Properties

Label 8007.2.a.f.1.7
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 1.7
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.27518 q^{2} -1.00000 q^{3} +3.17643 q^{4} +2.61308 q^{5} +2.27518 q^{6} +3.54577 q^{7} -2.67658 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.27518 q^{2} -1.00000 q^{3} +3.17643 q^{4} +2.61308 q^{5} +2.27518 q^{6} +3.54577 q^{7} -2.67658 q^{8} +1.00000 q^{9} -5.94522 q^{10} +2.60663 q^{11} -3.17643 q^{12} -6.26473 q^{13} -8.06724 q^{14} -2.61308 q^{15} -0.263166 q^{16} -1.00000 q^{17} -2.27518 q^{18} +2.01130 q^{19} +8.30026 q^{20} -3.54577 q^{21} -5.93053 q^{22} -8.87413 q^{23} +2.67658 q^{24} +1.82820 q^{25} +14.2534 q^{26} -1.00000 q^{27} +11.2629 q^{28} -5.96949 q^{29} +5.94522 q^{30} +1.87052 q^{31} +5.95191 q^{32} -2.60663 q^{33} +2.27518 q^{34} +9.26538 q^{35} +3.17643 q^{36} +1.22700 q^{37} -4.57606 q^{38} +6.26473 q^{39} -6.99412 q^{40} +6.75629 q^{41} +8.06724 q^{42} -8.80703 q^{43} +8.27976 q^{44} +2.61308 q^{45} +20.1902 q^{46} -7.43338 q^{47} +0.263166 q^{48} +5.57246 q^{49} -4.15947 q^{50} +1.00000 q^{51} -19.8994 q^{52} -3.46416 q^{53} +2.27518 q^{54} +6.81133 q^{55} -9.49052 q^{56} -2.01130 q^{57} +13.5816 q^{58} +8.10288 q^{59} -8.30026 q^{60} +9.35388 q^{61} -4.25577 q^{62} +3.54577 q^{63} -13.0153 q^{64} -16.3702 q^{65} +5.93053 q^{66} -0.624312 q^{67} -3.17643 q^{68} +8.87413 q^{69} -21.0804 q^{70} +12.4781 q^{71} -2.67658 q^{72} -6.92684 q^{73} -2.79164 q^{74} -1.82820 q^{75} +6.38875 q^{76} +9.24249 q^{77} -14.2534 q^{78} -1.93136 q^{79} -0.687676 q^{80} +1.00000 q^{81} -15.3718 q^{82} +17.5002 q^{83} -11.2629 q^{84} -2.61308 q^{85} +20.0375 q^{86} +5.96949 q^{87} -6.97684 q^{88} -0.0410964 q^{89} -5.94522 q^{90} -22.2133 q^{91} -28.1880 q^{92} -1.87052 q^{93} +16.9123 q^{94} +5.25569 q^{95} -5.95191 q^{96} +12.3898 q^{97} -12.6783 q^{98} +2.60663 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} + O(q^{10}) \) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} - 20q^{10} + 5q^{11} - 45q^{12} - 8q^{13} + 4q^{14} - q^{15} + 39q^{16} - 48q^{17} - q^{18} - 6q^{19} + 6q^{20} + 13q^{21} - 35q^{22} - 8q^{23} + 6q^{24} + 13q^{25} + 17q^{26} - 48q^{27} - 38q^{28} + q^{29} + 20q^{30} - 21q^{31} - 3q^{32} - 5q^{33} + q^{34} + 19q^{35} + 45q^{36} - 58q^{37} - 14q^{38} + 8q^{39} - 54q^{40} - 3q^{41} - 4q^{42} - 33q^{43} + 2q^{44} + q^{45} - 26q^{46} + 9q^{47} - 39q^{48} + 11q^{49} + 4q^{50} + 48q^{51} - 31q^{52} - 33q^{53} + q^{54} - 21q^{55} + 6q^{57} - 55q^{58} + 77q^{59} - 6q^{60} - 29q^{61} - 46q^{62} - 13q^{63} + 24q^{64} - 49q^{65} + 35q^{66} - 44q^{67} - 45q^{68} + 8q^{69} + 4q^{70} + 22q^{71} - 6q^{72} - 63q^{73} - 16q^{74} - 13q^{75} - 46q^{76} - 30q^{77} - 17q^{78} - 46q^{79} - 14q^{80} + 48q^{81} - 75q^{82} + 11q^{83} + 38q^{84} - q^{85} + 8q^{86} - q^{87} - 116q^{88} + 10q^{89} - 20q^{90} - 67q^{91} - 64q^{92} + 21q^{93} - 16q^{94} - 8q^{95} + 3q^{96} - 96q^{97} - 46q^{98} + 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.27518 −1.60879 −0.804396 0.594093i \(-0.797511\pi\)
−0.804396 + 0.594093i \(0.797511\pi\)
\(3\) −1.00000 −0.577350
\(4\) 3.17643 1.58821
\(5\) 2.61308 1.16861 0.584303 0.811536i \(-0.301368\pi\)
0.584303 + 0.811536i \(0.301368\pi\)
\(6\) 2.27518 0.928837
\(7\) 3.54577 1.34017 0.670087 0.742283i \(-0.266257\pi\)
0.670087 + 0.742283i \(0.266257\pi\)
\(8\) −2.67658 −0.946313
\(9\) 1.00000 0.333333
\(10\) −5.94522 −1.88004
\(11\) 2.60663 0.785927 0.392964 0.919554i \(-0.371450\pi\)
0.392964 + 0.919554i \(0.371450\pi\)
\(12\) −3.17643 −0.916955
\(13\) −6.26473 −1.73752 −0.868761 0.495231i \(-0.835083\pi\)
−0.868761 + 0.495231i \(0.835083\pi\)
\(14\) −8.06724 −2.15606
\(15\) −2.61308 −0.674695
\(16\) −0.263166 −0.0657916
\(17\) −1.00000 −0.242536
\(18\) −2.27518 −0.536264
\(19\) 2.01130 0.461424 0.230712 0.973022i \(-0.425895\pi\)
0.230712 + 0.973022i \(0.425895\pi\)
\(20\) 8.30026 1.85600
\(21\) −3.54577 −0.773750
\(22\) −5.93053 −1.26439
\(23\) −8.87413 −1.85038 −0.925192 0.379499i \(-0.876096\pi\)
−0.925192 + 0.379499i \(0.876096\pi\)
\(24\) 2.67658 0.546354
\(25\) 1.82820 0.365640
\(26\) 14.2534 2.79531
\(27\) −1.00000 −0.192450
\(28\) 11.2629 2.12848
\(29\) −5.96949 −1.10851 −0.554253 0.832348i \(-0.686996\pi\)
−0.554253 + 0.832348i \(0.686996\pi\)
\(30\) 5.94522 1.08544
\(31\) 1.87052 0.335956 0.167978 0.985791i \(-0.446276\pi\)
0.167978 + 0.985791i \(0.446276\pi\)
\(32\) 5.95191 1.05216
\(33\) −2.60663 −0.453755
\(34\) 2.27518 0.390190
\(35\) 9.26538 1.56613
\(36\) 3.17643 0.529404
\(37\) 1.22700 0.201717 0.100859 0.994901i \(-0.467841\pi\)
0.100859 + 0.994901i \(0.467841\pi\)
\(38\) −4.57606 −0.742335
\(39\) 6.26473 1.00316
\(40\) −6.99412 −1.10587
\(41\) 6.75629 1.05516 0.527578 0.849507i \(-0.323100\pi\)
0.527578 + 0.849507i \(0.323100\pi\)
\(42\) 8.06724 1.24480
\(43\) −8.80703 −1.34306 −0.671530 0.740978i \(-0.734362\pi\)
−0.671530 + 0.740978i \(0.734362\pi\)
\(44\) 8.27976 1.24822
\(45\) 2.61308 0.389535
\(46\) 20.1902 2.97688
\(47\) −7.43338 −1.08427 −0.542135 0.840291i \(-0.682384\pi\)
−0.542135 + 0.840291i \(0.682384\pi\)
\(48\) 0.263166 0.0379848
\(49\) 5.57246 0.796066
\(50\) −4.15947 −0.588239
\(51\) 1.00000 0.140028
