Properties

Label 8007.2.a.f.1.37
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 1.37
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.67933 q^{2} -1.00000 q^{3} +0.820135 q^{4} +3.59386 q^{5} -1.67933 q^{6} +1.09506 q^{7} -1.98138 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.67933 q^{2} -1.00000 q^{3} +0.820135 q^{4} +3.59386 q^{5} -1.67933 q^{6} +1.09506 q^{7} -1.98138 q^{8} +1.00000 q^{9} +6.03526 q^{10} -1.52969 q^{11} -0.820135 q^{12} -0.0461842 q^{13} +1.83896 q^{14} -3.59386 q^{15} -4.96765 q^{16} -1.00000 q^{17} +1.67933 q^{18} -1.91613 q^{19} +2.94745 q^{20} -1.09506 q^{21} -2.56885 q^{22} -5.70497 q^{23} +1.98138 q^{24} +7.91581 q^{25} -0.0775583 q^{26} -1.00000 q^{27} +0.898094 q^{28} -8.96107 q^{29} -6.03526 q^{30} +1.93639 q^{31} -4.37954 q^{32} +1.52969 q^{33} -1.67933 q^{34} +3.93548 q^{35} +0.820135 q^{36} -6.02148 q^{37} -3.21781 q^{38} +0.0461842 q^{39} -7.12079 q^{40} -4.24287 q^{41} -1.83896 q^{42} -0.305192 q^{43} -1.25455 q^{44} +3.59386 q^{45} -9.58051 q^{46} +5.72249 q^{47} +4.96765 q^{48} -5.80085 q^{49} +13.2932 q^{50} +1.00000 q^{51} -0.0378772 q^{52} +0.193461 q^{53} -1.67933 q^{54} -5.49749 q^{55} -2.16972 q^{56} +1.91613 q^{57} -15.0486 q^{58} -2.32265 q^{59} -2.94745 q^{60} -14.8783 q^{61} +3.25183 q^{62} +1.09506 q^{63} +2.58062 q^{64} -0.165979 q^{65} +2.56885 q^{66} -4.82522 q^{67} -0.820135 q^{68} +5.70497 q^{69} +6.60895 q^{70} -8.61413 q^{71} -1.98138 q^{72} +14.1239 q^{73} -10.1120 q^{74} -7.91581 q^{75} -1.57149 q^{76} -1.67510 q^{77} +0.0775583 q^{78} +4.00757 q^{79} -17.8530 q^{80} +1.00000 q^{81} -7.12516 q^{82} -3.07445 q^{83} -0.898094 q^{84} -3.59386 q^{85} -0.512517 q^{86} +8.96107 q^{87} +3.03090 q^{88} -2.17593 q^{89} +6.03526 q^{90} -0.0505743 q^{91} -4.67885 q^{92} -1.93639 q^{93} +9.60993 q^{94} -6.88631 q^{95} +4.37954 q^{96} -15.4254 q^{97} -9.74152 q^{98} -1.52969 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} + O(q^{10}) \) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} - 20q^{10} + 5q^{11} - 45q^{12} - 8q^{13} + 4q^{14} - q^{15} + 39q^{16} - 48q^{17} - q^{18} - 6q^{19} + 6q^{20} + 13q^{21} - 35q^{22} - 8q^{23} + 6q^{24} + 13q^{25} + 17q^{26} - 48q^{27} - 38q^{28} + q^{29} + 20q^{30} - 21q^{31} - 3q^{32} - 5q^{33} + q^{34} + 19q^{35} + 45q^{36} - 58q^{37} - 14q^{38} + 8q^{39} - 54q^{40} - 3q^{41} - 4q^{42} - 33q^{43} + 2q^{44} + q^{45} - 26q^{46} + 9q^{47} - 39q^{48} + 11q^{49} + 4q^{50} + 48q^{51} - 31q^{52} - 33q^{53} + q^{54} - 21q^{55} + 6q^{57} - 55q^{58} + 77q^{59} - 6q^{60} - 29q^{61} - 46q^{62} - 13q^{63} + 24q^{64} - 49q^{65} + 35q^{66} - 44q^{67} - 45q^{68} + 8q^{69} + 4q^{70} + 22q^{71} - 6q^{72} - 63q^{73} - 16q^{74} - 13q^{75} - 46q^{76} - 30q^{77} - 17q^{78} - 46q^{79} - 14q^{80} + 48q^{81} - 75q^{82} + 11q^{83} + 38q^{84} - q^{85} + 8q^{86} - q^{87} - 116q^{88} + 10q^{89} - 20q^{90} - 67q^{91} - 64q^{92} + 21q^{93} - 16q^{94} - 8q^{95} + 3q^{96} - 96q^{97} - 46q^{98} + 5q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.67933 1.18746 0.593731 0.804663i \(-0.297654\pi\)
0.593731 + 0.804663i \(0.297654\pi\)
\(3\) −1.00000 −0.577350
\(4\) 0.820135 0.410067
\(5\) 3.59386 1.60722 0.803611 0.595155i \(-0.202909\pi\)
0.803611 + 0.595155i \(0.202909\pi\)
\(6\) −1.67933 −0.685582
\(7\) 1.09506 0.413892 0.206946 0.978352i \(-0.433647\pi\)
0.206946 + 0.978352i \(0.433647\pi\)
\(8\) −1.98138 −0.700523
\(9\) 1.00000 0.333333
\(10\) 6.03526 1.90852
\(11\) −1.52969 −0.461220 −0.230610 0.973046i \(-0.574072\pi\)
−0.230610 + 0.973046i \(0.574072\pi\)
\(12\) −0.820135 −0.236752
\(13\) −0.0461842 −0.0128092 −0.00640459 0.999979i \(-0.502039\pi\)
−0.00640459 + 0.999979i \(0.502039\pi\)
\(14\) 1.83896 0.491482
\(15\) −3.59386 −0.927930
\(16\) −4.96765 −1.24191
\(17\) −1.00000 −0.242536
\(18\) 1.67933 0.395821
\(19\) −1.91613 −0.439591 −0.219796 0.975546i \(-0.570539\pi\)
−0.219796 + 0.975546i \(0.570539\pi\)
\(20\) 2.94745 0.659069
\(21\) −1.09506 −0.238961
\(22\) −2.56885 −0.547681
\(23\) −5.70497 −1.18957 −0.594785 0.803885i \(-0.702763\pi\)
−0.594785 + 0.803885i \(0.702763\pi\)
\(24\) 1.98138 0.404447
\(25\) 7.91581 1.58316
\(26\) −0.0775583 −0.0152104
\(27\) −1.00000 −0.192450
\(28\) 0.898094 0.169724
\(29\) −8.96107 −1.66403 −0.832014 0.554754i \(-0.812812\pi\)
−0.832014 + 0.554754i \(0.812812\pi\)
\(30\) −6.03526 −1.10188
\(31\) 1.93639 0.347786 0.173893 0.984765i \(-0.444365\pi\)
0.173893 + 0.984765i \(0.444365\pi\)
\(32\) −4.37954 −0.774201
\(33\) 1.52969 0.266285
\(34\) −1.67933 −0.288002
\(35\) 3.93548 0.665217
\(36\) 0.820135 0.136689
\(37\) −6.02148 −0.989925 −0.494962 0.868914i \(-0.664818\pi\)
−0.494962 + 0.868914i \(0.664818\pi\)
\(38\) −3.21781 −0.521998
\(39\) 0.0461842 0.00739539
\(40\) −7.12079 −1.12590
\(41\) −4.24287 −0.662625 −0.331312 0.943521i \(-0.607491\pi\)
−0.331312 + 0.943521i \(0.607491\pi\)
\(42\) −1.83896 −0.283757
\(43\) −0.305192 −0.0465414 −0.0232707 0.999729i \(-0.507408\pi\)
−0.0232707 + 0.999729i \(0.507408\pi\)
\(44\) −1.25455 −0.189131
\(45\) 3.59386 0.535741
\(46\) −9.58051 −1.41257
\(47\) 5.72249 0.834712 0.417356 0.908743i \(-0.362957\pi\)
0.417356 + 0.908743i \(0.362957\pi\)
\(48\) 4.96765 0.717018
\(49\) −5.80085 −0.828693
\(50\) 13.2932 1.87995
