Properties

Label 6037.2.a.b.1.7
Level $6037$
Weight $2$
Character 6037.1
Self dual yes
Analytic conductor $48.206$
Analytic rank $0$
Dimension $259$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 6037 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6037.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(48.2056877002\)
Analytic rank: \(0\)
Dimension: \(259\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) \(=\) 6037.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.60200 q^{2} -2.50808 q^{3} +4.77039 q^{4} +0.421972 q^{5} +6.52603 q^{6} -1.06326 q^{7} -7.20855 q^{8} +3.29049 q^{9} +O(q^{10})\) \(q-2.60200 q^{2} -2.50808 q^{3} +4.77039 q^{4} +0.421972 q^{5} +6.52603 q^{6} -1.06326 q^{7} -7.20855 q^{8} +3.29049 q^{9} -1.09797 q^{10} -2.57042 q^{11} -11.9645 q^{12} +3.70300 q^{13} +2.76660 q^{14} -1.05834 q^{15} +9.21585 q^{16} -5.32295 q^{17} -8.56184 q^{18} -7.54727 q^{19} +2.01297 q^{20} +2.66674 q^{21} +6.68822 q^{22} +4.06815 q^{23} +18.0797 q^{24} -4.82194 q^{25} -9.63520 q^{26} -0.728563 q^{27} -5.07216 q^{28} -2.06786 q^{29} +2.75380 q^{30} -5.40445 q^{31} -9.56252 q^{32} +6.44682 q^{33} +13.8503 q^{34} -0.448665 q^{35} +15.6969 q^{36} -8.73603 q^{37} +19.6380 q^{38} -9.28743 q^{39} -3.04181 q^{40} -5.87862 q^{41} -6.93885 q^{42} -5.00492 q^{43} -12.2619 q^{44} +1.38849 q^{45} -10.5853 q^{46} +4.68277 q^{47} -23.1141 q^{48} -5.86948 q^{49} +12.5467 q^{50} +13.3504 q^{51} +17.6648 q^{52} -10.3864 q^{53} +1.89572 q^{54} -1.08464 q^{55} +7.66455 q^{56} +18.9292 q^{57} +5.38057 q^{58} +12.4664 q^{59} -5.04870 q^{60} -10.1115 q^{61} +14.0624 q^{62} -3.49864 q^{63} +6.44995 q^{64} +1.56256 q^{65} -16.7746 q^{66} -10.2037 q^{67} -25.3926 q^{68} -10.2033 q^{69} +1.16743 q^{70} -6.16132 q^{71} -23.7196 q^{72} +11.7691 q^{73} +22.7311 q^{74} +12.0938 q^{75} -36.0035 q^{76} +2.73302 q^{77} +24.1659 q^{78} -0.169344 q^{79} +3.88883 q^{80} -8.04416 q^{81} +15.2962 q^{82} +4.24867 q^{83} +12.7214 q^{84} -2.24614 q^{85} +13.0228 q^{86} +5.18637 q^{87} +18.5290 q^{88} -4.85615 q^{89} -3.61286 q^{90} -3.93724 q^{91} +19.4067 q^{92} +13.5548 q^{93} -12.1846 q^{94} -3.18474 q^{95} +23.9836 q^{96} -8.55369 q^{97} +15.2724 q^{98} -8.45792 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 259q + 47q^{2} + 29q^{3} + 273q^{4} + 38q^{5} + 24q^{6} + 42q^{7} + 141q^{8} + 286q^{9} + O(q^{10}) \) \( 259q + 47q^{2} + 29q^{3} + 273q^{4} + 38q^{5} + 24q^{6} + 42q^{7} + 141q^{8} + 286q^{9} + 18q^{10} + 108q^{11} + 46q^{12} + 33q^{13} + 35q^{14} + 40q^{15} + 301q^{16} + 67q^{17} + 117q^{18} + 69q^{19} + 103q^{20} + 24q^{21} + 42q^{22} + 162q^{23} + 45q^{24} + 291q^{25} + 41q^{26} + 101q^{27} + 87q^{28} + 78q^{29} + 48q^{30} + 25q^{31} + 314q^{32} + 67q^{33} + 9q^{34} + 252q^{35} + 337q^{36} + 49q^{37} + 59q^{38} + 93q^{39} + 44q^{40} + 60q^{41} + 38q^{42} + 178q^{43} + 171q^{44} + 67q^{45} + 43q^{46} + 185q^{47} + 67q^{48} + 273q^{49} + 204q^{50} + 145q^{51} + 83q^{52} + 112q^{53} + 60q^{54} + 57q^{55} + 93q^{56} + 109q^{57} + 63q^{58} + 228q^{59} + 53q^{60} + 20q^{61} + 126q^{62} + 153q^{63} + 345q^{64} + 113q^{65} + 5q^{66} + 208q^{67} + 166q^{68} + 10q^{69} + 69q^{70} + 150q^{71} + 331q^{72} + 75q^{73} + 84q^{74} + 72q^{75} + 102q^{76} + 166q^{77} + 69q^{78} + 52q^{79} + 180q^{80} + 327q^{81} + 43q^{82} + 434q^{83} + 75q^{85} + 133q^{86} + 144q^{87} + 111q^{88} + 78q^{89} - 8q^{90} + 35q^{91} + 372q^{92} + 160q^{93} + 36q^{94} + 154q^{95} + 60q^{96} + 35q^{97} + 254q^{98} + 234q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.60200 −1.83989 −0.919945 0.392047i \(-0.871767\pi\)
−0.919945 + 0.392047i \(0.871767\pi\)
\(3\) −2.50808 −1.44804 −0.724022 0.689777i \(-0.757708\pi\)
−0.724022 + 0.689777i \(0.757708\pi\)
\(4\) 4.77039 2.38520
\(5\) 0.421972 0.188712 0.0943558 0.995539i \(-0.469921\pi\)
0.0943558 + 0.995539i \(0.469921\pi\)
\(6\) 6.52603 2.66424
\(7\) −1.06326 −0.401874 −0.200937 0.979604i \(-0.564399\pi\)
−0.200937 + 0.979604i \(0.564399\pi\)
\(8\) −7.20855 −2.54861
\(9\) 3.29049 1.09683
\(10\) −1.09797 −0.347209
\(11\) −2.57042 −0.775010 −0.387505 0.921868i \(-0.626663\pi\)
−0.387505 + 0.921868i \(0.626663\pi\)
\(12\) −11.9645 −3.45387
\(13\) 3.70300 1.02703 0.513514 0.858081i \(-0.328344\pi\)
0.513514 + 0.858081i \(0.328344\pi\)
\(14\) 2.76660 0.739404
\(15\) −1.05834 −0.273263
\(16\) 9.21585 2.30396
\(17\) −5.32295 −1.29101 −0.645503 0.763758i \(-0.723352\pi\)
−0.645503 + 0.763758i \(0.723352\pi\)
\(18\) −8.56184 −2.01804
\(19\) −7.54727 −1.73146 −0.865732 0.500508i \(-0.833146\pi\)
−0.865732 + 0.500508i \(0.833146\pi\)
\(20\) 2.01297 0.450114
\(21\) 2.66674 0.581931
\(22\) 6.68822 1.42593
\(23\) 4.06815 0.848268 0.424134 0.905599i \(-0.360579\pi\)
0.424134 + 0.905599i \(0.360579\pi\)
\(24\) 18.0797 3.69049
\(25\) −4.82194 −0.964388
\(26\) −9.63520 −1.88962
\(27\) −0.728563 −0.140212
\(28\) −5.07216 −0.958548
\(29\) −2.06786 −0.383992 −0.191996 0.981396i \(-0.561496\pi\)
−0.191996 + 0.981396i \(0.561496\pi\)
\(30\) 2.75380 0.502773
\(31\) −5.40445 −0.970668 −0.485334 0.874329i \(-0.661302\pi\)
−0.485334 + 0.874329i \(0.661302\pi\)
\(32\) −9.56252 −1.69043
\(33\) 6.44682 1.12225
\(34\) 13.8503 2.37531
\(35\) −0.448665 −0.0758383
\(36\) 15.6969 2.61615
\(37\) −8.73603 −1.43619 −0.718097 0.695943i \(-0.754987\pi\)
