Properties

Label 177.4.a.a.1.4
Level $177$
Weight $4$
Character 177.1
Self dual yes
Analytic conductor $10.443$
Analytic rank $1$
Dimension $7$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(10.4433380710\)
Analytic rank: \(1\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
Defining polynomial: \(x^{7} - x^{6} - 34 x^{5} + 25 x^{4} + 315 x^{3} - 146 x^{2} - 736 x + 512\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(0.775001\) of defining polynomial
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.77500 q^{2} +3.00000 q^{3} -4.84937 q^{4} +6.23028 q^{5} -5.32500 q^{6} -18.0779 q^{7} +22.8076 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q-1.77500 q^{2} +3.00000 q^{3} -4.84937 q^{4} +6.23028 q^{5} -5.32500 q^{6} -18.0779 q^{7} +22.8076 q^{8} +9.00000 q^{9} -11.0588 q^{10} +13.3400 q^{11} -14.5481 q^{12} -66.3734 q^{13} +32.0883 q^{14} +18.6908 q^{15} -1.68865 q^{16} -97.6720 q^{17} -15.9750 q^{18} +109.769 q^{19} -30.2129 q^{20} -54.2336 q^{21} -23.6785 q^{22} -147.736 q^{23} +68.4229 q^{24} -86.1836 q^{25} +117.813 q^{26} +27.0000 q^{27} +87.6663 q^{28} -173.639 q^{29} -33.1763 q^{30} +148.613 q^{31} -179.464 q^{32} +40.0199 q^{33} +173.368 q^{34} -112.630 q^{35} -43.6443 q^{36} -446.332 q^{37} -194.840 q^{38} -199.120 q^{39} +142.098 q^{40} +182.883 q^{41} +96.2648 q^{42} -223.613 q^{43} -64.6904 q^{44} +56.0725 q^{45} +262.231 q^{46} -529.113 q^{47} -5.06595 q^{48} -16.1904 q^{49} +152.976 q^{50} -293.016 q^{51} +321.869 q^{52} +398.029 q^{53} -47.9250 q^{54} +83.1117 q^{55} -412.314 q^{56} +329.306 q^{57} +308.210 q^{58} -59.0000 q^{59} -90.6388 q^{60} +788.427 q^{61} -263.789 q^{62} -162.701 q^{63} +332.058 q^{64} -413.525 q^{65} -71.0354 q^{66} +288.375 q^{67} +473.648 q^{68} -443.207 q^{69} +199.919 q^{70} -139.803 q^{71} +205.269 q^{72} +549.077 q^{73} +792.240 q^{74} -258.551 q^{75} -532.310 q^{76} -241.158 q^{77} +353.439 q^{78} -190.617 q^{79} -10.5208 q^{80} +81.0000 q^{81} -324.617 q^{82} +410.618 q^{83} +262.999 q^{84} -608.524 q^{85} +396.914 q^{86} -520.918 q^{87} +304.253 q^{88} +1291.81 q^{89} -99.5288 q^{90} +1199.89 q^{91} +716.425 q^{92} +445.840 q^{93} +939.176 q^{94} +683.891 q^{95} -538.392 q^{96} +1488.11 q^{97} +28.7380 q^{98} +120.060 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q - 8q^{2} + 21q^{3} + 22q^{4} - 28q^{5} - 24q^{6} - 59q^{7} - 117q^{8} + 63q^{9} + O(q^{10}) \) \( 7q - 8q^{2} + 21q^{3} + 22q^{4} - 28q^{5} - 24q^{6} - 59q^{7} - 117q^{8} + 63q^{9} - 79q^{10} - 131q^{11} + 66q^{12} - 123q^{13} - 117q^{14} - 84q^{15} + 202q^{16} - 235q^{17} - 72q^{18} - 80q^{19} + 61q^{20} - 177q^{21} + 688q^{22} - 274q^{23} - 351q^{24} + 193q^{25} - 180q^{26} + 189q^{27} - 118q^{28} - 406q^{29} - 237q^{30} - 346q^{31} - 854q^{32} - 393q^{33} + 178q^{34} - 424q^{35} + 198q^{36} - 157q^{37} - 129q^{38} - 369q^{39} - 590q^{40} - 825q^{41} - 351q^{42} - 815q^{43} - 1690q^{44} - 252q^{45} + 1457q^{46} - 1196q^{47} + 606q^{48} + 914q^{49} + 713q^{50} - 705q^{51} + 1030q^{52} - 900q^{53} - 216q^{54} - 1044q^{55} + 2172q^{56} - 240q^{57} + 1242q^{58} - 413q^{59} + 183q^{60} + 420q^{61} + 646q^{62} - 531q^{63} + 3541q^{64} + 190q^{65} + 2064q^{66} + 1316q^{67} - 611q^{68} - 822q^{69} + 4658q^{70} - 173q^{71} - 1053q^{72} - 418q^{73} + 660q^{74} + 579q^{75} + 1540q^{76} - 753q^{77} - 540q^{78} + 2635q^{79} + 6155q^{80} + 567q^{81} - 125q^{82} + 457q^{83} - 354q^{84} + 1270q^{85} + 3482q^{86} - 1218q^{87} + 7685q^{88} + 592q^{89} - 711q^{90} + 3179q^{91} - 3500q^{92} - 1038q^{93} + 2064q^{94} - 2250q^{95} - 2562q^{96} - 1906q^{97} + 2994q^{98} - 1179q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.77500 −0.627558 −0.313779 0.949496i \(-0.601595\pi\)
−0.313779 + 0.949496i \(0.601595\pi\)
\(3\) 3.00000 0.577350
\(4\) −4.84937 −0.606171
\(5\) 6.23028 0.557253 0.278627 0.960399i \(-0.410121\pi\)
0.278627 + 0.960399i \(0.410121\pi\)
\(6\) −5.32500 −0.362321
\(7\) −18.0779 −0.976114 −0.488057 0.872812i \(-0.662294\pi\)
−0.488057 + 0.872812i \(0.662294\pi\)
\(8\) 22.8076 1.00797
\(9\) 9.00000 0.333333
\(10\) −11.0588 −0.349709
\(11\) 13.3400 0.365650 0.182825 0.983145i \(-0.441476\pi\)
0.182825 + 0.983145i \(0.441476\pi\)
\(12\) −14.5481 −0.349973
\(13\) −66.3734 −1.41605 −0.708026 0.706187i \(-0.750414\pi\)
−0.708026 + 0.706187i \(0.750414\pi\)
\(14\) 32.0883 0.612568
\(15\) 18.6908 0.321730
\(16\) −1.68865 −0.0263851
\(17\) −97.6720 −1.39347 −0.696733 0.717330i \(-0.745364\pi\)
−0.696733 + 0.717330i \(0.745364\pi\)
\(18\) −15.9750 −0.209186
\(19\) 109.769 1.32540 0.662702 0.748883i \(-0.269409\pi\)
0.662702 + 0.748883i \(0.269409\pi\)
\(20\) −30.2129 −0.337791
\(21\) −54.2336 −0.563559
\(22\) −23.6785 −0.229466
\(23\) −147.736 −1.33935 −0.669674 0.742655i \(-0.733566\pi\)
−0.669674 + 0.742655i \(0.733566\pi\)
\(24\) 68.4229 0.581949
\(25\) −86.1836 −0.689469
\(26\) 117.813 0.888654
\(27\) 27.0000 0.192450
\(28\) 87.6663 0.591692
\(29\) −173.639 −1.11186 −0.555931 0.831228i \(-0.687638\pi\)
−0.555931 + 0.831228i \(0.687638\pi\)
\(30\) −33.1763 −0.201904
\(31\) 148.613 0.861024 0.430512 0.902585i \(-0.358333\pi\)
0.430512 + 0.902585i \(0.358333\pi\)
\(32\) −179.464 −0.991407
\(33\) 40.0199 0.211108
\(34\) 173.368 0.874481
\(35\) −112.630 −0.543943
\(36\) −43.6443 −0.202057
\(37\) −446.332 −1.98315 −0.991574 0.129539i \(-0.958650\pi\)
