Properties

Label 8007.2.a.f.1.39
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 1.39
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.82604 q^{2} -1.00000 q^{3} +1.33443 q^{4} -0.167627 q^{5} -1.82604 q^{6} +3.32340 q^{7} -1.21535 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.82604 q^{2} -1.00000 q^{3} +1.33443 q^{4} -0.167627 q^{5} -1.82604 q^{6} +3.32340 q^{7} -1.21535 q^{8} +1.00000 q^{9} -0.306095 q^{10} -0.790492 q^{11} -1.33443 q^{12} -2.24590 q^{13} +6.06866 q^{14} +0.167627 q^{15} -4.88815 q^{16} -1.00000 q^{17} +1.82604 q^{18} +7.55949 q^{19} -0.223688 q^{20} -3.32340 q^{21} -1.44347 q^{22} +0.417165 q^{23} +1.21535 q^{24} -4.97190 q^{25} -4.10112 q^{26} -1.00000 q^{27} +4.43485 q^{28} -2.98837 q^{29} +0.306095 q^{30} -8.95148 q^{31} -6.49528 q^{32} +0.790492 q^{33} -1.82604 q^{34} -0.557092 q^{35} +1.33443 q^{36} -1.22329 q^{37} +13.8039 q^{38} +2.24590 q^{39} +0.203726 q^{40} -9.37300 q^{41} -6.06866 q^{42} -2.86920 q^{43} -1.05486 q^{44} -0.167627 q^{45} +0.761762 q^{46} +4.19886 q^{47} +4.88815 q^{48} +4.04495 q^{49} -9.07891 q^{50} +1.00000 q^{51} -2.99701 q^{52} +3.33576 q^{53} -1.82604 q^{54} +0.132508 q^{55} -4.03910 q^{56} -7.55949 q^{57} -5.45688 q^{58} +5.24784 q^{59} +0.223688 q^{60} -4.29098 q^{61} -16.3458 q^{62} +3.32340 q^{63} -2.08435 q^{64} +0.376475 q^{65} +1.44347 q^{66} -2.10530 q^{67} -1.33443 q^{68} -0.417165 q^{69} -1.01727 q^{70} +3.75354 q^{71} -1.21535 q^{72} +12.0241 q^{73} -2.23378 q^{74} +4.97190 q^{75} +10.0876 q^{76} -2.62712 q^{77} +4.10112 q^{78} -10.6687 q^{79} +0.819389 q^{80} +1.00000 q^{81} -17.1155 q^{82} -6.26459 q^{83} -4.43485 q^{84} +0.167627 q^{85} -5.23929 q^{86} +2.98837 q^{87} +0.960726 q^{88} +5.46315 q^{89} -0.306095 q^{90} -7.46402 q^{91} +0.556680 q^{92} +8.95148 q^{93} +7.66730 q^{94} -1.26718 q^{95} +6.49528 q^{96} +1.46789 q^{97} +7.38626 q^{98} -0.790492 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} + O(q^{10}) \) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} - 20q^{10} + 5q^{11} - 45q^{12} - 8q^{13} + 4q^{14} - q^{15} + 39q^{16} - 48q^{17} - q^{18} - 6q^{19} + 6q^{20} + 13q^{21} - 35q^{22} - 8q^{23} + 6q^{24} + 13q^{25} + 17q^{26} - 48q^{27} - 38q^{28} + q^{29} + 20q^{30} - 21q^{31} - 3q^{32} - 5q^{33} + q^{34} + 19q^{35} + 45q^{36} - 58q^{37} - 14q^{38} + 8q^{39} - 54q^{40} - 3q^{41} - 4q^{42} - 33q^{43} + 2q^{44} + q^{45} - 26q^{46} + 9q^{47} - 39q^{48} + 11q^{49} + 4q^{50} + 48q^{51} - 31q^{52} - 33q^{53} + q^{54} - 21q^{55} + 6q^{57} - 55q^{58} + 77q^{59} - 6q^{60} - 29q^{61} - 46q^{62} - 13q^{63} + 24q^{64} - 49q^{65} + 35q^{66} - 44q^{67} - 45q^{68} + 8q^{69} + 4q^{70} + 22q^{71} - 6q^{72} - 63q^{73} - 16q^{74} - 13q^{75} - 46q^{76} - 30q^{77} - 17q^{78} - 46q^{79} - 14q^{80} + 48q^{81} - 75q^{82} + 11q^{83} + 38q^{84} - q^{85} + 8q^{86} - q^{87} - 116q^{88} + 10q^{89} - 20q^{90} - 67q^{91} - 64q^{92} + 21q^{93} - 16q^{94} - 8q^{95} + 3q^{96} - 96q^{97} - 46q^{98} + 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.82604 1.29121 0.645604 0.763673i \(-0.276606\pi\)
0.645604 + 0.763673i \(0.276606\pi\)
\(3\) −1.00000 −0.577350
\(4\) 1.33443 0.667217
\(5\) −0.167627 −0.0749653 −0.0374826 0.999297i \(-0.511934\pi\)
−0.0374826 + 0.999297i \(0.511934\pi\)
\(6\) −1.82604 −0.745479
\(7\) 3.32340 1.25613 0.628063 0.778163i \(-0.283848\pi\)
0.628063 + 0.778163i \(0.283848\pi\)
\(8\) −1.21535 −0.429692
\(9\) 1.00000 0.333333
\(10\) −0.306095 −0.0967957
\(11\) −0.790492 −0.238342 −0.119171 0.992874i \(-0.538024\pi\)
−0.119171 + 0.992874i \(0.538024\pi\)
\(12\) −1.33443 −0.385218
\(13\) −2.24590 −0.622901 −0.311451 0.950262i \(-0.600815\pi\)
−0.311451 + 0.950262i \(0.600815\pi\)
\(14\) 6.06866 1.62192
\(15\) 0.167627 0.0432812
\(16\) −4.88815 −1.22204
\(17\) −1.00000 −0.242536
\(18\) 1.82604 0.430403
\(19\) 7.55949 1.73426 0.867132 0.498078i \(-0.165961\pi\)
0.867132 + 0.498078i \(0.165961\pi\)
\(20\) −0.223688 −0.0500181
\(21\) −3.32340 −0.725224
\(22\) −1.44347 −0.307749
\(23\) 0.417165 0.0869850 0.0434925 0.999054i \(-0.486152\pi\)
0.0434925 + 0.999054i \(0.486152\pi\)
\(24\) 1.21535 0.248083
\(25\) −4.97190 −0.994380
\(26\) −4.10112 −0.804295
\(27\) −1.00000 −0.192450
\(28\) 4.43485 0.838108
\(29\) −2.98837 −0.554925 −0.277463 0.960736i \(-0.589494\pi\)
−0.277463 + 0.960736i \(0.589494\pi\)
\(30\) 0.306095 0.0558850
\(31\) −8.95148 −1.60773 −0.803867 0.594809i \(-0.797228\pi\)
−0.803867 + 0.594809i \(0.797228\pi\)
\(32\) −6.49528 −1.14821
\(33\) 0.790492 0.137607
\(34\) −1.82604 −0.313164
\(35\) −0.557092 −0.0941658
\(36\) 1.33443 0.222406
\(37\) −1.22329 −0.201107 −0.100554 0.994932i \(-0.532061\pi\)
−0.100554 + 0.994932i \(0.532061\pi\)
\(38\) 13.8039 2.23930
\(39\) 2.24590 0.359632
\(40\) 0.203726 0.0322120
\(41\) −9.37300 −1.46382 −0.731908 0.681404i \(-0.761370\pi\)
−0.731908 + 0.681404i \(0.761370\pi\)
\(42\) −6.06866 −0.936415
\(43\) −2.86920 −0.437549 −0.218775 0.975775i \(-0.570206\pi\)
−0.218775 + 0.975775i \(0.570206\pi\)
\(44\) −1.05486 −0.159026
\(45\) −0.167627 −0.0249884
\(46\) 0.761762 0.112316
\(47\) 4.19886 0.612467 0.306233 0.951956i \(-0.400931\pi\)
0.306233 + 0.951956i \(0.400931\pi\)
\(48\) 4.88815 0.705544
\(49\) 4.04495 0.577851
\(50\) −9.07891 −1.28395