−0.718097 + 0.695943i \(0.754987\pi\)
\(38\) 19.6380 3.18570
\(39\) −9.28743 −1.48718
\(40\) −3.04181 −0.480952
\(41\) −5.87862 −0.918087 −0.459043 0.888414i \(-0.651808\pi\)
−0.459043 + 0.888414i \(0.651808\pi\)
\(42\) −6.93885 −1.07069
\(43\) −5.00492 −0.763243 −0.381622 0.924319i \(-0.624634\pi\)
−0.381622 + 0.924319i \(0.624634\pi\)
\(44\) −12.2619 −1.84855
\(45\) 1.38849 0.206984
\(46\) −10.5853 −1.56072
\(47\) 4.68277 0.683052 0.341526 0.939872i \(-0.389056\pi\)
0.341526 + 0.939872i \(0.389056\pi\)
\(48\) −23.1141 −3.33624
\(49\) −5.86948 −0.838497
\(50\) 12.5467 1.77437
\(51\) 13.3504 1.86943
\(52\) 17.6648 2.44966
\(53\) −10.3864 −1.42668 −0.713339 0.700820i \(-0.752818\pi\)
−0.713339 + 0.700820i \(0.752818\pi\)
\(54\) 1.89572 0.257975
\(55\) −1.08464 −0.146253
\(56\) 7.66455 1.02422
\(57\) 18.9292 2.50723
\(58\) 5.38057 0.706504
\(59\) 12.4664 1.62299 0.811496 0.584358i \(-0.198654\pi\)
0.811496 + 0.584358i \(0.198654\pi\)
\(60\) −5.04870 −0.651785
\(61\) −10.1115 −1.29465 −0.647325 0.762214i \(-0.724112\pi\)
−0.647325 + 0.762214i \(0.724112\pi\)
\(62\) 14.0624 1.78592
\(63\) −3.49864 −0.440787
\(64\) 6.44995 0.806243
\(65\) 1.56256 0.193812
\(66\) −16.7746 −2.06481
\(67\) −10.2037 −1.24659 −0.623293 0.781989i \(-0.714205\pi\)
−0.623293 + 0.781989i \(0.714205\pi\)
\(68\) −25.3926 −3.07930
\(69\) −10.2033 −1.22833
\(70\) 1.16743 0.139534
\(71\) −6.16132 −0.731214 −0.365607 0.930769i \(-0.619139\pi\)
−0.365607 + 0.930769i \(0.619139\pi\)
\(72\) −23.7196 −2.79539
\(73\) 11.7691 1.37747 0.688733 0.725015i \(-0.258167\pi\)
0.688733 + 0.725015i \(0.258167\pi\)
\(74\) 22.7311 2.64244
\(75\) 12.0938 1.39648
\(76\) −36.0035 −4.12988
\(77\) 2.73302 0.311456
\(78\) 24.1659 2.73625
\(79\) −0.169344 −0.0190526 −0.00952632 0.999955i \(-0.503032\pi\)
−0.00952632 + 0.999955i \(0.503032\pi\)
\(80\) 3.88883 0.434785
\(81\) −8.04416 −0.893796
\(82\) 15.2962 1.68918
\(83\) 4.24867 0.466352 0.233176 0.972435i \(-0.425088\pi\)
0.233176 + 0.972435i \(0.425088\pi\)
\(84\) 12.7214 1.38802
\(85\) −2.24614 −0.243628
\(86\) 13.0228 1.40428
\(87\) 5.18637 0.556037
\(88\) 18.5290 1.97520
\(89\) −4.85615 −0.514751 −0.257376 0.966311i \(-0.582858\pi\)
−0.257376 + 0.966311i \(0.582858\pi\)
\(90\) −3.61286 −0.380828
\(91\) −3.93724 −0.412735
\(92\) 19.4067 2.02329
\(93\) 13.5548 1.40557
\(94\) −12.1846 −1.25674
\(95\) −3.18474 −0.326747
\(96\) 23.9836 2.44782
\(97\) −8.55369 −0.868496 −0.434248 0.900793i \(-0.642986\pi\)
−0.434248 + 0.900793i \(0.642986\pi\)
\(98\) 15.2724 1.54274
\(99\) −8.45792 −0.850053
\(100\) −23.0025 −2.30025
\(101\) 9.07104 0.902602 0.451301 0.892372i \(-0.350960\pi\)
0.451301 + 0.892372i \(0.350960\pi\)
\(102\) −34.7377 −3.43955
\(103\) −1.04588 −0.103054 −0.0515270 0.998672i \(-0.516409\pi\)
−0.0515270 + 0.998672i \(0.516409\pi\)
\(104\) −26.6933 −2.61749
\(105\) 1.12529 0.109817
\(106\) 27.0253 2.62493
\(107\) 9.99804 0.966547 0.483273 0.875469i \(-0.339448\pi\)
0.483273 + 0.875469i \(0.339448\pi\)
\(108\) −3.47553 −0.334433
\(109\) −2.85821 −0.273767 −0.136883 0.990587i \(-0.543709\pi\)
−0.136883 + 0.990587i \(0.543709\pi\)
\(110\) 2.82224 0.269090
\(111\) 21.9107 2.07967
\(112\) −9.79883 −0.925902
\(113\) 10.9654 1.03154 0.515770 0.856727i \(-0.327506\pi\)
0.515770 + 0.856727i \(0.327506\pi\)
\(114\) −49.2537 −4.61303
\(115\) 1.71665 0.160078
\(116\) −9.86451 −0.915897
\(117\) 12.1847 1.12647
\(118\) −32.4376 −2.98613
\(119\) 5.65967 0.518821
\(120\) 7.62911 0.696439
\(121\) −4.39296 −0.399360
\(122\) 26.3102 2.38201
\(123\) 14.7441 1.32943
\(124\) −25.7813 −2.31523
\(125\) −4.14458 −0.370703
\(126\) 9.10344 0.810999
\(127\) −13.6068 −1.20741 −0.603704 0.797208i \(-0.706309\pi\)
−0.603704 + 0.797208i \(0.706309\pi\)
\(128\) 2.34229 0.207031
\(129\) 12.5528 1.10521
\(130\) −4.06578 −0.356593
\(131\) 2.43434 0.212689 0.106345 0.994329i \(-0.466085\pi\)
0.106345 + 0.994329i \(0.466085\pi\)
\(132\) 30.7539 2.67678
\(133\) 8.02470 0.695830
\(134\) 26.5501 2.29358
\(135\) −0.307433 −0.0264596
\(136\) 38.3708 3.29027
\(137\) 4.34294 0.371042 0.185521 0.982640i \(-0.440603\pi\)
0.185521 + 0.982640i \(0.440603\pi\)
\(138\) 26.5489 2.25999
\(139\) 10.8969 0.924263 0.462132 0.886811i \(-0.347085\pi\)
0.462132 + 0.886811i \(0.347085\pi\)
\(140\) −2.14031 −0.180889
\(141\) −11.7448 −0.989089
\(142\) 16.0317 1.34535
\(143\) −9.51825 −0.795956
\(144\) 30.3246 2.52705
\(145\) −0.872580 −0.0724638
\(146\) −30.6231 −2.53439
\(147\) 14.7212 1.21418
\(148\) −41.6743 −3.42560
\(149\) −18.8882 −1.54738 −0.773690 0.633564i \(-0.781591\pi\)
−0.773690 + 0.633564i \(0.781591\pi\)
\(150\) −31.4681 −2.56936
\(151\) −1.76685 −0.143784 −0.0718920 0.997412i \(-0.522904\pi\)
−0.0718920 + 0.997412i \(0.522904\pi\)
\(152\) 54.4049 4.41282
\(153\) −17.5151 −1.41601
\(154\) −7.11130 −0.573045
\(155\) −2.28053 −0.183176
\(156\) −44.3047 −3.54721
\(157\) 4.33460 0.345939 0.172969 0.984927i \(-0.444664\pi\)
0.172969 + 0.984927i \(0.444664\pi\)
\(158\) 0.440632 0.0350548
\(159\) 26.0499 2.06589
\(160\) −4.03512 −0.319004
\(161\) −4.32549 −0.340897
\(162\) 20.9309 1.64449
\(163\) −4.06005 −0.318007 −0.159004 0.987278i \(-0.550828\pi\)
−0.159004 + 0.987278i \(0.550828\pi\)
\(164\) −28.0433 −2.18982
\(165\) 2.72038 0.211781
