Properties

Label 8034.2.a.bc.1.7
Level 8034
Weight 2
Character 8034.1
Self dual yes
Analytic conductor 64.152
Analytic rank 0
Dimension 15
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8034.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(64.1518129839\)
Analytic rank: \(0\)
Dimension: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
Defining polynomial: \(x^{15} - x^{14} - 48 x^{13} + 44 x^{12} + 872 x^{11} - 707 x^{10} - 7580 x^{9} + 5112 x^{8} + 33191 x^{7} - 16428 x^{6} - 71361 x^{5} + 21747 x^{4} + 65434 x^{3} - 11840 x^{2} - 17600 x + 2048\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(0.676512\) of defining polynomial
Character \(\chi\) \(=\) 8034.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.676512 q^{5} -1.00000 q^{6} -2.72085 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.676512 q^{5} -1.00000 q^{6} -2.72085 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.676512 q^{10} -5.27216 q^{11} -1.00000 q^{12} -1.00000 q^{13} -2.72085 q^{14} +0.676512 q^{15} +1.00000 q^{16} +1.01679 q^{17} +1.00000 q^{18} +4.84704 q^{19} -0.676512 q^{20} +2.72085 q^{21} -5.27216 q^{22} -5.02811 q^{23} -1.00000 q^{24} -4.54233 q^{25} -1.00000 q^{26} -1.00000 q^{27} -2.72085 q^{28} +6.30498 q^{29} +0.676512 q^{30} -3.04264 q^{31} +1.00000 q^{32} +5.27216 q^{33} +1.01679 q^{34} +1.84069 q^{35} +1.00000 q^{36} -1.00182 q^{37} +4.84704 q^{38} +1.00000 q^{39} -0.676512 q^{40} +9.67843 q^{41} +2.72085 q^{42} -8.83597 q^{43} -5.27216 q^{44} -0.676512 q^{45} -5.02811 q^{46} -8.64110 q^{47} -1.00000 q^{48} +0.402999 q^{49} -4.54233 q^{50} -1.01679 q^{51} -1.00000 q^{52} -2.36350 q^{53} -1.00000 q^{54} +3.56668 q^{55} -2.72085 q^{56} -4.84704 q^{57} +6.30498 q^{58} -13.7006 q^{59} +0.676512 q^{60} +11.9378 q^{61} -3.04264 q^{62} -2.72085 q^{63} +1.00000 q^{64} +0.676512 q^{65} +5.27216 q^{66} +2.97048 q^{67} +1.01679 q^{68} +5.02811 q^{69} +1.84069 q^{70} +15.6217 q^{71} +1.00000 q^{72} +1.34277 q^{73} -1.00182 q^{74} +4.54233 q^{75} +4.84704 q^{76} +14.3447 q^{77} +1.00000 q^{78} -5.10293 q^{79} -0.676512 q^{80} +1.00000 q^{81} +9.67843 q^{82} -0.744233 q^{83} +2.72085 q^{84} -0.687874 q^{85} -8.83597 q^{86} -6.30498 q^{87} -5.27216 q^{88} +13.8862 q^{89} -0.676512 q^{90} +2.72085 q^{91} -5.02811 q^{92} +3.04264 q^{93} -8.64110 q^{94} -3.27908 q^{95} -1.00000 q^{96} -2.57742 q^{97} +0.402999 q^{98} -5.27216 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15q + 15q^{2} - 15q^{3} + 15q^{4} - q^{5} - 15q^{6} + 5q^{7} + 15q^{8} + 15q^{9} + O(q^{10}) \) \( 15q + 15q^{2} - 15q^{3} + 15q^{4} - q^{5} - 15q^{6} + 5q^{7} + 15q^{8} + 15q^{9} - q^{10} + 3q^{11} - 15q^{12} - 15q^{13} + 5q^{14} + q^{15} + 15q^{16} - 2q^{17} + 15q^{18} + 8q^{19} - q^{20} - 5q^{21} + 3q^{22} + 3q^{23} - 15q^{24} + 22q^{25} - 15q^{26} - 15q^{27} + 5q^{28} + 26q^{29} + q^{30} + 15q^{32} - 3q^{33} - 2q^{34} - 8q^{35} + 15q^{36} + 25q^{37} + 8q^{38} + 15q^{39} - q^{40} - q^{41} - 5q^{42} + 10q^{43} + 3q^{44} - q^{45} + 3q^{46} - 3q^{47} - 15q^{48} + 32q^{49} + 22q^{50} + 2q^{51} - 15q^{52} + 13q^{53} - 15q^{54} - 2q^{55} + 5q^{56} - 8q^{57} + 26q^{58} + 28q^{59} + q^{60} + 22q^{61} + 5q^{63} + 15q^{64} + q^{65} - 3q^{66} + 29q^{67} - 2q^{68} - 3q^{69} - 8q^{70} + 18q^{71} + 15q^{72} + 23q^{73} + 25q^{74} - 22q^{75} + 8q^{76} + 17q^{77} + 15q^{78} + 27q^{79} - q^{80} + 15q^{81} - q^{82} + 7q^{83} - 5q^{84} + 43q^{85} + 10q^{86} - 26q^{87} + 3q^{88} + 35q^{89} - q^{90} - 5q^{91} + 3q^{92} - 3q^{94} + 6q^{95} - 15q^{96} + 19q^{97} + 32q^{98} + 3q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −1.00000 −0.577350
\(4\) 1.00000 0.500000
\(5\) −0.676512 −0.302546 −0.151273 0.988492i \(-0.548337\pi\)
−0.151273 + 0.988492i \(0.548337\pi\)
\(6\) −1.00000 −0.408248
\(7\) −2.72085 −1.02838 −0.514191 0.857675i \(-0.671908\pi\)
−0.514191 + 0.857675i \(0.671908\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) −0.676512 −0.213932
\(11\) −5.27216 −1.58962 −0.794809 0.606860i \(-0.792429\pi\)
−0.794809 + 0.606860i \(0.792429\pi\)
\(12\) −1.00000 −0.288675
\(13\) −1.00000 −0.277350
\(14\) −2.72085 −0.727176
\(15\) 0.676512 0.174675
\(16\) 1.00000 0.250000
\(17\) 1.01679 0.246609 0.123304 0.992369i \(-0.460651\pi\)
0.123304 + 0.992369i \(0.460651\pi\)
\(18\) 1.00000 0.235702
\(19\) 4.84704 1.11199 0.555994 0.831186i \(-0.312338\pi\)
0.555994 + 0.831186i \(0.312338\pi\)
\(20\) −0.676512 −0.151273
\(21\) 2.72085 0.593737
\(22\) −5.27216 −1.12403
\(23\) −5.02811 −1.04843 −0.524217 0.851585i \(-0.675642\pi\)
−0.524217 + 0.851585i \(0.675642\pi\)
\(24\) −1.00000 −0.204124
\(25\) −4.54233 −0.908466
\(26\) −1.00000 −0.196116
\(27\) −1.00000 −0.192450
\(28\) −2.72085 −0.514191
\(29\) 6.30498 1.17081 0.585403 0.810743i \(-0.300936\pi\)
0.585403 + 0.810743i \(0.300936\pi\)
\(30\) 0.676512 0.123514
\(31\) −3.04264 −0.546474 −0.273237 0.961947i \(-0.588094\pi\)
−0.273237 + 0.961947i \(0.588094\pi\)
\(32\) 1.00000 0.176777
\(33\) 5.27216 0.917766
\(34\) 1.01679 0.174379
\(35\) 1.84069 0.311133
\(36\) 1.00000 0.166667
\(37\) −1.00182 −0.164698 −0.0823489 0.996604i \(-0.526242\pi\)
−0.0823489 + 0.996604i \(0.526242\pi\)
\(38\) 4.84704 0.786294
\(39\) 1.00000 0.160128
\(40\) −0.676512 −0.106966
\(41\) 9.67843 1.51152 0.755759 0.654850i \(-0.227268\pi\)
0.755759 + 0.654850i \(0.227268\pi\)