\(52\) −19.8994 −2.75956
\(53\) −3.46416 −0.475839 −0.237920 0.971285i \(-0.576466\pi\)
−0.237920 + 0.971285i \(0.576466\pi\)
\(54\) 2.27518 0.309612
\(55\) 6.81133 0.918439
\(56\) −9.49052 −1.26822
\(57\) −2.01130 −0.266403
\(58\) 13.5816 1.78336
\(59\) 8.10288 1.05491 0.527453 0.849585i \(-0.323147\pi\)
0.527453 + 0.849585i \(0.323147\pi\)
\(60\) −8.30026 −1.07156
\(61\) 9.35388 1.19764 0.598821 0.800883i \(-0.295636\pi\)
0.598821 + 0.800883i \(0.295636\pi\)
\(62\) −4.25577 −0.540483
\(63\) 3.54577 0.446725
\(64\) −13.0153 −1.62691
\(65\) −16.3702 −2.03048
\(66\) 5.93053 0.729998
\(67\) −0.624312 −0.0762718 −0.0381359 0.999273i \(-0.512142\pi\)
−0.0381359 + 0.999273i \(0.512142\pi\)
\(68\) −3.17643 −0.385198
\(69\) 8.87413 1.06832
\(70\) −21.0804 −2.51959
\(71\) 12.4781 1.48088 0.740438 0.672125i \(-0.234618\pi\)
0.740438 + 0.672125i \(0.234618\pi\)
\(72\) −2.67658 −0.315438
\(73\) −6.92684 −0.810726 −0.405363 0.914156i \(-0.632855\pi\)
−0.405363 + 0.914156i \(0.632855\pi\)
\(74\) −2.79164 −0.324522
\(75\) −1.82820 −0.211102
\(76\) 6.38875 0.732839
\(77\) 9.24249 1.05328
\(78\) −14.2534 −1.61387
\(79\) −1.93136 −0.217296 −0.108648 0.994080i \(-0.534652\pi\)
−0.108648 + 0.994080i \(0.534652\pi\)
\(80\) −0.687676 −0.0768845
\(81\) 1.00000 0.111111
\(82\) −15.3718 −1.69753
\(83\) 17.5002 1.92089 0.960447 0.278462i \(-0.0898247\pi\)
0.960447 + 0.278462i \(0.0898247\pi\)
\(84\) −11.2629 −1.22888
\(85\) −2.61308 −0.283429
\(86\) 20.0375 2.16070
\(87\) 5.96949 0.639996
\(88\) −6.97684 −0.743734
\(89\) −0.0410964 −0.00435621 −0.00217810 0.999998i \(-0.500693\pi\)
−0.00217810 + 0.999998i \(0.500693\pi\)
\(90\) −5.94522 −0.626681
\(91\) −22.2133 −2.32858
\(92\) −28.1880 −2.93881
\(93\) −1.87052 −0.193964
\(94\) 16.9123 1.74437
\(95\) 5.25569 0.539222
\(96\) −5.95191 −0.607464
\(97\) 12.3898 1.25800 0.628999 0.777406i \(-0.283465\pi\)
0.628999 + 0.777406i \(0.283465\pi\)
\(98\) −12.6783 −1.28070
\(99\) 2.60663 0.261976
\(100\) 5.80714 0.580714
\(101\) −11.5200 −1.14628 −0.573139 0.819458i \(-0.694275\pi\)
−0.573139 + 0.819458i \(0.694275\pi\)
\(102\) −2.27518 −0.225276
\(103\) −17.3391 −1.70847 −0.854234 0.519888i \(-0.825974\pi\)
−0.854234 + 0.519888i \(0.825974\pi\)
\(104\) 16.7680 1.64424
\(105\) −9.26538 −0.904208
\(106\) 7.88158 0.765527
\(107\) −7.48347 −0.723455 −0.361727 0.932284i \(-0.617813\pi\)
−0.361727 + 0.932284i \(0.617813\pi\)
\(108\) −3.17643 −0.305652
\(109\) 1.60493 0.153724 0.0768621 0.997042i \(-0.475510\pi\)
0.0768621 + 0.997042i \(0.475510\pi\)
\(110\) −15.4970 −1.47758
\(111\) −1.22700 −0.116462
\(112\) −0.933127 −0.0881722
\(113\) −1.86353 −0.175306 −0.0876529 0.996151i \(-0.527937\pi\)
−0.0876529 + 0.996151i \(0.527937\pi\)
\(114\) 4.57606 0.428587
\(115\) −23.1888 −2.16237
\(116\) −18.9616 −1.76054
\(117\) −6.26473 −0.579174
\(118\) −18.4355 −1.69712
\(119\) −3.54577 −0.325040
\(120\) 6.99412 0.638473
\(121\) −4.20550 −0.382318
\(122\) −21.2817 −1.92676
\(123\) −6.75629 −0.609194
\(124\) 5.94158 0.533569
\(125\) −8.28818 −0.741317
\(126\) −8.06724 −0.718687
\(127\) −8.33178 −0.739326 −0.369663 0.929166i \(-0.620527\pi\)
−0.369663 + 0.929166i \(0.620527\pi\)
\(128\) 17.7083 1.56521
\(129\) 8.80703 0.775416
\(130\) 37.2452 3.26662
\(131\) −15.5784 −1.36109 −0.680546 0.732705i \(-0.738257\pi\)
−0.680546 + 0.732705i \(0.738257\pi\)
\(132\) −8.27976 −0.720660
\(133\) 7.13160 0.618388
\(134\) 1.42042 0.122706
\(135\) −2.61308 −0.224898
\(136\) 2.67658 0.229515
\(137\) −12.7444 −1.08882 −0.544412 0.838818i \(-0.683247\pi\)
−0.544412 + 0.838818i \(0.683247\pi\)
\(138\) −20.1902 −1.71870
\(139\) −5.36138 −0.454746 −0.227373 0.973808i \(-0.573014\pi\)
−0.227373 + 0.973808i \(0.573014\pi\)
\(140\) 29.4308 2.48736
\(141\) 7.43338 0.626004
\(142\) −28.3898 −2.38242
\(143\) −16.3298 −1.36557
\(144\) −0.263166 −0.0219305
\(145\) −15.5988 −1.29541
\(146\) 15.7598 1.30429
\(147\) −5.57246 −0.459609
\(148\) 3.89747 0.320370
\(149\) 21.8993 1.79406 0.897030 0.441971i \(-0.145720\pi\)
0.897030 + 0.441971i \(0.145720\pi\)
\(150\) 4.15947 0.339620
\(151\) −19.0277 −1.54845 −0.774227 0.632908i \(-0.781861\pi\)
−0.774227 + 0.632908i \(0.781861\pi\)
\(152\) −5.38340 −0.436651
\(153\) −1.00000 −0.0808452
\(154\) −21.0283 −1.69451
\(155\) 4.88783 0.392600
\(156\) 19.8994 1.59323
\(157\) −1.00000 −0.0798087
\(158\) 4.39420 0.349583
\(159\) 3.46416 0.274726
\(160\) 15.5528 1.22956
\(161\) −31.4656 −2.47984
\(162\) −2.27518 −0.178755
\(163\) −13.9254 −1.09072 −0.545361 0.838201i \(-0.683608\pi\)
−0.545361 + 0.838201i \(0.683608\pi\)
\(164\) 21.4609 1.67581
\(165\) −6.81133 −0.530261
\(166\) −39.8160 −3.09032
\(167\) 6.04651 0.467893 0.233947 0.972249i \(-0.424836\pi\)
0.233947 + 0.972249i \(0.424836\pi\)
\(168\) 9.49052 0.732210
\(169\) 26.2468 2.01898
\(170\) 5.94522 0.455978
\(171\) 2.01130 0.153808
\(172\) −27.9749 −2.13307
\(173\) 4.42199 0.336198 0.168099 0.985770i \(-0.446237\pi\)
0.168099 + 0.985770i \(0.446237\pi\)
\(174\) −13.5816 −1.02962
\(175\) 6.48237 0.490021
\(176\) −0.685977 −0.0517074
\(177\) −8.10288 −0.609050
\(178\) 0.0935015 0.00700823
\(179\) 12.7749 0.954837 0.477419 0.878676i \(-0.341573\pi\)
0.477419 + 0.878676i \(0.341573\pi\)
