Properties

Label 43.4.a.b.1.4
Level 43
Weight 4
Character 43.1
Self dual yes
Analytic conductor 2.537
Analytic rank 0
Dimension 6
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 43.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(2.53708213025\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\mathbb{Q}[x]/(x^{6} - \cdots)\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(-0.847740\) of \(x^{6} - 32 x^{4} - 16 x^{3} + 251 x^{2} + 276 x + 60\)
Character \(\chi\) \(=\) 43.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.84774 q^{2} +9.49653 q^{3} -4.58586 q^{4} +2.98245 q^{5} +17.5471 q^{6} -26.0720 q^{7} -23.2554 q^{8} +63.1842 q^{9} +O(q^{10})\) \(q+1.84774 q^{2} +9.49653 q^{3} -4.58586 q^{4} +2.98245 q^{5} +17.5471 q^{6} -26.0720 q^{7} -23.2554 q^{8} +63.1842 q^{9} +5.51080 q^{10} -36.8506 q^{11} -43.5497 q^{12} +89.5430 q^{13} -48.1743 q^{14} +28.3230 q^{15} -6.28309 q^{16} -28.8042 q^{17} +116.748 q^{18} -58.8677 q^{19} -13.6771 q^{20} -247.594 q^{21} -68.0904 q^{22} +2.63139 q^{23} -220.846 q^{24} -116.105 q^{25} +165.452 q^{26} +343.624 q^{27} +119.563 q^{28} +173.812 q^{29} +52.3335 q^{30} +57.9476 q^{31} +174.434 q^{32} -349.953 q^{33} -53.2227 q^{34} -77.7586 q^{35} -289.753 q^{36} +52.0754 q^{37} -108.772 q^{38} +850.348 q^{39} -69.3581 q^{40} +142.704 q^{41} -457.489 q^{42} -43.0000 q^{43} +168.992 q^{44} +188.444 q^{45} +4.86213 q^{46} -106.853 q^{47} -59.6676 q^{48} +336.750 q^{49} -214.532 q^{50} -273.540 q^{51} -410.631 q^{52} +244.652 q^{53} +634.928 q^{54} -109.905 q^{55} +606.315 q^{56} -559.039 q^{57} +321.160 q^{58} -127.799 q^{59} -129.885 q^{60} -443.613 q^{61} +107.072 q^{62} -1647.34 q^{63} +372.573 q^{64} +267.058 q^{65} -646.622 q^{66} -117.896 q^{67} +132.092 q^{68} +24.9891 q^{69} -143.678 q^{70} +816.799 q^{71} -1469.37 q^{72} -620.953 q^{73} +96.2217 q^{74} -1102.59 q^{75} +269.959 q^{76} +960.770 q^{77} +1571.22 q^{78} +377.771 q^{79} -18.7390 q^{80} +1557.27 q^{81} +263.680 q^{82} -1453.23 q^{83} +1135.43 q^{84} -85.9072 q^{85} -79.4528 q^{86} +1650.62 q^{87} +856.975 q^{88} +627.993 q^{89} +348.195 q^{90} -2334.57 q^{91} -12.0672 q^{92} +550.302 q^{93} -197.436 q^{94} -175.570 q^{95} +1656.52 q^{96} -817.163 q^{97} +622.227 q^{98} -2328.38 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 6q^{2} + 7q^{3} + 22q^{4} + 43q^{5} - 3q^{6} + 8q^{7} + 54q^{8} + 81q^{9} + O(q^{10}) \) \( 6q + 6q^{2} + 7q^{3} + 22q^{4} + 43q^{5} - 3q^{6} + 8q^{7} + 54q^{8} + 81q^{9} + 57q^{10} - 28q^{11} - 157q^{12} + 56q^{13} - 184q^{14} - 124q^{15} - 54q^{16} + 19q^{17} - 81q^{18} - 75q^{19} + 135q^{20} - 18q^{21} - 504q^{22} + 131q^{23} - 567q^{24} + 105q^{25} + 44q^{26} + 238q^{27} - 404q^{28} + 515q^{29} - 396q^{30} + 237q^{31} + 558q^{32} + 540q^{33} - 107q^{34} + 198q^{35} + 73q^{36} + 269q^{37} + 527q^{38} + 290q^{39} + 613q^{40} + 471q^{41} + 362q^{42} - 258q^{43} - 428q^{44} + 334q^{45} - 67q^{46} + 415q^{47} - 989q^{48} + 350q^{49} + 1335q^{50} - 1241q^{51} - 8q^{52} + 450q^{53} + 402q^{54} - 1732q^{55} - 780q^{56} - 1000q^{57} - 1055q^{58} + 356q^{59} - 2732q^{60} - 1328q^{61} + 1603q^{62} - 2290q^{63} + 466q^{64} - 62q^{65} + 156q^{66} - 632q^{67} + 571q^{68} - 1130q^{69} - 1902q^{70} - 144q^{71} + 567q^{72} + 864q^{73} + 1207q^{74} - 2494q^{75} + 1005q^{76} + 2660q^{77} + 2222q^{78} - 1613q^{79} + 2399q^{80} - 102q^{81} + 1673q^{82} - 682q^{83} + 3758q^{84} + 84q^{85} - 258q^{86} + 449q^{87} - 608q^{88} + 3378q^{89} + 930q^{90} - 3900q^{91} + 3491q^{92} + 1879q^{93} + 3197q^{94} - 79q^{95} - 591q^{96} - 55q^{97} + 2398q^{98} - 1612q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.84774 0.653275 0.326637 0.945150i \(-0.394084\pi\)
0.326637 + 0.945150i \(0.394084\pi\)
\(3\) 9.49653 1.82761 0.913804 0.406154i \(-0.133130\pi\)
0.913804 + 0.406154i \(0.133130\pi\)
\(4\) −4.58586 −0.573232
\(5\) 2.98245 0.266759 0.133379 0.991065i \(-0.457417\pi\)
0.133379 + 0.991065i \(0.457417\pi\)
\(6\) 17.5471 1.19393
\(7\) −26.0720 −1.40776 −0.703878 0.710321i \(-0.748550\pi\)
−0.703878 + 0.710321i \(0.748550\pi\)
\(8\) −23.2554 −1.02775
\(9\) 63.1842 2.34015
\(10\) 5.51080 0.174267
\(11\) −36.8506 −1.01008 −0.505040 0.863096i \(-0.668522\pi\)
−0.505040 + 0.863096i \(0.668522\pi\)
\(12\) −43.5497 −1.04764
\(13\) 89.5430 1.91037 0.955183 0.296016i \(-0.0956581\pi\)
0.955183 + 0.296016i \(0.0956581\pi\)
\(14\) −48.1743 −0.919652
\(15\) 28.3230 0.487531
\(16\) −6.28309 −0.0981733
\(17\) −28.8042 −0.410944 −0.205472 0.978663i \(-0.565873\pi\)
−0.205472 + 0.978663i \(0.565873\pi\)
\(18\) 116.748 1.52876
\(19\) −58.8677 −0.710799 −0.355400 0.934714i \(-0.615655\pi\)
−0.355400 + 0.934714i \(0.615655\pi\)
\(20\) −13.6771 −0.152915
\(21\) −247.594 −2.57283
\(22\) −68.0904 −0.659860
\(23\) 2.63139 0.0238558 0.0119279 0.999929i \(-0.496203\pi\)
0.0119279 + 0.999929i \(0.496203\pi\)
\(24\) −220.846 −1.87833
\(25\) −116.105 −0.928840
\(26\) 165.452 1.24799
\(27\) 343.624 2.44928
\(28\) 119.563 0.806971
\(29\) 173.812 1.11297 0.556486 0.830857i \(-0.312149\pi\)
0.556486 + 0.830857i \(0.312149\pi\)
\(30\) 52.3335 0.318492
\(31\) 57.9476 0.335732 0.167866 0.985810i \(-0.446312\pi\)
0.167866 + 0.985810i \(0.446312\pi\)
\(32\) 174.434 0.963619
\(33\) −349.953 −1.84603
\(34\) −53.2227 −0.268459
\(35\) −77.7586 −0.375531
\(36\) −289.753 −1.34145
