Properties

Label 2166.4.a.s.1.1
Level $2166$
Weight $4$
Character 2166.1
Self dual yes
Analytic conductor $127.798$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2166 = 2 \cdot 3 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2166.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(127.798137072\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.1524.1
Defining polynomial: \(x^{3} - x^{2} - 7 x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{3}\cdot 3 \)
Twist minimal: no (minimal twist has level 114)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(3.13264\) of defining polynomial
Character \(\chi\) \(=\) 2166.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -12.9884 q^{5} +6.00000 q^{6} -25.6033 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -12.9884 q^{5} +6.00000 q^{6} -25.6033 q^{7} -8.00000 q^{8} +9.00000 q^{9} +25.9768 q^{10} +26.7726 q^{11} -12.0000 q^{12} -8.59165 q^{13} +51.2065 q^{14} +38.9652 q^{15} +16.0000 q^{16} +8.16936 q^{17} -18.0000 q^{18} -51.9536 q^{20} +76.8098 q^{21} -53.5452 q^{22} +156.900 q^{23} +24.0000 q^{24} +43.6984 q^{25} +17.1833 q^{26} -27.0000 q^{27} -102.413 q^{28} -207.357 q^{29} -77.9304 q^{30} +94.5197 q^{31} -32.0000 q^{32} -80.3178 q^{33} -16.3387 q^{34} +332.545 q^{35} +36.0000 q^{36} +197.387 q^{37} +25.7749 q^{39} +103.907 q^{40} -376.738 q^{41} -153.620 q^{42} -508.244 q^{43} +107.090 q^{44} -116.896 q^{45} -313.800 q^{46} -366.487 q^{47} -48.0000 q^{48} +312.527 q^{49} -87.3968 q^{50} -24.5081 q^{51} -34.3666 q^{52} -203.329 q^{53} +54.0000 q^{54} -347.733 q^{55} +204.826 q^{56} +414.715 q^{58} +592.204 q^{59} +155.861 q^{60} -509.060 q^{61} -189.039 q^{62} -230.429 q^{63} +64.0000 q^{64} +111.592 q^{65} +160.636 q^{66} -250.719 q^{67} +32.6774 q^{68} -470.701 q^{69} -665.090 q^{70} -115.436 q^{71} -72.0000 q^{72} -832.671 q^{73} -394.775 q^{74} -131.095 q^{75} -685.466 q^{77} -51.5499 q^{78} +369.429 q^{79} -207.814 q^{80} +81.0000 q^{81} +753.476 q^{82} -1288.29 q^{83} +307.239 q^{84} -106.107 q^{85} +1016.49 q^{86} +622.072 q^{87} -214.181 q^{88} +61.0743 q^{89} +233.791 q^{90} +219.974 q^{91} +627.601 q^{92} -283.559 q^{93} +732.975 q^{94} +96.0000 q^{96} +247.510 q^{97} -625.053 q^{98} +240.954 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q - 6q^{2} - 9q^{3} + 12q^{4} + 2q^{5} + 18q^{6} - 17q^{7} - 24q^{8} + 27q^{9} + O(q^{10}) \) \( 3q - 6q^{2} - 9q^{3} + 12q^{4} + 2q^{5} + 18q^{6} - 17q^{7} - 24q^{8} + 27q^{9} - 4q^{10} - 52q^{11} - 36q^{12} + 75q^{13} + 34q^{14} - 6q^{15} + 48q^{16} - 48q^{17} - 54q^{18} + 8q^{20} + 51q^{21} + 104q^{22} - 238q^{23} + 72q^{24} + 229q^{25} - 150q^{26} - 81q^{27} - 68q^{28} - 8q^{29} + 12q^{30} + 107q^{31} - 96q^{32} + 156q^{33} + 96q^{34} - 294q^{35} + 108q^{36} + 305q^{37} - 225q^{39} - 16q^{40} + 16q^{41} - 102q^{42} - 331q^{43} - 208q^{44} + 18q^{45} + 476q^{46} - 766q^{47} - 144q^{48} + 1142q^{49} - 458q^{50} + 144q^{51} + 300q^{52} - 118q^{53} + 162q^{54} - 1400q^{55} + 136q^{56} + 16q^{58} + 936q^{59} - 24q^{60} - 399q^{61} - 214q^{62} - 153q^{63} + 192q^{64} + 370q^{65} - 312q^{66} + 61q^{67} - 192q^{68} + 714q^{69} + 588q^{70} + 974q^{71} - 216q^{72} + 91q^{73} - 610q^{74} - 687q^{75} - 36q^{77} + 450q^{78} - 321q^{79} + 32q^{80} + 243q^{81} - 32q^{82} - 2148q^{83} + 204q^{84} - 1680q^{85} + 662q^{86} + 24q^{87} + 416q^{88} + 1116q^{89} - 36q^{90} + 1367q^{91} - 952q^{92} - 321q^{93} + 1532q^{94} + 288q^{96} + 1382q^{97} - 2284q^{98} - 468q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.00000 −0.707107
\(3\) −3.00000 −0.577350
\(4\) 4.00000 0.500000
\(5\) −12.9884 −1.16172 −0.580859 0.814004i \(-0.697283\pi\)
−0.580859 + 0.814004i \(0.697283\pi\)
\(6\) 6.00000 0.408248
\(7\) −25.6033 −1.38245 −0.691223 0.722642i \(-0.742928\pi\)
−0.691223 + 0.722642i \(0.742928\pi\)
\(8\) −8.00000 −0.353553
\(9\) 9.00000 0.333333
\(10\) 25.9768 0.821458
\(11\) 26.7726 0.733841 0.366920 0.930252i \(-0.380412\pi\)
0.366920 + 0.930252i \(0.380412\pi\)
\(12\) −12.0000 −0.288675
\(13\) −8.59165 −0.183300 −0.0916498 0.995791i \(-0.529214\pi\)
−0.0916498 + 0.995791i \(0.529214\pi\)
\(14\) 51.2065 0.977537
\(15\) 38.9652 0.670718