\(180\) 8.30026 0.618665
\(181\) −9.03612 −0.671650 −0.335825 0.941924i \(-0.609015\pi\)
−0.335825 + 0.941924i \(0.609015\pi\)
\(182\) 50.5391 3.74620
\(183\) −9.35388 −0.691459
\(184\) 23.7523 1.75104
\(185\) 3.20625 0.235728
\(186\) 4.25577 0.312048
\(187\) −2.60663 −0.190615
\(188\) −23.6116 −1.72205
\(189\) −3.54577 −0.257917
\(190\) −11.9576 −0.867497
\(191\) 16.9747 1.22825 0.614123 0.789211i \(-0.289510\pi\)
0.614123 + 0.789211i \(0.289510\pi\)
\(192\) 13.0153 0.939299
\(193\) 24.4329 1.75872 0.879358 0.476162i \(-0.157972\pi\)
0.879358 + 0.476162i \(0.157972\pi\)
\(194\) −28.1891 −2.02386
\(195\) 16.3702 1.17230
\(196\) 17.7005 1.26432
\(197\) −16.1379 −1.14978 −0.574888 0.818232i \(-0.694954\pi\)
−0.574888 + 0.818232i \(0.694954\pi\)
\(198\) −5.93053 −0.421465
\(199\) −21.3513 −1.51355 −0.756777 0.653673i \(-0.773227\pi\)
−0.756777 + 0.653673i \(0.773227\pi\)
\(200\) −4.89332 −0.346010
\(201\) 0.624312 0.0440356
\(202\) 26.2099 1.84412
\(203\) −21.1664 −1.48559
\(204\) 3.17643 0.222394
\(205\) 17.6547 1.23306
\(206\) 39.4494 2.74857
\(207\) −8.87413 −0.616795
\(208\) 1.64867 0.114314
\(209\) 5.24271 0.362646
\(210\) 21.0804 1.45468
\(211\) −21.0376 −1.44829 −0.724144 0.689649i \(-0.757765\pi\)
−0.724144 + 0.689649i \(0.757765\pi\)
\(212\) −11.0037 −0.755735
\(213\) −12.4781 −0.854984
\(214\) 17.0262 1.16389
\(215\) −23.0135 −1.56951
\(216\) 2.67658 0.182118
\(217\) 6.63243 0.450239
\(218\) −3.65149 −0.247310
\(219\) 6.92684 0.468073
\(220\) 21.6357 1.45868
\(221\) 6.26473 0.421411
\(222\) 2.79164 0.187363
\(223\) −10.4258 −0.698162 −0.349081 0.937093i \(-0.613506\pi\)
−0.349081 + 0.937093i \(0.613506\pi\)
\(224\) 21.1041 1.41007
\(225\) 1.82820 0.121880
\(226\) 4.23985 0.282031
\(227\) 14.8548 0.985947 0.492973 0.870044i \(-0.335910\pi\)
0.492973 + 0.870044i \(0.335910\pi\)
\(228\) −6.38875 −0.423105
\(229\) 4.09762 0.270778 0.135389 0.990792i \(-0.456772\pi\)
0.135389 + 0.990792i \(0.456772\pi\)
\(230\) 52.7587 3.47880
\(231\) −9.24249 −0.608111
\(232\) 15.9778 1.04899
\(233\) 25.5973 1.67694 0.838469 0.544949i \(-0.183451\pi\)
0.838469 + 0.544949i \(0.183451\pi\)
\(234\) 14.2534 0.931771
\(235\) −19.4240 −1.26709
\(236\) 25.7382 1.67541
\(237\) 1.93136 0.125456
\(238\) 8.06724 0.522922
\(239\) −3.45532 −0.223506 −0.111753 0.993736i \(-0.535647\pi\)
−0.111753 + 0.993736i \(0.535647\pi\)
\(240\) 0.687676 0.0443893
\(241\) 2.48706 0.160206 0.0801029 0.996787i \(-0.474475\pi\)
0.0801029 + 0.996787i \(0.474475\pi\)
\(242\) 9.56825 0.615070
\(243\) −1.00000 −0.0641500
\(244\) 29.7119 1.90211
\(245\) 14.5613 0.930287
\(246\) 15.3718 0.980067
\(247\) −12.6002 −0.801734
\(248\) −5.00660 −0.317919
\(249\) −17.5002 −1.10903
\(250\) 18.8571 1.19263
\(251\) −6.99590 −0.441577 −0.220789 0.975322i \(-0.570863\pi\)
−0.220789 + 0.975322i \(0.570863\pi\)
\(252\) 11.2629 0.709494
\(253\) −23.1315 −1.45427
\(254\) 18.9563 1.18942
\(255\) 2.61308 0.163638
\(256\) −14.2589 −0.891180
\(257\) −4.95624 −0.309162 −0.154581 0.987980i \(-0.549403\pi\)
−0.154581 + 0.987980i \(0.549403\pi\)
\(258\) −20.0375 −1.24748
\(259\) 4.35065 0.270336
\(260\) −51.9989 −3.22483
\(261\) −5.96949 −0.369502
\(262\) 35.4436 2.18971
\(263\) −6.67551 −0.411630 −0.205815 0.978591i \(-0.565984\pi\)
−0.205815 + 0.978591i \(0.565984\pi\)
\(264\) 6.97684 0.429395
\(265\) −9.05214 −0.556069
\(266\) −16.2256 −0.994858
\(267\) 0.0410964 0.00251506
\(268\) −1.98308 −0.121136
\(269\) −14.2545 −0.869110 −0.434555 0.900645i \(-0.643094\pi\)
−0.434555 + 0.900645i \(0.643094\pi\)
\(270\) 5.94522 0.361815
\(271\) −20.4057 −1.23956 −0.619780 0.784776i \(-0.712778\pi\)
−0.619780 + 0.784776i \(0.712778\pi\)
\(272\) 0.263166 0.0159568
\(273\) 22.2133 1.34441
\(274\) 28.9957 1.75169
\(275\) 4.76543 0.287366
\(276\) 28.1880 1.69672
\(277\) −27.0901 −1.62769 −0.813845 0.581083i \(-0.802629\pi\)
−0.813845 + 0.581083i \(0.802629\pi\)
\(278\) 12.1981 0.731592
\(279\) 1.87052 0.111985
\(280\) −24.7995 −1.48205
\(281\) −29.4109 −1.75451 −0.877255 0.480026i \(-0.840627\pi\)
−0.877255 + 0.480026i \(0.840627\pi\)
\(282\) −16.9123 −1.00711
\(283\) −31.9225 −1.89759 −0.948797 0.315886i \(-0.897698\pi\)
−0.948797 + 0.315886i \(0.897698\pi\)
\(284\) 39.6357 2.35195
\(285\) −5.25569 −0.311320
\(286\) 37.1532 2.19691
\(287\) 23.9562 1.41409
\(288\) 5.95191 0.350719
\(289\) 1.00000 0.0588235
\(290\) 35.4899 2.08404
\(291\) −12.3898 −0.726306
\(292\) −22.0026 −1.28761
\(293\) 23.7604 1.38810 0.694050 0.719927i \(-0.255825\pi\)
0.694050 + 0.719927i \(0.255825\pi\)
\(294\) 12.6783 0.739415
\(295\) 21.1735 1.23277
\(296\) −3.28416 −0.190888
\(297\) −2.60663 −0.151252
\(298\) −49.8247 −2.88627
\(299\) 55.5940 3.21508
\(300\) −5.80714 −0.335275
\(301\) −31.2277 −1.79993
\(302\) 43.2914 2.49114
\(303\) 11.5200 0.661804
\(304\) −0.529306 −0.0303578
\(305\) 24.4425 1.39957
\(306\) 2.27518 0.130063
\(307\) −0.229041 −0.0130721 −0.00653604 0.999979i \(-0.502080\pi\)
−0.00653604 + 0.999979i \(0.502080\pi\)
\(308\) 29.3581 1.67283
\(309\) 17.3391 0.986385
\(310\) −11.1207 −0.631612
\(311\) 26.6277 1.50992 0.754958 0.655773i \(-0.227657\pi\)
0.754958 + 0.655773i \(0.227657\pi\)
\(312\) −16.7680 −0.949303