\(166\) −11.0550 −0.858037
\(167\) 21.6107 1.67229 0.836144 0.548510i \(-0.184805\pi\)
0.836144 + 0.548510i \(0.184805\pi\)
\(168\) −19.2233 −1.48311
\(169\) 0.712206 0.0547851
\(170\) 5.84445 0.448248
\(171\) −24.8342 −1.89912
\(172\) −23.8754 −1.82048
\(173\) −16.2724 −1.23717 −0.618584 0.785718i \(-0.712294\pi\)
−0.618584 + 0.785718i \(0.712294\pi\)
\(174\) −13.4949 −1.02305
\(175\) 5.12697 0.387562
\(176\) −23.6886 −1.78559
\(177\) −31.2669 −2.35016
\(178\) 12.6357 0.947086
\(179\) −4.86042 −0.363285 −0.181642 0.983365i \(-0.558141\pi\)
−0.181642 + 0.983365i \(0.558141\pi\)
\(180\) 6.62366 0.493698
\(181\) −1.15380 −0.0857610 −0.0428805 0.999080i \(-0.513653\pi\)
−0.0428805 + 0.999080i \(0.513653\pi\)
\(182\) 10.2447 0.759388
\(183\) 25.3606 1.87471
\(184\) −29.3255 −2.16190
\(185\) −3.68636 −0.271027
\(186\) −35.2696 −2.58609
\(187\) 13.6822 1.00054
\(188\) 22.3386 1.62921
\(189\) 0.774651 0.0563475
\(190\) 8.28668 0.601179
\(191\) −19.4965 −1.41071 −0.705357 0.708852i \(-0.749213\pi\)
−0.705357 + 0.708852i \(0.749213\pi\)
\(192\) −16.1770 −1.16748
\(193\) −13.0698 −0.940784 −0.470392 0.882458i \(-0.655887\pi\)
−0.470392 + 0.882458i \(0.655887\pi\)
\(194\) 22.2567 1.59794
\(195\) −3.91904 −0.280648
\(196\) −27.9997 −1.99998
\(197\) 3.07879 0.219355 0.109677 0.993967i \(-0.465018\pi\)
0.109677 + 0.993967i \(0.465018\pi\)
\(198\) 22.0075 1.56400
\(199\) 9.40233 0.666513 0.333257 0.942836i \(-0.391852\pi\)
0.333257 + 0.942836i \(0.391852\pi\)
\(200\) 34.7592 2.45785
\(201\) 25.5918 1.80511
\(202\) −23.6028 −1.66069
\(203\) 2.19867 0.154316
\(204\) 63.6867 4.45896
\(205\) −2.48062 −0.173254
\(206\) 2.72139 0.189608
\(207\) 13.3862 0.930405
\(208\) 34.1263 2.36623
\(209\) 19.3996 1.34190
\(210\) −2.92800 −0.202051
\(211\) −13.2029 −0.908926 −0.454463 0.890766i \(-0.650169\pi\)
−0.454463 + 0.890766i \(0.650169\pi\)
\(212\) −49.5470 −3.40290
\(213\) 15.4531 1.05883
\(214\) −26.0149 −1.77834
\(215\) −2.11194 −0.144033
\(216\) 5.25188 0.357345
\(217\) 5.74633 0.390086
\(218\) 7.43705 0.503700
\(219\) −29.5178 −1.99463
\(220\) −5.17418 −0.348843
\(221\) −19.7109 −1.32590
\(222\) −57.0116 −3.82637
\(223\) 8.33033 0.557840 0.278920 0.960314i \(-0.410023\pi\)
0.278920 + 0.960314i \(0.410023\pi\)
\(224\) 10.1674 0.679340
\(225\) −15.8665 −1.05777
\(226\) −28.5320 −1.89792
\(227\) 10.4967 0.696693 0.348346 0.937366i \(-0.386743\pi\)
0.348346 + 0.937366i \(0.386743\pi\)
\(228\) 90.2997 5.98024
\(229\) −24.3460 −1.60883 −0.804415 0.594067i \(-0.797521\pi\)
−0.804415 + 0.594067i \(0.797521\pi\)
\(230\) −4.46671 −0.294526
\(231\) −6.85463 −0.451002
\(232\) 14.9063 0.978646
\(233\) −25.0042 −1.63808 −0.819041 0.573735i \(-0.805494\pi\)
−0.819041 + 0.573735i \(0.805494\pi\)
\(234\) −31.7045 −2.07259
\(235\) 1.97600 0.128900
\(236\) 59.4698 3.87115
\(237\) 0.424728 0.0275890
\(238\) −14.7265 −0.954574
\(239\) 0.610822 0.0395108 0.0197554 0.999805i \(-0.493711\pi\)
0.0197554 + 0.999805i \(0.493711\pi\)
\(240\) −9.75352 −0.629587
\(241\) −0.802165 −0.0516720 −0.0258360 0.999666i \(-0.508225\pi\)
−0.0258360 + 0.999666i \(0.508225\pi\)
\(242\) 11.4305 0.734779
\(243\) 22.3611 1.43447
\(244\) −48.2360 −3.08799
\(245\) −2.47676 −0.158234
\(246\) −38.3641 −2.44600
\(247\) −27.9476 −1.77826
\(248\) 38.9583 2.47385
\(249\) −10.6560 −0.675298
\(250\) 10.7842 0.682053
\(251\) −4.14027 −0.261332 −0.130666 0.991426i \(-0.541712\pi\)
−0.130666 + 0.991426i \(0.541712\pi\)
\(252\) −16.6899 −1.05136
\(253\) −10.4568 −0.657416
\(254\) 35.4049 2.22150
\(255\) 5.63350 0.352784
\(256\) −18.9945 −1.18716
\(257\) −13.2371 −0.825709 −0.412854 0.910797i \(-0.635468\pi\)
−0.412854 + 0.910797i \(0.635468\pi\)
\(258\) −32.6623 −2.03346
\(259\) 9.28865 0.577169
\(260\) 7.45404 0.462280
\(261\) −6.80427 −0.421174
\(262\) −6.33414 −0.391324
\(263\) −22.9404 −1.41456 −0.707281 0.706932i \(-0.750079\pi\)
−0.707281 + 0.706932i \(0.750079\pi\)
\(264\) −46.4722 −2.86017
\(265\) −4.38276 −0.269231
\(266\) −20.8803 −1.28025
\(267\) 12.1796 0.745382
\(268\) −48.6758 −2.97335
\(269\) −0.280355 −0.0170936 −0.00854679 0.999963i \(-0.502721\pi\)
−0.00854679 + 0.999963i \(0.502721\pi\)
\(270\) 0.799941 0.0486828
\(271\) −32.1628 −1.95375 −0.976874 0.213816i \(-0.931411\pi\)
−0.976874 + 0.213816i \(0.931411\pi\)
\(272\) −49.0555 −2.97443
\(273\) 9.87494 0.597659
\(274\) −11.3003 −0.682677
\(275\) 12.3944 0.747410
\(276\) −48.6736 −2.92980
\(277\) 13.7852 0.828274 0.414137 0.910215i \(-0.364083\pi\)
0.414137 + 0.910215i \(0.364083\pi\)
\(278\) −28.3537 −1.70054
\(279\) −17.7833 −1.06466
\(280\) 3.23423 0.193282
\(281\) −16.2375 −0.968650 −0.484325 0.874888i \(-0.660935\pi\)
−0.484325 + 0.874888i \(0.660935\pi\)
\(282\) 30.5599 1.81981
\(283\) −8.19036 −0.486867 −0.243433 0.969918i \(-0.578274\pi\)
−0.243433 + 0.969918i \(0.578274\pi\)
\(284\) −29.3919 −1.74409
\(285\) 7.98759 0.473144
\(286\) 24.7665 1.46447
\(287\) 6.25050 0.368955
\(288\) −31.4653 −1.85411
\(289\) 11.3338 0.666696
\(290\) 2.27045 0.133326
\(291\) 21.4534 1.25762
\(292\) 56.1431 3.28553
\(293\) 8.36765 0.488843 0.244422 0.969669i \(-0.421402\pi\)
0.244422 + 0.969669i \(0.421402\pi\)
\(294\) −38.3044 −2.23396
\(295\) 5.26049 0.306278
\(296\) 62.9741 3.66030
\(297\) 1.87271 0.108666
\(298\) 49.1470 2.84701