\(16\) 16.0000 0.250000
\(17\) 8.16936 0.116551 0.0582753 0.998301i \(-0.481440\pi\)
0.0582753 + 0.998301i \(0.481440\pi\)
\(18\) −18.0000 −0.235702
\(19\) 0 0
\(20\) −51.9536 −0.580859
\(21\) 76.8098 0.798155
\(22\) −53.5452 −0.518904
\(23\) 156.900 1.42243 0.711217 0.702973i \(-0.248145\pi\)
0.711217 + 0.702973i \(0.248145\pi\)
\(24\) 24.0000 0.204124
\(25\) 43.6984 0.349587
\(26\) 17.1833 0.129612
\(27\) −27.0000 −0.192450
\(28\) −102.413 −0.691223
\(29\) −207.357 −1.32777 −0.663884 0.747835i \(-0.731093\pi\)
−0.663884 + 0.747835i \(0.731093\pi\)
\(30\) −77.9304 −0.474269
\(31\) 94.5197 0.547621 0.273810 0.961784i \(-0.411716\pi\)
0.273810 + 0.961784i \(0.411716\pi\)
\(32\) −32.0000 −0.176777
\(33\) −80.3178 −0.423683
\(34\) −16.3387 −0.0824138
\(35\) 332.545 1.60601
\(36\) 36.0000 0.166667
\(37\) 197.387 0.877035 0.438517 0.898723i \(-0.355504\pi\)
0.438517 + 0.898723i \(0.355504\pi\)
\(38\) 0 0
\(39\) 25.7749 0.105828
\(40\) 103.907 0.410729
\(41\) −376.738 −1.43504 −0.717519 0.696539i \(-0.754722\pi\)
−0.717519 + 0.696539i \(0.754722\pi\)
\(42\) −153.620 −0.564381
\(43\) −508.244 −1.80248 −0.901238 0.433325i \(-0.857340\pi\)
−0.901238 + 0.433325i \(0.857340\pi\)
\(44\) 107.090 0.366920
\(45\) −116.896 −0.387239
\(46\) −313.800 −1.00581
\(47\) −366.487 −1.13740 −0.568699 0.822546i \(-0.692553\pi\)
−0.568699 + 0.822546i \(0.692553\pi\)
\(48\) −48.0000 −0.144338
\(49\) 312.527 0.911156
\(50\) −87.3968 −0.247196
\(51\) −24.5081 −0.0672906
\(52\) −34.3666 −0.0916498
\(53\) −203.329 −0.526970 −0.263485 0.964663i \(-0.584872\pi\)
−0.263485 + 0.964663i \(0.584872\pi\)
\(54\) 54.0000 0.136083
\(55\) −347.733 −0.852516
\(56\) 204.826 0.488768
\(57\) 0 0
\(58\) 414.715 0.938874
\(59\) 592.204 1.30675 0.653376 0.757033i \(-0.273352\pi\)
0.653376 + 0.757033i \(0.273352\pi\)
\(60\) 155.861 0.335359
\(61\) −509.060 −1.06850 −0.534250 0.845327i \(-0.679406\pi\)
−0.534250 + 0.845327i \(0.679406\pi\)
\(62\) −189.039 −0.387226
\(63\) −230.429 −0.460815
\(64\) 64.0000 0.125000
\(65\) 111.592 0.212942
\(66\) 160.636 0.299589
\(67\) −250.719 −0.457167 −0.228584 0.973524i \(-0.573409\pi\)
−0.228584 + 0.973524i \(0.573409\pi\)
\(68\) 32.6774 0.0582753
\(69\) −470.701 −0.821242
\(70\) −665.090 −1.13562
\(71\) −115.436 −0.192954 −0.0964771 0.995335i \(-0.530757\pi\)
−0.0964771 + 0.995335i \(0.530757\pi\)
\(72\) −72.0000 −0.117851
\(73\) −832.671 −1.33502 −0.667512 0.744599i \(-0.732641\pi\)
−0.667512 + 0.744599i \(0.732641\pi\)
\(74\) −394.775 −0.620157
\(75\) −131.095 −0.201834
\(76\) 0 0
\(77\) −685.466 −1.01449
\(78\) −51.5499 −0.0748318
\(79\) 369.429 0.526127 0.263064 0.964778i \(-0.415267\pi\)
0.263064 + 0.964778i \(0.415267\pi\)
\(80\) −207.814 −0.290429
\(81\) 81.0000 0.111111
\(82\) 753.476 1.01473
\(83\) −1288.29 −1.70371 −0.851854 0.523780i \(-0.824521\pi\)
−0.851854 + 0.523780i \(0.824521\pi\)
\(84\) 307.239 0.399078
\(85\) −106.107 −0.135399
\(86\) 1016.49 1.27454
\(87\) 622.072 0.766588
\(88\) −214.181 −0.259452
\(89\) 61.0743 0.0727401 0.0363700 0.999338i \(-0.488421\pi\)
0.0363700 + 0.999338i \(0.488421\pi\)
\(90\) 233.791 0.273819
\(91\) 219.974 0.253402
\(92\) 627.601 0.711217
\(93\) −283.559 −0.316169
\(94\) 732.975 0.804261
\(95\) 0 0
\(96\) 96.0000 0.102062
\(97\) 247.510 0.259081 0.129541 0.991574i \(-0.458650\pi\)
0.129541 + 0.991574i \(0.458650\pi\)
\(98\) −625.053 −0.644285
\(99\) 240.954 0.244614
\(100\) 174.794 0.174794
\(101\) −846.012 −0.833478 −0.416739 0.909026i \(-0.636827\pi\)
−0.416739 + 0.909026i \(0.636827\pi\)
\(102\) 49.0162 0.0475816
\(103\) −1422.55 −1.36085 −0.680427 0.732816i \(-0.738206\pi\)
−0.680427 + 0.732816i \(0.738206\pi\)
\(104\) 68.7332 0.0648062
\(105\) −997.636 −0.927231
\(106\) 406.659 0.372624
\(107\) 286.239 0.258615 0.129307 0.991605i \(-0.458725\pi\)
0.129307 + 0.991605i \(0.458725\pi\)
\(108\) −108.000 −0.0962250
\(109\) −32.2854 −0.0283705 −0.0141852 0.999899i \(-0.504515\pi\)
−0.0141852 + 0.999899i \(0.504515\pi\)
\(110\) 695.467 0.602820
\(111\) −592.162 −0.506356
\(112\) −409.652 −0.345611
\(113\) −297.098 −0.247333 −0.123666 0.992324i \(-0.539465\pi\)
−0.123666 + 0.992324i \(0.539465\pi\)
\(114\) 0 0
