Properties

Label 8003.2.a.b.1.8
Level 8003
Weight 2
Character 8003.1
Self dual yes
Analytic conductor 63.904
Analytic rank 1
Dimension 153
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 8003 = 53 \cdot 151 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8003.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(63.9042767376\)
Analytic rank: \(1\)
Dimension: \(153\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) \(=\) 8003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.55291 q^{2} -0.169380 q^{3} +4.51736 q^{4} -0.762748 q^{5} +0.432413 q^{6} +0.998481 q^{7} -6.42660 q^{8} -2.97131 q^{9} +O(q^{10})\) \(q-2.55291 q^{2} -0.169380 q^{3} +4.51736 q^{4} -0.762748 q^{5} +0.432413 q^{6} +0.998481 q^{7} -6.42660 q^{8} -2.97131 q^{9} +1.94723 q^{10} +3.25596 q^{11} -0.765151 q^{12} -2.38564 q^{13} -2.54904 q^{14} +0.129194 q^{15} +7.37183 q^{16} -5.61636 q^{17} +7.58549 q^{18} -0.236108 q^{19} -3.44561 q^{20} -0.169123 q^{21} -8.31217 q^{22} +0.0343603 q^{23} +1.08854 q^{24} -4.41822 q^{25} +6.09033 q^{26} +1.01142 q^{27} +4.51050 q^{28} +4.27471 q^{29} -0.329822 q^{30} +1.74002 q^{31} -5.96642 q^{32} -0.551494 q^{33} +14.3381 q^{34} -0.761590 q^{35} -13.4225 q^{36} -0.632150 q^{37} +0.602764 q^{38} +0.404080 q^{39} +4.90188 q^{40} +3.96974 q^{41} +0.431756 q^{42} +3.03857 q^{43} +14.7083 q^{44} +2.26636 q^{45} -0.0877189 q^{46} +0.324569 q^{47} -1.24864 q^{48} -6.00304 q^{49} +11.2793 q^{50} +0.951299 q^{51} -10.7768 q^{52} -1.00000 q^{53} -2.58207 q^{54} -2.48347 q^{55} -6.41684 q^{56} +0.0399921 q^{57} -10.9129 q^{58} +13.5090 q^{59} +0.583618 q^{60} +9.22106 q^{61} -4.44212 q^{62} -2.96680 q^{63} +0.488101 q^{64} +1.81964 q^{65} +1.40792 q^{66} -8.81790 q^{67} -25.3711 q^{68} -0.00581996 q^{69} +1.94427 q^{70} +14.2107 q^{71} +19.0954 q^{72} +7.81582 q^{73} +1.61382 q^{74} +0.748358 q^{75} -1.06659 q^{76} +3.25101 q^{77} -1.03158 q^{78} -0.258786 q^{79} -5.62285 q^{80} +8.74262 q^{81} -10.1344 q^{82} -7.55717 q^{83} -0.763989 q^{84} +4.28387 q^{85} -7.75720 q^{86} -0.724050 q^{87} -20.9247 q^{88} +9.59998 q^{89} -5.78582 q^{90} -2.38202 q^{91} +0.155218 q^{92} -0.294725 q^{93} -0.828595 q^{94} +0.180091 q^{95} +1.01059 q^{96} +9.21304 q^{97} +15.3252 q^{98} -9.67446 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 153q - 9q^{2} - 17q^{3} + 137q^{4} - 31q^{5} - 10q^{6} - 17q^{7} - 30q^{8} + 136q^{9} + O(q^{10}) \) \( 153q - 9q^{2} - 17q^{3} + 137q^{4} - 31q^{5} - 10q^{6} - 17q^{7} - 30q^{8} + 136q^{9} - 34q^{10} - q^{11} - 60q^{12} - 101q^{13} - 16q^{14} - 14q^{15} + 97q^{16} - 12q^{17} - 45q^{18} - 45q^{19} - 52q^{20} - 76q^{21} - 46q^{22} - 28q^{23} - 30q^{24} + 84q^{25} - 22q^{26} - 68q^{27} - 64q^{28} - 14q^{29} - q^{30} - 70q^{31} - 54q^{32} - 85q^{33} - 59q^{34} - 16q^{35} + 87q^{36} - 167q^{37} - 48q^{38} - 28q^{39} - 68q^{40} - 38q^{41} + 2q^{42} - 71q^{43} - 10q^{44} - 151q^{45} - 37q^{46} - 37q^{47} - 166q^{48} + 74q^{49} - 3q^{50} - 11q^{51} - 183q^{52} - 153q^{53} - 40q^{54} - 88q^{55} - 69q^{56} - 26q^{57} - 43q^{58} - 34q^{59} - 12q^{60} - 90q^{61} - 37q^{62} - 36q^{63} + 58q^{64} - 19q^{65} + 52q^{66} - 86q^{67} - 22q^{68} - 81q^{69} - 144q^{70} - 50q^{71} - 190q^{72} - 171q^{73} - 14q^{74} - 69q^{75} - 88q^{76} - 72q^{77} - 61q^{78} - 13q^{79} - 84q^{80} + 117q^{81} - 124q^{82} - 72q^{83} - 106q^{84} - 193q^{85} - 44q^{86} - 65q^{87} - 89q^{88} - 10q^{89} - 152q^{90} - 67q^{91} - 29q^{92} - 129q^{93} - 43q^{94} - 29q^{95} - 106q^{96} - 177q^{97} - 69q^{98} - 11q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.55291 −1.80518 −0.902591 0.430500i \(-0.858337\pi\)
−0.902591 + 0.430500i \(0.858337\pi\)
\(3\) −0.169380 −0.0977917 −0.0488958 0.998804i \(-0.515570\pi\)
−0.0488958 + 0.998804i \(0.515570\pi\)
\(4\) 4.51736 2.25868
\(5\) −0.762748 −0.341111 −0.170556 0.985348i \(-0.554556\pi\)
−0.170556 + 0.985348i \(0.554556\pi\)
\(6\) 0.432413 0.176532
\(7\) 0.998481 0.377390 0.188695 0.982036i \(-0.439574\pi\)
0.188695 + 0.982036i \(0.439574\pi\)
\(8\) −6.42660 −2.27215
\(9\) −2.97131 −0.990437
\(10\) 1.94723 0.615768
\(11\) 3.25596 0.981708 0.490854 0.871242i \(-0.336685\pi\)
0.490854 + 0.871242i \(0.336685\pi\)
\(12\) −0.765151 −0.220880
\(13\) −2.38564 −0.661657 −0.330829 0.943691i \(-0.607328\pi\)
−0.330829 + 0.943691i \(0.607328\pi\)
\(14\) −2.54904 −0.681258
\(15\) 0.129194 0.0333578
\(16\) 7.37183 1.84296
\(17\) −5.61636 −1.36217 −0.681083 0.732206i \(-0.738491\pi\)
−0.681083 + 0.732206i \(0.738491\pi\)
\(18\) 7.58549 1.78792
\(19\) −0.236108 −0.0541670 −0.0270835 0.999633i \(-0.508622\pi\)
−0.0270835 + 0.999633i \(0.508622\pi\)
\(20\) −3.44561 −0.770462
\(21\) −0.169123 −0.0369056
\(22\) −8.31217 −1.77216
\(23\) 0.0343603 0.00716463 0.00358231 0.999994i \(-0.498860\pi\)
0.00358231 + 0.999994i \(0.498860\pi\)
\(24\) 1.08854 0.222197
\(25\) −4.41822 −0.883643
\(26\) 6.09033 1.19441
\(27\) 1.01142 0.194648
\(28\) 4.51050 0.852404
\(29\) 4.27471 0.793793 0.396896 0.917863i \(-0.370087\pi\)
0.396896 + 0.917863i \(0.370087\pi\)
\(30\) −0.329822 −0.0602170
\(31\) 1.74002 0.312517 0.156258 0.987716i \(-0.450057\pi\)
0.156258 + 0.987716i \(0.450057\pi\)
\(32\) −5.96642 −1.05472
\(33\) −0.551494 −0.0960028
\(34\) 14.3381 2.45896
\(35\) −0.761590 −0.128732
\(36\) −13.4225 −2.23708
\(37\) −0.632150 −0.103925 −0.0519624 0.998649i \(-0.516548\pi\)