\(299\) 15.0644 0.871194
\(300\) 57.6923 3.33087
\(301\) 5.32152 0.306728
\(302\) 4.59733 0.264547
\(303\) −22.7509 −1.30701
\(304\) −69.5546 −3.98923
\(305\) −4.26679 −0.244316
\(306\) 45.5743 2.60531
\(307\) 9.47421 0.540722 0.270361 0.962759i \(-0.412857\pi\)
0.270361 + 0.962759i \(0.412857\pi\)
\(308\) 13.0376 0.742884
\(309\) 2.62317 0.149227
\(310\) 5.93393 0.337024
\(311\) −4.92648 −0.279355 −0.139678 0.990197i \(-0.544607\pi\)
−0.139678 + 0.990197i \(0.544607\pi\)
\(312\) 66.9489 3.79024
\(313\) 13.6944 0.774051 0.387025 0.922069i \(-0.373503\pi\)
0.387025 + 0.922069i \(0.373503\pi\)
\(314\) −11.2786 −0.636490
\(315\) −1.47633 −0.0831816
\(316\) −0.807835 −0.0454443
\(317\) 16.7011 0.938026 0.469013 0.883191i \(-0.344610\pi\)
0.469013 + 0.883191i \(0.344610\pi\)
\(318\) −67.7817 −3.80101
\(319\) 5.31527 0.297598
\(320\) 2.72170 0.152148
\(321\) −25.0759 −1.39960
\(322\) 11.2549 0.627212
\(323\) 40.1738 2.23533
\(324\) −38.3738 −2.13188
\(325\) −17.8556 −0.990453
\(326\) 10.5642 0.585099
\(327\) 7.16862 0.396426
\(328\) 42.3764 2.33984
\(329\) −4.97899 −0.274501
\(330\) −7.07842 −0.389654
\(331\) 2.46233 0.135342 0.0676710 0.997708i \(-0.478443\pi\)
0.0676710 + 0.997708i \(0.478443\pi\)
\(332\) 20.2678 1.11234
\(333\) −28.7458 −1.57526
\(334\) −56.2310 −3.07683
\(335\) −4.30569 −0.235245
\(336\) 24.5763 1.34075
\(337\) 0.572821 0.0312035 0.0156018 0.999878i \(-0.495034\pi\)
0.0156018 + 0.999878i \(0.495034\pi\)
\(338\) −1.85316 −0.100799
\(339\) −27.5022 −1.49371
\(340\) −10.7150 −0.581100
\(341\) 13.8917 0.752277
\(342\) 64.6185 3.49417
\(343\) 13.6836 0.738844
\(344\) 36.0782 1.94521
\(345\) −4.30549 −0.231800
\(346\) 42.3408 2.27625
\(347\) 0.813396 0.0436654 0.0218327 0.999762i \(-0.493050\pi\)
0.0218327 + 0.999762i \(0.493050\pi\)
\(348\) 24.7410 1.32626
\(349\) 19.5749 1.04782 0.523910 0.851774i \(-0.324473\pi\)
0.523910 + 0.851774i \(0.324473\pi\)
\(350\) −13.3404 −0.713072
\(351\) −2.69787 −0.144002
\(352\) 24.5797 1.31010
\(353\) −28.9414 −1.54040 −0.770198 0.637805i \(-0.779842\pi\)
−0.770198 + 0.637805i \(0.779842\pi\)
\(354\) 81.3563 4.32404
\(355\) −2.59990 −0.137989
\(356\) −23.1657 −1.22778
\(357\) −14.1949 −0.751276
\(358\) 12.6468 0.668404
\(359\) −28.5449 −1.50654 −0.753272 0.657709i \(-0.771525\pi\)
−0.753272 + 0.657709i \(0.771525\pi\)
\(360\) −10.0090 −0.527522
\(361\) 37.9614 1.99797
\(362\) 3.00217 0.157791
\(363\) 11.0179 0.578291
\(364\) −18.7822 −0.984455
\(365\) 4.96622 0.259944
\(366\) −65.9882 −3.44926
\(367\) 26.8132 1.39964 0.699819 0.714320i \(-0.253264\pi\)
0.699819 + 0.714320i \(0.253264\pi\)
\(368\) 37.4915 1.95438
\(369\) −19.3435 −1.00698
\(370\) 9.59190 0.498659
\(371\) 11.0434 0.573344
\(372\) 64.6618 3.35256
\(373\) −25.0671 −1.29793 −0.648963 0.760820i \(-0.724797\pi\)
−0.648963 + 0.760820i \(0.724797\pi\)
\(374\) −35.6011 −1.84089
\(375\) 10.3950 0.536794
\(376\) −33.7560 −1.74083
\(377\) −7.65729 −0.394371
\(378\) −2.01564 −0.103673
\(379\) −0.889645 −0.0456980 −0.0228490 0.999739i \(-0.507274\pi\)
−0.0228490 + 0.999739i \(0.507274\pi\)
\(380\) −15.1925 −0.779356
\(381\) 34.1270 1.74838
\(382\) 50.7297 2.59556
\(383\) −30.3780 −1.55224 −0.776122 0.630582i \(-0.782816\pi\)
−0.776122 + 0.630582i \(0.782816\pi\)
\(384\) −5.87466 −0.299790
\(385\) 1.15326 0.0587754
\(386\) 34.0076 1.73094
\(387\) −16.4686 −0.837147
\(388\) −40.8045 −2.07153
\(389\) −18.9050 −0.958524 −0.479262 0.877672i \(-0.659096\pi\)
−0.479262 + 0.877672i \(0.659096\pi\)
\(390\) 10.1973 0.516362
\(391\) −21.6546 −1.09512
\(392\) 42.3105 2.13700
\(393\) −6.10552 −0.307983
\(394\) −8.01101 −0.403589
\(395\) −0.0714583 −0.00359546
\(396\) −40.3476 −2.02754
\(397\) −23.0434 −1.15652 −0.578258 0.815854i \(-0.696267\pi\)
−0.578258 + 0.815854i \(0.696267\pi\)
\(398\) −24.4648 −1.22631
\(399\) −20.1266 −1.00759
\(400\) −44.4383 −2.22191
\(401\) −32.5008 −1.62301 −0.811506 0.584343i \(-0.801352\pi\)
−0.811506 + 0.584343i \(0.801352\pi\)
\(402\) −66.5899 −3.32120
\(403\) −20.0127 −0.996903
\(404\) 43.2724 2.15288
\(405\) −3.39441 −0.168670
\(406\) −5.72094 −0.283925
\(407\) 22.4552 1.11306
\(408\) −96.2371 −4.76445
\(409\) −8.06276 −0.398678 −0.199339 0.979931i \(-0.563879\pi\)
−0.199339 + 0.979931i \(0.563879\pi\)
\(410\) 6.45456 0.318768
\(411\) −10.8924 −0.537285
\(412\) −4.98928 −0.245804
\(413\) −13.2550 −0.652238
\(414\) −34.8308 −1.71184
\(415\) 1.79282 0.0880061
\(416\) −35.4100 −1.73612
\(417\) −27.3303 −1.33837
\(418\) −50.4778 −2.46895
\(419\) 9.49540 0.463880 0.231940 0.972730i \(-0.425493\pi\)
0.231940 + 0.972730i \(0.425493\pi\)
\(420\) 5.36808 0.261935
\(421\) 7.72704 0.376593 0.188296 0.982112i \(-0.439703\pi\)
0.188296 + 0.982112i \(0.439703\pi\)
\(422\) 34.3540 1.67232
\(423\) 15.4086 0.749191
\(424\) 74.8707 3.63604
\(425\) 25.6670 1.24503
\(426\) −40.2089 −1.94813
\(427\) 10.7512 0.520286
\(428\) 47.6946 2.30540
\(429\) 23.8726 1.15258
\(430\) 5.49526 0.265005
\(431\) 24.2334 1.16728 0.583641 0.812012i \(-0.301628\pi\)
0.583641 + 0.812012i \(0.301628\pi\)
\(432\) −6.71433 −0.323043
\(433\) −18.0024 −0.865141 −0.432571 0.901600i \(-0.642393\pi\)
−0.432571 + 0.901600i \(0.642393\pi\)
\(434\) −14.9519 −0.717716
\(435\) 2.18850 0.104931
\(436\) −13.6348 −0.652987
\(437\) −30.7034 −1.46875