\(37\) 52.0754 0.231382 0.115691 0.993285i \(-0.463092\pi\)
0.115691 + 0.993285i \(0.463092\pi\)
\(38\) −108.772 −0.464347
\(39\) 850.348 3.49140
\(40\) −69.3581 −0.274162
\(41\) 142.704 0.543577 0.271788 0.962357i \(-0.412385\pi\)
0.271788 + 0.962357i \(0.412385\pi\)
\(42\) −457.489 −1.68076
\(43\) −43.0000 −0.152499
\(44\) 168.992 0.579010
\(45\) 188.444 0.624257
\(46\) 4.86213 0.0155844
\(47\) −106.853 −0.331618 −0.165809 0.986158i \(-0.553024\pi\)
−0.165809 + 0.986158i \(0.553024\pi\)
\(48\) −59.6676 −0.179422
\(49\) 336.750 0.981779
\(50\) −214.532 −0.606788
\(51\) −273.540 −0.751045
\(52\) −410.631 −1.09508
\(53\) 244.652 0.634067 0.317033 0.948414i \(-0.397313\pi\)
0.317033 + 0.948414i \(0.397313\pi\)
\(54\) 634.928 1.60005
\(55\) −109.905 −0.269448
\(56\) 606.315 1.44683
\(57\) −559.039 −1.29906
\(58\) 321.160 0.727076
\(59\) −127.799 −0.281999 −0.141000 0.990010i \(-0.545032\pi\)
−0.141000 + 0.990010i \(0.545032\pi\)
\(60\) −129.885 −0.279468
\(61\) −443.613 −0.931128 −0.465564 0.885014i \(-0.654149\pi\)
−0.465564 + 0.885014i \(0.654149\pi\)
\(62\) 107.072 0.219325
\(63\) −1647.34 −3.29437
\(64\) 372.573 0.727681
\(65\) 267.058 0.509607
\(66\) −646.622 −1.20597
\(67\) −117.896 −0.214975 −0.107487 0.994206i \(-0.534280\pi\)
−0.107487 + 0.994206i \(0.534280\pi\)
\(68\) 132.092 0.235566
\(69\) 24.9891 0.0435991
\(70\) −143.678 −0.245325
\(71\) 816.799 1.36530 0.682650 0.730746i \(-0.260827\pi\)
0.682650 + 0.730746i \(0.260827\pi\)
\(72\) −1469.37 −2.40510
\(73\) −620.953 −0.995576 −0.497788 0.867299i \(-0.665854\pi\)
−0.497788 + 0.867299i \(0.665854\pi\)
\(74\) 96.2217 0.151156
\(75\) −1102.59 −1.69756
\(76\) 269.959 0.407453
\(77\) 960.770 1.42195
\(78\) 1571.22 2.28085
\(79\) 377.771 0.538007 0.269003 0.963139i \(-0.413306\pi\)
0.269003 + 0.963139i \(0.413306\pi\)
\(80\) −18.7390 −0.0261886
\(81\) 1557.27 2.13617
\(82\) 263.680 0.355105
\(83\) −1453.23 −1.92184 −0.960919 0.276829i \(-0.910716\pi\)
−0.960919 + 0.276829i \(0.910716\pi\)
\(84\) 1135.43 1.47483
\(85\) −85.9072 −0.109623
\(86\) −79.4528 −0.0996235
\(87\) 1650.62 2.03408
\(88\) 856.975 1.03811
\(89\) 627.993 0.747945 0.373973 0.927440i \(-0.377995\pi\)
0.373973 + 0.927440i \(0.377995\pi\)
\(90\) 348.195 0.407811
\(91\) −2334.57 −2.68933
\(92\) −12.0672 −0.0136749
\(93\) 550.302 0.613587
\(94\) −197.436 −0.216638
\(95\) −175.570 −0.189612
\(96\) 1656.52 1.76112
\(97\) −817.163 −0.855365 −0.427682 0.903929i \(-0.640670\pi\)
−0.427682 + 0.903929i \(0.640670\pi\)
\(98\) 622.227 0.641372
\(99\) −2328.38 −2.36374
\(100\) 532.441 0.532441
\(101\) 513.438 0.505832 0.252916 0.967488i \(-0.418610\pi\)
0.252916 + 0.967488i \(0.418610\pi\)
\(102\) −505.431 −0.490639
\(103\) 689.788 0.659872 0.329936 0.944003i \(-0.392973\pi\)
0.329936 + 0.944003i \(0.392973\pi\)
\(104\) −2082.36 −1.96338
\(105\) −738.437 −0.686325
\(106\) 452.053 0.414220
\(107\) 320.710 0.289759 0.144879 0.989449i \(-0.453721\pi\)
0.144879 + 0.989449i \(0.453721\pi\)
\(108\) −1575.81 −1.40400
\(109\) −1691.51 −1.48640 −0.743200 0.669069i \(-0.766693\pi\)
−0.743200 + 0.669069i \(0.766693\pi\)
\(110\) −203.076 −0.176023
\(111\) 494.535 0.422876
\(112\) 163.813 0.138204
\(113\) 856.360 0.712916 0.356458 0.934311i \(-0.383984\pi\)
0.356458 + 0.934311i \(0.383984\pi\)
\(114\) −1032.96 −0.848645
\(115\) 7.84801 0.00636374
\(116\) −797.079 −0.637990
\(117\) 5657.70 4.47055
\(118\) −236.139 −0.184223
\(119\) 750.984 0.578509
\(120\) −658.662 −0.501061
\(121\) 26.9674 0.0202610
\(122\) −819.682 −0.608283
\(123\) 1355.19 0.993445
\(124\) −265.739 −0.192452
\(125\) −719.084 −0.514535
\(126\) −3043.85 −2.15213
\(127\) −2233.72 −1.56071 −0.780357 0.625335i \(-0.784962\pi\)
−0.780357 + 0.625335i \(0.784962\pi\)
\(128\) −707.051 −0.488243
\(129\) −408.351 −0.278708
\(130\) 493.454 0.332913
\(131\) −2051.51 −1.36825 −0.684126 0.729364i \(-0.739816\pi\)
−0.684126 + 0.729364i \(0.739816\pi\)
\(132\) 1604.83 1.05820
\(133\) 1534.80 1.00063
\(134\) −217.841 −0.140437
\(135\) 1024.84 0.653367
\(136\) 669.853 0.422349
\(137\) 2594.49 1.61797 0.808986 0.587827i \(-0.200017\pi\)
0.808986 + 0.587827i \(0.200017\pi\)
\(138\) 46.1734 0.0284822
\(139\) 1140.44 0.695905 0.347953 0.937512i \(-0.386877\pi\)
0.347953 + 0.937512i \(0.386877\pi\)
\(140\) 356.590 0.215267
\(141\) −1014.73 −0.606068
\(142\) 1509.23 0.891916
\(143\) −3299.71 −1.92962
\(144\) −396.992 −0.229741
\(145\) 518.388 0.296895
\(146\) −1147.36 −0.650385
\(147\) 3197.96 1.79431
\(148\) −238.810 −0.132636
\(149\) −2112.03 −1.16124 −0.580618 0.814176i \(-0.697189\pi\)
−0.580618 + 0.814176i \(0.697189\pi\)
\(150\) −2037.31 −1.10897
\(151\) −1351.31 −0.728265 −0.364132 0.931347i \(-0.618634\pi\)
−0.364132 + 0.931347i \(0.618634\pi\)
\(152\) 1368.99 0.730526
\(153\) −1819.97 −0.961672
\(154\) 1775.25 0.928922
\(155\) 172.826 0.0895595
\(156\) −3899.57 −2.00138
\(157\) −1506.02 −0.765562 −0.382781 0.923839i \(-0.625034\pi\)
−0.382781 + 0.923839i \(0.625034\pi\)
\(158\) 698.022 0.351466
\(159\) 2323.35 1.15883
\(160\) 520.240 0.257054
\(161\) −68.6057 −0.0335832
\(162\) 2877.43 1.39551
\(163\) −1258.30 −0.604647 −0.302323 0.953205i \(-0.597762\pi\)
−0.302323 + 0.953205i \(0.597762\pi\)
\(164\) −654.420 −0.311595
\(165\) −1043.72 −0.492445
\(166\) −2685.19 −1.25549
\(167\) 2764.50 1.28098 0.640489 0.767967i \(-0.278732\pi\)