\(51\) 1.00000 0.140028
\(52\) −2.99701 −0.415610
\(53\) 3.33576 0.458202 0.229101 0.973403i \(-0.426421\pi\)
0.229101 + 0.973403i \(0.426421\pi\)
\(54\) −1.82604 −0.248493
\(55\) 0.132508 0.0178674
\(56\) −4.03910 −0.539747
\(57\) −7.55949 −1.00128
\(58\) −5.45688 −0.716524
\(59\) 5.24784 0.683210 0.341605 0.939844i \(-0.389029\pi\)
0.341605 + 0.939844i \(0.389029\pi\)
\(60\) 0.223688 0.0288780
\(61\) −4.29098 −0.549404 −0.274702 0.961529i \(-0.588579\pi\)
−0.274702 + 0.961529i \(0.588579\pi\)
\(62\) −16.3458 −2.07592
\(63\) 3.32340 0.418708
\(64\) −2.08435 −0.260543
\(65\) 0.376475 0.0466960
\(66\) 1.44347 0.177679
\(67\) −2.10530 −0.257203 −0.128602 0.991696i \(-0.541049\pi\)
−0.128602 + 0.991696i \(0.541049\pi\)
\(68\) −1.33443 −0.161824
\(69\) −0.417165 −0.0502208
\(70\) −1.01727 −0.121588
\(71\) 3.75354 0.445463 0.222731 0.974880i \(-0.428503\pi\)
0.222731 + 0.974880i \(0.428503\pi\)
\(72\) −1.21535 −0.143231
\(73\) 12.0241 1.40732 0.703658 0.710539i \(-0.251549\pi\)
0.703658 + 0.710539i \(0.251549\pi\)
\(74\) −2.23378 −0.259671
\(75\) 4.97190 0.574106
\(76\) 10.0876 1.15713
\(77\) −2.62712 −0.299388
\(78\) 4.10112 0.464360
\(79\) −10.6687 −1.20032 −0.600159 0.799880i \(-0.704896\pi\)
−0.600159 + 0.799880i \(0.704896\pi\)
\(80\) 0.819389 0.0916105
\(81\) 1.00000 0.111111
\(82\) −17.1155 −1.89009
\(83\) −6.26459 −0.687628 −0.343814 0.939038i \(-0.611719\pi\)
−0.343814 + 0.939038i \(0.611719\pi\)
\(84\) −4.43485 −0.483882
\(85\) 0.167627 0.0181817
\(86\) −5.23929 −0.564967
\(87\) 2.98837 0.320386
\(88\) 0.960726 0.102414
\(89\) 5.46315 0.579093 0.289547 0.957164i \(-0.406495\pi\)
0.289547 + 0.957164i \(0.406495\pi\)
\(90\) −0.306095 −0.0322652
\(91\) −7.46402 −0.782442
\(92\) 0.556680 0.0580379
\(93\) 8.95148 0.928225
\(94\) 7.66730 0.790822
\(95\) −1.26718 −0.130010
\(96\) 6.49528 0.662921
\(97\) 1.46789 0.149042 0.0745209 0.997219i \(-0.476257\pi\)
0.0745209 + 0.997219i \(0.476257\pi\)
\(98\) 7.38626 0.746125
\(99\) −0.790492 −0.0794474
\(100\) −6.63467 −0.663467
\(101\) −11.5861 −1.15286 −0.576432 0.817145i \(-0.695555\pi\)
−0.576432 + 0.817145i \(0.695555\pi\)
\(102\) 1.82604 0.180805
\(103\) −17.6860 −1.74266 −0.871328 0.490701i \(-0.836741\pi\)
−0.871328 + 0.490701i \(0.836741\pi\)
\(104\) 2.72956 0.267656
\(105\) 0.557092 0.0543666
\(106\) 6.09125 0.591635
\(107\) −12.8920 −1.24632 −0.623160 0.782095i \(-0.714151\pi\)
−0.623160 + 0.782095i \(0.714151\pi\)
\(108\) −1.33443 −0.128406
\(109\) 8.10349 0.776173 0.388087 0.921623i \(-0.373136\pi\)
0.388087 + 0.921623i \(0.373136\pi\)
\(110\) 0.241966 0.0230705
\(111\) 1.22329 0.116109
\(112\) −16.2453 −1.53503
\(113\) 18.4938 1.73975 0.869873 0.493276i \(-0.164201\pi\)
0.869873 + 0.493276i \(0.164201\pi\)
\(114\) −13.8039 −1.29286
\(115\) −0.0699284 −0.00652085
\(116\) −3.98778 −0.370256
\(117\) −2.24590 −0.207634
\(118\) 9.58278 0.882166
\(119\) −3.32340 −0.304655
\(120\) −0.203726 −0.0185976
\(121\) −10.3751 −0.943193
\(122\) −7.83552 −0.709395
\(123\) 9.37300 0.845135
\(124\) −11.9452 −1.07271
\(125\) 1.67156 0.149509
\(126\) 6.06866 0.540639
\(127\) 3.10262 0.275313 0.137656 0.990480i \(-0.456043\pi\)
0.137656 + 0.990480i \(0.456043\pi\)
\(128\) 9.18444 0.811798
\(129\) 2.86920 0.252619
\(130\) 0.687460 0.0602942
\(131\) −13.0950 −1.14412 −0.572058 0.820213i \(-0.693855\pi\)
−0.572058 + 0.820213i \(0.693855\pi\)
\(132\) 1.05486 0.0918137
\(133\) 25.1232 2.17845
\(134\) −3.84437 −0.332103
\(135\) 0.167627 0.0144271
\(136\) 1.21535 0.104216
\(137\) 3.91930 0.334848 0.167424 0.985885i \(-0.446455\pi\)
0.167424 + 0.985885i \(0.446455\pi\)
\(138\) −0.761762 −0.0648455
\(139\) −16.4286 −1.39345 −0.696727 0.717336i \(-0.745361\pi\)
−0.696727 + 0.717336i \(0.745361\pi\)
\(140\) −0.743403 −0.0628290
\(141\) −4.19886 −0.353608
\(142\) 6.85412 0.575185
\(143\) 1.77537 0.148464
\(144\) −4.88815 −0.407346
\(145\) 0.500932 0.0416001
\(146\) 21.9565 1.81714
\(147\) −4.04495 −0.333622
\(148\) −1.63240 −0.134182
\(149\) −21.0121 −1.72138 −0.860691 0.509128i \(-0.829968\pi\)
−0.860691 + 0.509128i \(0.829968\pi\)
\(150\) 9.07891 0.741290
\(151\) −11.2749 −0.917542 −0.458771 0.888555i \(-0.651710\pi\)
−0.458771 + 0.888555i \(0.651710\pi\)
\(152\) −9.18744 −0.745200
\(153\) −1.00000 −0.0808452
\(154\) −4.79723 −0.386572
\(155\) 1.50051 0.120524
\(156\) 2.99701 0.239953
\(157\) −1.00000 −0.0798087
\(158\) −19.4815 −1.54986
\(159\) −3.33576 −0.264543
\(160\) 1.08879 0.0860761
\(161\) 1.38641 0.109264
\(162\) 1.82604 0.143468
\(163\) 0.929838 0.0728305 0.0364153 0.999337i \(-0.488406\pi\)
0.0364153 + 0.999337i \(0.488406\pi\)
\(164\) −12.5076 −0.976683
\(165\) −0.132508 −0.0103157
\(166\) −11.4394 −0.887871
\(167\) 6.00705 0.464839 0.232420 0.972616i \(-0.425336\pi\)
0.232420 + 0.972616i \(0.425336\pi\)
\(168\) 4.03910 0.311623
\(169\) −7.95592 −0.611994
\(170\) 0.306095 0.0234764
\(171\) 7.55949 0.578088
\(172\) −3.82876 −0.291940
\(173\) 13.1729 1.00151 0.500757 0.865588i \(-0.333055\pi\)
0.500757 + 0.865588i \(0.333055\pi\)
\(174\) 5.45688 0.413685
\(175\) −16.5236 −1.24907
\(176\) 3.86405 0.291263
\(177\) −5.24784 −0.394452
\(178\) 9.97595 0.747729
\(179\) 3.81256 0.284964 0.142482 0.989797i \(-0.454492\pi\)
0.142482 + 0.989797i \(0.454492\pi\)