−0.0519624 + 0.998649i \(0.516548\pi\)
\(38\) 0.602764 0.0977812
\(39\) 0.404080 0.0647046
\(40\) 4.90188 0.775055
\(41\) 3.96974 0.619969 0.309984 0.950742i \(-0.399676\pi\)
0.309984 + 0.950742i \(0.399676\pi\)
\(42\) 0.431756 0.0666214
\(43\) 3.03857 0.463377 0.231689 0.972790i \(-0.425575\pi\)
0.231689 + 0.972790i \(0.425575\pi\)
\(44\) 14.7083 2.21736
\(45\) 2.26636 0.337849
\(46\) −0.0877189 −0.0129335
\(47\) 0.324569 0.0473432 0.0236716 0.999720i \(-0.492464\pi\)
0.0236716 + 0.999720i \(0.492464\pi\)
\(48\) −1.24864 −0.180226
\(49\) −6.00304 −0.857576
\(50\) 11.2793 1.59514
\(51\) 0.951299 0.133209
\(52\) −10.7768 −1.49447
\(53\) −1.00000 −0.137361
\(54\) −2.58207 −0.351375
\(55\) −2.48347 −0.334872
\(56\) −6.41684 −0.857486
\(57\) 0.0399921 0.00529708
\(58\) −10.9129 −1.43294
\(59\) 13.5090 1.75872 0.879361 0.476156i \(-0.157970\pi\)
0.879361 + 0.476156i \(0.157970\pi\)
\(60\) 0.583618 0.0753447
\(61\) 9.22106 1.18064 0.590318 0.807171i \(-0.299002\pi\)
0.590318 + 0.807171i \(0.299002\pi\)
\(62\) −4.44212 −0.564150
\(63\) −2.96680 −0.373781
\(64\) 0.488101 0.0610127
\(65\) 1.81964 0.225699
\(66\) 1.40792 0.173302
\(67\) −8.81790 −1.07728 −0.538639 0.842537i \(-0.681061\pi\)
−0.538639 + 0.842537i \(0.681061\pi\)
\(68\) −25.3711 −3.07670
\(69\) −0.00581996 −0.000700641 0
\(70\) 1.94427 0.232385
\(71\) 14.2107 1.68650 0.843252 0.537519i \(-0.180638\pi\)
0.843252 + 0.537519i \(0.180638\pi\)
\(72\) 19.0954 2.25042
\(73\) 7.81582 0.914773 0.457386 0.889268i \(-0.348786\pi\)
0.457386 + 0.889268i \(0.348786\pi\)
\(74\) 1.61382 0.187603
\(75\) 0.748358 0.0864129
\(76\) −1.06659 −0.122346
\(77\) 3.25101 0.370487
\(78\) −1.03158 −0.116803
\(79\) −0.258786 −0.0291157 −0.0145579 0.999894i \(-0.504634\pi\)
−0.0145579 + 0.999894i \(0.504634\pi\)
\(80\) −5.62285 −0.628653
\(81\) 8.74262 0.971402
\(82\) −10.1344 −1.11916
\(83\) −7.55717 −0.829507 −0.414754 0.909934i \(-0.636132\pi\)
−0.414754 + 0.909934i \(0.636132\pi\)
\(84\) −0.763989 −0.0833580
\(85\) 4.28387 0.464651
\(86\) −7.75720 −0.836480
\(87\) −0.724050 −0.0776263
\(88\) −20.9247 −2.23058
\(89\) 9.59998 1.01760 0.508798 0.860886i \(-0.330090\pi\)
0.508798 + 0.860886i \(0.330090\pi\)
\(90\) −5.78582 −0.609879
\(91\) −2.38202 −0.249703
\(92\) 0.155218 0.0161826
\(93\) −0.294725 −0.0305615
\(94\) −0.828595 −0.0854631
\(95\) 0.180091 0.0184770
\(96\) 1.01059 0.103143
\(97\) 9.21304 0.935442 0.467721 0.883876i \(-0.345075\pi\)
0.467721 + 0.883876i \(0.345075\pi\)
\(98\) 15.3252 1.54808
\(99\) −9.67446 −0.972319
\(100\) −19.9587 −1.99587
\(101\) −6.01080 −0.598097 −0.299048 0.954238i \(-0.596669\pi\)
−0.299048 + 0.954238i \(0.596669\pi\)
\(102\) −2.42858 −0.240466
\(103\) −1.75012 −0.172445 −0.0862225 0.996276i \(-0.527480\pi\)
−0.0862225 + 0.996276i \(0.527480\pi\)
\(104\) 15.3316 1.50338
\(105\) 0.128998 0.0125889
\(106\) 2.55291 0.247961
\(107\) 7.05450 0.681984 0.340992 0.940066i \(-0.389237\pi\)
0.340992 + 0.940066i \(0.389237\pi\)
\(108\) 4.56895 0.439648
\(109\) −15.2490 −1.46059 −0.730296 0.683131i \(-0.760618\pi\)
−0.730296 + 0.683131i \(0.760618\pi\)
\(110\) 6.34009 0.604504
\(111\) 0.107074 0.0101630
\(112\) 7.36063 0.695514
\(113\) −12.5740 −1.18286 −0.591431 0.806355i \(-0.701437\pi\)
−0.591431 + 0.806355i \(0.701437\pi\)
\(114\) −0.102096 −0.00956219
\(115\) −0.0262083 −0.00244394
\(116\) 19.3104 1.79292
\(117\) 7.08847 0.655330
\(118\) −34.4873 −3.17481
\(119\) −5.60783 −0.514069
\(120\) −0.830281 −0.0757939
\(121\) −0.398752 −0.0362502
\(122\) −23.5406 −2.13126
\(123\) −0.672395 −0.0606278
\(124\) 7.86030 0.705876
\(125\) 7.18373 0.642532
\(126\) 7.57397 0.674743
\(127\) −6.02956 −0.535037 −0.267518 0.963553i \(-0.586204\pi\)
−0.267518 + 0.963553i \(0.586204\pi\)
\(128\) 10.6868 0.944586
\(129\) −0.514673 −0.0453144
\(130\) −4.64539 −0.407427
\(131\) −19.5158 −1.70510 −0.852552 0.522642i \(-0.824946\pi\)
−0.852552 + 0.522642i \(0.824946\pi\)
\(132\) −2.49130 −0.216840
\(133\) −0.235750 −0.0204421
\(134\) 22.5113 1.94468
\(135\) −0.771460 −0.0663967
\(136\) 36.0941 3.09504
\(137\) −0.456732 −0.0390213 −0.0195106 0.999810i \(-0.506211\pi\)
−0.0195106 + 0.999810i \(0.506211\pi\)
\(138\) 0.0148578 0.00126478
\(139\) 13.5613 1.15025 0.575126 0.818065i \(-0.304953\pi\)
0.575126 + 0.818065i \(0.304953\pi\)
\(140\) −3.44038 −0.290765
\(141\) −0.0549755 −0.00462977
\(142\) −36.2788 −3.04445
\(143\) −7.76754 −0.649554
\(144\) −21.9040 −1.82533
\(145\) −3.26052 −0.270772
\(146\) −19.9531 −1.65133
\(147\) 1.01679 0.0838638
\(148\) −2.85565 −0.234733
\(149\) 7.22946 0.592260 0.296130 0.955148i \(-0.404304\pi\)
0.296130 + 0.955148i \(0.404304\pi\)
\(150\) −1.91049 −0.155991
\(151\) −1.00000 −0.0813788
\(152\) 1.51737 0.123075
\(153\) 16.6879 1.34914
\(154\) −8.29955 −0.668796
\(155\) −1.32720 −0.106603
\(156\) 1.82537 0.146147
\(157\) 0.772562 0.0616572 0.0308286 0.999525i \(-0.490185\pi\)
0.0308286 + 0.999525i \(0.490185\pi\)
\(158\) 0.660658 0.0525592
\(159\) 0.169380 0.0134327
\(160\) 4.55088 0.359779
\(161\) 0.0343082 0.00270386
\(162\) −22.3191 −1.75356
\(163\) −1.65366 −0.129525 −0.0647624 0.997901i \(-0.520629\pi\)
−0.0647624 + 0.997901i \(0.520629\pi\)
\(164\) 17.9327 1.40031
\(165\) 0.420651 0.0327477
\(166\) 19.2928 1.49741
\(167\) −0.0974749 −0.00754284 −0.00377142 0.999993i \(-0.501200\pi\)
−0.00377142 + 0.999993i \(0.501200\pi\)
