\(769\) −11.0315 −0.397806 −0.198903 0.980019i \(-0.563738\pi\)
−0.198903 + 0.980019i \(0.563738\pi\)
\(770\) 4.78959 0.172605
\(771\) 13.0568 0.470229
\(772\) 104.326 3.75477
\(773\) −31.8047 −1.14394 −0.571968 0.820276i \(-0.693820\pi\)
−0.571968 + 0.820276i \(0.693820\pi\)
\(774\) 3.00090 0.107865
\(775\) −1.37141 −0.0492626
\(776\) −76.6777 −2.75257
\(777\) −8.97060 −0.321819
\(778\) −64.7484 −2.32134
\(779\) −3.82810 −0.137156
\(780\) −46.7595 −1.67426
\(781\) 14.2215 0.508885
\(782\) 9.12253 0.326221
\(783\) −10.0517 −0.359218
\(784\) −110.981 −3.96361
\(785\) −2.04412 −0.0729578
\(786\) −20.5179 −0.731849
\(787\) −17.2294 −0.614162 −0.307081 0.951683i \(-0.599352\pi\)
−0.307081 + 0.951683i \(0.599352\pi\)
\(788\) −49.7141 −1.77099
\(789\) −16.2349 −0.577979
\(790\) 89.5769 3.18700
\(791\) 9.39237 0.333954
\(792\) −11.0351 −0.392116
\(793\) −8.03819 −0.285444
\(794\) 28.2099 1.00113
\(795\) 24.8348 0.880801
\(796\) −67.3571 −2.38741
\(797\) −21.3036 −0.754611 −0.377305 0.926089i \(-0.623149\pi\)
−0.377305 + 0.926089i \(0.623149\pi\)
\(798\) 12.3293 0.436454
\(799\) −1.11157 −0.0393247
\(800\) 22.7342 0.803774
\(801\) −3.21069 −0.113444
\(802\) 27.2140 0.960961
\(803\) −9.46112 −0.333876
\(804\) 38.0659 1.34248
\(805\) −5.31729 −0.187410
\(806\) −18.5178 −0.652260
\(807\) −9.51640 −0.334993
\(808\) −11.8516 −0.416939
\(809\) 12.0795 0.424691 0.212346 0.977195i \(-0.431890\pi\)
0.212346 + 0.977195i \(0.431890\pi\)
\(810\) −5.68506 −0.199752
\(811\) −30.5260 −1.07191 −0.535956 0.844246i \(-0.680049\pi\)
−0.535956 + 0.844246i \(0.680049\pi\)
\(812\) −45.7155 −1.60430
\(813\) −1.55394 −0.0544992
\(814\) 33.4210 1.17141
\(815\) −22.7439 −0.796685
\(816\) 17.4195 0.609804
\(817\) 6.03170 0.211022
\(818\) 96.1828 3.36295
\(819\) −3.16324 −0.110533
\(820\) 8.02790 0.280347
\(821\) 1.96496 0.0685775 0.0342887 0.999412i \(-0.489083\pi\)
0.0342887 + 0.999412i \(0.489083\pi\)
\(822\) −50.7308 −1.76944
\(823\) −53.1025 −1.85104 −0.925518 0.378704i \(-0.876370\pi\)
−0.925518 + 0.378704i \(0.876370\pi\)
\(824\) −83.6970 −2.91572
\(825\) 0.872791 0.0303867
\(826\) 7.91678 0.275460
\(827\) 32.6068 1.13385 0.566925 0.823769i \(-0.308133\pi\)
0.566925 + 0.823769i \(0.308133\pi\)
\(828\) 18.8111 0.653732
\(829\) −40.0549 −1.39116 −0.695582 0.718447i \(-0.744853\pi\)
−0.695582 + 0.718447i \(0.744853\pi\)
\(830\) −81.7438 −2.83737
\(831\) 17.9592 0.622999
\(832\) 168.009 5.82466
\(833\) 6.37108 0.220745
\(834\) 16.4259 0.568782
\(835\) −1.51869 −0.0525565
\(836\) −34.0573 −1.17790
\(837\) −1.66926 −0.0576982
\(838\) −2.53397 −0.0875346
\(839\) −3.59882 −0.124245 −0.0621225 0.998069i \(-0.519787\pi\)
−0.0621225 + 0.998069i \(0.519787\pi\)
\(840\) −16.8389 −0.580996
\(841\) 72.0365 2.48402
\(842\) −64.3149 −2.21644
\(843\) −29.8844 −1.02927
\(844\) 86.0673 2.96256
\(845\) 5.94848 0.204634
\(846\) −3.09148 −0.106287
\(847\) 7.82845 0.268989