\(42\) 2.72085 0.419836
\(43\) −8.83597 −1.34747 −0.673737 0.738972i \(-0.735312\pi\)
−0.673737 + 0.738972i \(0.735312\pi\)
\(44\) −5.27216 −0.794809
\(45\) −0.676512 −0.100849
\(46\) −5.02811 −0.741355
\(47\) −8.64110 −1.26043 −0.630217 0.776419i \(-0.717034\pi\)
−0.630217 + 0.776419i \(0.717034\pi\)
\(48\) −1.00000 −0.144338
\(49\) 0.402999 0.0575712
\(50\) −4.54233 −0.642383
\(51\) −1.01679 −0.142380
\(52\) −1.00000 −0.138675
\(53\) −2.36350 −0.324652 −0.162326 0.986737i \(-0.551900\pi\)
−0.162326 + 0.986737i \(0.551900\pi\)
\(54\) −1.00000 −0.136083
\(55\) 3.56668 0.480932
\(56\) −2.72085 −0.363588
\(57\) −4.84704 −0.642006
\(58\) 6.30498 0.827884
\(59\) −13.7006 −1.78367 −0.891833 0.452365i \(-0.850580\pi\)
−0.891833 + 0.452365i \(0.850580\pi\)
\(60\) 0.676512 0.0873374
\(61\) 11.9378 1.52848 0.764242 0.644930i \(-0.223113\pi\)
0.764242 + 0.644930i \(0.223113\pi\)
\(62\) −3.04264 −0.386416
\(63\) −2.72085 −0.342794
\(64\) 1.00000 0.125000
\(65\) 0.676512 0.0839110
\(66\) 5.27216 0.648959
\(67\) 2.97048 0.362902 0.181451 0.983400i \(-0.441921\pi\)
0.181451 + 0.983400i \(0.441921\pi\)
\(68\) 1.01679 0.123304
\(69\) 5.02811 0.605314
\(70\) 1.84069 0.220004
\(71\) 15.6217 1.85395 0.926977 0.375119i \(-0.122398\pi\)
0.926977 + 0.375119i \(0.122398\pi\)
\(72\) 1.00000 0.117851
\(73\) 1.34277 0.157159 0.0785796 0.996908i \(-0.474962\pi\)
0.0785796 + 0.996908i \(0.474962\pi\)
\(74\) −1.00182 −0.116459
\(75\) 4.54233 0.524503
\(76\) 4.84704 0.555994
\(77\) 14.3447 1.63474
\(78\) 1.00000 0.113228
\(79\) −5.10293 −0.574125 −0.287062 0.957912i \(-0.592679\pi\)
−0.287062 + 0.957912i \(0.592679\pi\)
\(80\) −0.676512 −0.0756364
\(81\) 1.00000 0.111111
\(82\) 9.67843 1.06880
\(83\) −0.744233 −0.0816902 −0.0408451 0.999165i \(-0.513005\pi\)
−0.0408451 + 0.999165i \(0.513005\pi\)
\(84\) 2.72085 0.296869
\(85\) −0.687874 −0.0746104
\(86\) −8.83597 −0.952807
\(87\) −6.30498 −0.675965
\(88\) −5.27216 −0.562015
\(89\) 13.8862 1.47194 0.735969 0.677016i \(-0.236727\pi\)
0.735969 + 0.677016i \(0.236727\pi\)
\(90\) −0.676512 −0.0713107
\(91\) 2.72085 0.285222
\(92\) −5.02811 −0.524217
\(93\) 3.04264 0.315507
\(94\) −8.64110 −0.891262
\(95\) −3.27908 −0.336427
\(96\) −1.00000 −0.102062
\(97\) −2.57742 −0.261697 −0.130849 0.991402i \(-0.541770\pi\)
−0.130849 + 0.991402i \(0.541770\pi\)
\(98\) 0.402999 0.0407090
\(99\) −5.27216 −0.529873
\(100\) −4.54233 −0.454233
\(101\) 8.50857 0.846634 0.423317 0.905982i \(-0.360866\pi\)
0.423317 + 0.905982i \(0.360866\pi\)
\(102\) −1.01679 −0.100678
\(103\) −1.00000 −0.0985329
\(104\) −1.00000 −0.0980581
\(105\) −1.84069 −0.179633
\(106\) −2.36350 −0.229564
\(107\) −17.8523 −1.72585 −0.862925 0.505332i \(-0.831370\pi\)
−0.862925 + 0.505332i \(0.831370\pi\)
\(108\) −1.00000 −0.0962250
\(109\) −0.493205 −0.0472405 −0.0236202 0.999721i \(-0.507519\pi\)
−0.0236202 + 0.999721i \(0.507519\pi\)
\(110\) 3.56668 0.340070
\(111\) 1.00182 0.0950883
\(112\) −2.72085 −0.257096
\(113\) −10.3192 −0.970746 −0.485373 0.874307i \(-0.661316\pi\)
−0.485373 + 0.874307i \(0.661316\pi\)
\(114\) −4.84704 −0.453967
\(115\) 3.40158 0.317199
\(116\) 6.30498 0.585403
\(117\) −1.00000 −0.0924500
\(118\) −13.7006 −1.26124
\(119\) −2.76654 −0.253608
\(120\) 0.676512 0.0617568
\(121\) 16.7957 1.52688
\(122\) 11.9378 1.08080
\(123\) −9.67843 −0.872675
\(124\) −3.04264 −0.273237
\(125\) 6.45551 0.577398
\(126\) −2.72085 −0.242392
\(127\) 14.1251 1.25340 0.626698 0.779262i \(-0.284406\pi\)
0.626698 + 0.779262i \(0.284406\pi\)
\(128\) 1.00000 0.0883883
\(129\) 8.83597 0.777964
\(130\) 0.676512 0.0593341
\(131\) −6.29354 −0.549870 −0.274935 0.961463i \(-0.588656\pi\)
−0.274935 + 0.961463i \(0.588656\pi\)
\(132\) 5.27216 0.458883
\(133\) −13.1881 −1.14355
\(134\) 2.97048 0.256611
\(135\) 0.676512 0.0582249
\(136\) 1.01679 0.0871893
\(137\) −6.42562 −0.548978 −0.274489 0.961590i \(-0.588509\pi\)
−0.274489 + 0.961590i \(0.588509\pi\)
\(138\) 5.02811 0.428021
\(139\) 18.3900 1.55982 0.779909 0.625893i \(-0.215265\pi\)
0.779909 + 0.625893i \(0.215265\pi\)
\(140\) 1.84069 0.155566
\(141\) 8.64110 0.727712
\(142\) 15.6217 1.31094
\(143\) 5.27216 0.440881
\(144\) 1.00000 0.0833333
\(145\) −4.26540 −0.354222
\(146\) 1.34277 0.111128
\(147\) −0.402999 −0.0332388
\(148\) −1.00182 −0.0823489
\(149\) 14.0749 1.15306 0.576531 0.817075i \(-0.304406\pi\)
0.576531 + 0.817075i \(0.304406\pi\)
\(150\) 4.54233 0.370880
\(151\) 23.4183 1.90575 0.952877 0.303358i \(-0.0981077\pi\)
0.952877 + 0.303358i \(0.0981077\pi\)
\(152\) 4.84704 0.393147
\(153\) 1.01679 0.0822029
\(154\) 14.3447 1.15593
\(155\) 2.05838 0.165333
\(156\) 1.00000 0.0800641
\(157\) 4.71578 0.376360 0.188180 0.982135i \(-0.439741\pi\)
0.188180 + 0.982135i \(0.439741\pi\)
\(158\) −5.10293 −0.405967
\(159\) 2.36350 0.187438
\(160\) −0.676512 −0.0534830
\(161\) 13.6807 1.07819
\(162\) 1.00000 0.0785674
\(163\) 14.3157 1.12129 0.560647 0.828055i \(-0.310552\pi\)
0.560647 + 0.828055i \(0.310552\pi\)
\(164\) 9.67843 0.755759
\(165\) −3.56668 −0.277666
\(166\) −0.744233 −0.0577637
\(167\) 5.09109 0.393960 0.196980 0.980407i \(-0.436887\pi\)
0.196980 + 0.980407i \(0.436887\pi\)
\(168\) 2.72085 0.209918
\(169\) 1.00000 0.0769231
\(170\) −0.687874 −0.0527575
\(171\) 4.84704 0.370663
\(172\) −8.83597 −0.673737