\(180\) −0.223688 −0.0166727
\(181\) −3.28420 −0.244112 −0.122056 0.992523i \(-0.538949\pi\)
−0.122056 + 0.992523i \(0.538949\pi\)
\(182\) −13.6296 −1.01030
\(183\) 4.29098 0.317199
\(184\) −0.507003 −0.0373767
\(185\) 0.205057 0.0150761
\(186\) 16.3458 1.19853
\(187\) 0.790492 0.0578065
\(188\) 5.60310 0.408648
\(189\) −3.32340 −0.241741
\(190\) −2.31392 −0.167869
\(191\) 16.1713 1.17011 0.585056 0.810993i \(-0.301072\pi\)
0.585056 + 0.810993i \(0.301072\pi\)
\(192\) 2.08435 0.150425
\(193\) 15.8666 1.14210 0.571050 0.820915i \(-0.306536\pi\)
0.571050 + 0.820915i \(0.306536\pi\)
\(194\) 2.68043 0.192444
\(195\) −0.376475 −0.0269599
\(196\) 5.39773 0.385552
\(197\) 15.0792 1.07435 0.537173 0.843472i \(-0.319492\pi\)
0.537173 + 0.843472i \(0.319492\pi\)
\(198\) −1.44347 −0.102583
\(199\) −17.3826 −1.23222 −0.616109 0.787661i \(-0.711292\pi\)
−0.616109 + 0.787661i \(0.711292\pi\)
\(200\) 6.04261 0.427277
\(201\) 2.10530 0.148496
\(202\) −21.1568 −1.48859
\(203\) −9.93152 −0.697056
\(204\) 1.33443 0.0934291
\(205\) 1.57117 0.109735
\(206\) −32.2955 −2.25013
\(207\) 0.417165 0.0289950
\(208\) 10.9783 0.761210
\(209\) −5.97571 −0.413349
\(210\) 1.01727 0.0701986
\(211\) −2.15143 −0.148111 −0.0740553 0.997254i \(-0.523594\pi\)
−0.0740553 + 0.997254i \(0.523594\pi\)
\(212\) 4.45136 0.305720
\(213\) −3.75354 −0.257188
\(214\) −23.5414 −1.60926
\(215\) 0.480957 0.0328010
\(216\) 1.21535 0.0826942
\(217\) −29.7493 −2.01951
\(218\) 14.7973 1.00220
\(219\) −12.0241 −0.812514
\(220\) 0.176823 0.0119214
\(221\) 2.24590 0.151076
\(222\) 2.23378 0.149921
\(223\) −6.40349 −0.428809 −0.214405 0.976745i \(-0.568781\pi\)
−0.214405 + 0.976745i \(0.568781\pi\)
\(224\) −21.5864 −1.44230
\(225\) −4.97190 −0.331460
\(226\) 33.7704 2.24637
\(227\) −10.0649 −0.668032 −0.334016 0.942567i \(-0.608404\pi\)
−0.334016 + 0.942567i \(0.608404\pi\)
\(228\) −10.0876 −0.668070
\(229\) 2.39902 0.158532 0.0792658 0.996854i \(-0.474742\pi\)
0.0792658 + 0.996854i \(0.474742\pi\)
\(230\) −0.127692 −0.00841978
\(231\) 2.62712 0.172852
\(232\) 3.63192 0.238447
\(233\) −18.1937 −1.19191 −0.595953 0.803019i \(-0.703226\pi\)
−0.595953 + 0.803019i \(0.703226\pi\)
\(234\) −4.10112 −0.268098
\(235\) −0.703844 −0.0459137
\(236\) 7.00289 0.455849
\(237\) 10.6687 0.693004
\(238\) −6.06866 −0.393373
\(239\) −7.50963 −0.485758 −0.242879 0.970057i \(-0.578092\pi\)
−0.242879 + 0.970057i \(0.578092\pi\)
\(240\) −0.819389 −0.0528913
\(241\) −15.4902 −0.997809 −0.498904 0.866657i \(-0.666264\pi\)
−0.498904 + 0.866657i \(0.666264\pi\)
\(242\) −18.9454 −1.21786
\(243\) −1.00000 −0.0641500
\(244\) −5.72603 −0.366572
\(245\) −0.678045 −0.0433187
\(246\) 17.1155 1.09124
\(247\) −16.9779 −1.08028
\(248\) 10.8792 0.690830
\(249\) 6.26459 0.397002
\(250\) 3.05235 0.193047
\(251\) −4.47396 −0.282394 −0.141197 0.989982i \(-0.545095\pi\)
−0.141197 + 0.989982i \(0.545095\pi\)
\(252\) 4.43485 0.279369
\(253\) −0.329766 −0.0207322
\(254\) 5.66551 0.355486
\(255\) −0.167627 −0.0104972
\(256\) 20.9399 1.30874
\(257\) 12.9682 0.808933 0.404467 0.914553i \(-0.367457\pi\)
0.404467 + 0.914553i \(0.367457\pi\)
\(258\) 5.23929 0.326184
\(259\) −4.06547 −0.252616
\(260\) 0.502381 0.0311564
\(261\) −2.98837 −0.184975
\(262\) −23.9121 −1.47729
\(263\) −6.98264 −0.430568 −0.215284 0.976551i \(-0.569068\pi\)
−0.215284 + 0.976551i \(0.569068\pi\)
\(264\) −0.960726 −0.0591286
\(265\) −0.559166 −0.0343493
\(266\) 45.8760 2.81284
\(267\) −5.46315 −0.334340
\(268\) −2.80938 −0.171610
\(269\) −16.6172 −1.01317 −0.506583 0.862191i \(-0.669092\pi\)
−0.506583 + 0.862191i \(0.669092\pi\)
\(270\) 0.306095 0.0186283
\(271\) −4.42732 −0.268940 −0.134470 0.990918i \(-0.542933\pi\)
−0.134470 + 0.990918i \(0.542933\pi\)
\(272\) 4.88815 0.296388
\(273\) 7.46402 0.451743
\(274\) 7.15680 0.432358
\(275\) 3.93025 0.237003
\(276\) −0.556680 −0.0335082
\(277\) 7.02563 0.422129 0.211065 0.977472i \(-0.432307\pi\)
0.211065 + 0.977472i \(0.432307\pi\)
\(278\) −29.9993 −1.79924
\(279\) −8.95148 −0.535911
\(280\) 0.677063 0.0404623
\(281\) 10.4169 0.621419 0.310709 0.950505i \(-0.399433\pi\)
0.310709 + 0.950505i \(0.399433\pi\)
\(282\) −7.66730 −0.456581
\(283\) −11.8295 −0.703193 −0.351596 0.936152i \(-0.614361\pi\)
−0.351596 + 0.936152i \(0.614361\pi\)
\(284\) 5.00885 0.297220
\(285\) 1.26718 0.0750611
\(286\) 3.24190 0.191698
\(287\) −31.1502 −1.83874
\(288\) −6.49528 −0.382738
\(289\) 1.00000 0.0588235
\(290\) 0.914724 0.0537144
\(291\) −1.46789 −0.0860494
\(292\) 16.0454 0.938985
\(293\) 1.93768 0.113201 0.0566003 0.998397i \(-0.481974\pi\)
0.0566003 + 0.998397i \(0.481974\pi\)
\(294\) −7.38626 −0.430776
\(295\) −0.879682 −0.0512170
\(296\) 1.48673 0.0864141
\(297\) 0.790492 0.0458690
\(298\) −38.3691 −2.22266
\(299\) −0.936913 −0.0541831
\(300\) 6.63467 0.383053
\(301\) −9.53549 −0.549616
\(302\) −20.5885 −1.18474
\(303\) 11.5861 0.665606
\(304\) −36.9519 −2.11934
\(305\) 0.719287 0.0411862
\(306\) −1.82604 −0.104388
\(307\) −15.8996 −0.907436 −0.453718 0.891145i \(-0.649903\pi\)
−0.453718 + 0.891145i \(0.649903\pi\)
\(308\) −3.50571 −0.199757
\(309\) 17.6860 1.00612
\(310\) 2.74000 0.155622
\(311\) −10.4760 −0.594042 −0.297021 0.954871i \(-0.595993\pi\)
−0.297021 + 0.954871i \(0.595993\pi\)