\(313\) −3.03505 −0.171551 −0.0857755 0.996314i \(-0.527337\pi\)
−0.0857755 + 0.996314i \(0.527337\pi\)
\(314\) 2.27518 0.128396
\(315\) 9.26538 0.522045
\(316\) −6.13484 −0.345112
\(317\) 14.1657 0.795623 0.397811 0.917467i \(-0.369770\pi\)
0.397811 + 0.917467i \(0.369770\pi\)
\(318\) −7.88158 −0.441977
\(319\) −15.5602 −0.871205
\(320\) −34.0101 −1.90122
\(321\) 7.48347 0.417687
\(322\) 71.5898 3.98954
\(323\) −2.01130 −0.111912
\(324\) 3.17643 0.176468
\(325\) −11.4532 −0.635307
\(326\) 31.6828 1.75475
\(327\) −1.60493 −0.0887527
\(328\) −18.0837 −0.998508
\(329\) −26.3570 −1.45311
\(330\) 15.4970 0.853080
\(331\) 2.25886 0.124158 0.0620792 0.998071i \(-0.480227\pi\)
0.0620792 + 0.998071i \(0.480227\pi\)
\(332\) 55.5880 3.05079
\(333\) 1.22700 0.0672391
\(334\) −13.7569 −0.752743
\(335\) −1.63138 −0.0891317
\(336\) 0.933127 0.0509062
\(337\) −3.65934 −0.199337 −0.0996684 0.995021i \(-0.531778\pi\)
−0.0996684 + 0.995021i \(0.531778\pi\)
\(338\) −59.7161 −3.24813
\(339\) 1.86353 0.101213
\(340\) −8.30026 −0.450145
\(341\) 4.87575 0.264037
\(342\) −4.57606 −0.247445
\(343\) −5.06173 −0.273308
\(344\) 23.5727 1.27096
\(345\) 23.1888 1.24844
\(346\) −10.0608 −0.540873
\(347\) 3.15473 0.169355 0.0846774 0.996408i \(-0.473014\pi\)
0.0846774 + 0.996408i \(0.473014\pi\)
\(348\) 18.9616 1.01645
\(349\) −32.3893 −1.73376 −0.866879 0.498518i \(-0.833878\pi\)
−0.866879 + 0.498518i \(0.833878\pi\)
\(350\) −14.7485 −0.788342
\(351\) 6.26473 0.334386
\(352\) 15.5144 0.826920
\(353\) −3.49864 −0.186214 −0.0931069 0.995656i \(-0.529680\pi\)
−0.0931069 + 0.995656i \(0.529680\pi\)
\(354\) 18.4355 0.979835
\(355\) 32.6063 1.73056
\(356\) −0.130540 −0.00691859
\(357\) 3.54577 0.187662
\(358\) −29.0650 −1.53614
\(359\) −7.56706 −0.399374 −0.199687 0.979860i \(-0.563993\pi\)
−0.199687 + 0.979860i \(0.563993\pi\)
\(360\) −6.99412 −0.368622
\(361\) −14.9547 −0.787088
\(362\) 20.5588 1.08055
\(363\) 4.20550 0.220731
\(364\) −70.5588 −3.69828
\(365\) −18.1004 −0.947419
\(366\) 21.2817 1.11241
\(367\) 28.3209 1.47834 0.739169 0.673520i \(-0.235219\pi\)
0.739169 + 0.673520i \(0.235219\pi\)
\(368\) 2.33537 0.121740
\(369\) 6.75629 0.351718
\(370\) −7.29478 −0.379238
\(371\) −12.2831 −0.637708
\(372\) −5.94158 −0.308056
\(373\) 17.1973 0.890442 0.445221 0.895421i \(-0.353125\pi\)
0.445221 + 0.895421i \(0.353125\pi\)
\(374\) 5.93053 0.306661
\(375\) 8.28818 0.428000
\(376\) 19.8960 1.02606
\(377\) 37.3972 1.92605
\(378\) 8.06724 0.414934
\(379\) 27.4516 1.41010 0.705048 0.709160i \(-0.250925\pi\)
0.705048 + 0.709160i \(0.250925\pi\)
\(380\) 16.6943 0.856400
\(381\) 8.33178 0.426850
\(382\) −38.6204 −1.97599
\(383\) 6.60303 0.337399 0.168700 0.985668i \(-0.446043\pi\)
0.168700 + 0.985668i \(0.446043\pi\)
\(384\) −17.7083 −0.903673
\(385\) 24.1514 1.23087
\(386\) −55.5890 −2.82941
\(387\) −8.80703 −0.447687
\(388\) 39.3554 1.99797
\(389\) −28.2248 −1.43106 −0.715528 0.698584i \(-0.753814\pi\)
−0.715528 + 0.698584i \(0.753814\pi\)
\(390\) −37.2452 −1.88598
\(391\) 8.87413 0.448784
\(392\) −14.9151 −0.753327
\(393\) 15.5784 0.785827
\(394\) 36.7165 1.84975
\(395\) −5.04682 −0.253933
\(396\) 8.27976 0.416074
\(397\) −10.6310 −0.533554 −0.266777 0.963758i \(-0.585959\pi\)
−0.266777 + 0.963758i \(0.585959\pi\)
\(398\) 48.5780 2.43499
\(399\) −7.13160 −0.357026
\(400\) −0.481121 −0.0240560
\(401\) −11.9271 −0.595613 −0.297806 0.954626i \(-0.596255\pi\)
−0.297806 + 0.954626i \(0.596255\pi\)
\(402\) −1.42042 −0.0708441
\(403\) −11.7183 −0.583730
\(404\) −36.5923 −1.82053
\(405\) 2.61308 0.129845
\(406\) 48.1573 2.39001
\(407\) 3.19833 0.158535
\(408\) −2.67658 −0.132510
\(409\) −10.7613 −0.532110 −0.266055 0.963958i \(-0.585720\pi\)
−0.266055 + 0.963958i \(0.585720\pi\)
\(410\) −40.1677 −1.98374
\(411\) 12.7444 0.628633
\(412\) −55.0763 −2.71341
\(413\) 28.7309 1.41376
\(414\) 20.1902 0.992295
\(415\) 45.7294 2.24477
\(416\) −37.2871 −1.82815
\(417\) 5.36138 0.262548
\(418\) −11.9281 −0.583421
\(419\) 9.97199 0.487164 0.243582 0.969880i \(-0.421678\pi\)
0.243582 + 0.969880i \(0.421678\pi\)
\(420\) −29.4308 −1.43608
\(421\) −26.2315 −1.27844 −0.639221 0.769023i \(-0.720743\pi\)
−0.639221 + 0.769023i \(0.720743\pi\)
\(422\) 47.8642 2.32999
\(423\) −7.43338 −0.361424
\(424\) 9.27211 0.450293
\(425\) −1.82820 −0.0886807
\(426\) 28.3898 1.37549
\(427\) 33.1667 1.60505
\(428\) −23.7707 −1.14900
\(429\) 16.3298 0.788410
\(430\) 52.3598 2.52501
\(431\) −8.75436 −0.421683 −0.210841 0.977520i \(-0.567620\pi\)
−0.210841 + 0.977520i \(0.567620\pi\)
\(432\) 0.263166 0.0126616
\(433\) −15.8567 −0.762024 −0.381012 0.924570i \(-0.624424\pi\)
−0.381012 + 0.924570i \(0.624424\pi\)
\(434\) −15.0900 −0.724341
\(435\) 15.5988 0.747903
\(436\) 5.09793 0.244147
\(437\) −17.8485 −0.853811
\(438\) −15.7598 −0.753032
\(439\) 31.0956 1.48411 0.742056 0.670338i \(-0.233851\pi\)
0.742056 + 0.670338i \(0.233851\pi\)
\(440\) −18.2311 −0.869131
\(441\) 5.57246 0.265355
\(442\) −14.2534 −0.677963
\(443\) −20.4594 −0.972057 −0.486028 0.873943i \(-0.661555\pi\)
−0.486028 + 0.873943i \(0.661555\pi\)
\(444\) −3.89747 −0.184966
\(445\) −0.107388 −0.00509069
\(446\) 23.7205 1.12320
\(447\) −21.8993 −1.03580