\(438\) 76.8054 3.66990
\(439\) −34.0158 −1.62349 −0.811743 0.584015i \(-0.801481\pi\)
−0.811743 + 0.584015i \(0.801481\pi\)
\(440\) 7.81871 0.372742
\(441\) −19.3134 −0.919688
\(442\) 51.2877 2.43951
\(443\) 3.31827 0.157656 0.0788280 0.996888i \(-0.474882\pi\)
0.0788280 + 0.996888i \(0.474882\pi\)
\(444\) 104.523 4.96042
\(445\) −2.04916 −0.0971396
\(446\) −21.6755 −1.02637
\(447\) 47.3731 2.24067
\(448\) −6.85796 −0.324008
\(449\) 23.7116 1.11902 0.559511 0.828823i \(-0.310989\pi\)
0.559511 + 0.828823i \(0.310989\pi\)
\(450\) 41.2847 1.94618
\(451\) 15.1105 0.711526
\(452\) 52.3093 2.46042
\(453\) 4.43140 0.208205
\(454\) −27.3125 −1.28184
\(455\) −1.66141 −0.0778880
\(456\) −136.452 −6.38996
\(457\) 18.3282 0.857357 0.428678 0.903457i \(-0.358979\pi\)
0.428678 + 0.903457i \(0.358979\pi\)
\(458\) 63.3483 2.96007
\(459\) 3.87811 0.181015
\(460\) 8.18907 0.381818
\(461\) −36.6549 −1.70719 −0.853595 0.520938i \(-0.825582\pi\)
−0.853595 + 0.520938i \(0.825582\pi\)
\(462\) 17.8357 0.829794
\(463\) 32.5430 1.51240 0.756202 0.654339i \(-0.227053\pi\)
0.756202 + 0.654339i \(0.227053\pi\)
\(464\) −19.0571 −0.884704
\(465\) 5.71976 0.265247
\(466\) 65.0610 3.01389
\(467\) 3.23763 0.149820 0.0749098 0.997190i \(-0.476133\pi\)
0.0749098 + 0.997190i \(0.476133\pi\)
\(468\) 58.1256 2.68686
\(469\) 10.8492 0.500970
\(470\) −5.14154 −0.237162
\(471\) −10.8715 −0.500934
\(472\) −89.8650 −4.13637
\(473\) 12.8647 0.591521
\(474\) −1.10514 −0.0507608
\(475\) 36.3925 1.66980
\(476\) 26.9989 1.23749
\(477\) −34.1762 −1.56482
\(478\) −1.58936 −0.0726955
\(479\) 29.1690 1.33277 0.666383 0.745610i \(-0.267842\pi\)
0.666383 + 0.745610i \(0.267842\pi\)
\(480\) 10.1204 0.461931
\(481\) −32.3495 −1.47501
\(482\) 2.08723 0.0950708
\(483\) 10.8487 0.493633
\(484\) −20.9561 −0.952552
\(485\) −3.60942 −0.163895
\(486\) −58.1836 −2.63926
\(487\) −5.90908 −0.267766 −0.133883 0.990997i \(-0.542745\pi\)
−0.133883 + 0.990997i \(0.542745\pi\)
\(488\) 72.8896 3.29956
\(489\) 10.1829 0.460488
\(490\) 6.44452 0.291134
\(491\) 3.33601 0.150552 0.0752759 0.997163i \(-0.476016\pi\)
0.0752759 + 0.997163i \(0.476016\pi\)
\(492\) 70.3351 3.17095
\(493\) 11.0071 0.495736
\(494\) 72.7195 3.27180
\(495\) −3.56901 −0.160415
\(496\) −49.8066 −2.23638
\(497\) 6.55107 0.293856
\(498\) 27.7269 1.24247
\(499\) 3.78987 0.169658 0.0848289 0.996396i \(-0.472966\pi\)
0.0848289 + 0.996396i \(0.472966\pi\)
\(500\) −19.7713 −0.884199
\(501\) −54.2015 −2.42154
\(502\) 10.7730 0.480822
\(503\) 20.3327 0.906589 0.453295 0.891361i \(-0.350249\pi\)
0.453295 + 0.891361i \(0.350249\pi\)
\(504\) 25.2201 1.12339
\(505\) 3.82773 0.170332
\(506\) 27.2087 1.20957
\(507\) −1.78627 −0.0793312
\(508\) −64.9098 −2.87991
\(509\) 32.4268 1.43729 0.718647 0.695375i \(-0.244762\pi\)
0.718647 + 0.695375i \(0.244762\pi\)
\(510\) −14.6584 −0.649083
\(511\) −12.5136 −0.553568
\(512\) 44.7391 1.97721
\(513\) 5.49866 0.242772
\(514\) 34.4429 1.51921
\(515\) −0.441334 −0.0194475
\(516\) 59.8816 2.63614
\(517\) −12.0367 −0.529372
\(518\) −24.1691 −1.06193
\(519\) 40.8126 1.79147
\(520\) −11.2638 −0.493951
\(521\) −33.7507 −1.47865 −0.739323 0.673351i \(-0.764855\pi\)
−0.739323 + 0.673351i \(0.764855\pi\)
\(522\) 17.7047 0.774913
\(523\) −0.964432 −0.0421717 −0.0210858 0.999778i \(-0.506712\pi\)
−0.0210858 + 0.999778i \(0.506712\pi\)
\(524\) 11.6127 0.507305
\(525\) −12.8589 −0.561207
\(526\) 59.6908 2.60264
\(527\) 28.7676 1.25314
\(528\) 59.4129 2.58562
\(529\) −6.45015 −0.280441
\(530\) 11.4039 0.495355
\(531\) 41.0206 1.78014
\(532\) 38.2810 1.65969
\(533\) −21.7685 −0.942900
\(534\) −31.6914 −1.37142
\(535\) 4.21889 0.182399
\(536\) 73.5542 3.17706
\(537\) 12.1903 0.526052
\(538\) 0.729484 0.0314503
\(539\) 15.0870 0.649844
\(540\) −1.46658 −0.0631114
\(541\) 24.4964 1.05318 0.526591 0.850119i \(-0.323470\pi\)
0.526591 + 0.850119i \(0.323470\pi\)
\(542\) 83.6874 3.59468
\(543\) 2.89382 0.124186
\(544\) 50.9008 2.18236
\(545\) −1.20608 −0.0516629
\(546\) −25.6946 −1.09963
\(547\) 44.4606 1.90100 0.950500 0.310725i \(-0.100572\pi\)
0.950500 + 0.310725i \(0.100572\pi\)
\(548\) 20.7175 0.885008
\(549\) −33.2719 −1.42001
\(550\) −32.2502 −1.37515
\(551\) 15.6067 0.664869
\(552\) 73.5507 3.13053
\(553\) 0.180056 0.00765676
\(554\) −35.8691 −1.52393
\(555\) 9.24570 0.392458
\(556\) 51.9825 2.20455
\(557\) 13.4324 0.569151 0.284575 0.958654i \(-0.408147\pi\)
0.284575 + 0.958654i \(0.408147\pi\)
\(558\) 46.2720 1.95885
\(559\) −18.5332 −0.783872
\(560\) −4.13483 −0.174729
\(561\) −34.3161 −1.44883
\(562\) 42.2500 1.78221
\(563\) −6.80148 −0.286648 −0.143324 0.989676i \(-0.545779\pi\)
−0.143324 + 0.989676i \(0.545779\pi\)
\(564\) −56.0272 −2.35917
\(565\) 4.62710 0.194664
\(566\) 21.3113 0.895781
\(567\) 8.55302 0.359193
\(568\) 44.4142 1.86358
\(569\) 38.6875 1.62187 0.810933 0.585139i \(-0.198960\pi\)
0.810933 + 0.585139i \(0.198960\pi\)
\(570\) −20.7837 −0.870533
\(571\) 15.5090 0.649030 0.324515 0.945881i \(-0.394799\pi\)
0.324515 + 0.945881i \(0.394799\pi\)
\(572\) −45.4058 −1.89851
\(573\) 48.8987 2.04277
\(574\) −16.2638 −0.678837
\(575\) −19.6164 −0.818059
\(576\) 21.2235 0.884311
\(577\) 16.8797 0.702711 0.351356 0.936242i \(-0.385721\pi\)
0.351356 + 0.936242i \(0.385721\pi\)
\(578\) −29.4906 −1.22665