\(115\) −2037.88 −1.65247
\(116\) −829.429 −0.663884
\(117\) −77.3248 −0.0610999
\(118\) −1184.41 −0.924014
\(119\) −209.162 −0.161125
\(120\) −311.721 −0.237135
\(121\) −614.227 −0.461478
\(122\) 1018.12 0.755543
\(123\) 1130.21 0.828520
\(124\) 378.079 0.273810
\(125\) 1055.98 0.755596
\(126\) 460.859 0.325846
\(127\) 2667.19 1.86358 0.931792 0.362994i \(-0.118245\pi\)
0.931792 + 0.362994i \(0.118245\pi\)
\(128\) −128.000 −0.0883883
\(129\) 1524.73 1.04066
\(130\) −223.183 −0.150573
\(131\) 822.276 0.548417 0.274208 0.961670i \(-0.411584\pi\)
0.274208 + 0.961670i \(0.411584\pi\)
\(132\) −321.271 −0.211842
\(133\) 0 0
\(134\) 501.438 0.323266
\(135\) 350.687 0.223573
\(136\) −65.3549 −0.0412069
\(137\) −2445.22 −1.52489 −0.762443 0.647055i \(-0.776000\pi\)
−0.762443 + 0.647055i \(0.776000\pi\)
\(138\) 941.401 0.580706
\(139\) 1504.34 0.917961 0.458980 0.888446i \(-0.348215\pi\)
0.458980 + 0.888446i \(0.348215\pi\)
\(140\) 1330.18 0.803006
\(141\) 1099.46 0.656677
\(142\) 230.872 0.136439
\(143\) −230.021 −0.134513
\(144\) 144.000 0.0833333
\(145\) 2693.24 1.54249
\(146\) 1665.34 0.944004
\(147\) −937.580 −0.526056
\(148\) 789.550 0.438517
\(149\) −720.747 −0.396281 −0.198141 0.980174i \(-0.563490\pi\)
−0.198141 + 0.980174i \(0.563490\pi\)
\(150\) 262.191 0.142718
\(151\) 1801.25 0.970752 0.485376 0.874306i \(-0.338683\pi\)
0.485376 + 0.874306i \(0.338683\pi\)
\(152\) 0 0
\(153\) 73.5243 0.0388502
\(154\) 1370.93 0.717356
\(155\) −1227.66 −0.636180
\(156\) 103.100 0.0529140
\(157\) 3829.11 1.94647 0.973236 0.229808i \(-0.0738097\pi\)
0.973236 + 0.229808i \(0.0738097\pi\)
\(158\) −738.859 −0.372028
\(159\) 609.988 0.304247
\(160\) 415.629 0.205365
\(161\) −4017.16 −1.96644
\(162\) −162.000 −0.0785674
\(163\) −956.496 −0.459623 −0.229812 0.973235i \(-0.573811\pi\)
−0.229812 + 0.973235i \(0.573811\pi\)
\(164\) −1506.95 −0.717519
\(165\) 1043.20 0.492200
\(166\) 2576.57 1.20470
\(167\) −2779.77 −1.28805 −0.644027 0.765003i \(-0.722737\pi\)
−0.644027 + 0.765003i \(0.722737\pi\)
\(168\) −614.478 −0.282191
\(169\) −2123.18 −0.966401
\(170\) 212.214 0.0957415
\(171\) 0 0
\(172\) −2032.97 −0.901238
\(173\) −309.552 −0.136039 −0.0680196 0.997684i \(-0.521668\pi\)
−0.0680196 + 0.997684i \(0.521668\pi\)
\(174\) −1244.14 −0.542059
\(175\) −1118.82 −0.483286
\(176\) 428.362 0.183460
\(177\) −1776.61 −0.754454
\(178\) −122.149 −0.0514350
\(179\) 4650.29 1.94178 0.970890 0.239524i \(-0.0769913\pi\)
0.970890 + 0.239524i \(0.0769913\pi\)
\(180\) −467.582 −0.193620
\(181\) −269.728 −0.110767 −0.0553833 0.998465i \(-0.517638\pi\)
−0.0553833 + 0.998465i \(0.517638\pi\)
\(182\) −439.948 −0.179182
\(183\) 1527.18 0.616899
\(184\) −1255.20 −0.502906
\(185\) −2563.75 −1.01887
\(186\) 567.118 0.223565
\(187\) 218.715 0.0855296
\(188\) −1465.95 −0.568699
\(189\) 691.288 0.266052
\(190\) 0 0
\(191\) −1949.96 −0.738715 −0.369357 0.929287i \(-0.620422\pi\)
−0.369357 + 0.929287i \(0.620422\pi\)
\(192\) −192.000 −0.0721688
\(193\) 2931.30 1.09326 0.546631 0.837374i \(-0.315910\pi\)
0.546631 + 0.837374i \(0.315910\pi\)
\(194\) −495.021 −0.183198
\(195\) −334.775 −0.122942
\(196\) 1250.11 0.455578
\(197\) −1236.48 −0.447186 −0.223593 0.974683i \(-0.571779\pi\)
−0.223593 + 0.974683i \(0.571779\pi\)
\(198\) −481.907 −0.172968
\(199\) −4509.01 −1.60621 −0.803103 0.595840i \(-0.796819\pi\)
−0.803103 + 0.595840i \(0.796819\pi\)
\(200\) −349.587 −0.123598
\(201\) 752.157 0.263946
\(202\) 1692.02 0.589358
\(203\) 5309.02 1.83557
\(204\) −98.0323 −0.0336453
\(205\) 4893.22 1.66711
\(206\) 2845.10 0.962269
\(207\) 1412.10 0.474144
\(208\) −137.466 −0.0458249
\(209\) 0 0
\(210\) 1995.27 0.655651
\(211\) −1.90470 −0.000621444 0 −0.000310722 1.00000i \(-0.500099\pi\)
−0.000310722 1.00000i \(0.500099\pi\)
\(212\) −813.317 −0.263485
\(213\) 346.308 0.111402
\(214\) −572.479 −0.182868
\(215\) 6601.27 2.09397
\(216\) 216.000 0.0680414
\(217\) −2420.01 −0.757056
\(218\) 64.5708 0.0200610
\(219\) 2498.01 0.770776
\(220\) −1390.93 −0.426258
\(221\) −70.1883 −0.0213637
\(222\) 1184.32 0.358048
\(223\) −4660.23 −1.39943 −0.699713 0.714424i \(-0.746689\pi\)
−0.699713 + 0.714424i \(0.746689\pi\)