−0.991574 + 0.129539i \(0.958650\pi\)
\(38\) −194.840 −0.831768
\(39\) −199.120 −0.817557
\(40\) 142.098 0.561692
\(41\) 182.883 0.696622 0.348311 0.937379i \(-0.386755\pi\)
0.348311 + 0.937379i \(0.386755\pi\)
\(42\) 96.2648 0.353666
\(43\) −223.613 −0.793040 −0.396520 0.918026i \(-0.629782\pi\)
−0.396520 + 0.918026i \(0.629782\pi\)
\(44\) −64.6904 −0.221647
\(45\) 56.0725 0.185751
\(46\) 262.231 0.840519
\(47\) −529.113 −1.64211 −0.821053 0.570851i \(-0.806613\pi\)
−0.821053 + 0.570851i \(0.806613\pi\)
\(48\) −5.06595 −0.0152335
\(49\) −16.1904 −0.0472023
\(50\) 152.976 0.432681
\(51\) −293.016 −0.804518
\(52\) 321.869 0.858369
\(53\) 398.029 1.03157 0.515787 0.856717i \(-0.327500\pi\)
0.515787 + 0.856717i \(0.327500\pi\)
\(54\) −47.9250 −0.120774
\(55\) 83.1117 0.203760
\(56\) −412.314 −0.983889
\(57\) 329.306 0.765223
\(58\) 308.210 0.697758
\(59\) −59.0000 −0.130189
\(60\) −90.6388 −0.195024
\(61\) 788.427 1.65488 0.827440 0.561554i \(-0.189796\pi\)
0.827440 + 0.561554i \(0.189796\pi\)
\(62\) −263.789 −0.540342
\(63\) −162.701 −0.325371
\(64\) 332.058 0.648550
\(65\) −413.525 −0.789099
\(66\) −71.0354 −0.132483
\(67\) 288.375 0.525829 0.262915 0.964819i \(-0.415316\pi\)
0.262915 + 0.964819i \(0.415316\pi\)
\(68\) 473.648 0.844680
\(69\) −443.207 −0.773273
\(70\) 199.919 0.341355
\(71\) −139.803 −0.233684 −0.116842 0.993150i \(-0.537277\pi\)
−0.116842 + 0.993150i \(0.537277\pi\)
\(72\) 205.269 0.335988
\(73\) 549.077 0.880336 0.440168 0.897915i \(-0.354919\pi\)
0.440168 + 0.897915i \(0.354919\pi\)
\(74\) 792.240 1.24454
\(75\) −258.551 −0.398065
\(76\) −532.310 −0.803422
\(77\) −241.158 −0.356916
\(78\) 353.439 0.513065
\(79\) −190.617 −0.271469 −0.135735 0.990745i \(-0.543339\pi\)
−0.135735 + 0.990745i \(0.543339\pi\)
\(80\) −10.5208 −0.0147032
\(81\) 81.0000 0.111111
\(82\) −324.617 −0.437171
\(83\) 410.618 0.543026 0.271513 0.962435i \(-0.412476\pi\)
0.271513 + 0.962435i \(0.412476\pi\)
\(84\) 262.999 0.341614
\(85\) −608.524 −0.776514
\(86\) 396.914 0.497679
\(87\) −520.918 −0.641934
\(88\) 304.253 0.368562
\(89\) 1291.81 1.53856 0.769281 0.638911i \(-0.220615\pi\)
0.769281 + 0.638911i \(0.220615\pi\)
\(90\) −99.5288 −0.116570
\(91\) 1199.89 1.38223
\(92\) 716.425 0.811875
\(93\) 445.840 0.497112
\(94\) 939.176 1.03052
\(95\) 683.891 0.738586
\(96\) −538.392 −0.572389
\(97\) 1488.11 1.55768 0.778839 0.627225i \(-0.215809\pi\)
0.778839 + 0.627225i \(0.215809\pi\)
\(98\) 28.7380 0.0296222
\(99\) 120.060 0.121883
\(100\) 417.936 0.417936
\(101\) −1287.68 −1.26861 −0.634303 0.773085i \(-0.718713\pi\)
−0.634303 + 0.773085i \(0.718713\pi\)
\(102\) 520.104 0.504882
\(103\) −469.022 −0.448680 −0.224340 0.974511i \(-0.572023\pi\)
−0.224340 + 0.974511i \(0.572023\pi\)
\(104\) −1513.82 −1.42733
\(105\) −337.891 −0.314045
\(106\) −706.501 −0.647372
\(107\) −1237.22 −1.11782 −0.558908 0.829230i \(-0.688779\pi\)
−0.558908 + 0.829230i \(0.688779\pi\)
\(108\) −130.933 −0.116658
\(109\) 2145.12 1.88500 0.942501 0.334204i \(-0.108468\pi\)
0.942501 + 0.334204i \(0.108468\pi\)
\(110\) −147.523 −0.127871
\(111\) −1339.00 −1.14497
\(112\) 30.5272 0.0257549
\(113\) 1114.62 0.927919 0.463960 0.885856i \(-0.346428\pi\)
0.463960 + 0.885856i \(0.346428\pi\)
\(114\) −584.519 −0.480222
\(115\) −920.435 −0.746357
\(116\) 842.041 0.673979
\(117\) −597.360 −0.472017
\(118\) 104.725 0.0817011
\(119\) 1765.70 1.36018
\(120\) 426.294 0.324293
\(121\) −1153.05 −0.866300
\(122\) −1399.46 −1.03853
\(123\) 548.649 0.402195
\(124\) −720.681 −0.521928
\(125\) −1315.73 −0.941462
\(126\) 288.794 0.204189
\(127\) −1267.75 −0.885782 −0.442891 0.896576i \(-0.646047\pi\)
−0.442891 + 0.896576i \(0.646047\pi\)
\(128\) 846.308 0.584404
\(129\) −670.840 −0.457862
\(130\) 734.007 0.495205
\(131\) −2119.49 −1.41359 −0.706796 0.707418i \(-0.749860\pi\)
−0.706796 + 0.707418i \(0.749860\pi\)
\(132\) −194.071 −0.127968
\(133\) −1984.39 −1.29375
\(134\) −511.865 −0.329988
\(135\) 168.218 0.107243
\(136\) −2227.67 −1.40457
\(137\) −845.583 −0.527322 −0.263661 0.964615i \(-0.584930\pi\)
−0.263661 + 0.964615i \(0.584930\pi\)
\(138\) 786.693 0.485274
\(139\) −1390.93 −0.848754 −0.424377 0.905486i \(-0.639507\pi\)
−0.424377 + 0.905486i \(0.639507\pi\)
\(140\) 546.186 0.329722
\(141\) −1587.34 −0.948071
\(142\) 248.151 0.146650
\(143\) −885.418 −0.517779
\(144\) −15.1978 −0.00879504
\(145\) −1081.82 −0.619589
\(146\) −974.612 −0.552462
\(147\) −48.5712 −0.0272523
\(148\) 2164.43 1.20213
\(149\) −1007.80 −0.554110 −0.277055 0.960854i \(-0.589358\pi\)
−0.277055 + 0.960854i \(0.589358\pi\)
\(150\) 458.928 0.249809
\(151\) −1926.18 −1.03808 −0.519041 0.854750i \(-0.673711\pi\)
−0.519041 + 0.854750i \(0.673711\pi\)
\(152\) 2503.57 1.33596
\(153\) −879.048 −0.464489
\(154\) 428.056 0.223985
\(155\) 925.903 0.479808
\(156\) 965.607 0.495580
\(157\) −1235.58 −0.628092 −0.314046 0.949408i \(-0.601685\pi\)
−0.314046 + 0.949408i \(0.601685\pi\)
\(158\) 338.345 0.170363
\(159\) 1194.09 0.595580
\(160\) −1118.11 −0.552465
\(161\) 2670.75 1.30736
\(162\) −143.775 −0.0697286
\(163\) 3664.53 1.76091 0.880454 0.474131i \(-0.157238\pi\)
0.880454 + 0.474131i \(0.157238\pi\)
\(164\) −886.867 −0.422272
\(165\) 249.335 0.117641
\(166\) −728.847 −0.340780
\(167\) 3953.29 1.83183 0.915913 0.401377i \(-0.131468\pi\)
