Properties

Label 105.4.a.g.1.2
Level 105
Weight 4
Character 105.1
Self dual yes
Analytic conductor 6.195
Analytic rank 0
Dimension 2
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 105.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(6.19520055060\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{41}) \)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(3.70156\) of \(x^{2} - x - 10\)
Character \(\chi\) \(=\) 105.1

$q$-expansion

\(f(q)\) \(=\) \(q+4.70156 q^{2} +3.00000 q^{3} +14.1047 q^{4} -5.00000 q^{5} +14.1047 q^{6} +7.00000 q^{7} +28.7016 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q+4.70156 q^{2} +3.00000 q^{3} +14.1047 q^{4} -5.00000 q^{5} +14.1047 q^{6} +7.00000 q^{7} +28.7016 q^{8} +9.00000 q^{9} -23.5078 q^{10} +24.5969 q^{11} +42.3141 q^{12} -35.0156 q^{13} +32.9109 q^{14} -15.0000 q^{15} +22.1047 q^{16} -18.4187 q^{17} +42.3141 q^{18} -67.4031 q^{19} -70.5234 q^{20} +21.0000 q^{21} +115.644 q^{22} -145.675 q^{23} +86.1047 q^{24} +25.0000 q^{25} -164.628 q^{26} +27.0000 q^{27} +98.7328 q^{28} +214.419 q^{29} -70.5234 q^{30} -88.6594 q^{31} -125.686 q^{32} +73.7906 q^{33} -86.5969 q^{34} -35.0000 q^{35} +126.942 q^{36} +162.125 q^{37} -316.900 q^{38} -105.047 q^{39} -143.508 q^{40} -337.769 q^{41} +98.7328 q^{42} +122.156 q^{43} +346.931 q^{44} -45.0000 q^{45} -684.900 q^{46} +354.219 q^{47} +66.3141 q^{48} +49.0000 q^{49} +117.539 q^{50} -55.2562 q^{51} -493.884 q^{52} +676.691 q^{53} +126.942 q^{54} -122.984 q^{55} +200.911 q^{56} -202.209 q^{57} +1008.10 q^{58} +501.319 q^{59} -211.570 q^{60} -708.931 q^{61} -416.837 q^{62} +63.0000 q^{63} -767.758 q^{64} +175.078 q^{65} +346.931 q^{66} -907.956 q^{67} -259.791 q^{68} -437.025 q^{69} -164.555 q^{70} +430.334 q^{71} +258.314 q^{72} +41.3406 q^{73} +762.241 q^{74} +75.0000 q^{75} -950.700 q^{76} +172.178 q^{77} -493.884 q^{78} +890.388 q^{79} -110.523 q^{80} +81.0000 q^{81} -1588.04 q^{82} -1057.15 q^{83} +296.198 q^{84} +92.0937 q^{85} +574.325 q^{86} +643.256 q^{87} +705.969 q^{88} +1473.72 q^{89} -211.570 q^{90} -245.109 q^{91} -2054.70 q^{92} -265.978 q^{93} +1665.38 q^{94} +337.016 q^{95} -377.058 q^{96} +555.034 q^{97} +230.377 q^{98} +221.372 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 3q^{2} + 6q^{3} + 9q^{4} - 10q^{5} + 9q^{6} + 14q^{7} + 51q^{8} + 18q^{9} + O(q^{10}) \) \( 2q + 3q^{2} + 6q^{3} + 9q^{4} - 10q^{5} + 9q^{6} + 14q^{7} + 51q^{8} + 18q^{9} - 15q^{10} + 62q^{11} + 27q^{12} - 6q^{13} + 21q^{14} - 30q^{15} + 25q^{16} + 40q^{17} + 27q^{18} - 122q^{19} - 45q^{20} + 42q^{21} + 52q^{22} + 16q^{23} + 153q^{24} + 50q^{25} - 214q^{26} + 54q^{27} + 63q^{28} + 352q^{29} - 45q^{30} + 66q^{31} - 309q^{32} + 186q^{33} - 186q^{34} - 70q^{35} + 81q^{36} - 188q^{37} - 224q^{38} - 18q^{39} - 255q^{40} + 16q^{41} + 63q^{42} - 396q^{43} + 156q^{44} - 90q^{45} - 960q^{46} - 188q^{47} + 75q^{48} + 98q^{49} + 75q^{50} + 120q^{51} - 642q^{52} + 982q^{53} + 81q^{54} - 310q^{55} + 357q^{56} - 366q^{57} + 774q^{58} + 516q^{59} - 135q^{60} - 880q^{61} - 680q^{62} + 126q^{63} - 479q^{64} + 30q^{65} + 156q^{66} - 356q^{67} - 558q^{68} + 48q^{69} - 105q^{70} + 310q^{71} + 459q^{72} + 326q^{73} + 1358q^{74} + 150q^{75} - 672q^{76} + 434q^{77} - 642q^{78} + 1832q^{79} - 125q^{80} + 162q^{81} - 2190q^{82} - 680q^{83} + 189q^{84} - 200q^{85} + 1456q^{86} + 1056q^{87} + 1540q^{88} + 796q^{89} - 135q^{90} - 42q^{91} - 2880q^{92} + 198q^{93} + 2588q^{94} + 610q^{95} - 927q^{96} - 670q^{97} + 147q^{98} + 558q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.70156 1.66225 0.831127 0.556083i \(-0.187696\pi\)
0.831127 + 0.556083i \(0.187696\pi\)
\(3\) 3.00000 0.577350
\(4\) 14.1047 1.76309
\(5\) −5.00000 −0.447214
\(6\) 14.1047 0.959702
\(7\) 7.00000 0.377964
\(8\) 28.7016 1.26844
\(9\) 9.00000 0.333333
\(10\) −23.5078 −0.743382
\(11\) 24.5969 0.674203 0.337102 0.941468i \(-0.390553\pi\)
0.337102 + 0.941468i \(0.390553\pi\)
\(12\) 42.3141 1.01792
\(13\) −35.0156 −0.747045 −0.373523 0.927621i \(-0.621850\pi\)
−0.373523 + 0.927621i \(0.621850\pi\)
\(14\) 32.9109 0.628273
\(15\) −15.0000 −0.258199
\(16\) 22.1047 0.345386
\(17\) −18.4187 −0.262777 −0.131388 0.991331i \(-0.541943\pi\)
−0.131388 + 0.991331i \(0.541943\pi\)
\(18\) 42.3141 0.554084
\(19\) −67.4031 −0.813860 −0.406930 0.913459i \(-0.633401\pi\)
−0.406930 + 0.913459i \(0.633401\pi\)
\(20\) −70.5234 −0.788476
\(21\) 21.0000 0.218218
\(22\) 115.644 1.12070
\(23\) −145.675 −1.32067 −0.660333 0.750973i \(-0.729585\pi\)
−0.660333 + 0.750973i \(0.729585\pi\)
\(24\) 86.1047 0.732335
\(25\) 25.0000 0.200000
\(26\) −164.628 −1.24178
\(27\) 27.0000 0.192450
\(28\) 98.7328 0.666384
\(29\) 214.419 1.37298 0.686492 0.727137i \(-0.259149\pi\)
0.686492 + 0.727137i \(0.259149\pi\)
\(30\) −70.5234 −0.429192
\(31\) −88.6594 −0.513667 −0.256834 0.966456i \(-0.582679\pi\)
−0.256834 + 0.966456i \(0.582679\pi\)
\(32\) −125.686 −0.694323
\(33\) 73.7906 0.389251
\(34\) −86.5969 −0.436801
\(35\) −35.0000 −0.169031
\(36\) 126.942 0.587695
\(37\) 162.125 0.720356 0.360178 0.932884i \(-0.382716\pi\)
0.360178 + 0.932884i \(0.382716\pi\)
\(38\) −316.900 −1.35284
\(39\) −105.047 −0.431307
\(40\) −143.508 −0.567264
\(41\) −337.769 −1.28660 −0.643300 0.765614i \(-0.722435\pi\)
−0.643300 + 0.765614i \(0.722435\pi\)
\(42\) 98.7328 0.362733