\(51\) 1.00000 0.140028
\(52\) −0.0378772 −0.00525263
\(53\) 0.193461 0.0265740 0.0132870 0.999912i \(-0.495770\pi\)
0.0132870 + 0.999912i \(0.495770\pi\)
\(54\) −1.67933 −0.228527
\(55\) −5.49749 −0.741282
\(56\) −2.16972 −0.289941
\(57\) 1.91613 0.253798
\(58\) −15.0486 −1.97597
\(59\) −2.32265 −0.302383 −0.151191 0.988505i \(-0.548311\pi\)
−0.151191 + 0.988505i \(0.548311\pi\)
\(60\) −2.94745 −0.380514
\(61\) −14.8783 −1.90497 −0.952485 0.304587i \(-0.901482\pi\)
−0.952485 + 0.304587i \(0.901482\pi\)
\(62\) 3.25183 0.412983
\(63\) 1.09506 0.137964
\(64\) 2.58062 0.322577
\(65\) −0.165979 −0.0205872
\(66\) 2.56885 0.316204
\(67\) −4.82522 −0.589495 −0.294747 0.955575i \(-0.595236\pi\)
−0.294747 + 0.955575i \(0.595236\pi\)
\(68\) −0.820135 −0.0994559
\(69\) 5.70497 0.686798
\(70\) 6.60895 0.789920
\(71\) −8.61413 −1.02231 −0.511155 0.859489i \(-0.670782\pi\)
−0.511155 + 0.859489i \(0.670782\pi\)
\(72\) −1.98138 −0.233508
\(73\) 14.1239 1.65307 0.826537 0.562883i \(-0.190308\pi\)
0.826537 + 0.562883i \(0.190308\pi\)
\(74\) −10.1120 −1.17550
\(75\) −7.91581 −0.914039
\(76\) −1.57149 −0.180262
\(77\) −1.67510 −0.190895
\(78\) 0.0775583 0.00878174
\(79\) 4.00757 0.450887 0.225443 0.974256i \(-0.427617\pi\)
0.225443 + 0.974256i \(0.427617\pi\)
\(80\) −17.8530 −1.99603
\(81\) 1.00000 0.111111
\(82\) −7.12516 −0.786842
\(83\) −3.07445 −0.337465 −0.168732 0.985662i \(-0.553967\pi\)
−0.168732 + 0.985662i \(0.553967\pi\)
\(84\) −0.898094 −0.0979900
\(85\) −3.59386 −0.389809
\(86\) −0.512517 −0.0552662
\(87\) 8.96107 0.960727
\(88\) 3.03090 0.323095
\(89\) −2.17593 −0.230648 −0.115324 0.993328i \(-0.536791\pi\)
−0.115324 + 0.993328i \(0.536791\pi\)
\(90\) 6.03526 0.636172
\(91\) −0.0505743 −0.00530162
\(92\) −4.67885 −0.487803
\(93\) −1.93639 −0.200794
\(94\) 9.60993 0.991189
\(95\) −6.88631 −0.706521
\(96\) 4.37954 0.446985
\(97\) −15.4254 −1.56621 −0.783105 0.621889i \(-0.786365\pi\)
−0.783105 + 0.621889i \(0.786365\pi\)
\(98\) −9.74152 −0.984042
\(99\) −1.52969 −0.153740
\(100\) 6.49203 0.649203
\(101\) 11.1376 1.10823 0.554116 0.832440i \(-0.313057\pi\)
0.554116 + 0.832440i \(0.313057\pi\)
\(102\) 1.67933 0.166278
\(103\) 4.16853 0.410737 0.205369 0.978685i \(-0.434161\pi\)
0.205369 + 0.978685i \(0.434161\pi\)
\(104\) 0.0915083 0.00897313
\(105\) −3.93548 −0.384063
\(106\) 0.324885 0.0315556
\(107\) 9.95303 0.962196 0.481098 0.876667i \(-0.340238\pi\)
0.481098 + 0.876667i \(0.340238\pi\)
\(108\) −0.820135 −0.0789175
\(109\) −6.25723 −0.599334 −0.299667 0.954044i \(-0.596876\pi\)
−0.299667 + 0.954044i \(0.596876\pi\)
\(110\) −9.23208 −0.880245
\(111\) 6.02148 0.571533
\(112\) −5.43986 −0.514018
\(113\) 3.19648 0.300700 0.150350 0.988633i \(-0.451960\pi\)
0.150350 + 0.988633i \(0.451960\pi\)
\(114\) 3.21781 0.301376
\(115\) −20.5029 −1.91190
\(116\) −7.34928 −0.682364
\(117\) −0.0461842 −0.00426973
\(118\) −3.90048 −0.359068
\(119\) −1.09506 −0.100384
\(120\) 7.12079 0.650036
\(121\) −8.66004 −0.787277
\(122\) −24.9855 −2.26208
\(123\) 4.24287 0.382567
\(124\) 1.58810 0.142616
\(125\) 10.4790 0.937270
\(126\) 1.83896 0.163827
\(127\) −6.53383 −0.579784 −0.289892 0.957059i \(-0.593619\pi\)
−0.289892 + 0.957059i \(0.593619\pi\)
\(128\) 13.0928 1.15725
\(129\) 0.305192 0.0268707
\(130\) −0.278733 −0.0244465
\(131\) 6.42075 0.560983 0.280492 0.959856i \(-0.409502\pi\)
0.280492 + 0.959856i \(0.409502\pi\)
\(132\) 1.25455 0.109195
\(133\) −2.09828 −0.181944
\(134\) −8.10312 −0.700003
\(135\) −3.59386 −0.309310
\(136\) 1.98138 0.169902
\(137\) 8.79125 0.751087 0.375543 0.926805i \(-0.377456\pi\)
0.375543 + 0.926805i \(0.377456\pi\)
\(138\) 9.58051 0.815547
\(139\) −0.593136 −0.0503091 −0.0251546 0.999684i \(-0.508008\pi\)
−0.0251546 + 0.999684i \(0.508008\pi\)
\(140\) 3.22762 0.272784
\(141\) −5.72249 −0.481921
\(142\) −14.4659 −1.21395
\(143\) 0.0706476 0.00590785
\(144\) −4.96765 −0.413971
\(145\) −32.2048 −2.67446
\(146\) 23.7186 1.96296
\(147\) 5.80085 0.478446
\(148\) −4.93842 −0.405936
\(149\) 9.44340 0.773634 0.386817 0.922157i \(-0.373575\pi\)
0.386817 + 0.922157i \(0.373575\pi\)
\(150\) −13.2932 −1.08539
\(151\) 15.8001 1.28580 0.642899 0.765951i \(-0.277732\pi\)
0.642899 + 0.765951i \(0.277732\pi\)
\(152\) 3.79659 0.307944
\(153\) −1.00000 −0.0808452
\(154\) −2.81304 −0.226681
\(155\) 6.95911 0.558969
\(156\) 0.0378772 0.00303261
\(157\) −1.00000 −0.0798087
\(158\) 6.73001 0.535411
\(159\) −0.193461 −0.0153425
\(160\) −15.7395 −1.24431
\(161\) −6.24727 −0.492354
\(162\) 1.67933 0.131940
\(163\) 8.56463 0.670834 0.335417 0.942070i \(-0.391123\pi\)
0.335417 + 0.942070i \(0.391123\pi\)
\(164\) −3.47972 −0.271721
\(165\) 5.49749 0.427979
\(166\) −5.16300 −0.400727
\(167\) −12.1584 −0.940844 −0.470422 0.882442i \(-0.655898\pi\)
−0.470422 + 0.882442i \(0.655898\pi\)
\(168\) 2.16972 0.167398
\(169\) −12.9979 −0.999836
\(170\) −6.03526 −0.462883
\(171\) −1.91613 −0.146530
\(172\) −0.250299 −0.0190851
\(173\) −13.0161 −0.989598 −0.494799 0.869007i \(-0.664758\pi\)
−0.494799 + 0.869007i \(0.664758\pi\)
\(174\) 15.0486 1.14083
\(175\) 8.66826 0.655259
\(176\) 7.59897 0.572794
\(177\) 2.32265 0.174581
\(178\) −3.65409 −0.273886
\(179\) 5.06732 0.378749 0.189375 0.981905i \(-0.439354\pi\)
0.189375 + 0.981905i \(0.439354\pi\)