0.640489 + 0.767967i \(0.278732\pi\)
\(168\) 5757.89 2.64423
\(169\) 5820.95 2.64950
\(170\) −158.734 −0.0716139
\(171\) −3719.51 −1.66338
\(172\) 197.192 0.0874170
\(173\) 1004.21 0.441322 0.220661 0.975351i \(-0.429179\pi\)
0.220661 + 0.975351i \(0.429179\pi\)
\(174\) 3049.91 1.32881
\(175\) 3027.09 1.30758
\(176\) 231.536 0.0991628
\(177\) −1213.64 −0.515384
\(178\) 1160.37 0.488614
\(179\) 2666.39 1.11338 0.556692 0.830719i \(-0.312070\pi\)
0.556692 + 0.830719i \(0.312070\pi\)
\(180\) −864.176 −0.357844
\(181\) 3016.21 1.23863 0.619317 0.785141i \(-0.287409\pi\)
0.619317 + 0.785141i \(0.287409\pi\)
\(182\) −4313.67 −1.75687
\(183\) −4212.79 −1.70174
\(184\) −61.1941 −0.0245179
\(185\) 155.312 0.0617232
\(186\) 1016.81 0.400841
\(187\) 1061.45 0.415086
\(188\) 490.010 0.190094
\(189\) −8958.98 −3.44799
\(190\) −324.408 −0.123869
\(191\) 1413.15 0.535352 0.267676 0.963509i \(-0.413744\pi\)
0.267676 + 0.963509i \(0.413744\pi\)
\(192\) 3538.15 1.32992
\(193\) −1246.60 −0.464934 −0.232467 0.972604i \(-0.574680\pi\)
−0.232467 + 0.972604i \(0.574680\pi\)
\(194\) −1509.91 −0.558788
\(195\) 2536.12 0.931362
\(196\) −1544.29 −0.562787
\(197\) −4931.17 −1.78341 −0.891704 0.452619i \(-0.850490\pi\)
−0.891704 + 0.452619i \(0.850490\pi\)
\(198\) −4302.23 −1.54417
\(199\) 552.461 0.196799 0.0983993 0.995147i \(-0.468628\pi\)
0.0983993 + 0.995147i \(0.468628\pi\)
\(200\) 2700.07 0.954618
\(201\) −1119.60 −0.392889
\(202\) 948.700 0.330447
\(203\) −4531.64 −1.56679
\(204\) 1254.42 0.430523
\(205\) 425.609 0.145004
\(206\) 1274.55 0.431078
\(207\) 166.262 0.0558263
\(208\) −562.607 −0.187547
\(209\) 2169.31 0.717964
\(210\) −1364.44 −0.448359
\(211\) 2302.22 0.751145 0.375572 0.926793i \(-0.377446\pi\)
0.375572 + 0.926793i \(0.377446\pi\)
\(212\) −1121.94 −0.363467
\(213\) 7756.76 2.49523
\(214\) 592.588 0.189292
\(215\) −128.246 −0.0406803
\(216\) −7991.12 −2.51725
\(217\) −1510.81 −0.472629
\(218\) −3125.48 −0.971028
\(219\) −5896.90 −1.81952
\(220\) 504.010 0.154456
\(221\) −2579.21 −0.785053
\(222\) 913.773 0.276254
\(223\) 2558.41 0.768269 0.384135 0.923277i \(-0.374500\pi\)
0.384135 + 0.923277i \(0.374500\pi\)
\(224\) −4547.84 −1.35654
\(225\) −7336.00 −2.17363
\(226\) 1582.33 0.465730
\(227\) 3622.76 1.05926 0.529628 0.848230i \(-0.322331\pi\)
0.529628 + 0.848230i \(0.322331\pi\)
\(228\) 2563.67 0.744664
\(229\) 1155.46 0.333428 0.166714 0.986005i \(-0.446684\pi\)
0.166714 + 0.986005i \(0.446684\pi\)
\(230\) 14.5011 0.00415727
\(231\) 9123.98 2.59876
\(232\) −4042.08 −1.14386
\(233\) 527.800 0.148401 0.0742003 0.997243i \(-0.476360\pi\)
0.0742003 + 0.997243i \(0.476360\pi\)
\(234\) 10454.0 2.92050
\(235\) −318.683 −0.0884620
\(236\) 586.066 0.161651
\(237\) 3587.51 0.983266
\(238\) 1387.62 0.377925
\(239\) −1341.41 −0.363048 −0.181524 0.983387i \(-0.558103\pi\)
−0.181524 + 0.983387i \(0.558103\pi\)
\(240\) −177.956 −0.0478625
\(241\) −3738.93 −0.999361 −0.499680 0.866210i \(-0.666549\pi\)
−0.499680 + 0.866210i \(0.666549\pi\)
\(242\) 49.8287 0.0132360
\(243\) 5510.79 1.45480
\(244\) 2034.34 0.533752
\(245\) 1004.34 0.261898
\(246\) 2504.05 0.648993
\(247\) −5271.19 −1.35789
\(248\) −1347.59 −0.345050
\(249\) −13800.6 −3.51237
\(250\) −1328.68 −0.336133
\(251\) −1741.62 −0.437969 −0.218985 0.975728i \(-0.570274\pi\)
−0.218985 + 0.975728i \(0.570274\pi\)
\(252\) 7554.46 1.88844
\(253\) −96.9684 −0.0240963
\(254\) −4127.33 −1.01957
\(255\) −815.821 −0.200348
\(256\) −4287.03 −1.04664
\(257\) 4121.68 1.00040 0.500200 0.865910i \(-0.333260\pi\)
0.500200 + 0.865910i \(0.333260\pi\)
\(258\) −754.527 −0.182073
\(259\) −1357.71 −0.325730
\(260\) −1224.69 −0.292123
\(261\) 10982.2 2.60452
\(262\) −3790.65 −0.893844
\(263\) 4315.46 1.01180 0.505898 0.862593i \(-0.331161\pi\)
0.505898 + 0.862593i \(0.331161\pi\)
\(264\) 8138.30 1.89726
\(265\) 729.663 0.169143
\(266\) 2835.91 0.653688
\(267\) 5963.76 1.36695
\(268\) 540.654 0.123230
\(269\) 5195.44 1.17759 0.588794 0.808283i \(-0.299603\pi\)
0.588794 + 0.808283i \(0.299603\pi\)
\(270\) 1893.64 0.426828
\(271\) −7874.15 −1.76502 −0.882510 0.470294i \(-0.844148\pi\)
−0.882510 + 0.470294i \(0.844148\pi\)
\(272\) 180.979 0.0403437
\(273\) −22170.3 −4.91504
\(274\) 4793.94 1.05698
\(275\) 4278.54 0.938202
\(276\) −114.596 −0.0249924
\(277\) −175.471 −0.0380615 −0.0190307 0.999819i \(-0.506058\pi\)
−0.0190307 + 0.999819i \(0.506058\pi\)
\(278\) 2107.24 0.454617
\(279\) 3661.37 0.785665
\(280\) 1808.31 0.385954
\(281\) 7263.01 1.54190 0.770951 0.636894i \(-0.219781\pi\)
0.770951 + 0.636894i \(0.219781\pi\)
\(282\) −1874.96 −0.395929
\(283\) 2314.68 0.486196 0.243098 0.970002i \(-0.421836\pi\)
0.243098 + 0.970002i \(0.421836\pi\)
\(284\) −3745.72 −0.782633
\(285\) −1667.31 −0.346536
\(286\) −6097.01 −1.26057
\(287\) −3720.58 −0.765224
\(288\) 11021.4 2.25502
\(289\) −4083.32 −0.831125
\(290\) 957.846 0.193954
\(291\) −7760.22 −1.56327
\(292\) 2847.60 0.570696
\(293\) 8723.52 1.73936 0.869681 0.493614i \(-0.164324\pi\)
0.869681 + 0.493614i \(0.164324\pi\)
\(294\) 5909.00 1.17218
\(295\) −381.153 −0.0752258
\(296\) −1211.03 −0.237804
\(297\) −12662.8 −2.47397
\(298\) −3902.48 −0.758607
\(299\) 235.623 0.0455733
\(300\) 5056.34 0.973093
\(301\) 1121.10 0.214681
\(302\) −2496.87 −0.475757
\(303\) 4875.88 0.924462