\(579\) 32.7801 1.36230
\(580\) −4.16255 −0.172840
\(581\) −4.51743 −0.187415
\(582\) −55.8216 −2.31388
\(583\) 26.6973 1.10569
\(584\) −84.8380 −3.51062
\(585\) 5.14159 0.212579
\(586\) −21.7726 −0.899418
\(587\) −1.92631 −0.0795073 −0.0397537 0.999210i \(-0.512657\pi\)
−0.0397537 + 0.999210i \(0.512657\pi\)
\(588\) 70.2257 2.89606
\(589\) 40.7889 1.68068
\(590\) −13.6878 −0.563517
\(591\) −7.72187 −0.317635
\(592\) −80.5099 −3.30894
\(593\) 38.1126 1.56510 0.782549 0.622589i \(-0.213919\pi\)
0.782549 + 0.622589i \(0.213919\pi\)
\(594\) −4.87279 −0.199933
\(595\) 2.38822 0.0979077
\(596\) −90.1040 −3.69080
\(597\) −23.5818 −0.965140
\(598\) −39.1974 −1.60290
\(599\) 22.1264 0.904061 0.452030 0.892002i \(-0.350700\pi\)
0.452030 + 0.892002i \(0.350700\pi\)
\(600\) −87.1790 −3.55907
\(601\) 21.1754 0.863761 0.431881 0.901931i \(-0.357850\pi\)
0.431881 + 0.901931i \(0.357850\pi\)
\(602\) −13.8466 −0.564345
\(603\) −33.5753 −1.36729
\(604\) −8.42855 −0.342953
\(605\) −1.85371 −0.0753639
\(606\) 59.1979 2.40475
\(607\) −25.5581 −1.03737 −0.518685 0.854965i \(-0.673578\pi\)
−0.518685 + 0.854965i \(0.673578\pi\)
\(608\) 72.1709 2.92692
\(609\) −5.51445 −0.223457
\(610\) 11.1022 0.449514
\(611\) 17.3403 0.701513
\(612\) −83.5539 −3.37747
\(613\) 24.8431 1.00340 0.501701 0.865041i \(-0.332708\pi\)
0.501701 + 0.865041i \(0.332708\pi\)
\(614\) −24.6519 −0.994868
\(615\) 6.22159 0.250879
\(616\) −19.7011 −0.793779
\(617\) 7.68846 0.309526 0.154763 0.987952i \(-0.450539\pi\)
0.154763 + 0.987952i \(0.450539\pi\)
\(618\) −6.82547 −0.274561
\(619\) 8.41073 0.338056 0.169028 0.985611i \(-0.445937\pi\)
0.169028 + 0.985611i \(0.445937\pi\)
\(620\) −10.8790 −0.436912
\(621\) −2.96390 −0.118937
\(622\) 12.8187 0.513983
\(623\) 5.16334 0.206865
\(624\) −85.5916 −3.42641
\(625\) 22.3608 0.894432
\(626\) −35.6327 −1.42417
\(627\) −48.6559 −1.94313
\(628\) 20.6777 0.825132
\(629\) 46.5015 1.85413
\(630\) 3.84140 0.153045
\(631\) 10.2435 0.407787 0.203893 0.978993i \(-0.434640\pi\)
0.203893 + 0.978993i \(0.434640\pi\)
\(632\) 1.22072 0.0485577
\(633\) 33.1140 1.31616
\(634\) −43.4562 −1.72586
\(635\) −5.74169 −0.227852
\(636\) 124.268 4.92755
\(637\) −21.7347 −0.861160
\(638\) −13.8303 −0.547547
\(639\) −20.2737 −0.802016
\(640\) 0.988381 0.0390692
\(641\) 48.7454 1.92533 0.962665 0.270697i \(-0.0872541\pi\)
0.962665 + 0.270697i \(0.0872541\pi\)
\(642\) 65.2475 2.57511
\(643\) −28.6616 −1.13030 −0.565151 0.824988i \(-0.691182\pi\)
−0.565151 + 0.824988i \(0.691182\pi\)
\(644\) −20.6343 −0.813105
\(645\) 5.29692 0.208566
\(646\) −104.532 −4.11276
\(647\) −5.39033 −0.211916 −0.105958 0.994371i \(-0.533791\pi\)
−0.105958 + 0.994371i \(0.533791\pi\)
\(648\) 57.9867 2.27793
\(649\) −32.0439 −1.25783
\(650\) 46.4603 1.82232
\(651\) −14.4123 −0.564862
\(652\) −19.3680 −0.758510
\(653\) −38.6182 −1.51125 −0.755623 0.655007i \(-0.772666\pi\)
−0.755623 + 0.655007i \(0.772666\pi\)
\(654\) −18.6527 −0.729380
\(655\) 1.02722 0.0401369
\(656\) −54.1765 −2.11524
\(657\) 38.7260 1.51084
\(658\) 12.9553 0.505051
\(659\) −18.5992 −0.724522 −0.362261 0.932077i \(-0.617995\pi\)
−0.362261 + 0.932077i \(0.617995\pi\)
\(660\) 12.9773 0.505140
\(661\) −47.1983 −1.83580 −0.917901 0.396809i \(-0.870117\pi\)
−0.917901 + 0.396809i \(0.870117\pi\)
\(662\) −6.40698 −0.249014
\(663\) 49.4366 1.91996
\(664\) −30.6268 −1.18855
\(665\) 3.38620 0.131311
\(666\) 74.7964 2.89830
\(667\) −8.41237 −0.325728
\(668\) 103.092 3.98873
\(669\) −20.8932 −0.807777
\(670\) 11.2034 0.432825
\(671\) 25.9909 1.00337
\(672\) −25.5008 −0.983713
\(673\) 34.1681 1.31708 0.658542 0.752544i \(-0.271174\pi\)
0.658542 + 0.752544i \(0.271174\pi\)
\(674\) −1.49048 −0.0574111
\(675\) 3.51309 0.135219
\(676\) 3.39750 0.130673
\(677\) 15.0137 0.577023 0.288511 0.957476i \(-0.406840\pi\)
0.288511 + 0.957476i \(0.406840\pi\)
\(678\) 71.5606 2.74827
\(679\) 9.09478 0.349026
\(680\) 16.1914 0.620912
\(681\) −26.3267 −1.00884
\(682\) −36.1461 −1.38411
\(683\) 16.0899 0.615663 0.307831 0.951441i \(-0.400397\pi\)
0.307831 + 0.951441i \(0.400397\pi\)
\(684\) −118.469 −4.52977
\(685\) 1.83260 0.0700200
\(686\) −35.6046 −1.35939
\(687\) 61.0619 2.32966
\(688\) −46.1246 −1.75848
\(689\) −38.4607 −1.46524
\(690\) 11.2029 0.426486
\(691\) 8.37173 0.318476 0.159238 0.987240i \(-0.449096\pi\)
0.159238 + 0.987240i \(0.449096\pi\)
\(692\) −77.6258 −2.95089
\(693\) 8.99295 0.341614
\(694\) −2.11646 −0.0803395
\(695\) 4.59819 0.174419
\(696\) −37.3862 −1.41712
\(697\) 31.2916 1.18526
\(698\) −50.9338 −1.92787
\(699\) 62.7127 2.37201
\(700\) 24.4576 0.924412
\(701\) 51.2471 1.93557 0.967787 0.251769i \(-0.0810122\pi\)
0.967787 + 0.251769i \(0.0810122\pi\)
\(702\) 7.01985 0.264947
\(703\) 65.9332 2.48672
\(704\) −16.5790 −0.624846
\(705\) −4.95597 −0.186653
\(706\) 75.3055 2.83416
\(707\) −9.64486 −0.362732
\(708\) −149.155 −5.60560
\(709\) −41.5781 −1.56150 −0.780749 0.624845i \(-0.785162\pi\)
−0.780749 + 0.624845i \(0.785162\pi\)
\(710\) 6.76495 0.253884
\(711\) −0.557223 −0.0208975
\(712\) 35.0058 1.31190
\(713\) −21.9861 −0.823387
\(714\) 36.9352 1.38226
\(715\) −4.01644 −0.150206
\(716\) −23.1861 −0.866505
\(717\) −1.53199 −0.0572133
\(718\) 74.2738 2.77187
\(719\) −19.1472 −0.714070 −0.357035 0.934091i \(-0.616212\pi\)