\(312\) −2.72956 −0.154531
\(313\) −18.9373 −1.07040 −0.535201 0.844725i \(-0.679764\pi\)
−0.535201 + 0.844725i \(0.679764\pi\)
\(314\) −1.82604 −0.103050
\(315\) −0.557092 −0.0313886
\(316\) −14.2366 −0.800873
\(317\) −10.4507 −0.586970 −0.293485 0.955964i \(-0.594815\pi\)
−0.293485 + 0.955964i \(0.594815\pi\)
\(318\) −6.09125 −0.341580
\(319\) 2.36228 0.132262
\(320\) 0.349394 0.0195317
\(321\) 12.8920 0.719563
\(322\) 2.53164 0.141083
\(323\) −7.55949 −0.420621
\(324\) 1.33443 0.0741352
\(325\) 11.1664 0.619401
\(326\) 1.69792 0.0940393
\(327\) −8.10349 −0.448124
\(328\) 11.3915 0.628990
\(329\) 13.9545 0.769335
\(330\) −0.241966 −0.0133198
\(331\) −15.2077 −0.835889 −0.417945 0.908473i \(-0.637249\pi\)
−0.417945 + 0.908473i \(0.637249\pi\)
\(332\) −8.35968 −0.458797
\(333\) −1.22329 −0.0670357
\(334\) 10.9691 0.600204
\(335\) 0.352906 0.0192813
\(336\) 16.2453 0.886252
\(337\) −33.4952 −1.82460 −0.912301 0.409521i \(-0.865696\pi\)
−0.912301 + 0.409521i \(0.865696\pi\)
\(338\) −14.5279 −0.790211
\(339\) −18.4938 −1.00444
\(340\) 0.223688 0.0121312
\(341\) 7.07607 0.383191
\(342\) 13.8039 0.746432
\(343\) −9.82078 −0.530272
\(344\) 3.48709 0.188011
\(345\) 0.0699284 0.00376482
\(346\) 24.0542 1.29316
\(347\) 1.36704 0.0733868 0.0366934 0.999327i \(-0.488318\pi\)
0.0366934 + 0.999327i \(0.488318\pi\)
\(348\) 3.98778 0.213767
\(349\) −1.63934 −0.0877518 −0.0438759 0.999037i \(-0.513971\pi\)
−0.0438759 + 0.999037i \(0.513971\pi\)
\(350\) −30.1728 −1.61280
\(351\) 2.24590 0.119877
\(352\) 5.13446 0.273668
\(353\) 21.5686 1.14798 0.573990 0.818862i \(-0.305395\pi\)
0.573990 + 0.818862i \(0.305395\pi\)
\(354\) −9.58278 −0.509319
\(355\) −0.629196 −0.0333942
\(356\) 7.29022 0.386381
\(357\) 3.32340 0.175893
\(358\) 6.96190 0.367948
\(359\) 29.8507 1.57546 0.787730 0.616020i \(-0.211256\pi\)
0.787730 + 0.616020i \(0.211256\pi\)
\(360\) 0.203726 0.0107373
\(361\) 38.1458 2.00767
\(362\) −5.99708 −0.315200
\(363\) 10.3751 0.544553
\(364\) −9.96025 −0.522059
\(365\) −2.01557 −0.105500
\(366\) 7.83552 0.409569
\(367\) −10.7930 −0.563388 −0.281694 0.959504i \(-0.590896\pi\)
−0.281694 + 0.959504i \(0.590896\pi\)
\(368\) −2.03917 −0.106299
\(369\) −9.37300 −0.487939
\(370\) 0.374442 0.0194663
\(371\) 11.0861 0.575560
\(372\) 11.9452 0.619328
\(373\) −2.07987 −0.107692 −0.0538458 0.998549i \(-0.517148\pi\)
−0.0538458 + 0.998549i \(0.517148\pi\)
\(374\) 1.44347 0.0746402
\(375\) −1.67156 −0.0863192
\(376\) −5.10310 −0.263172
\(377\) 6.71158 0.345664
\(378\) −6.06866 −0.312138
\(379\) 31.6435 1.62542 0.812708 0.582671i \(-0.197992\pi\)
0.812708 + 0.582671i \(0.197992\pi\)
\(380\) −1.69096 −0.0867446
\(381\) −3.10262 −0.158952
\(382\) 29.5295 1.51086
\(383\) 14.9047 0.761592 0.380796 0.924659i \(-0.375650\pi\)
0.380796 + 0.924659i \(0.375650\pi\)
\(384\) −9.18444 −0.468692
\(385\) 0.440377 0.0224437
\(386\) 28.9731 1.47469
\(387\) −2.86920 −0.145850
\(388\) 1.95881 0.0994433
\(389\) −17.3086 −0.877583 −0.438792 0.898589i \(-0.644593\pi\)
−0.438792 + 0.898589i \(0.644593\pi\)
\(390\) −0.687460 −0.0348109
\(391\) −0.417165 −0.0210970
\(392\) −4.91605 −0.248298
\(393\) 13.0950 0.660556
\(394\) 27.5352 1.38720
\(395\) 1.78836 0.0899822
\(396\) −1.05486 −0.0530087
\(397\) 30.4420 1.52784 0.763921 0.645310i \(-0.223272\pi\)
0.763921 + 0.645310i \(0.223272\pi\)
\(398\) −31.7413 −1.59105
\(399\) −25.1232 −1.25773
\(400\) 24.3034 1.21517
\(401\) −31.4646 −1.57127 −0.785633 0.618693i \(-0.787663\pi\)
−0.785633 + 0.618693i \(0.787663\pi\)
\(402\) 3.84437 0.191740
\(403\) 20.1042 1.00146
\(404\) −15.4609 −0.769210
\(405\) −0.167627 −0.00832948
\(406\) −18.1354 −0.900044
\(407\) 0.966999 0.0479324
\(408\) −1.21535 −0.0601689
\(409\) −25.1796 −1.24505 −0.622527 0.782599i \(-0.713894\pi\)
−0.622527 + 0.782599i \(0.713894\pi\)
\(410\) 2.86903 0.141691
\(411\) −3.91930 −0.193325
\(412\) −23.6008 −1.16273
\(413\) 17.4406 0.858198
\(414\) 0.761762 0.0374386
\(415\) 1.05012 0.0515482
\(416\) 14.5878 0.715224
\(417\) 16.4286 0.804511
\(418\) −10.9119 −0.533719
\(419\) 39.4605 1.92777 0.963886 0.266315i \(-0.0858060\pi\)
0.963886 + 0.266315i \(0.0858060\pi\)
\(420\) 0.743403 0.0362743
\(421\) 3.15855 0.153938 0.0769692 0.997033i \(-0.475476\pi\)
0.0769692 + 0.997033i \(0.475476\pi\)
\(422\) −3.92861 −0.191242
\(423\) 4.19886 0.204156
\(424\) −4.05413 −0.196886
\(425\) 4.97190 0.241173
\(426\) −6.85412 −0.332083
\(427\) −14.2606 −0.690120
\(428\) −17.2036 −0.831565
\(429\) −1.77537 −0.0857156
\(430\) 0.878248 0.0423529
\(431\) 8.80135 0.423946 0.211973 0.977276i \(-0.432011\pi\)
0.211973 + 0.977276i \(0.432011\pi\)
\(432\) 4.88815 0.235181
\(433\) 12.8301 0.616573 0.308287 0.951293i \(-0.400244\pi\)
0.308287 + 0.951293i \(0.400244\pi\)
\(434\) −54.3235 −2.60761
\(435\) −0.500932 −0.0240179
\(436\) 10.8136 0.517876
\(437\) 3.15356 0.150855
\(438\) −21.9565 −1.04912
\(439\) −21.6115 −1.03146 −0.515731 0.856750i \(-0.672480\pi\)
−0.515731 + 0.856750i \(0.672480\pi\)
\(440\) −0.161044 −0.00767748
\(441\) 4.04495 0.192617
\(442\) 4.10112 0.195070
\(443\) −38.4004 −1.82446 −0.912230 0.409679i \(-0.865641\pi\)
−0.912230 + 0.409679i \(0.865641\pi\)
\(444\) 1.63240 0.0774701
\(445\) −0.915774 −0.0434119
\(446\) −11.6930 −0.553682