\(168\) 1.08689 0.0838550
\(169\) −7.30873 −0.562210
\(170\) −10.9363 −0.838779
\(171\) 0.701551 0.0536490
\(172\) 13.7263 1.04662
\(173\) 15.7605 1.19825 0.599125 0.800656i \(-0.295515\pi\)
0.599125 + 0.800656i \(0.295515\pi\)
\(174\) 1.84844 0.140130
\(175\) −4.41150 −0.333478
\(176\) 24.0023 1.80924
\(177\) −2.28816 −0.171988
\(178\) −24.5079 −1.83695
\(179\) 23.8386 1.78178 0.890892 0.454215i \(-0.150080\pi\)
0.890892 + 0.454215i \(0.150080\pi\)
\(180\) 10.2380 0.763094
\(181\) −0.399625 −0.0297039 −0.0148520 0.999890i \(-0.504728\pi\)
−0.0148520 + 0.999890i \(0.504728\pi\)
\(182\) 6.08108 0.450759
\(183\) −1.56186 −0.115456
\(184\) −0.220820 −0.0162791
\(185\) 0.482171 0.0354499
\(186\) 0.752407 0.0551691
\(187\) −18.2866 −1.33725
\(188\) 1.46619 0.106933
\(189\) 1.00989 0.0734583
\(190\) −0.459757 −0.0333543
\(191\) −6.94831 −0.502762 −0.251381 0.967888i \(-0.580885\pi\)
−0.251381 + 0.967888i \(0.580885\pi\)
\(192\) −0.0826747 −0.00596653
\(193\) −19.1235 −1.37654 −0.688268 0.725456i \(-0.741629\pi\)
−0.688268 + 0.725456i \(0.741629\pi\)
\(194\) −23.5201 −1.68864
\(195\) −0.308211 −0.0220715
\(196\) −27.1179 −1.93699
\(197\) 8.89670 0.633864 0.316932 0.948448i \(-0.397347\pi\)
0.316932 + 0.948448i \(0.397347\pi\)
\(198\) 24.6980 1.75521
\(199\) −14.6032 −1.03519 −0.517597 0.855624i \(-0.673173\pi\)
−0.517597 + 0.855624i \(0.673173\pi\)
\(200\) 28.3941 2.00777
\(201\) 1.49358 0.105349
\(202\) 15.3450 1.07967
\(203\) 4.26821 0.299570
\(204\) 4.29736 0.300876
\(205\) −3.02791 −0.211478
\(206\) 4.46791 0.311294
\(207\) −0.102095 −0.00709611
\(208\) −17.5865 −1.21941
\(209\) −0.768759 −0.0531761
\(210\) −0.329321 −0.0227253
\(211\) −20.8058 −1.43233 −0.716165 0.697931i \(-0.754104\pi\)
−0.716165 + 0.697931i \(0.754104\pi\)
\(212\) −4.51736 −0.310254
\(213\) −2.40702 −0.164926
\(214\) −18.0095 −1.23111
\(215\) −2.31766 −0.158063
\(216\) −6.50000 −0.442269
\(217\) 1.73738 0.117941
\(218\) 38.9294 2.63663
\(219\) −1.32384 −0.0894571
\(220\) −11.2188 −0.756368
\(221\) 13.3986 0.901288
\(222\) −0.273350 −0.0183460
\(223\) −23.7859 −1.59282 −0.796411 0.604756i \(-0.793271\pi\)
−0.796411 + 0.604756i \(0.793271\pi\)
\(224\) −5.95736 −0.398043
\(225\) 13.1279 0.875193
\(226\) 32.1003 2.13528
\(227\) 22.8458 1.51633 0.758165 0.652063i \(-0.226096\pi\)
0.758165 + 0.652063i \(0.226096\pi\)
\(228\) 0.180659 0.0119644
\(229\) 6.02333 0.398033 0.199017 0.979996i \(-0.436225\pi\)
0.199017 + 0.979996i \(0.436225\pi\)
\(230\) 0.0669075 0.00441175
\(231\) −0.550657 −0.0362305
\(232\) −27.4718 −1.80361
\(233\) −27.0992 −1.77533 −0.887665 0.460490i \(-0.847674\pi\)
−0.887665 + 0.460490i \(0.847674\pi\)
\(234\) −18.0963 −1.18299
\(235\) −0.247564 −0.0161493
\(236\) 61.0250 3.97239
\(237\) 0.0438332 0.00284727
\(238\) 14.3163 0.927988
\(239\) −26.7586 −1.73087 −0.865434 0.501023i \(-0.832957\pi\)
−0.865434 + 0.501023i \(0.832957\pi\)
\(240\) 0.952399 0.0614771
\(241\) 27.5376 1.77385 0.886925 0.461913i \(-0.152837\pi\)
0.886925 + 0.461913i \(0.152837\pi\)
\(242\) 1.01798 0.0654381
\(243\) −4.51509 −0.289643
\(244\) 41.6548 2.66668
\(245\) 4.57880 0.292529
\(246\) 1.71656 0.109444
\(247\) 0.563270 0.0358400
\(248\) −11.1824 −0.710084
\(249\) 1.28003 0.0811189
\(250\) −18.3394 −1.15989
\(251\) −26.9056 −1.69827 −0.849133 0.528179i \(-0.822875\pi\)
−0.849133 + 0.528179i \(0.822875\pi\)
\(252\) −13.4021 −0.844253
\(253\) 0.111876 0.00703357
\(254\) 15.3929 0.965838
\(255\) −0.725602 −0.0454390
\(256\) −28.2586 −1.76616
\(257\) 4.90814 0.306161 0.153081 0.988214i \(-0.451081\pi\)
0.153081 + 0.988214i \(0.451081\pi\)
\(258\) 1.31392 0.0818008
\(259\) −0.631190 −0.0392202
\(260\) 8.21998 0.509782
\(261\) −12.7015 −0.786202
\(262\) 49.8222 3.07802
\(263\) −17.0341 −1.05037 −0.525185 0.850988i \(-0.676004\pi\)
−0.525185 + 0.850988i \(0.676004\pi\)
\(264\) 3.54423 0.218132
\(265\) 0.762748 0.0468553
\(266\) 0.601849 0.0369017
\(267\) −1.62605 −0.0995124
\(268\) −39.8336 −2.43323
\(269\) −19.9660 −1.21735 −0.608674 0.793420i \(-0.708298\pi\)
−0.608674 + 0.793420i \(0.708298\pi\)
\(270\) 1.96947 0.119858
\(271\) −0.484274 −0.0294176 −0.0147088 0.999892i \(-0.504682\pi\)
−0.0147088 + 0.999892i \(0.504682\pi\)
\(272\) −41.4028 −2.51041
\(273\) 0.403466 0.0244189
\(274\) 1.16600 0.0704405
\(275\) −14.3855 −0.867479
\(276\) −0.0262909 −0.00158252
\(277\) −9.62834 −0.578511 −0.289255 0.957252i \(-0.593408\pi\)
−0.289255 + 0.957252i \(0.593408\pi\)
\(278\) −34.6207 −2.07641
\(279\) −5.17014 −0.309528
\(280\) 4.89443 0.292498
\(281\) −2.67286 −0.159449 −0.0797246 0.996817i \(-0.525404\pi\)
−0.0797246 + 0.996817i \(0.525404\pi\)
\(282\) 0.140348 0.00835758
\(283\) −9.10043 −0.540964 −0.270482 0.962725i \(-0.587183\pi\)
−0.270482 + 0.962725i \(0.587183\pi\)
\(284\) 64.1950 3.80927
\(285\) −0.0305039 −0.00180689
\(286\) 19.8298 1.17256
\(287\) 3.96371 0.233970
\(288\) 17.7281 1.04464
\(289\) 14.5435 0.855499
\(290\) 8.32383 0.488792
\(291\) −1.56051 −0.0914784
\(292\) 35.3069 2.06618
\(293\) 14.2652 0.833381 0.416691 0.909048i \(-0.363190\pi\)
0.416691 + 0.909048i \(0.363190\pi\)
\(294\) −2.59579 −0.151389
\(295\) −10.3040 −0.599920
\(296\) 4.06257 0.236132
\(297\) 3.29314 0.191088
\(298\) −18.4562 −1.06914
\(299\) −0.0819714 −0.00474053
\(300\) 3.38060 0.195179
\(301\) 3.03395 0.174874
\(302\) 2.55291 0.146904
\(303\) 1.01811 0.0584889