\(848\) −211.636 −7.26762
\(849\) 7.24127 0.248520
\(850\) −2.28492 −0.0783721
\(851\) −37.1033 −1.27188
\(852\) −76.7725 −2.63018
\(853\) −3.43592 −0.117644 −0.0588218 0.998269i \(-0.518734\pi\)
−0.0588218 + 0.998269i \(0.518734\pi\)
\(854\) −4.44475 −0.152096
\(855\) −11.4267 −0.390786
\(856\) 27.4006 0.936533
\(857\) 46.2970 1.58148 0.790739 0.612154i \(-0.209697\pi\)
0.790739 + 0.612154i \(0.209697\pi\)
\(858\) 11.7850 0.402334
\(859\) −19.2192 −0.655752 −0.327876 0.944721i \(-0.606333\pi\)
−0.327876 + 0.944721i \(0.606333\pi\)
\(860\) −12.6491 −0.431329
\(861\) 0.543081 0.0185081
\(862\) −37.5641 −1.27944
\(863\) −19.4991 −0.663758 −0.331879 0.943322i \(-0.607683\pi\)
−0.331879 + 0.943322i \(0.607683\pi\)
\(864\) 27.6717 0.941410
\(865\) −37.6056 −1.27863
\(866\) 72.5307 2.46469
\(867\) −1.00000 −0.0339618
\(868\) −7.59187 −0.257685
\(869\) −16.7390 −0.567830
\(870\) 57.1444 1.93738
\(871\) −26.4755 −0.897087
\(872\) −148.853 −5.04079
\(873\) 7.38175 0.249835
\(874\) 50.9954 1.72494
\(875\) 9.43720 0.319036
\(876\) 51.0744 1.72564
\(877\) 32.1612 1.08601 0.543003 0.839731i \(-0.317287\pi\)
0.543003 + 0.839731i \(0.317287\pi\)
\(878\) 13.2653 0.447682
\(879\) −15.2781 −0.515317
\(880\) 37.8276 1.27517
\(881\) 23.8548 0.803690 0.401845 0.915708i \(-0.368369\pi\)
0.401845 + 0.915708i \(0.368369\pi\)
\(882\) 17.7191 0.596633
\(883\) −29.7984 −1.00280 −0.501398 0.865217i \(-0.667181\pi\)
−0.501398 + 0.865217i \(0.667181\pi\)
\(884\) −22.8751 −0.769373
\(885\) −7.33720 −0.246637
\(886\) −86.8542 −2.91792
\(887\) 51.1668 1.71801 0.859007 0.511964i \(-0.171082\pi\)
0.859007 + 0.511964i \(0.171082\pi\)
\(888\) −117.499 −3.94301
\(889\) −2.74586 −0.0920931
\(890\) 18.2529 0.611840
\(891\) 1.06235 0.0355900
\(892\) 1.80840 0.0605496
\(893\) −6.21375 −0.207935
\(894\) −47.4928 −1.58840
\(895\) −34.2596 −1.14517
\(896\) 49.0114 1.63736
\(897\) −13.0835 −0.436844
\(898\) −39.0558 −1.30331
\(899\) 16.7789 0.559608
\(900\) −4.71163 −0.157054
\(901\) 12.1494 0.404755
\(902\) −2.02331 −0.0673689
\(903\) −0.855698 −0.0284759
\(904\) 123.024 4.09170
\(905\) 13.6645 0.454223
\(906\) −36.2473 −1.20424
\(907\) −50.9600 −1.69210 −0.846049 0.533105i \(-0.821025\pi\)
−0.846049 + 0.533105i \(0.821025\pi\)
\(908\) 85.3729 2.83320
\(909\) 1.14096 0.0378431
\(910\) 17.9832 0.596137
\(911\) −15.2408 −0.504951 −0.252476 0.967603i \(-0.581245\pi\)
−0.252476 + 0.967603i \(0.581245\pi\)
\(912\) 97.3758 3.22443
\(913\) 15.2752 0.505535
\(914\) −10.1244 −0.334885
\(915\) 4.11935 0.136182
\(916\) −147.218 −4.86423
\(917\) 5.85061 0.193204
\(918\) −2.78117 −0.0917924
\(919\) 44.2760 1.46053 0.730266 0.683163i \(-0.239396\pi\)
0.730266 + 0.683163i \(0.239396\pi\)
\(920\) −69.6472 −2.29620
\(921\) 30.5663 1.00720
\(922\) −32.1644 −1.05928
\(923\) 53.3966 1.75757
\(924\) 4.83160 0.158948
\(925\) 9.29326 0.305561
\(926\) −98.3404 −3.23167
