Properties

Label 966.4.a.m.1.1
Level $966$
Weight $4$
Character 966.1
Self dual yes
Analytic conductor $56.996$
Analytic rank $0$
Dimension $5$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 966.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(56.9958450655\)
Analytic rank: \(0\)
Dimension: \(5\)
Coefficient field: \(\mathbb{Q}[x]/(x^{5} - \cdots)\)
Defining polynomial: \( x^{5} - x^{4} - 351x^{3} - 663x^{2} + 18451x - 19243 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-13.0148\) of defining polynomial
Character \(\chi\) \(=\) 966.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -12.7819 q^{5} +6.00000 q^{6} -7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -12.7819 q^{5} +6.00000 q^{6} -7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +25.5638 q^{10} -4.56319 q^{11} -12.0000 q^{12} -70.6646 q^{13} +14.0000 q^{14} +38.3456 q^{15} +16.0000 q^{16} -78.3781 q^{17} -18.0000 q^{18} -43.1688 q^{19} -51.1275 q^{20} +21.0000 q^{21} +9.12638 q^{22} -23.0000 q^{23} +24.0000 q^{24} +38.3765 q^{25} +141.329 q^{26} -27.0000 q^{27} -28.0000 q^{28} +166.607 q^{29} -76.6913 q^{30} -147.257 q^{31} -32.0000 q^{32} +13.6896 q^{33} +156.756 q^{34} +89.4732 q^{35} +36.0000 q^{36} -363.445 q^{37} +86.3375 q^{38} +211.994 q^{39} +102.255 q^{40} -295.204 q^{41} -42.0000 q^{42} -456.253 q^{43} -18.2528 q^{44} -115.037 q^{45} +46.0000 q^{46} -117.941 q^{47} -48.0000 q^{48} +49.0000 q^{49} -76.7529 q^{50} +235.134 q^{51} -282.658 q^{52} -221.354 q^{53} +54.0000 q^{54} +58.3262 q^{55} +56.0000 q^{56} +129.506 q^{57} -333.215 q^{58} -22.7176 q^{59} +153.383 q^{60} -399.012 q^{61} +294.514 q^{62} -63.0000 q^{63} +64.0000 q^{64} +903.226 q^{65} -27.3791 q^{66} +446.717 q^{67} -313.512 q^{68} +69.0000 q^{69} -178.946 q^{70} +321.137 q^{71} -72.0000 q^{72} -519.488 q^{73} +726.889 q^{74} -115.129 q^{75} -172.675 q^{76} +31.9423 q^{77} -423.988 q^{78} +85.1065 q^{79} -204.510 q^{80} +81.0000 q^{81} +590.408 q^{82} -163.878 q^{83} +84.0000 q^{84} +1001.82 q^{85} +912.506 q^{86} -499.822 q^{87} +36.5055 q^{88} -955.704 q^{89} +230.074 q^{90} +494.652 q^{91} -92.0000 q^{92} +441.772 q^{93} +235.882 q^{94} +551.778 q^{95} +96.0000 q^{96} -476.957 q^{97} -98.0000 q^{98} -41.0687 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q - 10 q^{2} - 15 q^{3} + 20 q^{4} + 10 q^{5} + 30 q^{6} - 35 q^{7} - 40 q^{8} + 45 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 5 q - 10 q^{2} - 15 q^{3} + 20 q^{4} + 10 q^{5} + 30 q^{6} - 35 q^{7} - 40 q^{8} + 45 q^{9} - 20 q^{10} + 4 q^{11} - 60 q^{12} + 24 q^{13} + 70 q^{14} - 30 q^{15} + 80 q^{16} + 28 q^{17} - 90 q^{18} - 160 q^{19} + 40 q^{20} + 105 q^{21} - 8 q^{22} - 115 q^{23} + 120 q^{24} + 219 q^{25} - 48 q^{26} - 135 q^{27} - 140 q^{28} + 79 q^{29} + 60 q^{30} - 162 q^{31} - 160 q^{32} - 12 q^{33} - 56 q^{34} - 70 q^{35} + 180 q^{36} + 301 q^{37} + 320 q^{38} - 72 q^{39} - 80 q^{40} + 251 q^{41} - 210 q^{42} - 380 q^{43} + 16 q^{44} + 90 q^{45} + 230 q^{46} - 505 q^{47} - 240 q^{48} + 245 q^{49} - 438 q^{50} - 84 q^{51} + 96 q^{52} + 93 q^{53} + 270 q^{54} - 503 q^{55} + 280 q^{56} + 480 q^{57} - 158 q^{58} + 637 q^{59} - 120 q^{60} - 679 q^{61} + 324 q^{62} - 315 q^{63} + 320 q^{64} + 961 q^{65} + 24 q^{66} - 1483 q^{67} + 112 q^{68} + 345 q^{69} + 140 q^{70} + 95 q^{71} - 360 q^{72} - 1310 q^{73} - 602 q^{74} - 657 q^{75} - 640 q^{76} - 28 q^{77} + 144 q^{78} + 494 q^{79} + 160 q^{80} + 405 q^{81} - 502 q^{82} - 482 q^{83} + 420 q^{84} - 291 q^{85} + 760 q^{86} - 237 q^{87} - 32 q^{88} + 661 q^{89} - 180 q^{90} - 168 q^{91} - 460 q^{92} + 486 q^{93} + 1010 q^{94} - 629 q^{95} + 480 q^{96} - 1905 q^{97} - 490 q^{98} + 36 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.00000 −0.707107
\(3\) −3.00000 −0.577350
\(4\) 4.00000 0.500000
\(5\) −12.7819 −1.14325 −0.571623 0.820516i \(-0.693686\pi\)
−0.571623 + 0.820516i \(0.693686\pi\)
\(6\) 6.00000 0.408248
\(7\) −7.00000 −0.377964
\(8\) −8.00000 −0.353553
\(9\) 9.00000 0.333333
\(10\) 25.5638 0.808397
\(11\) −4.56319 −0.125078 −0.0625388 0.998043i \(-0.519920\pi\)
−0.0625388 + 0.998043i \(0.519920\pi\)
\(12\) −12.0000 −0.288675
\(13\) −70.6646 −1.50760 −0.753801 0.657102i \(-0.771782\pi\)
−0.753801 + 0.657102i \(0.771782\pi\)
\(14\) 14.0000 0.267261
\(15\) 38.3456 0.660053
\(16\) 16.0000 0.250000
\(17\) −78.3781 −1.11820 −0.559102 0.829099i \(-0.688854\pi\)
−0.559102 + 0.829099i \(0.688854\pi\)
\(18\) −18.0000 −0.235702
\(19\) −43.1688 −0.521242 −0.260621 0.965441i \(-0.583927\pi\)
−0.260621 + 0.965441i \(0.583927\pi\)
\(20\) −51.1275 −0.571623
\(21\) 21.0000 0.218218
\(22\) 9.12638 0.0884432
\(23\) −23.0000 −0.208514
\(24\) 24.0000 0.204124
\(25\) 38.3765 0.307012
\(26\) 141.329 1.06604
\(27\) −27.0000 −0.192450
\(28\) −28.0000 −0.188982
\(29\) 166.607 1.06684 0.533418 0.845852i \(-0.320907\pi\)
0.533418 + 0.845852i \(0.320907\pi\)
\(30\) −76.6913 −0.466728
\(31\) −147.257 −0.853167 −0.426584 0.904448i \(-0.640283\pi\)
−0.426584 + 0.904448i \(0.640283\pi\)
\(32\) −32.0000 −0.176777
\(33\) 13.6896 0.0722136
\(34\) 156.756 0.790690
\(35\) 89.4732 0.432106
\(36\) 36.0000 0.166667
\(37\) −363.445 −1.61486 −0.807432 0.589961i \(-0.799143\pi\)
−0.807432 + 0.589961i \(0.799143\pi\)
\(38\) 86.3375 0.368574
\(39\) 211.994 0.870415
\(40\) 102.255 0.404199