\(304\) −1.74055 −0.0998274
\(305\) −7.03335 −0.402728
\(306\) −42.6029 −2.43544
\(307\) 10.1713 0.580506 0.290253 0.956950i \(-0.406261\pi\)
0.290253 + 0.956950i \(0.406261\pi\)
\(308\) 14.6860 0.836812
\(309\) 0.296436 0.0168637
\(310\) 3.38822 0.192438
\(311\) −6.47695 −0.367274 −0.183637 0.982994i \(-0.558787\pi\)
−0.183637 + 0.982994i \(0.558787\pi\)
\(312\) −2.59686 −0.147018
\(313\) −34.7056 −1.96168 −0.980838 0.194827i \(-0.937585\pi\)
−0.980838 + 0.194827i \(0.937585\pi\)
\(314\) −1.97228 −0.111302
\(315\) 2.26292 0.127501
\(316\) −1.16903 −0.0657631
\(317\) 18.8186 1.05696 0.528478 0.848947i \(-0.322763\pi\)
0.528478 + 0.848947i \(0.322763\pi\)
\(318\) −0.432413 −0.0242485
\(319\) 13.9183 0.779273
\(320\) −0.372298 −0.0208121
\(321\) −1.19489 −0.0666924
\(322\) −0.0875857 −0.00488096
\(323\) 1.32607 0.0737845
\(324\) 39.4936 2.19409
\(325\) 10.5403 0.584669
\(326\) 4.22165 0.233816
\(327\) 2.58288 0.142834
\(328\) −25.5119 −1.40866
\(329\) 0.324076 0.0178669
\(330\) −1.07389 −0.0591155
\(331\) −14.5066 −0.797355 −0.398678 0.917091i \(-0.630531\pi\)
−0.398678 + 0.917091i \(0.630531\pi\)
\(332\) −34.1385 −1.87359
\(333\) 1.87831 0.102931
\(334\) 0.248845 0.0136162
\(335\) 6.72584 0.367472
\(336\) −1.24674 −0.0680155
\(337\) −25.1291 −1.36887 −0.684435 0.729074i \(-0.739951\pi\)
−0.684435 + 0.729074i \(0.739951\pi\)
\(338\) 18.6585 1.01489
\(339\) 2.12979 0.115674
\(340\) 19.3518 1.04950
\(341\) 5.66543 0.306800
\(342\) −1.79100 −0.0968461
\(343\) −12.9833 −0.701032
\(344\) −19.5277 −1.05286
\(345\) 0.00443916 0.000238997 0
\(346\) −40.2352 −2.16306
\(347\) 12.1097 0.650085 0.325042 0.945699i \(-0.394621\pi\)
0.325042 + 0.945699i \(0.394621\pi\)
\(348\) −3.27080 −0.175333
\(349\) −9.60542 −0.514167 −0.257083 0.966389i \(-0.582761\pi\)
−0.257083 + 0.966389i \(0.582761\pi\)
\(350\) 11.2622 0.601989
\(351\) −2.41289 −0.128790
\(352\) −19.4264 −1.03543
\(353\) −9.19399 −0.489347 −0.244673 0.969606i \(-0.578681\pi\)
−0.244673 + 0.969606i \(0.578681\pi\)
\(354\) 5.84146 0.310470
\(355\) −10.8392 −0.575286
\(356\) 43.3666 2.29842
\(357\) 0.949855 0.0502716
\(358\) −60.8580 −3.21644
\(359\) 25.6514 1.35383 0.676915 0.736061i \(-0.263316\pi\)
0.676915 + 0.736061i \(0.263316\pi\)
\(360\) −14.5650 −0.767643
\(361\) −18.9443 −0.997066
\(362\) 1.02021 0.0536209
\(363\) 0.0675406 0.00354496
\(364\) −10.7604 −0.564000
\(365\) −5.96150 −0.312039
\(366\) 3.98730 0.208420
\(367\) 20.9507 1.09362 0.546809 0.837257i \(-0.315842\pi\)
0.546809 + 0.837257i \(0.315842\pi\)
\(368\) 0.253298 0.0132041
\(369\) −11.7953 −0.614040
\(370\) −1.23094 −0.0639936
\(371\) −0.998481 −0.0518386
\(372\) −1.33138 −0.0690288
\(373\) 6.23367 0.322767 0.161384 0.986892i \(-0.448404\pi\)
0.161384 + 0.986892i \(0.448404\pi\)
\(374\) 46.6841 2.41398
\(375\) −1.21678 −0.0628343
\(376\) −2.08587 −0.107571
\(377\) −10.1979 −0.525219
\(378\) −2.57815 −0.132606
\(379\) −5.01634 −0.257672 −0.128836 0.991666i \(-0.541124\pi\)
−0.128836 + 0.991666i \(0.541124\pi\)
\(380\) 0.813537 0.0417336
\(381\) 1.02129 0.0523221
\(382\) 17.7384 0.907577
\(383\) −17.2339 −0.880611 −0.440306 0.897848i \(-0.645130\pi\)
−0.440306 + 0.897848i \(0.645130\pi\)
\(384\) −1.81013 −0.0923726
\(385\) −2.47970 −0.126377
\(386\) 48.8205 2.48490
\(387\) −9.02853 −0.458946
\(388\) 41.6186 2.11286
\(389\) 7.33855 0.372079 0.186040 0.982542i \(-0.440435\pi\)
0.186040 + 0.982542i \(0.440435\pi\)
\(390\) 0.786836 0.0398430
\(391\) −0.192980 −0.00975942
\(392\) 38.5791 1.94854
\(393\) 3.30559 0.166745
\(394\) −22.7125 −1.14424
\(395\) 0.197389 0.00993171
\(396\) −43.7030 −2.19616
\(397\) 37.4051 1.87731 0.938653 0.344862i \(-0.112074\pi\)
0.938653 + 0.344862i \(0.112074\pi\)
\(398\) 37.2807 1.86871
\(399\) 0.0399313 0.00199907
\(400\) −32.5703 −1.62852
\(401\) 38.6015 1.92767 0.963835 0.266501i \(-0.0858676\pi\)
0.963835 + 0.266501i \(0.0858676\pi\)
\(402\) −3.81297 −0.190174
\(403\) −4.15106 −0.206779
\(404\) −27.1529 −1.35091
\(405\) −6.66842 −0.331356
\(406\) −10.8964 −0.540778
\(407\) −2.05825 −0.102024
\(408\) −6.11362 −0.302669
\(409\) 23.7642 1.17506 0.587532 0.809201i \(-0.300100\pi\)
0.587532 + 0.809201i \(0.300100\pi\)
\(410\) 7.72999 0.381757
\(411\) 0.0773614 0.00381595
\(412\) −7.90594 −0.389498
\(413\) 13.4885 0.663725
\(414\) 0.260640 0.0128098
\(415\) 5.76422 0.282954
\(416\) 14.2337 0.697866
\(417\) −2.29701 −0.112485
\(418\) 1.96257 0.0959926
\(419\) 17.9562 0.877220 0.438610 0.898678i \(-0.355471\pi\)
0.438610 + 0.898678i \(0.355471\pi\)
\(420\) 0.582731 0.0284344
\(421\) 1.08410 0.0528359 0.0264180 0.999651i \(-0.491590\pi\)
0.0264180 + 0.999651i \(0.491590\pi\)
\(422\) 53.1153 2.58561
\(423\) −0.964394 −0.0468905
\(424\) 6.42660 0.312103
\(425\) 24.8143 1.20367
\(426\) 6.14490 0.297721
\(427\) 9.20705 0.445561
\(428\) 31.8677 1.54038
\(429\) 1.31567 0.0635210
\(430\) 5.91679 0.285333
\(431\) −9.53990 −0.459521 −0.229761 0.973247i \(-0.573794\pi\)
−0.229761 + 0.973247i \(0.573794\pi\)
\(432\) 7.45602 0.358728
\(433\) 27.7840 1.33521 0.667607 0.744514i \(-0.267319\pi\)
0.667607 + 0.744514i \(0.267319\pi\)
\(434\) −4.43537 −0.212905
\(435\) 0.552268 0.0264792
\(436\) −68.8854 −3.29901
\(437\) −0.00811277 −0.000388086 0
\(438\) 3.37966 0.161486
\(439\) 23.5155 1.12233 0.561166 0.827703i \(-0.310353\pi\)
0.561166 + 0.827703i \(0.310353\pi\)