\(448\) −46.1492 −2.18035
\(449\) 27.5789 1.30153 0.650764 0.759280i \(-0.274449\pi\)
0.650764 + 0.759280i \(0.274449\pi\)
\(450\) −4.15947 −0.196080
\(451\) 17.6111 0.829276
\(452\) −5.91935 −0.278423
\(453\) 19.0277 0.894000
\(454\) −33.7973 −1.58618
\(455\) −58.0451 −2.72119
\(456\) 5.38340 0.252101
\(457\) −4.17445 −0.195273 −0.0976363 0.995222i \(-0.531128\pi\)
−0.0976363 + 0.995222i \(0.531128\pi\)
\(458\) −9.32281 −0.435626
\(459\) 1.00000 0.0466760
\(460\) −73.6576 −3.43430
\(461\) 4.42469 0.206078 0.103039 0.994677i \(-0.467143\pi\)
0.103039 + 0.994677i \(0.467143\pi\)
\(462\) 21.0283 0.978325
\(463\) 5.35314 0.248781 0.124391 0.992233i \(-0.460302\pi\)
0.124391 + 0.992233i \(0.460302\pi\)
\(464\) 1.57097 0.0729304
\(465\) −4.88783 −0.226668
\(466\) −58.2385 −2.69785
\(467\) −5.66484 −0.262138 −0.131069 0.991373i \(-0.541841\pi\)
−0.131069 + 0.991373i \(0.541841\pi\)
\(468\) −19.8994 −0.919852
\(469\) −2.21366 −0.102217
\(470\) 44.1931 2.03848
\(471\) 1.00000 0.0460776
\(472\) −21.6880 −0.998271
\(473\) −22.9566 −1.05555
\(474\) −4.39420 −0.201832
\(475\) 3.67706 0.168715
\(476\) −11.2629 −0.516233
\(477\) −3.46416 −0.158613
\(478\) 7.86147 0.359575
\(479\) −15.6358 −0.714417 −0.357209 0.934025i \(-0.616271\pi\)
−0.357209 + 0.934025i \(0.616271\pi\)
\(480\) −15.5528 −0.709886
\(481\) −7.68681 −0.350489
\(482\) −5.65851 −0.257738
\(483\) 31.4656 1.43173
\(484\) −13.3585 −0.607203
\(485\) 32.3757 1.47010
\(486\) 2.27518 0.103204
\(487\) −4.13638 −0.187437 −0.0937187 0.995599i \(-0.529875\pi\)
−0.0937187 + 0.995599i \(0.529875\pi\)
\(488\) −25.0364 −1.13334
\(489\) 13.9254 0.629729
\(490\) −33.1295 −1.49664
\(491\) 10.3555 0.467338 0.233669 0.972316i \(-0.424927\pi\)
0.233669 + 0.972316i \(0.424927\pi\)
\(492\) −21.4609 −0.967530
\(493\) 5.96949 0.268852
\(494\) 28.6678 1.28982
\(495\) 6.81133 0.306146
\(496\) −0.492259 −0.0221031
\(497\) 44.2444 1.98463
\(498\) 39.8160 1.78420
\(499\) 4.63554 0.207515 0.103758 0.994603i \(-0.466913\pi\)
0.103758 + 0.994603i \(0.466913\pi\)
\(500\) −26.3268 −1.17737
\(501\) −6.04651 −0.270138
\(502\) 15.9169 0.710406
\(503\) −9.62014 −0.428941 −0.214470 0.976730i \(-0.568803\pi\)
−0.214470 + 0.976730i \(0.568803\pi\)
\(504\) −9.49052 −0.422741
\(505\) −30.1026 −1.33955
\(506\) 52.6283 2.33962
\(507\) −26.2468 −1.16566
\(508\) −26.4653 −1.17421
\(509\) 14.8763 0.659381 0.329691 0.944089i \(-0.393056\pi\)
0.329691 + 0.944089i \(0.393056\pi\)
\(510\) −5.94522 −0.263259
\(511\) −24.5610 −1.08651
\(512\) −2.97511 −0.131483
\(513\) −2.01130 −0.0888010
\(514\) 11.2763 0.497377
\(515\) −45.3084 −1.99653
\(516\) 27.9749 1.23153
\(517\) −19.3761 −0.852158
\(518\) −9.89850 −0.434915
\(519\) −4.42199 −0.194104
\(520\) 43.8162 1.92147
\(521\) −37.9700 −1.66350 −0.831748 0.555153i \(-0.812660\pi\)
−0.831748 + 0.555153i \(0.812660\pi\)
\(522\) 13.5816 0.594452
\(523\) −17.8279 −0.779562 −0.389781 0.920908i \(-0.627449\pi\)
−0.389781 + 0.920908i \(0.627449\pi\)
\(524\) −49.4837 −2.16170
\(525\) −6.48237 −0.282914
\(526\) 15.1880 0.662227
\(527\) −1.87052 −0.0814812
\(528\) 0.685977 0.0298533
\(529\) 55.7502 2.42392
\(530\) 20.5952 0.894599
\(531\) 8.10288 0.351635
\(532\) 22.6530 0.982132
\(533\) −42.3263 −1.83336
\(534\) −0.0935015 −0.00404621
\(535\) −19.5549 −0.845434
\(536\) 1.67102 0.0721770
\(537\) −12.7749 −0.551276
\(538\) 32.4314 1.39822
\(539\) 14.5253 0.625650
\(540\) −8.30026 −0.357187
\(541\) 30.5975 1.31549 0.657744 0.753242i \(-0.271511\pi\)
0.657744 + 0.753242i \(0.271511\pi\)
\(542\) 46.4266 1.99419
\(543\) 9.03612 0.387777
\(544\) −5.95191 −0.255186
\(545\) 4.19381 0.179643
\(546\) −50.5391 −2.16287
\(547\) 5.72836 0.244927 0.122464 0.992473i \(-0.460921\pi\)
0.122464 + 0.992473i \(0.460921\pi\)
\(548\) −40.4815 −1.72929
\(549\) 9.35388 0.399214
\(550\) −10.8422 −0.462313
\(551\) −12.0064 −0.511491
\(552\) −23.7523 −1.01097
\(553\) −6.84817 −0.291214
\(554\) 61.6349 2.61861
\(555\) −3.20625 −0.136098
\(556\) −17.0300 −0.722234
\(557\) −30.6480 −1.29860 −0.649299 0.760533i \(-0.724938\pi\)
−0.649299 + 0.760533i \(0.724938\pi\)
\(558\) −4.25577 −0.180161
\(559\) 55.1736 2.33360
\(560\) −2.43834 −0.103039
\(561\) 2.60663 0.110052
\(562\) 66.9151 2.82264
\(563\) −5.47566 −0.230771 −0.115386 0.993321i \(-0.536810\pi\)
−0.115386 + 0.993321i \(0.536810\pi\)
\(564\) 23.6116 0.994228
\(565\) −4.86955 −0.204863
\(566\) 72.6293 3.05284
\(567\) 3.54577 0.148908
\(568\) −33.3986 −1.40137
\(569\) −39.1643 −1.64185 −0.820926 0.571035i \(-0.806542\pi\)
−0.820926 + 0.571035i \(0.806542\pi\)
\(570\) 11.9576 0.500850
\(571\) −12.3200 −0.515576 −0.257788 0.966201i \(-0.582994\pi\)
−0.257788 + 0.966201i \(0.582994\pi\)
\(572\) −51.8704 −2.16881
\(573\) −16.9747 −0.709128
\(574\) −54.5046 −2.27498
\(575\) −16.2237 −0.676574
\(576\) −13.0153 −0.542304
\(577\) −35.0333 −1.45845 −0.729227 0.684272i \(-0.760120\pi\)
−0.729227 + 0.684272i \(0.760120\pi\)
\(578\) −2.27518 −0.0946349
\(579\) −24.4329 −1.01539
\(580\) −49.5483 −2.05738
\(581\) 62.0516 2.57433
\(582\) 28.1891 1.16848
\(583\) −9.02978 −0.373975
\(584\) 18.5402 0.767201
\(585\) −16.3702 −0.676826
\(586\) −54.0592 −2.23316
\(587\) −26.5707 −1.09669 −0.548344 0.836253i \(-0.684742\pi\)