\(304\) 369.871 0.0697815
\(305\) −1323.06 −0.248387
\(306\) −3362.83 −0.628236
\(307\) 1579.68 0.293672 0.146836 0.989161i \(-0.453091\pi\)
0.146836 + 0.989161i \(0.453091\pi\)
\(308\) −4405.95 −0.815105
\(309\) 6550.59 1.20599
\(310\) 319.338 0.0585070
\(311\) −5604.24 −1.02182 −0.510912 0.859633i \(-0.670692\pi\)
−0.510912 + 0.859633i \(0.670692\pi\)
\(312\) −19775.2 −3.58830
\(313\) 3429.86 0.619384 0.309692 0.950837i \(-0.399774\pi\)
0.309692 + 0.950837i \(0.399774\pi\)
\(314\) −2782.73 −0.500123
\(315\) −4913.11 −0.878802
\(316\) −1732.40 −0.308403
\(317\) 4493.00 0.796064 0.398032 0.917372i \(-0.369693\pi\)
0.398032 + 0.917372i \(0.369693\pi\)
\(318\) 4292.94 0.757032
\(319\) −6405.09 −1.12419
\(320\) 1111.18 0.194115
\(321\) 3045.63 0.529566
\(322\) −126.766 −0.0219390
\(323\) 1695.64 0.292098
\(324\) −7141.40 −1.22452
\(325\) −10396.4 −1.77442
\(326\) −2325.01 −0.395001
\(327\) −16063.5 −2.71656
\(328\) −3318.64 −0.558662
\(329\) 2785.86 0.466837
\(330\) −1928.52 −0.321702
\(331\) 4433.87 0.736277 0.368139 0.929771i \(-0.379995\pi\)
0.368139 + 0.929771i \(0.379995\pi\)
\(332\) 6664.30 1.10166
\(333\) 3290.34 0.541470
\(334\) 5108.07 0.836831
\(335\) −351.620 −0.0573463
\(336\) 1555.65 0.252583
\(337\) 6498.33 1.05040 0.525202 0.850977i \(-0.323990\pi\)
0.525202 + 0.850977i \(0.323990\pi\)
\(338\) 10755.6 1.73085
\(339\) 8132.45 1.30293
\(340\) 393.958 0.0628393
\(341\) −2135.41 −0.339116
\(342\) −6872.69 −1.08664
\(343\) 162.945 0.0256507
\(344\) 999.982 0.156731
\(345\) 74.5289 0.0116304
\(346\) 1855.52 0.288305
\(347\) −11973.6 −1.85237 −0.926187 0.377064i \(-0.876934\pi\)
−0.926187 + 0.377064i \(0.876934\pi\)
\(348\) −7569.49 −1.16600
\(349\) 5611.30 0.860648 0.430324 0.902674i \(-0.358399\pi\)
0.430324 + 0.902674i \(0.358399\pi\)
\(350\) 5593.28 0.854209
\(351\) 30769.1 4.67902
\(352\) −6427.99 −0.973332
\(353\) −2022.00 −0.304874 −0.152437 0.988313i \(-0.548712\pi\)
−0.152437 + 0.988313i \(0.548712\pi\)
\(354\) −2242.50 −0.336688
\(355\) 2436.07 0.364206
\(356\) −2879.88 −0.428746
\(357\) 7131.74 1.05729
\(358\) 4926.81 0.727346
\(359\) 10135.3 1.49003 0.745014 0.667049i \(-0.232443\pi\)
0.745014 + 0.667049i \(0.232443\pi\)
\(360\) −4382.34 −0.641582
\(361\) −3393.59 −0.494765
\(362\) 5573.17 0.809169
\(363\) 256.097 0.0370292
\(364\) 10706.0 1.54161
\(365\) −1851.96 −0.265579
\(366\) −7784.13 −1.11170
\(367\) −4379.58 −0.622922 −0.311461 0.950259i \(-0.600818\pi\)
−0.311461 + 0.950259i \(0.600818\pi\)
\(368\) −16.5333 −0.00234200
\(369\) 9016.64 1.27205
\(370\) 286.977 0.0403222
\(371\) −6378.57 −0.892612
\(372\) −2523.60 −0.351728
\(373\) 4392.98 0.609813 0.304906 0.952382i \(-0.401375\pi\)
0.304906 + 0.952382i \(0.401375\pi\)
\(374\) 1961.29 0.271165
\(375\) −6828.81 −0.940369
\(376\) 2484.90 0.340821
\(377\) 15563.7 2.12618
\(378\) −16553.9 −2.25248
\(379\) −878.629 −0.119082 −0.0595411 0.998226i \(-0.518964\pi\)
−0.0595411 + 0.998226i \(0.518964\pi\)
\(380\) 805.140 0.108692
\(381\) −21212.6 −2.85237
\(382\) 2611.14 0.349732
\(383\) 5061.60 0.675289 0.337644 0.941274i \(-0.390370\pi\)
0.337644 + 0.941274i \(0.390370\pi\)
\(384\) −6714.54 −0.892317
\(385\) 2865.45 0.379317
\(386\) −2303.39 −0.303730
\(387\) −2716.92 −0.356870
\(388\) 3747.39 0.490322
\(389\) −3417.17 −0.445392 −0.222696 0.974888i \(-0.571486\pi\)
−0.222696 + 0.974888i \(0.571486\pi\)
\(390\) 4686.10 0.608436
\(391\) −75.7952 −0.00980339
\(392\) −7831.26 −1.00903
\(393\) −19482.2 −2.50063
\(394\) −9111.52 −1.16506
\(395\) 1126.68 0.143518
\(396\) 10677.6 1.35497
\(397\) 7634.34 0.965130 0.482565 0.875860i \(-0.339705\pi\)
0.482565 + 0.875860i \(0.339705\pi\)
\(398\) 1020.80 0.128564
\(399\) 14575.3 1.82876
\(400\) 729.498 0.0911872
\(401\) −8402.74 −1.04642 −0.523208 0.852205i \(-0.675265\pi\)
−0.523208 + 0.852205i \(0.675265\pi\)
\(402\) −2068.74 −0.256665
\(403\) 5188.80 0.641372
\(404\) −2354.55 −0.289959
\(405\) 4644.48 0.569842
\(406\) −8373.30 −1.02355
\(407\) −1919.01 −0.233714
\(408\) 6361.28 0.771888
\(409\) −11792.8 −1.42571 −0.712857 0.701310i \(-0.752599\pi\)
−0.712857 + 0.701310i \(0.752599\pi\)
\(410\) 786.414 0.0947274
\(411\) 24638.7 2.95702
\(412\) −3163.27 −0.378260
\(413\) 3331.97 0.396986
\(414\) 307.210 0.0364699
\(415\) −4334.19 −0.512667
\(416\) 15619.3 1.84086
\(417\) 10830.2 1.27184
\(418\) 4008.32 0.469028
\(419\) −10631.9 −1.23962 −0.619811 0.784751i \(-0.712791\pi\)
−0.619811 + 0.784751i \(0.712791\pi\)
\(420\) 3386.37 0.393423
\(421\) −3136.52 −0.363099 −0.181550 0.983382i \(-0.558111\pi\)
−0.181550 + 0.983382i \(0.558111\pi\)
\(422\) 4253.91 0.490704
\(423\) −6751.39 −0.776037
\(424\) −5689.48 −0.651664
\(425\) 3344.31 0.381701
\(426\) 14332.5 1.63007
\(427\) 11565.9 1.31080
\(428\) −1470.73 −0.166099
\(429\) −31335.8 −3.52659
\(430\) −236.964 −0.0265754
\(431\) −170.380 −0.0190416 −0.00952080 0.999955i \(-0.503031\pi\)
−0.00952080 + 0.999955i \(0.503031\pi\)
\(432\) −2159.02 −0.240454
\(433\) 2093.65 0.232365 0.116183 0.993228i \(-0.462934\pi\)
0.116183 + 0.993228i \(0.462934\pi\)
\(434\) −2791.59 −0.308757
\(435\) 4922.89 0.542608
\(436\) 7757.04 0.852052
\(437\) −154.904 −0.0169567
\(438\) −10895.9 −1.18865
\(439\) −10860.1 −1.18070 −0.590348 0.807149i \(-0.701010\pi\)
−0.590348 + 0.807149i \(0.701010\pi\)
\(440\) 2555.89 0.276926
\(441\) 21277.3 2.29751