\(440\) 15.9603 0.760877
\(441\) 17.8369 0.849375
\(442\) −34.2055 −1.62699
\(443\) 4.86448 0.231118 0.115559 0.993301i \(-0.463134\pi\)
0.115559 + 0.993301i \(0.463134\pi\)
\(444\) 0.483690 0.0229549
\(445\) −7.32237 −0.347114
\(446\) 60.7233 2.87533
\(447\) −1.22453 −0.0579181
\(448\) 0.487360 0.0230256
\(449\) 27.7489 1.30955 0.654776 0.755823i \(-0.272763\pi\)
0.654776 + 0.755823i \(0.272763\pi\)
\(450\) −33.5143 −1.57988
\(451\) 12.9253 0.608628
\(452\) −56.8013 −2.67171
\(453\) 0.169380 0.00795817
\(454\) −58.3233 −2.73725
\(455\) 1.81688 0.0851766
\(456\) −0.257013 −0.0120357
\(457\) −13.7244 −0.642001 −0.321001 0.947079i \(-0.604019\pi\)
−0.321001 + 0.947079i \(0.604019\pi\)
\(458\) −15.3770 −0.718522
\(459\) −5.68050 −0.265143
\(460\) −0.118392 −0.00552007
\(461\) 12.9906 0.605031 0.302516 0.953144i \(-0.402174\pi\)
0.302516 + 0.953144i \(0.402174\pi\)
\(462\) 1.40578 0.0654027
\(463\) 18.0506 0.838881 0.419440 0.907783i \(-0.362226\pi\)
0.419440 + 0.907783i \(0.362226\pi\)
\(464\) 31.5124 1.46293
\(465\) 0.224801 0.0104249
\(466\) 69.1820 3.20479
\(467\) −20.6379 −0.955009 −0.477504 0.878629i \(-0.658459\pi\)
−0.477504 + 0.878629i \(0.658459\pi\)
\(468\) 32.0212 1.48018
\(469\) −8.80451 −0.406554
\(470\) 0.632010 0.0291524
\(471\) −0.130857 −0.00602956
\(472\) −86.8169 −3.99607
\(473\) 9.89345 0.454901
\(474\) −0.111902 −0.00513985
\(475\) 1.04318 0.0478643
\(476\) −25.3326 −1.16112
\(477\) 2.97131 0.136047
\(478\) 68.3123 3.12453
\(479\) 8.19536 0.374456 0.187228 0.982317i \(-0.440050\pi\)
0.187228 + 0.982317i \(0.440050\pi\)
\(480\) −0.770828 −0.0351833
\(481\) 1.50808 0.0687626
\(482\) −70.3010 −3.20212
\(483\) −0.00581112 −0.000264415 0
\(484\) −1.80131 −0.0818775
\(485\) −7.02723 −0.319090
\(486\) 11.5266 0.522858
\(487\) −2.73244 −0.123819 −0.0619093 0.998082i \(-0.519719\pi\)
−0.0619093 + 0.998082i \(0.519719\pi\)
\(488\) −59.2601 −2.68258
\(489\) 0.280097 0.0126664
\(490\) −11.6893 −0.528068
\(491\) −21.5899 −0.974339 −0.487169 0.873308i \(-0.661971\pi\)
−0.487169 + 0.873308i \(0.661971\pi\)
\(492\) −3.03745 −0.136939
\(493\) −24.0083 −1.08128
\(494\) −1.43798 −0.0646977
\(495\) 7.37917 0.331669
\(496\) 12.8271 0.575955
\(497\) 14.1892 0.636470
\(498\) −3.26782 −0.146434
\(499\) −20.7945 −0.930888 −0.465444 0.885077i \(-0.654105\pi\)
−0.465444 + 0.885077i \(0.654105\pi\)
\(500\) 32.4515 1.45127
\(501\) 0.0165103 0.000737626 0
\(502\) 68.6876 3.06568
\(503\) −25.0163 −1.11542 −0.557710 0.830036i \(-0.688320\pi\)
−0.557710 + 0.830036i \(0.688320\pi\)
\(504\) 19.0664 0.849286
\(505\) 4.58473 0.204018
\(506\) −0.285609 −0.0126969
\(507\) 1.23795 0.0549794
\(508\) −27.2377 −1.20848
\(509\) −16.6451 −0.737783 −0.368891 0.929472i \(-0.620263\pi\)
−0.368891 + 0.929472i \(0.620263\pi\)
\(510\) 1.85240 0.0820256
\(511\) 7.80395 0.345226
\(512\) 50.7681 2.24366
\(513\) −0.238805 −0.0105435
\(514\) −12.5301 −0.552677
\(515\) 1.33490 0.0588229
\(516\) −2.32496 −0.102351
\(517\) 1.05678 0.0464772
\(518\) 1.61137 0.0707996
\(519\) −2.66952 −0.117179
\(520\) −11.6941 −0.512821
\(521\) 25.4052 1.11302 0.556511 0.830841i \(-0.312140\pi\)
0.556511 + 0.830841i \(0.312140\pi\)
\(522\) 32.4258 1.41924
\(523\) −37.7426 −1.65037 −0.825185 0.564862i \(-0.808929\pi\)
−0.825185 + 0.564862i \(0.808929\pi\)
\(524\) −88.1600 −3.85129
\(525\) 0.747221 0.0326114
\(526\) 43.4867 1.89611
\(527\) −9.77258 −0.425700
\(528\) −4.06552 −0.176929
\(529\) −22.9988 −0.999949
\(530\) −1.94723 −0.0845822
\(531\) −40.1394 −1.74190
\(532\) −1.06497 −0.0461722
\(533\) −9.47036 −0.410207
\(534\) 4.15115 0.179638
\(535\) −5.38081 −0.232633
\(536\) 56.6691 2.44773
\(537\) −4.03779 −0.174244
\(538\) 50.9715 2.19754
\(539\) −19.5456 −0.841889
\(540\) −3.48496 −0.149969
\(541\) 35.7933 1.53887 0.769437 0.638723i \(-0.220537\pi\)
0.769437 + 0.638723i \(0.220537\pi\)
\(542\) 1.23631 0.0531041
\(543\) 0.0676886 0.00290479
\(544\) 33.5096 1.43671
\(545\) 11.6312 0.498225
\(546\) −1.03001 −0.0440805
\(547\) 14.8935 0.636800 0.318400 0.947956i \(-0.396854\pi\)
0.318400 + 0.947956i \(0.396854\pi\)
\(548\) −2.06322 −0.0881366
\(549\) −27.3986 −1.16934
\(550\) 36.7250 1.56596
\(551\) −1.00929 −0.0429974
\(552\) 0.0374026 0.00159196
\(553\) −0.258393 −0.0109880
\(554\) 24.5803 1.04432
\(555\) −0.0816702 −0.00346671
\(556\) 61.2612 2.59805
\(557\) −20.3983 −0.864304 −0.432152 0.901801i \(-0.642246\pi\)
−0.432152 + 0.901801i \(0.642246\pi\)
\(558\) 13.1989 0.558755
\(559\) −7.24893 −0.306597
\(560\) −5.61431 −0.237248
\(561\) 3.09739 0.130772
\(562\) 6.82357 0.287835
\(563\) 3.22812 0.136049 0.0680246 0.997684i \(-0.478330\pi\)
0.0680246 + 0.997684i \(0.478330\pi\)
\(564\) −0.248344 −0.0104572
\(565\) 9.59080 0.403488
\(566\) 23.2326 0.976539
\(567\) 8.72934 0.366598
\(568\) −91.3267 −3.83198
\(569\) −25.7502 −1.07950 −0.539752 0.841824i \(-0.681482\pi\)
−0.539752 + 0.841824i \(0.681482\pi\)
\(570\) 0.0778737 0.00326177
\(571\) 4.35595 0.182291 0.0911454 0.995838i \(-0.470947\pi\)
0.0911454 + 0.995838i \(0.470947\pi\)
\(572\) −35.0888 −1.46713
\(573\) 1.17691 0.0491659
\(574\) −10.1190 −0.422359
\(575\) −0.151811 −0.00633097
\(576\) −1.45030 −0.0604292
\(577\) 38.1063 1.58639 0.793193 0.608970i \(-0.208417\pi\)
0.793193 + 0.608970i \(0.208417\pi\)
\(578\) −37.1282 −1.54433
\(579\) 3.23913 0.134614
\(580\) −14.7290 −0.611587