−0.548344 + 0.836253i \(0.684742\pi\)
\(588\) −17.7005 −0.729957
\(589\) 3.76218 0.155018
\(590\) −48.1734 −1.98327
\(591\) 16.1379 0.663823
\(592\) −0.322905 −0.0132713
\(593\) −37.2391 −1.52923 −0.764613 0.644489i \(-0.777070\pi\)
−0.764613 + 0.644489i \(0.777070\pi\)
\(594\) 5.93053 0.243333
\(595\) −9.26538 −0.379844
\(596\) 69.5615 2.84935
\(597\) 21.3513 0.873850
\(598\) −126.486 −5.17240
\(599\) 22.9797 0.938927 0.469464 0.882952i \(-0.344447\pi\)
0.469464 + 0.882952i \(0.344447\pi\)
\(600\) 4.89332 0.199769
\(601\) −39.6585 −1.61771 −0.808853 0.588011i \(-0.799911\pi\)
−0.808853 + 0.588011i \(0.799911\pi\)
\(602\) 71.0485 2.89572
\(603\) −0.624312 −0.0254239
\(604\) −60.4401 −2.45927
\(605\) −10.9893 −0.446779
\(606\) −26.2099 −1.06471
\(607\) −18.6044 −0.755130 −0.377565 0.925983i \(-0.623238\pi\)
−0.377565 + 0.925983i \(0.623238\pi\)
\(608\) 11.9711 0.485491
\(609\) 21.1664 0.857706
\(610\) −55.6109 −2.25162
\(611\) 46.5681 1.88394
\(612\) −3.17643 −0.128399
\(613\) 38.5118 1.55548 0.777738 0.628588i \(-0.216367\pi\)
0.777738 + 0.628588i \(0.216367\pi\)
\(614\) 0.521109 0.0210302
\(615\) −17.6547 −0.711908
\(616\) −24.7382 −0.996732
\(617\) 11.7116 0.471493 0.235746 0.971815i \(-0.424247\pi\)
0.235746 + 0.971815i \(0.424247\pi\)
\(618\) −39.4494 −1.58689
\(619\) −4.34468 −0.174627 −0.0873137 0.996181i \(-0.527828\pi\)
−0.0873137 + 0.996181i \(0.527828\pi\)
\(620\) 15.5258 0.623532
\(621\) 8.87413 0.356107
\(622\) −60.5826 −2.42914
\(623\) −0.145718 −0.00583807
\(624\) −1.64867 −0.0659994
\(625\) −30.7987 −1.23195
\(626\) 6.90526 0.275990
\(627\) −5.24271 −0.209374
\(628\) −3.17643 −0.126753
\(629\) −1.22700 −0.0489237
\(630\) −21.0804 −0.839862
\(631\) 41.8931 1.66774 0.833869 0.551963i \(-0.186121\pi\)
0.833869 + 0.551963i \(0.186121\pi\)
\(632\) 5.16945 0.205630
\(633\) 21.0376 0.836169
\(634\) −32.2294 −1.27999
\(635\) −21.7716 −0.863981
\(636\) 11.0037 0.436324
\(637\) −34.9099 −1.38318
\(638\) 35.4023 1.40159
\(639\) 12.4781 0.493625
\(640\) 46.2732 1.82911
\(641\) −26.6015 −1.05069 −0.525347 0.850888i \(-0.676065\pi\)
−0.525347 + 0.850888i \(0.676065\pi\)
\(642\) −17.0262 −0.671971
\(643\) −37.2983 −1.47090 −0.735452 0.677577i \(-0.763030\pi\)
−0.735452 + 0.677577i \(0.763030\pi\)
\(644\) −99.9482 −3.93851
\(645\) 23.0135 0.906156
\(646\) 4.57606 0.180043
\(647\) −13.9677 −0.549127 −0.274563 0.961569i \(-0.588533\pi\)
−0.274563 + 0.961569i \(0.588533\pi\)
\(648\) −2.67658 −0.105146
\(649\) 21.1212 0.829079
\(650\) 26.0580 1.02208
\(651\) −6.63243 −0.259946
\(652\) −44.2331 −1.73230
\(653\) 9.15541 0.358279 0.179139 0.983824i \(-0.442669\pi\)
0.179139 + 0.983824i \(0.442669\pi\)
\(654\) 3.65149 0.142785
\(655\) −40.7077 −1.59058
\(656\) −1.77803 −0.0694204
\(657\) −6.92684 −0.270242
\(658\) 59.9669 2.33775
\(659\) −4.77018 −0.185820 −0.0929100 0.995675i \(-0.529617\pi\)
−0.0929100 + 0.995675i \(0.529617\pi\)
\(660\) −21.6357 −0.842168
\(661\) −19.7353 −0.767614 −0.383807 0.923413i \(-0.625387\pi\)
−0.383807 + 0.923413i \(0.625387\pi\)
\(662\) −5.13931 −0.199745
\(663\) −6.26473 −0.243302
\(664\) −46.8406 −1.81777
\(665\) 18.6355 0.722652
\(666\) −2.79164 −0.108174
\(667\) 52.9740 2.05116
\(668\) 19.2063 0.743114
\(669\) 10.4258 0.403084
\(670\) 3.71167 0.143394
\(671\) 24.3821 0.941259
\(672\) −21.1041 −0.814107
\(673\) 21.8824 0.843503 0.421752 0.906711i \(-0.361415\pi\)
0.421752 + 0.906711i \(0.361415\pi\)
\(674\) 8.32564 0.320692
\(675\) −1.82820 −0.0703674
\(676\) 83.3710 3.20658
\(677\) 31.3801 1.20604 0.603018 0.797727i \(-0.293965\pi\)
0.603018 + 0.797727i \(0.293965\pi\)
\(678\) −4.23985 −0.162830
\(679\) 43.9315 1.68594
\(680\) 6.99412 0.268212
\(681\) −14.8548 −0.569237
\(682\) −11.0932 −0.424780
\(683\) 17.0362 0.651873 0.325937 0.945392i \(-0.394320\pi\)
0.325937 + 0.945392i \(0.394320\pi\)
\(684\) 6.38875 0.244280
\(685\) −33.3021 −1.27241
\(686\) 11.5163 0.439695
\(687\) −4.09762 −0.156334
\(688\) 2.31771 0.0883621
\(689\) 21.7020 0.826782
\(690\) −52.7587 −2.00849
\(691\) −27.4752 −1.04520 −0.522602 0.852577i \(-0.675039\pi\)
−0.522602 + 0.852577i \(0.675039\pi\)
\(692\) 14.0461 0.533954
\(693\) 9.24249 0.351093
\(694\) −7.17757 −0.272457
\(695\) −14.0097 −0.531419
\(696\) −15.9778 −0.605637
\(697\) −6.75629 −0.255913
\(698\) 73.6913 2.78926
\(699\) −25.5973 −0.968181
\(700\) 20.5908 0.778258
\(701\) 8.64248 0.326422 0.163211 0.986591i \(-0.447815\pi\)
0.163211 + 0.986591i \(0.447815\pi\)
\(702\) −14.2534 −0.537958
\(703\) 2.46786 0.0930772
\(704\) −33.9260 −1.27864
\(705\) 19.4240 0.731552
\(706\) 7.96002 0.299579
\(707\) −40.8471 −1.53621
\(708\) −25.7382 −0.967301
\(709\) 14.5344 0.545851 0.272925 0.962035i \(-0.412009\pi\)
0.272925 + 0.962035i \(0.412009\pi\)
\(710\) −74.1850 −2.78411
\(711\) −1.93136 −0.0724318
\(712\) 0.109998 0.00412234
\(713\) −16.5993 −0.621647
\(714\) −8.06724 −0.301909
\(715\) −42.6711 −1.59581
\(716\) 40.5784 1.51649
\(717\) 3.45532 0.129041
\(718\) 17.2164 0.642510
\(719\) −22.8626 −0.852631 −0.426315 0.904575i \(-0.640189\pi\)
−0.426315 + 0.904575i \(0.640189\pi\)
\(720\) −0.687676 −0.0256282
\(721\) −61.4803 −2.28965
\(722\) 34.0245 1.26626