\(41\) −295.204 −1.12447 −0.562233 0.826979i \(-0.690058\pi\)
−0.562233 + 0.826979i \(0.690058\pi\)
\(42\) −42.0000 −0.154303
\(43\) −456.253 −1.61809 −0.809046 0.587746i \(-0.800015\pi\)
−0.809046 + 0.587746i \(0.800015\pi\)
\(44\) −18.2528 −0.0625388
\(45\) −115.037 −0.381082
\(46\) 46.0000 0.147442
\(47\) −117.941 −0.366031 −0.183016 0.983110i \(-0.558586\pi\)
−0.183016 + 0.983110i \(0.558586\pi\)
\(48\) −48.0000 −0.144338
\(49\) 49.0000 0.142857
\(50\) −76.7529 −0.217090
\(51\) 235.134 0.645596
\(52\) −282.658 −0.753801
\(53\) −221.354 −0.573685 −0.286842 0.957978i \(-0.592606\pi\)
−0.286842 + 0.957978i \(0.592606\pi\)
\(54\) 54.0000 0.136083
\(55\) 58.3262 0.142994
\(56\) 56.0000 0.133631
\(57\) 129.506 0.300939
\(58\) −333.215 −0.754367
\(59\) −22.7176 −0.0501284 −0.0250642 0.999686i \(-0.507979\pi\)
−0.0250642 + 0.999686i \(0.507979\pi\)
\(60\) 153.383 0.330027
\(61\) −399.012 −0.837512 −0.418756 0.908099i \(-0.637534\pi\)
−0.418756 + 0.908099i \(0.637534\pi\)
\(62\) 294.514 0.603280
\(63\) −63.0000 −0.125988
\(64\) 64.0000 0.125000
\(65\) 903.226 1.72356
\(66\) −27.3791 −0.0510627
\(67\) 446.717 0.814555 0.407278 0.913304i \(-0.366478\pi\)
0.407278 + 0.913304i \(0.366478\pi\)
\(68\) −313.512 −0.559102
\(69\) 69.0000 0.120386
\(70\) −178.946 −0.305545
\(71\) 321.137 0.536788 0.268394 0.963309i \(-0.413507\pi\)
0.268394 + 0.963309i \(0.413507\pi\)
\(72\) −72.0000 −0.117851
\(73\) −519.488 −0.832897 −0.416449 0.909159i \(-0.636725\pi\)
−0.416449 + 0.909159i \(0.636725\pi\)
\(74\) 726.889 1.14188
\(75\) −115.129 −0.177253
\(76\) −172.675 −0.260621
\(77\) 31.9423 0.0472749
\(78\) −423.988 −0.615476
\(79\) 85.1065 0.121205 0.0606027 0.998162i \(-0.480698\pi\)
0.0606027 + 0.998162i \(0.480698\pi\)
\(80\) −204.510 −0.285812
\(81\) 81.0000 0.111111
\(82\) 590.408 0.795118
\(83\) −163.878 −0.216723 −0.108361 0.994112i \(-0.534560\pi\)
−0.108361 + 0.994112i \(0.534560\pi\)
\(84\) 84.0000 0.109109
\(85\) 1001.82 1.27838
\(86\) 912.506 1.14416
\(87\) −499.822 −0.615938
\(88\) 36.5055 0.0442216
\(89\) −955.704 −1.13825 −0.569126 0.822251i \(-0.692718\pi\)
−0.569126 + 0.822251i \(0.692718\pi\)
\(90\) 230.074 0.269466
\(91\) 494.652 0.569820
\(92\) −92.0000 −0.104257
\(93\) 441.772 0.492576
\(94\) 235.882 0.258823
\(95\) 551.778 0.595908
\(96\) 96.0000 0.102062
\(97\) −476.957 −0.499255 −0.249627 0.968342i \(-0.580308\pi\)
−0.249627 + 0.968342i \(0.580308\pi\)
\(98\) −98.0000 −0.101015
\(99\) −41.0687 −0.0416925
\(100\) 153.506 0.153506
\(101\) 1340.97 1.32110 0.660552 0.750780i \(-0.270322\pi\)
0.660552 + 0.750780i \(0.270322\pi\)
\(102\) −470.268 −0.456505
\(103\) −1349.60 −1.29107 −0.645536 0.763730i \(-0.723366\pi\)
−0.645536 + 0.763730i \(0.723366\pi\)
\(104\) 565.317 0.533018
\(105\) −268.419 −0.249477
\(106\) 442.708 0.405656
\(107\) 816.118 0.737356 0.368678 0.929557i \(-0.379810\pi\)
0.368678 + 0.929557i \(0.379810\pi\)
\(108\) −108.000 −0.0962250
\(109\) −793.928 −0.697656 −0.348828 0.937187i \(-0.613420\pi\)
−0.348828 + 0.937187i \(0.613420\pi\)
\(110\) −116.652 −0.101112
\(111\) 1090.33 0.932342
\(112\) −112.000 −0.0944911
\(113\) −756.248 −0.629574 −0.314787 0.949162i \(-0.601933\pi\)
−0.314787 + 0.949162i \(0.601933\pi\)
\(114\) −259.013 −0.212796
\(115\) 293.983 0.238383
\(116\) 666.430 0.533418
\(117\) −635.981 −0.502534
\(118\) 45.4351 0.0354461
\(119\) 548.647 0.422642
\(120\) −306.765 −0.233364
\(121\) −1310.18 −0.984356
\(122\) 798.024 0.592211
\(123\) 885.612 0.649211
\(124\) −589.029 −0.426584
\(125\) 1107.21 0.792256
\(126\) 126.000 0.0890871
\(127\) 250.192 0.174811 0.0874053 0.996173i \(-0.472142\pi\)
0.0874053 + 0.996173i \(0.472142\pi\)
\(128\) −128.000 −0.0883883
\(129\) 1368.76 0.934205
\(130\) −1806.45 −1.21874
\(131\) 1623.93 1.08308 0.541541 0.840675i \(-0.317841\pi\)
0.541541 + 0.840675i \(0.317841\pi\)
\(132\) 54.7583 0.0361068
\(133\) 302.181 0.197011
\(134\) −893.434 −0.575977
\(135\) 345.111 0.220018
\(136\) 627.025 0.395345
\(137\) 1110.52 0.692539 0.346270 0.938135i \(-0.387448\pi\)
0.346270 + 0.938135i \(0.387448\pi\)
\(138\) −138.000 −0.0851257
\(139\) −352.003 −0.214795 −0.107398 0.994216i \(-0.534252\pi\)
−0.107398 + 0.994216i \(0.534252\pi\)
\(140\) 357.893 0.216053
\(141\) 353.823 0.211328
\(142\) −642.274 −0.379566
\(143\) 322.456 0.188567
\(144\) 144.000 0.0833333
\(145\) −2129.56 −1.21966
\(146\) 1038.98 0.588947
\(147\) −147.000 −0.0824786
\(148\) −1453.78 −0.807432
\(149\) 552.442 0.303744 0.151872 0.988400i \(-0.451470\pi\)
0.151872 + 0.988400i \(0.451470\pi\)
\(150\) 230.259 0.125337
\(151\) 2159.00 1.16356 0.581779 0.813347i \(-0.302357\pi\)
0.581779 + 0.813347i \(0.302357\pi\)
\(152\) 345.350 0.184287
\(153\) −705.403 −0.372735
\(154\) −63.8847 −0.0334284
\(155\) 1882.22 0.975380
\(156\) 847.975 0.435207
\(157\) 1335.03 0.678643 0.339321 0.940670i \(-0.389803\pi\)
0.339321 + 0.940670i \(0.389803\pi\)
\(158\) −170.213 −0.0857052
\(159\) 664.062 0.331217
\(160\) 409.020 0.202099
\(161\) 161.000 0.0788110
\(162\) −162.000 −0.0785674
\(163\) 1555.57 0.747493 0.373747 0.927531i \(-0.378073\pi\)
0.373747 + 0.927531i \(0.378073\pi\)
\(164\) −1180.82 −0.562233
\(165\) −174.978 −0.0825579
\(166\) 327.757 0.153246
\(167\) −2422.61 −1.12256 −0.561279 0.827627i \(-0.689690\pi\)
−0.561279 + 0.827627i \(0.689690\pi\)