\(442\) −4765.72 −0.512855
\(443\) 8256.28 0.885480 0.442740 0.896650i \(-0.354006\pi\)
0.442740 + 0.896650i \(0.354006\pi\)
\(444\) −2267.87 −0.242406
\(445\) 1872.96 0.199521
\(446\) 4727.29 0.501891
\(447\) −20057.0 −2.12229
\(448\) −9713.73 −1.02440
\(449\) −6792.03 −0.713888 −0.356944 0.934126i \(-0.616181\pi\)
−0.356944 + 0.934126i \(0.616181\pi\)
\(450\) −13555.0 −1.41998
\(451\) −5258.73 −0.549056
\(452\) −3927.14 −0.408666
\(453\) −12832.8 −1.33098
\(454\) 6693.93 0.691986
\(455\) −6962.74 −0.717403
\(456\) 13000.7 1.33512
\(457\) 4004.62 0.409908 0.204954 0.978772i \(-0.434295\pi\)
0.204954 + 0.978772i \(0.434295\pi\)
\(458\) 2134.99 0.217820
\(459\) −9897.82 −1.00652
\(460\) −35.9898 −0.00364790
\(461\) 1164.36 0.117635 0.0588175 0.998269i \(-0.481267\pi\)
0.0588175 + 0.998269i \(0.481267\pi\)
\(462\) 16858.8 1.69771
\(463\) 2566.99 0.257664 0.128832 0.991666i \(-0.458877\pi\)
0.128832 + 0.991666i \(0.458877\pi\)
\(464\) −1092.08 −0.109264
\(465\) 1641.25 0.163680
\(466\) 975.237 0.0969463
\(467\) −7654.43 −0.758469 −0.379234 0.925301i \(-0.623813\pi\)
−0.379234 + 0.925301i \(0.623813\pi\)
\(468\) −25945.4 −2.56266
\(469\) 3073.79 0.302632
\(470\) −588.843 −0.0577900
\(471\) −14301.9 −1.39915
\(472\) 2972.01 0.289826
\(473\) 1584.58 0.154036
\(474\) 6628.79 0.642343
\(475\) 6834.84 0.660218
\(476\) −3443.90 −0.331620
\(477\) 15458.1 1.48381
\(478\) −2478.57 −0.237170
\(479\) −8754.20 −0.835051 −0.417526 0.908665i \(-0.637103\pi\)
−0.417526 + 0.908665i \(0.637103\pi\)
\(480\) 4940.48 0.469794
\(481\) 4662.98 0.442024
\(482\) −6908.58 −0.652857
\(483\) −651.517 −0.0613769
\(484\) −123.668 −0.0116142
\(485\) −2437.15 −0.228176
\(486\) 10182.5 0.950386
\(487\) −9406.39 −0.875245 −0.437623 0.899159i \(-0.644179\pi\)
−0.437623 + 0.899159i \(0.644179\pi\)
\(488\) 10316.4 0.956970
\(489\) −11949.5 −1.10506
\(490\) 1855.76 0.171092
\(491\) 6362.18 0.584768 0.292384 0.956301i \(-0.405551\pi\)
0.292384 + 0.956301i \(0.405551\pi\)
\(492\) −6214.73 −0.569475
\(493\) −5006.53 −0.457369
\(494\) −9739.80 −0.887073
\(495\) −6944.27 −0.630549
\(496\) −364.090 −0.0329599
\(497\) −21295.6 −1.92201
\(498\) −25500.0 −2.29454
\(499\) 11574.8 1.03840 0.519198 0.854654i \(-0.326231\pi\)
0.519198 + 0.854654i \(0.326231\pi\)
\(500\) 3297.62 0.294948
\(501\) 26253.2 2.34113
\(502\) −3218.07 −0.286114
\(503\) 11443.5 1.01439 0.507196 0.861831i \(-0.330682\pi\)
0.507196 + 0.861831i \(0.330682\pi\)
\(504\) 38309.5 3.38580
\(505\) 1531.31 0.134935
\(506\) −179.172 −0.0157415
\(507\) 55278.8 4.84225
\(508\) 10243.5 0.894651
\(509\) −17397.9 −1.51502 −0.757511 0.652822i \(-0.773585\pi\)
−0.757511 + 0.652822i \(0.773585\pi\)
\(510\) −1507.42 −0.130882
\(511\) 16189.5 1.40153
\(512\) −2264.91 −0.195499
\(513\) −20228.4 −1.74095
\(514\) 7615.79 0.653537
\(515\) 2057.26 0.176027
\(516\) 1872.64 0.159764
\(517\) 3937.58 0.334961
\(518\) −2508.70 −0.212791
\(519\) 9536.53 0.806565
\(520\) −6210.54 −0.523750
\(521\) −23236.4 −1.95394 −0.976972 0.213369i \(-0.931556\pi\)
−0.976972 + 0.213369i \(0.931556\pi\)
\(522\) 20292.2 1.70147
\(523\) −6523.69 −0.545432 −0.272716 0.962095i \(-0.587922\pi\)
−0.272716 + 0.962095i \(0.587922\pi\)
\(524\) 9407.91 0.784325
\(525\) 28746.9 2.38975
\(526\) 7973.85 0.660981
\(527\) −1669.13 −0.137967
\(528\) 2198.79 0.181231
\(529\) −12160.1 −0.999431
\(530\) 1348.23 0.110497
\(531\) −8074.85 −0.659922
\(532\) −7038.37 −0.573594
\(533\) 12778.2 1.03843
\(534\) 11019.5 0.892995
\(535\) 956.502 0.0772957
\(536\) 2741.72 0.220941
\(537\) 25321.5 2.03483
\(538\) 9599.82 0.769289
\(539\) −12409.5 −0.991675
\(540\) −4699.78 −0.374531
\(541\) −13311.4 −1.05786 −0.528930 0.848666i \(-0.677406\pi\)
−0.528930 + 0.848666i \(0.677406\pi\)
\(542\) −14549.4 −1.15304
\(543\) 28643.5 2.26374
\(544\) −5024.42 −0.395993
\(545\) −5044.86 −0.396510
\(546\) −40964.9 −3.21088
\(547\) −24529.8 −1.91740 −0.958700 0.284420i \(-0.908199\pi\)
−0.958700 + 0.284420i \(0.908199\pi\)
\(548\) −11898.0 −0.927474
\(549\) −28029.3 −2.17898
\(550\) 7905.63 0.612904
\(551\) −10231.9 −0.791099
\(552\) −581.132 −0.0448091
\(553\) −9849.25 −0.757383
\(554\) −324.225 −0.0248646
\(555\) 1474.93 0.112806
\(556\) −5229.89 −0.398915
\(557\) −1732.87 −0.131821 −0.0659104 0.997826i \(-0.520995\pi\)
−0.0659104 + 0.997826i \(0.520995\pi\)
\(558\) 6765.27 0.513255
\(559\) −3850.35 −0.291328
\(560\) 488.564 0.0368672
\(561\) 10080.1 0.758615
\(562\) 13420.1 1.00729
\(563\) 13482.0 1.00924 0.504618 0.863343i \(-0.331634\pi\)
0.504618 + 0.863343i \(0.331634\pi\)
\(564\) 4653.40 0.347417
\(565\) 2554.05 0.190177
\(566\) 4276.92 0.317619
\(567\) −40601.1 −3.00721
\(568\) −18995.0 −1.40319
\(569\) 23053.6 1.69852 0.849261 0.527973i \(-0.177048\pi\)
0.849261 + 0.527973i \(0.177048\pi\)
\(570\) −3080.76 −0.226384
\(571\) 8791.94 0.644363 0.322181 0.946678i \(-0.395584\pi\)
0.322181 + 0.946678i \(0.395584\pi\)
\(572\) 15132.0 1.10612
\(573\) 13420.1 0.978414
\(574\) −6874.68 −0.499901
\(575\) −305.518 −0.0221582
\(576\) 23540.7 1.70289
\(577\) −12464.3 −0.899302 −0.449651 0.893204i \(-0.648452\pi\)
−0.449651 + 0.893204i \(0.648452\pi\)
\(578\) −7544.91 −0.542953
\(579\) −11838.4 −0.849718
\(580\) −2377.25 −0.170190
\(581\) 37888.6 2.70548
\(582\) −14338.9 −1.02125
\(583\) −9015.58 −0.640458
\(584\) 14440.5 1.02321