\(173\) 8.23408 0.626025 0.313013 0.949749i \(-0.398662\pi\)
0.313013 + 0.949749i \(0.398662\pi\)
\(174\) −6.30498 −0.477979
\(175\) 12.3590 0.934251
\(176\) −5.27216 −0.397404
\(177\) 13.7006 1.02980
\(178\) 13.8862 1.04082
\(179\) 21.3025 1.59223 0.796113 0.605148i \(-0.206886\pi\)
0.796113 + 0.605148i \(0.206886\pi\)
\(180\) −0.676512 −0.0504243
\(181\) 8.88993 0.660783 0.330392 0.943844i \(-0.392819\pi\)
0.330392 + 0.943844i \(0.392819\pi\)
\(182\) 2.72085 0.201682
\(183\) −11.9378 −0.882471
\(184\) −5.02811 −0.370677
\(185\) 0.677742 0.0498286
\(186\) 3.04264 0.223097
\(187\) −5.36070 −0.392014
\(188\) −8.64110 −0.630217
\(189\) 2.72085 0.197912
\(190\) −3.27908 −0.237890
\(191\) −11.8651 −0.858532 −0.429266 0.903178i \(-0.641228\pi\)
−0.429266 + 0.903178i \(0.641228\pi\)
\(192\) −1.00000 −0.0721688
\(193\) 10.6974 0.770019 0.385009 0.922913i \(-0.374198\pi\)
0.385009 + 0.922913i \(0.374198\pi\)
\(194\) −2.57742 −0.185048
\(195\) −0.676512 −0.0484461
\(196\) 0.402999 0.0287856
\(197\) −27.1432 −1.93387 −0.966936 0.255021i \(-0.917918\pi\)
−0.966936 + 0.255021i \(0.917918\pi\)
\(198\) −5.27216 −0.374676
\(199\) 16.0741 1.13946 0.569731 0.821831i \(-0.307047\pi\)
0.569731 + 0.821831i \(0.307047\pi\)
\(200\) −4.54233 −0.321191
\(201\) −2.97048 −0.209522
\(202\) 8.50857 0.598661
\(203\) −17.1549 −1.20404
\(204\) −1.01679 −0.0711898
\(205\) −6.54758 −0.457303
\(206\) −1.00000 −0.0696733
\(207\) −5.02811 −0.349478
\(208\) −1.00000 −0.0693375
\(209\) −25.5544 −1.76764
\(210\) −1.84069 −0.127019
\(211\) 13.8759 0.955258 0.477629 0.878562i \(-0.341496\pi\)
0.477629 + 0.878562i \(0.341496\pi\)
\(212\) −2.36350 −0.162326
\(213\) −15.6217 −1.07038
\(214\) −17.8523 −1.22036
\(215\) 5.97765 0.407672
\(216\) −1.00000 −0.0680414
\(217\) 8.27855 0.561985
\(218\) −0.493205 −0.0334041
\(219\) −1.34277 −0.0907359
\(220\) 3.56668 0.240466
\(221\) −1.01679 −0.0683969
\(222\) 1.00182 0.0672376
\(223\) 3.62805 0.242952 0.121476 0.992594i \(-0.461237\pi\)
0.121476 + 0.992594i \(0.461237\pi\)
\(224\) −2.72085 −0.181794
\(225\) −4.54233 −0.302822
\(226\) −10.3192 −0.686421
\(227\) 12.8428 0.852406 0.426203 0.904627i \(-0.359851\pi\)
0.426203 + 0.904627i \(0.359851\pi\)
\(228\) −4.84704 −0.321003
\(229\) 16.1697 1.06852 0.534261 0.845320i \(-0.320590\pi\)
0.534261 + 0.845320i \(0.320590\pi\)
\(230\) 3.40158 0.224294
\(231\) −14.3447 −0.943815
\(232\) 6.30498 0.413942
\(233\) −3.08086 −0.201834 −0.100917 0.994895i \(-0.532178\pi\)
−0.100917 + 0.994895i \(0.532178\pi\)
\(234\) −1.00000 −0.0653720
\(235\) 5.84581 0.381339
\(236\) −13.7006 −0.891833
\(237\) 5.10293 0.331471
\(238\) −2.76654 −0.179328
\(239\) 16.9163 1.09422 0.547111 0.837060i \(-0.315728\pi\)
0.547111 + 0.837060i \(0.315728\pi\)
\(240\) 0.676512 0.0436687
\(241\) −29.6909 −1.91256 −0.956281 0.292450i \(-0.905530\pi\)
−0.956281 + 0.292450i \(0.905530\pi\)
\(242\) 16.7957 1.07967
\(243\) −1.00000 −0.0641500
\(244\) 11.9378 0.764242
\(245\) −0.272634 −0.0174179
\(246\) −9.67843 −0.617074
\(247\) −4.84704 −0.308410
\(248\) −3.04264 −0.193208
\(249\) 0.744233 0.0471638
\(250\) 6.45551 0.408282
\(251\) −3.96047 −0.249983 −0.124991 0.992158i \(-0.539890\pi\)
−0.124991 + 0.992158i \(0.539890\pi\)
\(252\) −2.72085 −0.171397
\(253\) 26.5090 1.66661
\(254\) 14.1251 0.886285
\(255\) 0.687874 0.0430763
\(256\) 1.00000 0.0625000
\(257\) 28.3377 1.76766 0.883828 0.467812i \(-0.154957\pi\)
0.883828 + 0.467812i \(0.154957\pi\)
\(258\) 8.83597 0.550104
\(259\) 2.72579 0.169372
\(260\) 0.676512 0.0419555
\(261\) 6.30498 0.390268
\(262\) −6.29354 −0.388817
\(263\) −5.13158 −0.316427 −0.158213 0.987405i \(-0.550573\pi\)
−0.158213 + 0.987405i \(0.550573\pi\)
\(264\) 5.27216 0.324479
\(265\) 1.59894 0.0982221
\(266\) −13.1881 −0.808611
\(267\) −13.8862 −0.849823
\(268\) 2.97048 0.181451
\(269\) 4.33267 0.264168 0.132084 0.991239i \(-0.457833\pi\)
0.132084 + 0.991239i \(0.457833\pi\)
\(270\) 0.676512 0.0411712
\(271\) −15.4148 −0.936385 −0.468193 0.883626i \(-0.655095\pi\)
−0.468193 + 0.883626i \(0.655095\pi\)
\(272\) 1.01679 0.0616522
\(273\) −2.72085 −0.164673
\(274\) −6.42562 −0.388186
\(275\) 23.9479 1.44411
\(276\) 5.02811 0.302657
\(277\) −26.4488 −1.58915 −0.794576 0.607164i \(-0.792307\pi\)
−0.794576 + 0.607164i \(0.792307\pi\)
\(278\) 18.3900 1.10296
\(279\) −3.04264 −0.182158
\(280\) 1.84069 0.110002
\(281\) −1.70942 −0.101976 −0.0509879 0.998699i \(-0.516237\pi\)
−0.0509879 + 0.998699i \(0.516237\pi\)
\(282\) 8.64110 0.514570
\(283\) −4.39481 −0.261244 −0.130622 0.991432i \(-0.541697\pi\)
−0.130622 + 0.991432i \(0.541697\pi\)
\(284\) 15.6217 0.926977
\(285\) 3.27908 0.194236
\(286\) 5.27216 0.311750
\(287\) −26.3335 −1.55442
\(288\) 1.00000 0.0589256
\(289\) −15.9661 −0.939184
\(290\) −4.26540 −0.250473
\(291\) 2.57742 0.151091
\(292\) 1.34277 0.0785796
\(293\) −2.45624 −0.143495 −0.0717475 0.997423i \(-0.522858\pi\)
−0.0717475 + 0.997423i \(0.522858\pi\)
\(294\) −0.402999 −0.0235034
\(295\) 9.26862 0.539640
\(296\) −1.00182 −0.0582295
\(297\) 5.27216 0.305922
\(298\) 14.0749 0.815338
\(299\) 5.02811 0.290783
\(300\) 4.54233 0.262252
\(301\) 24.0413 1.38572
\(302\) 23.4183 1.34757
\(303\) −8.50857 −0.488804
\(304\) 4.84704 0.277997
\(305\) −8.07610 −0.462436
\(306\) 1.01679 0.0581262