0.915913 + 0.401377i \(0.131468\pi\)
\(168\) −1236.94 −0.568048
\(169\) 2208.43 1.00520
\(170\) 1080.13 0.487307
\(171\) 987.919 0.441802
\(172\) 1084.38 0.480718
\(173\) −2225.27 −0.977945 −0.488973 0.872299i \(-0.662628\pi\)
−0.488973 + 0.872299i \(0.662628\pi\)
\(174\) 924.630 0.402851
\(175\) 1558.02 0.673000
\(176\) −22.5265 −0.00964772
\(177\) −177.000 −0.0751646
\(178\) −2292.97 −0.965536
\(179\) −2130.61 −0.889662 −0.444831 0.895615i \(-0.646736\pi\)
−0.444831 + 0.895615i \(0.646736\pi\)
\(180\) −271.917 −0.112597
\(181\) 1429.58 0.587072 0.293536 0.955948i \(-0.405168\pi\)
0.293536 + 0.955948i \(0.405168\pi\)
\(182\) −2129.81 −0.867427
\(183\) 2365.28 0.955446
\(184\) −3369.50 −1.35002
\(185\) −2780.77 −1.10512
\(186\) −791.366 −0.311967
\(187\) −1302.94 −0.509521
\(188\) 2565.86 0.995398
\(189\) −488.103 −0.187853
\(190\) −1213.91 −0.463506
\(191\) −920.502 −0.348718 −0.174359 0.984682i \(-0.555785\pi\)
−0.174359 + 0.984682i \(0.555785\pi\)
\(192\) 996.173 0.374441
\(193\) −1870.05 −0.697458 −0.348729 0.937224i \(-0.613387\pi\)
−0.348729 + 0.937224i \(0.613387\pi\)
\(194\) −2641.40 −0.977532
\(195\) −1240.57 −0.455587
\(196\) 78.5132 0.0286127
\(197\) −476.512 −0.172335 −0.0861676 0.996281i \(-0.527462\pi\)
−0.0861676 + 0.996281i \(0.527462\pi\)
\(198\) −213.106 −0.0764888
\(199\) 4164.08 1.48334 0.741668 0.670767i \(-0.234035\pi\)
0.741668 + 0.670767i \(0.234035\pi\)
\(200\) −1965.64 −0.694960
\(201\) 865.124 0.303588
\(202\) 2285.64 0.796123
\(203\) 3139.03 1.08530
\(204\) 1420.94 0.487676
\(205\) 1139.41 0.388195
\(206\) 832.514 0.281573
\(207\) −1329.62 −0.446450
\(208\) 112.081 0.0373627
\(209\) 1464.31 0.484634
\(210\) 599.757 0.197082
\(211\) −2499.21 −0.815415 −0.407707 0.913113i \(-0.633672\pi\)
−0.407707 + 0.913113i \(0.633672\pi\)
\(212\) −1930.19 −0.625311
\(213\) −419.410 −0.134918
\(214\) 2196.06 0.701494
\(215\) −1393.18 −0.441924
\(216\) 615.807 0.193983
\(217\) −2686.61 −0.840457
\(218\) −3807.59 −1.18295
\(219\) 1647.23 0.508262
\(220\) −403.040 −0.123513
\(221\) 6482.82 1.97322
\(222\) 2376.72 0.718536
\(223\) 2567.55 0.771013 0.385506 0.922705i \(-0.374027\pi\)
0.385506 + 0.922705i \(0.374027\pi\)
\(224\) 3244.33 0.967726
\(225\) −775.652 −0.229823
\(226\) −1978.46 −0.582323
\(227\) −969.018 −0.283330 −0.141665 0.989915i \(-0.545246\pi\)
−0.141665 + 0.989915i \(0.545246\pi\)
\(228\) −1596.93 −0.463856
\(229\) 4217.16 1.21693 0.608467 0.793579i \(-0.291785\pi\)
0.608467 + 0.793579i \(0.291785\pi\)
\(230\) 1633.77 0.468382
\(231\) −723.475 −0.206065
\(232\) −3960.30 −1.12072
\(233\) 382.087 0.107431 0.0537154 0.998556i \(-0.482894\pi\)
0.0537154 + 0.998556i \(0.482894\pi\)
\(234\) 1060.32 0.296218
\(235\) −3296.52 −0.915070
\(236\) 286.113 0.0789168
\(237\) −571.851 −0.156733
\(238\) −3134.12 −0.853593
\(239\) −4069.70 −1.10145 −0.550726 0.834686i \(-0.685649\pi\)
−0.550726 + 0.834686i \(0.685649\pi\)
\(240\) −31.5623 −0.00848890
\(241\) 4573.11 1.22232 0.611162 0.791506i \(-0.290703\pi\)
0.611162 + 0.791506i \(0.290703\pi\)
\(242\) 2046.66 0.543653
\(243\) 243.000 0.0641500
\(244\) −3823.37 −1.00314
\(245\) −100.871 −0.0263036
\(246\) −973.852 −0.252401
\(247\) −7285.73 −1.87684
\(248\) 3389.52 0.867882
\(249\) 1231.85 0.313516
\(250\) 2335.43 0.590822
\(251\) 4263.66 1.07219 0.536095 0.844158i \(-0.319899\pi\)
0.536095 + 0.844158i \(0.319899\pi\)
\(252\) 788.997 0.197231
\(253\) −1970.79 −0.489733
\(254\) 2250.25 0.555879
\(255\) −1825.57 −0.448321
\(256\) −4158.66 −1.01530
\(257\) 3758.60 0.912277 0.456138 0.889909i \(-0.349232\pi\)
0.456138 + 0.889909i \(0.349232\pi\)
\(258\) 1190.74 0.287335
\(259\) 8068.73 1.93578
\(260\) 2005.34 0.478329
\(261\) −1562.75 −0.370621
\(262\) 3762.09 0.887110
\(263\) −2832.72 −0.664157 −0.332078 0.943252i \(-0.607750\pi\)
−0.332078 + 0.943252i \(0.607750\pi\)
\(264\) 912.760 0.212790
\(265\) 2479.83 0.574848
\(266\) 3522.29 0.811900
\(267\) 3875.44 0.888289
\(268\) −1398.44 −0.318743
\(269\) −7351.53 −1.66629 −0.833143 0.553058i \(-0.813461\pi\)
−0.833143 + 0.553058i \(0.813461\pi\)
\(270\) −298.587 −0.0673015
\(271\) −4053.05 −0.908507 −0.454253 0.890872i \(-0.650094\pi\)
−0.454253 + 0.890872i \(0.650094\pi\)
\(272\) 164.934 0.0367668
\(273\) 3599.67 0.798029
\(274\) 1500.91 0.330925
\(275\) −1149.69 −0.252104
\(276\) 2149.28 0.468736
\(277\) 3054.14 0.662475 0.331238 0.943547i \(-0.392534\pi\)
0.331238 + 0.943547i \(0.392534\pi\)
\(278\) 2468.90 0.532642
\(279\) 1337.52 0.287008
\(280\) −2568.83 −0.548275
\(281\) −3512.24 −0.745632 −0.372816 0.927905i \(-0.621608\pi\)
−0.372816 + 0.927905i \(0.621608\pi\)
\(282\) 2817.53 0.594969
\(283\) −7955.47 −1.67104 −0.835518 0.549463i \(-0.814832\pi\)
−0.835518 + 0.549463i \(0.814832\pi\)
\(284\) 677.958 0.141653
\(285\) 2051.67 0.426423
\(286\) 1571.62 0.324936
\(287\) −3306.13 −0.679982
\(288\) −1615.17 −0.330469
\(289\) 4626.82 0.941750
\(290\) 1920.24 0.388828
\(291\) 4464.33 0.899325
\(292\) −2662.68 −0.533635
\(293\) 4933.26 0.983632 0.491816 0.870699i \(-0.336333\pi\)
0.491816 + 0.870699i \(0.336333\pi\)
\(294\) 86.2139 0.0171024
\(295\) −367.587 −0.0725482
\(296\) −10179.8 −1.99895
\(297\) 360.179 0.0703694
\(298\) 1788.85 0.347736
\(299\) 9805.72 1.89659
\(300\) 1253.81 0.241296
\(301\) 4042.46 0.774098