\(585\) 16873.8 1.19256
\(586\) 16118.8 1.13628
\(587\) −24395.5 −1.71535 −0.857674 0.514193i \(-0.828091\pi\)
−0.857674 + 0.514193i \(0.828091\pi\)
\(588\) −14665.4 −1.02855
\(589\) −3411.24 −0.238638
\(590\) −704.273 −0.0491431
\(591\) −46829.0 −3.25937
\(592\) −327.194 −0.0227155
\(593\) −8779.99 −0.608012 −0.304006 0.952670i \(-0.598324\pi\)
−0.304006 + 0.952670i \(0.598324\pi\)
\(594\) −23397.5 −1.61618
\(595\) 2239.77 0.154322
\(596\) 9685.46 0.665658
\(597\) 5246.46 0.359671
\(598\) 435.370 0.0297719
\(599\) −14440.3 −0.985001 −0.492501 0.870312i \(-0.663917\pi\)
−0.492501 + 0.870312i \(0.663917\pi\)
\(600\) 25641.3 1.74467
\(601\) 7456.08 0.506056 0.253028 0.967459i \(-0.418573\pi\)
0.253028 + 0.967459i \(0.418573\pi\)
\(602\) 2071.50 0.140246
\(603\) −7449.16 −0.503074
\(604\) 6196.91 0.417464
\(605\) 80.4290 0.00540480
\(606\) 9009.37 0.603928
\(607\) −6832.01 −0.456842 −0.228421 0.973563i \(-0.573356\pi\)
−0.228421 + 0.973563i \(0.573356\pi\)
\(608\) −10268.5 −0.684939
\(609\) −43034.9 −2.86348
\(610\) −2444.66 −0.162265
\(611\) −9567.89 −0.633512
\(612\) 8346.12 0.551261
\(613\) 12239.8 0.806460 0.403230 0.915099i \(-0.367887\pi\)
0.403230 + 0.915099i \(0.367887\pi\)
\(614\) 2918.84 0.191849
\(615\) 4041.81 0.265010
\(616\) −22343.1 −1.46141
\(617\) 4307.99 0.281091 0.140546 0.990074i \(-0.455114\pi\)
0.140546 + 0.990074i \(0.455114\pi\)
\(618\) 12103.8 0.787842
\(619\) 21923.8 1.42357 0.711786 0.702396i \(-0.247887\pi\)
0.711786 + 0.702396i \(0.247887\pi\)
\(620\) −792.556 −0.0513384
\(621\) 904.210 0.0584295
\(622\) −10355.2 −0.667531
\(623\) −16373.0 −1.05292
\(624\) −5342.81 −0.342762
\(625\) 12368.5 0.791583
\(626\) 6337.49 0.404628
\(627\) 20600.9 1.31216
\(628\) 6906.38 0.438845
\(629\) −1499.99 −0.0950850
\(630\) −9078.16 −0.574099
\(631\) 13249.3 0.835891 0.417945 0.908472i \(-0.362750\pi\)
0.417945 + 0.908472i \(0.362750\pi\)
\(632\) −8785.21 −0.552938
\(633\) 21863.1 1.37280
\(634\) 8301.91 0.520049
\(635\) −6661.97 −0.416334
\(636\) −10654.5 −0.664276
\(637\) 30153.6 1.87556
\(638\) −11835.0 −0.734405
\(639\) 51608.8 3.19501
\(640\) −2108.75 −0.130243
\(641\) −6897.79 −0.425033 −0.212517 0.977157i \(-0.568166\pi\)
−0.212517 + 0.977157i \(0.568166\pi\)
\(642\) 5627.54 0.345952
\(643\) −570.068 −0.0349631 −0.0174816 0.999847i \(-0.505565\pi\)
−0.0174816 + 0.999847i \(0.505565\pi\)
\(644\) 314.616 0.0192509
\(645\) −1217.89 −0.0743477
\(646\) 3133.10 0.190821
\(647\) 15788.1 0.959341 0.479670 0.877449i \(-0.340756\pi\)
0.479670 + 0.877449i \(0.340756\pi\)
\(648\) −36214.9 −2.19545
\(649\) 4709.46 0.284842
\(650\) −19209.8 −1.15919
\(651\) −14347.5 −0.863782
\(652\) 5770.37 0.346603
\(653\) 21960.3 1.31604 0.658019 0.753001i \(-0.271394\pi\)
0.658019 + 0.753001i \(0.271394\pi\)
\(654\) −29681.2 −1.77466
\(655\) −6118.52 −0.364993
\(656\) −896.623 −0.0533647
\(657\) −39234.4 −2.32980
\(658\) 5147.55 0.304973
\(659\) −12142.6 −0.717766 −0.358883 0.933383i \(-0.616842\pi\)
−0.358883 + 0.933383i \(0.616842\pi\)
\(660\) 4786.34 0.282285
\(661\) 3554.01 0.209130 0.104565 0.994518i \(-0.466655\pi\)
0.104565 + 0.994518i \(0.466655\pi\)
\(662\) 8192.65 0.480992
\(663\) −24493.6 −1.43477
\(664\) 33795.4 1.97518
\(665\) 4577.47 0.266927
\(666\) 6079.69 0.353729
\(667\) 457.369 0.0265508
\(668\) −12677.6 −0.734297
\(669\) 24296.1 1.40410
\(670\) −649.702 −0.0374629
\(671\) 16347.4 0.940514
\(672\) −43188.7 −2.47923
\(673\) 20271.0 1.16106 0.580528 0.814240i \(-0.302846\pi\)
0.580528 + 0.814240i \(0.302846\pi\)
\(674\) 12007.2 0.686203
\(675\) −39896.5 −2.27499
\(676\) −26694.0 −1.51878
\(677\) 26668.2 1.51395 0.756973 0.653447i \(-0.226678\pi\)
0.756973 + 0.653447i \(0.226678\pi\)
\(678\) 15026.7 0.851173
\(679\) 21305.1 1.20415
\(680\) 1997.81 0.112665
\(681\) 34403.7 1.93591
\(682\) −3945.67 −0.221536
\(683\) −5584.15 −0.312843 −0.156421 0.987690i \(-0.549996\pi\)
−0.156421 + 0.987690i \(0.549996\pi\)
\(684\) 17057.1 0.953502
\(685\) 7737.95 0.431608
\(686\) 301.079 0.0167569
\(687\) 10972.9 0.609377
\(688\) 270.173 0.0149713
\(689\) 21906.9 1.21130
\(690\) 137.710 0.00759787
\(691\) −2702.39 −0.148776 −0.0743878 0.997229i \(-0.523700\pi\)
−0.0743878 + 0.997229i \(0.523700\pi\)
\(692\) −4605.17 −0.252980
\(693\) 60705.4 3.32757
\(694\) −22124.0 −1.21011
\(695\) 3401.31 0.185639
\(696\) −38385.7 −2.09053
\(697\) −4110.48 −0.223379
\(698\) 10368.2 0.562240
\(699\) 5012.27 0.271218
\(700\) −13881.8 −0.749547
\(701\) −19885.1 −1.07140 −0.535700 0.844408i \(-0.679952\pi\)
−0.535700 + 0.844408i \(0.679952\pi\)
\(702\) 56853.4 3.05669
\(703\) −3065.56 −0.164466
\(704\) −13729.5 −0.735016
\(705\) −3026.38 −0.161674
\(706\) −3736.14 −0.199166
\(707\) −13386.4 −0.712088
\(708\) 5565.59 0.295435
\(709\) −7798.56 −0.413090 −0.206545 0.978437i \(-0.566222\pi\)
−0.206545 + 0.978437i \(0.566222\pi\)
\(710\) 4501.22 0.237926
\(711\) 23869.1 1.25902
\(712\) −14604.2 −0.768703
\(713\) 152.483 0.00800916
\(714\) 13177.6 0.690700
\(715\) −9841.24 −0.514744
\(716\) −12227.7 −0.638227
\(717\) −12738.7 −0.663509
\(718\) 18727.4 0.973398
\(719\) 1118.09 0.0579939 0.0289970 0.999579i \(-0.490769\pi\)
0.0289970 + 0.999579i \(0.490769\pi\)
\(720\) −1184.01 −0.0612853
\(721\) −17984.2 −0.928939
\(722\) −6270.47 −0.323217
\(723\) −35506.9 −1.82644
\(724\) −13831.9 −0.710025