\(581\) −7.54569 −0.313048
\(582\) 3.98383 0.165135
\(583\) −3.25596 −0.134848
\(584\) −50.2292 −2.07850
\(585\) −5.40672 −0.223540
\(586\) −36.4178 −1.50440
\(587\) −45.8227 −1.89131 −0.945653 0.325177i \(-0.894576\pi\)
−0.945653 + 0.325177i \(0.894576\pi\)
\(588\) 4.59323 0.189422
\(589\) −0.410834 −0.0169281
\(590\) 26.3051 1.08296
\(591\) −1.50692 −0.0619866
\(592\) −4.66010 −0.191529
\(593\) 3.16572 0.130001 0.0650003 0.997885i \(-0.479295\pi\)
0.0650003 + 0.997885i \(0.479295\pi\)
\(594\) −8.40710 −0.344948
\(595\) 4.27736 0.175355
\(596\) 32.6581 1.33773
\(597\) 2.47349 0.101233
\(598\) 0.209266 0.00855751
\(599\) −2.11033 −0.0862257 −0.0431128 0.999070i \(-0.513727\pi\)
−0.0431128 + 0.999070i \(0.513727\pi\)
\(600\) −4.80940 −0.196343
\(601\) −40.9755 −1.67142 −0.835712 0.549168i \(-0.814945\pi\)
−0.835712 + 0.549168i \(0.814945\pi\)
\(602\) −7.74542 −0.315680
\(603\) 26.2007 1.06698
\(604\) −4.51736 −0.183809
\(605\) 0.304147 0.0123653
\(606\) −2.59914 −0.105583
\(607\) −36.3526 −1.47551 −0.737753 0.675070i \(-0.764113\pi\)
−0.737753 + 0.675070i \(0.764113\pi\)
\(608\) 1.40872 0.0571312
\(609\) −0.722951 −0.0292954
\(610\) 17.9555 0.726998
\(611\) −0.774304 −0.0313250
\(612\) 75.3855 3.04728
\(613\) −37.1747 −1.50147 −0.750735 0.660603i \(-0.770301\pi\)
−0.750735 + 0.660603i \(0.770301\pi\)
\(614\) −25.9664 −1.04792
\(615\) 0.512868 0.0206808
\(616\) −20.8929 −0.841801
\(617\) 24.6099 0.990756 0.495378 0.868677i \(-0.335030\pi\)
0.495378 + 0.868677i \(0.335030\pi\)
\(618\) −0.756776 −0.0304420
\(619\) 29.5641 1.18828 0.594140 0.804362i \(-0.297493\pi\)
0.594140 + 0.804362i \(0.297493\pi\)
\(620\) −5.99543 −0.240782
\(621\) 0.0347528 0.00139458
\(622\) 16.5351 0.662996
\(623\) 9.58540 0.384031
\(624\) 2.97881 0.119248
\(625\) 16.6117 0.664468
\(626\) 88.6003 3.54118
\(627\) 0.130212 0.00520018
\(628\) 3.48994 0.139264
\(629\) 3.55038 0.141563
\(630\) −5.77704 −0.230163
\(631\) −30.8086 −1.22647 −0.613236 0.789900i \(-0.710132\pi\)
−0.613236 + 0.789900i \(0.710132\pi\)
\(632\) 1.66312 0.0661552
\(633\) 3.52409 0.140070
\(634\) −48.0421 −1.90800
\(635\) 4.59903 0.182507
\(636\) 0.765151 0.0303402
\(637\) 14.3211 0.567422
\(638\) −35.5321 −1.40673
\(639\) −42.2245 −1.67038
\(640\) −8.15131 −0.322209
\(641\) −23.5705 −0.930978 −0.465489 0.885054i \(-0.654122\pi\)
−0.465489 + 0.885054i \(0.654122\pi\)
\(642\) 3.05045 0.120392
\(643\) −31.9327 −1.25930 −0.629651 0.776878i \(-0.716802\pi\)
−0.629651 + 0.776878i \(0.716802\pi\)
\(644\) 0.154982 0.00610716
\(645\) 0.392566 0.0154573
\(646\) −3.38534 −0.133194
\(647\) 34.0811 1.33987 0.669934 0.742421i \(-0.266323\pi\)
0.669934 + 0.742421i \(0.266323\pi\)
\(648\) −56.1853 −2.20717
\(649\) 43.9847 1.72655
\(650\) −26.9084 −1.05543
\(651\) −0.294277 −0.0115336
\(652\) −7.47019 −0.292555
\(653\) 45.6180 1.78517 0.892584 0.450881i \(-0.148890\pi\)
0.892584 + 0.450881i \(0.148890\pi\)
\(654\) −6.59387 −0.257841
\(655\) 14.8857 0.581631
\(656\) 29.2642 1.14258
\(657\) −23.2232 −0.906024
\(658\) −0.827337 −0.0322530
\(659\) −17.7410 −0.691090 −0.345545 0.938402i \(-0.612306\pi\)
−0.345545 + 0.938402i \(0.612306\pi\)
\(660\) 1.90023 0.0739665
\(661\) −36.0502 −1.40219 −0.701095 0.713068i \(-0.747305\pi\)
−0.701095 + 0.713068i \(0.747305\pi\)
\(662\) 37.0341 1.43937
\(663\) −2.26946 −0.0881384
\(664\) 48.5669 1.88476
\(665\) 0.179818 0.00697304
\(666\) −4.79517 −0.185809
\(667\) 0.146880 0.00568723
\(668\) −0.440329 −0.0170369
\(669\) 4.02886 0.155765
\(670\) −17.1705 −0.663353
\(671\) 30.0234 1.15904
\(672\) 1.00906 0.0389253
\(673\) −17.0259 −0.656300 −0.328150 0.944626i \(-0.606425\pi\)
−0.328150 + 0.944626i \(0.606425\pi\)
\(674\) 64.1525 2.47106
\(675\) −4.46868 −0.171999
\(676\) −33.0161 −1.26985
\(677\) 0.925431 0.0355672 0.0177836 0.999842i \(-0.494339\pi\)
0.0177836 + 0.999842i \(0.494339\pi\)
\(678\) −5.43716 −0.208813
\(679\) 9.19904 0.353027
\(680\) −27.5307 −1.05575
\(681\) −3.86963 −0.148284
\(682\) −14.4633 −0.553830
\(683\) −39.6444 −1.51695 −0.758476 0.651701i \(-0.774056\pi\)
−0.758476 + 0.651701i \(0.774056\pi\)
\(684\) 3.16916 0.121176
\(685\) 0.348372 0.0133106
\(686\) 33.1452 1.26549
\(687\) −1.02023 −0.0389243
\(688\) 22.3998 0.853984
\(689\) 2.38564 0.0908856
\(690\) −0.0113328 −0.000431432 0
\(691\) 13.4582 0.511974 0.255987 0.966680i \(-0.417600\pi\)
0.255987 + 0.966680i \(0.417600\pi\)
\(692\) 71.1959 2.70646
\(693\) −9.65976 −0.366944
\(694\) −30.9151 −1.17352
\(695\) −10.3438 −0.392364
\(696\) 4.65318 0.176378
\(697\) −22.2955 −0.844501
\(698\) 24.5218 0.928164
\(699\) 4.59007 0.173612
\(700\) −19.9284 −0.753221
\(701\) 26.1009 0.985817 0.492908 0.870081i \(-0.335934\pi\)
0.492908 + 0.870081i \(0.335934\pi\)
\(702\) 6.15989 0.232490
\(703\) 0.149256 0.00562929
\(704\) 1.58924 0.0598966
\(705\) 0.0419325 0.00157927
\(706\) 23.4715 0.883360
\(707\) −6.00167 −0.225716
\(708\) −10.3364 −0.388467
\(709\) −43.6199 −1.63818 −0.819090 0.573664i \(-0.805521\pi\)
−0.819090 + 0.573664i \(0.805521\pi\)
\(710\) 27.6716 1.03850
\(711\) 0.768934 0.0288373
\(712\) −61.6953 −2.31213
\(713\) 0.0597877 0.00223907
\(714\) −2.42490 −0.0907494
\(715\) 5.92467 0.221570
\(716\) 107.688 4.02448
\(717\) 4.53237 0.169264
\(718\) −65.4859 −2.44391
\(719\) 15.3015 0.570650 0.285325 0.958431i \(-0.407899\pi\)
0.285325 + 0.958431i \(0.407899\pi\)