\(224\) 819.304 0.244384
\(225\) 393.286 0.116529
\(226\) 594.195 0.174891
\(227\) −4045.15 −1.18276 −0.591380 0.806393i \(-0.701416\pi\)
−0.591380 + 0.806393i \(0.701416\pi\)
\(228\) 0 0
\(229\) 5062.73 1.46094 0.730468 0.682947i \(-0.239302\pi\)
0.730468 + 0.682947i \(0.239302\pi\)
\(230\) 4075.76 1.16847
\(231\) 2056.40 0.585719
\(232\) 1658.86 0.469437
\(233\) 433.089 0.121771 0.0608854 0.998145i \(-0.480608\pi\)
0.0608854 + 0.998145i \(0.480608\pi\)
\(234\) 154.650 0.0432041
\(235\) 4760.08 1.32133
\(236\) 2368.82 0.653376
\(237\) −1108.29 −0.303760
\(238\) 418.325 0.113933
\(239\) −4165.22 −1.12730 −0.563652 0.826012i \(-0.690604\pi\)
−0.563652 + 0.826012i \(0.690604\pi\)
\(240\) 623.443 0.167679
\(241\) 4169.42 1.11442 0.557212 0.830370i \(-0.311871\pi\)
0.557212 + 0.830370i \(0.311871\pi\)
\(242\) 1228.45 0.326314
\(243\) −243.000 −0.0641500
\(244\) −2036.24 −0.534250
\(245\) −4059.22 −1.05851
\(246\) −2260.43 −0.585852
\(247\) 0 0
\(248\) −756.158 −0.193613
\(249\) 3864.86 0.983636
\(250\) −2111.95 −0.534287
\(251\) −7132.25 −1.79356 −0.896780 0.442477i \(-0.854100\pi\)
−0.896780 + 0.442477i \(0.854100\pi\)
\(252\) −921.717 −0.230408
\(253\) 4200.63 1.04384
\(254\) −5334.38 −1.31775
\(255\) 318.321 0.0781726
\(256\) 256.000 0.0625000
\(257\) −1077.52 −0.261532 −0.130766 0.991413i \(-0.541744\pi\)
−0.130766 + 0.991413i \(0.541744\pi\)
\(258\) −3049.46 −0.735857
\(259\) −5053.76 −1.21245
\(260\) 446.367 0.106471
\(261\) −1866.22 −0.442590
\(262\) −1644.55 −0.387789
\(263\) 2489.16 0.583606 0.291803 0.956478i \(-0.405745\pi\)
0.291803 + 0.956478i \(0.405745\pi\)
\(264\) 642.543 0.149795
\(265\) 2640.92 0.612191
\(266\) 0 0
\(267\) −183.223 −0.0419965
\(268\) −1002.88 −0.228584
\(269\) −6181.28 −1.40104 −0.700519 0.713634i \(-0.747048\pi\)
−0.700519 + 0.713634i \(0.747048\pi\)
\(270\) −701.373 −0.158090
\(271\) 6032.71 1.35226 0.676128 0.736784i \(-0.263657\pi\)
0.676128 + 0.736784i \(0.263657\pi\)
\(272\) 130.710 0.0291377
\(273\) −659.923 −0.146302
\(274\) 4890.45 1.07826
\(275\) 1169.92 0.256541
\(276\) −1882.80 −0.410621
\(277\) 912.717 0.197978 0.0989889 0.995089i \(-0.468439\pi\)
0.0989889 + 0.995089i \(0.468439\pi\)
\(278\) −3008.68 −0.649096
\(279\) 850.677 0.182540
\(280\) −2660.36 −0.567811
\(281\) −334.886 −0.0710948 −0.0355474 0.999368i \(-0.511317\pi\)
−0.0355474 + 0.999368i \(0.511317\pi\)
\(282\) −2198.92 −0.464340
\(283\) −2776.94 −0.583293 −0.291646 0.956526i \(-0.594203\pi\)
−0.291646 + 0.956526i \(0.594203\pi\)
\(284\) −461.744 −0.0964771
\(285\) 0 0
\(286\) 460.042 0.0951149
\(287\) 9645.72 1.98386
\(288\) −288.000 −0.0589256
\(289\) −4846.26 −0.986416
\(290\) −5386.48 −1.09071
\(291\) −742.531 −0.149581
\(292\) −3330.68 −0.667512
\(293\) −3067.85 −0.611692 −0.305846 0.952081i \(-0.598939\pi\)
−0.305846 + 0.952081i \(0.598939\pi\)
\(294\) 1875.16 0.371978
\(295\) −7691.78 −1.51808
\(296\) −1579.10 −0.310079
\(297\) −722.861 −0.141228
\(298\) 1441.49 0.280213
\(299\) −1348.03 −0.260731
\(300\) −524.381 −0.100917
\(301\) 13012.7 2.49182
\(302\) −3602.50 −0.686425
\(303\) 2538.04 0.481209
\(304\) 0 0
\(305\) 6611.88 1.24129
\(306\) −147.049 −0.0274713
\(307\) −7487.81 −1.39203 −0.696013 0.718029i \(-0.745044\pi\)
−0.696013 + 0.718029i \(0.745044\pi\)
\(308\) −2741.86 −0.507247
\(309\) 4267.65 0.785690
\(310\) 2455.32 0.449847
\(311\) −6681.88 −1.21831 −0.609156 0.793051i \(-0.708492\pi\)
−0.609156 + 0.793051i \(0.708492\pi\)
\(312\) −206.200 −0.0374159
\(313\) 8162.02 1.47394 0.736972 0.675923i \(-0.236255\pi\)
0.736972 + 0.675923i \(0.236255\pi\)
\(314\) −7658.22 −1.37636
\(315\) 2992.91 0.535337
\(316\) 1477.72 0.263064
\(317\) −2839.54 −0.503106 −0.251553 0.967844i \(-0.580941\pi\)
−0.251553 + 0.967844i \(0.580941\pi\)
\(318\) −1219.98 −0.215135
\(319\) −5551.50 −0.974371
\(320\) −831.257 −0.145215
\(321\) −858.718 −0.149311
\(322\) 8034.31 1.39048
\(323\) 0 0
\(324\) 324.000 0.0555556
\(325\) −375.442 −0.0640792
\(326\) 1912.99 0.325003
\(327\) 96.8562 0.0163797
\(328\) 3013.90 0.507363
\(329\) 9383.27 1.57239
\(330\) −2086.40 −0.348038
\(331\) 11056.2 1.83597 0.917984 0.396617i \(-0.129816\pi\)
0.917984 + 0.396617i \(0.129816\pi\)