\(180\) 2.94745 0.219690
\(181\) −5.21426 −0.387573 −0.193786 0.981044i \(-0.562077\pi\)
−0.193786 + 0.981044i \(0.562077\pi\)
\(182\) −0.0849307 −0.00629548
\(183\) 14.8783 1.09983
\(184\) 11.3037 0.833321
\(185\) −21.6403 −1.59103
\(186\) −3.25183 −0.238436
\(187\) 1.52969 0.111862
\(188\) 4.69322 0.342288
\(189\) −1.09506 −0.0796536
\(190\) −11.5644 −0.838967
\(191\) 5.91599 0.428066 0.214033 0.976826i \(-0.431340\pi\)
0.214033 + 0.976826i \(0.431340\pi\)
\(192\) −2.58062 −0.186240
\(193\) 22.8297 1.64332 0.821660 0.569978i \(-0.193048\pi\)
0.821660 + 0.569978i \(0.193048\pi\)
\(194\) −25.9042 −1.85982
\(195\) 0.165979 0.0118860
\(196\) −4.75748 −0.339820
\(197\) −0.855946 −0.0609836 −0.0304918 0.999535i \(-0.509707\pi\)
−0.0304918 + 0.999535i \(0.509707\pi\)
\(198\) −2.56885 −0.182560
\(199\) 19.4670 1.37998 0.689988 0.723820i \(-0.257616\pi\)
0.689988 + 0.723820i \(0.257616\pi\)
\(200\) −15.6842 −1.10904
\(201\) 4.82522 0.340345
\(202\) 18.7036 1.31598
\(203\) −9.81288 −0.688729
\(204\) 0.820135 0.0574209
\(205\) −15.2483 −1.06499
\(206\) 7.00031 0.487735
\(207\) −5.70497 −0.396523
\(208\) 0.229427 0.0159079
\(209\) 2.93110 0.202748
\(210\) −6.60895 −0.456061
\(211\) −9.18507 −0.632327 −0.316163 0.948705i \(-0.602395\pi\)
−0.316163 + 0.948705i \(0.602395\pi\)
\(212\) 0.158664 0.0108971
\(213\) 8.61413 0.590231
\(214\) 16.7144 1.14257
\(215\) −1.09682 −0.0748023
\(216\) 1.98138 0.134816
\(217\) 2.12046 0.143946
\(218\) −10.5079 −0.711687
\(219\) −14.1239 −0.954402
\(220\) −4.50869 −0.303976
\(221\) 0.0461842 0.00310668
\(222\) 10.1120 0.678674
\(223\) −15.0124 −1.00530 −0.502652 0.864489i \(-0.667642\pi\)
−0.502652 + 0.864489i \(0.667642\pi\)
\(224\) −4.79585 −0.320436
\(225\) 7.91581 0.527721
\(226\) 5.36794 0.357070
\(227\) 19.0896 1.26702 0.633509 0.773735i \(-0.281614\pi\)
0.633509 + 0.773735i \(0.281614\pi\)
\(228\) 1.57149 0.104074
\(229\) −14.5725 −0.962978 −0.481489 0.876452i \(-0.659904\pi\)
−0.481489 + 0.876452i \(0.659904\pi\)
\(230\) −34.4310 −2.27031
\(231\) 1.67510 0.110213
\(232\) 17.7553 1.16569
\(233\) −9.19047 −0.602087 −0.301044 0.953610i \(-0.597335\pi\)
−0.301044 + 0.953610i \(0.597335\pi\)
\(234\) −0.0775583 −0.00507014
\(235\) 20.5658 1.34157
\(236\) −1.90488 −0.123997
\(237\) −4.00757 −0.260320
\(238\) −1.83896 −0.119202
\(239\) −29.9619 −1.93808 −0.969038 0.246911i \(-0.920584\pi\)
−0.969038 + 0.246911i \(0.920584\pi\)
\(240\) 17.8530 1.15241
\(241\) −0.260683 −0.0167921 −0.00839604 0.999965i \(-0.502673\pi\)
−0.00839604 + 0.999965i \(0.502673\pi\)
\(242\) −14.5430 −0.934861
\(243\) −1.00000 −0.0641500
\(244\) −12.2022 −0.781166
\(245\) −20.8474 −1.33189
\(246\) 7.12516 0.454284
\(247\) 0.0884951 0.00563081
\(248\) −3.83672 −0.243632
\(249\) 3.07445 0.194835
\(250\) 17.5976 1.11297
\(251\) 28.8017 1.81795 0.908974 0.416853i \(-0.136867\pi\)
0.908974 + 0.416853i \(0.136867\pi\)
\(252\) 0.898094 0.0565746
\(253\) 8.72685 0.548653
\(254\) −10.9724 −0.688472
\(255\) 3.59386 0.225056
\(256\) 16.8258 1.05161
\(257\) −13.0022 −0.811057 −0.405529 0.914082i \(-0.632913\pi\)
−0.405529 + 0.914082i \(0.632913\pi\)
\(258\) 0.512517 0.0319079
\(259\) −6.59386 −0.409722
\(260\) −0.136125 −0.00844214
\(261\) −8.96107 −0.554676
\(262\) 10.7825 0.666147
\(263\) 11.3986 0.702866 0.351433 0.936213i \(-0.385695\pi\)
0.351433 + 0.936213i \(0.385695\pi\)
\(264\) −3.03090 −0.186539
\(265\) 0.695273 0.0427103
\(266\) −3.52369 −0.216051
\(267\) 2.17593 0.133165
\(268\) −3.95733 −0.241733
\(269\) −10.6849 −0.651473 −0.325736 0.945461i \(-0.605612\pi\)
−0.325736 + 0.945461i \(0.605612\pi\)
\(270\) −6.03526 −0.367294
\(271\) −10.3987 −0.631677 −0.315839 0.948813i \(-0.602286\pi\)
−0.315839 + 0.948813i \(0.602286\pi\)
\(272\) 4.96765 0.301208
\(273\) 0.0505743 0.00306089
\(274\) 14.7634 0.891888
\(275\) −12.1087 −0.730185
\(276\) 4.67885 0.281633
\(277\) −4.41176 −0.265077 −0.132538 0.991178i \(-0.542313\pi\)
−0.132538 + 0.991178i \(0.542313\pi\)
\(278\) −0.996069 −0.0597402
\(279\) 1.93639 0.115929
\(280\) −7.79767 −0.466000
\(281\) −2.71894 −0.162198 −0.0810992 0.996706i \(-0.525843\pi\)
−0.0810992 + 0.996706i \(0.525843\pi\)
\(282\) −9.60993 −0.572263
\(283\) −9.80213 −0.582676 −0.291338 0.956620i \(-0.594100\pi\)
−0.291338 + 0.956620i \(0.594100\pi\)
\(284\) −7.06475 −0.419216
\(285\) 6.88631 0.407910
\(286\) 0.118640 0.00701535
\(287\) −4.64618 −0.274255
\(288\) −4.37954 −0.258067
\(289\) 1.00000 0.0588235
\(290\) −54.0823 −3.17582
\(291\) 15.4254 0.904252
\(292\) 11.5835 0.677871
\(293\) 18.5396 1.08309 0.541547 0.840670i \(-0.317839\pi\)
0.541547 + 0.840670i \(0.317839\pi\)
\(294\) 9.74152 0.568137
\(295\) −8.34726 −0.485996
\(296\) 11.9308 0.693465
\(297\) 1.52969 0.0887617
\(298\) 15.8585 0.918661
\(299\) 0.263479 0.0152374
\(300\) −6.49203 −0.374817
\(301\) −0.334203 −0.0192631
\(302\) 26.5336 1.52684
\(303\) −11.1376 −0.639837
\(304\) 9.51868 0.545934
\(305\) −53.4704 −3.06171
\(306\) −1.67933 −0.0960007
\(307\) 12.4781 0.712161 0.356080 0.934455i \(-0.384113\pi\)
0.356080 + 0.934455i \(0.384113\pi\)
\(308\) −1.37381 −0.0782799
\(309\) −4.16853 −0.237139
\(310\) 11.6866 0.663755
\(311\) −5.40547 −0.306516 −0.153258 0.988186i \(-0.548977\pi\)
−0.153258 + 0.988186i \(0.548977\pi\)