\(168\) −168.000 −0.0771517
\(169\) 2796.49 1.27287
\(170\) −2003.64 −0.903953
\(171\) −388.519 −0.173747
\(172\) −1825.01 −0.809046
\(173\) 1552.30 0.682193 0.341096 0.940028i \(-0.389202\pi\)
0.341096 + 0.940028i \(0.389202\pi\)
\(174\) 999.645 0.435534
\(175\) −268.635 −0.116039
\(176\) −73.0110 −0.0312694
\(177\) 68.1527 0.0289416
\(178\) 1911.41 0.804865
\(179\) 3121.09 1.30325 0.651624 0.758542i \(-0.274088\pi\)
0.651624 + 0.758542i \(0.274088\pi\)
\(180\) −460.148 −0.190541
\(181\) −808.858 −0.332166 −0.166083 0.986112i \(-0.553112\pi\)
−0.166083 + 0.986112i \(0.553112\pi\)
\(182\) −989.304 −0.402924
\(183\) 1197.04 0.483538
\(184\) 184.000 0.0737210
\(185\) 4645.51 1.84619
\(186\) −883.543 −0.348304
\(187\) 357.654 0.139862
\(188\) −471.764 −0.183016
\(189\) 189.000 0.0727393
\(190\) −1103.56 −0.421370
\(191\) −2975.03 −1.12705 −0.563523 0.826100i \(-0.690555\pi\)
−0.563523 + 0.826100i \(0.690555\pi\)
\(192\) −192.000 −0.0721688
\(193\) 950.504 0.354501 0.177251 0.984166i \(-0.443280\pi\)
0.177251 + 0.984166i \(0.443280\pi\)
\(194\) 953.915 0.353026
\(195\) −2709.68 −0.995098
\(196\) 196.000 0.0714286
\(197\) −1721.87 −0.622731 −0.311366 0.950290i \(-0.600786\pi\)
−0.311366 + 0.950290i \(0.600786\pi\)
\(198\) 82.1374 0.0294811
\(199\) 2116.67 0.754004 0.377002 0.926212i \(-0.376955\pi\)
0.377002 + 0.926212i \(0.376955\pi\)
\(200\) −307.012 −0.108545
\(201\) −1340.15 −0.470284
\(202\) −2681.94 −0.934161
\(203\) −1166.25 −0.403226
\(204\) 940.537 0.322798
\(205\) 3773.26 1.28554
\(206\) 2699.21 0.912926
\(207\) −207.000 −0.0695048
\(208\) −1130.63 −0.376901
\(209\) 196.987 0.0651957
\(210\) 536.839 0.176407
\(211\) −872.114 −0.284544 −0.142272 0.989828i \(-0.545441\pi\)
−0.142272 + 0.989828i \(0.545441\pi\)
\(212\) −885.415 −0.286842
\(213\) −963.411 −0.309915
\(214\) −1632.24 −0.521390
\(215\) 5831.77 1.84988
\(216\) 216.000 0.0680414
\(217\) 1030.80 0.322467
\(218\) 1587.86 0.493317
\(219\) 1558.46 0.480874
\(220\) 233.305 0.0714972
\(221\) 5538.56 1.68581
\(222\) −2180.67 −0.659265
\(223\) 2471.17 0.742070 0.371035 0.928619i \(-0.379003\pi\)
0.371035 + 0.928619i \(0.379003\pi\)
\(224\) 224.000 0.0668153
\(225\) 345.388 0.102337
\(226\) 1512.50 0.445176
\(227\) 2923.30 0.854742 0.427371 0.904076i \(-0.359440\pi\)
0.427371 + 0.904076i \(0.359440\pi\)
\(228\) 518.025 0.150470
\(229\) 5006.00 1.44457 0.722284 0.691597i \(-0.243092\pi\)
0.722284 + 0.691597i \(0.243092\pi\)
\(230\) −587.966 −0.168562
\(231\) −95.8270 −0.0272942
\(232\) −1332.86 −0.377183
\(233\) 2162.09 0.607910 0.303955 0.952686i \(-0.401693\pi\)
0.303955 + 0.952686i \(0.401693\pi\)
\(234\) 1271.96 0.355345
\(235\) 1507.51 0.418464
\(236\) −90.8702 −0.0250642
\(237\) −255.319 −0.0699780
\(238\) −1097.29 −0.298853
\(239\) −2815.63 −0.762041 −0.381021 0.924567i \(-0.624427\pi\)
−0.381021 + 0.924567i \(0.624427\pi\)
\(240\) 613.530 0.165013
\(241\) 5516.45 1.47446 0.737231 0.675640i \(-0.236133\pi\)
0.737231 + 0.675640i \(0.236133\pi\)
\(242\) 2620.35 0.696045
\(243\) −243.000 −0.0641500
\(244\) −1596.05 −0.418756
\(245\) −626.312 −0.163321
\(246\) −1771.22 −0.459062
\(247\) 3050.50 0.785825
\(248\) 1178.06 0.301640
\(249\) 491.635 0.125125
\(250\) −2214.42 −0.560210
\(251\) −5526.99 −1.38988 −0.694941 0.719067i \(-0.744570\pi\)
−0.694941 + 0.719067i \(0.744570\pi\)
\(252\) −252.000 −0.0629941
\(253\) 104.953 0.0260805
\(254\) −500.384 −0.123610
\(255\) −3005.46 −0.738075
\(256\) 256.000 0.0625000
\(257\) 3872.51 0.939925 0.469962 0.882686i \(-0.344267\pi\)
0.469962 + 0.882686i \(0.344267\pi\)
\(258\) −2737.52 −0.660583
\(259\) 2544.11 0.610361
\(260\) 3612.91 0.861780
\(261\) 1499.47 0.355612
\(262\) −3247.86 −0.765854
\(263\) −2293.87 −0.537817 −0.268908 0.963166i \(-0.586663\pi\)
−0.268908 + 0.963166i \(0.586663\pi\)
\(264\) −109.517 −0.0255314
\(265\) 2829.32 0.655863
\(266\) −604.363 −0.139308
\(267\) 2867.11 0.657170
\(268\) 1786.87 0.407278
\(269\) −1112.28 −0.252108 −0.126054 0.992023i \(-0.540231\pi\)
−0.126054 + 0.992023i \(0.540231\pi\)
\(270\) −690.222 −0.155576
\(271\) −6593.76 −1.47802 −0.739009 0.673696i \(-0.764706\pi\)
−0.739009 + 0.673696i \(0.764706\pi\)
\(272\) −1254.05 −0.279551
\(273\) −1483.96 −0.328986
\(274\) −2221.03 −0.489699
\(275\) −175.119 −0.0384003
\(276\) 276.000 0.0601929
\(277\) −7047.11 −1.52859 −0.764296 0.644865i \(-0.776913\pi\)
−0.764296 + 0.644865i \(0.776913\pi\)
\(278\) 704.006 0.151883
\(279\) −1325.32 −0.284389
\(280\) −715.785 −0.152773
\(281\) −1606.77 −0.341110 −0.170555 0.985348i \(-0.554556\pi\)
−0.170555 + 0.985348i \(0.554556\pi\)
\(282\) −707.647 −0.149432
\(283\) −7435.54 −1.56183 −0.780913 0.624640i \(-0.785246\pi\)
−0.780913 + 0.624640i \(0.785246\pi\)
\(284\) 1284.55 0.268394
\(285\) −1655.33 −0.344047
\(286\) −644.912 −0.133337
\(287\) 2066.43 0.425008
\(288\) −288.000 −0.0589256
\(289\) 1230.12 0.250381
\(290\) 4259.11 0.862427
\(291\) 1430.87 0.288245
\(292\) −2077.95 −0.416449
\(293\) −984.078 −0.196213 −0.0981066 0.995176i \(-0.531279\pi\)
−0.0981066 + 0.995176i \(0.531279\pi\)
\(294\) 294.000 0.0583212
\(295\) 290.373 0.0573091
\(296\) 2907.56 0.570940
\(297\) 123.206 0.0240712
\(298\) −1104.88 −0.214779
\(299\) 1625.29 0.314357
\(300\) −460.517 −0.0886266
\(301\) 3193.77 0.611581
\(302\) −4318.01 −0.822760
\(303\) −4022.91 −0.762740