\(302\) 3418.97 0.651456
\(303\) −3863.05 −0.732430
\(304\) −185.361 −0.0349710
\(305\) 4912.12 0.922188
\(306\) 1560.31 0.291494
\(307\) −4362.63 −0.811037 −0.405518 0.914087i \(-0.632909\pi\)
−0.405518 + 0.914087i \(0.632909\pi\)
\(308\) 1169.47 0.216352
\(309\) −1407.07 −0.259046
\(310\) −1643.48 −0.301107
\(311\) −3542.33 −0.645875 −0.322937 0.946420i \(-0.604670\pi\)
−0.322937 + 0.946420i \(0.604670\pi\)
\(312\) −4541.46 −0.824069
\(313\) −1808.65 −0.326616 −0.163308 0.986575i \(-0.552216\pi\)
−0.163308 + 0.986575i \(0.552216\pi\)
\(314\) 2193.16 0.394164
\(315\) −1013.67 −0.181314
\(316\) 924.372 0.164557
\(317\) 302.078 0.0535217 0.0267609 0.999642i \(-0.491481\pi\)
0.0267609 + 0.999642i \(0.491481\pi\)
\(318\) −2119.50 −0.373761
\(319\) −2316.34 −0.406552
\(320\) 2068.81 0.361407
\(321\) −3711.65 −0.645371
\(322\) −4740.58 −0.820442
\(323\) −10721.3 −1.84691
\(324\) −392.799 −0.0673524
\(325\) 5720.30 0.976323
\(326\) −6504.54 −1.10507
\(327\) 6435.36 1.08831
\(328\) 4171.13 0.702171
\(329\) 9565.23 1.60288
\(330\) −442.570 −0.0738263
\(331\) −4133.17 −0.686343 −0.343172 0.939273i \(-0.611501\pi\)
−0.343172 + 0.939273i \(0.611501\pi\)
\(332\) −1991.24 −0.329167
\(333\) −4016.99 −0.661050
\(334\) −7017.10 −1.14958
\(335\) 1796.66 0.293020
\(336\) 91.5815 0.0148696
\(337\) −3246.37 −0.524750 −0.262375 0.964966i \(-0.584506\pi\)
−0.262375 + 0.964966i \(0.584506\pi\)
\(338\) −3919.96 −0.630821
\(339\) 3343.87 0.535734
\(340\) 2950.96 0.470701
\(341\) 1982.50 0.314833
\(342\) −1753.56 −0.277256
\(343\) 6493.40 1.02219
\(344\) −5100.10 −0.799357
\(345\) −2761.31 −0.430909
\(346\) 3949.87 0.613717
\(347\) 463.911 0.0717696 0.0358848 0.999356i \(-0.488575\pi\)
0.0358848 + 0.999356i \(0.488575\pi\)
\(348\) 2526.12 0.389122
\(349\) −6606.06 −1.01322 −0.506611 0.862175i \(-0.669102\pi\)
−0.506611 + 0.862175i \(0.669102\pi\)
\(350\) −2765.48 −0.422346
\(351\) −1792.08 −0.272519
\(352\) −2394.04 −0.362508
\(353\) −6284.55 −0.947572 −0.473786 0.880640i \(-0.657113\pi\)
−0.473786 + 0.880640i \(0.657113\pi\)
\(354\) 314.175 0.0471701
\(355\) −871.014 −0.130221
\(356\) −6264.48 −0.932632
\(357\) 5297.11 0.785301
\(358\) 3781.84 0.558314
\(359\) 5773.93 0.848848 0.424424 0.905464i \(-0.360477\pi\)
0.424424 + 0.905464i \(0.360477\pi\)
\(360\) 1278.88 0.187231
\(361\) 5190.19 0.756698
\(362\) −2537.51 −0.368421
\(363\) −3459.14 −0.500159
\(364\) −5818.71 −0.837866
\(365\) 3420.90 0.490570
\(366\) −4198.38 −0.599597
\(367\) −669.964 −0.0952911 −0.0476456 0.998864i \(-0.515172\pi\)
−0.0476456 + 0.998864i \(0.515172\pi\)
\(368\) 249.474 0.0353389
\(369\) 1645.95 0.232207
\(370\) 4935.88 0.693524
\(371\) −7195.51 −1.00693
\(372\) −2162.04 −0.301335
\(373\) 3345.79 0.464446 0.232223 0.972663i \(-0.425400\pi\)
0.232223 + 0.972663i \(0.425400\pi\)
\(374\) 2312.72 0.319754
\(375\) −3947.20 −0.543553
\(376\) −12067.8 −1.65519
\(377\) 11525.0 1.57445
\(378\) 866.383 0.117889
\(379\) 6881.01 0.932595 0.466298 0.884628i \(-0.345588\pi\)
0.466298 + 0.884628i \(0.345588\pi\)
\(380\) −3316.44 −0.447710
\(381\) −3803.24 −0.511406
\(382\) 1633.89 0.218841
\(383\) −4080.85 −0.544444 −0.272222 0.962235i \(-0.587758\pi\)
−0.272222 + 0.962235i \(0.587758\pi\)
\(384\) 2538.92 0.337406
\(385\) −1502.48 −0.198893
\(386\) 3319.35 0.437695
\(387\) −2012.52 −0.264347
\(388\) −7216.40 −0.944219
\(389\) −4698.80 −0.612439 −0.306220 0.951961i \(-0.599064\pi\)
−0.306220 + 0.951961i \(0.599064\pi\)
\(390\) 2202.02 0.285907
\(391\) 14429.6 1.86634
\(392\) −369.265 −0.0475783
\(393\) −6358.46 −0.816138
\(394\) 845.809 0.108150
\(395\) −1187.60 −0.151277
\(396\) −582.214 −0.0738822
\(397\) 10293.0 1.30124 0.650620 0.759404i \(-0.274509\pi\)
0.650620 + 0.759404i \(0.274509\pi\)
\(398\) −7391.25 −0.930879
\(399\) −5953.16 −0.746944
\(400\) 145.534 0.0181917
\(401\) 7673.35 0.955583 0.477792 0.878473i \(-0.341437\pi\)
0.477792 + 0.878473i \(0.341437\pi\)
\(402\) −1535.60 −0.190519
\(403\) −9863.97 −1.21925
\(404\) 6244.45 0.768992
\(405\) 504.653 0.0619170
\(406\) −5571.78 −0.681091
\(407\) −5954.05 −0.725138
\(408\) −6683.01 −0.810927
\(409\) 3707.61 0.448239 0.224119 0.974562i \(-0.428049\pi\)
0.224119 + 0.974562i \(0.428049\pi\)
\(410\) −2022.46 −0.243615
\(411\) −2536.75 −0.304449
\(412\) 2274.46 0.271977
\(413\) 1066.59 0.127079
\(414\) 2360.08 0.280173
\(415\) 2558.27 0.302603
\(416\) 11911.6 1.40388
\(417\) −4172.78 −0.490029
\(418\) −2599.16 −0.304136
\(419\) −11357.0 −1.32416 −0.662082 0.749431i \(-0.730327\pi\)
−0.662082 + 0.749431i \(0.730327\pi\)
\(420\) 1638.56 0.190365
\(421\) 3814.03 0.441531 0.220766 0.975327i \(-0.429144\pi\)
0.220766 + 0.975327i \(0.429144\pi\)
\(422\) 4436.10 0.511720
\(423\) −4762.01 −0.547369
\(424\) 9078.10 1.03979
\(425\) 8417.72 0.960752
\(426\) 744.453 0.0846687
\(427\) −14253.1 −1.61535
\(428\) 5999.72 0.677588
\(429\) −2656.26 −0.298940
\(430\) 2472.89 0.277333
\(431\) −1307.09 −0.146079 −0.0730396 0.997329i \(-0.523270\pi\)
−0.0730396 + 0.997329i \(0.523270\pi\)
\(432\) −45.5935 −0.00507782
\(433\) 7915.74 0.878536 0.439268 0.898356i \(-0.355238\pi\)
0.439268 + 0.898356i \(0.355238\pi\)
\(434\) 4768.74 0.527435
\(435\) −3245.47 −0.357720
\(436\) −10402.5 −1.14263
\(437\) −16216.8 −1.77518
\(438\) −2923.83 −0.318964
\(439\) 2570.45 0.279456 0.139728 0.990190i \(-0.455377\pi\)