\(312\) −0.0915083 −0.00518064
\(313\) 22.9439 1.29687 0.648433 0.761272i \(-0.275425\pi\)
0.648433 + 0.761272i \(0.275425\pi\)
\(314\) −1.67933 −0.0947698
\(315\) 3.93548 0.221739
\(316\) 3.28674 0.184894
\(317\) 32.7680 1.84043 0.920217 0.391410i \(-0.128012\pi\)
0.920217 + 0.391410i \(0.128012\pi\)
\(318\) −0.324885 −0.0182186
\(319\) 13.7077 0.767483
\(320\) 9.27437 0.518453
\(321\) −9.95303 −0.555524
\(322\) −10.4912 −0.584652
\(323\) 1.91613 0.106617
\(324\) 0.820135 0.0455630
\(325\) −0.365585 −0.0202790
\(326\) 14.3828 0.796590
\(327\) 6.25723 0.346026
\(328\) 8.40673 0.464184
\(329\) 6.26645 0.345481
\(330\) 9.23208 0.508210
\(331\) −3.68621 −0.202613 −0.101306 0.994855i \(-0.532302\pi\)
−0.101306 + 0.994855i \(0.532302\pi\)
\(332\) −2.52146 −0.138383
\(333\) −6.02148 −0.329975
\(334\) −20.4179 −1.11722
\(335\) −17.3412 −0.947449
\(336\) 5.43986 0.296768
\(337\) 12.2642 0.668074 0.334037 0.942560i \(-0.391589\pi\)
0.334037 + 0.942560i \(0.391589\pi\)
\(338\) −21.8277 −1.18727
\(339\) −3.19648 −0.173609
\(340\) −2.94745 −0.159848
\(341\) −2.96208 −0.160406
\(342\) −3.21781 −0.173999
\(343\) −14.0177 −0.756882
\(344\) 0.604702 0.0326033
\(345\) 20.5029 1.10384
\(346\) −21.8583 −1.17511
\(347\) 9.28716 0.498561 0.249280 0.968431i \(-0.419806\pi\)
0.249280 + 0.968431i \(0.419806\pi\)
\(348\) 7.34928 0.393963
\(349\) −29.4998 −1.57909 −0.789544 0.613695i \(-0.789683\pi\)
−0.789544 + 0.613695i \(0.789683\pi\)
\(350\) 14.5568 0.778095
\(351\) 0.0461842 0.00246513
\(352\) 6.69935 0.357077
\(353\) −15.0848 −0.802882 −0.401441 0.915885i \(-0.631491\pi\)
−0.401441 + 0.915885i \(0.631491\pi\)
\(354\) 3.90048 0.207308
\(355\) −30.9580 −1.64308
\(356\) −1.78455 −0.0945812
\(357\) 1.09506 0.0579565
\(358\) 8.50968 0.449750
\(359\) 3.23478 0.170725 0.0853626 0.996350i \(-0.472795\pi\)
0.0853626 + 0.996350i \(0.472795\pi\)
\(360\) −7.12079 −0.375299
\(361\) −15.3284 −0.806759
\(362\) −8.75644 −0.460228
\(363\) 8.66004 0.454534
\(364\) −0.0414777 −0.00217402
\(365\) 50.7591 2.65686
\(366\) 24.9855 1.30601
\(367\) 0.561855 0.0293286 0.0146643 0.999892i \(-0.495332\pi\)
0.0146643 + 0.999892i \(0.495332\pi\)
\(368\) 28.3403 1.47734
\(369\) −4.24287 −0.220875
\(370\) −36.3412 −1.88929
\(371\) 0.211851 0.0109988
\(372\) −1.58810 −0.0823392
\(373\) 27.4552 1.42158 0.710789 0.703405i \(-0.248338\pi\)
0.710789 + 0.703405i \(0.248338\pi\)
\(374\) 2.56885 0.132832
\(375\) −10.4790 −0.541133
\(376\) −11.3384 −0.584735
\(377\) 0.413859 0.0213148
\(378\) −1.83896 −0.0945857
\(379\) 9.73443 0.500024 0.250012 0.968243i \(-0.419565\pi\)
0.250012 + 0.968243i \(0.419565\pi\)
\(380\) −5.64770 −0.289721
\(381\) 6.53383 0.334738
\(382\) 9.93488 0.508313
\(383\) −16.8676 −0.861892 −0.430946 0.902378i \(-0.641820\pi\)
−0.430946 + 0.902378i \(0.641820\pi\)
\(384\) −13.0928 −0.668138
\(385\) −6.02007 −0.306811
\(386\) 38.3386 1.95138
\(387\) −0.305192 −0.0155138
\(388\) −12.6509 −0.642252
\(389\) 11.4566 0.580873 0.290437 0.956894i \(-0.406199\pi\)
0.290437 + 0.956894i \(0.406199\pi\)
\(390\) 0.278733 0.0141142
\(391\) 5.70497 0.288513
\(392\) 11.4937 0.580519
\(393\) −6.42075 −0.323884
\(394\) −1.43741 −0.0724158
\(395\) 14.4026 0.724675
\(396\) −1.25455 −0.0630437
\(397\) −32.8386 −1.64812 −0.824061 0.566501i \(-0.808297\pi\)
−0.824061 + 0.566501i \(0.808297\pi\)
\(398\) 32.6914 1.63867
\(399\) 2.09828 0.105045
\(400\) −39.3230 −1.96615
\(401\) −36.5893 −1.82718 −0.913590 0.406636i \(-0.866702\pi\)
−0.913590 + 0.406636i \(0.866702\pi\)
\(402\) 8.10312 0.404147
\(403\) −0.0894306 −0.00445486
\(404\) 9.13432 0.454449
\(405\) 3.59386 0.178580
\(406\) −16.4790 −0.817840
\(407\) 9.21100 0.456573
\(408\) −1.98138 −0.0980928
\(409\) −12.4925 −0.617715 −0.308858 0.951108i \(-0.599947\pi\)
−0.308858 + 0.951108i \(0.599947\pi\)
\(410\) −25.6068 −1.26463
\(411\) −8.79125 −0.433640
\(412\) 3.41875 0.168430
\(413\) −2.54343 −0.125154
\(414\) −9.58051 −0.470856
\(415\) −11.0491 −0.542381
\(416\) 0.202266 0.00991688
\(417\) 0.593136 0.0290460
\(418\) 4.92226 0.240756
\(419\) −27.6888 −1.35269 −0.676344 0.736586i \(-0.736437\pi\)
−0.676344 + 0.736586i \(0.736437\pi\)
\(420\) −3.22762 −0.157492
\(421\) 21.9880 1.07163 0.535815 0.844335i \(-0.320004\pi\)
0.535815 + 0.844335i \(0.320004\pi\)
\(422\) −15.4247 −0.750864
\(423\) 5.72249 0.278237
\(424\) −0.383320 −0.0186157
\(425\) −7.91581 −0.383973
\(426\) 14.4659 0.700877
\(427\) −16.2926 −0.788452
\(428\) 8.16283 0.394565
\(429\) −0.0706476 −0.00341090
\(430\) −1.84191 −0.0888250
\(431\) 4.78198 0.230340 0.115170 0.993346i \(-0.463259\pi\)
0.115170 + 0.993346i \(0.463259\pi\)
\(432\) 4.96765 0.239006
\(433\) −17.8643 −0.858503 −0.429251 0.903185i \(-0.641223\pi\)
−0.429251 + 0.903185i \(0.641223\pi\)
\(434\) 3.56094 0.170931
\(435\) 32.2048 1.54410
\(436\) −5.13177 −0.245767
\(437\) 10.9315 0.522924
\(438\) −23.7186 −1.13332
\(439\) 12.3881 0.591252 0.295626 0.955304i \(-0.404472\pi\)
0.295626 + 0.955304i \(0.404472\pi\)
\(440\) 10.8926 0.519285
\(441\) −5.80085 −0.276231
\(442\) 0.0775583 0.00368907
\(443\) −19.2163 −0.912995 −0.456498 0.889725i \(-0.650896\pi\)
−0.456498 + 0.889725i \(0.650896\pi\)
\(444\) 4.93842 0.234367
\(445\) −7.81998 −0.370703
\(446\) −25.2107 −1.19376
