Properties

Label 4003.2.a.c.1.9
Level 4003
Weight 2
Character 4003.1
Self dual yes
Analytic conductor 31.964
Analytic rank 0
Dimension 179
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4003 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4003.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(31.9641159291\)
Analytic rank: \(0\)
Dimension: \(179\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) = 4003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.60379 q^{2} +0.316007 q^{3} +4.77975 q^{4} +1.57805 q^{5} -0.822817 q^{6} +2.80041 q^{7} -7.23789 q^{8} -2.90014 q^{9} +O(q^{10})\) \(q-2.60379 q^{2} +0.316007 q^{3} +4.77975 q^{4} +1.57805 q^{5} -0.822817 q^{6} +2.80041 q^{7} -7.23789 q^{8} -2.90014 q^{9} -4.10892 q^{10} +1.05246 q^{11} +1.51043 q^{12} +1.29122 q^{13} -7.29169 q^{14} +0.498675 q^{15} +9.28647 q^{16} +2.11989 q^{17} +7.55137 q^{18} +4.99475 q^{19} +7.54268 q^{20} +0.884949 q^{21} -2.74039 q^{22} +7.80822 q^{23} -2.28722 q^{24} -2.50975 q^{25} -3.36208 q^{26} -1.86448 q^{27} +13.3852 q^{28} +6.12200 q^{29} -1.29845 q^{30} -6.15798 q^{31} -9.70430 q^{32} +0.332584 q^{33} -5.51976 q^{34} +4.41919 q^{35} -13.8619 q^{36} +7.71921 q^{37} -13.0053 q^{38} +0.408036 q^{39} -11.4218 q^{40} +2.40798 q^{41} -2.30423 q^{42} -10.2280 q^{43} +5.03049 q^{44} -4.57657 q^{45} -20.3310 q^{46} +3.26833 q^{47} +2.93459 q^{48} +0.842299 q^{49} +6.53488 q^{50} +0.669901 q^{51} +6.17172 q^{52} -7.78005 q^{53} +4.85474 q^{54} +1.66083 q^{55} -20.2690 q^{56} +1.57838 q^{57} -15.9404 q^{58} +9.71469 q^{59} +2.38354 q^{60} +4.92650 q^{61} +16.0341 q^{62} -8.12158 q^{63} +6.69505 q^{64} +2.03762 q^{65} -0.865981 q^{66} -12.3095 q^{67} +10.1325 q^{68} +2.46745 q^{69} -11.5067 q^{70} +9.20342 q^{71} +20.9909 q^{72} -1.59934 q^{73} -20.0992 q^{74} -0.793099 q^{75} +23.8736 q^{76} +2.94732 q^{77} -1.06244 q^{78} -5.44023 q^{79} +14.6545 q^{80} +8.11123 q^{81} -6.26989 q^{82} +11.0791 q^{83} +4.22983 q^{84} +3.34530 q^{85} +26.6317 q^{86} +1.93460 q^{87} -7.61758 q^{88} +15.9788 q^{89} +11.9164 q^{90} +3.61596 q^{91} +37.3213 q^{92} -1.94596 q^{93} -8.51006 q^{94} +7.88198 q^{95} -3.06663 q^{96} -4.95819 q^{97} -2.19317 q^{98} -3.05228 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 179q + 22q^{2} + 16q^{3} + 196q^{4} + 61q^{5} + 7q^{6} + 21q^{7} + 60q^{8} + 221q^{9} + O(q^{10}) \) \( 179q + 22q^{2} + 16q^{3} + 196q^{4} + 61q^{5} + 7q^{6} + 21q^{7} + 60q^{8} + 221q^{9} + 9q^{10} + 46q^{11} + 33q^{12} + 47q^{13} + 22q^{14} + 36q^{15} + 222q^{16} + 103q^{17} + 43q^{18} + 12q^{19} + 102q^{20} + 50q^{21} + 39q^{22} + 121q^{23} - 3q^{24} + 246q^{25} + 52q^{26} + 49q^{27} + 41q^{28} + 138q^{29} + 28q^{30} + 5q^{31} + 137q^{32} + 63q^{33} + 2q^{34} + 72q^{35} + 279q^{36} + 118q^{37} + 123q^{38} + q^{39} + 9q^{40} + 50q^{41} + 48q^{42} + 48q^{43} + 108q^{44} + 158q^{45} + 13q^{46} + 85q^{47} + 50q^{48} + 230q^{49} + 78q^{50} + 15q^{51} + 41q^{52} + 399q^{53} - 5q^{54} + 24q^{55} + 53q^{56} + 45q^{57} + 27q^{58} + 48q^{59} + 66q^{60} + 46q^{61} + 81q^{62} + 78q^{63} + 252q^{64} + 153q^{65} + 6q^{66} + 70q^{67} + 240q^{68} + 120q^{69} - 31q^{70} + 86q^{71} + 89q^{72} + 45q^{73} + 68q^{74} + 17q^{75} - 13q^{76} + 362q^{77} + 69q^{78} + 31q^{79} + 169q^{80} + 303q^{81} + 25q^{82} + 106q^{83} + 13q^{84} + 115q^{85} + 95q^{86} + 32q^{87} + 83q^{88} + 105q^{89} - 38q^{90} + 3q^{91} + 310q^{92} + 298q^{93} - 17q^{94} + 102q^{95} - 82q^{96} + 34q^{97} + 81q^{98} + 58q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.60379 −1.84116 −0.920580 0.390553i \(-0.872284\pi\)
−0.920580 + 0.390553i \(0.872284\pi\)
\(3\) 0.316007 0.182447 0.0912233 0.995830i \(-0.470922\pi\)
0.0912233 + 0.995830i \(0.470922\pi\)
\(4\) 4.77975 2.38987
\(5\) 1.57805 0.705726 0.352863 0.935675i \(-0.385208\pi\)
0.352863 + 0.935675i \(0.385208\pi\)
\(6\) −0.822817 −0.335914
\(7\) 2.80041 1.05846 0.529228 0.848480i \(-0.322482\pi\)
0.529228 + 0.848480i \(0.322482\pi\)
\(8\) −7.23789 −2.55898
\(9\) −2.90014 −0.966713
\(10\) −4.10892 −1.29936
\(11\) 1.05246 0.317328 0.158664 0.987333i \(-0.449281\pi\)
0.158664 + 0.987333i \(0.449281\pi\)
\(12\) 1.51043 0.436024
\(13\) 1.29122 0.358121 0.179061 0.983838i \(-0.442694\pi\)
0.179061 + 0.983838i \(0.442694\pi\)
\(14\) −7.29169 −1.94879
\(15\) 0.498675 0.128757
\(16\) 9.28647 2.32162
\(17\) 2.11989 0.514149 0.257075 0.966392i \(-0.417241\pi\)
0.257075 + 0.966392i \(0.417241\pi\)
\(18\) 7.55137 1.77987
\(19\) 4.99475 1.14587 0.572937 0.819599i \(-0.305804\pi\)
0.572937 + 0.819599i \(0.305804\pi\)
\(20\) 7.54268 1.68660
\(21\) 0.884949 0.193112
\(22\) −2.74039 −0.584252
\(23\) 7.80822 1.62813 0.814063 0.580776i \(-0.197251\pi\)
0.814063 + 0.580776i \(0.197251\pi\)
\(24\) −2.28722 −0.466877
\(25\) −2.50975 −0.501951
\(26\) −3.36208 −0.659359
\(27\) −1.86448 −0.358820
\(28\) 13.3852 2.52957
\(29\) 6.12200 1.13683 0.568414 0.822743i \(-0.307557\pi\)
0.568414 + 0.822743i \(0.307557\pi\)
\(30\) −1.29845 −0.237063
\(31\) −6.15798 −1.10601 −0.553003 0.833179i \(-0.686518\pi\)
−0.553003 + 0.833179i \(0.686518\pi\)
\(32\) −9.70430 −1.71549
\(33\) 0.332584 0.0578955
\(34\) −5.51976 −0.946632
\(35\) 4.41919 0.746980
\(36\) −13.8619 −2.31032
\(37\) 7.71921 1.26903 0.634515 0.772911i \(-0.281200\pi\)
0.634515 + 0.772911i \(0.281200\pi\)