0.139728 + 0.990190i \(0.455377\pi\)
\(440\) 1895.58 0.205383
\(441\) −145.713 −0.0157341
\(442\) −11507.0 −1.23831
\(443\) −633.121 −0.0679017 −0.0339509 0.999424i \(-0.510809\pi\)
−0.0339509 + 0.999424i \(0.510809\pi\)
\(444\) 6493.29 0.694049
\(445\) 8048.36 0.857369
\(446\) −4557.40 −0.483855
\(447\) −3023.41 −0.319915
\(448\) −6002.90 −0.633059
\(449\) 10146.6 1.06648 0.533238 0.845965i \(-0.320975\pi\)
0.533238 + 0.845965i \(0.320975\pi\)
\(450\) 1376.78 0.144227
\(451\) 2439.65 0.254720
\(452\) −5405.22 −0.562478
\(453\) −5778.54 −0.599336
\(454\) 1720.01 0.177806
\(455\) 7475.65 0.770250
\(456\) 7510.71 0.771318
\(457\) −7173.92 −0.734315 −0.367157 0.930159i \(-0.619669\pi\)
−0.367157 + 0.930159i \(0.619669\pi\)
\(458\) −7485.47 −0.763697
\(459\) −2637.14 −0.268173
\(460\) 4463.53 0.452420
\(461\) −15959.8 −1.61242 −0.806208 0.591632i \(-0.798484\pi\)
−0.806208 + 0.591632i \(0.798484\pi\)
\(462\) 1284.17 0.129318
\(463\) 10486.8 1.05262 0.526308 0.850294i \(-0.323576\pi\)
0.526308 + 0.850294i \(0.323576\pi\)
\(464\) 293.216 0.0293366
\(465\) 2777.71 0.277018
\(466\) −678.205 −0.0674190
\(467\) −11871.2 −1.17630 −0.588150 0.808752i \(-0.700144\pi\)
−0.588150 + 0.808752i \(0.700144\pi\)
\(468\) 2896.82 0.286123
\(469\) −5213.20 −0.513269
\(470\) 5851.33 0.574259
\(471\) −3706.75 −0.362629
\(472\) −1345.65 −0.131226
\(473\) −2983.00 −0.289975
\(474\) 1015.04 0.0983590
\(475\) −9460.27 −0.913825
\(476\) −8562.54 −0.824503
\(477\) 3582.26 0.343858
\(478\) 7223.72 0.691225
\(479\) −9570.85 −0.912950 −0.456475 0.889736i \(-0.650888\pi\)
−0.456475 + 0.889736i \(0.650888\pi\)
\(480\) −3354.33 −0.318966
\(481\) 29624.6 2.80824
\(482\) −8117.28 −0.767078
\(483\) 8012.24 0.754803
\(484\) 5591.54 0.525126
\(485\) 9271.34 0.868021
\(486\) −431.325 −0.0402578
\(487\) 11208.2 1.04290 0.521451 0.853281i \(-0.325391\pi\)
0.521451 + 0.853281i \(0.325391\pi\)
\(488\) 17982.2 1.66806
\(489\) 10993.6 1.01666
\(490\) 179.046 0.0165071
\(491\) 7720.19 0.709587 0.354793 0.934945i \(-0.384551\pi\)
0.354793 + 0.934945i \(0.384551\pi\)
\(492\) −2660.60 −0.243799
\(493\) 16959.7 1.54934
\(494\) 12932.2 1.17783
\(495\) 748.006 0.0679199
\(496\) −250.956 −0.0227182
\(497\) 2527.35 0.228103
\(498\) −2186.54 −0.196750
\(499\) −3679.73 −0.330115 −0.165057 0.986284i \(-0.552781\pi\)
−0.165057 + 0.986284i \(0.552781\pi\)
\(500\) 6380.48 0.570687
\(501\) 11859.9 1.05761
\(502\) −7568.00 −0.672861
\(503\) 15306.9 1.35686 0.678431 0.734664i \(-0.262660\pi\)
0.678431 + 0.734664i \(0.262660\pi\)
\(504\) −3710.82 −0.327963
\(505\) −8022.62 −0.706935
\(506\) 3498.15 0.307336
\(507\) 6625.28 0.580353
\(508\) 6147.77 0.536935
\(509\) −9361.34 −0.815195 −0.407597 0.913162i \(-0.633633\pi\)
−0.407597 + 0.913162i \(0.633633\pi\)
\(510\) 3240.39 0.281347
\(511\) −9926.14 −0.859308
\(512\) 611.164 0.0527537
\(513\) 2963.76 0.255074
\(514\) −6671.52 −0.572506
\(515\) −2922.14 −0.250029
\(516\) 3253.15 0.277543
\(517\) −7058.34 −0.600436
\(518\) −14322.0 −1.21481
\(519\) −6675.82 −0.564617
\(520\) −9431.53 −0.795385
\(521\) −5933.23 −0.498924 −0.249462 0.968385i \(-0.580254\pi\)
−0.249462 + 0.968385i \(0.580254\pi\)
\(522\) 2773.89 0.232586
\(523\) 17269.3 1.44385 0.721925 0.691972i \(-0.243258\pi\)
0.721925 + 0.691972i \(0.243258\pi\)
\(524\) 10278.2 0.856879
\(525\) 4674.05 0.388557
\(526\) 5028.09 0.416797
\(527\) −14515.4 −1.19981
\(528\) −67.5795 −0.00557012
\(529\) 9658.83 0.793855
\(530\) −4401.70 −0.360750
\(531\) −531.000 −0.0433963
\(532\) 9623.03 0.784231
\(533\) −12138.6 −0.986453
\(534\) −6878.91 −0.557453
\(535\) −7708.21 −0.622907
\(536\) 6577.15 0.530018
\(537\) −6391.84 −0.513647
\(538\) 13049.0 1.04569
\(539\) −215.979 −0.0172595
\(540\) −815.750 −0.0650079
\(541\) −1132.58 −0.0900067 −0.0450034 0.998987i \(-0.514330\pi\)
−0.0450034 + 0.998987i \(0.514330\pi\)
\(542\) 7194.17 0.570141
\(543\) 4288.75 0.338946
\(544\) 17528.6 1.38149
\(545\) 13364.7 1.05042
\(546\) −6389.42 −0.500809
\(547\) 8546.77 0.668069 0.334034 0.942561i \(-0.391590\pi\)
0.334034 + 0.942561i \(0.391590\pi\)
\(548\) 4100.55 0.319647
\(549\) 7095.84 0.551627
\(550\) 2040.69 0.158210
\(551\) −19060.2 −1.47367
\(552\) −10108.5 −0.779433
\(553\) 3445.95 0.264985
\(554\) −5421.11 −0.415741
\(555\) −8342.32 −0.638039
\(556\) 6745.12 0.514490
\(557\) −16689.2 −1.26956 −0.634778 0.772695i \(-0.718908\pi\)
−0.634778 + 0.772695i \(0.718908\pi\)
\(558\) −2374.10 −0.180114
\(559\) 14842.0 1.12299
\(560\) 190.193 0.0143520
\(561\) −3908.82 −0.294172
\(562\) 6234.23 0.467927
\(563\) −6844.25 −0.512346 −0.256173 0.966631i \(-0.582462\pi\)
−0.256173 + 0.966631i \(0.582462\pi\)
\(564\) 7697.59 0.574693
\(565\) 6944.41 0.517086
\(566\) 14121.0 1.04867
\(567\) −1464.31 −0.108457
\(568\) −3188.58 −0.235546
\(569\) −12047.3 −0.887611 −0.443806 0.896123i \(-0.646372\pi\)
−0.443806 + 0.896123i \(0.646372\pi\)
\(570\) −3641.72 −0.267605
\(571\) −14990.8 −1.09868 −0.549338 0.835600i \(-0.685120\pi\)
−0.549338 + 0.835600i \(0.685120\pi\)
\(572\) 4293.72 0.313863
\(573\) −2761.51 −0.201333
\(574\) 5868.39 0.426728
\(575\) 12732.4 0.923439
\(576\) 2988.52 0.216183
\(577\) −5773.70 −0.416572 −0.208286 0.978068i \(-0.566788\pi\)
−0.208286 + 0.978068i \(0.566788\pi\)
\(578\) −8212.61 −0.591002
\(579\) −5610.16 −0.402677