\(725\) −20180.5 −1.03377
\(726\) 473.200 0.0241902
\(727\) −1741.54 −0.0888449 −0.0444225 0.999013i \(-0.514145\pi\)
−0.0444225 + 0.999013i \(0.514145\pi\)
\(728\) 54291.3 2.76397
\(729\) 10287.2 0.522642
\(730\) −3421.95 −0.173496
\(731\) 1238.58 0.0626683
\(732\) 19319.2 0.975491
\(733\) −9461.10 −0.476744 −0.238372 0.971174i \(-0.576614\pi\)
−0.238372 + 0.971174i \(0.576614\pi\)
\(734\) −8092.33 −0.406939
\(735\) 9537.77 0.478648
\(736\) 459.003 0.0229879
\(737\) 4344.54 0.217141
\(738\) 16660.4 0.831000
\(739\) 30605.3 1.52346 0.761728 0.647897i \(-0.224351\pi\)
0.761728 + 0.647897i \(0.224351\pi\)
\(740\) −712.240 −0.0353817
\(741\) −50058.1 −2.48169
\(742\) −11785.9 −0.583121
\(743\) 14556.5 0.718745 0.359373 0.933194i \(-0.382991\pi\)
0.359373 + 0.933194i \(0.382991\pi\)
\(744\) −12797.5 −0.630616
\(745\) −6299.03 −0.309770
\(746\) 8117.10 0.398375
\(747\) −91821.1 −4.49740
\(748\) −4867.67 −0.237941
\(749\) −8361.55 −0.407910
\(750\) −12617.9 −0.614319
\(751\) −17528.3 −0.851685 −0.425843 0.904797i \(-0.640022\pi\)
−0.425843 + 0.904797i \(0.640022\pi\)
\(752\) 671.364 0.0325560
\(753\) −16539.4 −0.800436
\(754\) 28757.7 1.38898
\(755\) −4030.22 −0.194271
\(756\) 41084.6 1.97650
\(757\) −37789.1 −1.81436 −0.907179 0.420744i \(-0.861769\pi\)
−0.907179 + 0.420744i \(0.861769\pi\)
\(758\) −1623.48 −0.0777934
\(759\) −920.864 −0.0440385
\(760\) 4082.96 0.194874
\(761\) 3292.90 0.156856 0.0784281 0.996920i \(-0.475010\pi\)
0.0784281 + 0.996920i \(0.475010\pi\)
\(762\) −39195.4 −1.86338
\(763\) 44101.2 2.09249
\(764\) −6480.52 −0.306881
\(765\) −5427.98 −0.256534
\(766\) 9352.52 0.441149
\(767\) −11443.5 −0.538722
\(768\) −40711.9 −1.91285
\(769\) −28023.9 −1.31413 −0.657065 0.753834i \(-0.728202\pi\)
−0.657065 + 0.753834i \(0.728202\pi\)
\(770\) 5294.61 0.247798
\(771\) 39141.6 1.82834
\(772\) 5716.73 0.266515
\(773\) 22131.0 1.02975 0.514875 0.857265i \(-0.327838\pi\)
0.514875 + 0.857265i \(0.327838\pi\)
\(774\) −5020.16 −0.233134
\(775\) −6728.01 −0.311841
\(776\) 19003.5 0.879103
\(777\) −12893.5 −0.595306
\(778\) −6314.04 −0.290963
\(779\) −8400.67 −0.386374
\(780\) −11630.3 −0.533887
\(781\) −30099.6 −1.37906
\(782\) −140.050 −0.00640431
\(783\) 59726.2 2.72598
\(784\) −2115.83 −0.0963845
\(785\) −4491.63 −0.204220
\(786\) −35998.0 −1.63360
\(787\) 5390.88 0.244173 0.122087 0.992519i \(-0.461041\pi\)
0.122087 + 0.992519i \(0.461041\pi\)
\(788\) 22613.6 1.02231
\(789\) 40981.9 1.84917
\(790\) 2081.82 0.0937567
\(791\) −22327.0 −1.00361
\(792\) 54147.3 2.42934
\(793\) −39722.4 −1.77880
\(794\) 14106.3 0.630495
\(795\) 6929.27 0.309127
\(796\) −2533.51 −0.112811
\(797\) 43815.4 1.94733 0.973664 0.227986i \(-0.0732142\pi\)
0.973664 + 0.227986i \(0.0732142\pi\)
\(798\) 26931.3 1.19469
\(799\) 3077.80 0.136276
\(800\) −20252.6 −0.895047
\(801\) 39679.2 1.75031
\(802\) −15526.1 −0.683597
\(803\) 22882.5 1.00561
\(804\) 5134.34 0.225217
\(805\) −204.613 −0.00895860
\(806\) 9587.56 0.418992
\(807\) 49338.6 2.15217
\(808\) −11940.2 −0.519870
\(809\) −19752.4 −0.858415 −0.429208 0.903206i \(-0.641207\pi\)
−0.429208 + 0.903206i \(0.641207\pi\)
\(810\) 8581.79 0.372263
\(811\) 21280.3 0.921398 0.460699 0.887556i \(-0.347599\pi\)
0.460699 + 0.887556i \(0.347599\pi\)
\(812\) 20781.5 0.898135
\(813\) −74777.1 −3.22577
\(814\) −3545.83 −0.152680
\(815\) −3752.81 −0.161295
\(816\) 1718.68 0.0737325
\(817\) 2531.31 0.108396
\(818\) −21790.0 −0.931383
\(819\) −147508. −6.29345
\(820\) −1951.78 −0.0831208
\(821\) −19716.5 −0.838136 −0.419068 0.907955i \(-0.637643\pi\)
−0.419068 + 0.907955i \(0.637643\pi\)
\(822\) 45525.9 1.93175
\(823\) 16269.0 0.689065 0.344532 0.938774i \(-0.388037\pi\)
0.344532 + 0.938774i \(0.388037\pi\)
\(824\) −16041.3 −0.678185
\(825\) 40631.3 1.71467
\(826\) 6156.61 0.259341
\(827\) −27410.0 −1.15253 −0.576263 0.817264i \(-0.695490\pi\)
−0.576263 + 0.817264i \(0.695490\pi\)
\(828\) −762.455 −0.0320014
\(829\) −25392.8 −1.06385 −0.531923 0.846792i \(-0.678531\pi\)
−0.531923 + 0.846792i \(0.678531\pi\)
\(830\) −8008.45 −0.334913
\(831\) −1666.37 −0.0695615
\(832\) 33361.3 1.39014
\(833\) −9699.82 −0.403456
\(834\) 20011.4 0.830863
\(835\) 8244.99 0.341712
\(836\) −9948.15 −0.411560
\(837\) 19912.2 0.822302
\(838\) −19645.0 −0.809814
\(839\) −20579.5 −0.846823 −0.423412 0.905937i \(-0.639168\pi\)
−0.423412 + 0.905937i \(0.639168\pi\)
\(840\) 17172.6 0.705372
\(841\) 5821.76 0.238704
\(842\) −5795.48 −0.237203
\(843\) 68973.4 2.81799
\(844\) −10557.7 −0.430580
\(845\) 17360.7 0.706777
\(846\) −12474.8 −0.506966
\(847\) −703.094 −0.0285225
\(848\) −1537.17 −0.0622484
\(849\) 21981.4 0.888575
\(850\) 6179.42 0.249356
\(851\) 137.031 0.00551980
\(852\) −35571.4 −1.43035
\(853\) 6873.98 0.275921 0.137961 0.990438i \(-0.455945\pi\)
0.137961 + 0.990438i \(0.455945\pi\)
\(854\) 21370.8 0.856314
\(855\) −11093.3 −0.443721
\(856\) −7458.23 −0.297800
\(857\) −20623.8 −0.822049 −0.411025 0.911624i \(-0.634829\pi\)
−0.411025 + 0.911624i \(0.634829\pi\)
\(858\) −57900.5 −2.30384
\(859\) 40959.1 1.62690 0.813450 0.581635i \(-0.197587\pi\)
0.813450 + 0.581635i \(0.197587\pi\)
\(860\) 588.115 0.0233193
\(861\) −35332.7 −1.39853
\(862\) −314.819 −0.0124394
\(863\) 33784.0 1.33258 0.666292 0.745691i \(-0.267880\pi\)
0.666292 + 0.745691i \(0.267880\pi\)
\(864\) 59939.6 2.36017