\(447\) 21.0121 0.993840
\(448\) −6.92711 −0.327275
\(449\) 22.9394 1.08258 0.541289 0.840837i \(-0.317936\pi\)
0.541289 + 0.840837i \(0.317936\pi\)
\(450\) −9.07891 −0.427984
\(451\) 7.40928 0.348889
\(452\) 24.6787 1.16079
\(453\) 11.2749 0.529743
\(454\) −18.3790 −0.862568
\(455\) 1.25118 0.0586560
\(456\) 9.18744 0.430241
\(457\) −29.3028 −1.37073 −0.685364 0.728201i \(-0.740357\pi\)
−0.685364 + 0.728201i \(0.740357\pi\)
\(458\) 4.38071 0.204697
\(459\) 1.00000 0.0466760
\(460\) −0.0933148 −0.00435082
\(461\) 36.5452 1.70208 0.851040 0.525100i \(-0.175972\pi\)
0.851040 + 0.525100i \(0.175972\pi\)
\(462\) 4.79723 0.223187
\(463\) 26.5273 1.23283 0.616413 0.787423i \(-0.288585\pi\)
0.616413 + 0.787423i \(0.288585\pi\)
\(464\) 14.6076 0.678140
\(465\) −1.50051 −0.0695847
\(466\) −33.2224 −1.53900
\(467\) 16.4222 0.759927 0.379964 0.925001i \(-0.375937\pi\)
0.379964 + 0.925001i \(0.375937\pi\)
\(468\) −2.99701 −0.138537
\(469\) −6.99674 −0.323079
\(470\) −1.28525 −0.0592842
\(471\) 1.00000 0.0460776
\(472\) −6.37797 −0.293570
\(473\) 2.26808 0.104286
\(474\) 19.4815 0.894813
\(475\) −37.5850 −1.72452
\(476\) −4.43485 −0.203271
\(477\) 3.33576 0.152734
\(478\) −13.7129 −0.627214
\(479\) 27.1235 1.23930 0.619652 0.784877i \(-0.287274\pi\)
0.619652 + 0.784877i \(0.287274\pi\)
\(480\) −1.08879 −0.0496961
\(481\) 2.74739 0.125270
\(482\) −28.2857 −1.28838
\(483\) −1.38641 −0.0630836
\(484\) −13.8449 −0.629314
\(485\) −0.246059 −0.0111730
\(486\) −1.82604 −0.0828310
\(487\) −27.7682 −1.25830 −0.629149 0.777285i \(-0.716597\pi\)
−0.629149 + 0.777285i \(0.716597\pi\)
\(488\) 5.21506 0.236075
\(489\) −0.929838 −0.0420487
\(490\) −1.23814 −0.0559335
\(491\) −0.640190 −0.0288914 −0.0144457 0.999896i \(-0.504598\pi\)
−0.0144457 + 0.999896i \(0.504598\pi\)
\(492\) 12.5076 0.563888
\(493\) 2.98837 0.134589
\(494\) −31.0023 −1.39486
\(495\) 0.132508 0.00595580
\(496\) 43.7562 1.96471
\(497\) 12.4745 0.559557
\(498\) 11.4394 0.512612
\(499\) −16.2768 −0.728650 −0.364325 0.931272i \(-0.618700\pi\)
−0.364325 + 0.931272i \(0.618700\pi\)
\(500\) 2.23059 0.0997551
\(501\) −6.00705 −0.268375
\(502\) −8.16965 −0.364629
\(503\) 11.2630 0.502191 0.251095 0.967962i \(-0.419209\pi\)
0.251095 + 0.967962i \(0.419209\pi\)
\(504\) −4.03910 −0.179916
\(505\) 1.94215 0.0864247
\(506\) −0.602167 −0.0267696
\(507\) 7.95592 0.353335
\(508\) 4.14024 0.183693
\(509\) −6.48398 −0.287397 −0.143699 0.989621i \(-0.545900\pi\)
−0.143699 + 0.989621i \(0.545900\pi\)
\(510\) −0.306095 −0.0135541
\(511\) 39.9609 1.76776
\(512\) 19.8683 0.878061
\(513\) −7.55949 −0.333759
\(514\) 23.6805 1.04450
\(515\) 2.96466 0.130639
\(516\) 3.82876 0.168552
\(517\) −3.31917 −0.145977
\(518\) −7.42372 −0.326180
\(519\) −13.1729 −0.578225
\(520\) −0.457550 −0.0200649
\(521\) −35.6849 −1.56338 −0.781691 0.623666i \(-0.785643\pi\)
−0.781691 + 0.623666i \(0.785643\pi\)
\(522\) −5.45688 −0.238841
\(523\) 9.54047 0.417176 0.208588 0.978004i \(-0.433113\pi\)
0.208588 + 0.978004i \(0.433113\pi\)
\(524\) −17.4744 −0.763374
\(525\) 16.5236 0.721149
\(526\) −12.7506 −0.555953
\(527\) 8.95148 0.389933
\(528\) −3.86405 −0.168161
\(529\) −22.8260 −0.992434
\(530\) −1.02106 −0.0443520
\(531\) 5.24784 0.227737
\(532\) 33.5252 1.45350
\(533\) 21.0508 0.911813
\(534\) −9.97595 −0.431702
\(535\) 2.16106 0.0934307
\(536\) 2.55868 0.110518
\(537\) −3.81256 −0.164524
\(538\) −30.3437 −1.30821
\(539\) −3.19750 −0.137726
\(540\) 0.223688 0.00962599
\(541\) 9.65625 0.415155 0.207577 0.978219i \(-0.433442\pi\)
0.207577 + 0.978219i \(0.433442\pi\)
\(542\) −8.08447 −0.347258
\(543\) 3.28420 0.140938
\(544\) 6.49528 0.278483
\(545\) −1.35837 −0.0581860
\(546\) 13.6296 0.583294
\(547\) 37.9903 1.62435 0.812173 0.583416i \(-0.198284\pi\)
0.812173 + 0.583416i \(0.198284\pi\)
\(548\) 5.23004 0.223416
\(549\) −4.29098 −0.183135
\(550\) 7.17680 0.306020
\(551\) −22.5905 −0.962388
\(552\) 0.507003 0.0215795
\(553\) −35.4562 −1.50775
\(554\) 12.8291 0.545057
\(555\) −0.205057 −0.00870417
\(556\) −21.9229 −0.929737
\(557\) −45.7237 −1.93738 −0.968688 0.248282i \(-0.920134\pi\)
−0.968688 + 0.248282i \(0.920134\pi\)
\(558\) −16.3458 −0.691973
\(559\) 6.44395 0.272550
\(560\) 2.72315 0.115074
\(561\) −0.790492 −0.0333746
\(562\) 19.0217 0.802381
\(563\) 19.1959 0.809010 0.404505 0.914536i \(-0.367444\pi\)
0.404505 + 0.914536i \(0.367444\pi\)
\(564\) −5.60310 −0.235933
\(565\) −3.10006 −0.130421
\(566\) −21.6012 −0.907968
\(567\) 3.32340 0.139569
\(568\) −4.56187 −0.191412
\(569\) 46.7144 1.95837 0.979184 0.202972i \(-0.0650602\pi\)
0.979184 + 0.202972i \(0.0650602\pi\)
\(570\) 2.31392 0.0969195
\(571\) −10.9140 −0.456736 −0.228368 0.973575i \(-0.573339\pi\)
−0.228368 + 0.973575i \(0.573339\pi\)
\(572\) 2.36911 0.0990575
\(573\) −16.1713 −0.675565
\(574\) −56.8815 −2.37419
\(575\) −2.07410 −0.0864961
\(576\) −2.08435 −0.0868478
\(577\) −13.3027 −0.553800 −0.276900 0.960899i \(-0.589307\pi\)
−0.276900 + 0.960899i \(0.589307\pi\)
\(578\) 1.82604 0.0759534
\(579\) −15.8666 −0.659392
\(580\) 0.668461 0.0277563
\(581\) −20.8197 −0.863747
\(582\) −2.68043 −0.111108
\(583\) −2.63689 −0.109209
\(584\) −14.6135 −0.604712
\(585\) 0.376475 0.0155653
\(586\) 3.53829 0.146166