\(43\) 122.156 0.433224 0.216612 0.976258i \(-0.430499\pi\)
0.216612 + 0.976258i \(0.430499\pi\)
\(44\) 346.931 1.18868
\(45\) −45.0000 −0.149071
\(46\) −684.900 −2.19528
\(47\) 354.219 1.09932 0.549661 0.835388i \(-0.314757\pi\)
0.549661 + 0.835388i \(0.314757\pi\)
\(48\) 66.3141 0.199409
\(49\) 49.0000 0.142857
\(50\) 117.539 0.332451
\(51\) −55.2562 −0.151714
\(52\) −493.884 −1.31710
\(53\) 676.691 1.75378 0.876892 0.480687i \(-0.159613\pi\)
0.876892 + 0.480687i \(0.159613\pi\)
\(54\) 126.942 0.319901
\(55\) −122.984 −0.301513
\(56\) 200.911 0.479426
\(57\) −202.209 −0.469882
\(58\) 1008.10 2.28225
\(59\) 501.319 1.10621 0.553103 0.833113i \(-0.313444\pi\)
0.553103 + 0.833113i \(0.313444\pi\)
\(60\) −211.570 −0.455227
\(61\) −708.931 −1.48802 −0.744011 0.668167i \(-0.767079\pi\)
−0.744011 + 0.668167i \(0.767079\pi\)
\(62\) −416.837 −0.853845
\(63\) 63.0000 0.125988
\(64\) −767.758 −1.49953
\(65\) 175.078 0.334089
\(66\) 346.931 0.647035
\(67\) −907.956 −1.65559 −0.827795 0.561031i \(-0.810405\pi\)
−0.827795 + 0.561031i \(0.810405\pi\)
\(68\) −259.791 −0.463298
\(69\) −437.025 −0.762487
\(70\) −164.555 −0.280972
\(71\) 430.334 0.719314 0.359657 0.933085i \(-0.382894\pi\)
0.359657 + 0.933085i \(0.382894\pi\)
\(72\) 258.314 0.422814
\(73\) 41.3406 0.0662816 0.0331408 0.999451i \(-0.489449\pi\)
0.0331408 + 0.999451i \(0.489449\pi\)
\(74\) 762.241 1.19741
\(75\) 75.0000 0.115470
\(76\) −950.700 −1.43490
\(77\) 172.178 0.254825
\(78\) −493.884 −0.716941
\(79\) 890.388 1.26806 0.634028 0.773310i \(-0.281400\pi\)
0.634028 + 0.773310i \(0.281400\pi\)
\(80\) −110.523 −0.154461
\(81\) 81.0000 0.111111
\(82\) −1588.04 −2.13866
\(83\) −1057.15 −1.39804 −0.699020 0.715102i \(-0.746380\pi\)
−0.699020 + 0.715102i \(0.746380\pi\)
\(84\) 296.198 0.384737
\(85\) 92.0937 0.117517
\(86\) 574.325 0.720129
\(87\) 643.256 0.792693
\(88\) 705.969 0.855188
\(89\) 1473.72 1.75522 0.877610 0.479376i \(-0.159137\pi\)
0.877610 + 0.479376i \(0.159137\pi\)
\(90\) −211.570 −0.247794
\(91\) −245.109 −0.282356
\(92\) −2054.70 −2.32845
\(93\) −265.978 −0.296566
\(94\) 1665.38 1.82735
\(95\) 337.016 0.363969
\(96\) −377.058 −0.400868
\(97\) 555.034 0.580981 0.290491 0.956878i \(-0.406181\pi\)
0.290491 + 0.956878i \(0.406181\pi\)
\(98\) 230.377 0.237465
\(99\) 221.372 0.224734
\(100\) 352.617 0.352617
\(101\) 1890.14 1.86214 0.931071 0.364838i \(-0.118876\pi\)
0.931071 + 0.364838i \(0.118876\pi\)
\(102\) −259.791 −0.252187
\(103\) 662.700 0.633959 0.316979 0.948432i \(-0.397331\pi\)
0.316979 + 0.948432i \(0.397331\pi\)
\(104\) −1005.00 −0.947583
\(105\) −105.000 −0.0975900
\(106\) 3181.50 2.91523
\(107\) 1614.53 1.45872 0.729358 0.684132i \(-0.239819\pi\)
0.729358 + 0.684132i \(0.239819\pi\)
\(108\) 380.827 0.339306
\(109\) 217.206 0.190868 0.0954339 0.995436i \(-0.469576\pi\)
0.0954339 + 0.995436i \(0.469576\pi\)
\(110\) −578.219 −0.501191
\(111\) 486.375 0.415898
\(112\) 154.733 0.130544
\(113\) −1658.20 −1.38044 −0.690221 0.723598i \(-0.742487\pi\)
−0.690221 + 0.723598i \(0.742487\pi\)
\(114\) −950.700 −0.781063
\(115\) 728.375 0.590620
\(116\) 3024.31 2.42069
\(117\) −315.141 −0.249015
\(118\) 2356.98 1.83879
\(119\) −128.931 −0.0993202
\(120\) −430.523 −0.327510
\(121\) −725.994 −0.545450
\(122\) −3333.08 −2.47347
\(123\) −1013.31 −0.742819
\(124\) −1250.51 −0.905640
\(125\) −125.000 −0.0894427
\(126\) 296.198 0.209424
\(127\) −1108.81 −0.774734 −0.387367 0.921926i \(-0.626615\pi\)
−0.387367 + 0.921926i \(0.626615\pi\)
\(128\) −2604.17 −1.79827
\(129\) 366.469 0.250122
\(130\) 823.141 0.555340
\(131\) 185.488 0.123711 0.0618554 0.998085i \(-0.480298\pi\)
0.0618554 + 0.998085i \(0.480298\pi\)
\(132\) 1040.79 0.686284
\(133\) −471.822 −0.307610
\(134\) −4268.81 −2.75201
\(135\) −135.000 −0.0860663
\(136\) −528.647 −0.333317
\(137\) −37.9907 −0.0236917 −0.0118458 0.999930i \(-0.503771\pi\)
−0.0118458 + 0.999930i \(0.503771\pi\)
\(138\) −2054.70 −1.26745
\(139\) 183.609 0.112040 0.0560199 0.998430i \(-0.482159\pi\)
0.0560199 + 0.998430i \(0.482159\pi\)
\(140\) −493.664 −0.298016
\(141\) 1062.66 0.634694
\(142\) 2023.24 1.19568
\(143\) −861.275 −0.503660
\(144\) 198.942 0.115129
\(145\) −1072.09 −0.614018
\(146\) 194.366 0.110177
\(147\) 147.000 0.0824786
\(148\) 2286.72 1.27005
\(149\) −1383.34 −0.760587 −0.380293 0.924866i \(-0.624177\pi\)
−0.380293 + 0.924866i \(0.624177\pi\)
\(150\) 352.617 0.191940
\(151\) 765.256 0.412422 0.206211 0.978508i \(-0.433887\pi\)
0.206211 + 0.978508i \(0.433887\pi\)
\(152\) −1934.57 −1.03233
\(153\) −165.769 −0.0875922
\(154\) 809.506 0.423584
\(155\) 443.297 0.229719
\(156\) −1481.65 −0.760431
\(157\) −2366.76 −1.20311 −0.601554 0.798832i \(-0.705452\pi\)
−0.601554 + 0.798832i \(0.705452\pi\)
\(158\) 4186.21 2.10783
\(159\) 2030.07 1.01255
\(160\) 628.430 0.310511
\(161\) −1019.72 −0.499165
\(162\) 380.827 0.184695
\(163\) −3137.69 −1.50775 −0.753875 0.657018i \(-0.771817\pi\)
−0.753875 + 0.657018i \(0.771817\pi\)
\(164\) −4764.12 −2.26839
\(165\) −368.953 −0.174079
\(166\) −4970.26 −2.32390
\(167\) 146.469 0.0678688 0.0339344 0.999424i \(-0.489196\pi\)
0.0339344 + 0.999424i \(0.489196\pi\)
\(168\) 602.733 0.276797
\(169\) −970.906 −0.441924
\(170\) 432.984 0.195343
\(171\) −606.628 −0.271287
\(172\) 1722.98 0.763812
\(173\) −1424.12 −0.625860 −0.312930 0.949776i \(-0.601311\pi\)