\(332\) −5153.14 −0.851854
\(333\) 1776.49 0.292345
\(334\) 5559.54 0.910791
\(335\) 3256.44 0.531099
\(336\) 1228.96 0.199539
\(337\) −5050.33 −0.816347 −0.408174 0.912904i \(-0.633834\pi\)
−0.408174 + 0.912904i \(0.633834\pi\)
\(338\) 4246.37 0.683349
\(339\) 891.293 0.142798
\(340\) −424.428 −0.0676995
\(341\) 2530.54 0.401866
\(342\) 0 0
\(343\) 780.217 0.122822
\(344\) 4065.95 0.637271
\(345\) 6113.65 0.954051
\(346\) 619.104 0.0961943
\(347\) −6014.85 −0.930531 −0.465265 0.885171i \(-0.654041\pi\)
−0.465265 + 0.885171i \(0.654041\pi\)
\(348\) 2488.29 0.383294
\(349\) −2514.51 −0.385669 −0.192834 0.981231i \(-0.561768\pi\)
−0.192834 + 0.981231i \(0.561768\pi\)
\(350\) 2237.64 0.341735
\(351\) 231.975 0.0352760
\(352\) −856.724 −0.129726
\(353\) 4578.03 0.690266 0.345133 0.938554i \(-0.387834\pi\)
0.345133 + 0.938554i \(0.387834\pi\)
\(354\) 3553.23 0.533480
\(355\) 1499.33 0.224158
\(356\) 244.297 0.0363700
\(357\) 627.487 0.0930255
\(358\) −9300.57 −1.37305
\(359\) 7972.44 1.17206 0.586029 0.810290i \(-0.300690\pi\)
0.586029 + 0.810290i \(0.300690\pi\)
\(360\) 935.164 0.136910
\(361\) 0 0
\(362\) 539.456 0.0783238
\(363\) 1842.68 0.266434
\(364\) 879.897 0.126701
\(365\) 10815.1 1.55092
\(366\) −3054.36 −0.436213
\(367\) 5465.50 0.777376 0.388688 0.921369i \(-0.372928\pi\)
0.388688 + 0.921369i \(0.372928\pi\)
\(368\) 2510.40 0.355608
\(369\) −3390.64 −0.478346
\(370\) 5127.49 0.720447
\(371\) 5205.89 0.728508
\(372\) −1134.24 −0.158084
\(373\) 9245.54 1.28342 0.641710 0.766947i \(-0.278225\pi\)
0.641710 + 0.766947i \(0.278225\pi\)
\(374\) −437.430 −0.0604786
\(375\) −3167.93 −0.436243
\(376\) 2931.90 0.402131
\(377\) 1781.54 0.243379
\(378\) −1382.58 −0.188127
\(379\) 6098.42 0.826530 0.413265 0.910611i \(-0.364388\pi\)
0.413265 + 0.910611i \(0.364388\pi\)
\(380\) 0 0
\(381\) −8001.58 −1.07594
\(382\) 3899.93 0.522350
\(383\) 4529.81 0.604341 0.302170 0.953254i \(-0.402289\pi\)
0.302170 + 0.953254i \(0.402289\pi\)
\(384\) 384.000 0.0510310
\(385\) 8903.10 1.17856
\(386\) −5862.60 −0.773053
\(387\) −4574.19 −0.600825
\(388\) 990.042 0.129541
\(389\) −5558.92 −0.724546 −0.362273 0.932072i \(-0.617999\pi\)
−0.362273 + 0.932072i \(0.617999\pi\)
\(390\) 669.550 0.0869334
\(391\) 1281.77 0.165786
\(392\) −2500.21 −0.322142
\(393\) −2466.83 −0.316629
\(394\) 2472.96 0.316208
\(395\) −4798.29 −0.611211
\(396\) 963.814 0.122307
\(397\) 9391.66 1.18729 0.593645 0.804727i \(-0.297689\pi\)
0.593645 + 0.804727i \(0.297689\pi\)
\(398\) 9018.01 1.13576
\(399\) 0 0
\(400\) 699.175 0.0873968
\(401\) 9532.13 1.18706 0.593531 0.804811i \(-0.297733\pi\)
0.593531 + 0.804811i \(0.297733\pi\)
\(402\) −1504.31 −0.186638
\(403\) −812.080 −0.100379
\(404\) −3384.05 −0.416739
\(405\) −1052.06 −0.129080
\(406\) −10618.0 −1.29794
\(407\) 5284.58 0.643604
\(408\) 196.065 0.0237908
\(409\) 6579.49 0.795439 0.397720 0.917507i \(-0.369802\pi\)
0.397720 + 0.917507i \(0.369802\pi\)
\(410\) −9786.44 −1.17882
\(411\) 7335.67 0.880394
\(412\) −5690.20 −0.680427
\(413\) −15162.4 −1.80652
\(414\) −2824.20 −0.335271
\(415\) 16732.8 1.97923
\(416\) 274.933 0.0324031
\(417\) −4513.02 −0.529985
\(418\) 0 0
\(419\) 4136.42 0.482285 0.241143 0.970490i \(-0.422478\pi\)
0.241143 + 0.970490i \(0.422478\pi\)
\(420\) −3990.54 −0.463616
\(421\) 7792.46 0.902093 0.451047 0.892500i \(-0.351051\pi\)
0.451047 + 0.892500i \(0.351051\pi\)
\(422\) 3.80939 0.000439428 0
\(423\) −3298.39 −0.379132
\(424\) 1626.63 0.186312
\(425\) 356.988 0.0407446
\(426\) −692.617 −0.0787732
\(427\) 13033.6 1.47714
\(428\) 1144.96 0.129307
\(429\) 690.063 0.0776610
\(430\) −13202.5 −1.48066
\(431\) −7350.59 −0.821498 −0.410749 0.911749i \(-0.634733\pi\)
−0.410749 + 0.911749i \(0.634733\pi\)
\(432\) −432.000 −0.0481125
\(433\) 10692.6 1.18673 0.593365 0.804933i \(-0.297799\pi\)
0.593365 + 0.804933i \(0.297799\pi\)
\(434\) 4840.02 0.535319
\(435\) −8079.72 −0.890558
\(436\) −129.142 −0.0141852
\(437\) 0 0
\(438\) −4996.02 −0.545021
\(439\) −9619.66 −1.04583 −0.522917 0.852384i \(-0.675156\pi\)
−0.522917 + 0.852384i \(0.675156\pi\)
\(440\) 2781.87 0.301410
\(441\) 2812.74 0.303719
\(442\) 140.377 0.0151064