\(587\) 20.2978 0.837779 0.418889 0.908037i \(-0.362420\pi\)
0.418889 + 0.908037i \(0.362420\pi\)
\(588\) −5.39773 −0.222598
\(589\) −67.6686 −2.78824
\(590\) −1.60634 −0.0661318
\(591\) −15.0792 −0.620274
\(592\) 5.97962 0.245761
\(593\) 18.9889 0.779782 0.389891 0.920861i \(-0.372513\pi\)
0.389891 + 0.920861i \(0.372513\pi\)
\(594\) 1.44347 0.0592264
\(595\) 0.557092 0.0228386
\(596\) −28.0393 −1.14853
\(597\) 17.3826 0.711422
\(598\) −1.71084 −0.0699616
\(599\) 29.0150 1.18552 0.592761 0.805379i \(-0.298038\pi\)
0.592761 + 0.805379i \(0.298038\pi\)
\(600\) −6.04261 −0.246689
\(601\) 40.1606 1.63818 0.819092 0.573661i \(-0.194477\pi\)
0.819092 + 0.573661i \(0.194477\pi\)
\(602\) −17.4122 −0.709669
\(603\) −2.10530 −0.0857344
\(604\) −15.0457 −0.612199
\(605\) 1.73916 0.0707067
\(606\) 21.1568 0.859436
\(607\) 24.9201 1.01148 0.505739 0.862687i \(-0.331220\pi\)
0.505739 + 0.862687i \(0.331220\pi\)
\(608\) −49.1009 −1.99131
\(609\) 9.93152 0.402445
\(610\) 1.31345 0.0531800
\(611\) −9.43024 −0.381507
\(612\) −1.33443 −0.0539413
\(613\) 18.3843 0.742537 0.371268 0.928526i \(-0.378923\pi\)
0.371268 + 0.928526i \(0.378923\pi\)
\(614\) −29.0333 −1.17169
\(615\) −1.57117 −0.0633557
\(616\) 3.19287 0.128645
\(617\) −24.2759 −0.977312 −0.488656 0.872476i \(-0.662513\pi\)
−0.488656 + 0.872476i \(0.662513\pi\)
\(618\) 32.2955 1.29911
\(619\) −13.4919 −0.542285 −0.271143 0.962539i \(-0.587402\pi\)
−0.271143 + 0.962539i \(0.587402\pi\)
\(620\) 2.00234 0.0804158
\(621\) −0.417165 −0.0167403
\(622\) −19.1297 −0.767031
\(623\) 18.1562 0.727413
\(624\) −10.9783 −0.439485
\(625\) 24.5793 0.983172
\(626\) −34.5804 −1.38211
\(627\) 5.97571 0.238647
\(628\) −1.33443 −0.0532497
\(629\) 1.22329 0.0487757
\(630\) −1.01727 −0.0405292
\(631\) 2.20017 0.0875873 0.0437937 0.999041i \(-0.486056\pi\)
0.0437937 + 0.999041i \(0.486056\pi\)
\(632\) 12.9662 0.515767
\(633\) 2.15143 0.0855117
\(634\) −19.0834 −0.757900
\(635\) −0.520084 −0.0206389
\(636\) −4.45136 −0.176508
\(637\) −9.08458 −0.359944
\(638\) 4.31362 0.170778
\(639\) 3.75354 0.148488
\(640\) −1.53956 −0.0608566
\(641\) −24.6827 −0.974908 −0.487454 0.873149i \(-0.662074\pi\)
−0.487454 + 0.873149i \(0.662074\pi\)
\(642\) 23.5414 0.929105
\(643\) 12.4848 0.492352 0.246176 0.969225i \(-0.420826\pi\)
0.246176 + 0.969225i \(0.420826\pi\)
\(644\) 1.85007 0.0729028
\(645\) −0.480957 −0.0189377
\(646\) −13.8039 −0.543109
\(647\) −25.6869 −1.00985 −0.504927 0.863162i \(-0.668481\pi\)
−0.504927 + 0.863162i \(0.668481\pi\)
\(648\) −1.21535 −0.0477435
\(649\) −4.14837 −0.162838
\(650\) 20.3903 0.799775
\(651\) 29.7493 1.16597
\(652\) 1.24081 0.0485938
\(653\) 4.38199 0.171480 0.0857402 0.996318i \(-0.472674\pi\)
0.0857402 + 0.996318i \(0.472674\pi\)
\(654\) −14.7973 −0.578621
\(655\) 2.19508 0.0857690
\(656\) 45.8166 1.78884
\(657\) 12.0241 0.469105
\(658\) 25.4815 0.993371
\(659\) 29.0589 1.13197 0.565986 0.824415i \(-0.308496\pi\)
0.565986 + 0.824415i \(0.308496\pi\)
\(660\) −0.176823 −0.00688284
\(661\) −7.59455 −0.295394 −0.147697 0.989033i \(-0.547186\pi\)
−0.147697 + 0.989033i \(0.547186\pi\)
\(662\) −27.7699 −1.07931
\(663\) −2.24590 −0.0872237
\(664\) 7.61369 0.295468
\(665\) −4.21133 −0.163308
\(666\) −2.23378 −0.0865571
\(667\) −1.24664 −0.0482702
\(668\) 8.01601 0.310149
\(669\) 6.40349 0.247573
\(670\) 0.644421 0.0248962
\(671\) 3.39199 0.130946
\(672\) 21.5864 0.832712
\(673\) −49.2062 −1.89676 −0.948380 0.317135i \(-0.897279\pi\)
−0.948380 + 0.317135i \(0.897279\pi\)
\(674\) −61.1637 −2.35594
\(675\) 4.97190 0.191369
\(676\) −10.6166 −0.408333
\(677\) 33.6580 1.29358 0.646791 0.762667i \(-0.276110\pi\)
0.646791 + 0.762667i \(0.276110\pi\)
\(678\) −33.7704 −1.29694
\(679\) 4.87839 0.187215
\(680\) −0.203726 −0.00781255
\(681\) 10.0649 0.385688
\(682\) 12.9212 0.494779
\(683\) −15.4901 −0.592714 −0.296357 0.955077i \(-0.595772\pi\)
−0.296357 + 0.955077i \(0.595772\pi\)
\(684\) 10.0876 0.385710
\(685\) −0.656982 −0.0251020
\(686\) −17.9332 −0.684692
\(687\) −2.39902 −0.0915283
\(688\) 14.0251 0.534702
\(689\) −7.49180 −0.285415
\(690\) 0.127692 0.00486116
\(691\) 50.9101 1.93671 0.968356 0.249571i \(-0.0802896\pi\)
0.968356 + 0.249571i \(0.0802896\pi\)
\(692\) 17.5783 0.668227
\(693\) −2.62712 −0.0997959
\(694\) 2.49628 0.0947576
\(695\) 2.75388 0.104461
\(696\) −3.63192 −0.137667
\(697\) 9.37300 0.355028
\(698\) −2.99350 −0.113306
\(699\) 18.1937 0.688148
\(700\) −22.0496 −0.833398
\(701\) 6.08252 0.229733 0.114867 0.993381i \(-0.463356\pi\)
0.114867 + 0.993381i \(0.463356\pi\)
\(702\) 4.10112 0.154787
\(703\) −9.24742 −0.348773
\(704\) 1.64766 0.0620985
\(705\) 0.703844 0.0265083
\(706\) 39.3852 1.48228
\(707\) −38.5053 −1.44814
\(708\) −7.00289 −0.263185
\(709\) 15.5988 0.585825 0.292912 0.956139i \(-0.405376\pi\)
0.292912 + 0.956139i \(0.405376\pi\)
\(710\) −1.14894 −0.0431189
\(711\) −10.6687 −0.400106
\(712\) −6.63966 −0.248832
\(713\) −3.73425 −0.139849
\(714\) 6.06866 0.227114
\(715\) −0.297600 −0.0111296
\(716\) 5.08761 0.190133
\(717\) 7.50963 0.280452
\(718\) 54.5087 2.03425
\(719\) −6.88361 −0.256715 −0.128358 0.991728i \(-0.540971\pi\)
−0.128358 + 0.991728i \(0.540971\pi\)
\(720\) 0.819389 0.0305368
\(721\) −58.7777 −2.18899
\(722\) 69.6559 2.59233