\(580\) 5246.16 0.375577
\(581\) −7423.10 −0.530055
\(582\) −7924.19 −0.564379
\(583\) 5309.69 0.377195
\(584\) 12523.1 0.887348
\(585\) −3721.72 −0.263033
\(586\) −8756.54 −0.617286
\(587\) −1595.79 −0.112207 −0.0561034 0.998425i \(-0.517868\pi\)
−0.0561034 + 0.998425i \(0.517868\pi\)
\(588\) 235.540 0.0165195
\(589\) 16313.1 1.14121
\(590\) 652.467 0.0455282
\(591\) −1429.53 −0.0994978
\(592\) 753.698 0.0523256
\(593\) 5301.19 0.367106 0.183553 0.983010i \(-0.441240\pi\)
0.183553 + 0.983010i \(0.441240\pi\)
\(594\) −639.318 −0.0441608
\(595\) 11000.8 0.757966
\(596\) 4887.20 0.335885
\(597\) 12492.2 0.856405
\(598\) −17405.2 −1.19022
\(599\) 12610.9 0.860211 0.430105 0.902779i \(-0.358476\pi\)
0.430105 + 0.902779i \(0.358476\pi\)
\(600\) −5896.93 −0.401236
\(601\) −27751.9 −1.88357 −0.941783 0.336221i \(-0.890851\pi\)
−0.941783 + 0.336221i \(0.890851\pi\)
\(602\) −7175.37 −0.485791
\(603\) 2595.37 0.175276
\(604\) 9340.76 0.629255
\(605\) −7183.80 −0.482749
\(606\) 6856.91 0.459642
\(607\) −20229.0 −1.35267 −0.676334 0.736595i \(-0.736433\pi\)
−0.676334 + 0.736595i \(0.736433\pi\)
\(608\) −19699.5 −1.31402
\(609\) 9417.09 0.626601
\(610\) −8719.02 −0.578726
\(611\) 35119.0 2.32531
\(612\) 4262.83 0.281560
\(613\) −21903.1 −1.44316 −0.721580 0.692331i \(-0.756584\pi\)
−0.721580 + 0.692331i \(0.756584\pi\)
\(614\) 7743.67 0.508972
\(615\) 3418.24 0.224125
\(616\) −5500.25 −0.359759
\(617\) 8023.42 0.523519 0.261759 0.965133i \(-0.415697\pi\)
0.261759 + 0.965133i \(0.415697\pi\)
\(618\) 2497.54 0.162566
\(619\) −6262.61 −0.406649 −0.203324 0.979111i \(-0.565175\pi\)
−0.203324 + 0.979111i \(0.565175\pi\)
\(620\) −4490.05 −0.290846
\(621\) −3988.86 −0.257758
\(622\) 6287.64 0.405324
\(623\) −23353.2 −1.50181
\(624\) 336.244 0.0215714
\(625\) 2575.56 0.164836
\(626\) 3210.35 0.204970
\(627\) 4392.93 0.279804
\(628\) 5991.81 0.380731
\(629\) 43594.1 2.76345
\(630\) 1799.27 0.113785
\(631\) −6018.53 −0.379705 −0.189852 0.981813i \(-0.560801\pi\)
−0.189852 + 0.981813i \(0.560801\pi\)
\(632\) −4347.53 −0.273632
\(633\) −7497.62 −0.470780
\(634\) −536.189 −0.0335880
\(635\) −7898.42 −0.493605
\(636\) −5790.56 −0.361023
\(637\) 1074.61 0.0668409
\(638\) 4111.51 0.255135
\(639\) −1258.23 −0.0778948
\(640\) 5272.74 0.325661
\(641\) 3669.06 0.226083 0.113041 0.993590i \(-0.463941\pi\)
0.113041 + 0.993590i \(0.463941\pi\)
\(642\) 6588.19 0.405008
\(643\) −9099.99 −0.558116 −0.279058 0.960274i \(-0.590022\pi\)
−0.279058 + 0.960274i \(0.590022\pi\)
\(644\) −12951.4 −0.792482
\(645\) −4179.53 −0.255145
\(646\) 19030.4 1.15904
\(647\) −1873.56 −0.113844 −0.0569222 0.998379i \(-0.518129\pi\)
−0.0569222 + 0.998379i \(0.518129\pi\)
\(648\) 1847.42 0.111996
\(649\) −787.058 −0.0476036
\(650\) −10153.5 −0.612699
\(651\) −8059.84 −0.485238
\(652\) −17770.7 −1.06741
\(653\) −23009.5 −1.37892 −0.689458 0.724325i \(-0.742151\pi\)
−0.689458 + 0.724325i \(0.742151\pi\)
\(654\) −11422.8 −0.682975
\(655\) −13205.0 −0.787729
\(656\) −308.825 −0.0183805
\(657\) 4941.69 0.293445
\(658\) −16978.3 −1.00590
\(659\) −10038.1 −0.593368 −0.296684 0.954976i \(-0.595881\pi\)
−0.296684 + 0.954976i \(0.595881\pi\)
\(660\) −1209.12 −0.0713104
\(661\) −21406.5 −1.25963 −0.629816 0.776744i \(-0.716870\pi\)
−0.629816 + 0.776744i \(0.716870\pi\)
\(662\) 7336.38 0.430720
\(663\) 19448.5 1.13924
\(664\) 9365.23 0.547351
\(665\) −12363.3 −0.720944
\(666\) 7130.16 0.414847
\(667\) 25652.7 1.48917
\(668\) −19171.0 −1.11040
\(669\) 7702.65 0.445144
\(670\) −3189.07 −0.183887
\(671\) 10517.6 0.605107
\(672\) 9732.98 0.558717
\(673\) −934.831 −0.0535439 −0.0267720 0.999642i \(-0.508523\pi\)
−0.0267720 + 0.999642i \(0.508523\pi\)
\(674\) 5762.30 0.329311
\(675\) −2326.96 −0.132688
\(676\) −10709.5 −0.609324
\(677\) −3937.51 −0.223531 −0.111766 0.993735i \(-0.535651\pi\)
−0.111766 + 0.993735i \(0.535651\pi\)
\(678\) −5935.37 −0.336204
\(679\) −26901.9 −1.52047
\(680\) −13879.0 −0.782699
\(681\) −2907.05 −0.163581
\(682\) −3518.93 −0.197576
\(683\) −12374.6 −0.693268 −0.346634 0.938001i \(-0.612675\pi\)
−0.346634 + 0.938001i \(0.612675\pi\)
\(684\) −4790.79 −0.267807
\(685\) −5268.22 −0.293852
\(686\) −11525.8 −0.641482
\(687\) 12651.5 0.702598
\(688\) 377.605 0.0209245
\(689\) −26418.5 −1.46076
\(690\) 4901.32 0.270420
\(691\) −5887.06 −0.324102 −0.162051 0.986782i \(-0.551811\pi\)
−0.162051 + 0.986782i \(0.551811\pi\)
\(692\) 10791.2 0.592802
\(693\) −2170.42 −0.118972
\(694\) −823.443 −0.0450396
\(695\) −8665.87 −0.472971
\(696\) −11880.9 −0.647047
\(697\) −17862.5 −0.970720
\(698\) 11725.8 0.635855
\(699\) 1146.26 0.0620252
\(700\) −7555.40 −0.407953
\(701\) 7809.40 0.420766 0.210383 0.977619i \(-0.432529\pi\)
0.210383 + 0.977619i \(0.432529\pi\)
\(702\) 3180.95 0.171022
\(703\) −48993.3 −2.62847
\(704\) 4429.64 0.237142
\(705\) −9889.56 −0.528316
\(706\) 11155.1 0.594656
\(707\) 23278.6 1.23830
\(708\) 858.339 0.0455626
\(709\) 13649.5 0.723018 0.361509 0.932369i \(-0.382262\pi\)
0.361509 + 0.932369i \(0.382262\pi\)
\(710\) 1546.05 0.0817215
\(711\) −1715.55 −0.0904898
\(712\) 29463.2 1.55082
\(713\) −21955.5 −1.15321
\(714\) −9402.37 −0.492822
\(715\) −5516.41 −0.288534
\(716\) 10332.1 0.539288
\(717\) −12209.1 −0.635923
\(718\) −10248.7 −0.532701
\(719\) 475.869 0.0246828 0.0123414 0.999924i \(-0.496072\pi\)