−0.312930 + 0.949776i \(0.601311\pi\)
\(174\) 3024.31 1.31766
\(175\) 175.000 0.0755929
\(176\) 543.706 0.232860
\(177\) 1503.96 0.638668
\(178\) 6928.81 2.91762
\(179\) 1244.70 0.519737 0.259869 0.965644i \(-0.416321\pi\)
0.259869 + 0.965644i \(0.416321\pi\)
\(180\) −634.711 −0.262825
\(181\) −3879.09 −1.59299 −0.796493 0.604648i \(-0.793314\pi\)
−0.796493 + 0.604648i \(0.793314\pi\)
\(182\) −1152.40 −0.469348
\(183\) −2126.79 −0.859110
\(184\) −4181.10 −1.67519
\(185\) −810.625 −0.322153
\(186\) −1250.51 −0.492968
\(187\) −453.044 −0.177165
\(188\) 4996.14 1.93820
\(189\) 189.000 0.0727393
\(190\) 1584.50 0.605009
\(191\) 1574.90 0.596628 0.298314 0.954468i \(-0.403576\pi\)
0.298314 + 0.954468i \(0.403576\pi\)
\(192\) −2303.27 −0.865752
\(193\) −4775.67 −1.78114 −0.890572 0.454843i \(-0.849695\pi\)
−0.890572 + 0.454843i \(0.849695\pi\)
\(194\) 2609.53 0.965738
\(195\) 525.234 0.192886
\(196\) 691.130 0.251869
\(197\) −2803.58 −1.01394 −0.506971 0.861963i \(-0.669235\pi\)
−0.506971 + 0.861963i \(0.669235\pi\)
\(198\) 1040.79 0.373566
\(199\) 4102.92 1.46155 0.730774 0.682620i \(-0.239159\pi\)
0.730774 + 0.682620i \(0.239159\pi\)
\(200\) 717.539 0.253688
\(201\) −2723.87 −0.955855
\(202\) 8886.63 3.09535
\(203\) 1500.93 0.518940
\(204\) −779.372 −0.267485
\(205\) 1688.84 0.575385
\(206\) 3115.72 1.05380
\(207\) −1311.07 −0.440222
\(208\) −774.009 −0.258019
\(209\) −1657.91 −0.548707
\(210\) −493.664 −0.162219
\(211\) −823.512 −0.268687 −0.134343 0.990935i \(-0.542893\pi\)
−0.134343 + 0.990935i \(0.542893\pi\)
\(212\) 9544.51 3.09207
\(213\) 1291.00 0.415296
\(214\) 7590.82 2.42476
\(215\) −610.781 −0.193744
\(216\) 774.942 0.244112
\(217\) −620.616 −0.194148
\(218\) 1021.21 0.317271
\(219\) 124.022 0.0382677
\(220\) −1734.66 −0.531593
\(221\) 644.944 0.196306
\(222\) 2286.72 0.691328
\(223\) 817.194 0.245396 0.122698 0.992444i \(-0.460845\pi\)
0.122698 + 0.992444i \(0.460845\pi\)
\(224\) −879.802 −0.262430
\(225\) 225.000 0.0666667
\(226\) −7796.12 −2.29465
\(227\) 3655.85 1.06893 0.534465 0.845190i \(-0.320513\pi\)
0.534465 + 0.845190i \(0.320513\pi\)
\(228\) −2852.10 −0.828443
\(229\) 939.393 0.271078 0.135539 0.990772i \(-0.456723\pi\)
0.135539 + 0.990772i \(0.456723\pi\)
\(230\) 3424.50 0.981760
\(231\) 516.534 0.147123
\(232\) 6154.15 1.74155
\(233\) −7.64701 −0.00215010 −0.00107505 0.999999i \(-0.500342\pi\)
−0.00107505 + 0.999999i \(0.500342\pi\)
\(234\) −1481.65 −0.413926
\(235\) −1771.09 −0.491631
\(236\) 7070.94 1.95034
\(237\) 2671.16 0.732112
\(238\) −606.178 −0.165095
\(239\) −889.115 −0.240636 −0.120318 0.992735i \(-0.538391\pi\)
−0.120318 + 0.992735i \(0.538391\pi\)
\(240\) −331.570 −0.0891782
\(241\) 2140.23 0.572051 0.286026 0.958222i \(-0.407666\pi\)
0.286026 + 0.958222i \(0.407666\pi\)
\(242\) −3413.30 −0.906676
\(243\) 243.000 0.0641500
\(244\) −9999.25 −2.62351
\(245\) −245.000 −0.0638877
\(246\) −4764.12 −1.23475
\(247\) 2360.16 0.607990
\(248\) −2544.66 −0.651557
\(249\) −3171.45 −0.807158
\(250\) −587.695 −0.148676
\(251\) −6749.81 −1.69739 −0.848693 0.528886i \(-0.822610\pi\)
−0.848693 + 0.528886i \(0.822610\pi\)
\(252\) 888.595 0.222128
\(253\) −3583.15 −0.890398
\(254\) −5213.15 −1.28780
\(255\) 276.281 0.0678486
\(256\) −6101.62 −1.48965
\(257\) 3068.64 0.744811 0.372405 0.928070i \(-0.378533\pi\)
0.372405 + 0.928070i \(0.378533\pi\)
\(258\) 1722.98 0.415766
\(259\) 1134.87 0.272269
\(260\) 2469.42 0.589027
\(261\) 1929.77 0.457662
\(262\) 872.081 0.205639
\(263\) −4674.12 −1.09589 −0.547944 0.836515i \(-0.684589\pi\)
−0.547944 + 0.836515i \(0.684589\pi\)
\(264\) 2117.91 0.493743
\(265\) −3383.45 −0.784316
\(266\) −2218.30 −0.511326
\(267\) 4421.17 1.01338
\(268\) −12806.4 −2.91895
\(269\) 2417.38 0.547919 0.273960 0.961741i \(-0.411667\pi\)
0.273960 + 0.961741i \(0.411667\pi\)
\(270\) −634.711 −0.143064
\(271\) 7724.30 1.73143 0.865715 0.500537i \(-0.166864\pi\)
0.865715 + 0.500537i \(0.166864\pi\)
\(272\) −407.141 −0.0907593
\(273\) −735.328 −0.163019
\(274\) −178.616 −0.0393816
\(275\) 614.922 0.134841
\(276\) −6164.10 −1.34433
\(277\) −4576.17 −0.992620 −0.496310 0.868145i \(-0.665312\pi\)
−0.496310 + 0.868145i \(0.665312\pi\)
\(278\) 863.250 0.186239
\(279\) −797.934 −0.171222
\(280\) −1004.55 −0.214406
\(281\) −1358.56 −0.288415 −0.144208 0.989547i \(-0.546063\pi\)
−0.144208 + 0.989547i \(0.546063\pi\)
\(282\) 4996.14 1.05502
\(283\) 3885.04 0.816048 0.408024 0.912971i \(-0.366218\pi\)
0.408024 + 0.912971i \(0.366218\pi\)
\(284\) 6069.73 1.26821
\(285\) 1011.05 0.210138
\(286\) −4049.34 −0.837211
\(287\) −2364.38 −0.486289
\(288\) −1131.17 −0.231441
\(289\) −4573.75 −0.930948
\(290\) −5040.52 −1.02065
\(291\) 1665.10 0.335430
\(292\) 583.097 0.116860
\(293\) −4033.91 −0.804312 −0.402156 0.915571i \(-0.631739\pi\)
−0.402156 + 0.915571i \(0.631739\pi\)
\(294\) 691.130 0.137100
\(295\) −2506.59 −0.494710
\(296\) 4653.24 0.913730
\(297\) 664.116 0.129750
\(298\) −6503.85 −1.26429
\(299\) 5100.90 0.986598
\(300\) 1057.85 0.203584
\(301\) 855.093 0.163743
\(302\) 3597.90 0.685549
\(303\) 5670.43 1.07511
\(304\) −1489.92 −0.281096
\(305\) 3544.66 0.665464
\(306\) −779.372 −0.145600
\(307\) −4620.36 −0.858950 −0.429475 0.903079i \(-0.641301\pi\)
−0.429475 + 0.903079i \(0.641301\pi\)
\(308\) 2428.52 0.449278