\(447\) −9.44340 −0.446658
\(448\) 2.82592 0.133512
\(449\) −8.50966 −0.401596 −0.200798 0.979633i \(-0.564353\pi\)
−0.200798 + 0.979633i \(0.564353\pi\)
\(450\) 13.2932 0.626648
\(451\) 6.49028 0.305616
\(452\) 2.62155 0.123307
\(453\) −15.8001 −0.742356
\(454\) 32.0576 1.50454
\(455\) −0.181757 −0.00852088
\(456\) −3.79659 −0.177791
\(457\) −30.1291 −1.40938 −0.704689 0.709516i \(-0.748914\pi\)
−0.704689 + 0.709516i \(0.748914\pi\)
\(458\) −24.4720 −1.14350
\(459\) 1.00000 0.0466760
\(460\) −16.8151 −0.784008
\(461\) 16.4091 0.764249 0.382124 0.924111i \(-0.375193\pi\)
0.382124 + 0.924111i \(0.375193\pi\)
\(462\) 2.81304 0.130874
\(463\) −31.4518 −1.46169 −0.730844 0.682545i \(-0.760873\pi\)
−0.730844 + 0.682545i \(0.760873\pi\)
\(464\) 44.5154 2.06658
\(465\) −6.95911 −0.322721
\(466\) −15.4338 −0.714956
\(467\) 4.39800 0.203515 0.101757 0.994809i \(-0.467553\pi\)
0.101757 + 0.994809i \(0.467553\pi\)
\(468\) −0.0378772 −0.00175088
\(469\) −5.28389 −0.243987
\(470\) 34.5367 1.59306
\(471\) 1.00000 0.0460776
\(472\) 4.60204 0.211826
\(473\) 0.466850 0.0214658
\(474\) −6.73001 −0.309120
\(475\) −15.1678 −0.695944
\(476\) −0.898094 −0.0411641
\(477\) 0.193461 0.00885799
\(478\) −50.3158 −2.30139
\(479\) −15.6060 −0.713056 −0.356528 0.934285i \(-0.616040\pi\)
−0.356528 + 0.934285i \(0.616040\pi\)
\(480\) 15.7395 0.718404
\(481\) 0.278097 0.0126801
\(482\) −0.437772 −0.0199400
\(483\) 6.24727 0.284261
\(484\) −7.10240 −0.322836
\(485\) −55.4366 −2.51725
\(486\) −1.67933 −0.0761758
\(487\) 40.2640 1.82454 0.912268 0.409594i \(-0.134330\pi\)
0.912268 + 0.409594i \(0.134330\pi\)
\(488\) 29.4795 1.33447
\(489\) −8.56463 −0.387306
\(490\) −35.0096 −1.58157
\(491\) −30.9388 −1.39625 −0.698124 0.715976i \(-0.745982\pi\)
−0.698124 + 0.715976i \(0.745982\pi\)
\(492\) 3.47972 0.156878
\(493\) 8.96107 0.403586
\(494\) 0.148612 0.00668637
\(495\) −5.49749 −0.247094
\(496\) −9.61931 −0.431920
\(497\) −9.43296 −0.423126
\(498\) 5.16300 0.231360
\(499\) −5.81475 −0.260304 −0.130152 0.991494i \(-0.541547\pi\)
−0.130152 + 0.991494i \(0.541547\pi\)
\(500\) 8.59419 0.384344
\(501\) 12.1584 0.543197
\(502\) 48.3674 2.15874
\(503\) −26.0840 −1.16303 −0.581514 0.813536i \(-0.697539\pi\)
−0.581514 + 0.813536i \(0.697539\pi\)
\(504\) −2.16972 −0.0966471
\(505\) 40.0269 1.78117
\(506\) 14.6552 0.651504
\(507\) 12.9979 0.577256
\(508\) −5.35862 −0.237750
\(509\) −4.63729 −0.205544 −0.102772 0.994705i \(-0.532771\pi\)
−0.102772 + 0.994705i \(0.532771\pi\)
\(510\) 6.03526 0.267246
\(511\) 15.4664 0.684195
\(512\) 2.07045 0.0915017
\(513\) 1.91613 0.0845994
\(514\) −21.8350 −0.963100
\(515\) 14.9811 0.660146
\(516\) 0.250299 0.0110188
\(517\) −8.75366 −0.384985
\(518\) −11.0732 −0.486530
\(519\) 13.0161 0.571345
\(520\) 0.328868 0.0144218
\(521\) −14.0071 −0.613662 −0.306831 0.951764i \(-0.599269\pi\)
−0.306831 + 0.951764i \(0.599269\pi\)
\(522\) −15.0486 −0.658657
\(523\) 19.8939 0.869901 0.434951 0.900454i \(-0.356766\pi\)
0.434951 + 0.900454i \(0.356766\pi\)
\(524\) 5.26588 0.230041
\(525\) −8.66826 −0.378314
\(526\) 19.1419 0.834627
\(527\) −1.93639 −0.0843505
\(528\) −7.59897 −0.330703
\(529\) 9.54673 0.415075
\(530\) 1.16759 0.0507168
\(531\) −2.32265 −0.100794
\(532\) −1.72087 −0.0746091
\(533\) 0.195953 0.00848768
\(534\) 3.65409 0.158128
\(535\) 35.7698 1.54646
\(536\) 9.56059 0.412955
\(537\) −5.06732 −0.218671
\(538\) −17.9435 −0.773599
\(539\) 8.87352 0.382209
\(540\) −2.94745 −0.126838
\(541\) −28.7557 −1.23631 −0.618153 0.786058i \(-0.712119\pi\)
−0.618153 + 0.786058i \(0.712119\pi\)
\(542\) −17.4628 −0.750093
\(543\) 5.21426 0.223765
\(544\) 4.37954 0.187771
\(545\) −22.4876 −0.963263
\(546\) 0.0849307 0.00363470
\(547\) −4.15252 −0.177549 −0.0887745 0.996052i \(-0.528295\pi\)
−0.0887745 + 0.996052i \(0.528295\pi\)
\(548\) 7.21001 0.307996
\(549\) −14.8783 −0.634990
\(550\) −20.3345 −0.867067
\(551\) 17.1706 0.731493
\(552\) −11.3037 −0.481118
\(553\) 4.38851 0.186619
\(554\) −7.40878 −0.314769
\(555\) 21.6403 0.918581
\(556\) −0.486451 −0.0206301
\(557\) −33.7307 −1.42922 −0.714609 0.699524i \(-0.753395\pi\)
−0.714609 + 0.699524i \(0.753395\pi\)
\(558\) 3.25183 0.137661
\(559\) 0.0140951 0.000596157 0
\(560\) −19.5501 −0.826141
\(561\) −1.52969 −0.0645837
\(562\) −4.56599 −0.192605
\(563\) 33.3227 1.40439 0.702193 0.711987i \(-0.252204\pi\)
0.702193 + 0.711987i \(0.252204\pi\)
\(564\) −4.69322 −0.197620
\(565\) 11.4877 0.483291
\(566\) −16.4610 −0.691906
\(567\) 1.09506 0.0459880
\(568\) 17.0679 0.716151
\(569\) −37.3867 −1.56733 −0.783665 0.621183i \(-0.786652\pi\)
−0.783665 + 0.621183i \(0.786652\pi\)
\(570\) 11.5644 0.484378
\(571\) 0.500722 0.0209546 0.0104773 0.999945i \(-0.496665\pi\)
0.0104773 + 0.999945i \(0.496665\pi\)
\(572\) 0.0579405 0.00242261
\(573\) −5.91599 −0.247144
\(574\) −7.80245 −0.325668
\(575\) −45.1595 −1.88328
\(576\) 2.58062 0.107526
\(577\) −8.80915 −0.366730 −0.183365 0.983045i \(-0.558699\pi\)
−0.183365 + 0.983045i \(0.558699\pi\)
\(578\) 1.67933 0.0698507
\(579\) −22.8297 −0.948772
\(580\) −26.4123 −1.09671
\(581\) −3.36670 −0.139674
\(582\) 25.9042 1.07377
\(583\) −0.295936 −0.0122564
\(584\) −27.9847 −1.15802
\(585\) −0.165979 −0.00686240
\(586\) 31.1340 1.28613