\(443\) 12604.5 1.35182 0.675909 0.736985i \(-0.263751\pi\)
0.675909 + 0.736985i \(0.263751\pi\)
\(444\) −2368.65 −0.253178
\(445\) −793.258 −0.0845034
\(446\) 9320.45 0.989543
\(447\) 2162.24 0.228793
\(448\) −1638.61 −0.172806
\(449\) 14957.9 1.57218 0.786088 0.618114i \(-0.212103\pi\)
0.786088 + 0.618114i \(0.212103\pi\)
\(450\) −786.572 −0.0823985
\(451\) −10086.3 −1.05309
\(452\) −1188.39 −0.123666
\(453\) −5403.75 −0.560464
\(454\) 8090.31 0.836337
\(455\) −2857.11 −0.294381
\(456\) 0 0
\(457\) −2003.50 −0.205076 −0.102538 0.994729i \(-0.532696\pi\)
−0.102538 + 0.994729i \(0.532696\pi\)
\(458\) −10125.5 −1.03304
\(459\) −220.573 −0.0224302
\(460\) −8151.53 −0.826233
\(461\) −1134.66 −0.114634 −0.0573170 0.998356i \(-0.518255\pi\)
−0.0573170 + 0.998356i \(0.518255\pi\)
\(462\) −4112.80 −0.414166
\(463\) −2934.33 −0.294536 −0.147268 0.989097i \(-0.547048\pi\)
−0.147268 + 0.989097i \(0.547048\pi\)
\(464\) −3317.72 −0.331942
\(465\) 3682.98 0.367299
\(466\) −866.178 −0.0861050
\(467\) −930.578 −0.0922098 −0.0461049 0.998937i \(-0.514681\pi\)
−0.0461049 + 0.998937i \(0.514681\pi\)
\(468\) −309.299 −0.0305499
\(469\) 6419.23 0.632009
\(470\) −9520.16 −0.934324
\(471\) −11487.3 −1.12380
\(472\) −4737.63 −0.462007
\(473\) −13607.0 −1.32273
\(474\) 2216.58 0.214791
\(475\) 0 0
\(476\) −836.649 −0.0805625
\(477\) −1829.96 −0.175657
\(478\) 8330.45 0.797125
\(479\) 15599.2 1.48799 0.743994 0.668187i \(-0.232929\pi\)
0.743994 + 0.668187i \(0.232929\pi\)
\(480\) −1246.89 −0.118567
\(481\) −1695.88 −0.160760
\(482\) −8338.84 −0.788016
\(483\) 12051.5 1.13532
\(484\) −2456.91 −0.230739
\(485\) −3214.76 −0.300979
\(486\) 486.000 0.0453609
\(487\) 13580.1 1.26360 0.631799 0.775132i \(-0.282317\pi\)
0.631799 + 0.775132i \(0.282317\pi\)
\(488\) 4072.48 0.377772
\(489\) 2869.49 0.265364
\(490\) 8118.44 0.748477
\(491\) 796.977 0.0732527 0.0366264 0.999329i \(-0.488339\pi\)
0.0366264 + 0.999329i \(0.488339\pi\)
\(492\) 4520.85 0.414260
\(493\) −1693.98 −0.154752
\(494\) 0 0
\(495\) −3129.60 −0.284172
\(496\) 1512.32 0.136905
\(497\) 2955.54 0.266749
\(498\) −7729.71 −0.695535
\(499\) 8901.33 0.798553 0.399277 0.916830i \(-0.369261\pi\)
0.399277 + 0.916830i \(0.369261\pi\)
\(500\) 4223.91 0.377798
\(501\) 8339.30 0.743658
\(502\) 14264.5 1.26824
\(503\) −20225.1 −1.79283 −0.896416 0.443214i \(-0.853838\pi\)
−0.896416 + 0.443214i \(0.853838\pi\)
\(504\) 1843.43 0.162923
\(505\) 10988.3 0.968266
\(506\) −8401.26 −0.738106
\(507\) 6369.55 0.557952
\(508\) 10668.8 0.931792
\(509\) 21066.4 1.83448 0.917240 0.398335i \(-0.130412\pi\)
0.917240 + 0.398335i \(0.130412\pi\)
\(510\) −636.641 −0.0552764
\(511\) 21319.1 1.84560
\(512\) −512.000 −0.0441942
\(513\) 0 0
\(514\) 2155.03 0.184931
\(515\) 18476.6 1.58093
\(516\) 6098.92 0.520330
\(517\) −9811.82 −0.834668
\(518\) 10107.5 0.857334
\(519\) 928.656 0.0785423
\(520\) −892.734 −0.0752865
\(521\) −1660.93 −0.139668 −0.0698338 0.997559i \(-0.522247\pi\)
−0.0698338 + 0.997559i \(0.522247\pi\)
\(522\) 3732.43 0.312958
\(523\) 22315.8 1.86578 0.932889 0.360165i \(-0.117280\pi\)
0.932889 + 0.360165i \(0.117280\pi\)
\(524\) 3289.10 0.274208
\(525\) 3356.47 0.279025
\(526\) −4978.32 −0.412672
\(527\) 772.166 0.0638255
\(528\) −1285.09 −0.105921
\(529\) 12450.7 1.02332
\(530\) −5281.84 −0.432884
\(531\) 5329.84 0.435584
\(532\) 0 0
\(533\) 3236.80 0.263042
\(534\) 366.446 0.0296960
\(535\) −3717.79 −0.300437
\(536\) 2005.75 0.161633
\(537\) −13950.9 −1.12109
\(538\) 12362.6 0.990683
\(539\) 8367.16 0.668644
\(540\) 1402.75 0.111786
\(541\) −11379.8 −0.904357 −0.452178 0.891927i \(-0.649353\pi\)
−0.452178 + 0.891927i \(0.649353\pi\)
\(542\) −12065.4 −0.956189
\(543\) 809.185 0.0639511
\(544\) −261.420 −0.0206034
\(545\) 419.336 0.0329585
\(546\) 1319.85 0.103451
\(547\) −16531.0 −1.29216 −0.646081 0.763269i \(-0.723593\pi\)
−0.646081 + 0.763269i \(0.723593\pi\)
\(548\) −9780.89 −0.762443
\(549\) −4581.54 −0.356167
\(550\) −2339.84 −0.181402
\(551\) 0 0
\(552\) 3765.61 0.290353
\(553\) −9458.59 −0.727342
\(554\) −1825.43 −0.139991
\(555\) 7691.24 0.588243
\(556\) 6017.36 0.458980
\(557\) −7325.32 −0.557242 −0.278621 0.960401i \(-0.589877\pi\)