\(304\) −690.700 −0.130310
\(305\) 5100.12 0.957483
\(306\) 1410.81 0.263563
\(307\) −7577.17 −1.40864 −0.704319 0.709883i \(-0.748748\pi\)
−0.704319 + 0.709883i \(0.748748\pi\)
\(308\) 127.769 0.0236374
\(309\) 4048.81 0.745401
\(310\) −3764.45 −0.689698
\(311\) −2223.18 −0.405353 −0.202677 0.979246i \(-0.564964\pi\)
−0.202677 + 0.979246i \(0.564964\pi\)
\(312\) −1695.95 −0.307738
\(313\) −3421.67 −0.617904 −0.308952 0.951078i \(-0.599978\pi\)
−0.308952 + 0.951078i \(0.599978\pi\)
\(314\) −2670.06 −0.479873
\(315\) 805.258 0.144035
\(316\) 340.426 0.0606027
\(317\) −1190.22 −0.210882 −0.105441 0.994426i \(-0.533625\pi\)
−0.105441 + 0.994426i \(0.533625\pi\)
\(318\) −1328.12 −0.234206
\(319\) −760.262 −0.133437
\(320\) −818.040 −0.142906
\(321\) −2448.35 −0.425713
\(322\) −322.000 −0.0557278
\(323\) 3383.48 0.582855
\(324\) 324.000 0.0555556
\(325\) −2711.86 −0.462852
\(326\) −3111.13 −0.528557
\(327\) 2381.78 0.402792
\(328\) 2361.63 0.397559
\(329\) 825.588 0.138347
\(330\) 349.957 0.0583773
\(331\) −7499.16 −1.24529 −0.622645 0.782504i \(-0.713942\pi\)
−0.622645 + 0.782504i \(0.713942\pi\)
\(332\) −655.513 −0.108361
\(333\) −3271.00 −0.538288
\(334\) 4845.22 0.793768
\(335\) −5709.89 −0.931237
\(336\) 336.000 0.0545545
\(337\) 3476.33 0.561922 0.280961 0.959719i \(-0.409347\pi\)
0.280961 + 0.959719i \(0.409347\pi\)
\(338\) −5592.97 −0.900052
\(339\) 2268.74 0.363485
\(340\) 4007.28 0.639191
\(341\) 671.963 0.106712
\(342\) 777.038 0.122858
\(343\) −343.000 −0.0539949
\(344\) 3650.02 0.572082
\(345\) −881.950 −0.137631
\(346\) −3104.60 −0.482383
\(347\) 7365.59 1.13950 0.569749 0.821819i \(-0.307041\pi\)
0.569749 + 0.821819i \(0.307041\pi\)
\(348\) −1999.29 −0.307969
\(349\) −4338.06 −0.665361 −0.332680 0.943040i \(-0.607953\pi\)
−0.332680 + 0.943040i \(0.607953\pi\)
\(350\) 537.270 0.0820523
\(351\) 1907.94 0.290138
\(352\) 146.022 0.0221108
\(353\) 1473.91 0.222233 0.111117 0.993807i \(-0.464557\pi\)
0.111117 + 0.993807i \(0.464557\pi\)
\(354\) −136.305 −0.0204648
\(355\) −4104.73 −0.613681
\(356\) −3822.81 −0.569126
\(357\) −1645.94 −0.244012
\(358\) −6242.18 −0.921535
\(359\) 1733.26 0.254813 0.127406 0.991851i \(-0.459335\pi\)
0.127406 + 0.991851i \(0.459335\pi\)
\(360\) 920.295 0.134733
\(361\) −4995.46 −0.728307
\(362\) 1617.72 0.234876
\(363\) 3930.53 0.568318
\(364\) 1978.61 0.284910
\(365\) 6640.04 0.952207
\(366\) −2394.07 −0.341913
\(367\) 3146.54 0.447543 0.223771 0.974642i \(-0.428163\pi\)
0.223771 + 0.974642i \(0.428163\pi\)
\(368\) −368.000 −0.0521286
\(369\) −2656.84 −0.374822
\(370\) −9291.01 −1.30545
\(371\) 1549.48 0.216832
\(372\) 1767.09 0.246288
\(373\) 10403.0 1.44409 0.722043 0.691848i \(-0.243203\pi\)
0.722043 + 0.691848i \(0.243203\pi\)
\(374\) −715.308 −0.0988976
\(375\) −3321.64 −0.457409
\(376\) 943.529 0.129412
\(377\) −11773.2 −1.60836
\(378\) −378.000 −0.0514344
\(379\) −5985.36 −0.811207 −0.405604 0.914049i \(-0.632939\pi\)
−0.405604 + 0.914049i \(0.632939\pi\)
\(380\) 2207.11 0.297954
\(381\) −750.576 −0.100927
\(382\) 5950.07 0.796942
\(383\) −2885.03 −0.384904 −0.192452 0.981306i \(-0.561644\pi\)
−0.192452 + 0.981306i \(0.561644\pi\)
\(384\) 384.000 0.0510310
\(385\) −408.283 −0.0540468
\(386\) −1901.01 −0.250670
\(387\) −4106.28 −0.539364
\(388\) −1907.83 −0.249627
\(389\) 11285.6 1.47095 0.735476 0.677551i \(-0.236959\pi\)
0.735476 + 0.677551i \(0.236959\pi\)
\(390\) 5419.36 0.703641
\(391\) 1802.70 0.233162
\(392\) −392.000 −0.0505076
\(393\) −4871.80 −0.625317
\(394\) 3443.74 0.440338
\(395\) −1087.82 −0.138568
\(396\) −164.275 −0.0208463
\(397\) −2475.74 −0.312982 −0.156491 0.987679i \(-0.550018\pi\)
−0.156491 + 0.987679i \(0.550018\pi\)
\(398\) −4233.34 −0.533161
\(399\) −906.544 −0.113744
\(400\) 614.023 0.0767529
\(401\) −7899.41 −0.983734 −0.491867 0.870670i \(-0.663685\pi\)
−0.491867 + 0.870670i \(0.663685\pi\)
\(402\) 2680.30 0.332541
\(403\) 10405.9 1.28624
\(404\) 5363.88 0.660552
\(405\) −1035.33 −0.127027
\(406\) 2332.50 0.285124
\(407\) 1658.47 0.201983
\(408\) −1881.07 −0.228253
\(409\) −11771.3 −1.42311 −0.711554 0.702631i \(-0.752008\pi\)
−0.711554 + 0.702631i \(0.752008\pi\)
\(410\) −7546.53 −0.909016
\(411\) −3331.55 −0.399838
\(412\) −5398.42 −0.645536
\(413\) 159.023 0.0189467
\(414\) 414.000 0.0491473
\(415\) 2094.67 0.247767
\(416\) 2261.27 0.266509
\(417\) 1056.01 0.124012
\(418\) −393.975 −0.0461003
\(419\) −1052.14 −0.122674 −0.0613370 0.998117i \(-0.519536\pi\)
−0.0613370 + 0.998117i \(0.519536\pi\)
\(420\) −1073.68 −0.124738
\(421\) −10346.9 −1.19780 −0.598902 0.800823i \(-0.704396\pi\)
−0.598902 + 0.800823i \(0.704396\pi\)
\(422\) 1744.23 0.201203
\(423\) −1061.47 −0.122010
\(424\) 1770.83 0.202828
\(425\) −3007.87 −0.343302
\(426\) 1926.82 0.219143
\(427\) 2793.08 0.316550
\(428\) 3264.47 0.368678
\(429\) −967.368 −0.108869
\(430\) −11663.5 −1.30806
\(431\) 5904.08 0.659836 0.329918 0.944010i \(-0.392979\pi\)
0.329918 + 0.944010i \(0.392979\pi\)
\(432\) −432.000 −0.0481125
\(433\) −8543.55 −0.948214 −0.474107 0.880467i \(-0.657229\pi\)
−0.474107 + 0.880467i \(0.657229\pi\)
\(434\) −2061.60 −0.228019
\(435\) 6388.67 0.704168
\(436\) −3175.71 −0.348828
\(437\) 992.881 0.108686
\(438\) −3116.93 −0.340029
\(439\) 17210.9 1.87114 0.935572 0.353135i \(-0.114884\pi\)