\(309\) 1988.10 0.366016
\(310\) 2084.19 0.381851
\(311\) 6675.89 1.21722 0.608609 0.793470i \(-0.291728\pi\)
0.608609 + 0.793470i \(0.291728\pi\)
\(312\) −3015.01 −0.547087
\(313\) 2836.78 0.512283 0.256141 0.966639i \(-0.417549\pi\)
0.256141 + 0.966639i \(0.417549\pi\)
\(314\) −11127.5 −1.99987
\(315\) −315.000 −0.0563436
\(316\) 12558.6 2.23569
\(317\) 4010.63 0.710597 0.355299 0.934753i \(-0.384379\pi\)
0.355299 + 0.934753i \(0.384379\pi\)
\(318\) 9544.51 1.68311
\(319\) 5274.03 0.925671
\(320\) 3838.79 0.670609
\(321\) 4843.59 0.842190
\(322\) −4794.30 −0.829739
\(323\) 1241.48 0.213863
\(324\) 1142.48 0.195898
\(325\) −875.391 −0.149409
\(326\) −14752.1 −2.50626
\(327\) 651.619 0.110198
\(328\) −9694.49 −1.63198
\(329\) 2479.53 0.415504
\(330\) −1734.66 −0.289363
\(331\) 11087.5 1.84117 0.920583 0.390546i \(-0.127714\pi\)
0.920583 + 0.390546i \(0.127714\pi\)
\(332\) −14910.8 −2.46486
\(333\) 1459.12 0.240119
\(334\) 688.631 0.112815
\(335\) 4539.78 0.740402
\(336\) 464.198 0.0753693
\(337\) 12118.7 1.95890 0.979450 0.201689i \(-0.0646431\pi\)
0.979450 + 0.201689i \(0.0646431\pi\)
\(338\) −4564.78 −0.734589
\(339\) −4974.59 −0.796999
\(340\) 1298.95 0.207193
\(341\) −2180.74 −0.346316
\(342\) −2852.10 −0.450947
\(343\) 343.000 0.0539949
\(344\) 3506.07 0.549520
\(345\) 2185.12 0.340995
\(346\) −6695.58 −1.04034
\(347\) −6361.22 −0.984116 −0.492058 0.870562i \(-0.663755\pi\)
−0.492058 + 0.870562i \(0.663755\pi\)
\(348\) 9072.93 1.39759
\(349\) −3115.18 −0.477799 −0.238899 0.971044i \(-0.576787\pi\)
−0.238899 + 0.971044i \(0.576787\pi\)
\(350\) 822.773 0.125655
\(351\) −945.422 −0.143769
\(352\) −3091.48 −0.468115
\(353\) −11927.4 −1.79839 −0.899194 0.437550i \(-0.855846\pi\)
−0.899194 + 0.437550i \(0.855846\pi\)
\(354\) 7070.94 1.06163
\(355\) −2151.67 −0.321687
\(356\) 20786.4 3.09460
\(357\) −386.794 −0.0573426
\(358\) 5852.02 0.863935
\(359\) −6143.95 −0.903245 −0.451623 0.892209i \(-0.649155\pi\)
−0.451623 + 0.892209i \(0.649155\pi\)
\(360\) −1291.57 −0.189088
\(361\) −2315.82 −0.337632
\(362\) −18237.8 −2.64794
\(363\) −2177.98 −0.314916
\(364\) −3457.19 −0.497819
\(365\) −206.703 −0.0296420
\(366\) −9999.25 −1.42806
\(367\) −1927.67 −0.274178 −0.137089 0.990559i \(-0.543775\pi\)
−0.137089 + 0.990559i \(0.543775\pi\)
\(368\) −3220.10 −0.456139
\(369\) −3039.92 −0.428867
\(370\) −3811.20 −0.535500
\(371\) 4736.83 0.662868
\(372\) −3751.54 −0.522871
\(373\) 10452.0 1.45090 0.725449 0.688276i \(-0.241632\pi\)
0.725449 + 0.688276i \(0.241632\pi\)
\(374\) −2130.01 −0.294493
\(375\) −375.000 −0.0516398
\(376\) 10166.6 1.39443
\(377\) −7508.01 −1.02568
\(378\) 888.595 0.120911
\(379\) 7066.43 0.957726 0.478863 0.877890i \(-0.341049\pi\)
0.478863 + 0.877890i \(0.341049\pi\)
\(380\) 4753.50 0.641709
\(381\) −3326.44 −0.447293
\(382\) 7404.51 0.991747
\(383\) 7168.04 0.956318 0.478159 0.878273i \(-0.341304\pi\)
0.478159 + 0.878273i \(0.341304\pi\)
\(384\) −7812.52 −1.03823
\(385\) −860.891 −0.113961
\(386\) −22453.1 −2.96071
\(387\) 1099.41 0.144408
\(388\) 7828.58 1.02432
\(389\) −7414.06 −0.966344 −0.483172 0.875525i \(-0.660515\pi\)
−0.483172 + 0.875525i \(0.660515\pi\)
\(390\) 2469.42 0.320626
\(391\) 2683.15 0.347040
\(392\) 1406.38 0.181206
\(393\) 556.463 0.0714245
\(394\) −13181.2 −1.68543
\(395\) −4451.94 −0.567092
\(396\) 3122.38 0.396226
\(397\) −8936.01 −1.12969 −0.564843 0.825198i \(-0.691063\pi\)
−0.564843 + 0.825198i \(0.691063\pi\)
\(398\) 19290.1 2.42946
\(399\) −1415.47 −0.177599
\(400\) 552.617 0.0690771
\(401\) 1782.91 0.222031 0.111015 0.993819i \(-0.464590\pi\)
0.111015 + 0.993819i \(0.464590\pi\)
\(402\) −12806.4 −1.58887
\(403\) 3104.46 0.383733
\(404\) 26659.9 3.28312
\(405\) −405.000 −0.0496904
\(406\) 7056.72 0.862609
\(407\) 3987.77 0.485667
\(408\) −1585.94 −0.192441
\(409\) −8759.92 −1.05905 −0.529524 0.848295i \(-0.677629\pi\)
−0.529524 + 0.848295i \(0.677629\pi\)
\(410\) 7940.20 0.956436
\(411\) −113.972 −0.0136784
\(412\) 9347.17 1.11772
\(413\) 3509.23 0.418106
\(414\) −6164.10 −0.731761
\(415\) 5285.75 0.625222
\(416\) 4400.97 0.518691
\(417\) 550.828 0.0646862
\(418\) −7794.75 −0.912090
\(419\) −3212.74 −0.374588 −0.187294 0.982304i \(-0.559972\pi\)
−0.187294 + 0.982304i \(0.559972\pi\)
\(420\) −1480.99 −0.172060
\(421\) 15757.8 1.82420 0.912101 0.409965i \(-0.134459\pi\)
0.912101 + 0.409965i \(0.134459\pi\)
\(422\) −3871.79 −0.446626
\(423\) 3187.97 0.366440
\(424\) 19422.1 2.22457
\(425\) −460.469 −0.0525553
\(426\) 6069.73 0.690327
\(427\) −4962.52 −0.562419
\(428\) 22772.5 2.57184
\(429\) −2583.82 −0.290788
\(430\) −2871.63 −0.322051
\(431\) −405.917 −0.0453650 −0.0226825 0.999743i \(-0.507221\pi\)
−0.0226825 + 0.999743i \(0.507221\pi\)
\(432\) 596.827 0.0664695
\(433\) −7845.25 −0.870713 −0.435357 0.900258i \(-0.643378\pi\)
−0.435357 + 0.900258i \(0.643378\pi\)
\(434\) −2917.86 −0.322723
\(435\) −3216.28 −0.354503
\(436\) 3063.63 0.336516
\(437\) 9818.95 1.07484
\(438\) 583.097 0.0636106
\(439\) 423.029 0.0459911 0.0229955 0.999736i \(-0.492680\pi\)
0.0229955 + 0.999736i \(0.492680\pi\)
\(440\) −3529.84 −0.382452
\(441\) 441.000 0.0476190
\(442\) 3032.24 0.326310
\(443\) −16058.7 −1.72229 −0.861143 0.508362i \(-0.830251\pi\)
−0.861143 + 0.508362i \(0.830251\pi\)
\(444\) 6860.17 0.733264
\(445\) −7368.62 −0.784958