\(307\) −11.7261 −0.669242 −0.334621 0.942353i \(-0.608608\pi\)
−0.334621 + 0.942353i \(0.608608\pi\)
\(308\) 14.3447 0.817368
\(309\) 1.00000 0.0568880
\(310\) 2.05838 0.116908
\(311\) −1.75340 −0.0994264 −0.0497132 0.998764i \(-0.515831\pi\)
−0.0497132 + 0.998764i \(0.515831\pi\)
\(312\) 1.00000 0.0566139
\(313\) 21.0420 1.18936 0.594681 0.803962i \(-0.297278\pi\)
0.594681 + 0.803962i \(0.297278\pi\)
\(314\) 4.71578 0.266127
\(315\) 1.84069 0.103711
\(316\) −5.10293 −0.287062
\(317\) 25.9164 1.45561 0.727804 0.685785i \(-0.240541\pi\)
0.727804 + 0.685785i \(0.240541\pi\)
\(318\) 2.36350 0.132539
\(319\) −33.2409 −1.86113
\(320\) −0.676512 −0.0378182
\(321\) 17.8523 0.996420
\(322\) 13.6807 0.762397
\(323\) 4.92844 0.274226
\(324\) 1.00000 0.0555556
\(325\) 4.54233 0.251963
\(326\) 14.3157 0.792875
\(327\) 0.493205 0.0272743
\(328\) 9.67843 0.534402
\(329\) 23.5111 1.29621
\(330\) −3.56668 −0.196340
\(331\) −18.0656 −0.992974 −0.496487 0.868044i \(-0.665377\pi\)
−0.496487 + 0.868044i \(0.665377\pi\)
\(332\) −0.744233 −0.0408451
\(333\) −1.00182 −0.0548993
\(334\) 5.09109 0.278572
\(335\) −2.00957 −0.109794
\(336\) 2.72085 0.148434
\(337\) 1.94031 0.105696 0.0528478 0.998603i \(-0.483170\pi\)
0.0528478 + 0.998603i \(0.483170\pi\)
\(338\) 1.00000 0.0543928
\(339\) 10.3192 0.560460
\(340\) −0.687874 −0.0373052
\(341\) 16.0413 0.868685
\(342\) 4.84704 0.262098
\(343\) 17.9494 0.969178
\(344\) −8.83597 −0.476404
\(345\) −3.40158 −0.183135
\(346\) 8.23408 0.442667
\(347\) 0.229716 0.0123318 0.00616590 0.999981i \(-0.498037\pi\)
0.00616590 + 0.999981i \(0.498037\pi\)
\(348\) −6.30498 −0.337982
\(349\) 19.8807 1.06419 0.532095 0.846684i \(-0.321405\pi\)
0.532095 + 0.846684i \(0.321405\pi\)
\(350\) 12.3590 0.660615
\(351\) 1.00000 0.0533761
\(352\) −5.27216 −0.281007
\(353\) −10.2245 −0.544195 −0.272098 0.962270i \(-0.587717\pi\)
−0.272098 + 0.962270i \(0.587717\pi\)
\(354\) 13.7006 0.728178
\(355\) −10.5683 −0.560905
\(356\) 13.8862 0.735969
\(357\) 2.76654 0.146421
\(358\) 21.3025 1.12587
\(359\) −4.10661 −0.216739 −0.108369 0.994111i \(-0.534563\pi\)
−0.108369 + 0.994111i \(0.534563\pi\)
\(360\) −0.676512 −0.0356553
\(361\) 4.49382 0.236517
\(362\) 8.88993 0.467244
\(363\) −16.7957 −0.881547
\(364\) 2.72085 0.142611
\(365\) −0.908400 −0.0475478
\(366\) −11.9378 −0.624001
\(367\) 24.2806 1.26744 0.633718 0.773564i \(-0.281528\pi\)
0.633718 + 0.773564i \(0.281528\pi\)
\(368\) −5.02811 −0.262109
\(369\) 9.67843 0.503839
\(370\) 0.677742 0.0352341
\(371\) 6.43073 0.333867
\(372\) 3.04264 0.157754
\(373\) −2.09879 −0.108671 −0.0543355 0.998523i \(-0.517304\pi\)
−0.0543355 + 0.998523i \(0.517304\pi\)
\(374\) −5.36070 −0.277195
\(375\) −6.45551 −0.333361
\(376\) −8.64110 −0.445631
\(377\) −6.30498 −0.324723
\(378\) 2.72085 0.139945
\(379\) −2.52123 −0.129507 −0.0647534 0.997901i \(-0.520626\pi\)
−0.0647534 + 0.997901i \(0.520626\pi\)
\(380\) −3.27908 −0.168213
\(381\) −14.1251 −0.723649
\(382\) −11.8651 −0.607074
\(383\) 2.79825 0.142984 0.0714918 0.997441i \(-0.477224\pi\)
0.0714918 + 0.997441i \(0.477224\pi\)
\(384\) −1.00000 −0.0510310
\(385\) −9.70440 −0.494582
\(386\) 10.6974 0.544485
\(387\) −8.83597 −0.449158
\(388\) −2.57742 −0.130849
\(389\) −21.9755 −1.11420 −0.557102 0.830444i \(-0.688087\pi\)
−0.557102 + 0.830444i \(0.688087\pi\)
\(390\) −0.676512 −0.0342565
\(391\) −5.11255 −0.258553
\(392\) 0.402999 0.0203545
\(393\) 6.29354 0.317467
\(394\) −27.1432 −1.36745
\(395\) 3.45220 0.173699
\(396\) −5.27216 −0.264936
\(397\) −18.4038 −0.923658 −0.461829 0.886969i \(-0.652807\pi\)
−0.461829 + 0.886969i \(0.652807\pi\)
\(398\) 16.0741 0.805721
\(399\) 13.1881 0.660228
\(400\) −4.54233 −0.227117
\(401\) 9.25701 0.462273 0.231136 0.972921i \(-0.425756\pi\)
0.231136 + 0.972921i \(0.425756\pi\)
\(402\) −2.97048 −0.148154
\(403\) 3.04264 0.151565
\(404\) 8.50857 0.423317
\(405\) −0.676512 −0.0336162
\(406\) −17.1549 −0.851382
\(407\) 5.28175 0.261807
\(408\) −1.01679 −0.0503388
\(409\) −6.19590 −0.306367 −0.153184 0.988198i \(-0.548953\pi\)
−0.153184 + 0.988198i \(0.548953\pi\)
\(410\) −6.54758 −0.323362
\(411\) 6.42562 0.316952
\(412\) −1.00000 −0.0492665
\(413\) 37.2772 1.83429
\(414\) −5.02811 −0.247118
\(415\) 0.503483 0.0247150
\(416\) −1.00000 −0.0490290
\(417\) −18.3900 −0.900562
\(418\) −25.5544 −1.24991
\(419\) 15.4153 0.753087 0.376543 0.926399i \(-0.377113\pi\)
0.376543 + 0.926399i \(0.377113\pi\)
\(420\) −1.84069 −0.0898163
\(421\) −25.8241 −1.25859 −0.629294 0.777167i \(-0.716656\pi\)
−0.629294 + 0.777167i \(0.716656\pi\)
\(422\) 13.8759 0.675469
\(423\) −8.64110 −0.420145
\(424\) −2.36350 −0.114782
\(425\) −4.61861 −0.224036
\(426\) −15.6217 −0.756873
\(427\) −32.4810 −1.57187
\(428\) −17.8523 −0.862925
\(429\) −5.27216 −0.254543
\(430\) 5.97765 0.288268
\(431\) −7.57974 −0.365103 −0.182552 0.983196i \(-0.558436\pi\)
−0.182552 + 0.983196i \(0.558436\pi\)
\(432\) −1.00000 −0.0481125
\(433\) −16.0633 −0.771954 −0.385977 0.922508i \(-0.626136\pi\)
−0.385977 + 0.922508i \(0.626136\pi\)
\(434\) 8.27855 0.397383
\(435\) 4.26540 0.204510
\(436\) −0.493205 −0.0236202
\(437\) −24.3715 −1.16585
\(438\) −1.34277 −0.0641600
\(439\) 34.5792 1.65037 0.825187 0.564859i \(-0.191069\pi\)
0.825187 + 0.564859i \(0.191069\pi\)
\(440\) 3.56668 0.170035
\(441\) 0.402999 0.0191904