\(38\) −13.0053 −2.10974
\(39\) 0.408036 0.0653380
\(40\) −11.4218 −1.80594
\(41\) 2.40798 0.376064 0.188032 0.982163i \(-0.439789\pi\)
0.188032 + 0.982163i \(0.439789\pi\)
\(42\) −2.30423 −0.355550
\(43\) −10.2280 −1.55976 −0.779880 0.625929i \(-0.784720\pi\)
−0.779880 + 0.625929i \(0.784720\pi\)
\(44\) 5.03049 0.758374
\(45\) −4.57657 −0.682235
\(46\) −20.3310 −2.99764
\(47\) 3.26833 0.476735 0.238367 0.971175i \(-0.423388\pi\)
0.238367 + 0.971175i \(0.423388\pi\)
\(48\) 2.93459 0.423572
\(49\) 0.842299 0.120328
\(50\) 6.53488 0.924172
\(51\) 0.669901 0.0938048
\(52\) 6.17172 0.855864
\(53\) −7.78005 −1.06867 −0.534336 0.845272i \(-0.679438\pi\)
−0.534336 + 0.845272i \(0.679438\pi\)
\(54\) 4.85474 0.660646
\(55\) 1.66083 0.223947
\(56\) −20.2690 −2.70857
\(57\) 1.57838 0.209061
\(58\) −15.9404 −2.09308
\(59\) 9.71469 1.26475 0.632373 0.774664i \(-0.282081\pi\)
0.632373 + 0.774664i \(0.282081\pi\)
\(60\) 2.38354 0.307714
\(61\) 4.92650 0.630774 0.315387 0.948963i \(-0.397866\pi\)
0.315387 + 0.948963i \(0.397866\pi\)
\(62\) 16.0341 2.03633
\(63\) −8.12158 −1.02322
\(64\) 6.69505 0.836881
\(65\) 2.03762 0.252735
\(66\) −0.865981 −0.106595
\(67\) −12.3095 −1.50384 −0.751919 0.659255i \(-0.770872\pi\)
−0.751919 + 0.659255i \(0.770872\pi\)
\(68\) 10.1325 1.22875
\(69\) 2.46745 0.297046
\(70\) −11.5067 −1.37531
\(71\) 9.20342 1.09225 0.546123 0.837705i \(-0.316103\pi\)
0.546123 + 0.837705i \(0.316103\pi\)
\(72\) 20.9909 2.47380
\(73\) −1.59934 −0.187188 −0.0935940 0.995610i \(-0.529836\pi\)
−0.0935940 + 0.995610i \(0.529836\pi\)
\(74\) −20.0992 −2.33649
\(75\) −0.793099 −0.0915792
\(76\) 23.8736 2.73850
\(77\) 2.94732 0.335878
\(78\) −1.06244 −0.120298
\(79\) −5.44023 −0.612074 −0.306037 0.952020i \(-0.599003\pi\)
−0.306037 + 0.952020i \(0.599003\pi\)
\(80\) 14.6545 1.63843
\(81\) 8.11123 0.901248
\(82\) −6.26989 −0.692394
\(83\) 11.0791 1.21609 0.608043 0.793904i \(-0.291955\pi\)
0.608043 + 0.793904i \(0.291955\pi\)
\(84\) 4.22983 0.461512
\(85\) 3.34530 0.362849
\(86\) 26.6317 2.87177
\(87\) 1.93460 0.207410
\(88\) −7.61758 −0.812036
\(89\) 15.9788 1.69375 0.846873 0.531795i \(-0.178482\pi\)
0.846873 + 0.531795i \(0.178482\pi\)
\(90\) 11.9164 1.25610
\(91\) 3.61596 0.379055
\(92\) 37.3213 3.89101
\(93\) −1.94596 −0.201787
\(94\) −8.51006 −0.877745
\(95\) 7.88198 0.808674
\(96\) −3.06663 −0.312986
\(97\) −4.95819 −0.503428 −0.251714 0.967802i \(-0.580994\pi\)
−0.251714 + 0.967802i \(0.580994\pi\)
\(98\) −2.19317 −0.221544
\(99\) −3.05228 −0.306765
\(100\) −11.9960 −1.19960
\(101\) −1.88212 −0.187277 −0.0936387 0.995606i \(-0.529850\pi\)
−0.0936387 + 0.995606i \(0.529850\pi\)
\(102\) −1.74428 −0.172710
\(103\) 1.29776 0.127872 0.0639360 0.997954i \(-0.479635\pi\)
0.0639360 + 0.997954i \(0.479635\pi\)
\(104\) −9.34573 −0.916425
\(105\) 1.39650 0.136284
\(106\) 20.2576 1.96760
\(107\) −15.1283 −1.46251 −0.731253 0.682106i \(-0.761064\pi\)
−0.731253 + 0.682106i \(0.761064\pi\)
\(108\) −8.91176 −0.857535
\(109\) 1.82182 0.174499 0.0872493 0.996187i \(-0.472192\pi\)
0.0872493 + 0.996187i \(0.472192\pi\)
\(110\) −4.32447 −0.412322
\(111\) 2.43932 0.231530
\(112\) 26.0059 2.45733
\(113\) −1.07750 −0.101363 −0.0506815 0.998715i \(-0.516139\pi\)
−0.0506815 + 0.998715i \(0.516139\pi\)
\(114\) −4.10977 −0.384915
\(115\) 12.3218 1.14901
\(116\) 29.2616 2.71687
\(117\) −3.74473 −0.346200
\(118\) −25.2951 −2.32860
\(119\) 5.93657 0.544204
\(120\) −3.60935 −0.329487
\(121\) −9.89233 −0.899303
\(122\) −12.8276 −1.16136
\(123\) 0.760939 0.0686116
\(124\) −29.4336 −2.64321
\(125\) −11.8508 −1.05997
\(126\) 21.1469 1.88392
\(127\) 20.2307 1.79518 0.897592 0.440827i \(-0.145315\pi\)
0.897592 + 0.440827i \(0.145315\pi\)
\(128\) 1.97606 0.174661
\(129\) −3.23213 −0.284573
\(130\) −5.30554 −0.465327
\(131\) 9.87709 0.862965 0.431483 0.902121i \(-0.357991\pi\)
0.431483 + 0.902121i \(0.357991\pi\)
\(132\) 1.58967 0.138363
\(133\) 13.9874 1.21286
\(134\) 32.0513 2.76881
\(135\) −2.94225 −0.253229
\(136\) −15.3435 −1.31570
\(137\) −8.27990 −0.707399 −0.353700 0.935359i \(-0.615077\pi\)
−0.353700 + 0.935359i \(0.615077\pi\)
\(138\) −6.42474 −0.546910
\(139\) 8.12202 0.688901 0.344450 0.938805i \(-0.388065\pi\)
0.344450 + 0.938805i \(0.388065\pi\)
\(140\) 21.1226 1.78519
\(141\) 1.03281 0.0869787
\(142\) −23.9638 −2.01100
\(143\) 1.35896 0.113642
\(144\) −26.9321 −2.24434
\(145\) 9.66084 0.802289
\(146\) 4.16434 0.344643
\(147\) 0.266172 0.0219535
\(148\) 36.8958 3.03282
\(149\) −14.6495 −1.20013 −0.600067 0.799950i \(-0.704859\pi\)
−0.600067 + 0.799950i \(0.704859\pi\)
\(150\) 2.06507 0.168612
\(151\) −7.03608 −0.572588 −0.286294 0.958142i \(-0.592423\pi\)
−0.286294 + 0.958142i \(0.592423\pi\)
\(152\) −36.1514 −2.93227
\(153\) −6.14798 −0.497035
\(154\) −7.67421 −0.618405
\(155\) −9.71761 −0.780537
\(156\) 1.95031 0.156150
\(157\) 14.1493 1.12924 0.564619 0.825352i \(-0.309023\pi\)
0.564619 + 0.825352i \(0.309023\pi\)
\(158\) 14.1652 1.12693
\(159\) −2.45855 −0.194976
\(160\) −15.3139 −1.21067
\(161\) 21.8662 1.72330
\(162\) −21.1200 −1.65934
\(163\) 20.7437 1.62477 0.812384 0.583122i \(-0.198169\pi\)
0.812384 + 0.583122i \(0.198169\pi\)
\(164\) 11.5095 0.898744
\(165\) 0.524835 0.0408584
\(166\) −28.8476 −2.23901