\(446\) 3842.09 0.407911
\(447\) −4150.01 −0.439125
\(448\) −5374.30 −0.566768
\(449\) 2186.75 0.229842 0.114921 0.993375i \(-0.463338\pi\)
0.114921 + 0.993375i \(0.463338\pi\)
\(450\) 1057.85 0.110817
\(451\) −8308.05 −0.867430
\(452\) −23388.3 −2.43384
\(453\) 2295.77 0.238112
\(454\) 17188.2 1.77683
\(455\) 1225.55 0.126274
\(456\) −5803.72 −0.596018
\(457\) −5799.22 −0.593602 −0.296801 0.954939i \(-0.595920\pi\)
−0.296801 + 0.954939i \(0.595920\pi\)
\(458\) 4416.62 0.450600
\(459\) −497.306 −0.0505714
\(460\) 10273.5 1.04131
\(461\) 9873.35 0.997500 0.498750 0.866746i \(-0.333793\pi\)
0.498750 + 0.866746i \(0.333793\pi\)
\(462\) 2428.52 0.244556
\(463\) −6181.84 −0.620506 −0.310253 0.950654i \(-0.600414\pi\)
−0.310253 + 0.950654i \(0.600414\pi\)
\(464\) 4739.66 0.474209
\(465\) 1329.89 0.132628
\(466\) −35.9529 −0.00357400
\(467\) 6145.50 0.608950 0.304475 0.952520i \(-0.401519\pi\)
0.304475 + 0.952520i \(0.401519\pi\)
\(468\) −4444.96 −0.439035
\(469\) −6355.69 −0.625754
\(470\) −8326.91 −0.817216
\(471\) −7100.28 −0.694615
\(472\) 14388.6 1.40316
\(473\) 3004.66 0.292081
\(474\) 12558.6 1.21696
\(475\) −1685.08 −0.162772
\(476\) −1818.53 −0.175110
\(477\) 6090.22 0.584595
\(478\) −4180.23 −0.399999
\(479\) 10879.4 1.03777 0.518887 0.854843i \(-0.326347\pi\)
0.518887 + 0.854843i \(0.326347\pi\)
\(480\) 1885.29 0.179274
\(481\) −5676.91 −0.538139
\(482\) 10062.4 0.950894
\(483\) −3059.17 −0.288193
\(484\) −10239.9 −0.961675
\(485\) −2775.17 −0.259823
\(486\) 1142.48 0.106634
\(487\) 8087.51 0.752526 0.376263 0.926513i \(-0.377209\pi\)
0.376263 + 0.926513i \(0.377209\pi\)
\(488\) −20347.4 −1.88747
\(489\) −9413.08 −0.870499
\(490\) −1151.88 −0.106197
\(491\) −6959.90 −0.639707 −0.319853 0.947467i \(-0.603634\pi\)
−0.319853 + 0.947467i \(0.603634\pi\)
\(492\) −14292.4 −1.30965
\(493\) −3949.32 −0.360788
\(494\) 11096.4 1.01063
\(495\) −1106.86 −0.100504
\(496\) −1959.79 −0.177413
\(497\) 3012.34 0.271875
\(498\) −14910.8 −1.34170
\(499\) 18632.0 1.67151 0.835756 0.549101i \(-0.185030\pi\)
0.835756 + 0.549101i \(0.185030\pi\)
\(500\) −1763.09 −0.157695
\(501\) 439.406 0.0391840
\(502\) −31734.6 −2.82149
\(503\) 4627.62 0.410209 0.205105 0.978740i \(-0.434247\pi\)
0.205105 + 0.978740i \(0.434247\pi\)
\(504\) 1808.20 0.159809
\(505\) −9450.72 −0.832775
\(506\) −16846.4 −1.48007
\(507\) −2912.72 −0.255145
\(508\) −15639.4 −1.36592
\(509\) −11351.8 −0.988528 −0.494264 0.869312i \(-0.664562\pi\)
−0.494264 + 0.869312i \(0.664562\pi\)
\(510\) 1298.95 0.112782
\(511\) 289.384 0.0250521
\(512\) −7853.76 −0.677911
\(513\) −1819.88 −0.156627
\(514\) 14427.4 1.23806
\(515\) −3313.50 −0.283515
\(516\) 5168.93 0.440987
\(517\) 8712.67 0.741166
\(518\) 5335.68 0.452580
\(519\) −4272.36 −0.361340
\(520\) 5025.02 0.423772
\(521\) 19096.1 1.60579 0.802893 0.596123i \(-0.203293\pi\)
0.802893 + 0.596123i \(0.203293\pi\)
\(522\) 9072.93 0.760750
\(523\) −3145.11 −0.262956 −0.131478 0.991319i \(-0.541972\pi\)
−0.131478 + 0.991319i \(0.541972\pi\)
\(524\) 2616.24 0.218113
\(525\) 525.000 0.0436436
\(526\) −21975.7 −1.82164
\(527\) 1632.99 0.134980
\(528\) 1631.12 0.134442
\(529\) 9054.20 0.744160
\(530\) −15907.5 −1.30373
\(531\) 4511.87 0.368735
\(532\) −6654.90 −0.542343
\(533\) 11827.2 0.961148
\(534\) 20786.4 1.68449
\(535\) −8072.66 −0.652358
\(536\) −26059.8 −2.10002
\(537\) 3734.09 0.300071
\(538\) 11365.5 0.910781
\(539\) 1205.25 0.0963148
\(540\) −1904.13 −0.151742
\(541\) 8776.12 0.697440 0.348720 0.937227i \(-0.386616\pi\)
0.348720 + 0.937227i \(0.386616\pi\)
\(542\) 36316.3 2.87808
\(543\) −11637.3 −0.919710
\(544\) 2314.98 0.182452
\(545\) −1086.03 −0.0853587
\(546\) −3457.19 −0.270978
\(547\) −13695.1 −1.07049 −0.535247 0.844696i \(-0.679781\pi\)
−0.535247 + 0.844696i \(0.679781\pi\)
\(548\) −535.847 −0.0417705
\(549\) −6380.38 −0.496007
\(550\) 2891.09 0.224139
\(551\) −14452.5 −1.11742
\(552\) −12543.3 −0.967171
\(553\) 6232.71 0.479280
\(554\) −21515.2 −1.64999
\(555\) −2431.87 −0.185995
\(556\) 2589.75 0.197536
\(557\) 7850.44 0.597188 0.298594 0.954380i \(-0.403482\pi\)
0.298594 + 0.954380i \(0.403482\pi\)
\(558\) −3751.54 −0.284615
\(559\) −4277.38 −0.323638
\(560\) −773.664 −0.0583808
\(561\) −1359.13 −0.102286
\(562\) −6387.33 −0.479419
\(563\) −4948.81 −0.370457 −0.185229 0.982695i \(-0.559303\pi\)
−0.185229 + 0.982695i \(0.559303\pi\)
\(564\) 14988.4 1.11902
\(565\) 8290.98 0.617353
\(566\) 18265.7 1.35648
\(567\) 567.000 0.0419961
\(568\) 12351.3 0.912408
\(569\) −8115.76 −0.597945 −0.298972 0.954262i \(-0.596644\pi\)
−0.298972 + 0.954262i \(0.596644\pi\)
\(570\) 4753.50 0.349302
\(571\) 5656.42 0.414560 0.207280 0.978282i \(-0.433539\pi\)
0.207280 + 0.978282i \(0.433539\pi\)
\(572\) −12148.0 −0.887996
\(573\) 4724.71 0.344463
\(574\) −11116.3 −0.808336
\(575\) −3641.87 −0.264133
\(576\) −6909.82 −0.499842
\(577\) −9536.77 −0.688078 −0.344039 0.938955i \(-0.611795\pi\)
−0.344039 + 0.938955i \(0.611795\pi\)
\(578\) −21503.8 −1.54747
\(579\) −14327.0 −1.02834
\(580\) −15121.5 −1.08257
\(581\) −7400.05 −0.528409
\(582\) 7828.58 0.557569
\(583\) 16644.5 1.18241
\(584\) 1186.54 0.0840743
\(585\) 1575.70 0.111363
\(586\) −18965.7 −1.33697
\(587\) −13089.6 −0.920383 −0.460191 0.887820i \(-0.652219\pi\)
−0.460191 + 0.887820i \(0.652219\pi\)