\(442\) −1.01679 −0.0483639
\(443\) 21.2435 1.00931 0.504654 0.863322i \(-0.331620\pi\)
0.504654 + 0.863322i \(0.331620\pi\)
\(444\) 1.00182 0.0475442
\(445\) −9.39420 −0.445328
\(446\) 3.62805 0.171793
\(447\) −14.0749 −0.665720
\(448\) −2.72085 −0.128548
\(449\) 35.5472 1.67757 0.838787 0.544460i \(-0.183265\pi\)
0.838787 + 0.544460i \(0.183265\pi\)
\(450\) −4.54233 −0.214128
\(451\) −51.0263 −2.40273
\(452\) −10.3192 −0.485373
\(453\) −23.4183 −1.10029
\(454\) 12.8428 0.602742
\(455\) −1.84069 −0.0862927
\(456\) −4.84704 −0.226984
\(457\) 24.4777 1.14502 0.572509 0.819898i \(-0.305970\pi\)
0.572509 + 0.819898i \(0.305970\pi\)
\(458\) 16.1697 0.755559
\(459\) −1.01679 −0.0474599
\(460\) 3.40158 0.158600
\(461\) −26.6751 −1.24238 −0.621191 0.783659i \(-0.713351\pi\)
−0.621191 + 0.783659i \(0.713351\pi\)
\(462\) −14.3447 −0.667378
\(463\) 7.77420 0.361298 0.180649 0.983548i \(-0.442180\pi\)
0.180649 + 0.983548i \(0.442180\pi\)
\(464\) 6.30498 0.292701
\(465\) −2.05838 −0.0954553
\(466\) −3.08086 −0.142718
\(467\) 22.4004 1.03657 0.518283 0.855209i \(-0.326571\pi\)
0.518283 + 0.855209i \(0.326571\pi\)
\(468\) −1.00000 −0.0462250
\(469\) −8.08222 −0.373202
\(470\) 5.84581 0.269647
\(471\) −4.71578 −0.217292
\(472\) −13.7006 −0.630621
\(473\) 46.5847 2.14197
\(474\) 5.10293 0.234385
\(475\) −22.0169 −1.01020
\(476\) −2.76654 −0.126804
\(477\) −2.36350 −0.108217
\(478\) 16.9163 0.773731
\(479\) −38.0641 −1.73919 −0.869597 0.493762i \(-0.835621\pi\)
−0.869597 + 0.493762i \(0.835621\pi\)
\(480\) 0.676512 0.0308784
\(481\) 1.00182 0.0456790
\(482\) −29.6909 −1.35239
\(483\) −13.6807 −0.622494
\(484\) 16.7957 0.763442
\(485\) 1.74366 0.0791754
\(486\) −1.00000 −0.0453609
\(487\) 17.7607 0.804815 0.402408 0.915461i \(-0.368173\pi\)
0.402408 + 0.915461i \(0.368173\pi\)
\(488\) 11.9378 0.540401
\(489\) −14.3157 −0.647380
\(490\) −0.272634 −0.0123163
\(491\) −31.1190 −1.40438 −0.702191 0.711989i \(-0.747795\pi\)
−0.702191 + 0.711989i \(0.747795\pi\)
\(492\) −9.67843 −0.436337
\(493\) 6.41086 0.288731
\(494\) −4.84704 −0.218079
\(495\) 3.56668 0.160311
\(496\) −3.04264 −0.136619
\(497\) −42.5042 −1.90657
\(498\) 0.744233 0.0333499
\(499\) 15.2463 0.682517 0.341258 0.939970i \(-0.389147\pi\)
0.341258 + 0.939970i \(0.389147\pi\)
\(500\) 6.45551 0.288699
\(501\) −5.09109 −0.227453
\(502\) −3.96047 −0.176764
\(503\) −42.7565 −1.90642 −0.953210 0.302310i \(-0.902242\pi\)
−0.953210 + 0.302310i \(0.902242\pi\)
\(504\) −2.72085 −0.121196
\(505\) −5.75615 −0.256145
\(506\) 26.5090 1.17847
\(507\) −1.00000 −0.0444116
\(508\) 14.1251 0.626698
\(509\) −11.1467 −0.494069 −0.247035 0.969007i \(-0.579456\pi\)
−0.247035 + 0.969007i \(0.579456\pi\)
\(510\) 0.687874 0.0304596
\(511\) −3.65347 −0.161620
\(512\) 1.00000 0.0441942
\(513\) −4.84704 −0.214002
\(514\) 28.3377 1.24992
\(515\) 0.676512 0.0298107
\(516\) 8.83597 0.388982
\(517\) 45.5573 2.00361
\(518\) 2.72579 0.119764
\(519\) −8.23408 −0.361436
\(520\) 0.676512 0.0296670
\(521\) 31.2470 1.36896 0.684479 0.729033i \(-0.260030\pi\)
0.684479 + 0.729033i \(0.260030\pi\)
\(522\) 6.30498 0.275961
\(523\) 8.46338 0.370078 0.185039 0.982731i \(-0.440759\pi\)
0.185039 + 0.982731i \(0.440759\pi\)
\(524\) −6.29354 −0.274935
\(525\) −12.3590 −0.539390
\(526\) −5.13158 −0.223748
\(527\) −3.09374 −0.134765
\(528\) 5.27216 0.229442
\(529\) 2.28192 0.0992141
\(530\) 1.59894 0.0694535
\(531\) −13.7006 −0.594555
\(532\) −13.1881 −0.571775
\(533\) −9.67843 −0.419219
\(534\) −13.8862 −0.600916
\(535\) 12.0773 0.522148
\(536\) 2.97048 0.128305
\(537\) −21.3025 −0.919272
\(538\) 4.33267 0.186795
\(539\) −2.12468 −0.0915162
\(540\) 0.676512 0.0291125
\(541\) −12.8504 −0.552480 −0.276240 0.961089i \(-0.589088\pi\)
−0.276240 + 0.961089i \(0.589088\pi\)
\(542\) −15.4148 −0.662124
\(543\) −8.88993 −0.381503
\(544\) 1.01679 0.0435947
\(545\) 0.333659 0.0142924
\(546\) −2.72085 −0.116441
\(547\) −11.5043 −0.491888 −0.245944 0.969284i \(-0.579098\pi\)
−0.245944 + 0.969284i \(0.579098\pi\)
\(548\) −6.42562 −0.274489
\(549\) 11.9378 0.509495
\(550\) 23.9479 1.02114
\(551\) 30.5605 1.30192
\(552\) 5.02811 0.214011
\(553\) 13.8843 0.590420
\(554\) −26.4488 −1.12370
\(555\) −0.677742 −0.0287686
\(556\) 18.3900 0.779909
\(557\) −37.2435 −1.57806 −0.789028 0.614357i \(-0.789416\pi\)
−0.789028 + 0.614357i \(0.789416\pi\)
\(558\) −3.04264 −0.128805
\(559\) 8.83597 0.373722
\(560\) 1.84069 0.0777832
\(561\) 5.36070 0.226329
\(562\) −1.70942 −0.0721077
\(563\) −13.2837 −0.559841 −0.279920 0.960023i \(-0.590308\pi\)
−0.279920 + 0.960023i \(0.590308\pi\)
\(564\) 8.64110 0.363856
\(565\) 6.98104 0.293695
\(566\) −4.39481 −0.184728
\(567\) −2.72085 −0.114265
\(568\) 15.6217 0.655472
\(569\) −4.29722 −0.180149 −0.0900745 0.995935i \(-0.528711\pi\)
−0.0900745 + 0.995935i \(0.528711\pi\)
\(570\) 3.27908 0.137346
\(571\) 43.0999 1.80368 0.901838 0.432074i \(-0.142218\pi\)
0.901838 + 0.432074i \(0.142218\pi\)
\(572\) 5.27216 0.220440
\(573\) 11.8651 0.495674
\(574\) −26.3335 −1.09914
\(575\) 22.8394 0.952467
\(576\) 1.00000 0.0416667
\(577\) 17.0048 0.707918 0.353959 0.935261i \(-0.384835\pi\)
0.353959 + 0.935261i \(0.384835\pi\)
\(578\) −15.9661 −0.664103
\(579\) −10.6974 −0.444570
\(580\) −4.26540 −0.177111
\(581\) 2.02494 0.0840088
\(582\) 2.57742 0.106838