\(723\) −2.48706 −0.0924948
\(724\) −28.7026 −1.06672
\(725\) −10.9134 −0.405314
\(726\) −9.56825 −0.355111
\(727\) 17.2472 0.639665 0.319832 0.947474i \(-0.396373\pi\)
0.319832 + 0.947474i \(0.396373\pi\)
\(728\) 59.4555 2.20357
\(729\) 1.00000 0.0370370
\(730\) 41.1816 1.52420
\(731\) 8.80703 0.325740
\(732\) −29.7119 −1.09818
\(733\) −14.0019 −0.517172 −0.258586 0.965988i \(-0.583257\pi\)
−0.258586 + 0.965988i \(0.583257\pi\)
\(734\) −64.4350 −2.37834
\(735\) −14.5613 −0.537101
\(736\) −52.8180 −1.94690
\(737\) −1.62735 −0.0599441
\(738\) −15.3718 −0.565842
\(739\) 42.3491 1.55784 0.778918 0.627126i \(-0.215769\pi\)
0.778918 + 0.627126i \(0.215769\pi\)
\(740\) 10.1844 0.374387
\(741\) 12.6002 0.462881
\(742\) 27.9463 1.02594
\(743\) 46.3646 1.70095 0.850475 0.526015i \(-0.176314\pi\)
0.850475 + 0.526015i \(0.176314\pi\)
\(744\) 5.00660 0.183551
\(745\) 57.2246 2.09655
\(746\) −39.1269 −1.43254
\(747\) 17.5002 0.640298
\(748\) −8.27976 −0.302738
\(749\) −26.5347 −0.969555
\(750\) −18.8571 −0.688563
\(751\) 0.00194241 7.08797e−5 0 3.54399e−5 1.00000i \(-0.499989\pi\)
3.54399e−5 1.00000i \(0.499989\pi\)
\(752\) 1.95622 0.0713359
\(753\) 6.99590 0.254945
\(754\) −85.0852 −3.09862
\(755\) −49.7210 −1.80953
\(756\) −11.2629 −0.409627
\(757\) −42.3578 −1.53952 −0.769760 0.638333i \(-0.779624\pi\)
−0.769760 + 0.638333i \(0.779624\pi\)
\(758\) −62.4573 −2.26855
\(759\) 23.1315 0.839622
\(760\) −14.0673 −0.510273
\(761\) −38.6416 −1.40076 −0.700379 0.713772i \(-0.746985\pi\)
−0.700379 + 0.713772i \(0.746985\pi\)
\(762\) −18.9563 −0.686713
\(763\) 5.69070 0.206017
\(764\) 53.9188 1.95072
\(765\) −2.61308 −0.0944762
\(766\) −15.0231 −0.542805
\(767\) −50.7623 −1.83292
\(768\) 14.2589 0.514523
\(769\) 9.97414 0.359677 0.179838 0.983696i \(-0.442443\pi\)
0.179838 + 0.983696i \(0.442443\pi\)
\(770\) −54.9487 −1.98021
\(771\) 4.95624 0.178495
\(772\) 77.6092 2.79322
\(773\) 30.8573 1.10986 0.554930 0.831897i \(-0.312745\pi\)
0.554930 + 0.831897i \(0.312745\pi\)
\(774\) 20.0375 0.720235
\(775\) 3.41969 0.122839
\(776\) −33.1624 −1.19046
\(777\) −4.35065 −0.156079
\(778\) 64.2164 2.30227
\(779\) 13.5889 0.486874
\(780\) 51.9989 1.86186
\(781\) 32.5257 1.16386
\(782\) −20.1902 −0.722001
\(783\) 5.96949 0.213332
\(784\) −1.46648 −0.0523744
\(785\) −2.61308 −0.0932649
\(786\) −35.4436 −1.26423
\(787\) −25.5568 −0.911003 −0.455501 0.890235i \(-0.650540\pi\)
−0.455501 + 0.890235i \(0.650540\pi\)
\(788\) −51.2607 −1.82609
\(789\) 6.67551 0.237655
\(790\) 11.4824 0.408525
\(791\) −6.60763 −0.234940
\(792\) −6.97684 −0.247911
\(793\) −58.5995 −2.08093
\(794\) 24.1874 0.858378
\(795\) 9.05214 0.321046
\(796\) −67.8208 −2.40385
\(797\) −14.0522 −0.497753 −0.248876 0.968535i \(-0.580061\pi\)
−0.248876 + 0.968535i \(0.580061\pi\)
\(798\) 16.2256 0.574381
\(799\) 7.43338 0.262974
\(800\) 10.8813 0.384711
\(801\) −0.0410964 −0.00145207
\(802\) 27.1363 0.958218
\(803\) −18.0557 −0.637172
\(804\) 1.98308 0.0699379
\(805\) −82.2222 −2.89795
\(806\) 26.6612 0.939101
\(807\) 14.2545 0.501781
\(808\) 30.8341 1.08474
\(809\) 3.20618 0.112723 0.0563616 0.998410i \(-0.482050\pi\)
0.0563616 + 0.998410i \(0.482050\pi\)
\(810\) −5.94522 −0.208894
\(811\) −22.9380 −0.805463 −0.402732 0.915318i \(-0.631939\pi\)
−0.402732 + 0.915318i \(0.631939\pi\)
\(812\) −67.2335 −2.35943
\(813\) 20.4057 0.715660
\(814\) −7.27676 −0.255050
\(815\) −36.3882 −1.27462
\(816\) −0.263166 −0.00921267
\(817\) −17.7136 −0.619720
\(818\) 24.4838 0.856055
\(819\) −22.2133 −0.776194
\(820\) 56.0790 1.95836
\(821\) 16.1588 0.563944 0.281972 0.959423i \(-0.409011\pi\)
0.281972 + 0.959423i \(0.409011\pi\)
\(822\) −28.9957 −1.01134
\(823\) 29.9380 1.04357 0.521786 0.853076i \(-0.325266\pi\)
0.521786 + 0.853076i \(0.325266\pi\)
\(824\) 46.4094 1.61675
\(825\) −4.76543 −0.165911
\(826\) −65.3679 −2.27444
\(827\) 8.11019 0.282019 0.141010 0.990008i \(-0.454965\pi\)
0.141010 + 0.990008i \(0.454965\pi\)
\(828\) −28.1880 −0.979602
\(829\) −33.6952 −1.17028 −0.585141 0.810932i \(-0.698961\pi\)
−0.585141 + 0.810932i \(0.698961\pi\)
\(830\) −104.042 −3.61137
\(831\) 27.0901 0.939747
\(832\) 81.5373 2.82680
\(833\) −5.57246 −0.193074
\(834\) −12.1981 −0.422385
\(835\) 15.8000 0.546783
\(836\) 16.6531 0.575959
\(837\) −1.87052 −0.0646547
\(838\) −22.6880 −0.783745
\(839\) 50.6960 1.75022 0.875110 0.483924i \(-0.160789\pi\)
0.875110 + 0.483924i \(0.160789\pi\)
\(840\) 24.7995 0.855664
\(841\) 6.63478 0.228786
\(842\) 59.6812 2.05675
\(843\) 29.4109 1.01297
\(844\) −66.8243 −2.30019
\(845\) 68.5850 2.35940
\(846\) 16.9123 0.581455
\(847\) −14.9117 −0.512373
\(848\) 0.911652 0.0313062
\(849\) 31.9225 1.09558
\(850\) 4.15947 0.142669
\(851\) −10.8886 −0.373255
\(852\) −39.6357 −1.35790
\(853\) 5.26761 0.180360 0.0901798 0.995926i \(-0.471256\pi\)
0.0901798 + 0.995926i \(0.471256\pi\)
\(854\) −75.4600 −2.58219
\(855\) 5.25569 0.179741
\(856\) 20.0301 0.684615
\(857\) −16.9689 −0.579647 −0.289824 0.957080i \(-0.593597\pi\)
−0.289824 + 0.957080i \(0.593597\pi\)
\(858\) −37.1532 −1.26839
\(859\) −46.2794 −1.57903 −0.789516 0.613730i \(-0.789668\pi\)
−0.789516 + 0.613730i \(0.789668\pi\)
\(860\) −73.1007 −2.49271