0.935572 + 0.353135i \(0.114884\pi\)
\(440\) −466.609 −0.0505562
\(441\) 441.000 0.0476190
\(442\) −11077.1 −1.19205
\(443\) −11853.5 −1.27128 −0.635642 0.771984i \(-0.719265\pi\)
−0.635642 + 0.771984i \(0.719265\pi\)
\(444\) 4361.34 0.466171
\(445\) 12215.7 1.30130
\(446\) −4942.34 −0.524723
\(447\) −1657.33 −0.175367
\(448\) −448.000 −0.0472456
\(449\) −13335.0 −1.40160 −0.700799 0.713359i \(-0.747173\pi\)
−0.700799 + 0.713359i \(0.747173\pi\)
\(450\) −690.776 −0.0723633
\(451\) 1347.07 0.140646
\(452\) −3024.99 −0.314787
\(453\) −6477.01 −0.671781
\(454\) −5846.61 −0.604394
\(455\) −6322.58 −0.651445
\(456\) −1036.05 −0.106398
\(457\) −16084.7 −1.64642 −0.823208 0.567740i \(-0.807818\pi\)
−0.823208 + 0.567740i \(0.807818\pi\)
\(458\) −10012.0 −1.02146
\(459\) 2116.21 0.215199
\(460\) 1175.93 0.119192
\(461\) 4358.86 0.440374 0.220187 0.975458i \(-0.429333\pi\)
0.220187 + 0.975458i \(0.429333\pi\)
\(462\) 191.654 0.0192999
\(463\) 521.026 0.0522984 0.0261492 0.999658i \(-0.491676\pi\)
0.0261492 + 0.999658i \(0.491676\pi\)
\(464\) 2665.72 0.266709
\(465\) −5646.67 −0.563136
\(466\) −4324.18 −0.429857
\(467\) 76.1495 0.00754556 0.00377278 0.999993i \(-0.498799\pi\)
0.00377278 + 0.999993i \(0.498799\pi\)
\(468\) −2543.93 −0.251267
\(469\) −3127.02 −0.307873
\(470\) −3015.02 −0.295899
\(471\) −4005.09 −0.391815
\(472\) 181.740 0.0177231
\(473\) 2081.97 0.202387
\(474\) 510.639 0.0494819
\(475\) −1656.66 −0.160027
\(476\) 2194.59 0.211321
\(477\) −1992.18 −0.191228
\(478\) 5631.26 0.538845
\(479\) −16679.8 −1.59106 −0.795532 0.605911i \(-0.792809\pi\)
−0.795532 + 0.605911i \(0.792809\pi\)
\(480\) −1227.06 −0.116682
\(481\) 25682.7 2.43457
\(482\) −11032.9 −1.04260
\(483\) −483.000 −0.0455016
\(484\) −5240.71 −0.492178
\(485\) 6096.41 0.570771
\(486\) 486.000 0.0453609
\(487\) −12398.8 −1.15368 −0.576839 0.816858i \(-0.695714\pi\)
−0.576839 + 0.816858i \(0.695714\pi\)
\(488\) 3192.10 0.296105
\(489\) −4666.70 −0.431565
\(490\) 1252.62 0.115485
\(491\) 14269.3 1.31154 0.655770 0.754960i \(-0.272344\pi\)
0.655770 + 0.754960i \(0.272344\pi\)
\(492\) 3542.45 0.324606
\(493\) −13058.4 −1.19294
\(494\) −6101.01 −0.555662
\(495\) 524.935 0.0476648
\(496\) −2356.12 −0.213292
\(497\) −2247.96 −0.202887
\(498\) −983.270 −0.0884767
\(499\) −11324.5 −1.01594 −0.507970 0.861375i \(-0.669604\pi\)
−0.507970 + 0.861375i \(0.669604\pi\)
\(500\) 4428.85 0.396128
\(501\) 7267.83 0.648109
\(502\) 11054.0 0.982795
\(503\) −16241.4 −1.43970 −0.719850 0.694130i \(-0.755789\pi\)
−0.719850 + 0.694130i \(0.755789\pi\)
\(504\) 504.000 0.0445435
\(505\) −17140.1 −1.51035
\(506\) −209.907 −0.0184417
\(507\) −8389.46 −0.734889
\(508\) 1000.77 0.0874053
\(509\) 22052.4 1.92035 0.960173 0.279405i \(-0.0901373\pi\)
0.960173 + 0.279405i \(0.0901373\pi\)
\(510\) 6010.91 0.521898
\(511\) 3636.42 0.314806
\(512\) −512.000 −0.0441942
\(513\) 1165.56 0.100313
\(514\) −7745.02 −0.664627
\(515\) 17250.5 1.47601
\(516\) 5475.04 0.467103
\(517\) 538.188 0.0457823
\(518\) −5088.23 −0.431590
\(519\) −4656.91 −0.393864
\(520\) −7225.81 −0.609371
\(521\) 6126.02 0.515136 0.257568 0.966260i \(-0.417079\pi\)
0.257568 + 0.966260i \(0.417079\pi\)
\(522\) −2998.93 −0.251456
\(523\) −11267.8 −0.942081 −0.471040 0.882112i \(-0.656121\pi\)
−0.471040 + 0.882112i \(0.656121\pi\)
\(524\) 6495.73 0.541541
\(525\) 805.906 0.0669954
\(526\) 4587.73 0.380294
\(527\) 11541.7 0.954015
\(528\) 219.033 0.0180534
\(529\) 529.000 0.0434783
\(530\) −5658.64 −0.463765
\(531\) −204.458 −0.0167095
\(532\) 1208.73 0.0985054
\(533\) 20860.5 1.69525
\(534\) −5734.22 −0.464689
\(535\) −10431.5 −0.842980
\(536\) −3573.74 −0.287989
\(537\) −9363.27 −0.752430
\(538\) 2224.57 0.178267
\(539\) −223.596 −0.0178682
\(540\) 1380.44 0.110009
\(541\) −2051.38 −0.163023 −0.0815117 0.996672i \(-0.525975\pi\)
−0.0815117 + 0.996672i \(0.525975\pi\)
\(542\) 13187.5 1.04512
\(543\) 2426.57 0.191776
\(544\) 2508.10 0.197672
\(545\) 10147.9 0.797592
\(546\) 2967.91 0.232628
\(547\) 8692.02 0.679422 0.339711 0.940530i \(-0.389671\pi\)
0.339711 + 0.940530i \(0.389671\pi\)
\(548\) 4442.07 0.346270
\(549\) −3591.11 −0.279171
\(550\) 350.238 0.0271531
\(551\) −7192.24 −0.556079
\(552\) −552.000 −0.0425628
\(553\) −595.745 −0.0458113
\(554\) 14094.2 1.08088
\(555\) −13936.5 −1.06590
\(556\) −1408.01 −0.107398
\(557\) 6835.31 0.519967 0.259983 0.965613i \(-0.416283\pi\)
0.259983 + 0.965613i \(0.416283\pi\)
\(558\) 2650.63 0.201093
\(559\) 32240.9 2.43944
\(560\) 1431.57 0.108027
\(561\) −1072.96 −0.0807496
\(562\) 3213.54 0.241201
\(563\) −5526.23 −0.413682 −0.206841 0.978375i \(-0.566318\pi\)
−0.206841 + 0.978375i \(0.566318\pi\)
\(564\) 1415.29 0.105664
\(565\) 9666.27 0.719758
\(566\) 14871.1 1.10438
\(567\) −567.000 −0.0419961
\(568\) −2569.10 −0.189783
\(569\) −17664.7 −1.30148 −0.650741 0.759300i \(-0.725542\pi\)
−0.650741 + 0.759300i \(0.725542\pi\)
\(570\) 3310.67 0.243278
\(571\) 14924.4 1.09381 0.546907 0.837194i \(-0.315805\pi\)
0.546907 + 0.837194i \(0.315805\pi\)
\(572\) 1289.82 0.0942837
\(573\) 8925.10 0.650701
\(574\) −4132.86 −0.300526
\(575\) −882.658 −0.0640164
\(576\) 576.000 0.0416667
\(577\) 16922.4 1.22095 0.610474 0.792036i \(-0.290979\pi\)
0.610474 + 0.792036i \(0.290979\pi\)
\(578\) −2460.25 −0.177046
\(579\) −2851.51 −0.204671