\(167\) 2.95856 0.228940 0.114470 0.993427i \(-0.463483\pi\)
0.114470 + 0.993427i \(0.463483\pi\)
\(168\) −6.40516 −0.494169
\(169\) −11.3327 −0.871749
\(170\) −8.71047 −0.668063
\(171\) −14.4855 −1.10773
\(172\) −48.8874 −3.72763
\(173\) −4.09080 −0.311018 −0.155509 0.987834i \(-0.549702\pi\)
−0.155509 + 0.987834i \(0.549702\pi\)
\(174\) −5.03729 −0.381876
\(175\) −7.02834 −0.531292
\(176\) 9.77363 0.736715
\(177\) 3.06991 0.230749
\(178\) −41.6054 −3.11846
\(179\) −0.743413 −0.0555653 −0.0277826 0.999614i \(-0.508845\pi\)
−0.0277826 + 0.999614i \(0.508845\pi\)
\(180\) −21.8748 −1.63045
\(181\) −20.8643 −1.55083 −0.775416 0.631450i \(-0.782460\pi\)
−0.775416 + 0.631450i \(0.782460\pi\)
\(182\) −9.41521 −0.697902
\(183\) 1.55681 0.115083
\(184\) −56.5150 −4.16634
\(185\) 12.1813 0.895587
\(186\) 5.06689 0.371522
\(187\) 2.23110 0.163154
\(188\) 15.6218 1.13934
\(189\) −5.22132 −0.379795
\(190\) −20.5231 −1.48890
\(191\) −5.63703 −0.407881 −0.203941 0.978983i \(-0.565375\pi\)
−0.203941 + 0.978983i \(0.565375\pi\)
\(192\) 2.11568 0.152686
\(193\) 6.48044 0.466472 0.233236 0.972420i \(-0.425069\pi\)
0.233236 + 0.972420i \(0.425069\pi\)
\(194\) 12.9101 0.926891
\(195\) 0.643902 0.0461107
\(196\) 4.02598 0.287570
\(197\) 20.7252 1.47661 0.738305 0.674467i \(-0.235626\pi\)
0.738305 + 0.674467i \(0.235626\pi\)
\(198\) 7.94750 0.564804
\(199\) −13.3778 −0.948325 −0.474163 0.880437i \(-0.657249\pi\)
−0.474163 + 0.880437i \(0.657249\pi\)
\(200\) 18.1653 1.28448
\(201\) −3.88987 −0.274370
\(202\) 4.90064 0.344808
\(203\) 17.1441 1.20328
\(204\) 3.20195 0.224182
\(205\) 3.79992 0.265398
\(206\) −3.37910 −0.235433
\(207\) −22.6449 −1.57393
\(208\) 11.9909 0.831421
\(209\) 5.25677 0.363619
\(210\) −3.63619 −0.250921
\(211\) −0.846497 −0.0582753 −0.0291376 0.999575i \(-0.509276\pi\)
−0.0291376 + 0.999575i \(0.509276\pi\)
\(212\) −37.1866 −2.55399
\(213\) 2.90835 0.199277
\(214\) 39.3909 2.69271
\(215\) −16.1404 −1.10076
\(216\) 13.4949 0.918214
\(217\) −17.2449 −1.17066
\(218\) −4.74364 −0.321280
\(219\) −0.505401 −0.0341518
\(220\) 7.93837 0.535204
\(221\) 2.73726 0.184128
\(222\) −6.35149 −0.426284
\(223\) −16.3250 −1.09321 −0.546603 0.837392i \(-0.684079\pi\)
−0.546603 + 0.837392i \(0.684079\pi\)
\(224\) −27.1760 −1.81577
\(225\) 7.27863 0.485242
\(226\) 2.80560 0.186626
\(227\) 7.25930 0.481817 0.240908 0.970548i \(-0.422555\pi\)
0.240908 + 0.970548i \(0.422555\pi\)
\(228\) 7.54424 0.499629
\(229\) −17.4767 −1.15489 −0.577446 0.816429i \(-0.695951\pi\)
−0.577446 + 0.816429i \(0.695951\pi\)
\(230\) −32.0834 −2.11551
\(231\) 0.931373 0.0612798
\(232\) −44.3104 −2.90912
\(233\) −25.1407 −1.64702 −0.823510 0.567301i \(-0.807987\pi\)
−0.823510 + 0.567301i \(0.807987\pi\)
\(234\) 9.75051 0.637411
\(235\) 5.15759 0.336444
\(236\) 46.4338 3.02258
\(237\) −1.71915 −0.111671
\(238\) −15.4576 −1.00197
\(239\) 8.78267 0.568104 0.284052 0.958809i \(-0.408321\pi\)
0.284052 + 0.958809i \(0.408321\pi\)
\(240\) 4.63093 0.298926
\(241\) 2.92332 0.188308 0.0941538 0.995558i \(-0.469985\pi\)
0.0941538 + 0.995558i \(0.469985\pi\)
\(242\) 25.7576 1.65576
\(243\) 8.15666 0.523250
\(244\) 23.5474 1.50747
\(245\) 1.32919 0.0849189
\(246\) −1.98133 −0.126325
\(247\) 6.44935 0.410362
\(248\) 44.5707 2.83024
\(249\) 3.50106 0.221871
\(250\) 30.8570 1.95157
\(251\) −17.5870 −1.11008 −0.555040 0.831824i \(-0.687297\pi\)
−0.555040 + 0.831824i \(0.687297\pi\)
\(252\) −38.8191 −2.44537
\(253\) 8.21783 0.516651
\(254\) −52.6766 −3.30522
\(255\) 1.05714 0.0662005
\(256\) −18.5354 −1.15846
\(257\) 17.8611 1.11414 0.557072 0.830464i \(-0.311925\pi\)
0.557072 + 0.830464i \(0.311925\pi\)
\(258\) 8.41580 0.523945
\(259\) 21.6169 1.34321
\(260\) 9.73930 0.604006
\(261\) −17.7547 −1.09899
\(262\) −25.7179 −1.58886
\(263\) 2.72274 0.167891 0.0839457 0.996470i \(-0.473248\pi\)
0.0839457 + 0.996470i \(0.473248\pi\)
\(264\) −2.40721 −0.148153
\(265\) −12.2773 −0.754189
\(266\) −36.4202 −2.23307
\(267\) 5.04940 0.309018
\(268\) −58.8360 −3.59398
\(269\) 3.74321 0.228228 0.114114 0.993468i \(-0.463597\pi\)
0.114114 + 0.993468i \(0.463597\pi\)
\(270\) 7.66102 0.466235
\(271\) 26.4914 1.60924 0.804619 0.593791i \(-0.202369\pi\)
0.804619 + 0.593791i \(0.202369\pi\)
\(272\) 19.6863 1.19366
\(273\) 1.14267 0.0691574
\(274\) 21.5591 1.30244
\(275\) −2.64141 −0.159283
\(276\) 11.7938 0.709903
\(277\) 13.6183 0.818246 0.409123 0.912479i \(-0.365835\pi\)
0.409123 + 0.912479i \(0.365835\pi\)
\(278\) −21.1481 −1.26838
\(279\) 17.8590 1.06919
\(280\) −31.9856 −1.91151
\(281\) −14.4616 −0.862709 −0.431355 0.902182i \(-0.641964\pi\)
−0.431355 + 0.902182i \(0.641964\pi\)
\(282\) −2.68924 −0.160142
\(283\) 26.0583 1.54901 0.774503 0.632570i \(-0.218000\pi\)
0.774503 + 0.632570i \(0.218000\pi\)
\(284\) 43.9900 2.61033
\(285\) 2.49076 0.147540
\(286\) −3.53845 −0.209233
\(287\) 6.74334 0.398047
\(288\) 28.1438 1.65839
\(289\) −12.5061 −0.735650
\(290\) −25.1548 −1.47714
\(291\) −1.56682 −0.0918487
\(292\) −7.64442 −0.447356
\(293\) −13.1572 −0.768651 −0.384326 0.923198i \(-0.625566\pi\)
−0.384326 + 0.923198i \(0.625566\pi\)
\(294\) −0.693058 −0.0404200
\(295\) 15.3303 0.892564
\(296\) −55.8707 −3.24742
\(297\) −1.96229 −0.113864
\(298\) 38.1443 2.20964
\(299\) 10.0822 0.583067
\(300\) −3.79081 −0.218863