\(588\) 2073.39 0.145417
\(589\) 5975.92 0.418053
\(590\) −11784.9 −0.822334
\(591\) −8410.73 −0.585400
\(592\) 3583.72 0.248801
\(593\) 4281.96 0.296524 0.148262 0.988948i \(-0.452632\pi\)
0.148262 + 0.988948i \(0.452632\pi\)
\(594\) 3122.38 0.215678
\(595\) 644.656 0.0444173
\(596\) −19511.5 −1.34098
\(597\) 12308.7 0.843825
\(598\) 23982.2 1.63997
\(599\) 3699.92 0.252378 0.126189 0.992006i \(-0.459725\pi\)
0.126189 + 0.992006i \(0.459725\pi\)
\(600\) 2152.62 0.146467
\(601\) −17286.1 −1.17323 −0.586616 0.809865i \(-0.699540\pi\)
−0.586616 + 0.809865i \(0.699540\pi\)
\(602\) 4020.28 0.272183
\(603\) −8171.61 −0.551863
\(604\) 10793.7 0.727135
\(605\) 3629.97 0.243933
\(606\) 26659.9 1.78710
\(607\) 14456.7 0.966689 0.483344 0.875430i \(-0.339422\pi\)
0.483344 + 0.875430i \(0.339422\pi\)
\(608\) 8471.63 0.565082
\(609\) 4502.79 0.299610
\(610\) 16665.4 1.10617
\(611\) −12403.2 −0.821243
\(612\) −2338.12 −0.154433
\(613\) 17981.9 1.18480 0.592400 0.805644i \(-0.298181\pi\)
0.592400 + 0.805644i \(0.298181\pi\)
\(614\) −21722.9 −1.42779
\(615\) 5066.53 0.332199
\(616\) 4941.78 0.323231
\(617\) 19614.7 1.27983 0.639916 0.768445i \(-0.278969\pi\)
0.639916 + 0.768445i \(0.278969\pi\)
\(618\) 9347.17 0.608412
\(619\) −10462.9 −0.679385 −0.339692 0.940537i \(-0.610323\pi\)
−0.339692 + 0.940537i \(0.610323\pi\)
\(620\) 6252.56 0.405014
\(621\) −3933.22 −0.254162
\(622\) 31387.1 2.02332
\(623\) 10316.1 0.663411
\(624\) −2322.03 −0.148967
\(625\) 625.000 0.0400000
\(626\) 13337.3 0.851544
\(627\) −4973.72 −0.316796
\(628\) −33382.4 −2.12118
\(629\) −2986.14 −0.189293
\(630\) −1480.99 −0.0936574
\(631\) 24481.9 1.54454 0.772272 0.635292i \(-0.219120\pi\)
0.772272 + 0.635292i \(0.219120\pi\)
\(632\) 25555.5 1.60846
\(633\) −2470.54 −0.155126
\(634\) 18856.2 1.18119
\(635\) 5544.06 0.346471
\(636\) 28633.5 1.78521
\(637\) −1715.77 −0.106721
\(638\) 24796.2 1.53870
\(639\) 3873.01 0.239771
\(640\) 13020.9 0.804211
\(641\) −1109.39 −0.0683595 −0.0341797 0.999416i \(-0.510882\pi\)
−0.0341797 + 0.999416i \(0.510882\pi\)
\(642\) 22772.5 1.39993
\(643\) 30112.5 1.84684 0.923422 0.383787i \(-0.125380\pi\)
0.923422 + 0.383787i \(0.125380\pi\)
\(644\) −14382.9 −0.880071
\(645\) −1832.34 −0.111858
\(646\) 5836.90 0.355495
\(647\) −4260.27 −0.258869 −0.129435 0.991588i \(-0.541316\pi\)
−0.129435 + 0.991588i \(0.541316\pi\)
\(648\) 2324.83 0.140938
\(649\) 12330.9 0.745808
\(650\) −4115.70 −0.248356
\(651\) −1861.85 −0.112091
\(652\) −44256.2 −2.65829
\(653\) −10576.8 −0.633844 −0.316922 0.948452i \(-0.602649\pi\)
−0.316922 + 0.948452i \(0.602649\pi\)
\(654\) 3063.63 0.183176
\(655\) −927.438 −0.0553252
\(656\) −7466.27 −0.444373
\(657\) 372.066 0.0220939
\(658\) 11657.7 0.690674
\(659\) 3394.70 0.200666 0.100333 0.994954i \(-0.468009\pi\)
0.100333 + 0.994954i \(0.468009\pi\)
\(660\) −5203.97 −0.306915
\(661\) −33174.4 −1.95210 −0.976048 0.217554i \(-0.930192\pi\)
−0.976048 + 0.217554i \(0.930192\pi\)
\(662\) 52128.7 3.06048
\(663\) 1934.83 0.113337
\(664\) −30341.9 −1.77333
\(665\) 2359.11 0.137567
\(666\) 6860.17 0.399138
\(667\) −31235.4 −1.81326
\(668\) 2065.89 0.119658
\(669\) 2451.58 0.141680
\(670\) 21344.1 1.23074
\(671\) −17437.5 −1.00323
\(672\) −2639.40 −0.151514
\(673\) 753.881 0.0431797 0.0215899 0.999767i \(-0.493127\pi\)
0.0215899 + 0.999767i \(0.493127\pi\)
\(674\) 56976.9 3.25619
\(675\) 675.000 0.0384900
\(676\) −13694.3 −0.779149
\(677\) 15668.8 0.889511 0.444756 0.895652i \(-0.353291\pi\)
0.444756 + 0.895652i \(0.353291\pi\)
\(678\) −23388.3 −1.32481
\(679\) 3885.24 0.219590
\(680\) 2643.23 0.149064
\(681\) 10967.5 0.617147
\(682\) −10252.9 −0.575665
\(683\) −11557.4 −0.647485 −0.323742 0.946145i \(-0.604941\pi\)
−0.323742 + 0.946145i \(0.604941\pi\)
\(684\) −8556.30 −0.478302
\(685\) 189.953 0.0105952
\(686\) 1612.64 0.0897532
\(687\) 2818.18 0.156507
\(688\) 2700.22 0.149630
\(689\) −23694.7 −1.31016
\(690\) 10273.5 0.566819
\(691\) −18503.1 −1.01866 −0.509328 0.860572i \(-0.670106\pi\)
−0.509328 + 0.860572i \(0.670106\pi\)
\(692\) −20086.8 −1.10344
\(693\) 1549.60 0.0849416
\(694\) −29907.7 −1.63585
\(695\) −918.046 −0.0501057
\(696\) 18462.5 1.00549
\(697\) 6221.28 0.338088
\(698\) −14646.2 −0.794223
\(699\) −22.9410 −0.00124136
\(700\) 2468.32 0.133277
\(701\) 22580.4 1.21662 0.608311 0.793699i \(-0.291847\pi\)
0.608311 + 0.793699i \(0.291847\pi\)
\(702\) −4444.96 −0.238980
\(703\) −10927.7 −0.586269
\(704\) −18884.4 −1.01099
\(705\) −5313.28 −0.283844
\(706\) −56077.4 −2.98938
\(707\) 13231.0 0.703823
\(708\) 21212.8 1.12603
\(709\) −27426.6 −1.45279 −0.726394 0.687278i \(-0.758805\pi\)
−0.726394 + 0.687278i \(0.758805\pi\)
\(710\) −10116.2 −0.534725
\(711\) 8013.49 0.422685
\(712\) 42298.2 2.22639
\(713\) 12915.5 0.678383
\(714\) −1818.53 −0.0953178
\(715\) 4306.37 0.225244
\(716\) 17556.1 0.916342
\(717\) −2667.35 −0.138931
\(718\) −28886.1 −1.50142
\(719\) 19383.0 1.00538 0.502688 0.864468i \(-0.332344\pi\)
0.502688 + 0.864468i \(0.332344\pi\)
\(720\) −994.711 −0.0514871
\(721\) 4638.90 0.239614
\(722\) −10888.0 −0.561230
\(723\) 6420.69 0.330274
\(724\) −54713.3 −2.80857
\(725\) 5360.47 0.274597
\(726\) −10239.9 −0.523469
\(727\) −12317.3 −0.628368 −0.314184 0.949362i \(-0.601731\pi\)
−0.314184 + 0.949362i \(0.601731\pi\)
\(728\) −7035.02 −0.358153