\(720\) 16.7072 0.622642
\(721\) −1.74747 −0.0650791
\(722\) 48.3630 1.79989
\(723\) −4.66432 −0.173468
\(724\) −1.80525 −0.0670916
\(725\) −18.8866 −0.701430
\(726\) −0.172425 −0.00639930
\(727\) −7.21452 −0.267572 −0.133786 0.991010i \(-0.542713\pi\)
−0.133786 + 0.991010i \(0.542713\pi\)
\(728\) 15.3083 0.567362
\(729\) −25.4631 −0.943077
\(730\) 15.2192 0.563288
\(731\) −17.0657 −0.631197
\(732\) −7.05550 −0.260779
\(733\) −13.9927 −0.516831 −0.258416 0.966034i \(-0.583200\pi\)
−0.258416 + 0.966034i \(0.583200\pi\)
\(734\) −53.4853 −1.97418
\(735\) −0.775558 −0.0286069
\(736\) −0.205008 −0.00755671
\(737\) −28.7107 −1.05757
\(738\) 30.1124 1.10845
\(739\) 38.4809 1.41554 0.707772 0.706441i \(-0.249701\pi\)
0.707772 + 0.706441i \(0.249701\pi\)
\(740\) 2.17814 0.0800701
\(741\) −0.0954067 −0.00350485
\(742\) 2.54904 0.0935780
\(743\) −22.4613 −0.824027 −0.412013 0.911178i \(-0.635174\pi\)
−0.412013 + 0.911178i \(0.635174\pi\)
\(744\) 1.89408 0.0694403
\(745\) −5.51426 −0.202027
\(746\) −15.9140 −0.582653
\(747\) 22.4547 0.821574
\(748\) −82.6072 −3.02042
\(749\) 7.04379 0.257374
\(750\) 3.10633 0.113427
\(751\) 8.93870 0.326178 0.163089 0.986611i \(-0.447854\pi\)
0.163089 + 0.986611i \(0.447854\pi\)
\(752\) 2.39266 0.0872515
\(753\) 4.55727 0.166076
\(754\) 26.0344 0.948115
\(755\) 0.762748 0.0277593
\(756\) 4.56202 0.165919
\(757\) −12.5755 −0.457066 −0.228533 0.973536i \(-0.573393\pi\)
−0.228533 + 0.973536i \(0.573393\pi\)
\(758\) 12.8063 0.465145
\(759\) −0.0189495 −0.000687824 0
\(760\) −1.15737 −0.0419824
\(761\) −52.1364 −1.88994 −0.944971 0.327153i \(-0.893911\pi\)
−0.944971 + 0.327153i \(0.893911\pi\)
\(762\) −2.60726 −0.0944509
\(763\) −15.2259 −0.551214
\(764\) −31.3880 −1.13558
\(765\) −12.7287 −0.460207
\(766\) 43.9966 1.58966
\(767\) −32.2276 −1.16367
\(768\) 4.78644 0.172716
\(769\) −15.3059 −0.551944 −0.275972 0.961166i \(-0.589000\pi\)
−0.275972 + 0.961166i \(0.589000\pi\)
\(770\) 6.33046 0.228134
\(771\) −0.831342 −0.0299400
\(772\) −86.3875 −3.10916
\(773\) −5.57430 −0.200494 −0.100247 0.994963i \(-0.531963\pi\)
−0.100247 + 0.994963i \(0.531963\pi\)
\(774\) 23.0490 0.828481
\(775\) −7.68779 −0.276153
\(776\) −59.2085 −2.12546
\(777\) 0.106911 0.00383541
\(778\) −18.7347 −0.671670
\(779\) −0.937289 −0.0335818
\(780\) −1.39230 −0.0498524
\(781\) 46.2695 1.65565
\(782\) 0.492661 0.0176175
\(783\) 4.32353 0.154510
\(784\) −44.2533 −1.58048
\(785\) −0.589270 −0.0210320
\(786\) −8.43888 −0.301005
\(787\) −5.10825 −0.182089 −0.0910447 0.995847i \(-0.529021\pi\)
−0.0910447 + 0.995847i \(0.529021\pi\)
\(788\) 40.1896 1.43170
\(789\) 2.88524 0.102717
\(790\) −0.503916 −0.0179285
\(791\) −12.5549 −0.446401
\(792\) 62.1739 2.20925
\(793\) −21.9981 −0.781176
\(794\) −95.4919 −3.38888
\(795\) −0.129194 −0.00458205
\(796\) −65.9680 −2.33817
\(797\) −46.8567 −1.65975 −0.829874 0.557950i \(-0.811588\pi\)
−0.829874 + 0.557950i \(0.811588\pi\)
\(798\) −0.101941 −0.00360868
\(799\) −1.82289 −0.0644894
\(800\) 26.3609 0.932000
\(801\) −28.5245 −1.00786
\(802\) −98.5464 −3.47979
\(803\) 25.4480 0.898039
\(804\) 6.74703 0.237949
\(805\) −0.0261685 −0.000922318 0
\(806\) 10.5973 0.373274
\(807\) 3.38184 0.119047
\(808\) 38.6290 1.35896
\(809\) −22.9741 −0.807728 −0.403864 0.914819i \(-0.632333\pi\)
−0.403864 + 0.914819i \(0.632333\pi\)
\(810\) 17.0239 0.598158
\(811\) −18.0720 −0.634595 −0.317297 0.948326i \(-0.602775\pi\)
−0.317297 + 0.948326i \(0.602775\pi\)
\(812\) 19.2811 0.676633
\(813\) 0.0820265 0.00287679
\(814\) 5.25454 0.184171
\(815\) 1.26133 0.0441824
\(816\) 7.01281 0.245498
\(817\) −0.717432 −0.0250998
\(818\) −60.6679 −2.12120
\(819\) 7.07771 0.247315
\(820\) −13.6782 −0.477662
\(821\) 34.7123 1.21147 0.605733 0.795668i \(-0.292880\pi\)
0.605733 + 0.795668i \(0.292880\pi\)
\(822\) −0.197497 −0.00688849
\(823\) 56.0970 1.95542 0.977710 0.209961i \(-0.0673336\pi\)
0.977710 + 0.209961i \(0.0673336\pi\)
\(824\) 11.2474 0.391820
\(825\) 2.43662 0.0848322
\(826\) −34.4349 −1.19814
\(827\) −12.6496 −0.439868 −0.219934 0.975515i \(-0.570584\pi\)
−0.219934 + 0.975515i \(0.570584\pi\)
\(828\) −0.461201 −0.0160278
\(829\) −8.61089 −0.299069 −0.149534 0.988757i \(-0.547777\pi\)
−0.149534 + 0.988757i \(0.547777\pi\)
\(830\) −14.7155 −0.510784
\(831\) 1.63085 0.0565735
\(832\) −1.16443 −0.0403695
\(833\) 33.7152 1.16816
\(834\) 5.86406 0.203056
\(835\) 0.0743488 0.00257295
\(836\) −3.47276 −0.120108
\(837\) 1.75989 0.0608308
\(838\) −45.8407 −1.58354
\(839\) −51.8300 −1.78937 −0.894685 0.446698i \(-0.852600\pi\)
−0.894685 + 0.446698i \(0.852600\pi\)
\(840\) −0.829020 −0.0286039
\(841\) −10.7269 −0.369893
\(842\) −2.76762 −0.0953784
\(843\) 0.452729 0.0155928
\(844\) −93.9872 −3.23517
\(845\) 5.57472 0.191776
\(846\) 2.46201 0.0846458
\(847\) −0.398146 −0.0136805
\(848\) −7.37183 −0.253150
\(849\) 1.54143 0.0529018
\(850\) −63.3487 −2.17284
\(851\) −0.0217209 −0.000744582 0
\(852\) −10.8734 −0.372515
\(853\) 11.4215 0.391063 0.195532 0.980697i \(-0.437357\pi\)
0.195532 + 0.980697i \(0.437357\pi\)
\(854\) −23.5048 −0.804318
\(855\) −0.535107 −0.0183003
\(856\) −45.3365 −1.54957
\(857\) −19.8844 −0.679239 −0.339619 0.940563i \(-0.610298\pi\)
−0.339619 + 0.940563i \(0.610298\pi\)
\(858\) −3.35878 −0.114667
\(859\) −46.8552 −1.59868 −0.799340 0.600879i \(-0.794817\pi\)
−0.799340 + 0.600879i \(0.794817\pi\)