\(580\) −8518.23 −0.609828
\(581\) 1147.15 0.0819135
\(582\) −2861.74 −0.203820
\(583\) 1010.08 0.0717551
\(584\) 4155.91 0.294474
\(585\) 8129.04 0.574520
\(586\) 1968.16 0.138744
\(587\) 9803.68 0.689338 0.344669 0.938724i \(-0.387991\pi\)
0.344669 + 0.938724i \(0.387991\pi\)
\(588\) −588.000 −0.0412393
\(589\) 6356.91 0.444706
\(590\) −580.746 −0.0405236
\(591\) 5165.61 0.359534
\(592\) −5815.12 −0.403716
\(593\) 8747.09 0.605734 0.302867 0.953033i \(-0.402056\pi\)
0.302867 + 0.953033i \(0.402056\pi\)
\(594\) −246.412 −0.0170209
\(595\) −7012.73 −0.483183
\(596\) 2209.77 0.151872
\(597\) −6350.01 −0.435324
\(598\) −3250.57 −0.222284
\(599\) −20587.5 −1.40431 −0.702157 0.712022i \(-0.747779\pi\)
−0.702157 + 0.712022i \(0.747779\pi\)
\(600\) 921.035 0.0626685
\(601\) −1385.33 −0.0940244 −0.0470122 0.998894i \(-0.514970\pi\)
−0.0470122 + 0.998894i \(0.514970\pi\)
\(602\) −6387.54 −0.432453
\(603\) 4020.46 0.271518
\(604\) 8636.02 0.581779
\(605\) 16746.5 1.12536
\(606\) 8045.82 0.539338
\(607\) −6297.96 −0.421131 −0.210565 0.977580i \(-0.567530\pi\)
−0.210565 + 0.977580i \(0.567530\pi\)
\(608\) 1381.40 0.0921434
\(609\) 3498.76 0.232803
\(610\) −10200.2 −0.677042
\(611\) 8334.26 0.551830
\(612\) −2821.61 −0.186367
\(613\) 20987.9 1.38286 0.691430 0.722444i \(-0.256981\pi\)
0.691430 + 0.722444i \(0.256981\pi\)
\(614\) 15154.3 0.996058
\(615\) −11319.8 −0.742208
\(616\) −255.539 −0.0167142
\(617\) −88.3741 −0.00576630 −0.00288315 0.999996i \(-0.500918\pi\)
−0.00288315 + 0.999996i \(0.500918\pi\)
\(618\) −8097.63 −0.527078
\(619\) −16529.3 −1.07330 −0.536648 0.843806i \(-0.680310\pi\)
−0.536648 + 0.843806i \(0.680310\pi\)
\(620\) 7528.90 0.487690
\(621\) 621.000 0.0401286
\(622\) 4446.36 0.286628
\(623\) 6689.93 0.430219
\(624\) 3391.90 0.217604
\(625\) −18949.3 −1.21276
\(626\) 6843.33 0.436924
\(627\) −590.962 −0.0376407
\(628\) 5340.12 0.339321
\(629\) 28486.1 1.80575
\(630\) −1610.52 −0.101848
\(631\) −5525.99 −0.348631 −0.174316 0.984690i \(-0.555771\pi\)
−0.174316 + 0.984690i \(0.555771\pi\)
\(632\) −680.852 −0.0428526
\(633\) 2616.34 0.164282
\(634\) 2380.44 0.149116
\(635\) −3197.92 −0.199852
\(636\) 2656.25 0.165609
\(637\) −3462.57 −0.215372
\(638\) 1520.52 0.0943544
\(639\) 2890.23 0.178929
\(640\) 1636.08 0.101050
\(641\) 2098.71 0.129320 0.0646601 0.997907i \(-0.479404\pi\)
0.0646601 + 0.997907i \(0.479404\pi\)
\(642\) 4896.71 0.301024
\(643\) −13772.3 −0.844677 −0.422338 0.906438i \(-0.638791\pi\)
−0.422338 + 0.906438i \(0.638791\pi\)
\(644\) 644.000 0.0394055
\(645\) −17495.3 −1.06803
\(646\) −6766.97 −0.412141
\(647\) −22099.9 −1.34287 −0.671436 0.741063i \(-0.734322\pi\)
−0.671436 + 0.741063i \(0.734322\pi\)
\(648\) −648.000 −0.0392837
\(649\) 103.665 0.00626994
\(650\) 5423.71 0.327285
\(651\) −3092.40 −0.186176
\(652\) 6222.27 0.373747
\(653\) −10236.7 −0.613467 −0.306734 0.951795i \(-0.599236\pi\)
−0.306734 + 0.951795i \(0.599236\pi\)
\(654\) −4763.57 −0.284817
\(655\) −20756.9 −1.23823
\(656\) −4723.27 −0.281117
\(657\) −4675.39 −0.277632
\(658\) −1651.18 −0.0978260
\(659\) −4648.69 −0.274791 −0.137396 0.990516i \(-0.543873\pi\)
−0.137396 + 0.990516i \(0.543873\pi\)
\(660\) −699.914 −0.0412790
\(661\) 1656.45 0.0974713 0.0487356 0.998812i \(-0.484481\pi\)
0.0487356 + 0.998812i \(0.484481\pi\)
\(662\) 14998.3 0.880553
\(663\) −16615.7 −0.973302
\(664\) 1311.03 0.0766230
\(665\) −3862.44 −0.225232
\(666\) 6542.00 0.380627
\(667\) −3831.97 −0.222451
\(668\) −9690.43 −0.561279
\(669\) −7413.50 −0.428434
\(670\) 11419.8 0.658484
\(671\) 1820.77 0.104754
\(672\) −672.000 −0.0385758
\(673\) 1740.37 0.0996826 0.0498413 0.998757i \(-0.484128\pi\)
0.0498413 + 0.998757i \(0.484128\pi\)
\(674\) −6952.66 −0.397339
\(675\) −1036.16 −0.0590844
\(676\) 11185.9 0.636433
\(677\) 12725.2 0.722406 0.361203 0.932487i \(-0.382366\pi\)
0.361203 + 0.932487i \(0.382366\pi\)
\(678\) −4537.49 −0.257022
\(679\) 3338.70 0.188700
\(680\) −8014.55 −0.451977
\(681\) −8769.91 −0.493485
\(682\) −1343.93 −0.0754569
\(683\) −19212.1 −1.07632 −0.538162 0.842841i \(-0.680881\pi\)
−0.538162 + 0.842841i \(0.680881\pi\)
\(684\) −1554.08 −0.0868736
\(685\) −14194.5 −0.791743
\(686\) 686.000 0.0381802
\(687\) −15018.0 −0.834022
\(688\) −7300.05 −0.404523
\(689\) 15641.9 0.864888
\(690\) 1763.90 0.0973196
\(691\) −24225.5 −1.33369 −0.666846 0.745195i \(-0.732356\pi\)
−0.666846 + 0.745195i \(0.732356\pi\)
\(692\) 6209.21 0.341096
\(693\) 287.481 0.0157583
\(694\) −14731.2 −0.805746
\(695\) 4499.26 0.245564
\(696\) 3998.58 0.217767
\(697\) 23137.5 1.25738
\(698\) 8676.12 0.470481
\(699\) −6486.26 −0.350977
\(700\) −1074.54 −0.0580197
\(701\) −3628.45 −0.195499 −0.0977494 0.995211i \(-0.531164\pi\)
−0.0977494 + 0.995211i \(0.531164\pi\)
\(702\) −3815.89 −0.205159
\(703\) 15689.5 0.841734
\(704\) −292.044 −0.0156347
\(705\) −4522.53 −0.241600
\(706\) −2947.82 −0.157143
\(707\) −9386.79 −0.499330
\(708\) 272.611 0.0144708
\(709\) 20542.5 1.08814 0.544069 0.839041i \(-0.316883\pi\)
0.544069 + 0.839041i \(0.316883\pi\)
\(710\) 8209.47 0.433938
\(711\) 765.958 0.0404018
\(712\) 7645.63 0.402433
\(713\) 3386.92 0.177898
\(714\) 3291.88 0.172543
\(715\) −4121.59 −0.215579
\(716\) 12484.4 0.651624
\(717\) 8446.89 0.439965
\(718\) −3466.52 −0.180180
\(719\) 615.398 0.0319200 0.0159600 0.999873i \(-0.494920\pi\)