\(729\) 729.000 0.0370370
\(730\) −971.828 −0.0492726
\(731\) −2249.96 −0.113841
\(732\) −29997.8 −1.51468
\(733\) 1234.02 0.0621822 0.0310911 0.999517i \(-0.490102\pi\)
0.0310911 + 0.999517i \(0.490102\pi\)
\(734\) −9063.05 −0.455754
\(735\) −735.000 −0.0368856
\(736\) 18309.3 0.916970
\(737\) −22332.9 −1.11620
\(738\) −14292.4 −0.712885
\(739\) −15257.3 −0.759473 −0.379736 0.925095i \(-0.623985\pi\)
−0.379736 + 0.925095i \(0.623985\pi\)
\(740\) −11433.6 −0.567984
\(741\) 7080.49 0.351023
\(742\) 22270.5 1.10186
\(743\) −35565.1 −1.75606 −0.878032 0.478602i \(-0.841144\pi\)
−0.878032 + 0.478602i \(0.841144\pi\)
\(744\) −7633.99 −0.376177
\(745\) 6916.69 0.340145
\(746\) 49140.8 2.41176
\(747\) −9514.35 −0.466013
\(748\) −6390.04 −0.312357
\(749\) 11301.7 0.551343
\(750\) −1763.09 −0.0858384
\(751\) 14266.7 0.693209 0.346605 0.938011i \(-0.387335\pi\)
0.346605 + 0.938011i \(0.387335\pi\)
\(752\) 7829.89 0.379690
\(753\) −20249.4 −0.979986
\(754\) −35299.4 −1.70494
\(755\) −3826.28 −0.184441
\(756\) 2665.79 0.128246
\(757\) −15927.9 −0.764744 −0.382372 0.924009i \(-0.624893\pi\)
−0.382372 + 0.924009i \(0.624893\pi\)
\(758\) 33223.3 1.59198
\(759\) −10749.4 −0.514071
\(760\) 9672.87 0.461674
\(761\) −2566.48 −0.122253 −0.0611266 0.998130i \(-0.519469\pi\)
−0.0611266 + 0.998130i \(0.519469\pi\)
\(762\) −15639.4 −0.743514
\(763\) 1520.44 0.0721413
\(764\) 22213.5 1.05191
\(765\) 828.844 0.0391724
\(766\) 33701.0 1.58964
\(767\) −17554.0 −0.826386
\(768\) −18304.9 −0.860052
\(769\) 14433.1 0.676816 0.338408 0.940999i \(-0.390112\pi\)
0.338408 + 0.940999i \(0.390112\pi\)
\(770\) −4047.53 −0.189432
\(771\) 9205.91 0.430017
\(772\) −67359.4 −3.14031
\(773\) −29443.2 −1.36999 −0.684993 0.728550i \(-0.740195\pi\)
−0.684993 + 0.728550i \(0.740195\pi\)
\(774\) 5168.93 0.240043
\(775\) −2216.48 −0.102733
\(776\) 15930.4 0.736941
\(777\) 3404.62 0.157195
\(778\) −34857.7 −1.60631
\(779\) 22766.7 1.04711
\(780\) 7408.27 0.340075
\(781\) 10584.9 0.484964
\(782\) 12615.0 0.576869
\(783\) 5789.31 0.264231
\(784\) 1083.13 0.0493408
\(785\) 11833.8 0.538046
\(786\) 2616.24 0.118726
\(787\) 26390.6 1.19533 0.597664 0.801747i \(-0.296096\pi\)
0.597664 + 0.801747i \(0.296096\pi\)
\(788\) −39543.6 −1.78767
\(789\) −14022.4 −0.632711
\(790\) −20931.1 −0.942650
\(791\) −11607.4 −0.521758
\(792\) 6353.72 0.285063
\(793\) 24823.7 1.11162
\(794\) −42013.2 −1.87783
\(795\) −10150.4 −0.452825
\(796\) 57870.3 2.57683
\(797\) −3738.33 −0.166146 −0.0830730 0.996543i \(-0.526473\pi\)
−0.0830730 + 0.996543i \(0.526473\pi\)
\(798\) −6654.90 −0.295214
\(799\) −6524.26 −0.288876
\(800\) −3142.15 −0.138865
\(801\) 13263.5 0.585073
\(802\) 8382.48 0.369072
\(803\) 1016.85 0.0446873
\(804\) −38419.3 −1.68525
\(805\) 5098.62 0.223233
\(806\) 14595.8 0.637861
\(807\) 7252.14 0.316341
\(808\) 54250.1 2.36202
\(809\) 43204.1 1.87760 0.938798 0.344468i \(-0.111941\pi\)
0.938798 + 0.344468i \(0.111941\pi\)
\(810\) −1904.13 −0.0825980
\(811\) −30192.4 −1.30727 −0.653637 0.756809i \(-0.726758\pi\)
−0.653637 + 0.756809i \(0.726758\pi\)
\(812\) 21170.2 0.914935
\(813\) 23172.9 0.999642
\(814\) 18748.7 0.807301
\(815\) 15688.5 0.674286
\(816\) −1221.42 −0.0523999
\(817\) −8233.71 −0.352584
\(818\) −41185.3 −1.76041
\(819\) −2205.98 −0.0941188
\(820\) 23820.6 1.01445
\(821\) −40274.7 −1.71206 −0.856028 0.516929i \(-0.827075\pi\)
−0.856028 + 0.516929i \(0.827075\pi\)
\(822\) −535.847 −0.0227370
\(823\) 25184.2 1.06667 0.533334 0.845905i \(-0.320939\pi\)
0.533334 + 0.845905i \(0.320939\pi\)
\(824\) 19020.5 0.804140
\(825\) 1844.77 0.0778503
\(826\) 16498.9 0.694999
\(827\) −38941.7 −1.63741 −0.818703 0.574218i \(-0.805306\pi\)
−0.818703 + 0.574218i \(0.805306\pi\)
\(828\) −18492.3 −0.776150
\(829\) −8327.05 −0.348867 −0.174433 0.984669i \(-0.555809\pi\)
−0.174433 + 0.984669i \(0.555809\pi\)
\(830\) 24851.3 1.03928
\(831\) −13728.5 −0.573089
\(832\) 26883.5 1.12021
\(833\) −902.519 −0.0375395
\(834\) 2589.75 0.107525
\(835\) −732.343 −0.0303518
\(836\) −23384.2 −0.967418
\(837\) −2393.80 −0.0988553
\(838\) −15104.9 −0.622660
\(839\) 8784.41 0.361468 0.180734 0.983532i \(-0.442153\pi\)
0.180734 + 0.983532i \(0.442153\pi\)
\(840\) −3013.66 −0.123787
\(841\) 21586.4 0.885087
\(842\) 74086.4 3.03229
\(843\) −4075.67 −0.166517
\(844\) −11615.4 −0.473718
\(845\) 4854.53 0.197634
\(846\) 14988.4 0.609117
\(847\) −5081.96 −0.206161
\(848\) 14958.0 0.605732
\(849\) 11655.1 0.471145
\(850\) −2164.92 −0.0873602
\(851\) −23617.6 −0.951350
\(852\) 18209.2 0.732203
\(853\) −9076.15 −0.364316 −0.182158 0.983269i \(-0.558308\pi\)
−0.182158 + 0.983269i \(0.558308\pi\)
\(854\) −23331.6 −0.934884
\(855\) 3033.14 0.121323
\(856\) 46339.6 1.85030
\(857\) 36396.7 1.45074 0.725372 0.688357i \(-0.241668\pi\)
0.725372 + 0.688357i \(0.241668\pi\)
\(858\) −12148.0 −0.483364
\(859\) 8915.27 0.354115 0.177058 0.984200i \(-0.443342\pi\)
0.177058 + 0.984200i \(0.443342\pi\)
\(860\) −8614.88 −0.341587
\(861\) −7093.14 −0.280759
\(862\) −1908.44 −0.0754081
\(863\) −6148.26 −0.242514 −0.121257 0.992621i \(-0.538692\pi\)
−0.121257 + 0.992621i \(0.538692\pi\)
\(864\) −3393.52 −0.133623
\(865\) 7120.59 0.279893
\(866\) −36884.9 −1.44735
\(867\) −13721.2 −0.537483
\(868\) −8753.59 −0.342300
\(869\) 21900.8 0.854928
\(870\) −15121.5 −0.589274