0.0123414 + 0.999924i \(0.496072\pi\)
\(720\) −94.6868 −0.00490107
\(721\) 8478.92 0.437963
\(722\) −9212.60 −0.474872
\(723\) 13719.3 0.705709
\(724\) −6932.57 −0.355866
\(725\) 14964.9 0.766594
\(726\) 6139.97 0.313878
\(727\) −8057.43 −0.411050 −0.205525 0.978652i \(-0.565890\pi\)
−0.205525 + 0.978652i \(0.565890\pi\)
\(728\) 27366.7 1.39324
\(729\) 729.000 0.0370370
\(730\) −6072.11 −0.307861
\(731\) 21840.8 1.10508
\(732\) −11470.1 −0.579164
\(733\) 28918.2 1.45719 0.728594 0.684946i \(-0.240174\pi\)
0.728594 + 0.684946i \(0.240174\pi\)
\(734\) 1189.19 0.0598007
\(735\) −302.612 −0.0151864
\(736\) 26513.2 1.32784
\(737\) 3846.91 0.192270
\(738\) −2921.56 −0.145724
\(739\) −25403.3 −1.26451 −0.632256 0.774760i \(-0.717871\pi\)
−0.632256 + 0.774760i \(0.717871\pi\)
\(740\) 13485.0 0.669890
\(741\) −21857.2 −1.08359
\(742\) 12772.0 0.631909
\(743\) −30468.3 −1.50441 −0.752204 0.658930i \(-0.771009\pi\)
−0.752204 + 0.658930i \(0.771009\pi\)
\(744\) 10168.6 0.501072
\(745\) −6278.89 −0.308779
\(746\) −5938.77 −0.291466
\(747\) 3695.56 0.181009
\(748\) 6318.44 0.308857
\(749\) 22366.3 1.09112
\(750\) 7006.29 0.341111
\(751\) −1951.23 −0.0948088 −0.0474044 0.998876i \(-0.515095\pi\)
−0.0474044 + 0.998876i \(0.515095\pi\)
\(752\) 893.485 0.0433272
\(753\) 12791.0 0.619029
\(754\) −20456.9 −0.988061
\(755\) −12000.6 −0.578474
\(756\) 2366.99 0.113871
\(757\) 13529.5 0.649588 0.324794 0.945785i \(-0.394705\pi\)
0.324794 + 0.945785i \(0.394705\pi\)
\(758\) −12213.8 −0.585257
\(759\) −5912.37 −0.282747
\(760\) 15597.9 0.744469
\(761\) 31379.5 1.49475 0.747376 0.664402i \(-0.231314\pi\)
0.747376 + 0.664402i \(0.231314\pi\)
\(762\) 6750.75 0.320937
\(763\) −38779.2 −1.83998
\(764\) 4463.86 0.211383
\(765\) −5476.72 −0.258838
\(766\) 7243.52 0.341670
\(767\) 3916.03 0.184354
\(768\) −12476.0 −0.586182
\(769\) −1805.38 −0.0846604 −0.0423302 0.999104i \(-0.513478\pi\)
−0.0423302 + 0.999104i \(0.513478\pi\)
\(770\) 2666.91 0.124817
\(771\) 11275.8 0.526703
\(772\) 9068.58 0.422779
\(773\) 27743.2 1.29089 0.645443 0.763808i \(-0.276673\pi\)
0.645443 + 0.763808i \(0.276673\pi\)
\(774\) 3572.23 0.165893
\(775\) −12808.0 −0.593649
\(776\) 33940.3 1.57008
\(777\) 24206.2 1.11762
\(778\) 8340.38 0.384341
\(779\) 20074.8 0.923306
\(780\) 6016.01 0.276164
\(781\) −1864.97 −0.0854467
\(782\) −25612.6 −1.17123
\(783\) −4688.26 −0.213978
\(784\) 27.3399 0.00124544
\(785\) −7698.04 −0.350006
\(786\) 11286.3 0.512173
\(787\) −2980.67 −0.135005 −0.0675027 0.997719i \(-0.521503\pi\)
−0.0675027 + 0.997719i \(0.521503\pi\)
\(788\) 2310.78 0.104465
\(789\) −8498.17 −0.383451
\(790\) 2107.99 0.0949352
\(791\) −20150.0 −0.905755
\(792\) 2738.28 0.122854
\(793\) −52330.6 −2.34340
\(794\) −18270.1 −0.816603
\(795\) 7439.49 0.331889
\(796\) −20193.2 −0.899156
\(797\) 26151.2 1.16226 0.581131 0.813810i \(-0.302610\pi\)
0.581131 + 0.813810i \(0.302610\pi\)
\(798\) 10566.9 0.468751
\(799\) 51679.5 2.28822
\(800\) 15466.8 0.683544
\(801\) 11626.3 0.512854
\(802\) −13620.2 −0.599684
\(803\) 7324.66 0.321895
\(804\) −4195.31 −0.184026
\(805\) 16639.5 0.728529
\(806\) 17508.6 0.765152
\(807\) −22054.6 −0.962030
\(808\) −29369.0 −1.27871
\(809\) −30368.8 −1.31979 −0.659895 0.751358i \(-0.729399\pi\)
−0.659895 + 0.751358i \(0.729399\pi\)
\(810\) −895.760 −0.0388565
\(811\) −5497.72 −0.238041 −0.119020 0.992892i \(-0.537975\pi\)
−0.119020 + 0.992892i \(0.537975\pi\)
\(812\) −15222.3 −0.657880
\(813\) −12159.2 −0.524527
\(814\) 10568.4 0.455066
\(815\) 22831.0 0.981272
\(816\) 494.801 0.0212273
\(817\) −24545.8 −1.05110
\(818\) −6581.02 −0.281296
\(819\) 10799.0 0.460742
\(820\) −5525.43 −0.235313
\(821\) −33287.7 −1.41504 −0.707521 0.706692i \(-0.750186\pi\)
−0.707521 + 0.706692i \(0.750186\pi\)
\(822\) 4502.74 0.191060
\(823\) −13109.6 −0.555253 −0.277626 0.960689i \(-0.589548\pi\)
−0.277626 + 0.960689i \(0.589548\pi\)
\(824\) −10697.3 −0.452254
\(825\) −3449.06 −0.145552
\(826\) −1893.21 −0.0797495
\(827\) 31629.7 1.32995 0.664977 0.746864i \(-0.268441\pi\)
0.664977 + 0.746864i \(0.268441\pi\)
\(828\) 6447.83 0.270625
\(829\) 23175.2 0.970938 0.485469 0.874254i \(-0.338649\pi\)
0.485469 + 0.874254i \(0.338649\pi\)
\(830\) −4540.92 −0.189901
\(831\) 9162.42 0.382480
\(832\) −22039.8 −0.918380
\(833\) 1581.35 0.0657748
\(834\) 7406.69 0.307521
\(835\) 24630.1 1.02079
\(836\) −7100.99 −0.293771
\(837\) 4012.56 0.165704
\(838\) 20158.7 0.830990
\(839\) 24731.6 1.01767 0.508837 0.860863i \(-0.330076\pi\)
0.508837 + 0.860863i \(0.330076\pi\)
\(840\) −7706.50 −0.316547
\(841\) 5761.61 0.236238
\(842\) −6769.91 −0.277086
\(843\) −10536.7 −0.430491
\(844\) 12119.6 0.494281
\(845\) 13759.1 0.560151
\(846\) 8452.58 0.343506
\(847\) 20844.6 0.845607
\(848\) −672.130 −0.0272182
\(849\) −23866.4 −0.964773
\(850\) −14941.5 −0.602927
\(851\) 65939.1 2.65613
\(852\) 2033.87 0.0817833
\(853\) 26779.6 1.07493 0.537466 0.843285i \(-0.319382\pi\)
0.537466 + 0.843285i \(0.319382\pi\)
\(854\) 25299.2 1.01373
\(855\) 6155.02 0.246195
\(856\) −28218.0 −1.12672
\(857\) 32339.7 1.28904 0.644518 0.764589i \(-0.277058\pi\)
0.644518 + 0.764589i \(0.277058\pi\)
\(858\) 4714.86 0.187602
\(859\) 41682.2 1.65562 0.827810 0.561009i \(-0.189587\pi\)
0.827810 + 0.561009i \(0.189587\pi\)
\(860\) 6756.02 0.267882