0.0159600 + 0.999873i \(0.494920\pi\)
\(720\) −1840.59 −0.0952705
\(721\) 9447.23 0.487980
\(722\) 9990.92 0.514991
\(723\) −16549.3 −0.851281
\(724\) −3235.43 −0.166083
\(725\) 6393.80 0.327531
\(726\) −7861.06 −0.401861
\(727\) 13930.0 0.710638 0.355319 0.934745i \(-0.384372\pi\)
0.355319 + 0.934745i \(0.384372\pi\)
\(728\) −3957.22 −0.201462
\(729\) 729.000 0.0370370
\(730\) −13280.1 −0.673312
\(731\) 35760.2 1.80936
\(732\) 4788.14 0.241769
\(733\) 38591.7 1.94463 0.972316 0.233668i \(-0.0750728\pi\)
0.972316 + 0.233668i \(0.0750728\pi\)
\(734\) −6293.08 −0.316460
\(735\) 1878.94 0.0942933
\(736\) 736.000 0.0368605
\(737\) −2038.46 −0.101883
\(738\) 5313.67 0.265039
\(739\) −3312.27 −0.164877 −0.0824383 0.996596i \(-0.526271\pi\)
−0.0824383 + 0.996596i \(0.526271\pi\)
\(740\) 18582.0 0.923093
\(741\) −9151.51 −0.453696
\(742\) −3098.95 −0.153324
\(743\) −31981.0 −1.57910 −0.789550 0.613687i \(-0.789686\pi\)
−0.789550 + 0.613687i \(0.789686\pi\)
\(744\) −3534.17 −0.174152
\(745\) −7061.25 −0.347254
\(746\) −20805.9 −1.02112
\(747\) −1474.90 −0.0722409
\(748\) 1430.62 0.0699312
\(749\) −5712.83 −0.278694
\(750\) 6643.27 0.323437
\(751\) 18460.9 0.897001 0.448500 0.893783i \(-0.351958\pi\)
0.448500 + 0.893783i \(0.351958\pi\)
\(752\) −1887.06 −0.0915079
\(753\) 16581.0 0.802449
\(754\) 23546.5 1.13728
\(755\) −27596.1 −1.33023
\(756\) 756.000 0.0363696
\(757\) 568.470 0.0272938 0.0136469 0.999907i \(-0.495656\pi\)
0.0136469 + 0.999907i \(0.495656\pi\)
\(758\) 11970.7 0.573610
\(759\) −314.860 −0.0150576
\(760\) −4414.22 −0.210685
\(761\) 29609.3 1.41043 0.705215 0.708994i \(-0.250851\pi\)
0.705215 + 0.708994i \(0.250851\pi\)
\(762\) 1501.15 0.0713662
\(763\) 5557.49 0.263689
\(764\) −11900.1 −0.563523
\(765\) 9016.37 0.426128
\(766\) 5770.07 0.272169
\(767\) 1605.33 0.0755737
\(768\) −768.000 −0.0360844
\(769\) −31575.5 −1.48068 −0.740339 0.672234i \(-0.765335\pi\)
−0.740339 + 0.672234i \(0.765335\pi\)
\(770\) 816.566 0.0382169
\(771\) −11617.5 −0.542666
\(772\) 3802.01 0.177251
\(773\) −33899.2 −1.57732 −0.788660 0.614830i \(-0.789225\pi\)
−0.788660 + 0.614830i \(0.789225\pi\)
\(774\) 8212.55 0.381388
\(775\) −5651.21 −0.261932
\(776\) 3815.66 0.176513
\(777\) −7632.34 −0.352392
\(778\) −22571.1 −1.04012
\(779\) 12743.6 0.586119
\(780\) −10838.7 −0.497549
\(781\) −1465.41 −0.0671402
\(782\) −3605.39 −0.164870
\(783\) −4498.40 −0.205313
\(784\) 784.000 0.0357143
\(785\) −17064.2 −0.775856
\(786\) 9743.59 0.442166
\(787\) −6835.67 −0.309613 −0.154807 0.987945i \(-0.549475\pi\)
−0.154807 + 0.987945i \(0.549475\pi\)
\(788\) −6887.47 −0.311366
\(789\) 6881.60 0.310509
\(790\) 2175.64 0.0979821
\(791\) 5293.74 0.237956
\(792\) 328.550 0.0147405
\(793\) 28196.0 1.26264
\(794\) 4951.48 0.221312
\(795\) −8487.95 −0.378663
\(796\) 8466.68 0.377002
\(797\) 567.471 0.0252206 0.0126103 0.999920i \(-0.495986\pi\)
0.0126103 + 0.999920i \(0.495986\pi\)
\(798\) 1813.09 0.0804293
\(799\) 9244.00 0.409298
\(800\) −1228.05 −0.0542725
\(801\) −8601.33 −0.379417
\(802\) 15798.8 0.695605
\(803\) 2370.52 0.104177
\(804\) −5360.61 −0.235142
\(805\) −2057.88 −0.0901004
\(806\) −20811.7 −0.909507
\(807\) 3336.85 0.145555
\(808\) −10727.8 −0.467081
\(809\) −453.037 −0.0196884 −0.00984421 0.999952i \(-0.503134\pi\)
−0.00984421 + 0.999952i \(0.503134\pi\)
\(810\) 2070.66 0.0898219
\(811\) −4837.90 −0.209472 −0.104736 0.994500i \(-0.533400\pi\)
−0.104736 + 0.994500i \(0.533400\pi\)
\(812\) −4665.01 −0.201613
\(813\) 19781.3 0.853334
\(814\) −3316.93 −0.142824
\(815\) −19883.1 −0.854568
\(816\) 3762.15 0.161399
\(817\) 19695.9 0.843417
\(818\) 23542.5 1.00629
\(819\) 4451.87 0.189940
\(820\) 15093.1 0.642771
\(821\) −16163.9 −0.687117 −0.343558 0.939131i \(-0.611632\pi\)
−0.343558 + 0.939131i \(0.611632\pi\)
\(822\) 6663.10 0.282728
\(823\) 36866.5 1.56146 0.780732 0.624866i \(-0.214847\pi\)
0.780732 + 0.624866i \(0.214847\pi\)
\(824\) 10796.8 0.456463
\(825\) 525.357 0.0221704
\(826\) −318.046 −0.0133974
\(827\) 7053.95 0.296602 0.148301 0.988942i \(-0.452620\pi\)
0.148301 + 0.988942i \(0.452620\pi\)
\(828\) −828.000 −0.0347524
\(829\) 25899.6 1.08508 0.542540 0.840030i \(-0.317463\pi\)
0.542540 + 0.840030i \(0.317463\pi\)
\(830\) −4189.35 −0.175198
\(831\) 21141.3 0.882533
\(832\) −4522.53 −0.188450
\(833\) −3840.53 −0.159743
\(834\) −2112.02 −0.0876897
\(835\) 30965.5 1.28336
\(836\) 787.949 0.0325978
\(837\) 3975.95 0.164192
\(838\) 2104.28 0.0867436
\(839\) −28305.1 −1.16472 −0.582359 0.812932i \(-0.697870\pi\)
−0.582359 + 0.812932i \(0.697870\pi\)
\(840\) 2147.36 0.0882034
\(841\) 3369.04 0.138138
\(842\) 20693.7 0.846975
\(843\) 4820.32 0.196940
\(844\) −3488.46 −0.142272
\(845\) −35744.3 −1.45520
\(846\) 2122.94 0.0862744
\(847\) 9171.24 0.372051
\(848\) −3541.66 −0.143421
\(849\) 22306.6 0.901721
\(850\) 6015.75 0.242751
\(851\) 8359.23 0.336722
\(852\) −3853.64 −0.154957
\(853\) 24137.4 0.968874 0.484437 0.874826i \(-0.339024\pi\)
0.484437 + 0.874826i \(0.339024\pi\)
\(854\) −5586.17 −0.223835
\(855\) 4966.00 0.198636
\(856\) −6528.95 −0.260695
\(857\) 45567.7 1.81629 0.908146 0.418653i \(-0.137498\pi\)
0.908146 + 0.418653i \(0.137498\pi\)
\(858\) 1934.74 0.0769823
\(859\) 12381.3 0.491788 0.245894 0.969297i \(-0.420919\pi\)