\(587\) 47.2663 1.95089 0.975444 0.220246i \(-0.0706860\pi\)
0.975444 + 0.220246i \(0.0706860\pi\)
\(588\) 4.75748 0.196195
\(589\) −3.71039 −0.152884
\(590\) −14.0178 −0.577102
\(591\) 0.855946 0.0352089
\(592\) 29.9126 1.22940
\(593\) −0.274025 −0.0112528 −0.00562642 0.999984i \(-0.501791\pi\)
−0.00562642 + 0.999984i \(0.501791\pi\)
\(594\) 2.56885 0.105401
\(595\) −3.93548 −0.161339
\(596\) 7.74486 0.317242
\(597\) −19.4670 −0.796730
\(598\) 0.442468 0.0180939
\(599\) 36.0529 1.47308 0.736542 0.676392i \(-0.236458\pi\)
0.736542 + 0.676392i \(0.236458\pi\)
\(600\) 15.6842 0.640305
\(601\) −14.6526 −0.597693 −0.298846 0.954301i \(-0.596602\pi\)
−0.298846 + 0.954301i \(0.596602\pi\)
\(602\) −0.561235 −0.0228742
\(603\) −4.82522 −0.196498
\(604\) 12.9582 0.527264
\(605\) −31.1230 −1.26533
\(606\) −18.7036 −0.759783
\(607\) −15.6217 −0.634064 −0.317032 0.948415i \(-0.602686\pi\)
−0.317032 + 0.948415i \(0.602686\pi\)
\(608\) 8.39179 0.340332
\(609\) 9.81288 0.397638
\(610\) −89.7943 −3.63566
\(611\) −0.264289 −0.0106920
\(612\) −0.820135 −0.0331520
\(613\) 12.0078 0.484991 0.242496 0.970152i \(-0.422034\pi\)
0.242496 + 0.970152i \(0.422034\pi\)
\(614\) 20.9547 0.845664
\(615\) 15.2483 0.614870
\(616\) 3.31901 0.133727
\(617\) 14.9841 0.603237 0.301619 0.953429i \(-0.402473\pi\)
0.301619 + 0.953429i \(0.402473\pi\)
\(618\) −7.00031 −0.281594
\(619\) −1.87009 −0.0751654 −0.0375827 0.999294i \(-0.511966\pi\)
−0.0375827 + 0.999294i \(0.511966\pi\)
\(620\) 5.70741 0.229215
\(621\) 5.70497 0.228933
\(622\) −9.07755 −0.363977
\(623\) −2.38277 −0.0954635
\(624\) −0.229427 −0.00918442
\(625\) −1.91902 −0.0767608
\(626\) 38.5303 1.53998
\(627\) −2.93110 −0.117057
\(628\) −0.820135 −0.0327269
\(629\) 6.02148 0.240092
\(630\) 6.60895 0.263307
\(631\) 45.2024 1.79948 0.899739 0.436428i \(-0.143756\pi\)
0.899739 + 0.436428i \(0.143756\pi\)
\(632\) −7.94051 −0.315856
\(633\) 9.18507 0.365074
\(634\) 55.0281 2.18545
\(635\) −23.4817 −0.931841
\(636\) −0.158664 −0.00629145
\(637\) 0.267907 0.0106149
\(638\) 23.0197 0.911357
\(639\) −8.61413 −0.340770
\(640\) 47.0536 1.85996
\(641\) −21.0744 −0.832388 −0.416194 0.909276i \(-0.636636\pi\)
−0.416194 + 0.909276i \(0.636636\pi\)
\(642\) −16.7144 −0.659664
\(643\) −10.7588 −0.424284 −0.212142 0.977239i \(-0.568044\pi\)
−0.212142 + 0.977239i \(0.568044\pi\)
\(644\) −5.12360 −0.201898
\(645\) 1.09682 0.0431872
\(646\) 3.21781 0.126603
\(647\) −43.4902 −1.70978 −0.854888 0.518812i \(-0.826374\pi\)
−0.854888 + 0.518812i \(0.826374\pi\)
\(648\) −1.98138 −0.0778359
\(649\) 3.55293 0.139465
\(650\) −0.613936 −0.0240806
\(651\) −2.12046 −0.0831073
\(652\) 7.02415 0.275087
\(653\) 18.7651 0.734334 0.367167 0.930155i \(-0.380328\pi\)
0.367167 + 0.930155i \(0.380328\pi\)
\(654\) 10.5079 0.410893
\(655\) 23.0752 0.901625
\(656\) 21.0771 0.822922
\(657\) 14.1239 0.551024
\(658\) 10.5234 0.410246
\(659\) −9.87754 −0.384774 −0.192387 0.981319i \(-0.561623\pi\)
−0.192387 + 0.981319i \(0.561623\pi\)
\(660\) 4.50869 0.175500
\(661\) 44.2858 1.72252 0.861259 0.508167i \(-0.169677\pi\)
0.861259 + 0.508167i \(0.169677\pi\)
\(662\) −6.19035 −0.240595
\(663\) −0.0461842 −0.00179364
\(664\) 6.09165 0.236402
\(665\) −7.54090 −0.292424
\(666\) −10.1120 −0.391833
\(667\) 51.1227 1.97948
\(668\) −9.97151 −0.385809
\(669\) 15.0124 0.580413
\(670\) −29.1215 −1.12506
\(671\) 22.7592 0.878609
\(672\) 4.79585 0.185004
\(673\) 33.3030 1.28374 0.641868 0.766815i \(-0.278160\pi\)
0.641868 + 0.766815i \(0.278160\pi\)
\(674\) 20.5956 0.793312
\(675\) −7.91581 −0.304680
\(676\) −10.6600 −0.410000
\(677\) −37.4141 −1.43794 −0.718970 0.695041i \(-0.755386\pi\)
−0.718970 + 0.695041i \(0.755386\pi\)
\(678\) −5.36794 −0.206154
\(679\) −16.8917 −0.648243
\(680\) 7.12079 0.273070
\(681\) −19.0896 −0.731513
\(682\) −4.97430 −0.190476
\(683\) −18.1151 −0.693156 −0.346578 0.938021i \(-0.612656\pi\)
−0.346578 + 0.938021i \(0.612656\pi\)
\(684\) −1.57149 −0.0600873
\(685\) 31.5945 1.20716
\(686\) −23.5402 −0.898769
\(687\) 14.5725 0.555976
\(688\) 1.51609 0.0578003
\(689\) −0.00893485 −0.000340391 0
\(690\) 34.4310 1.31076
\(691\) 39.2338 1.49252 0.746261 0.665653i \(-0.231847\pi\)
0.746261 + 0.665653i \(0.231847\pi\)
\(692\) −10.6750 −0.405802
\(693\) −1.67510 −0.0636318
\(694\) 15.5962 0.592022
\(695\) −2.13165 −0.0808579
\(696\) −17.7553 −0.673012
\(697\) 4.24287 0.160710
\(698\) −49.5397 −1.87511
\(699\) 9.19047 0.347615
\(700\) 7.10914 0.268700
\(701\) 45.6812 1.72535 0.862677 0.505756i \(-0.168786\pi\)
0.862677 + 0.505756i \(0.168786\pi\)
\(702\) 0.0775583 0.00292725
\(703\) 11.5380 0.435162
\(704\) −3.94755 −0.148779
\(705\) −20.5658 −0.774554
\(706\) −25.3323 −0.953392
\(707\) 12.1963 0.458688
\(708\) 1.90488 0.0715899
\(709\) −41.7290 −1.56717 −0.783583 0.621287i \(-0.786610\pi\)
−0.783583 + 0.621287i \(0.786610\pi\)
\(710\) −51.9885 −1.95109
\(711\) 4.00757 0.150296
\(712\) 4.31134 0.161574
\(713\) −11.0471 −0.413716
\(714\) 1.83896 0.0688212
\(715\) 0.253897 0.00949522
\(716\) 4.15588 0.155313
\(717\) 29.9619 1.11895
\(718\) 5.43225 0.202730
\(719\) 35.2895 1.31608 0.658038 0.752985i \(-0.271387\pi\)
0.658038 + 0.752985i \(0.271387\pi\)
\(720\) −17.8530 −0.665343
\(721\) 4.56477 0.170001
\(722\) −25.7414 −0.957997