−0.278621 + 0.960401i \(0.589877\pi\)
\(558\) −1701.35 −0.129075
\(559\) 4366.65 0.330393
\(560\) 5320.72 0.401503
\(561\) −656.146 −0.0493805
\(562\) 669.773 0.0502716
\(563\) 10864.0 0.813258 0.406629 0.913593i \(-0.366704\pi\)
0.406629 + 0.913593i \(0.366704\pi\)
\(564\) 4397.85 0.328338
\(565\) 3858.82 0.287331
\(566\) 5553.87 0.412450
\(567\) −2073.86 −0.153605
\(568\) 923.489 0.0682196
\(569\) −19930.0 −1.46838 −0.734192 0.678941i \(-0.762439\pi\)
−0.734192 + 0.678941i \(0.762439\pi\)
\(570\) 0 0
\(571\) 1218.32 0.0892906 0.0446453 0.999003i \(-0.485784\pi\)
0.0446453 + 0.999003i \(0.485784\pi\)
\(572\) −920.084 −0.0672564
\(573\) 5849.89 0.426497
\(574\) −19291.4 −1.40280
\(575\) 6856.29 0.497265
\(576\) 576.000 0.0416667
\(577\) −9186.43 −0.662801 −0.331400 0.943490i \(-0.607521\pi\)
−0.331400 + 0.943490i \(0.607521\pi\)
\(578\) 9692.52 0.697501
\(579\) −8793.90 −0.631195
\(580\) 10773.0 0.771246
\(581\) 32984.3 2.35528
\(582\) 1485.06 0.105769
\(583\) −5443.66 −0.386712
\(584\) 6661.36 0.472002
\(585\) 1004.33 0.0709808
\(586\) 6135.70 0.432531
\(587\) 544.891 0.0383136 0.0191568 0.999816i \(-0.493902\pi\)
0.0191568 + 0.999816i \(0.493902\pi\)
\(588\) −3750.32 −0.263028
\(589\) 0 0
\(590\) 15383.6 1.07344
\(591\) 3709.44 0.258183
\(592\) 3158.20 0.219259
\(593\) 12123.5 0.839551 0.419776 0.907628i \(-0.362109\pi\)
0.419776 + 0.907628i \(0.362109\pi\)
\(594\) 1445.72 0.0998631
\(595\) 2716.68 0.187182
\(596\) −2882.99 −0.198141
\(597\) 13527.0 0.927344
\(598\) 2696.06 0.184365
\(599\) −25305.2 −1.72612 −0.863058 0.505104i \(-0.831454\pi\)
−0.863058 + 0.505104i \(0.831454\pi\)
\(600\) 1048.76 0.0713592
\(601\) −15329.1 −1.04041 −0.520206 0.854041i \(-0.674145\pi\)
−0.520206 + 0.854041i \(0.674145\pi\)
\(602\) −26025.4 −1.76199
\(603\) −2256.47 −0.152389
\(604\) 7204.99 0.485376
\(605\) 7977.82 0.536107
\(606\) −5076.07 −0.340266
\(607\) −1137.90 −0.0760891 −0.0380446 0.999276i \(-0.512113\pi\)
−0.0380446 + 0.999276i \(0.512113\pi\)
\(608\) 0 0
\(609\) −15927.1 −1.05977
\(610\) −13223.8 −0.877728
\(611\) 3148.73 0.208484
\(612\) 294.097 0.0194251
\(613\) −12853.8 −0.846916 −0.423458 0.905916i \(-0.639184\pi\)
−0.423458 + 0.905916i \(0.639184\pi\)
\(614\) 14975.6 0.984311
\(615\) −14679.7 −0.962506
\(616\) 5483.73 0.358678
\(617\) −18031.2 −1.17651 −0.588257 0.808674i \(-0.700186\pi\)
−0.588257 + 0.808674i \(0.700186\pi\)
\(618\) −8535.30 −0.555567
\(619\) −28147.3 −1.82768 −0.913841 0.406071i \(-0.866898\pi\)
−0.913841 + 0.406071i \(0.866898\pi\)
\(620\) −4910.64 −0.318090
\(621\) −4236.31 −0.273747
\(622\) 13363.8 0.861476
\(623\) −1563.70 −0.100559
\(624\) 412.399 0.0264570
\(625\) −19177.8 −1.22738
\(626\) −16324.0 −1.04224
\(627\) 0 0
\(628\) 15316.4 0.973236
\(629\) 1612.53 0.102219
\(630\) −5985.81 −0.378541
\(631\) 1024.56 0.0646386 0.0323193 0.999478i \(-0.489711\pi\)
0.0323193 + 0.999478i \(0.489711\pi\)
\(632\) −2955.43 −0.186014
\(633\) 5.71409 0.000358791 0
\(634\) 5679.08 0.355749
\(635\) −34642.5 −2.16496
\(636\) 2439.95 0.152123
\(637\) −2685.12 −0.167015
\(638\) 11103.0 0.688984
\(639\) −1038.92 −0.0643180
\(640\) 1662.51 0.102682
\(641\) 17477.0 1.07691 0.538454 0.842655i \(-0.319009\pi\)
0.538454 + 0.842655i \(0.319009\pi\)
\(642\) 1717.44 0.105579
\(643\) −13432.5 −0.823833 −0.411917 0.911222i \(-0.635141\pi\)
−0.411917 + 0.911222i \(0.635141\pi\)
\(644\) −16068.6 −0.983218
\(645\) −19803.8 −1.20895
\(646\) 0 0
\(647\) −2658.09 −0.161515 −0.0807575 0.996734i \(-0.525734\pi\)
−0.0807575 + 0.996734i \(0.525734\pi\)
\(648\) −648.000 −0.0392837
\(649\) 15854.9 0.958948
\(650\) 750.883 0.0453109
\(651\) 7260.04 0.437086
\(652\) −3825.99 −0.229812
\(653\) −9989.77 −0.598668 −0.299334 0.954148i \(-0.596764\pi\)
−0.299334 + 0.954148i \(0.596764\pi\)
\(654\) −193.712 −0.0115822
\(655\) −10680.0 −0.637105
\(656\) −6027.81 −0.358760
\(657\) −7494.03 −0.445008
\(658\) −18766.5 −1.11185
\(659\) 20064.6 1.18605 0.593025 0.805184i \(-0.297934\pi\)
0.593025 + 0.805184i \(0.297934\pi\)
\(660\) 4172.80 0.246100
\(661\) 23719.1 1.39571 0.697855 0.716239i \(-0.254138\pi\)
0.697855 + 0.716239i \(0.254138\pi\)