−0.357035 + 0.934091i \(0.616212\pi\)
\(720\) 12.7961 0.476884
\(721\) 1.11205 0.0414147
\(722\) −98.7753 −3.67604
\(723\) 2.01190 0.0748233
\(724\) −5.50406 −0.204557
\(725\) 9.97111 0.370318
\(726\) −28.6686 −1.06399
\(727\) −40.1138 −1.48774 −0.743869 0.668326i \(-0.767011\pi\)
−0.743869 + 0.668326i \(0.767011\pi\)
\(728\) 28.3818 1.05190
\(729\) −31.9511 −1.18337
\(730\) −12.9221 −0.478268
\(731\) 26.6410 0.985352
\(732\) 120.980 4.47155
\(733\) −40.5800 −1.49886 −0.749429 0.662085i \(-0.769672\pi\)
−0.749429 + 0.662085i \(0.769672\pi\)
\(734\) −69.7679 −2.57518
\(735\) 6.21192 0.229130
\(736\) −38.9018 −1.43394
\(737\) 26.2279 0.966116
\(738\) 50.3318 1.85274
\(739\) −11.1808 −0.411293 −0.205647 0.978626i \(-0.565930\pi\)
−0.205647 + 0.978626i \(0.565930\pi\)
\(740\) −17.5854 −0.646451
\(741\) 70.0948 2.57500
\(742\) −28.7349 −1.05489
\(743\) 46.1368 1.69260 0.846298 0.532711i \(-0.178827\pi\)
0.846298 + 0.532711i \(0.178827\pi\)
\(744\) −97.7106 −3.58224
\(745\) −7.97028 −0.292009
\(746\) 65.2246 2.38804
\(747\) 13.9802 0.511508
\(748\) 65.2695 2.38649
\(749\) −10.6305 −0.388430
\(750\) −27.0477 −0.987642
\(751\) 36.1428 1.31887 0.659434 0.751762i \(-0.270796\pi\)
0.659434 + 0.751762i \(0.270796\pi\)
\(752\) 43.1557 1.57373
\(753\) 10.3842 0.378420
\(754\) 19.9243 0.725599
\(755\) −0.745560 −0.0271337
\(756\) 3.69539 0.134400
\(757\) −10.0781 −0.366294 −0.183147 0.983086i \(-0.558628\pi\)
−0.183147 + 0.983086i \(0.558628\pi\)
\(758\) 2.31485 0.0840793
\(759\) 26.2266 0.951966
\(760\) 22.9574 0.832751
\(761\) 4.37255 0.158505 0.0792523 0.996855i \(-0.474747\pi\)
0.0792523 + 0.996855i \(0.474747\pi\)
\(762\) −88.7984 −3.21683
\(763\) 3.03901 0.110020
\(764\) −93.0057 −3.36483
\(765\) −7.39088 −0.267218
\(766\) 79.0436 2.85596
\(767\) 46.1632 1.66686
\(768\) 47.6399 1.71906
\(769\) 24.0729 0.868091 0.434045 0.900891i \(-0.357086\pi\)
0.434045 + 0.900891i \(0.357086\pi\)
\(770\) −3.00077 −0.108140
\(771\) 33.1998 1.19566
\(772\) −62.3480 −2.24395
\(773\) −16.2792 −0.585523 −0.292761 0.956186i \(-0.594574\pi\)
−0.292761 + 0.956186i \(0.594574\pi\)
\(774\) 42.8513 1.54026
\(775\) 26.0599 0.936101
\(776\) 61.6597 2.21346
\(777\) −23.2967 −0.835765
\(778\) 49.1909 1.76358
\(779\) 44.3676 1.58963
\(780\) −18.6953 −0.669401
\(781\) 15.8372 0.566698
\(782\) 56.3451 2.01490
\(783\) 1.50657 0.0538403
\(784\) −54.0923 −1.93187
\(785\) 1.82908 0.0652827
\(786\) 15.8866 0.566655
\(787\) −8.51539 −0.303541 −0.151770 0.988416i \(-0.548497\pi\)
−0.151770 + 0.988416i \(0.548497\pi\)
\(788\) 14.6870 0.523204
\(789\) 57.5363 2.04835
\(790\) 0.185934 0.00661524
\(791\) −11.6591 −0.414549
\(792\) 60.9693 2.16645
\(793\) −37.4430 −1.32964
\(794\) 59.9590 2.12786
\(795\) 10.9923 0.389858
\(796\) 44.8528 1.58976
\(797\) −13.1161 −0.464596 −0.232298 0.972645i \(-0.574624\pi\)
−0.232298 + 0.972645i \(0.574624\pi\)
\(798\) 52.3694 1.85386
\(799\) −24.9262 −0.881824
\(800\) 46.1099 1.63023
\(801\) −15.9791 −0.564594
\(802\) 84.5670 2.98617
\(803\) −30.2514 −1.06755
\(804\) 122.083 4.30554
\(805\) −1.82524 −0.0643312
\(806\) 52.0730 1.83419
\(807\) 0.703155 0.0247522
\(808\) −65.3891 −2.30038
\(809\) −53.5738 −1.88356 −0.941778 0.336236i \(-0.890846\pi\)
−0.941778 + 0.336236i \(0.890846\pi\)
\(810\) 8.83225 0.310334
\(811\) −41.1700 −1.44567 −0.722837 0.691019i \(-0.757162\pi\)
−0.722837 + 0.691019i \(0.757162\pi\)
\(812\) 10.4885 0.368075
\(813\) 80.6669 2.82911
\(814\) −58.4284 −2.04792
\(815\) −1.71323 −0.0600117
\(816\) 123.035 4.30710
\(817\) 37.7735 1.32153
\(818\) 20.9793 0.733523
\(819\) −12.9554 −0.452700
\(820\) −11.8335 −0.413244
\(821\) 23.5848 0.823116 0.411558 0.911384i \(-0.364985\pi\)
0.411558 + 0.911384i \(0.364985\pi\)
\(822\) 28.3421 0.988545
\(823\) 19.0603 0.664400 0.332200 0.943209i \(-0.392209\pi\)
0.332200 + 0.943209i \(0.392209\pi\)
\(824\) 7.53931 0.262644
\(825\) −31.0862 −1.08228
\(826\) 34.4896 1.20005
\(827\) −4.98841 −0.173464 −0.0867320 0.996232i \(-0.527642\pi\)
−0.0867320 + 0.996232i \(0.527642\pi\)
\(828\) 63.8574 2.21920
\(829\) −1.17639 −0.0408578 −0.0204289 0.999791i \(-0.506503\pi\)
−0.0204289 + 0.999791i \(0.506503\pi\)
\(830\) −4.66491 −0.161922
\(831\) −34.5745 −1.19938
\(832\) 23.8842 0.828034
\(833\) 31.2430 1.08250
\(834\) 71.1135 2.46246
\(835\) 9.11912 0.315580
\(836\) 92.5439 3.20070
\(837\) 3.93748 0.136099
\(838\) −24.7070 −0.853489
\(839\) −15.9012 −0.548972 −0.274486 0.961591i \(-0.588508\pi\)
−0.274486 + 0.961591i \(0.588508\pi\)
\(840\) −8.11171 −0.279881
\(841\) −24.7239 −0.852550
\(842\) −20.1057 −0.692890
\(843\) 40.7251 1.40265
\(844\) −62.9831 −2.16797
\(845\) 0.300531 0.0103386
\(846\) −40.0931 −1.37843
\(847\) 4.67085 0.160492
\(848\) −95.7192 −3.28701
\(849\) 20.5421 0.705004
\(850\) −66.7854 −2.29072
\(851\) −35.5395 −1.21828
\(852\) 73.7174 2.52552
\(853\) 16.5186 0.565587 0.282793 0.959181i \(-0.408739\pi\)
0.282793 + 0.959181i \(0.408739\pi\)
\(854\) −27.9746 −0.957269
\(855\) −10.4793 −0.358386
\(856\) −72.0714 −2.46335
\(857\) −20.9190 −0.714580 −0.357290 0.933994i \(-0.616299\pi\)
−0.357290 + 0.933994i \(0.616299\pi\)
\(858\) −62.1164 −2.12062
\(859\) 19.8204 0.676264 0.338132 0.941099i \(-0.390205\pi\)
0.338132 + 0.941099i \(0.390205\pi\)