\(723\) 0.260683 0.00969491
\(724\) −4.27639 −0.158931
\(725\) −70.9341 −2.63443
\(726\) 14.5430 0.539742
\(727\) −15.0621 −0.558621 −0.279311 0.960201i \(-0.590106\pi\)
−0.279311 + 0.960201i \(0.590106\pi\)
\(728\) 0.100207 0.00371391
\(729\) 1.00000 0.0370370
\(730\) 85.2411 3.15492
\(731\) 0.305192 0.0112879
\(732\) 12.2022 0.451006
\(733\) −5.35920 −0.197947 −0.0989733 0.995090i \(-0.531556\pi\)
−0.0989733 + 0.995090i \(0.531556\pi\)
\(734\) 0.943537 0.0348266
\(735\) 20.8474 0.768969
\(736\) 24.9852 0.920966
\(737\) 7.38111 0.271887
\(738\) −7.12516 −0.262281
\(739\) 21.0427 0.774067 0.387033 0.922066i \(-0.373500\pi\)
0.387033 + 0.922066i \(0.373500\pi\)
\(740\) −17.7480 −0.652429
\(741\) −0.0884951 −0.00325095
\(742\) 0.355767 0.0130606
\(743\) 38.4467 1.41047 0.705236 0.708973i \(-0.250841\pi\)
0.705236 + 0.708973i \(0.250841\pi\)
\(744\) 3.83672 0.140661
\(745\) 33.9382 1.24340
\(746\) 46.1063 1.68807
\(747\) −3.07445 −0.112488
\(748\) 1.25455 0.0458710
\(749\) 10.8991 0.398246
\(750\) −17.5976 −0.642575
\(751\) −14.4525 −0.527377 −0.263689 0.964608i \(-0.584939\pi\)
−0.263689 + 0.964608i \(0.584939\pi\)
\(752\) −28.4273 −1.03664
\(753\) −28.8017 −1.04959
\(754\) 0.695005 0.0253106
\(755\) 56.7835 2.06656
\(756\) −0.898094 −0.0326633
\(757\) 16.9998 0.617867 0.308934 0.951084i \(-0.400028\pi\)
0.308934 + 0.951084i \(0.400028\pi\)
\(758\) 16.3473 0.593760
\(759\) −8.72685 −0.316765
\(760\) 13.6444 0.494934
\(761\) −7.92681 −0.287346 −0.143673 0.989625i \(-0.545891\pi\)
−0.143673 + 0.989625i \(0.545891\pi\)
\(762\) 10.9724 0.397489
\(763\) −6.85202 −0.248060
\(764\) 4.85191 0.175536
\(765\) −3.59386 −0.129936
\(766\) −28.3261 −1.02346
\(767\) 0.107270 0.00387328
\(768\) −16.8258 −0.607149
\(769\) −3.34933 −0.120780 −0.0603900 0.998175i \(-0.519234\pi\)
−0.0603900 + 0.998175i \(0.519234\pi\)
\(770\) −10.1097 −0.364327
\(771\) 13.0022 0.468264
\(772\) 18.7235 0.673872
\(773\) 30.4161 1.09399 0.546996 0.837135i \(-0.315771\pi\)
0.546996 + 0.837135i \(0.315771\pi\)
\(774\) −0.512517 −0.0184221
\(775\) 15.3281 0.550602
\(776\) 30.5635 1.09717
\(777\) 6.59386 0.236553
\(778\) 19.2394 0.689765
\(779\) 8.12991 0.291284
\(780\) 0.136125 0.00487407
\(781\) 13.1770 0.471509
\(782\) 9.58051 0.342598
\(783\) 8.96107 0.320242
\(784\) 28.8166 1.02916
\(785\) −3.59386 −0.128270
\(786\) −10.7825 −0.384600
\(787\) −8.20172 −0.292360 −0.146180 0.989258i \(-0.546698\pi\)
−0.146180 + 0.989258i \(0.546698\pi\)
\(788\) −0.701991 −0.0250074
\(789\) −11.3986 −0.405800
\(790\) 24.1867 0.860524
\(791\) 3.50033 0.124457
\(792\) 3.03090 0.107698
\(793\) 0.687141 0.0244011
\(794\) −55.1467 −1.95708
\(795\) −0.695273 −0.0246588
\(796\) 15.9655 0.565883
\(797\) −21.7121 −0.769083 −0.384541 0.923108i \(-0.625640\pi\)
−0.384541 + 0.923108i \(0.625640\pi\)
\(798\) 3.52369 0.124737
\(799\) −5.72249 −0.202447
\(800\) −34.6676 −1.22569
\(801\) −2.17593 −0.0768827
\(802\) −61.4453 −2.16971
\(803\) −21.6052 −0.762430
\(804\) 3.95733 0.139564
\(805\) −22.4518 −0.791322
\(806\) −0.150183 −0.00528998
\(807\) 10.6849 0.376128
\(808\) −22.0678 −0.776341
\(809\) −43.3879 −1.52544 −0.762718 0.646731i \(-0.776136\pi\)
−0.762718 + 0.646731i \(0.776136\pi\)
\(810\) 6.03526 0.212057
\(811\) −46.3570 −1.62781 −0.813907 0.580995i \(-0.802664\pi\)
−0.813907 + 0.580995i \(0.802664\pi\)
\(812\) −8.04788 −0.282425
\(813\) 10.3987 0.364699
\(814\) 15.4683 0.542163
\(815\) 30.7801 1.07818
\(816\) −4.96765 −0.173902
\(817\) 0.584790 0.0204592
\(818\) −20.9790 −0.733514
\(819\) −0.0505743 −0.00176721
\(820\) −12.5056 −0.436716
\(821\) −0.510003 −0.0177992 −0.00889961 0.999960i \(-0.502833\pi\)
−0.00889961 + 0.999960i \(0.502833\pi\)
\(822\) −14.7634 −0.514932
\(823\) −33.4611 −1.16638 −0.583190 0.812336i \(-0.698196\pi\)
−0.583190 + 0.812336i \(0.698196\pi\)
\(824\) −8.25943 −0.287731
\(825\) 12.1087 0.421573
\(826\) −4.27125 −0.148616
\(827\) −40.2051 −1.39807 −0.699035 0.715088i \(-0.746387\pi\)
−0.699035 + 0.715088i \(0.746387\pi\)
\(828\) −4.67885 −0.162601
\(829\) 16.1426 0.560655 0.280327 0.959904i \(-0.409557\pi\)
0.280327 + 0.959904i \(0.409557\pi\)
\(830\) −18.5551 −0.644057
\(831\) 4.41176 0.153042
\(832\) −0.119184 −0.00413195
\(833\) 5.80085 0.200988
\(834\) 0.996069 0.0344910
\(835\) −43.6955 −1.51214
\(836\) 2.40389 0.0831404
\(837\) −1.93639 −0.0669315
\(838\) −46.4985 −1.60627
\(839\) 49.4308 1.70654 0.853270 0.521469i \(-0.174616\pi\)
0.853270 + 0.521469i \(0.174616\pi\)
\(840\) 7.79767 0.269045
\(841\) 51.3008 1.76899
\(842\) 36.9251 1.27252
\(843\) 2.71894 0.0936453
\(844\) −7.53300 −0.259296
\(845\) −46.7125 −1.60696
\(846\) 9.60993 0.330396
\(847\) −9.48323 −0.325848
\(848\) −0.961048 −0.0330025
\(849\) 9.80213 0.336408
\(850\) −13.2932 −0.455954
\(851\) 34.3524 1.17758
\(852\) 7.06475 0.242034
\(853\) 17.4755 0.598351 0.299176 0.954198i \(-0.403288\pi\)
0.299176 + 0.954198i \(0.403288\pi\)
\(854\) −27.3605 −0.936258
\(855\) −6.88631 −0.235507
\(856\) −19.7207 −0.674040
\(857\) −15.6295 −0.533892 −0.266946 0.963711i \(-0.586015\pi\)
−0.266946 + 0.963711i \(0.586015\pi\)
\(858\) −0.118640 −0.00405031
\(859\) 7.67136 0.261743 0.130872 0.991399i \(-0.458222\pi\)
0.130872 + 0.991399i \(0.458222\pi\)
\(860\) −0.899538 −0.0306740