\(723\) 15.4902 0.576085
\(724\) −4.38254 −0.162876
\(725\) 14.8579 0.551807
\(726\) 18.9454 0.703131
\(727\) 33.4014 1.23879 0.619394 0.785080i \(-0.287378\pi\)
0.619394 + 0.785080i \(0.287378\pi\)
\(728\) 9.07142 0.336209
\(729\) 1.00000 0.0370370
\(730\) −3.68052 −0.136222
\(731\) 2.86920 0.106121
\(732\) 5.72603 0.211640
\(733\) 46.3072 1.71040 0.855198 0.518302i \(-0.173436\pi\)
0.855198 + 0.518302i \(0.173436\pi\)
\(734\) −19.7084 −0.727450
\(735\) 0.678045 0.0250101
\(736\) −2.70960 −0.0998773
\(737\) 1.66422 0.0613024
\(738\) −17.1155 −0.630030
\(739\) −16.4868 −0.606478 −0.303239 0.952915i \(-0.598068\pi\)
−0.303239 + 0.952915i \(0.598068\pi\)
\(740\) 0.273634 0.0100590
\(741\) 16.9779 0.623698
\(742\) 20.2436 0.743167
\(743\) −42.1914 −1.54785 −0.773926 0.633276i \(-0.781710\pi\)
−0.773926 + 0.633276i \(0.781710\pi\)
\(744\) −10.8792 −0.398851
\(745\) 3.52221 0.129044
\(746\) −3.79793 −0.139052
\(747\) −6.26459 −0.229209
\(748\) 1.05486 0.0385695
\(749\) −42.8453 −1.56553
\(750\) −3.05235 −0.111456
\(751\) 27.8285 1.01548 0.507738 0.861512i \(-0.330482\pi\)
0.507738 + 0.861512i \(0.330482\pi\)
\(752\) −20.5247 −0.748458
\(753\) 4.47396 0.163040
\(754\) 12.2556 0.446324
\(755\) 1.88999 0.0687838
\(756\) −4.43485 −0.161294
\(757\) −11.3376 −0.412072 −0.206036 0.978544i \(-0.566056\pi\)
−0.206036 + 0.978544i \(0.566056\pi\)
\(758\) 57.7823 2.09875
\(759\) 0.329766 0.0119697
\(760\) 1.54007 0.0558641
\(761\) −14.8333 −0.537706 −0.268853 0.963181i \(-0.586645\pi\)
−0.268853 + 0.963181i \(0.586645\pi\)
\(762\) −5.66551 −0.205240
\(763\) 26.9311 0.974971
\(764\) 21.5795 0.780719
\(765\) 0.167627 0.00606058
\(766\) 27.2165 0.983374
\(767\) −11.7861 −0.425573
\(768\) −20.9399 −0.755603
\(769\) −45.3793 −1.63642 −0.818210 0.574920i \(-0.805033\pi\)
−0.818210 + 0.574920i \(0.805033\pi\)
\(770\) 0.804147 0.0289795
\(771\) −12.9682 −0.467038
\(772\) 21.1729 0.762029
\(773\) −42.4650 −1.52736 −0.763680 0.645595i \(-0.776609\pi\)
−0.763680 + 0.645595i \(0.776609\pi\)
\(774\) −5.23929 −0.188322
\(775\) 44.5059 1.59870
\(776\) −1.78401 −0.0640421
\(777\) 4.06547 0.145848
\(778\) −31.6063 −1.13314
\(779\) −70.8550 −2.53864
\(780\) −0.502381 −0.0179881
\(781\) −2.96714 −0.106173
\(782\) −0.761762 −0.0272406
\(783\) 2.98837 0.106795
\(784\) −19.7724 −0.706156
\(785\) 0.167627 0.00598288
\(786\) 23.9121 0.852915
\(787\) 35.9496 1.28146 0.640732 0.767765i \(-0.278631\pi\)
0.640732 + 0.767765i \(0.278631\pi\)
\(788\) 20.1222 0.716822
\(789\) 6.98264 0.248589
\(790\) 3.26563 0.116186
\(791\) 61.4621 2.18534
\(792\) 0.960726 0.0341379
\(793\) 9.63713 0.342225
\(794\) 55.5885 1.97276
\(795\) 0.559166 0.0198316
\(796\) −23.1959 −0.822157
\(797\) −23.1830 −0.821183 −0.410592 0.911819i \(-0.634678\pi\)
−0.410592 + 0.911819i \(0.634678\pi\)
\(798\) −45.8760 −1.62399
\(799\) −4.19886 −0.148545
\(800\) 32.2939 1.14176
\(801\) 5.46315 0.193031
\(802\) −57.4557 −2.02883
\(803\) −9.50496 −0.335423
\(804\) 2.80938 0.0990792
\(805\) −0.232400 −0.00819101
\(806\) 36.7111 1.29309
\(807\) 16.6172 0.584952
\(808\) 14.0812 0.495376
\(809\) 7.71907 0.271388 0.135694 0.990751i \(-0.456674\pi\)
0.135694 + 0.990751i \(0.456674\pi\)
\(810\) −0.306095 −0.0107551
\(811\) −29.6601 −1.04151 −0.520754 0.853707i \(-0.674349\pi\)
−0.520754 + 0.853707i \(0.674349\pi\)
\(812\) −13.2530 −0.465088
\(813\) 4.42732 0.155273
\(814\) 1.76578 0.0618906
\(815\) −0.155866 −0.00545976
\(816\) −4.88815 −0.171120
\(817\) −21.6897 −0.758826
\(818\) −45.9791 −1.60762
\(819\) −7.46402 −0.260814
\(820\) 2.09662 0.0732173
\(821\) −41.8880 −1.46190 −0.730951 0.682430i \(-0.760923\pi\)
−0.730951 + 0.682430i \(0.760923\pi\)
\(822\) −7.15680 −0.249622
\(823\) −49.4767 −1.72465 −0.862325 0.506356i \(-0.830992\pi\)
−0.862325 + 0.506356i \(0.830992\pi\)
\(824\) 21.4948 0.748805
\(825\) −3.93025 −0.136834
\(826\) 31.8474 1.10811
\(827\) 31.8902 1.10893 0.554466 0.832207i \(-0.312923\pi\)
0.554466 + 0.832207i \(0.312923\pi\)
\(828\) 0.556680 0.0193460
\(829\) 10.8768 0.377765 0.188883 0.982000i \(-0.439513\pi\)
0.188883 + 0.982000i \(0.439513\pi\)
\(830\) 1.91756 0.0665595
\(831\) −7.02563 −0.243717
\(832\) 4.68124 0.162293
\(833\) −4.04495 −0.140149
\(834\) 29.9993 1.03879
\(835\) −1.00695 −0.0348468
\(836\) −7.97419 −0.275793
\(837\) 8.95148 0.309408
\(838\) 72.0566 2.48915
\(839\) −54.5822 −1.88439 −0.942193 0.335071i \(-0.891240\pi\)
−0.942193 + 0.335071i \(0.891240\pi\)
\(840\) −0.677063 −0.0233609
\(841\) −20.0697 −0.692058
\(842\) 5.76766 0.198767
\(843\) −10.4169 −0.358776
\(844\) −2.87094 −0.0988219
\(845\) 1.33363 0.0458783
\(846\) 7.66730 0.263607
\(847\) −34.4806 −1.18477
\(848\) −16.3057 −0.559941
\(849\) 11.8295 0.405988
\(850\) 9.07891 0.311404
\(851\) −0.510313 −0.0174933
\(852\) −5.00885 −0.171600
\(853\) −8.97469 −0.307288 −0.153644 0.988126i \(-0.549101\pi\)
−0.153644 + 0.988126i \(0.549101\pi\)
\(854\) −26.0405 −0.891089
\(855\) −1.26718 −0.0433365
\(856\) 15.6684 0.535533
\(857\) 21.7054 0.741442 0.370721 0.928744i \(-0.379111\pi\)
0.370721 + 0.928744i \(0.379111\pi\)
\(858\) −3.24190 −0.110677
\(859\) 51.6995 1.76396 0.881981 0.471284i \(-0.156209\pi\)
0.881981 + 0.471284i \(0.156209\pi\)
\(860\) 0.641805 0.0218854
\(861\) 31.1502 1.06159