\(301\) −28.6427 −1.65094
\(302\) 18.3205 1.05423
\(303\) −0.594761 −0.0341682
\(304\) 46.3836 2.66028
\(305\) 7.77428 0.445154
\(306\) 16.0081 0.915121
\(307\) 28.1992 1.60941 0.804707 0.593672i \(-0.202322\pi\)
0.804707 + 0.593672i \(0.202322\pi\)
\(308\) 14.0874 0.802705
\(309\) 0.410101 0.0233298
\(310\) 25.3027 1.43709
\(311\) 0.309272 0.0175372 0.00876859 0.999962i \(-0.497209\pi\)
0.00876859 + 0.999962i \(0.497209\pi\)
\(312\) −2.95332 −0.167199
\(313\) 28.9161 1.63444 0.817218 0.576328i \(-0.195515\pi\)
0.817218 + 0.576328i \(0.195515\pi\)
\(314\) −36.8419 −2.07911
\(315\) −12.8163 −0.722115
\(316\) −26.0029 −1.46278
\(317\) −22.0027 −1.23580 −0.617899 0.786258i \(-0.712016\pi\)
−0.617899 + 0.786258i \(0.712016\pi\)
\(318\) 6.40155 0.358981
\(319\) 6.44316 0.360748
\(320\) 10.5651 0.590609
\(321\) −4.78064 −0.266829
\(322\) −56.9351 −3.17287
\(323\) 10.5883 0.589151
\(324\) 38.7696 2.15387
\(325\) −3.24065 −0.179759
\(326\) −54.0122 −2.99146
\(327\) 0.575708 0.0318367
\(328\) −17.4287 −0.962339
\(329\) 9.15266 0.504603
\(330\) −1.36656 −0.0752268
\(331\) 20.2690 1.11409 0.557043 0.830483i \(-0.311936\pi\)
0.557043 + 0.830483i \(0.311936\pi\)
\(332\) 52.9551 2.90629
\(333\) −22.3868 −1.22679
\(334\) −7.70349 −0.421516
\(335\) −19.4249 −1.06130
\(336\) 8.21806 0.448332
\(337\) −24.8441 −1.35334 −0.676671 0.736285i \(-0.736578\pi\)
−0.676671 + 0.736285i \(0.736578\pi\)
\(338\) 29.5081 1.60503
\(339\) −0.340498 −0.0184933
\(340\) 15.9897 0.867162
\(341\) −6.48102 −0.350967
\(342\) 37.7172 2.03951
\(343\) −17.2441 −0.931093
\(344\) 74.0293 3.99139
\(345\) 3.89377 0.209633
\(346\) 10.6516 0.572634
\(347\) −27.5664 −1.47984 −0.739920 0.672695i \(-0.765137\pi\)
−0.739920 + 0.672695i \(0.765137\pi\)
\(348\) 9.24687 0.495684
\(349\) 34.9196 1.86920 0.934602 0.355694i \(-0.115756\pi\)
0.934602 + 0.355694i \(0.115756\pi\)
\(350\) 18.3003 0.978195
\(351\) −2.40747 −0.128501
\(352\) −10.2134 −0.544375
\(353\) 19.6082 1.04364 0.521821 0.853055i \(-0.325253\pi\)
0.521821 + 0.853055i \(0.325253\pi\)
\(354\) −7.99341 −0.424845
\(355\) 14.5235 0.770826
\(356\) 76.3745 4.04784
\(357\) 1.87600 0.0992883
\(358\) 1.93569 0.102305
\(359\) −2.13875 −0.112879 −0.0564393 0.998406i \(-0.517975\pi\)
−0.0564393 + 0.998406i \(0.517975\pi\)
\(360\) 33.1247 1.74582
\(361\) 5.94756 0.313029
\(362\) 54.3264 2.85533
\(363\) −3.12604 −0.164075
\(364\) 17.2834 0.905894
\(365\) −2.52383 −0.132103
\(366\) −4.05361 −0.211886
\(367\) 21.8872 1.14250 0.571252 0.820775i \(-0.306458\pi\)
0.571252 + 0.820775i \(0.306458\pi\)
\(368\) 72.5108 3.77989
\(369\) −6.98348 −0.363546
\(370\) −31.7176 −1.64892
\(371\) −21.7873 −1.13114
\(372\) −9.30121 −0.482245
\(373\) −14.4774 −0.749613 −0.374807 0.927103i \(-0.622291\pi\)
−0.374807 + 0.927103i \(0.622291\pi\)
\(374\) −5.80932 −0.300393
\(375\) −3.74493 −0.193387
\(376\) −23.6558 −1.21995
\(377\) 7.90488 0.407122
\(378\) 13.5953 0.699264
\(379\) −14.3066 −0.734881 −0.367440 0.930047i \(-0.619766\pi\)
−0.367440 + 0.930047i \(0.619766\pi\)
\(380\) 37.6738 1.93263
\(381\) 6.39304 0.327525
\(382\) 14.6777 0.750975
\(383\) −0.423718 −0.0216510 −0.0108255 0.999941i \(-0.503446\pi\)
−0.0108255 + 0.999941i \(0.503446\pi\)
\(384\) 0.624449 0.0318663
\(385\) 4.65102 0.237038
\(386\) −16.8737 −0.858850
\(387\) 29.6627 1.50784
\(388\) −23.6989 −1.20313
\(389\) 3.44354 0.174595 0.0872973 0.996182i \(-0.472177\pi\)
0.0872973 + 0.996182i \(0.472177\pi\)
\(390\) −1.67659 −0.0848973
\(391\) 16.5526 0.837100
\(392\) −6.09646 −0.307918
\(393\) 3.12123 0.157445
\(394\) −53.9642 −2.71868
\(395\) −8.58496 −0.431956
\(396\) −14.5891 −0.733130
\(397\) 1.88424 0.0945674 0.0472837 0.998881i \(-0.484944\pi\)
0.0472837 + 0.998881i \(0.484944\pi\)
\(398\) 34.8330 1.74602
\(399\) 4.42010 0.221282
\(400\) −23.3068 −1.16534
\(401\) 25.2574 1.26129 0.630646 0.776070i \(-0.282790\pi\)
0.630646 + 0.776070i \(0.282790\pi\)
\(402\) 10.1284 0.505160
\(403\) −7.95133 −0.396084
\(404\) −8.99603 −0.447569
\(405\) 12.7999 0.636034
\(406\) −44.6398 −2.21543
\(407\) 8.12415 0.402699
\(408\) −4.84866 −0.240045
\(409\) −28.1709 −1.39296 −0.696480 0.717576i \(-0.745252\pi\)
−0.696480 + 0.717576i \(0.745252\pi\)
\(410\) −9.89421 −0.488640
\(411\) −2.61650 −0.129063
\(412\) 6.20296 0.305598
\(413\) 27.2051 1.33868
\(414\) 58.9627 2.89786
\(415\) 17.4833 0.858223
\(416\) −12.5304 −0.614355
\(417\) 2.56661 0.125688
\(418\) −13.6876 −0.669480
\(419\) −0.273174 −0.0133454 −0.00667270 0.999978i \(-0.502124\pi\)
−0.00667270 + 0.999978i \(0.502124\pi\)
\(420\) 6.67489 0.325701
\(421\) −25.5604 −1.24574 −0.622870 0.782325i \(-0.714033\pi\)
−0.622870 + 0.782325i \(0.714033\pi\)
\(422\) 2.20411 0.107294
\(423\) −9.47861 −0.460866
\(424\) 56.3111 2.73471
\(425\) −5.32041 −0.258078
\(426\) −7.57273 −0.366900
\(427\) 13.7962 0.667647
\(428\) −72.3093 −3.49520
\(429\) 0.429441 0.0207336
\(430\) 42.0262 2.02668
\(431\) −16.5368 −0.796549 −0.398274 0.917266i \(-0.630391\pi\)
−0.398274 + 0.917266i \(0.630391\pi\)
\(432\) −17.3145 −0.833044
\(433\) −10.5317 −0.506121 −0.253060 0.967450i \(-0.581437\pi\)
−0.253060 + 0.967450i \(0.581437\pi\)
\(434\) 44.9021 2.15537
\(435\) 3.05289 0.146375
\(436\) 8.70783 0.417030
\(437\) 39.0001 1.86563
\(438\) 1.31596 0.0628790