\(860\) −10.4697 −0.357014
\(861\) −0.671373 −0.0228803
\(862\) 24.3545 0.829519
\(863\) −8.43346 −0.287078 −0.143539 0.989645i \(-0.545848\pi\)
−0.143539 + 0.989645i \(0.545848\pi\)
\(864\) −6.03457 −0.205300
\(865\) −12.0213 −0.408737
\(866\) −70.9301 −2.41030
\(867\) −2.46338 −0.0836606
\(868\) 7.84836 0.266391
\(869\) −0.842596 −0.0285831
\(870\) −1.40989 −0.0477998
\(871\) 21.0363 0.712789
\(872\) 97.9994 3.31868
\(873\) −27.3748 −0.926496
\(874\) 0.0207112 0.000700566 0
\(875\) 7.17282 0.242485
\(876\) −5.98028 −0.202055
\(877\) 43.4804 1.46823 0.734114 0.679026i \(-0.237598\pi\)
0.734114 + 0.679026i \(0.237598\pi\)
\(878\) −60.0330 −2.02601
\(879\) −2.41624 −0.0814977
\(880\) −18.3077 −0.617154
\(881\) −52.9936 −1.78540 −0.892699 0.450653i \(-0.851191\pi\)
−0.892699 + 0.450653i \(0.851191\pi\)
\(882\) −45.5360 −1.53328
\(883\) 3.90506 0.131416 0.0657079 0.997839i \(-0.479069\pi\)
0.0657079 + 0.997839i \(0.479069\pi\)
\(884\) 60.5263 2.03572
\(885\) 1.74529 0.0586672
\(886\) −12.4186 −0.417211
\(887\) −47.0119 −1.57851 −0.789253 0.614068i \(-0.789532\pi\)
−0.789253 + 0.614068i \(0.789532\pi\)
\(888\) −0.688119 −0.0230918
\(889\) −6.02040 −0.201918
\(890\) 18.6934 0.626603
\(891\) 28.4656 0.953633
\(892\) −107.450 −3.59768
\(893\) −0.0766334 −0.00256444
\(894\) 3.12611 0.104553
\(895\) −18.1829 −0.607787
\(896\) 10.6705 0.356478
\(897\) 0.0138843 0.000463584 0
\(898\) −70.8405 −2.36398
\(899\) 7.43808 0.248074
\(900\) 59.3034 1.97678
\(901\) 5.61636 0.187108
\(902\) −32.9971 −1.09868
\(903\) −0.513891 −0.0171012
\(904\) 80.8081 2.68764
\(905\) 0.304813 0.0101323
\(906\) −0.432413 −0.0143659
\(907\) 9.01943 0.299485 0.149743 0.988725i \(-0.452155\pi\)
0.149743 + 0.988725i \(0.452155\pi\)
\(908\) 103.203 3.42490
\(909\) 17.8599 0.592377
\(910\) −4.63833 −0.153759
\(911\) −42.2466 −1.39969 −0.699846 0.714293i \(-0.746748\pi\)
−0.699846 + 0.714293i \(0.746748\pi\)
\(912\) 0.294815 0.00976229
\(913\) −24.6058 −0.814334
\(914\) 35.0372 1.15893
\(915\) 1.19131 0.0393835
\(916\) 27.2096 0.899030
\(917\) −19.4862 −0.643490
\(918\) 14.5018 0.478632
\(919\) 60.3277 1.99003 0.995014 0.0997377i \(-0.0318004\pi\)
0.995014 + 0.0997377i \(0.0318004\pi\)
\(920\) 0.168430 0.00555298
\(921\) −1.72281 −0.0567686
\(922\) −33.1638 −1.09219
\(923\) −33.9017 −1.11589
\(924\) −2.48751 −0.0818332
\(925\) 2.79297 0.0918324
\(926\) −46.0815 −1.51433
\(927\) 5.20016 0.170796
\(928\) −25.5047 −0.837233
\(929\) −16.8834 −0.553927 −0.276963 0.960880i \(-0.589328\pi\)
−0.276963 + 0.960880i \(0.589328\pi\)
\(930\) −0.573897 −0.0188188
\(931\) 1.41737 0.0464523
\(932\) −122.417 −4.00990
\(933\) 1.09707 0.0359163
\(934\) 52.6868 1.72396
\(935\) 13.9481 0.456151
\(936\) −45.5548 −1.48901
\(937\) −36.3703 −1.18817 −0.594083 0.804404i \(-0.702485\pi\)
−0.594083 + 0.804404i \(0.702485\pi\)
\(938\) 22.4771 0.733905
\(939\) 5.87843 0.191835
\(940\) −1.11834 −0.0364761
\(941\) 55.5612 1.81124 0.905622 0.424086i \(-0.139404\pi\)
0.905622 + 0.424086i \(0.139404\pi\)
\(942\) 0.334066 0.0108844
\(943\) 0.136402 0.00444185
\(944\) 99.5860 3.24125
\(945\) −0.770288 −0.0250575
\(946\) −25.2571 −0.821179
\(947\) 8.40232 0.273039 0.136519 0.990637i \(-0.456408\pi\)
0.136519 + 0.990637i \(0.456408\pi\)
\(948\) 0.198011 0.00643108
\(949\) −18.6457 −0.605266
\(950\) −2.66314 −0.0864037
\(951\) −3.18749 −0.103361
\(952\) 36.0393 1.16804
\(953\) −32.9371 −1.06694 −0.533469 0.845819i \(-0.679112\pi\)
−0.533469 + 0.845819i \(0.679112\pi\)
\(954\) −7.58549 −0.245589
\(955\) 5.29981 0.171498
\(956\) −120.878 −3.90948
\(957\) −2.35748 −0.0762064
\(958\) −20.9220 −0.675960
\(959\) −0.456039 −0.0147263
\(960\) 0.0630600 0.00203525
\(961\) −27.9723 −0.902333
\(962\) −3.85000 −0.124129
\(963\) −20.9611 −0.675462
\(964\) 124.397 4.00656
\(965\) 14.5864 0.469552
\(966\) 0.0148353 0.000477317 0
\(967\) −24.6122 −0.791476 −0.395738 0.918364i \(-0.629511\pi\)
−0.395738 + 0.918364i \(0.629511\pi\)
\(968\) 2.56262 0.0823657
\(969\) −0.224610 −0.00721551
\(970\) 17.9399 0.576015
\(971\) 52.6849 1.69074 0.845369 0.534182i \(-0.179380\pi\)
0.845369 + 0.534182i \(0.179380\pi\)
\(972\) −20.3963 −0.654211
\(973\) 13.5407 0.434094
\(974\) 6.97567 0.223515
\(975\) −1.78531 −0.0571757
\(976\) 67.9760 2.17586
\(977\) −22.6088 −0.723320 −0.361660 0.932310i \(-0.617790\pi\)
−0.361660 + 0.932310i \(0.617790\pi\)
\(978\) −0.715064 −0.0228652
\(979\) 31.2571 0.998982
\(980\) 20.6841 0.660730
\(981\) 45.3096 1.44662
\(982\) 55.1171 1.75886
\(983\) −4.22584 −0.134783 −0.0673917 0.997727i \(-0.521468\pi\)
−0.0673917 + 0.997727i \(0.521468\pi\)
\(984\) 4.32121 0.137755
\(985\) −6.78594 −0.216218
\(986\) 61.2910 1.95190
\(987\) −0.0548920 −0.00174723
\(988\) 2.54449 0.0809511
\(989\) 0.104406 0.00331993
\(990\) −18.8384 −0.598723
\(991\) −43.9999 −1.39770 −0.698851 0.715267i \(-0.746305\pi\)
−0.698851 + 0.715267i \(0.746305\pi\)
\(992\) −10.3817 −0.329619
\(993\) 2.45713 0.0779747
\(994\) −36.2237 −1.14894
\(995\) 11.1386 0.353117
\(996\) 5.78238 0.183222
\(997\) −15.2447 −0.482805 −0.241402 0.970425i \(-0.577607\pi\)
−0.241402 + 0.970425i \(0.577607\pi\)
\(998\) 53.0864 1.68042
\(999\) −0.639370 −0.0202288
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 8003.2.a.b.1.8 153
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8003.2.a.b.1.8 153 1.1 even 1 trivial