0.245894 + 0.969297i \(0.420919\pi\)
\(860\) 23327.1 0.924938
\(861\) −6199.29 −0.245379
\(862\) −11808.2 −0.466574
\(863\) −12015.9 −0.473958 −0.236979 0.971515i \(-0.576157\pi\)
−0.236979 + 0.971515i \(0.576157\pi\)
\(864\) 864.000 0.0340207
\(865\) −19841.3 −0.779914
\(866\) 17087.1 0.670488
\(867\) −3690.37 −0.144558
\(868\) 4123.20 0.161233
\(869\) −388.357 −0.0151601
\(870\) −12777.3 −0.497922
\(871\) −31567.1 −1.22803
\(872\) 6351.42 0.246659
\(873\) −4292.62 −0.166418
\(874\) −1985.76 −0.0768529
\(875\) −7750.48 −0.299445
\(876\) 6233.86 0.240437
\(877\) 29870.9 1.15014 0.575069 0.818105i \(-0.304975\pi\)
0.575069 + 0.818105i \(0.304975\pi\)
\(878\) −34421.8 −1.32310
\(879\) 2952.23 0.113284
\(880\) 933.218 0.0357486
\(881\) −18857.5 −0.721143 −0.360571 0.932732i \(-0.617418\pi\)
−0.360571 + 0.932732i \(0.617418\pi\)
\(882\) −882.000 −0.0336718
\(883\) 43540.2 1.65939 0.829697 0.558213i \(-0.188513\pi\)
0.829697 + 0.558213i \(0.188513\pi\)
\(884\) 22154.2 0.842904
\(885\) −871.119 −0.0330874
\(886\) 23707.1 0.898934
\(887\) −26111.3 −0.988422 −0.494211 0.869342i \(-0.664543\pi\)
−0.494211 + 0.869342i \(0.664543\pi\)
\(888\) −8722.67 −0.329633
\(889\) −1751.34 −0.0660722
\(890\) −24431.4 −0.920159
\(891\) −369.618 −0.0138975
\(892\) 9884.67 0.371035
\(893\) 5091.37 0.190791
\(894\) 3314.65 0.124003
\(895\) −39893.4 −1.48993
\(896\) 896.000 0.0334077
\(897\) −4875.86 −0.181494
\(898\) 26670.0 0.991079
\(899\) −24534.2 −0.910189
\(900\) 1381.55 0.0511686
\(901\) 17349.3 0.641497
\(902\) −2694.15 −0.0994515
\(903\) −9581.31 −0.353096
\(904\) 6049.98 0.222588
\(905\) 10338.7 0.379747
\(906\) 12954.0 0.475021
\(907\) −3966.29 −0.145202 −0.0726012 0.997361i \(-0.523130\pi\)
−0.0726012 + 0.997361i \(0.523130\pi\)
\(908\) 11693.2 0.427371
\(909\) 12068.7 0.440368
\(910\) 12645.2 0.460641
\(911\) −17533.1 −0.637649 −0.318824 0.947814i \(-0.603288\pi\)
−0.318824 + 0.947814i \(0.603288\pi\)
\(912\) 2072.10 0.0752348
\(913\) 747.808 0.0271072
\(914\) 32169.5 1.16419
\(915\) −15300.4 −0.552803
\(916\) 20024.0 0.722284
\(917\) −11367.5 −0.409366
\(918\) −4232.42 −0.152168
\(919\) 47649.9 1.71036 0.855182 0.518328i \(-0.173445\pi\)
0.855182 + 0.518328i \(0.173445\pi\)
\(920\) −2351.87 −0.0842812
\(921\) 22731.5 0.813278
\(922\) −8717.72 −0.311391
\(923\) −22693.0 −0.809263
\(924\) −383.308 −0.0136471
\(925\) −13947.7 −0.495782
\(926\) −1042.05 −0.0369805
\(927\) −12146.4 −0.430358
\(928\) −5331.44 −0.188592
\(929\) 3997.24 0.141168 0.0705841 0.997506i \(-0.477514\pi\)
0.0705841 + 0.997506i \(0.477514\pi\)
\(930\) 11293.3 0.398197
\(931\) −2115.27 −0.0744631
\(932\) 8648.35 0.303955
\(933\) 6669.53 0.234031
\(934\) −152.299 −0.00533552
\(935\) −4571.49 −0.159897
\(936\) 5087.85 0.177673
\(937\) −56435.2 −1.96762 −0.983808 0.179225i \(-0.942641\pi\)
−0.983808 + 0.179225i \(0.942641\pi\)
\(938\) 6254.04 0.217699
\(939\) 10265.0 0.356747
\(940\) 6030.04 0.209232
\(941\) 42259.7 1.46400 0.732002 0.681302i \(-0.238586\pi\)
0.732002 + 0.681302i \(0.238586\pi\)
\(942\) 8010.18 0.277055
\(943\) 6789.69 0.234468
\(944\) −363.481 −0.0125321
\(945\) −2415.78 −0.0831589
\(946\) −4163.94 −0.143109
\(947\) −51670.3 −1.77303 −0.886514 0.462701i \(-0.846880\pi\)
−0.886514 + 0.462701i \(0.846880\pi\)
\(948\) −1021.28 −0.0349890
\(949\) 36709.4 1.25568
\(950\) 3313.33 0.113156
\(951\) 3570.66 0.121753
\(952\) −4389.17 −0.149426
\(953\) 50516.5 1.71709 0.858546 0.512736i \(-0.171368\pi\)
0.858546 + 0.512736i \(0.171368\pi\)
\(954\) 3984.37 0.135219
\(955\) 38026.5 1.28849
\(956\) −11262.5 −0.381021
\(957\) 2280.78 0.0770400
\(958\) 33359.6 1.12505
\(959\) −7773.62 −0.261755
\(960\) 2454.12 0.0825067
\(961\) −8106.30 −0.272106
\(962\) −51365.3 −1.72150
\(963\) 7345.06 0.245785
\(964\) 22065.8 0.737231
\(965\) −12149.2 −0.405282
\(966\) 966.000 0.0321745
\(967\) −87.5748 −0.00291232 −0.00145616 0.999999i \(-0.500464\pi\)
−0.00145616 + 0.999999i \(0.500464\pi\)
\(968\) 10481.4 0.348022
\(969\) −10150.5 −0.336511
\(970\) −12192.8 −0.403596
\(971\) −45984.9 −1.51980 −0.759900 0.650040i \(-0.774752\pi\)
−0.759900 + 0.650040i \(0.774752\pi\)
\(972\) −972.000 −0.0320750
\(973\) 2464.02 0.0811849
\(974\) 24797.5 0.815774
\(975\) 8135.57 0.267227
\(976\) −6384.19 −0.209378
\(977\) −26575.8 −0.870249 −0.435125 0.900370i \(-0.643296\pi\)
−0.435125 + 0.900370i \(0.643296\pi\)
\(978\) 9333.40 0.305163
\(979\) 4361.06 0.142370
\(980\) −2505.25 −0.0816604
\(981\) −7145.35 −0.232552
\(982\) −28538.7 −0.927399
\(983\) 7451.37 0.241772 0.120886 0.992666i \(-0.461426\pi\)
0.120886 + 0.992666i \(0.461426\pi\)
\(984\) −7084.90 −0.229531
\(985\) 22008.7 0.711935
\(986\) 26116.7 0.843536
\(987\) −2476.76 −0.0798746
\(988\) 12202.0 0.392913
\(989\) 10493.8 0.337395
\(990\) −1049.87 −0.0337041
\(991\) 50945.4 1.63303 0.816515 0.577324i \(-0.195903\pi\)
0.816515 + 0.577324i \(0.195903\pi\)
\(992\) 4712.23 0.150820
\(993\) 22497.5 0.718968
\(994\) 4495.92 0.143463
\(995\) −27055.0 −0.862012
\(996\) 1966.54 0.0625624
\(997\) −16659.1 −0.529187 −0.264593 0.964360i \(-0.585238\pi\)
−0.264593 + 0.964360i \(0.585238\pi\)
\(998\) 22649.0 0.718378
\(999\) 9813.01 0.310781
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 966.4.a.m.1.1 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
966.4.a.m.1.1 5 1.1 even 1 trivial