\(583\) 12.4608 0.516073
\(584\) 1.34277 0.0555642
\(585\) 0.676512 0.0279703
\(586\) −2.45624 −0.101466
\(587\) −0.310300 −0.0128075 −0.00640373 0.999979i \(-0.502038\pi\)
−0.00640373 + 0.999979i \(0.502038\pi\)
\(588\) −0.402999 −0.0166194
\(589\) −14.7478 −0.607673
\(590\) 9.26862 0.381583
\(591\) 27.1432 1.11652
\(592\) −1.00182 −0.0411745
\(593\) 34.7530 1.42714 0.713568 0.700586i \(-0.247078\pi\)
0.713568 + 0.700586i \(0.247078\pi\)
\(594\) 5.27216 0.216320
\(595\) 1.87160 0.0767280
\(596\) 14.0749 0.576531
\(597\) −16.0741 −0.657868
\(598\) 5.02811 0.205615
\(599\) −19.2572 −0.786827 −0.393414 0.919362i \(-0.628706\pi\)
−0.393414 + 0.919362i \(0.628706\pi\)
\(600\) 4.54233 0.185440
\(601\) −16.5213 −0.673917 −0.336959 0.941519i \(-0.609398\pi\)
−0.336959 + 0.941519i \(0.609398\pi\)
\(602\) 24.0413 0.979851
\(603\) 2.97048 0.120967
\(604\) 23.4183 0.952877
\(605\) −11.3625 −0.461952
\(606\) −8.50857 −0.345637
\(607\) −1.62313 −0.0658809 −0.0329404 0.999457i \(-0.510487\pi\)
−0.0329404 + 0.999457i \(0.510487\pi\)
\(608\) 4.84704 0.196574
\(609\) 17.1549 0.695151
\(610\) −8.07610 −0.326992
\(611\) 8.64110 0.349582
\(612\) 1.01679 0.0411015
\(613\) 29.4693 1.19025 0.595127 0.803632i \(-0.297102\pi\)
0.595127 + 0.803632i \(0.297102\pi\)
\(614\) −11.7261 −0.473225
\(615\) 6.54758 0.264024
\(616\) 14.3447 0.577966
\(617\) −9.07021 −0.365153 −0.182576 0.983192i \(-0.558444\pi\)
−0.182576 + 0.983192i \(0.558444\pi\)
\(618\) 1.00000 0.0402259
\(619\) −4.18897 −0.168369 −0.0841845 0.996450i \(-0.526829\pi\)
−0.0841845 + 0.996450i \(0.526829\pi\)
\(620\) 2.05838 0.0826667
\(621\) 5.02811 0.201771
\(622\) −1.75340 −0.0703051
\(623\) −37.7823 −1.51371
\(624\) 1.00000 0.0400320
\(625\) 18.3444 0.733777
\(626\) 21.0420 0.841006
\(627\) 25.5544 1.02054
\(628\) 4.71578 0.188180
\(629\) −1.01864 −0.0406159
\(630\) 1.84069 0.0733347
\(631\) −15.6492 −0.622986 −0.311493 0.950248i \(-0.600829\pi\)
−0.311493 + 0.950248i \(0.600829\pi\)
\(632\) −5.10293 −0.202984
\(633\) −13.8759 −0.551519
\(634\) 25.9164 1.02927
\(635\) −9.55578 −0.379210
\(636\) 2.36350 0.0937191
\(637\) −0.402999 −0.0159674
\(638\) −33.2409 −1.31602
\(639\) 15.6217 0.617985
\(640\) −0.676512 −0.0267415
\(641\) −6.08581 −0.240375 −0.120187 0.992751i \(-0.538350\pi\)
−0.120187 + 0.992751i \(0.538350\pi\)
\(642\) 17.8523 0.704575
\(643\) 20.2998 0.800545 0.400273 0.916396i \(-0.368915\pi\)
0.400273 + 0.916396i \(0.368915\pi\)
\(644\) 13.6807 0.539096
\(645\) −5.97765 −0.235370
\(646\) 4.92844 0.193907
\(647\) −40.1434 −1.57820 −0.789100 0.614264i \(-0.789453\pi\)
−0.789100 + 0.614264i \(0.789453\pi\)
\(648\) 1.00000 0.0392837
\(649\) 72.2318 2.83535
\(650\) 4.54233 0.178165
\(651\) −8.27855 −0.324462
\(652\) 14.3157 0.560647
\(653\) −9.92143 −0.388256 −0.194128 0.980976i \(-0.562188\pi\)
−0.194128 + 0.980976i \(0.562188\pi\)
\(654\) 0.493205 0.0192858
\(655\) 4.25766 0.166361
\(656\) 9.67843 0.377879
\(657\) 1.34277 0.0523864
\(658\) 23.5111 0.916558
\(659\) −3.80652 −0.148281 −0.0741405 0.997248i \(-0.523621\pi\)
−0.0741405 + 0.997248i \(0.523621\pi\)
\(660\) −3.56668 −0.138833
\(661\) −0.560567 −0.0218035 −0.0109018 0.999941i \(-0.503470\pi\)
−0.0109018 + 0.999941i \(0.503470\pi\)
\(662\) −18.0656 −0.702138
\(663\) 1.01679 0.0394890
\(664\) −0.744233 −0.0288818
\(665\) 8.92188 0.345976
\(666\) −1.00182 −0.0388197
\(667\) −31.7022 −1.22751
\(668\) 5.09109 0.196980
\(669\) −3.62805 −0.140269
\(670\) −2.00957 −0.0776364
\(671\) −62.9383 −2.42970
\(672\) 2.72085 0.104959
\(673\) 13.2680 0.511444 0.255722 0.966750i \(-0.417687\pi\)
0.255722 + 0.966750i \(0.417687\pi\)
\(674\) 1.94031 0.0747381
\(675\) 4.54233 0.174834
\(676\) 1.00000 0.0384615
\(677\) 28.8453 1.10861 0.554307 0.832312i \(-0.312983\pi\)
0.554307 + 0.832312i \(0.312983\pi\)
\(678\) 10.3192 0.396305
\(679\) 7.01276 0.269125
\(680\) −0.687874 −0.0263787
\(681\) −12.8428 −0.492137
\(682\) 16.0413 0.614253
\(683\) 6.72659 0.257386 0.128693 0.991684i \(-0.458922\pi\)
0.128693 + 0.991684i \(0.458922\pi\)
\(684\) 4.84704 0.185331
\(685\) 4.34701 0.166091
\(686\) 17.9494 0.685312
\(687\) −16.1697 −0.616911
\(688\) −8.83597 −0.336868
\(689\) 2.36350 0.0900424
\(690\) −3.40158 −0.129496
\(691\) 11.4509 0.435612 0.217806 0.975992i \(-0.430110\pi\)
0.217806 + 0.975992i \(0.430110\pi\)
\(692\) 8.23408 0.313013
\(693\) 14.3447 0.544912
\(694\) 0.229716 0.00871990
\(695\) −12.4411 −0.471916
\(696\) −6.30498 −0.238990
\(697\) 9.84097 0.372753
\(698\) 19.8807 0.752497
\(699\) 3.08086 0.116529
\(700\) 12.3590 0.467126
\(701\) 41.0431 1.55018 0.775088 0.631853i \(-0.217705\pi\)
0.775088 + 0.631853i \(0.217705\pi\)
\(702\) 1.00000 0.0377426
\(703\) −4.85585 −0.183142
\(704\) −5.27216 −0.198702
\(705\) −5.84581 −0.220166
\(706\) −10.2245 −0.384804
\(707\) −23.1505 −0.870664
\(708\) 13.7006 0.514900
\(709\) 25.2166 0.947030 0.473515 0.880786i \(-0.342985\pi\)
0.473515 + 0.880786i \(0.342985\pi\)
\(710\) −10.5683 −0.396620
\(711\) −5.10293 −0.191375
\(712\) 13.8862 0.520408
\(713\) 15.2987 0.572942
\(714\) 2.76654 0.103535
\(715\) −3.56668 −0.133386
\(716\) 21.3025 0.796113
\(717\) −16.9163 −0.631749
\(718\) −4.10661 −0.153257
\(719\) −22.2351 −0.829231 −0.414616 0.909997i \(-0.636084\pi\)
−0.414616 + 0.909997i \(0.636084\pi\)