\(927\) 8.05750 0.264643
\(928\) −278.147 −9.13063
\(929\) 25.8433 0.847891 0.423946 0.905688i \(-0.360645\pi\)
0.423946 + 0.905688i \(0.360645\pi\)
\(930\) 9.48985 0.311185
\(931\) 35.6147 1.16722
\(932\) 28.4823 0.932970
\(933\) −8.61773 −0.282132
\(934\) 86.8233 2.84095
\(935\) −2.17157 −0.0710179
\(936\) −41.4329 −1.35428
\(937\) −31.1207 −1.01667 −0.508334 0.861160i \(-0.669739\pi\)
−0.508334 + 0.861160i \(0.669739\pi\)
\(938\) −14.6397 −0.478004
\(939\) 27.7786 0.906520
\(940\) 13.0308 0.425019
\(941\) −57.4690 −1.87343 −0.936717 0.350086i \(-0.886152\pi\)
−0.936717 + 0.350086i \(0.886152\pi\)
\(942\) −2.78117 −0.0906155
\(943\) 2.24623 0.0731475
\(944\) 62.5258 2.03504
\(945\) 1.62108 0.0527336
\(946\) 3.18801 0.103651
\(947\) −22.7136 −0.738094 −0.369047 0.929411i \(-0.620316\pi\)
−0.369047 + 0.929411i \(0.620316\pi\)
\(948\) 90.3626 2.93484
\(949\) −35.5231 −1.15313
\(950\) −12.7728 −0.414405
\(951\) −13.5481 −0.439326
\(952\) −8.23770 −0.266986
\(953\) −15.1075 −0.489380 −0.244690 0.969601i \(-0.578686\pi\)
−0.244690 + 0.969601i \(0.578686\pi\)
\(954\) 33.7896 1.09398
\(955\) 16.7201 0.541051
\(956\) 5.86275 0.189615
\(957\) −10.6784 −0.345184
\(958\) −93.8698 −3.03280
\(959\) 14.4657 0.467123
\(960\) −86.1000 −2.77886
\(961\) −28.2136 −0.910115
\(962\) 125.484 4.04577
\(963\) −2.63785 −0.0850036
\(964\) −70.4081 −2.26769
\(965\) 37.1853 1.19704
\(966\) −7.23456 −0.232768
\(967\) −2.91823 −0.0938438 −0.0469219 0.998899i \(-0.514941\pi\)
−0.0469219 + 0.998899i \(0.514941\pi\)
\(968\) 102.539 3.29573
\(969\) −5.59005 −0.179578
\(970\) −41.9657 −1.34744
\(971\) −10.3346 −0.331654 −0.165827 0.986155i \(-0.553029\pi\)
−0.165827 + 0.986155i \(0.553029\pi\)
\(972\) −5.73492 −0.183948
\(973\) −4.68379 −0.150155
\(974\) −95.5147 −3.06049
\(975\) 3.27702 0.104949
\(976\) −35.1041 −1.12366
\(977\) 35.0864 1.12251 0.561256 0.827642i \(-0.310318\pi\)
0.561256 + 0.827642i \(0.310318\pi\)
\(978\) −30.9447 −0.989504
\(979\) −3.41087 −0.109012
\(980\) −74.6874 −2.38580
\(981\) 14.3300 0.457523
\(982\) 93.3044 2.97746
\(983\) −53.1689 −1.69582 −0.847912 0.530138i \(-0.822140\pi\)
−0.847912 + 0.530138i \(0.822140\pi\)
\(984\) 7.11340 0.226767
\(985\) −17.7198 −0.564600
\(986\) 27.9555 0.890284
\(987\) 0.881526 0.0280593
\(988\) −127.873 −4.06818
\(989\) −3.53925 −0.112542
\(990\) −6.03951 −0.191948
\(991\) −9.29409 −0.295236 −0.147618 0.989044i \(-0.547161\pi\)
−0.147618 + 0.989044i \(0.547161\pi\)
\(992\) −46.1913 −1.46658
\(993\) −21.0128 −0.666821
\(994\) 29.5259 0.936504
\(995\) −24.0083 −0.761116
\(996\) −82.4608 −2.61287
\(997\) −17.8074 −0.563966 −0.281983 0.959419i \(-0.590992\pi\)
−0.281983 + 0.959419i \(0.590992\pi\)
\(998\) −76.0167 −2.40627
\(999\) 11.3116 0.357884
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.1.1 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8007.2.a.f.1.1 48 1.1 even 1 trivial