\(439\) 9.90432 0.472708 0.236354 0.971667i \(-0.424048\pi\)
0.236354 + 0.971667i \(0.424048\pi\)
\(440\) −12.0209 −0.573075
\(441\) −2.44279 −0.116323
\(442\) −7.12725 −0.339009
\(443\) 32.6369 1.55062 0.775312 0.631578i \(-0.217593\pi\)
0.775312 + 0.631578i \(0.217593\pi\)
\(444\) 11.6593 0.553328
\(445\) 25.2153 1.19532
\(446\) 42.5071 2.01277
\(447\) −4.62934 −0.218960
\(448\) 18.7489 0.885802
\(449\) 37.4935 1.76943 0.884713 0.466136i \(-0.154354\pi\)
0.884713 + 0.466136i \(0.154354\pi\)
\(450\) −18.9521 −0.893409
\(451\) 2.53430 0.119336
\(452\) −5.15019 −0.242245
\(453\) −2.22345 −0.104467
\(454\) −18.9017 −0.887102
\(455\) 5.70617 0.267509
\(456\) −11.4241 −0.534983
\(457\) 26.4903 1.23916 0.619581 0.784932i \(-0.287302\pi\)
0.619581 + 0.784932i \(0.287302\pi\)
\(458\) 45.5057 2.12634
\(459\) −3.95251 −0.184487
\(460\) 58.8949 2.74599
\(461\) 4.02442 0.187436 0.0937179 0.995599i \(-0.470125\pi\)
0.0937179 + 0.995599i \(0.470125\pi\)
\(462\) −2.42510 −0.112826
\(463\) 5.17675 0.240584 0.120292 0.992739i \(-0.461617\pi\)
0.120292 + 0.992739i \(0.461617\pi\)
\(464\) 56.8518 2.63928
\(465\) −3.07083 −0.142406
\(466\) 65.4612 3.03243
\(467\) −3.19518 −0.147855 −0.0739276 0.997264i \(-0.523553\pi\)
−0.0739276 + 0.997264i \(0.523553\pi\)
\(468\) −17.8989 −0.827375
\(469\) −34.4715 −1.59175
\(470\) −13.4293 −0.619448
\(471\) 4.47128 0.206026
\(472\) −70.3138 −3.23646
\(473\) −10.7646 −0.494956
\(474\) 4.47631 0.205604
\(475\) −12.5356 −0.575173
\(476\) 28.3753 1.30058
\(477\) 22.5632 1.03310
\(478\) −22.8683 −1.04597
\(479\) −22.4429 −1.02544 −0.512722 0.858555i \(-0.671363\pi\)
−0.512722 + 0.858555i \(0.671363\pi\)
\(480\) −4.83929 −0.220883
\(481\) 9.96723 0.454466
\(482\) −7.61173 −0.346705
\(483\) 6.90988 0.314410
\(484\) −47.2828 −2.14922
\(485\) −7.82428 −0.355282
\(486\) −21.2383 −0.963387
\(487\) 17.1500 0.777140 0.388570 0.921419i \(-0.372969\pi\)
0.388570 + 0.921419i \(0.372969\pi\)
\(488\) −35.6575 −1.61414
\(489\) 6.55514 0.296434
\(490\) −3.46094 −0.156349
\(491\) −35.6549 −1.60908 −0.804541 0.593897i \(-0.797588\pi\)
−0.804541 + 0.593897i \(0.797588\pi\)
\(492\) 3.63709 0.163973
\(493\) 12.9780 0.584499
\(494\) −16.7928 −0.755543
\(495\) −4.81665 −0.216492
\(496\) −57.1859 −2.56772
\(497\) 25.7734 1.15609
\(498\) −9.11604 −0.408500
\(499\) −37.9495 −1.69886 −0.849428 0.527705i \(-0.823053\pi\)
−0.849428 + 0.527705i \(0.823053\pi\)
\(500\) −56.6437 −2.53318
\(501\) 0.934926 0.0417694
\(502\) 45.7928 2.04383
\(503\) 8.56576 0.381929 0.190964 0.981597i \(-0.438839\pi\)
0.190964 + 0.981597i \(0.438839\pi\)
\(504\) 58.7831 2.61841
\(505\) −2.97008 −0.132167
\(506\) −21.3975 −0.951237
\(507\) −3.58122 −0.159048
\(508\) 96.6976 4.29026
\(509\) −9.18837 −0.407267 −0.203634 0.979047i \(-0.565275\pi\)
−0.203634 + 0.979047i \(0.565275\pi\)
\(510\) −2.75257 −0.121886
\(511\) −4.47880 −0.198130
\(512\) 44.3101 1.95825
\(513\) −9.31264 −0.411163
\(514\) −46.5066 −2.05132
\(515\) 2.04793 0.0902426
\(516\) −15.4487 −0.680093
\(517\) 3.43978 0.151281
\(518\) −56.2861 −2.47307
\(519\) −1.29272 −0.0567442
\(520\) −14.7480 −0.646745
\(521\) 29.8781 1.30898 0.654492 0.756069i \(-0.272883\pi\)
0.654492 + 0.756069i \(0.272883\pi\)
\(522\) 46.2295 2.02341
\(523\) 30.1708 1.31928 0.659639 0.751582i \(-0.270709\pi\)
0.659639 + 0.751582i \(0.270709\pi\)
\(524\) 47.2100 2.06238
\(525\) −2.22100 −0.0969325
\(526\) −7.08946 −0.309115
\(527\) −13.0543 −0.568652
\(528\) 3.08854 0.134411
\(529\) 37.9683 1.65080
\(530\) 31.9676 1.38858
\(531\) −28.1740 −1.22265
\(532\) 66.8560 2.89858
\(533\) 3.10925 0.134676
\(534\) −13.1476 −0.568953
\(535\) −23.8732 −1.03213
\(536\) 89.0944 3.84829
\(537\) −0.234924 −0.0101377
\(538\) −9.74655 −0.420204
\(539\) 0.886485 0.0381836
\(540\) −14.0632 −0.605185
\(541\) −32.6813 −1.40508 −0.702540 0.711644i \(-0.747951\pi\)
−0.702540 + 0.711644i \(0.747951\pi\)
\(542\) −68.9782 −2.96287
\(543\) −6.59327 −0.282944
\(544\) −20.5721 −0.882020
\(545\) 2.87493 0.123148
\(546\) −2.97527 −0.127330
\(547\) −2.91069 −0.124452 −0.0622261 0.998062i \(-0.519820\pi\)
−0.0622261 + 0.998062i \(0.519820\pi\)
\(548\) −39.5758 −1.69059
\(549\) −14.2876 −0.609778
\(550\) 6.87769 0.293266
\(551\) 30.5779 1.30266
\(552\) −17.8591 −0.760135
\(553\) −15.2349 −0.647853
\(554\) −35.4593 −1.50652
\(555\) 3.84938 0.163397
\(556\) 38.8212 1.64639
\(557\) 39.1827 1.66022 0.830112 0.557597i \(-0.188276\pi\)
0.830112 + 0.557597i \(0.188276\pi\)
\(558\) −46.5012 −1.96855
\(559\) −13.2067 −0.558583
\(560\) 41.0387 1.73420
\(561\) 0.705043 0.0297669
\(562\) 37.6551 1.58839
\(563\) −11.1208 −0.468687 −0.234344 0.972154i \(-0.575294\pi\)
−0.234344 + 0.972154i \(0.575294\pi\)
\(564\) 4.93659 0.207868
\(565\) −1.70036 −0.0715345
\(566\) −67.8505 −2.85197
\(567\) 22.7148 0.953931
\(568\) −66.6133 −2.79503
\(569\) 6.35464 0.266400 0.133200 0.991089i \(-0.457475\pi\)
0.133200 + 0.991089i \(0.457475\pi\)
\(570\) −6.48543 −0.271645
\(571\) −19.9842 −0.836314 −0.418157 0.908375i \(-0.637324\pi\)
−0.418157 + 0.908375i \(0.637324\pi\)
\(572\) 6.49548 0.271590
\(573\) −1.78134 −0.0744166
\(574\) −17.5583 −0.732868
\(575\) −19.5967 −0.817239
\(576\) −19.4166 −0.809024
\(577\) 17.2186 0.716820 0.358410 0.933564i \(-0.383319\pi\)
0.358410 + 0.933564i \(0.383319\pi\)