\(861\) −9918.40 −0.392588
\(862\) 2320.08 0.0916732
\(863\) −15307.7 −0.603802 −0.301901 0.953339i \(-0.597621\pi\)
−0.301901 + 0.953339i \(0.597621\pi\)
\(864\) −4845.52 −0.190796
\(865\) −13864.1 −0.544963
\(866\) −14050.4 −0.551332
\(867\) 13880.5 0.543720
\(868\) 13028.4 0.509461
\(869\) −2542.82 −0.0992628
\(870\) 5760.71 0.224490
\(871\) −19140.4 −0.744601
\(872\) 48925.1 1.90002
\(873\) 13393.0 0.519226
\(874\) 28784.8 1.11403
\(875\) 23785.7 0.918974
\(876\) −7988.03 −0.308094
\(877\) −42064.0 −1.61961 −0.809807 0.586696i \(-0.800428\pi\)
−0.809807 + 0.586696i \(0.800428\pi\)
\(878\) −4562.56 −0.175374
\(879\) 14799.8 0.567900
\(880\) −140.346 −0.00537623
\(881\) −983.391 −0.0376065 −0.0188032 0.999823i \(-0.505986\pi\)
−0.0188032 + 0.999823i \(0.505986\pi\)
\(882\) 258.642 0.00987405
\(883\) 3067.46 0.116906 0.0584531 0.998290i \(-0.481383\pi\)
0.0584531 + 0.998290i \(0.481383\pi\)
\(884\) −31437.6 −1.19611
\(885\) −1102.76 −0.0418857
\(886\) 1123.79 0.0426123
\(887\) 15178.8 0.574583 0.287291 0.957843i \(-0.407245\pi\)
0.287291 + 0.957843i \(0.407245\pi\)
\(888\) −30539.3 −1.15409
\(889\) 22918.2 0.864624
\(890\) −14285.9 −0.538048
\(891\) 1080.54 0.0406278
\(892\) −12451.0 −0.467366
\(893\) −58080.1 −2.17646
\(894\) 5366.55 0.200765
\(895\) −13274.3 −0.495767
\(896\) −15299.4 −0.570445
\(897\) 29417.1 1.09499
\(898\) −18010.2 −0.669275
\(899\) −25805.1 −0.957340
\(900\) 3761.42 0.139312
\(901\) −38876.2 −1.43746
\(902\) −4330.38 −0.159851
\(903\) 12127.4 0.446925
\(904\) 25421.9 0.935310
\(905\) 8906.70 0.327148
\(906\) 10256.9 0.376118
\(907\) −2893.09 −0.105914 −0.0529568 0.998597i \(-0.516865\pi\)
−0.0529568 + 0.998597i \(0.516865\pi\)
\(908\) 4699.13 0.171747
\(909\) −11589.1 −0.422869
\(910\) −13269.3 −0.483377
\(911\) −2299.05 −0.0836124 −0.0418062 0.999126i \(-0.513311\pi\)
−0.0418062 + 0.999126i \(0.513311\pi\)
\(912\) −556.083 −0.0201905
\(913\) 5477.63 0.198557
\(914\) 12733.7 0.460825
\(915\) 14736.4 0.532425
\(916\) −20450.6 −0.737671
\(917\) 38315.8 1.37983
\(918\) 4680.93 0.168294
\(919\) −45794.9 −1.64378 −0.821891 0.569645i \(-0.807081\pi\)
−0.821891 + 0.569645i \(0.807081\pi\)
\(920\) −20993.0 −0.752301
\(921\) −13087.9 −0.468252
\(922\) 28328.7 1.01188
\(923\) 9279.22 0.330909
\(924\) 3508.40 0.124911
\(925\) 38466.5 1.36732
\(926\) −18614.0 −0.660578
\(927\) −4221.20 −0.149560
\(928\) 31162.0 1.10231
\(929\) −43137.0 −1.52344 −0.761721 0.647905i \(-0.775646\pi\)
−0.761721 + 0.647905i \(0.775646\pi\)
\(930\) −4930.44 −0.173844
\(931\) −1777.20 −0.0625621
\(932\) −1852.88 −0.0651214
\(933\) −10627.0 −0.372896
\(934\) 21071.4 0.738197
\(935\) −8117.69 −0.283932
\(936\) −13624.4 −0.475777
\(937\) 20420.6 0.711966 0.355983 0.934492i \(-0.384146\pi\)
0.355983 + 0.934492i \(0.384146\pi\)
\(938\) 9253.44 0.322106
\(939\) −5425.94 −0.188572
\(940\) 15986.1 0.554689
\(941\) −21235.7 −0.735668 −0.367834 0.929892i \(-0.619900\pi\)
−0.367834 + 0.929892i \(0.619900\pi\)
\(942\) 6579.49 0.227571
\(943\) −27018.3 −0.933020
\(944\) 99.6303 0.00343505
\(945\) −3041.02 −0.104682
\(946\) 5294.82 0.181976
\(947\) −21631.9 −0.742283 −0.371141 0.928576i \(-0.621034\pi\)
−0.371141 + 0.928576i \(0.621034\pi\)
\(948\) 2773.12 0.0950070
\(949\) −36444.1 −1.24660
\(950\) 16792.0 0.573478
\(951\) 906.234 0.0309008
\(952\) 40271.5 1.37102
\(953\) 869.752 0.0295635 0.0147818 0.999891i \(-0.495295\pi\)
0.0147818 + 0.999891i \(0.495295\pi\)
\(954\) −6358.51 −0.215791
\(955\) −5734.99 −0.194324
\(956\) 19735.5 0.667668
\(957\) −6949.03 −0.234723
\(958\) 16988.3 0.572929
\(959\) 15286.4 0.514726
\(960\) 6206.44 0.208658
\(961\) −7705.09 −0.258638
\(962\) −52583.6 −1.76233
\(963\) −11135.0 −0.372605
\(964\) −22176.7 −0.740937
\(965\) −11651.0 −0.388661
\(966\) −14221.7 −0.473682
\(967\) 45869.5 1.52540 0.762700 0.646752i \(-0.223873\pi\)
0.762700 + 0.646752i \(0.223873\pi\)
\(968\) −26298.3 −0.873200
\(969\) −32164.0 −1.06631
\(970\) −16456.6 −0.544733
\(971\) 4456.05 0.147272 0.0736361 0.997285i \(-0.476540\pi\)
0.0736361 + 0.997285i \(0.476540\pi\)
\(972\) −1178.40 −0.0388859
\(973\) 25145.0 0.828481
\(974\) −19894.6 −0.654481
\(975\) 17160.9 0.563680
\(976\) −1331.38 −0.0436642
\(977\) −34528.0 −1.13065 −0.565326 0.824867i \(-0.691250\pi\)
−0.565326 + 0.824867i \(0.691250\pi\)
\(978\) −19513.6 −0.638013
\(979\) 17232.7 0.562575
\(980\) 489.159 0.0159445
\(981\) 19306.1 0.628334
\(982\) −13703.3 −0.445307
\(983\) 17284.8 0.560834 0.280417 0.959878i \(-0.409527\pi\)
0.280417 + 0.959878i \(0.409527\pi\)
\(984\) 12513.4 0.405399
\(985\) −2968.80 −0.0960344
\(986\) −30103.5 −0.972303
\(987\) 28695.7 0.925425
\(988\) 35331.2 1.13769
\(989\) 33035.7 1.06216
\(990\) −1327.71 −0.0426237
\(991\) −49628.1 −1.59081 −0.795403 0.606081i \(-0.792741\pi\)
−0.795403 + 0.606081i \(0.792741\pi\)
\(992\) −26670.7 −0.853625
\(993\) −12399.5 −0.396260
\(994\) −4486.04 −0.143148
\(995\) 25943.4 0.826594
\(996\) −5973.71 −0.190045
\(997\) −1153.92 −0.0366549 −0.0183274 0.999832i \(-0.505834\pi\)
−0.0183274 + 0.999832i \(0.505834\pi\)
\(998\) 6531.53 0.207166
\(999\) −12051.0 −0.381657
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 177.4.a.a.1.4 7
3.2 odd 2 531.4.a.d.1.4 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.4.a.a.1.4 7 1.1 even 1 trivial
531.4.a.d.1.4 7 3.2 odd 2