\(871\) 31792.6 1.23680
\(872\) 6234.16 0.242105
\(873\) 4995.31 0.193660
\(874\) 46164.4 1.78665
\(875\) −875.000 −0.0338062
\(876\) 1749.29 0.0674692
\(877\) −14287.0 −0.550101 −0.275050 0.961430i \(-0.588694\pi\)
−0.275050 + 0.961430i \(0.588694\pi\)
\(878\) 1988.90 0.0764488
\(879\) −12101.7 −0.464370
\(880\) −2718.53 −0.104138
\(881\) −13315.9 −0.509221 −0.254610 0.967044i \(-0.581947\pi\)
−0.254610 + 0.967044i \(0.581947\pi\)
\(882\) 2073.39 0.0791549
\(883\) −5271.78 −0.200917 −0.100458 0.994941i \(-0.532031\pi\)
−0.100458 + 0.994941i \(0.532031\pi\)
\(884\) 9096.73 0.346104
\(885\) −7519.78 −0.285621
\(886\) −75501.1 −2.86288
\(887\) 2606.07 0.0986507 0.0493253 0.998783i \(-0.484293\pi\)
0.0493253 + 0.998783i \(0.484293\pi\)
\(888\) 13959.7 0.527542
\(889\) −7761.69 −0.292822
\(890\) −34644.0 −1.30480
\(891\) 1992.35 0.0749115
\(892\) 11526.3 0.432654
\(893\) −23875.4 −0.894694
\(894\) −19511.5 −0.729937
\(895\) −6223.48 −0.232434
\(896\) −18229.2 −0.679682
\(897\) 15302.7 0.569612
\(898\) 10281.1 0.382056
\(899\) −19010.2 −0.705258
\(900\) 3173.55 0.117539
\(901\) −12463.8 −0.460854
\(902\) −39060.8 −1.44189
\(903\) 2565.28 0.0945373
\(904\) −47592.8 −1.75101
\(905\) 19395.4 0.712405
\(906\) 10793.7 0.395802
\(907\) 18610.6 0.681317 0.340659 0.940187i \(-0.389350\pi\)
0.340659 + 0.940187i \(0.389350\pi\)
\(908\) 51564.6 1.88462
\(909\) 17011.3 0.620714
\(910\) 5761.98 0.209899
\(911\) 41091.7 1.49443 0.747216 0.664581i \(-0.231390\pi\)
0.747216 + 0.664581i \(0.231390\pi\)
\(912\) −4469.77 −0.162291
\(913\) −26002.6 −0.942563
\(914\) −27265.4 −0.986716
\(915\) 10634.0 0.384206
\(916\) 13249.8 0.477934
\(917\) 1298.41 0.0467583
\(918\) −2338.12 −0.0840624
\(919\) 38891.3 1.39598 0.697990 0.716107i \(-0.254078\pi\)
0.697990 + 0.716107i \(0.254078\pi\)
\(920\) 20905.5 0.749167
\(921\) −13861.1 −0.495915
\(922\) 46420.2 1.65810
\(923\) −15068.4 −0.537360
\(924\) 7285.56 0.259391
\(925\) 4053.12 0.144071
\(926\) −29064.3 −1.03144
\(927\) 5964.30 0.211320
\(928\) −26949.4 −0.953295
\(929\) 18699.4 0.660396 0.330198 0.943912i \(-0.392885\pi\)
0.330198 + 0.943912i \(0.392885\pi\)
\(930\) 6252.56 0.220462
\(931\) −3302.75 −0.116266
\(932\) −107.859 −0.00379080
\(933\) 20027.7 0.702761
\(934\) 28893.4 1.01223
\(935\) 2265.22 0.0792305
\(936\) −9045.03 −0.315861
\(937\) 21509.6 0.749933 0.374967 0.927038i \(-0.377654\pi\)
0.374967 + 0.927038i \(0.377654\pi\)
\(938\) −29881.7 −1.04016
\(939\) 8510.35 0.295767
\(940\) −24980.7 −0.866788
\(941\) −11241.7 −0.389448 −0.194724 0.980858i \(-0.562381\pi\)
−0.194724 + 0.980858i \(0.562381\pi\)
\(942\) −33382.4 −1.15463
\(943\) 49204.5 1.69917
\(944\) 11081.5 0.382068
\(945\) −945.000 −0.0325300
\(946\) 14126.6 0.485513
\(947\) −36556.3 −1.25441 −0.627203 0.778856i \(-0.715800\pi\)
−0.627203 + 0.778856i \(0.715800\pi\)
\(948\) 37675.9 1.29078
\(949\) −1447.57 −0.0495153
\(950\) −7922.50 −0.270568
\(951\) 12031.9 0.410263
\(952\) −3700.53 −0.125982
\(953\) −36633.4 −1.24520 −0.622598 0.782542i \(-0.713923\pi\)
−0.622598 + 0.782542i \(0.713923\pi\)
\(954\) 28633.5 0.971745
\(955\) −7874.52 −0.266820
\(956\) −12540.7 −0.424263
\(957\) 15822.1 0.534436
\(958\) 51150.3 1.72504
\(959\) −265.935 −0.00895462
\(960\) 11516.4 0.387176
\(961\) −21930.5 −0.736146
\(962\) −26690.3 −0.894523
\(963\) 14530.8 0.486239
\(964\) 30187.3 1.00858
\(965\) 23878.4 0.796551
\(966\) −14382.9 −0.479050
\(967\) −35515.8 −1.18109 −0.590544 0.807006i \(-0.701087\pi\)
−0.590544 + 0.807006i \(0.701087\pi\)
\(968\) −20837.2 −0.691871
\(969\) 3724.44 0.123474
\(970\) −13047.6 −0.431891
\(971\) −39661.0 −1.31080 −0.655398 0.755283i \(-0.727499\pi\)
−0.655398 + 0.755283i \(0.727499\pi\)
\(972\) 3427.44 0.113102
\(973\) 1285.26 0.0423471
\(974\) 38023.9 1.25089
\(975\) −2626.17 −0.0862613
\(976\) −15670.7 −0.513942
\(977\) 50325.3 1.64795 0.823977 0.566624i \(-0.191751\pi\)
0.823977 + 0.566624i \(0.191751\pi\)
\(978\) −44256.2 −1.44699
\(979\) 36249.0 1.18337
\(980\) −3455.65 −0.112639
\(981\) 1954.86 0.0636226
\(982\) −32722.4 −1.06335
\(983\) 51189.0 1.66091 0.830456 0.557084i \(-0.188080\pi\)
0.830456 + 0.557084i \(0.188080\pi\)
\(984\) −29083.5 −0.942223
\(985\) 14017.9 0.453449
\(986\) −18568.0 −0.599721
\(987\) 7438.59 0.239892
\(988\) 33289.3 1.07194
\(989\) −17795.1 −0.572145
\(990\) −5203.97 −0.167064
\(991\) −55137.3 −1.76740 −0.883700 0.468054i \(-0.844955\pi\)
−0.883700 + 0.468054i \(0.844955\pi\)
\(992\) 11143.2 0.356651
\(993\) 33262.6 1.06300
\(994\) 14162.7 0.451925
\(995\) −20514.6 −0.653624
\(996\) −44732.3 −1.42309
\(997\) 41606.5 1.32166 0.660828 0.750537i \(-0.270205\pi\)
0.660828 + 0.750537i \(0.270205\pi\)
\(998\) 87599.6 2.77848
\(999\) 4377.37 0.138633
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 105.4.a.g.1.2 2
3.2 odd 2 315.4.a.g.1.1 2
4.3 odd 2 1680.4.a.y.1.2 2
5.2 odd 4 525.4.d.j.274.4 4
5.3 odd 4 525.4.d.j.274.1 4
5.4 even 2 525.4.a.i.1.1 2
7.6 odd 2 735.4.a.q.1.2 2
15.14 odd 2 1575.4.a.y.1.2 2
21.20 even 2 2205.4.a.v.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.4.a.g.1.2 2 1.1 even 1 trivial
315.4.a.g.1.1 2 3.2 odd 2
525.4.a.i.1.1 2 5.4 even 2
525.4.d.j.274.1 4 5.3 odd 4
525.4.d.j.274.4 4 5.2 odd 4
735.4.a.q.1.2 2 7.6 odd 2
1575.4.a.y.1.2 2 15.14 odd 2
1680.4.a.y.1.2 2 4.3 odd 2
2205.4.a.v.1.1 2 21.20 even 2