\(720\) −0.676512 −0.0252121
\(721\) 2.72085 0.101330
\(722\) 4.49382 0.167243
\(723\) 29.6909 1.10422
\(724\) 8.88993 0.330392
\(725\) −28.6393 −1.06364
\(726\) −16.7957 −0.623348
\(727\) −30.4872 −1.13071 −0.565354 0.824848i \(-0.691260\pi\)
−0.565354 + 0.824848i \(0.691260\pi\)
\(728\) 2.72085 0.100841
\(729\) 1.00000 0.0370370
\(730\) −0.908400 −0.0336214
\(731\) −8.98436 −0.332299
\(732\) −11.9378 −0.441235
\(733\) −41.4654 −1.53156 −0.765780 0.643103i \(-0.777647\pi\)
−0.765780 + 0.643103i \(0.777647\pi\)
\(734\) 24.2806 0.896212
\(735\) 0.272634 0.0100562
\(736\) −5.02811 −0.185339
\(737\) −15.6609 −0.576876
\(738\) 9.67843 0.356268
\(739\) 50.7684 1.86755 0.933773 0.357866i \(-0.116495\pi\)
0.933773 + 0.357866i \(0.116495\pi\)
\(740\) 0.677742 0.0249143
\(741\) 4.84704 0.178061
\(742\) 6.43073 0.236080
\(743\) 15.2433 0.559223 0.279611 0.960113i \(-0.409794\pi\)
0.279611 + 0.960113i \(0.409794\pi\)
\(744\) 3.04264 0.111549
\(745\) −9.52185 −0.348854
\(746\) −2.09879 −0.0768421
\(747\) −0.744233 −0.0272301
\(748\) −5.36070 −0.196007
\(749\) 48.5734 1.77483
\(750\) −6.45551 −0.235722
\(751\) 12.7402 0.464898 0.232449 0.972609i \(-0.425326\pi\)
0.232449 + 0.972609i \(0.425326\pi\)
\(752\) −8.64110 −0.315109
\(753\) 3.96047 0.144328
\(754\) −6.30498 −0.229614
\(755\) −15.8428 −0.576577
\(756\) 2.72085 0.0989562
\(757\) 15.1143 0.549337 0.274668 0.961539i \(-0.411432\pi\)
0.274668 + 0.961539i \(0.411432\pi\)
\(758\) −2.52123 −0.0915752
\(759\) −26.5090 −0.962217
\(760\) −3.27908 −0.118945
\(761\) 7.05638 0.255794 0.127897 0.991787i \(-0.459177\pi\)
0.127897 + 0.991787i \(0.459177\pi\)
\(762\) −14.1251 −0.511697
\(763\) 1.34193 0.0485813
\(764\) −11.8651 −0.429266
\(765\) −0.687874 −0.0248701
\(766\) 2.79825 0.101105
\(767\) 13.7006 0.494700
\(768\) −1.00000 −0.0360844
\(769\) 15.4429 0.556887 0.278443 0.960453i \(-0.410182\pi\)
0.278443 + 0.960453i \(0.410182\pi\)
\(770\) −9.70440 −0.349722
\(771\) −28.3377 −1.02056
\(772\) 10.6974 0.385009
\(773\) −8.93806 −0.321480 −0.160740 0.986997i \(-0.551388\pi\)
−0.160740 + 0.986997i \(0.551388\pi\)
\(774\) −8.83597 −0.317602
\(775\) 13.8207 0.496453
\(776\) −2.57742 −0.0925240
\(777\) −2.72579 −0.0977872
\(778\) −21.9755 −0.787861
\(779\) 46.9118 1.68079
\(780\) −0.676512 −0.0242230
\(781\) −82.3601 −2.94708
\(782\) −5.11255 −0.182825
\(783\) −6.30498 −0.225322
\(784\) 0.402999 0.0143928
\(785\) −3.19028 −0.113866
\(786\) 6.29354 0.224483
\(787\) 54.3035 1.93571 0.967856 0.251507i \(-0.0809261\pi\)
0.967856 + 0.251507i \(0.0809261\pi\)
\(788\) −27.1432 −0.966936
\(789\) 5.13158 0.182689
\(790\) 3.45220 0.122824
\(791\) 28.0769 0.998298
\(792\) −5.27216 −0.187338
\(793\) −11.9378 −0.423925
\(794\) −18.4038 −0.653125
\(795\) −1.59894 −0.0567086
\(796\) 16.0741 0.569731
\(797\) 38.1146 1.35009 0.675044 0.737778i \(-0.264125\pi\)
0.675044 + 0.737778i \(0.264125\pi\)
\(798\) 13.1881 0.466852
\(799\) −8.78622 −0.310834
\(800\) −4.54233 −0.160596
\(801\) 13.8862 0.490646
\(802\) 9.25701 0.326876
\(803\) −7.07930 −0.249823
\(804\) −2.97048 −0.104761
\(805\) −9.25518 −0.326202
\(806\) 3.04264 0.107172
\(807\) −4.33267 −0.152517
\(808\) 8.50857 0.299330
\(809\) −39.7580 −1.39782 −0.698909 0.715211i \(-0.746331\pi\)
−0.698909 + 0.715211i \(0.746331\pi\)
\(810\) −0.676512 −0.0237702
\(811\) 37.2157 1.30682 0.653410 0.757004i \(-0.273338\pi\)
0.653410 + 0.757004i \(0.273338\pi\)
\(812\) −17.1549 −0.602018
\(813\) 15.4148 0.540622
\(814\) 5.28175 0.185125
\(815\) −9.68477 −0.339243
\(816\) −1.01679 −0.0355949
\(817\) −42.8283 −1.49837
\(818\) −6.19590 −0.216635
\(819\) 2.72085 0.0950740
\(820\) −6.54758 −0.228651
\(821\) 21.1159 0.736952 0.368476 0.929637i \(-0.379880\pi\)
0.368476 + 0.929637i \(0.379880\pi\)
\(822\) 6.42562 0.224119
\(823\) −33.4694 −1.16667 −0.583335 0.812232i \(-0.698252\pi\)
−0.583335 + 0.812232i \(0.698252\pi\)
\(824\) −1.00000 −0.0348367
\(825\) −23.9479 −0.833759
\(826\) 37.2772 1.29704
\(827\) −25.7208 −0.894401 −0.447201 0.894434i \(-0.647579\pi\)
−0.447201 + 0.894434i \(0.647579\pi\)
\(828\) −5.02811 −0.174739
\(829\) −22.7542 −0.790286 −0.395143 0.918620i \(-0.629305\pi\)
−0.395143 + 0.918620i \(0.629305\pi\)
\(830\) 0.503483 0.0174761
\(831\) 26.4488 0.917498
\(832\) −1.00000 −0.0346688
\(833\) 0.409766 0.0141976
\(834\) −18.3900 −0.636793
\(835\) −3.44419 −0.119191
\(836\) −25.5544 −0.883818
\(837\) 3.04264 0.105169
\(838\) 15.4153 0.532513
\(839\) 19.5982 0.676605 0.338303 0.941037i \(-0.390147\pi\)
0.338303 + 0.941037i \(0.390147\pi\)
\(840\) −1.84069 −0.0635097
\(841\) 10.7528 0.370785
\(842\) −25.8241 −0.889957
\(843\) 1.70942 0.0588757
\(844\) 13.8759 0.477629
\(845\) −0.676512 −0.0232727
\(846\) −8.64110 −0.297087
\(847\) −45.6986 −1.57022
\(848\) −2.36350 −0.0811631
\(849\) 4.39481 0.150829
\(850\) −4.61861 −0.158417
\(851\) 5.03725 0.172675
\(852\) −15.6217 −0.535190
\(853\) 39.9423 1.36760 0.683799 0.729670i \(-0.260327\pi\)
0.683799 + 0.729670i \(0.260327\pi\)
\(854\) −32.4810 −1.11148
\(855\) −3.27908 −0.112142
\(856\) −17.8523 −0.610180
\(857\) −54.7153 −1.86904 −0.934519 0.355912i \(-0.884170\pi\)
−0.934519 + 0.355912i \(0.884170\pi\)
\(858\) −5.27216 −0.179989
\(859\) −30.0969 −1.02689 −0.513446 0.858122i \(-0.671632\pi\)
−0.513446 + 0.858122i \(0.671632\pi\)