\(578\) 32.5632 1.35445
\(579\) 2.04786 0.0851063
\(580\) 46.1763 1.91737
\(581\) 31.0259 1.28717
\(582\) 4.07968 0.169108
\(583\) −8.18818 −0.339120
\(584\) 11.5758 0.479010
\(585\) −5.90938 −0.244323
\(586\) 34.2586 1.41521
\(587\) 0.550926 0.0227391 0.0113696 0.999935i \(-0.496381\pi\)
0.0113696 + 0.999935i \(0.496381\pi\)
\(588\) 1.27224 0.0524661
\(589\) −30.7576 −1.26734
\(590\) −39.9169 −1.64335
\(591\) 6.54931 0.269403
\(592\) 71.6842 2.94620
\(593\) 44.4417 1.82500 0.912501 0.409075i \(-0.134148\pi\)
0.912501 + 0.409075i \(0.134148\pi\)
\(594\) 5.10941 0.209642
\(595\) 9.36821 0.384059
\(596\) −70.0209 −2.86817
\(597\) −4.22747 −0.173019
\(598\) −26.2519 −1.07352
\(599\) 32.7136 1.33664 0.668320 0.743874i \(-0.267014\pi\)
0.668320 + 0.743874i \(0.267014\pi\)
\(600\) 5.74036 0.234349
\(601\) −24.3815 −0.994543 −0.497271 0.867595i \(-0.665665\pi\)
−0.497271 + 0.867595i \(0.665665\pi\)
\(602\) 74.5797 3.03964
\(603\) 35.6991 1.45378
\(604\) −33.6307 −1.36841
\(605\) −15.6106 −0.634661
\(606\) 1.54864 0.0629091
\(607\) −18.5698 −0.753725 −0.376863 0.926269i \(-0.622997\pi\)
−0.376863 + 0.926269i \(0.622997\pi\)
\(608\) −48.4706 −1.96574
\(609\) 5.41766 0.219535
\(610\) −20.2426 −0.819600
\(611\) 4.22015 0.170729
\(612\) −29.3858 −1.18785
\(613\) 20.3171 0.820601 0.410300 0.911950i \(-0.365424\pi\)
0.410300 + 0.911950i \(0.365424\pi\)
\(614\) −73.4250 −2.96319
\(615\) 1.20080 0.0484210
\(616\) −21.3323 −0.859505
\(617\) 39.9142 1.60689 0.803443 0.595381i \(-0.202999\pi\)
0.803443 + 0.595381i \(0.202999\pi\)
\(618\) −1.06782 −0.0429540
\(619\) 4.22030 0.169628 0.0848141 0.996397i \(-0.472970\pi\)
0.0848141 + 0.996397i \(0.472970\pi\)
\(620\) −46.4477 −1.86538
\(621\) −14.5583 −0.584205
\(622\) −0.805280 −0.0322888
\(623\) 44.7471 1.79276
\(624\) 3.78921 0.151690
\(625\) −6.15237 −0.246095
\(626\) −75.2917 −3.00926
\(627\) 1.66118 0.0663410
\(628\) 67.6301 2.69873
\(629\) 16.3639 0.652471
\(630\) 33.3709 1.32953
\(631\) −18.7980 −0.748336 −0.374168 0.927361i \(-0.622072\pi\)
−0.374168 + 0.927361i \(0.622072\pi\)
\(632\) 39.3758 1.56628
\(633\) −0.267499 −0.0106321
\(634\) 57.2906 2.27530
\(635\) 31.9251 1.26691
\(636\) −11.7512 −0.465967
\(637\) 1.08760 0.0430922
\(638\) −16.7767 −0.664194
\(639\) −26.6912 −1.05589
\(640\) 3.11833 0.123263
\(641\) −28.1705 −1.11267 −0.556335 0.830958i \(-0.687793\pi\)
−0.556335 + 0.830958i \(0.687793\pi\)
\(642\) 12.4478 0.491276
\(643\) 26.9209 1.06166 0.530829 0.847479i \(-0.321881\pi\)
0.530829 + 0.847479i \(0.321881\pi\)
\(644\) 104.515 4.11847
\(645\) −5.10046 −0.200831
\(646\) −27.5699 −1.08472
\(647\) 30.6505 1.20499 0.602497 0.798121i \(-0.294173\pi\)
0.602497 + 0.798121i \(0.294173\pi\)
\(648\) −58.7081 −2.30627
\(649\) 10.2243 0.401339
\(650\) 8.43800 0.330965
\(651\) −5.44950 −0.213583
\(652\) 99.1494 3.88299
\(653\) 9.10101 0.356150 0.178075 0.984017i \(-0.443013\pi\)
0.178075 + 0.984017i \(0.443013\pi\)
\(654\) −1.49902 −0.0586165
\(655\) 15.5866 0.609017
\(656\) 22.3617 0.873076
\(657\) 4.63830 0.180957
\(658\) −23.8317 −0.929055
\(659\) −13.7459 −0.535464 −0.267732 0.963493i \(-0.586274\pi\)
−0.267732 + 0.963493i \(0.586274\pi\)
\(660\) 2.50858 0.0976463
\(661\) 22.9405 0.892281 0.446140 0.894963i \(-0.352798\pi\)
0.446140 + 0.894963i \(0.352798\pi\)
\(662\) −52.7764 −2.05121
\(663\) 0.864992 0.0335935
\(664\) −80.1890 −3.11194
\(665\) 22.0728 0.855945
\(666\) 58.2906 2.25871
\(667\) 47.8020 1.85090
\(668\) 14.1412 0.547139
\(669\) −5.15883 −0.199452
\(670\) 50.5786 1.95402
\(671\) 5.18494 0.200163
\(672\) −8.58781 −0.331282
\(673\) 28.5212 1.09941 0.549705 0.835359i \(-0.314740\pi\)
0.549705 + 0.835359i \(0.314740\pi\)
\(674\) 64.6888 2.49172
\(675\) 4.67940 0.180110
\(676\) −54.1676 −2.08337
\(677\) −41.0183 −1.57646 −0.788230 0.615381i \(-0.789002\pi\)
−0.788230 + 0.615381i \(0.789002\pi\)
\(678\) 0.886588 0.0340492
\(679\) −13.8850 −0.532856
\(680\) −24.2129 −0.928522
\(681\) 2.29399 0.0879058
\(682\) 16.8752 0.646186
\(683\) 5.38299 0.205974 0.102987 0.994683i \(-0.467160\pi\)
0.102987 + 0.994683i \(0.467160\pi\)
\(684\) −69.2369 −2.64734
\(685\) −13.0661 −0.499230
\(686\) 44.9001 1.71429
\(687\) −5.52276 −0.210706
\(688\) −94.9823 −3.62117
\(689\) −10.0458 −0.382714
\(690\) −10.1386 −0.385969
\(691\) −17.1577 −0.652708 −0.326354 0.945248i \(-0.605820\pi\)
−0.326354 + 0.945248i \(0.605820\pi\)
\(692\) −19.5530 −0.743293
\(693\) −8.54763 −0.324698
\(694\) 71.7771 2.72462
\(695\) 12.8170 0.486175
\(696\) −14.0024 −0.530759
\(697\) 5.10466 0.193353
\(698\) −90.9235 −3.44151
\(699\) −7.94463 −0.300493
\(700\) −33.5937 −1.26972
\(701\) 4.88828 0.184628 0.0923139 0.995730i \(-0.470574\pi\)
0.0923139 + 0.995730i \(0.470574\pi\)
\(702\) 6.26855 0.236591
\(703\) 38.5555 1.45415
\(704\) 7.04627 0.265566
\(705\) 1.62983 0.0613831
\(706\) −51.0558 −1.92151
\(707\) −5.27070 −0.198225
\(708\) 14.6734 0.551460
\(709\) 46.9593 1.76359 0.881796 0.471631i \(-0.156335\pi\)
0.881796 + 0.471631i \(0.156335\pi\)
\(710\) −37.8161 −1.41921
\(711\) 15.7774 0.591700
\(712\) −115.653 −4.33426
\(713\) −48.0829 −1.80072
\(714\) −4.88471 −0.182806
\(715\) 2.14451 0.0802001
\(716\) −3.55332 −0.132794
\(717\) 2.77538 0.103649
\(718\) 5.56885 0.207828