\(862\) 16.0716 0.547402
\(863\) 41.7475 1.42110 0.710551 0.703646i \(-0.248446\pi\)
0.710551 + 0.703646i \(0.248446\pi\)
\(864\) 6.49528 0.220974
\(865\) −2.20813 −0.0750788
\(866\) 23.4282 0.796124
\(867\) −1.00000 −0.0339618
\(868\) −39.6985 −1.34745
\(869\) 8.43350 0.286087
\(870\) −0.914724 −0.0310120
\(871\) 4.72830 0.160212
\(872\) −9.84859 −0.333515
\(873\) 1.46789 0.0496806
\(874\) 5.75853 0.194785
\(875\) 5.55527 0.187802
\(876\) −16.0454 −0.542123
\(877\) 41.0439 1.38595 0.692977 0.720959i \(-0.256299\pi\)
0.692977 + 0.720959i \(0.256299\pi\)
\(878\) −39.4636 −1.33183
\(879\) −1.93768 −0.0653564
\(880\) −0.647720 −0.0218346
\(881\) −8.84113 −0.297865 −0.148933 0.988847i \(-0.547584\pi\)
−0.148933 + 0.988847i \(0.547584\pi\)
\(882\) 7.38626 0.248708
\(883\) 0.749367 0.0252182 0.0126091 0.999921i \(-0.495986\pi\)
0.0126091 + 0.999921i \(0.495986\pi\)
\(884\) 2.99701 0.100800
\(885\) 0.879682 0.0295702
\(886\) −70.1209 −2.35576
\(887\) 0.920209 0.0308976 0.0154488 0.999881i \(-0.495082\pi\)
0.0154488 + 0.999881i \(0.495082\pi\)
\(888\) −1.48673 −0.0498912
\(889\) 10.3112 0.345827
\(890\) −1.67224 −0.0560537
\(891\) −0.790492 −0.0264825
\(892\) −8.54503 −0.286109
\(893\) 31.7412 1.06218
\(894\) 38.3691 1.28325
\(895\) −0.639089 −0.0213624
\(896\) 30.5235 1.01972
\(897\) 0.936913 0.0312826
\(898\) 41.8884 1.39783
\(899\) 26.7503 0.892172
\(900\) −6.63467 −0.221156
\(901\) −3.33576 −0.111130
\(902\) 13.5297 0.450488
\(903\) 9.53549 0.317321
\(904\) −22.4764 −0.747555
\(905\) 0.550521 0.0183000
\(906\) 20.5885 0.684008
\(907\) −49.8197 −1.65424 −0.827118 0.562029i \(-0.810021\pi\)
−0.827118 + 0.562029i \(0.810021\pi\)
\(908\) −13.4310 −0.445722
\(909\) −11.5861 −0.384288
\(910\) 2.28470 0.0757371
\(911\) −17.5975 −0.583030 −0.291515 0.956566i \(-0.594159\pi\)
−0.291515 + 0.956566i \(0.594159\pi\)
\(912\) 36.9519 1.22360
\(913\) 4.95211 0.163891
\(914\) −53.5082 −1.76989
\(915\) −0.719287 −0.0237789
\(916\) 3.20133 0.105775
\(917\) −43.5199 −1.43715
\(918\) 1.82604 0.0602684
\(919\) 12.1033 0.399251 0.199626 0.979872i \(-0.436027\pi\)
0.199626 + 0.979872i \(0.436027\pi\)
\(920\) 0.0849876 0.00280196
\(921\) 15.8996 0.523909
\(922\) 66.7332 2.19774
\(923\) −8.43008 −0.277479
\(924\) 3.50571 0.115330
\(925\) 6.08206 0.199977
\(926\) 48.4399 1.59183
\(927\) −17.6860 −0.580885
\(928\) 19.4103 0.637173
\(929\) −52.3519 −1.71761 −0.858805 0.512302i \(-0.828793\pi\)
−0.858805 + 0.512302i \(0.828793\pi\)
\(930\) −2.74000 −0.0898483
\(931\) 30.5778 1.00215
\(932\) −24.2783 −0.795261
\(933\) 10.4760 0.342970
\(934\) 29.9876 0.981224
\(935\) −0.132508 −0.00433348
\(936\) 2.72956 0.0892186
\(937\) 38.4380 1.25571 0.627857 0.778329i \(-0.283932\pi\)
0.627857 + 0.778329i \(0.283932\pi\)
\(938\) −12.7763 −0.417162
\(939\) 18.9373 0.617997
\(940\) −0.939234 −0.0306344
\(941\) 50.9150 1.65978 0.829891 0.557926i \(-0.188403\pi\)
0.829891 + 0.557926i \(0.188403\pi\)
\(942\) 1.82604 0.0594957
\(943\) −3.91009 −0.127330
\(944\) −25.6522 −0.834909
\(945\) 0.557092 0.0181222
\(946\) 4.14161 0.134655
\(947\) −18.0649 −0.587031 −0.293516 0.955954i \(-0.594825\pi\)
−0.293516 + 0.955954i \(0.594825\pi\)
\(948\) 14.2366 0.462384
\(949\) −27.0050 −0.876619
\(950\) −68.6319 −2.22671
\(951\) 10.4507 0.338887
\(952\) 4.03910 0.130908
\(953\) 31.9241 1.03412 0.517061 0.855949i \(-0.327026\pi\)
0.517061 + 0.855949i \(0.327026\pi\)
\(954\) 6.09125 0.197212
\(955\) −2.71075 −0.0877178
\(956\) −10.0211 −0.324106
\(957\) −2.36228 −0.0763616
\(958\) 49.5286 1.60020
\(959\) 13.0254 0.420611
\(960\) −0.349394 −0.0112766
\(961\) 49.1290 1.58481
\(962\) 5.01684 0.161750
\(963\) −12.8920 −0.415440
\(964\) −20.6706 −0.665755
\(965\) −2.65967 −0.0856179
\(966\) −2.53164 −0.0814541
\(967\) 58.4931 1.88101 0.940506 0.339778i \(-0.110352\pi\)
0.940506 + 0.339778i \(0.110352\pi\)
\(968\) 12.6094 0.405282
\(969\) 7.55949 0.242846
\(970\) −0.449314 −0.0144266
\(971\) 46.3161 1.48635 0.743177 0.669095i \(-0.233318\pi\)
0.743177 + 0.669095i \(0.233318\pi\)
\(972\) −1.33443 −0.0428020
\(973\) −54.5987 −1.75035
\(974\) −50.7060 −1.62472
\(975\) −11.1664 −0.357611
\(976\) 20.9750 0.671393
\(977\) −3.33760 −0.106779 −0.0533897 0.998574i \(-0.517003\pi\)
−0.0533897 + 0.998574i \(0.517003\pi\)
\(978\) −1.69792 −0.0542936
\(979\) −4.31858 −0.138022
\(980\) −0.904807 −0.0289030
\(981\) 8.10349 0.258724
\(982\) −1.16901 −0.0373047
\(983\) −11.3562 −0.362208 −0.181104 0.983464i \(-0.557967\pi\)
−0.181104 + 0.983464i \(0.557967\pi\)
\(984\) −11.3915 −0.363147
\(985\) −2.52768 −0.0805387
\(986\) 5.45688 0.173783
\(987\) −13.9545 −0.444176
\(988\) −22.6559 −0.720779
\(989\) −1.19693 −0.0380602
\(990\) 0.241966 0.00769017
\(991\) 45.9817 1.46066 0.730328 0.683097i \(-0.239367\pi\)
0.730328 + 0.683097i \(0.239367\pi\)
\(992\) 58.1423 1.84602
\(993\) 15.2077 0.482601
\(994\) 22.7790 0.722504
\(995\) 2.91380 0.0923736
\(996\) 8.35968 0.264887
\(997\) −18.8695 −0.597604 −0.298802 0.954315i \(-0.596587\pi\)
−0.298802 + 0.954315i \(0.596587\pi\)
\(998\) −29.7222 −0.940838
\(999\) 1.22329 0.0387031
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.1.39 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8007.2.a.f.1.39 48 1.1 even 1 trivial