\(860\) 5.97765 0.203836
\(861\) 26.3335 0.897444
\(862\) −7.57974 −0.258167
\(863\) 30.9324 1.05295 0.526475 0.850191i \(-0.323513\pi\)
0.526475 + 0.850191i \(0.323513\pi\)
\(864\) −1.00000 −0.0340207
\(865\) −5.57046 −0.189401
\(866\) −16.0633 −0.545854
\(867\) 15.9661 0.542238
\(868\) 8.27855 0.280992
\(869\) 26.9035 0.912639
\(870\) 4.26540 0.144610
\(871\) −2.97048 −0.100651
\(872\) −0.493205 −0.0167020
\(873\) −2.57742 −0.0872325
\(874\) −24.3715 −0.824378
\(875\) −17.5644 −0.593786
\(876\) −1.34277 −0.0453680
\(877\) 32.5460 1.09900 0.549500 0.835494i \(-0.314818\pi\)
0.549500 + 0.835494i \(0.314818\pi\)
\(878\) 34.5792 1.16699
\(879\) 2.45624 0.0828469
\(880\) 3.56668 0.120233
\(881\) 7.14872 0.240847 0.120423 0.992723i \(-0.461575\pi\)
0.120423 + 0.992723i \(0.461575\pi\)
\(882\) 0.402999 0.0135697
\(883\) −7.51123 −0.252773 −0.126387 0.991981i \(-0.540338\pi\)
−0.126387 + 0.991981i \(0.540338\pi\)
\(884\) −1.01679 −0.0341985
\(885\) −9.26862 −0.311561
\(886\) 21.2435 0.713688
\(887\) 7.79271 0.261654 0.130827 0.991405i \(-0.458237\pi\)
0.130827 + 0.991405i \(0.458237\pi\)
\(888\) 1.00182 0.0336188
\(889\) −38.4321 −1.28897
\(890\) −9.39420 −0.314894
\(891\) −5.27216 −0.176624
\(892\) 3.62805 0.121476
\(893\) −41.8838 −1.40159
\(894\) −14.0749 −0.470735
\(895\) −14.4114 −0.481721
\(896\) −2.72085 −0.0908971
\(897\) −5.02811 −0.167884
\(898\) 35.5472 1.18622
\(899\) −19.1838 −0.639815
\(900\) −4.54233 −0.151411
\(901\) −2.40320 −0.0800621
\(902\) −51.0263 −1.69899
\(903\) −24.0413 −0.800045
\(904\) −10.3192 −0.343210
\(905\) −6.01415 −0.199917
\(906\) −23.4183 −0.778021
\(907\) −2.50049 −0.0830273 −0.0415136 0.999138i \(-0.513218\pi\)
−0.0415136 + 0.999138i \(0.513218\pi\)
\(908\) 12.8428 0.426203
\(909\) 8.50857 0.282211
\(910\) −1.84069 −0.0610181
\(911\) −23.9600 −0.793831 −0.396915 0.917855i \(-0.629919\pi\)
−0.396915 + 0.917855i \(0.629919\pi\)
\(912\) −4.84704 −0.160502
\(913\) 3.92372 0.129856
\(914\) 24.4777 0.809650
\(915\) 8.07610 0.266988
\(916\) 16.1697 0.534261
\(917\) 17.1238 0.565476
\(918\) −1.01679 −0.0335592
\(919\) −52.1127 −1.71904 −0.859519 0.511104i \(-0.829237\pi\)
−0.859519 + 0.511104i \(0.829237\pi\)
\(920\) 3.40158 0.112147
\(921\) 11.7261 0.386387
\(922\) −26.6751 −0.878496
\(923\) −15.6217 −0.514194
\(924\) −14.3447 −0.471907
\(925\) 4.55059 0.149622
\(926\) 7.77420 0.255476
\(927\) −1.00000 −0.0328443
\(928\) 6.30498 0.206971
\(929\) 16.1845 0.530995 0.265498 0.964112i \(-0.414464\pi\)
0.265498 + 0.964112i \(0.414464\pi\)
\(930\) −2.05838 −0.0674971
\(931\) 1.95335 0.0640185
\(932\) −3.08086 −0.100917
\(933\) 1.75340 0.0574039
\(934\) 22.4004 0.732963
\(935\) 3.62658 0.118602
\(936\) −1.00000 −0.0326860
\(937\) 12.5147 0.408837 0.204419 0.978884i \(-0.434470\pi\)
0.204419 + 0.978884i \(0.434470\pi\)
\(938\) −8.08222 −0.263894
\(939\) −21.0420 −0.686679
\(940\) 5.84581 0.190669
\(941\) −51.5353 −1.68000 −0.840002 0.542583i \(-0.817446\pi\)
−0.840002 + 0.542583i \(0.817446\pi\)
\(942\) −4.71578 −0.153648
\(943\) −48.6643 −1.58473
\(944\) −13.7006 −0.445916
\(945\) −1.84069 −0.0598775
\(946\) 46.5847 1.51460
\(947\) −42.8955 −1.39392 −0.696959 0.717111i \(-0.745464\pi\)
−0.696959 + 0.717111i \(0.745464\pi\)
\(948\) 5.10293 0.165736
\(949\) −1.34277 −0.0435881
\(950\) −22.0169 −0.714322
\(951\) −25.9164 −0.840396
\(952\) −2.76654 −0.0896640
\(953\) 13.4076 0.434314 0.217157 0.976137i \(-0.430322\pi\)
0.217157 + 0.976137i \(0.430322\pi\)
\(954\) −2.36350 −0.0765213
\(955\) 8.02692 0.259745
\(956\) 16.9163 0.547111
\(957\) 33.2409 1.07453
\(958\) −38.0641 −1.22980
\(959\) 17.4831 0.564559
\(960\) 0.676512 0.0218343
\(961\) −21.7423 −0.701366
\(962\) 1.00182 0.0322999
\(963\) −17.8523 −0.575283
\(964\) −29.6909 −0.956281
\(965\) −7.23695 −0.232966
\(966\) −13.6807 −0.440170
\(967\) 44.3002 1.42460 0.712299 0.701876i \(-0.247654\pi\)
0.712299 + 0.701876i \(0.247654\pi\)
\(968\) 16.7957 0.539835
\(969\) −4.92844 −0.158324
\(970\) 1.74366 0.0559855
\(971\) 4.94382 0.158655 0.0793274 0.996849i \(-0.474723\pi\)
0.0793274 + 0.996849i \(0.474723\pi\)
\(972\) −1.00000 −0.0320750
\(973\) −50.0363 −1.60409
\(974\) 17.7607 0.569090
\(975\) −4.54233 −0.145471
\(976\) 11.9378 0.382121
\(977\) 44.7955 1.43313 0.716567 0.697518i \(-0.245712\pi\)
0.716567 + 0.697518i \(0.245712\pi\)
\(978\) −14.3157 −0.457767
\(979\) −73.2105 −2.33982
\(980\) −0.272634 −0.00870896
\(981\) −0.493205 −0.0157468
\(982\) −31.1190 −0.993048
\(983\) 8.01746 0.255717 0.127859 0.991792i \(-0.459190\pi\)
0.127859 + 0.991792i \(0.459190\pi\)
\(984\) −9.67843 −0.308537
\(985\) 18.3627 0.585084
\(986\) 6.41086 0.204163
\(987\) −23.5111 −0.748367
\(988\) −4.84704 −0.154205
\(989\) 44.4283 1.41274
\(990\) 3.56668 0.113357
\(991\) −46.1093 −1.46471 −0.732356 0.680922i \(-0.761579\pi\)
−0.732356 + 0.680922i \(0.761579\pi\)
\(992\) −3.04264 −0.0966039
\(993\) 18.0656 0.573294
\(994\) −42.5042 −1.34815
\(995\) −10.8743 −0.344739
\(996\) 0.744233 0.0235819
\(997\) 6.11084 0.193532 0.0967662 0.995307i \(-0.469150\pi\)
0.0967662 + 0.995307i \(0.469150\pi\)
\(998\) 15.2463 0.482612
\(999\) 1.00182 0.0316961
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 8034.2.a.bc.1.7 15
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8034.2.a.bc.1.7 15 1.1 even 1 trivial