\(861\) −23.9562 −0.816426
\(862\) 19.9177 0.678400
\(863\) 13.7140 0.466829 0.233414 0.972377i \(-0.425010\pi\)
0.233414 + 0.972377i \(0.425010\pi\)
\(864\) −5.95191 −0.202488
\(865\) 11.5550 0.392883
\(866\) 36.0768 1.22594
\(867\) −1.00000 −0.0339618
\(868\) 21.0674 0.715076
\(869\) −5.03435 −0.170779
\(870\) −35.4899 −1.20322
\(871\) 3.91114 0.132524
\(872\) −4.29571 −0.145471
\(873\) 12.3898 0.419333
\(874\) 40.6086 1.37361
\(875\) −29.3879 −0.993494
\(876\) 22.0026 0.743399
\(877\) 30.9732 1.04589 0.522946 0.852366i \(-0.324833\pi\)
0.522946 + 0.852366i \(0.324833\pi\)
\(878\) −70.7480 −2.38763
\(879\) −23.7604 −0.801419
\(880\) −1.79251 −0.0604256
\(881\) −43.5601 −1.46758 −0.733789 0.679377i \(-0.762250\pi\)
−0.733789 + 0.679377i \(0.762250\pi\)
\(882\) −12.6783 −0.426901
\(883\) 7.62998 0.256769 0.128385 0.991724i \(-0.459021\pi\)
0.128385 + 0.991724i \(0.459021\pi\)
\(884\) 19.8994 0.669291
\(885\) −21.1735 −0.711739
\(886\) 46.5488 1.56384
\(887\) 39.0212 1.31020 0.655102 0.755540i \(-0.272625\pi\)
0.655102 + 0.755540i \(0.272625\pi\)
\(888\) 3.28416 0.110209
\(889\) −29.5426 −0.990825
\(890\) 0.244327 0.00818986
\(891\) 2.60663 0.0873253
\(892\) −33.1167 −1.10883
\(893\) −14.9508 −0.500308
\(894\) 49.8247 1.66639
\(895\) 33.3817 1.11583
\(896\) 62.7895 2.09765
\(897\) −55.5940 −1.85623
\(898\) −62.7468 −2.09389
\(899\) −11.1661 −0.372409
\(900\) 5.80714 0.193571
\(901\) 3.46416 0.115408
\(902\) −40.0684 −1.33413
\(903\) 31.2277 1.03919
\(904\) 4.98787 0.165894
\(905\) −23.6121 −0.784894
\(906\) −43.2914 −1.43826
\(907\) 15.5332 0.515770 0.257885 0.966176i \(-0.416974\pi\)
0.257885 + 0.966176i \(0.416974\pi\)
\(908\) 47.1851 1.56589
\(909\) −11.5200 −0.382093
\(910\) 132.063 4.37784
\(911\) 17.6789 0.585729 0.292864 0.956154i \(-0.405392\pi\)
0.292864 + 0.956154i \(0.405392\pi\)
\(912\) 0.529306 0.0175271
\(913\) 45.6164 1.50968
\(914\) 9.49761 0.314153
\(915\) −24.4425 −0.808043
\(916\) 13.0158 0.430054
\(917\) −55.2374 −1.82410
\(918\) −2.27518 −0.0750920
\(919\) 14.4888 0.477943 0.238971 0.971027i \(-0.423190\pi\)
0.238971 + 0.971027i \(0.423190\pi\)
\(920\) 62.0667 2.04628
\(921\) 0.229041 0.00754716
\(922\) −10.0669 −0.331537
\(923\) −78.1718 −2.57306
\(924\) −29.3581 −0.965810
\(925\) 2.24320 0.0737559
\(926\) −12.1793 −0.400238
\(927\) −17.3391 −0.569490
\(928\) −35.5298 −1.16632
\(929\) −49.8482 −1.63547 −0.817734 0.575597i \(-0.804770\pi\)
−0.817734 + 0.575597i \(0.804770\pi\)
\(930\) 11.1207 0.364661
\(931\) 11.2079 0.367324
\(932\) 81.3081 2.66334
\(933\) −26.6277 −0.871751
\(934\) 12.8885 0.421725
\(935\) −6.81133 −0.222754
\(936\) 16.7680 0.548080
\(937\) 31.3338 1.02363 0.511815 0.859095i \(-0.328973\pi\)
0.511815 + 0.859095i \(0.328973\pi\)
\(938\) 5.03647 0.164447
\(939\) 3.03505 0.0990450
\(940\) −61.6991 −2.01240
\(941\) 18.4634 0.601888 0.300944 0.953642i \(-0.402698\pi\)
0.300944 + 0.953642i \(0.402698\pi\)
\(942\) −2.27518 −0.0741292
\(943\) −59.9562 −1.95244
\(944\) −2.13241 −0.0694039
\(945\) −9.26538 −0.301403
\(946\) 52.2304 1.69816
\(947\) −15.0986 −0.490637 −0.245319 0.969442i \(-0.578893\pi\)
−0.245319 + 0.969442i \(0.578893\pi\)
\(948\) 6.13484 0.199250
\(949\) 43.3948 1.40865
\(950\) −8.36595 −0.271427
\(951\) −14.1657 −0.459353
\(952\) 9.49052 0.307590
\(953\) 11.6863 0.378558 0.189279 0.981923i \(-0.439385\pi\)
0.189279 + 0.981923i \(0.439385\pi\)
\(954\) 7.88158 0.255176
\(955\) 44.3563 1.43533
\(956\) −10.9756 −0.354976
\(957\) 15.5602 0.502991
\(958\) 35.5742 1.14935
\(959\) −45.1885 −1.45921
\(960\) 34.0101 1.09767
\(961\) −27.5011 −0.887134
\(962\) 17.4889 0.563863
\(963\) −7.48347 −0.241152
\(964\) 7.89997 0.254441
\(965\) 63.8451 2.05525
\(966\) −71.5898 −2.30336
\(967\) −28.3352 −0.911200 −0.455600 0.890185i \(-0.650575\pi\)
−0.455600 + 0.890185i \(0.650575\pi\)
\(968\) 11.2563 0.361793
\(969\) 2.01130 0.0646122
\(970\) −73.6604 −2.36509
\(971\) 55.6378 1.78550 0.892750 0.450552i \(-0.148773\pi\)
0.892750 + 0.450552i \(0.148773\pi\)
\(972\) −3.17643 −0.101884
\(973\) −19.0102 −0.609439
\(974\) 9.41100 0.301548
\(975\) 11.4532 0.366795
\(976\) −2.46163 −0.0787947
\(977\) −5.94578 −0.190222 −0.0951111 0.995467i \(-0.530321\pi\)
−0.0951111 + 0.995467i \(0.530321\pi\)
\(978\) −31.6828 −1.01310
\(979\) −0.107123 −0.00342366
\(980\) 46.2529 1.47749
\(981\) 1.60493 0.0512414
\(982\) −23.5606 −0.751850
\(983\) 10.1332 0.323199 0.161599 0.986856i \(-0.448335\pi\)
0.161599 + 0.986856i \(0.448335\pi\)
\(984\) 18.0837 0.576489
\(985\) −42.1696 −1.34363
\(986\) −13.5816 −0.432527
\(987\) 26.3570 0.838954
\(988\) −40.0237 −1.27332
\(989\) 78.1548 2.48518
\(990\) −15.4970 −0.492526
\(991\) 20.5491 0.652763 0.326382 0.945238i \(-0.394171\pi\)
0.326382 + 0.945238i \(0.394171\pi\)
\(992\) 11.1332 0.353479
\(993\) −2.25886 −0.0716829
\(994\) −100.664 −3.19286
\(995\) −55.7927 −1.76875
\(996\) −55.5880 −1.76137
\(997\) 23.4582 0.742929 0.371465 0.928447i \(-0.378856\pi\)
0.371465 + 0.928447i \(0.378856\pi\)
\(998\) −10.5467 −0.333849
\(999\) −1.22700 −0.0388205
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.1.7 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8007.2.a.f.1.7 48 1.1 even 1 trivial