\(719\) 19.9077 0.742431 0.371215 0.928547i \(-0.378941\pi\)
0.371215 + 0.928547i \(0.378941\pi\)
\(720\) −42.5002 −1.58389
\(721\) 3.63426 0.135347
\(722\) −15.4862 −0.576337
\(723\) 0.923790 0.0343561
\(724\) −99.7262 −3.70629
\(725\) −15.3647 −0.570631
\(726\) 8.13958 0.302088
\(727\) 33.7961 1.25343 0.626714 0.779249i \(-0.284399\pi\)
0.626714 + 0.779249i \(0.284399\pi\)
\(728\) −26.1719 −0.969995
\(729\) −21.7561 −0.805782
\(730\) 6.57154 0.243224
\(731\) −21.6823 −0.801950
\(732\) 7.44115 0.275033
\(733\) 47.7228 1.76268 0.881341 0.472480i \(-0.156641\pi\)
0.881341 + 0.472480i \(0.156641\pi\)
\(734\) −56.9899 −2.10353
\(735\) 0.420034 0.0154932
\(736\) −75.7733 −2.79304
\(737\) −12.9552 −0.477211
\(738\) 18.1836 0.669346
\(739\) −49.6785 −1.82745 −0.913727 0.406328i \(-0.866809\pi\)
−0.913727 + 0.406328i \(0.866809\pi\)
\(740\) 58.2235 2.14034
\(741\) 2.03804 0.0748692
\(742\) 56.7297 2.08261
\(743\) −38.4405 −1.41025 −0.705123 0.709085i \(-0.749108\pi\)
−0.705123 + 0.709085i \(0.749108\pi\)
\(744\) 14.0847 0.516369
\(745\) −23.1177 −0.846966
\(746\) 37.6963 1.38016
\(747\) −32.1308 −1.17561
\(748\) 10.6641 0.389918
\(749\) −42.3654 −1.54800
\(750\) 9.75102 0.356057
\(751\) 6.82033 0.248878 0.124439 0.992227i \(-0.460287\pi\)
0.124439 + 0.992227i \(0.460287\pi\)
\(752\) 30.3513 1.10680
\(753\) −5.55760 −0.202530
\(754\) −20.5827 −0.749577
\(755\) −11.1033 −0.404090
\(756\) −24.9566 −0.907663
\(757\) 8.52901 0.309992 0.154996 0.987915i \(-0.450464\pi\)
0.154996 + 0.987915i \(0.450464\pi\)
\(758\) 37.2514 1.35303
\(759\) 2.59689 0.0942612
\(760\) −57.0489 −2.06938
\(761\) 8.47951 0.307382 0.153691 0.988119i \(-0.450884\pi\)
0.153691 + 0.988119i \(0.450884\pi\)
\(762\) −16.6462 −0.603027
\(763\) 5.10184 0.184699
\(764\) −26.9436 −0.974784
\(765\) −9.70184 −0.350771
\(766\) 1.10328 0.0398630
\(767\) 12.5438 0.452932
\(768\) −5.85730 −0.211357
\(769\) 7.67339 0.276709 0.138355 0.990383i \(-0.455819\pi\)
0.138355 + 0.990383i \(0.455819\pi\)
\(770\) −12.1103 −0.436425
\(771\) 5.64423 0.203272
\(772\) 30.9748 1.11481
\(773\) −41.6953 −1.49967 −0.749837 0.661622i \(-0.769868\pi\)
−0.749837 + 0.661622i \(0.769868\pi\)
\(774\) −77.2356 −2.77618
\(775\) 15.4550 0.555160
\(776\) 35.8868 1.28826
\(777\) 6.83110 0.245065
\(778\) −8.96628 −0.321457
\(779\) 12.0273 0.430922
\(780\) 3.07769 0.110199
\(781\) 9.68622 0.346600
\(782\) −43.0995 −1.54124
\(783\) −11.4144 −0.407917
\(784\) 7.82199 0.279357
\(785\) 22.3283 0.796932
\(786\) −8.12704 −0.289882
\(787\) −19.7776 −0.704994 −0.352497 0.935813i \(-0.614667\pi\)
−0.352497 + 0.935813i \(0.614667\pi\)
\(788\) 99.0613 3.52891
\(789\) 0.860405 0.0306312
\(790\) 22.3535 0.795301
\(791\) −3.01745 −0.107288
\(792\) 22.0920 0.785006
\(793\) 6.36122 0.225894
\(794\) −4.90618 −0.174114
\(795\) −3.87972 −0.137599
\(796\) −63.9423 −2.26638
\(797\) −46.4327 −1.64473 −0.822366 0.568959i \(-0.807346\pi\)
−0.822366 + 0.568959i \(0.807346\pi\)
\(798\) −11.5090 −0.407415
\(799\) 6.92851 0.245113
\(800\) 24.3554 0.861093
\(801\) −46.3407 −1.63737
\(802\) −65.7650 −2.32224
\(803\) −1.68323 −0.0594001
\(804\) −18.5926 −0.655710
\(805\) 34.5060 1.21618
\(806\) 20.7036 0.729254
\(807\) 1.18288 0.0416394
\(808\) 13.6225 0.479239
\(809\) 27.6798 0.973171 0.486585 0.873633i \(-0.338242\pi\)
0.486585 + 0.873633i \(0.338242\pi\)
\(810\) −33.3284 −1.17104
\(811\) −10.3944 −0.364996 −0.182498 0.983206i \(-0.558418\pi\)
−0.182498 + 0.983206i \(0.558418\pi\)
\(812\) 81.9445 2.87569
\(813\) 8.37147 0.293600
\(814\) −21.1536 −0.741434
\(815\) 32.7346 1.14664
\(816\) 6.22101 0.217779
\(817\) −51.0865 −1.78729
\(818\) 73.3512 2.56466
\(819\) −10.4868 −0.366438
\(820\) 18.1627 0.634267
\(821\) 6.60043 0.230357 0.115178 0.993345i \(-0.463256\pi\)
0.115178 + 0.993345i \(0.463256\pi\)
\(822\) 6.81284 0.237625
\(823\) −16.2879 −0.567760 −0.283880 0.958860i \(-0.591622\pi\)
−0.283880 + 0.958860i \(0.591622\pi\)
\(824\) −9.39303 −0.327222
\(825\) −0.834704 −0.0290607
\(826\) −70.8366 −2.46472
\(827\) −21.8128 −0.758504 −0.379252 0.925293i \(-0.623819\pi\)
−0.379252 + 0.925293i \(0.623819\pi\)
\(828\) −108.237 −3.76150
\(829\) −51.6223 −1.79292 −0.896458 0.443129i \(-0.853868\pi\)
−0.896458 + 0.443129i \(0.853868\pi\)
\(830\) −45.5230 −1.58013
\(831\) 4.30349 0.149286
\(832\) 8.64481 0.299705
\(833\) 1.78558 0.0618668
\(834\) −6.68294 −0.231411
\(835\) 4.66877 0.161569
\(836\) 25.1260 0.869002
\(837\) 11.4815 0.396857
\(838\) 0.711288 0.0245710
\(839\) −29.8961 −1.03213 −0.516064 0.856550i \(-0.672603\pi\)
−0.516064 + 0.856550i \(0.672603\pi\)
\(840\) −10.1077 −0.348748
\(841\) 8.47893 0.292377
\(842\) 66.5542 2.29361
\(843\) −4.56998 −0.157398
\(844\) −4.04604 −0.139270
\(845\) −17.8836 −0.615216
\(846\) 24.6804 0.848528
\(847\) −27.7026 −0.951872
\(848\) −72.2492 −2.48105
\(849\) 8.23461 0.282611
\(850\) 13.8532 0.475162
\(851\) 60.2733 2.06614
\(852\) 13.9011 0.476246
\(853\) −11.5788 −0.396451 −0.198225 0.980156i \(-0.563518\pi\)
−0.198225 + 0.980156i \(0.563518\pi\)
\(854\) −35.9226 −1.22924
\(855\) −22.8588 −0.781756
\(856\) 109.497 3.74252
\(857\) 27.6406 0.944184 0.472092 0.881549i \(-0.343499\pi\)
0.472092 + 0.881549i \(0.343499\pi\)
\(858\) −1.11818 −0.0381739
\(859\) −38.4781 −1.31286 −0.656428 0.754388i \(-0.727934\pi\)