\(865\) 2995.01 0.117727
\(866\) 3868.52 0.151799
\(867\) −38777.4 −1.51897
\(868\) 6928.36 0.270926
\(869\) −13921.1 −0.543430
\(870\) 9096.22 0.354472
\(871\) −10556.8 −0.410680
\(872\) 39336.8 1.52765
\(873\) −51631.8 −2.00169
\(874\) −286.223 −0.0110774
\(875\) 18748.0 0.724340
\(876\) 27042.3 1.04301
\(877\) −37125.7 −1.42947 −0.714736 0.699395i \(-0.753453\pi\)
−0.714736 + 0.699395i \(0.753453\pi\)
\(878\) −20066.7 −0.771319
\(879\) 82843.2 3.17887
\(880\) 690.545 0.0264526
\(881\) −108.651 −0.00415499 −0.00207749 0.999998i \(-0.500661\pi\)
−0.00207749 + 0.999998i \(0.500661\pi\)
\(882\) 39314.9 1.50091
\(883\) −19622.4 −0.747843 −0.373921 0.927460i \(-0.621987\pi\)
−0.373921 + 0.927460i \(0.621987\pi\)
\(884\) 11827.9 0.450017
\(885\) −3619.64 −0.137483
\(886\) 15255.5 0.578462
\(887\) −26012.1 −0.984668 −0.492334 0.870406i \(-0.663856\pi\)
−0.492334 + 0.870406i \(0.663856\pi\)
\(888\) −11500.6 −0.434612
\(889\) 58237.6 2.19710
\(890\) 3460.74 0.130342
\(891\) −57386.2 −2.15770
\(892\) −11732.5 −0.440397
\(893\) 6290.17 0.235714
\(894\) −37060.1 −1.38644
\(895\) 7952.40 0.297005
\(896\) 18434.3 0.687327
\(897\) 2237.60 0.0832902
\(898\) −12549.9 −0.466365
\(899\) 10072.0 0.373660
\(900\) 33641.8 1.24599
\(901\) −7047.01 −0.260566
\(902\) −9716.78 −0.358684
\(903\) 10646.5 0.392353
\(904\) −19915.0 −0.732702
\(905\) 8995.70 0.330417
\(906\) −23711.6 −0.869498
\(907\) −42258.2 −1.54703 −0.773517 0.633776i \(-0.781504\pi\)
−0.773517 + 0.633776i \(0.781504\pi\)
\(908\) −16613.5 −0.607200
\(909\) 32441.2 1.18372
\(910\) −12865.3 −0.468661
\(911\) 6717.75 0.244313 0.122156 0.992511i \(-0.461019\pi\)
0.122156 + 0.992511i \(0.461019\pi\)
\(912\) 3512.50 0.127533
\(913\) 53552.4 1.94121
\(914\) 7399.49 0.267783
\(915\) −12564.4 −0.453954
\(916\) −5298.78 −0.191132
\(917\) 53486.9 1.92616
\(918\) −18288.6 −0.657532
\(919\) 46824.2 1.68073 0.840364 0.542023i \(-0.182341\pi\)
0.840364 + 0.542023i \(0.182341\pi\)
\(920\) −182.509 −0.00654036
\(921\) 15001.5 0.536717
\(922\) 2151.44 0.0768479
\(923\) 73138.7 2.60822
\(924\) −41841.3 −1.48969
\(925\) −6046.21 −0.214917
\(926\) 4743.14 0.168325
\(927\) 43583.7 1.54420
\(928\) 30318.7 1.07248
\(929\) 14300.0 0.505025 0.252513 0.967594i \(-0.418743\pi\)
0.252513 + 0.967594i \(0.418743\pi\)
\(930\) 3032.60 0.106928
\(931\) −19823.7 −0.697848
\(932\) −2420.41 −0.0850679
\(933\) −53220.8 −1.86749
\(934\) −14143.4 −0.495489
\(935\) 3165.73 0.110728
\(936\) −131572. −4.59462
\(937\) 44630.3 1.55604 0.778019 0.628241i \(-0.216225\pi\)
0.778019 + 0.628241i \(0.216225\pi\)
\(938\) 5679.56 0.197702
\(939\) 32571.8 1.13199
\(940\) 1461.43 0.0507092
\(941\) −12069.3 −0.418116 −0.209058 0.977903i \(-0.567040\pi\)
−0.209058 + 0.977903i \(0.567040\pi\)
\(942\) −26426.3 −0.914028
\(943\) 375.511 0.0129675
\(944\) 802.970 0.0276848
\(945\) −26719.7 −0.919781
\(946\) 2927.89 0.100628
\(947\) 23634.0 0.810984 0.405492 0.914099i \(-0.367100\pi\)
0.405492 + 0.914099i \(0.367100\pi\)
\(948\) −16451.8 −0.563640
\(949\) −55602.0 −1.90192
\(950\) 12629.0 0.431304
\(951\) 42668.0 1.45489
\(952\) −17464.4 −0.594564
\(953\) −31376.9 −1.06652 −0.533262 0.845950i \(-0.679034\pi\)
−0.533262 + 0.845950i \(0.679034\pi\)
\(954\) 28562.6 0.969339
\(955\) 4214.67 0.142810
\(956\) 6151.50 0.208110
\(957\) −60826.2 −2.05458
\(958\) −16175.5 −0.545518
\(959\) −67643.6 −2.27771
\(960\) 10552.4 0.354767
\(961\) −26433.1 −0.887284
\(962\) 8615.98 0.288763
\(963\) 20263.8 0.678080
\(964\) 17146.2 0.572865
\(965\) −3717.93 −0.124025
\(966\) −1203.83 −0.0400960
\(967\) 32665.7 1.08631 0.543154 0.839633i \(-0.317230\pi\)
0.543154 + 0.839633i \(0.317230\pi\)
\(968\) −627.137 −0.0208233
\(969\) 16102.7 0.533842
\(970\) −4503.22 −0.149062
\(971\) −41567.8 −1.37381 −0.686907 0.726745i \(-0.741032\pi\)
−0.686907 + 0.726745i \(0.741032\pi\)
\(972\) −25271.7 −0.833940
\(973\) −29733.6 −0.979665
\(974\) −17380.6 −0.571776
\(975\) −98729.6 −3.24295
\(976\) 2787.26 0.0914119
\(977\) −25363.2 −0.830542 −0.415271 0.909698i \(-0.636313\pi\)
−0.415271 + 0.909698i \(0.636313\pi\)
\(978\) −22079.5 −0.721907
\(979\) −23141.9 −0.755484
\(980\) −4605.77 −0.150128
\(981\) −106877. −3.47841
\(982\) 11755.7 0.382014
\(983\) −3961.23 −0.128528 −0.0642642 0.997933i \(-0.520470\pi\)
−0.0642642 + 0.997933i \(0.520470\pi\)
\(984\) −31515.6 −1.02102
\(985\) −14707.0 −0.475740
\(986\) −9250.76 −0.298787
\(987\) 26456.0 0.853196
\(988\) 24172.9 0.778384
\(989\) −113.150 −0.00363798
\(990\) −12831.2 −0.411922
\(991\) 27940.2 0.895610 0.447805 0.894131i \(-0.352206\pi\)
0.447805 + 0.894131i \(0.352206\pi\)
\(992\) 10108.0 0.323518
\(993\) 42106.4 1.34563
\(994\) −39348.8 −1.25560
\(995\) 1647.69 0.0524978
\(996\) 63287.7 2.01340
\(997\) −15531.3 −0.493363 −0.246681 0.969097i \(-0.579340\pi\)
−0.246681 + 0.969097i \(0.579340\pi\)
\(998\) 21387.2 0.678357
\(999\) 17894.4 0.566719
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 43.4.a.b.1.4 6
3.2 odd 2 387.4.a.h.1.3 6
4.3 odd 2 688.4.a.i.1.1 6
5.4 even 2 1075.4.a.b.1.3 6
7.6 odd 2 2107.4.a.c.1.4 6
43.42 odd 2 1849.4.a.c.1.3 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.4.a.b.1.4 6 1.1 even 1 trivial
387.4.a.h.1.3 6 3.2 odd 2
688.4.a.i.1.1 6 4.3 odd 2
1075.4.a.b.1.3 6 5.4 even 2
1849.4.a.c.1.3 6 43.42 odd 2
2107.4.a.c.1.4 6 7.6 odd 2