\(861\) 4.64618 0.158341
\(862\) 8.03050 0.273520
\(863\) 22.4197 0.763176 0.381588 0.924333i \(-0.375377\pi\)
0.381588 + 0.924333i \(0.375377\pi\)
\(864\) 4.37954 0.148995
\(865\) −46.7781 −1.59050
\(866\) −29.9999 −1.01944
\(867\) −1.00000 −0.0339618
\(868\) 1.73906 0.0590276
\(869\) −6.13035 −0.207958
\(870\) 54.0823 1.83356
\(871\) 0.222849 0.00755095
\(872\) 12.3979 0.419847
\(873\) −15.4254 −0.522070
\(874\) 18.3575 0.620953
\(875\) 11.4751 0.387929
\(876\) −11.5835 −0.391369
\(877\) 6.51262 0.219915 0.109958 0.993936i \(-0.464928\pi\)
0.109958 + 0.993936i \(0.464928\pi\)
\(878\) 20.8037 0.702089
\(879\) −18.5396 −0.625325
\(880\) 27.3096 0.920607
\(881\) −8.28718 −0.279202 −0.139601 0.990208i \(-0.544582\pi\)
−0.139601 + 0.990208i \(0.544582\pi\)
\(882\) −9.74152 −0.328014
\(883\) 13.4417 0.452348 0.226174 0.974087i \(-0.427378\pi\)
0.226174 + 0.974087i \(0.427378\pi\)
\(884\) 0.0378772 0.00127395
\(885\) 8.34726 0.280590
\(886\) −32.2705 −1.08415
\(887\) 15.7191 0.527794 0.263897 0.964551i \(-0.414992\pi\)
0.263897 + 0.964551i \(0.414992\pi\)
\(888\) −11.9308 −0.400372
\(889\) −7.15491 −0.239968
\(890\) −13.1323 −0.440195
\(891\) −1.52969 −0.0512466
\(892\) −12.3122 −0.412243
\(893\) −10.9651 −0.366932
\(894\) −15.8585 −0.530389
\(895\) 18.2112 0.608734
\(896\) 14.3373 0.478977
\(897\) −0.263479 −0.00879732
\(898\) −14.2905 −0.476880
\(899\) −17.3521 −0.578726
\(900\) 6.49203 0.216401
\(901\) −0.193461 −0.00644513
\(902\) 10.8993 0.362907
\(903\) 0.334203 0.0111216
\(904\) −6.33344 −0.210647
\(905\) −18.7393 −0.622915
\(906\) −26.5336 −0.881520
\(907\) 45.1858 1.50037 0.750185 0.661228i \(-0.229965\pi\)
0.750185 + 0.661228i \(0.229965\pi\)
\(908\) 15.6560 0.519563
\(909\) 11.1376 0.369410
\(910\) −0.305229 −0.0101182
\(911\) 52.5562 1.74127 0.870633 0.491933i \(-0.163710\pi\)
0.870633 + 0.491933i \(0.163710\pi\)
\(912\) −9.51868 −0.315195
\(913\) 4.70296 0.155645
\(914\) −50.5965 −1.67358
\(915\) 53.4704 1.76768
\(916\) −11.9514 −0.394886
\(917\) 7.03108 0.232187
\(918\) 1.67933 0.0554260
\(919\) 59.2062 1.95303 0.976517 0.215441i \(-0.0691188\pi\)
0.976517 + 0.215441i \(0.0691188\pi\)
\(920\) 40.6239 1.33933
\(921\) −12.4781 −0.411166
\(922\) 27.5563 0.907517
\(923\) 0.397837 0.0130950
\(924\) 1.37381 0.0451949
\(925\) −47.6649 −1.56721
\(926\) −52.8178 −1.73570
\(927\) 4.16853 0.136912
\(928\) 39.2454 1.28829
\(929\) 54.0557 1.77351 0.886755 0.462239i \(-0.152954\pi\)
0.886755 + 0.462239i \(0.152954\pi\)
\(930\) −11.6866 −0.383219
\(931\) 11.1152 0.364286
\(932\) −7.53742 −0.246896
\(933\) 5.40547 0.176967
\(934\) 7.38567 0.241666
\(935\) 5.49749 0.179787
\(936\) 0.0915083 0.00299104
\(937\) −56.3169 −1.83979 −0.919897 0.392160i \(-0.871728\pi\)
−0.919897 + 0.392160i \(0.871728\pi\)
\(938\) −8.87338 −0.289726
\(939\) −22.9439 −0.748746
\(940\) 16.8667 0.550133
\(941\) 32.9031 1.07261 0.536305 0.844024i \(-0.319820\pi\)
0.536305 + 0.844024i \(0.319820\pi\)
\(942\) 1.67933 0.0547154
\(943\) 24.2055 0.788238
\(944\) 11.5381 0.375533
\(945\) −3.93548 −0.128021
\(946\) 0.783994 0.0254898
\(947\) −24.3724 −0.791995 −0.395998 0.918252i \(-0.629601\pi\)
−0.395998 + 0.918252i \(0.629601\pi\)
\(948\) −3.28674 −0.106749
\(949\) −0.652299 −0.0211745
\(950\) −25.4716 −0.826408
\(951\) −32.7680 −1.06257
\(952\) 2.16972 0.0703211
\(953\) 19.9179 0.645204 0.322602 0.946535i \(-0.395442\pi\)
0.322602 + 0.946535i \(0.395442\pi\)
\(954\) 0.324885 0.0105185
\(955\) 21.2612 0.687997
\(956\) −24.5728 −0.794742
\(957\) −13.7077 −0.443106
\(958\) −26.2075 −0.846727
\(959\) 9.62691 0.310869
\(960\) −9.27437 −0.299329
\(961\) −27.2504 −0.879045
\(962\) 0.467015 0.0150572
\(963\) 9.95303 0.320732
\(964\) −0.213795 −0.00688588
\(965\) 82.0468 2.64118
\(966\) 10.4912 0.337549
\(967\) −23.6814 −0.761542 −0.380771 0.924669i \(-0.624341\pi\)
−0.380771 + 0.924669i \(0.624341\pi\)
\(968\) 17.1588 0.551505
\(969\) −1.91613 −0.0615551
\(970\) −93.0962 −2.98914
\(971\) −7.95210 −0.255195 −0.127598 0.991826i \(-0.540727\pi\)
−0.127598 + 0.991826i \(0.540727\pi\)
\(972\) −0.820135 −0.0263058
\(973\) −0.649517 −0.0208226
\(974\) 67.6164 2.16657
\(975\) 0.365585 0.0117081
\(976\) 73.9101 2.36580
\(977\) 58.5191 1.87219 0.936095 0.351747i \(-0.114412\pi\)
0.936095 + 0.351747i \(0.114412\pi\)
\(978\) −14.3828 −0.459911
\(979\) 3.32850 0.106379
\(980\) −17.0977 −0.546166
\(981\) −6.25723 −0.199778
\(982\) −51.9563 −1.65799
\(983\) 15.3438 0.489390 0.244695 0.969600i \(-0.421312\pi\)
0.244695 + 0.969600i \(0.421312\pi\)
\(984\) −8.40673 −0.267997
\(985\) −3.07615 −0.0980142
\(986\) 15.0486 0.479244
\(987\) −6.26645 −0.199463
\(988\) 0.0725779 0.00230901
\(989\) 1.74111 0.0553642
\(990\) −9.23208 −0.293415
\(991\) 15.1365 0.480825 0.240413 0.970671i \(-0.422717\pi\)
0.240413 + 0.970671i \(0.422717\pi\)
\(992\) −8.48051 −0.269256
\(993\) 3.68621 0.116978
\(994\) −15.8410 −0.502446
\(995\) 69.9615 2.21793
\(996\) 2.52146 0.0798956
\(997\) −37.3031 −1.18140 −0.590701 0.806890i \(-0.701149\pi\)
−0.590701 + 0.806890i \(0.701149\pi\)
\(998\) −9.76486 −0.309101
\(999\) 6.02148 0.190511
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.1.37 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8007.2.a.f.1.37 48 1.1 even 1 trivial