−0.656428 + 0.754388i \(0.727934\pi\)
\(860\) −77.1468 −2.63068
\(861\) 2.13094 0.0726223
\(862\) 43.0584 1.46657
\(863\) −22.9487 −0.781181 −0.390591 0.920564i \(-0.627729\pi\)
−0.390591 + 0.920564i \(0.627729\pi\)
\(864\) 18.0935 0.615554
\(865\) −6.45550 −0.219493
\(866\) 27.4224 0.931850
\(867\) −3.95200 −0.134217
\(868\) −82.4261 −2.79772
\(869\) −5.72562 −0.194228
\(870\) −7.94910 −0.269500
\(871\) −15.8943 −0.538557
\(872\) −13.1861 −0.446538
\(873\) 14.3794 0.486670
\(874\) −101.548 −3.43492
\(875\) −33.1870 −1.12193
\(876\) −2.41569 −0.0816185
\(877\) 14.9014 0.503184 0.251592 0.967833i \(-0.419046\pi\)
0.251592 + 0.967833i \(0.419046\pi\)
\(878\) −25.7888 −0.870331
\(879\) −4.15776 −0.140238
\(880\) 15.4233 0.519919
\(881\) 54.6260 1.84040 0.920198 0.391454i \(-0.128028\pi\)
0.920198 + 0.391454i \(0.128028\pi\)
\(882\) 6.36051 0.214170
\(883\) −5.20588 −0.175192 −0.0875960 0.996156i \(-0.527918\pi\)
−0.0875960 + 0.996156i \(0.527918\pi\)
\(884\) 13.0834 0.440042
\(885\) 4.84448 0.162845
\(886\) −84.9797 −2.85495
\(887\) −58.5267 −1.96514 −0.982568 0.185905i \(-0.940478\pi\)
−0.982568 + 0.185905i \(0.940478\pi\)
\(888\) −17.6555 −0.592481
\(889\) 56.6543 1.90012
\(890\) −65.6555 −2.20078
\(891\) 8.53673 0.285991
\(892\) −78.0296 −2.61262
\(893\) 16.3245 0.546279
\(894\) 12.0539 0.403141
\(895\) −1.17314 −0.0392139
\(896\) 5.53378 0.184871
\(897\) 3.18603 0.106379
\(898\) −97.6253 −3.25780
\(899\) −37.6992 −1.25734
\(900\) 34.7900 1.15967
\(901\) −16.4929 −0.549457
\(902\) −6.59880 −0.219716
\(903\) −9.05129 −0.301208
\(904\) 7.79884 0.259386
\(905\) −32.9250 −1.09446
\(906\) 5.78941 0.192340
\(907\) −3.69292 −0.122621 −0.0613107 0.998119i \(-0.519528\pi\)
−0.0613107 + 0.998119i \(0.519528\pi\)
\(908\) 34.6976 1.15148
\(909\) 5.45840 0.181044
\(910\) −14.8577 −0.492528
\(911\) 7.84245 0.259832 0.129916 0.991525i \(-0.458529\pi\)
0.129916 + 0.991525i \(0.458529\pi\)
\(912\) 14.6576 0.485360
\(913\) 11.6603 0.385898
\(914\) −68.9752 −2.28150
\(915\) 2.45673 0.0812169
\(916\) −83.5341 −2.76005
\(917\) 27.6599 0.913410
\(918\) 10.2915 0.339671
\(919\) −7.00565 −0.231095 −0.115548 0.993302i \(-0.536862\pi\)
−0.115548 + 0.993302i \(0.536862\pi\)
\(920\) −89.1836 −2.94030
\(921\) 8.91115 0.293632
\(922\) −10.4788 −0.345099
\(923\) 11.8837 0.391156
\(924\) 4.45172 0.146451
\(925\) −19.3733 −0.636990
\(926\) −13.4792 −0.442954
\(927\) −3.76368 −0.123616
\(928\) −59.4098 −1.95022
\(929\) 33.0564 1.08455 0.542273 0.840202i \(-0.317564\pi\)
0.542273 + 0.840202i \(0.317564\pi\)
\(930\) 7.99581 0.262193
\(931\) 4.20708 0.137881
\(932\) −120.166 −3.93617
\(933\) 0.0977320 0.00319960
\(934\) 8.31959 0.272225
\(935\) 3.52079 0.115142
\(936\) 27.1039 0.885920
\(937\) −32.8800 −1.07414 −0.537071 0.843537i \(-0.680469\pi\)
−0.537071 + 0.843537i \(0.680469\pi\)
\(938\) 89.7567 2.93066
\(939\) 9.13770 0.298198
\(940\) 24.6520 0.804059
\(941\) 6.45007 0.210266 0.105133 0.994458i \(-0.466473\pi\)
0.105133 + 0.994458i \(0.466473\pi\)
\(942\) −11.6423 −0.379326
\(943\) 18.8021 0.612279
\(944\) 90.2152 2.93626
\(945\) −8.23952 −0.268032
\(946\) 28.0288 0.911293
\(947\) −35.1309 −1.14160 −0.570801 0.821088i \(-0.693367\pi\)
−0.570801 + 0.821088i \(0.693367\pi\)
\(948\) −8.21710 −0.266879
\(949\) −2.06510 −0.0670360
\(950\) 32.6401 1.05899
\(951\) −6.95302 −0.225467
\(952\) −42.9682 −1.39261
\(953\) −35.5361 −1.15113 −0.575563 0.817758i \(-0.695217\pi\)
−0.575563 + 0.817758i \(0.695217\pi\)
\(954\) −58.7500 −1.90210
\(955\) −8.89552 −0.287852
\(956\) 41.9789 1.35770
\(957\) 2.03608 0.0658172
\(958\) 58.4368 1.88801
\(959\) −23.1871 −0.748751
\(960\) 3.33866 0.107755
\(961\) 6.92070 0.223248
\(962\) −25.9526 −0.836746
\(963\) 43.8741 1.41382
\(964\) 13.9727 0.450031
\(965\) 10.2265 0.329202
\(966\) −17.9919 −0.578880
\(967\) −57.7192 −1.85612 −0.928062 0.372425i \(-0.878526\pi\)
−0.928062 + 0.372425i \(0.878526\pi\)
\(968\) 71.5996 2.30130
\(969\) 3.34599 0.107489
\(970\) 20.3728 0.654131
\(971\) 37.2682 1.19599 0.597996 0.801499i \(-0.295964\pi\)
0.597996 + 0.801499i \(0.295964\pi\)
\(972\) 38.9868 1.25050
\(973\) 22.7450 0.729171
\(974\) −44.6550 −1.43084
\(975\) −1.02407 −0.0327965
\(976\) 45.7499 1.46442
\(977\) 34.3101 1.09768 0.548838 0.835929i \(-0.315070\pi\)
0.548838 + 0.835929i \(0.315070\pi\)
\(978\) −17.0682 −0.545782
\(979\) 16.8170 0.537474
\(980\) 6.35320 0.202945
\(981\) −5.28353 −0.168690
\(982\) 92.8379 2.96258
\(983\) −25.9514 −0.827721 −0.413860 0.910340i \(-0.635820\pi\)
−0.413860 + 0.910340i \(0.635820\pi\)
\(984\) −5.50759 −0.175576
\(985\) 32.7055 1.04208
\(986\) −33.7920 −1.07616
\(987\) 2.89231 0.0920631
\(988\) 30.8262 0.980713
\(989\) −79.8627 −2.53949
\(990\) 12.5416 0.398597
\(991\) −18.3337 −0.582390 −0.291195 0.956664i \(-0.594053\pi\)
−0.291195 + 0.956664i \(0.594053\pi\)
\(992\) 59.7589 1.89735
\(993\) 6.40515 0.203261
\(994\) −67.1085 −2.12855
\(995\) −21.1108 −0.669258
\(996\) 16.7342 0.530243
\(997\) 18.4122 0.583121 0.291560 0.956552i \(-0.405826\pi\)
0.291560 + 0.956552i \(0.405826\pi\)
\(998\) 98.8128 3.12787
\(999\) −14.3923 −0.455354
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 4003.2.a.c.1.9 179
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4003.2.a.c.1.9 179 1.1 even 1 trivial