\(860\) −10.0748 −0.343547
\(861\) −15.6768 −0.534263
\(862\) −63.0552 −2.14767
\(863\) 15.3542 0.522662 0.261331 0.965249i \(-0.415839\pi\)
0.261331 + 0.965249i \(0.415839\pi\)
\(864\) 6.96690 0.237019
\(865\) −6.86651 −0.233468
\(866\) 46.8423 1.59176
\(867\) −28.4262 −0.965404
\(868\) 27.4122 0.930432
\(869\) 0.435283 0.0147660
\(870\) −5.69448 −0.193061
\(871\) −37.7844 −1.28028
\(872\) 20.6035 0.697723
\(873\) −28.1458 −0.952591
\(874\) 79.8903 2.70233
\(875\) 4.40676 0.148976
\(876\) −140.812 −4.75759
\(877\) −0.156434 −0.00528242 −0.00264121 0.999997i \(-0.500841\pi\)
−0.00264121 + 0.999997i \(0.500841\pi\)
\(878\) 88.5090 2.98703
\(879\) −20.9868 −0.707866
\(880\) −9.99592 −0.336962
\(881\) −13.3979 −0.451388 −0.225694 0.974198i \(-0.572465\pi\)
−0.225694 + 0.974198i \(0.572465\pi\)
\(882\) 50.2535 1.69212
\(883\) −11.0318 −0.371250 −0.185625 0.982621i \(-0.559431\pi\)
−0.185625 + 0.982621i \(0.559431\pi\)
\(884\) −94.0287 −3.16253
\(885\) −13.1938 −0.443503
\(886\) −8.63414 −0.290070
\(887\) −36.8627 −1.23773 −0.618864 0.785498i \(-0.712407\pi\)
−0.618864 + 0.785498i \(0.712407\pi\)
\(888\) −157.944 −5.30027
\(889\) 14.4675 0.485226
\(890\) 5.33191 0.178726
\(891\) 20.6768 0.692700
\(892\) 39.7390 1.33056
\(893\) −35.3421 −1.18268
\(894\) −123.265 −4.12259
\(895\) −2.05096 −0.0685561
\(896\) −2.49046 −0.0832004
\(897\) −37.7827 −1.26153
\(898\) −61.6976 −2.05888
\(899\) 11.1757 0.372729
\(900\) −75.6895 −2.52298
\(901\) 55.2861 1.84185
\(902\) −39.3175 −1.30913
\(903\) −13.3468 −0.444155
\(904\) −79.0448 −2.62899
\(905\) −0.486870 −0.0161841
\(906\) −11.5305 −0.383075
\(907\) −21.4514 −0.712283 −0.356141 0.934432i \(-0.615908\pi\)
−0.356141 + 0.934432i \(0.615908\pi\)
\(908\) 50.0735 1.66175
\(909\) 29.8481 0.990000
\(910\) 4.32298 0.143305
\(911\) −21.3522 −0.707430 −0.353715 0.935353i \(-0.615082\pi\)
−0.353715 + 0.935353i \(0.615082\pi\)
\(912\) 174.449 5.77657
\(913\) −10.9208 −0.361427
\(914\) −47.6899 −1.57744
\(915\) 10.7015 0.353780
\(916\) −116.140 −3.83738
\(917\) −2.58833 −0.0854742
\(918\) −10.0908 −0.333047
\(919\) 26.7724 0.883140 0.441570 0.897227i \(-0.354422\pi\)
0.441570 + 0.897227i \(0.354422\pi\)
\(920\) −12.3745 −0.407976
\(921\) −23.7621 −0.782988
\(922\) 95.3760 3.14104
\(923\) −22.8154 −0.750977
\(924\) −32.6993 −1.07573
\(925\) 42.1246 1.38505
\(926\) −84.6769 −2.78266
\(927\) −3.44147 −0.113033
\(928\) 19.7740 0.649112
\(929\) −10.9798 −0.360236 −0.180118 0.983645i \(-0.557648\pi\)
−0.180118 + 0.983645i \(0.557648\pi\)
\(930\) −14.8828 −0.488026
\(931\) 44.2986 1.45183
\(932\) −119.280 −3.90715
\(933\) 12.3560 0.404518
\(934\) −8.42430 −0.275652
\(935\) 5.77351 0.188814
\(936\) −87.8338 −2.87094
\(937\) 49.0691 1.60302 0.801509 0.597983i \(-0.204031\pi\)
0.801509 + 0.597983i \(0.204031\pi\)
\(938\) −28.2296 −0.921730
\(939\) −34.3466 −1.12086
\(940\) 9.42628 0.307451
\(941\) −16.4162 −0.535153 −0.267576 0.963537i \(-0.586223\pi\)
−0.267576 + 0.963537i \(0.586223\pi\)
\(942\) 28.2877 0.921664
\(943\) −23.9151 −0.778784
\(944\) 114.889 3.73931
\(945\) 0.326881 0.0106334
\(946\) −33.4740 −1.08833
\(947\) 37.3421 1.21345 0.606727 0.794910i \(-0.292482\pi\)
0.606727 + 0.794910i \(0.292482\pi\)
\(948\) 2.02612 0.0658053
\(949\) 43.5809 1.41470
\(950\) −94.6932 −3.07225
\(951\) −41.8877 −1.35830
\(952\) −40.7981 −1.32227
\(953\) 22.6614 0.734074 0.367037 0.930206i \(-0.380372\pi\)
0.367037 + 0.930206i \(0.380372\pi\)
\(954\) 88.9264 2.87910
\(955\) −8.22696 −0.266218
\(956\) 2.91386 0.0942410
\(957\) −13.3311 −0.430934
\(958\) −75.8977 −2.45214
\(959\) −4.61766 −0.149112
\(960\) −6.82625 −0.220316
\(961\) −1.79190 −0.0578033
\(962\) 84.1733 2.71386
\(963\) 32.8984 1.06014
\(964\) −3.82664 −0.123248
\(965\) −5.51509 −0.177537
\(966\) −28.2283 −0.908231
\(967\) −43.1014 −1.38605 −0.693024 0.720914i \(-0.743722\pi\)
−0.693024 + 0.720914i \(0.743722\pi\)
\(968\) 31.6669 1.01781
\(969\) −100.759 −3.23685
\(970\) 9.39170 0.301549
\(971\) −56.4626 −1.81197 −0.905986 0.423308i \(-0.860869\pi\)
−0.905986 + 0.423308i \(0.860869\pi\)
\(972\) 106.671 3.42148
\(973\) −11.5862 −0.371437
\(974\) 15.3754 0.492660
\(975\) 44.7834 1.43422
\(976\) −93.1865 −2.98283
\(977\) −43.3163 −1.38581 −0.692906 0.721028i \(-0.743670\pi\)
−0.692906 + 0.721028i \(0.743670\pi\)
\(978\) −26.4960 −0.847248
\(979\) 12.4823 0.398937
\(980\) −11.8151 −0.377420
\(981\) −9.40489 −0.300275
\(982\) −8.68028 −0.276999
\(983\) −51.5548 −1.64434 −0.822171 0.569241i \(-0.807237\pi\)
−0.822171 + 0.569241i \(0.807237\pi\)
\(984\) −106.283 −3.38819
\(985\) 1.29916 0.0413948
\(986\) −28.6405 −0.912100
\(987\) 12.4877 0.397489
\(988\) −133.321 −4.24150
\(989\) −20.3608 −0.647435
\(990\) 9.28654 0.295146
\(991\) −29.5822 −0.939709 −0.469855 0.882744i \(-0.655694\pi\)
−0.469855 + 0.882744i \(0.655694\pi\)
\(992\) 51.6802 1.64085
\(993\) −6.17573 −0.195981
\(994\) −17.0459 −0.540662
\(995\) 3.96752 0.125779
\(996\) −50.8334 −1.61072
\(997\) −27.1639 −0.860289 −0.430144 0.902760i \(-0.641537\pi\)
−0.430144 + 0.902760i \(0.641537\pi\)
\(998\) −9.86123 −0.312152
\(999\) 6.36475 0.201372
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 6037.2.a.b.1.7 259
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6037.2.a.b.1.7 259 1.1 even 1 trivial