\(662\) −22112.5 −1.29823
\(663\) 210.565 0.0123343
\(664\) 10306.3 0.602351
\(665\) 0 0
\(666\) −3552.97 −0.206719
\(667\) −32534.4 −1.88866
\(668\) −11119.1 −0.644027
\(669\) 13980.7 0.807959
\(670\) −6512.88 −0.375544
\(671\) −13628.9 −0.784109
\(672\) −2457.91 −0.141095
\(673\) −10144.0 −0.581014 −0.290507 0.956873i \(-0.593824\pi\)
−0.290507 + 0.956873i \(0.593824\pi\)
\(674\) 10100.7 0.577245
\(675\) −1179.86 −0.0672781
\(676\) −8492.73 −0.483201
\(677\) −16883.4 −0.958469 −0.479234 0.877687i \(-0.659086\pi\)
−0.479234 + 0.877687i \(0.659086\pi\)
\(678\) −1782.59 −0.100973
\(679\) −6337.07 −0.358166
\(680\) 848.855 0.0478708
\(681\) 12135.5 0.682866
\(682\) −5061.08 −0.284162
\(683\) −16610.2 −0.930560 −0.465280 0.885164i \(-0.654046\pi\)
−0.465280 + 0.885164i \(0.654046\pi\)
\(684\) 0 0
\(685\) 31759.5 1.77149
\(686\) −1560.43 −0.0868479
\(687\) −15188.2 −0.843472
\(688\) −8131.90 −0.450619
\(689\) 1746.93 0.0965935
\(690\) −12227.3 −0.674616
\(691\) 24812.1 1.36598 0.682992 0.730426i \(-0.260678\pi\)
0.682992 + 0.730426i \(0.260678\pi\)
\(692\) −1238.21 −0.0680196
\(693\) −6169.19 −0.338165
\(694\) 12029.7 0.657984
\(695\) −19539.0 −1.06641
\(696\) −4976.58 −0.271030
\(697\) −3077.71 −0.167255
\(698\) 5029.01 0.272709
\(699\) −1299.27 −0.0703044
\(700\) −4475.29 −0.241643
\(701\) 13067.2 0.704051 0.352025 0.935990i \(-0.385493\pi\)
0.352025 + 0.935990i \(0.385493\pi\)
\(702\) −463.949 −0.0249439
\(703\) 0 0
\(704\) 1713.45 0.0917301
\(705\) −14280.2 −0.762873
\(706\) −9156.05 −0.488091
\(707\) 21660.7 1.15224
\(708\) −7106.45 −0.377227
\(709\) 10445.2 0.553284 0.276642 0.960973i \(-0.410778\pi\)
0.276642 + 0.960973i \(0.410778\pi\)
\(710\) −2998.66 −0.158504
\(711\) 3324.86 0.175376
\(712\) −488.595 −0.0257175
\(713\) 14830.2 0.778954
\(714\) −1254.97 −0.0657790
\(715\) 2987.60 0.156266
\(716\) 18601.1 0.970890
\(717\) 12495.7 0.650850
\(718\) −15944.9 −0.828771
\(719\) 648.001 0.0336111 0.0168055 0.999859i \(-0.494650\pi\)
0.0168055 + 0.999859i \(0.494650\pi\)
\(720\) −1870.33 −0.0968098
\(721\) 36421.9 1.88131
\(722\) 0 0
\(723\) −12508.3 −0.643413
\(724\) −1078.91 −0.0553833
\(725\) −9061.19 −0.464171
\(726\) −3685.36 −0.188398
\(727\) 16873.2 0.860789 0.430394 0.902641i \(-0.358375\pi\)
0.430394 + 0.902641i \(0.358375\pi\)
\(728\) −1759.79 −0.0895911
\(729\) 729.000 0.0370370
\(730\) −21630.1 −1.09667
\(731\) −4152.03 −0.210080
\(732\) 6108.72 0.308449
\(733\) −23662.1 −1.19233 −0.596166 0.802861i \(-0.703310\pi\)
−0.596166 + 0.802861i \(0.703310\pi\)
\(734\) −10931.0 −0.549688
\(735\) 12177.7 0.611129
\(736\) −5020.81 −0.251453
\(737\) −6712.41 −0.335488
\(738\) 6781.28 0.338242
\(739\) 17277.3 0.860021 0.430011 0.902824i \(-0.358510\pi\)
0.430011 + 0.902824i \(0.358510\pi\)
\(740\) −10255.0 −0.509433
\(741\) 0 0
\(742\) −10411.8 −0.515133
\(743\) 25798.5 1.27383 0.636915 0.770934i \(-0.280210\pi\)
0.636915 + 0.770934i \(0.280210\pi\)
\(744\) 2268.47 0.111783
\(745\) 9361.35 0.460367
\(746\) −18491.1 −0.907516
\(747\) −11594.6 −0.567902
\(748\) 874.861 0.0427648
\(749\) −7328.66 −0.357521
\(750\) 6335.86 0.308471
\(751\) 15156.5 0.736444 0.368222 0.929738i \(-0.379967\pi\)
0.368222 + 0.929738i \(0.379967\pi\)
\(752\) −5863.80 −0.284349
\(753\) 21396.7 1.03551
\(754\) −3563.08 −0.172095
\(755\) −23395.3 −1.12774
\(756\) 2765.15 0.133026
\(757\) 7454.91 0.357931 0.178965 0.983855i \(-0.442725\pi\)
0.178965 + 0.983855i \(0.442725\pi\)
\(758\) −12196.8 −0.584445
\(759\) −12601.9 −0.602661
\(760\) 0 0
\(761\) 23295.2 1.10966 0.554830 0.831964i \(-0.312783\pi\)
0.554830 + 0.831964i \(0.312783\pi\)
\(762\) 16003.2 0.760805
\(763\) 826.611 0.0392206
\(764\) −7799.86 −0.369357
\(765\) −954.962 −0.0451330
\(766\) −9059.62 −0.427333
\(767\) −5088.01 −0.239527
\(768\) −768.000 −0.0360844
\(769\) −37973.8 −1.78072 −0.890358 0.455260i \(-0.849546\pi\)
−0.890358 + 0.455260i \(0.849546\pi\)
\(770\) −17806.2 −0.833365
\(771\) 3232.55 0.150995
\(772\) 11725.2 0.546631
\(773\) 8339.37 0.388029 0.194014 0.980999i \(-0.437849\pi\)
0.194014 + 0.980999i \(0.437849\pi\)
\(774\) 9148.39 0.424847
\(775\) 4130.36 0.191441
\(776\) −1980.08 −0.0915990
\(777\) 15161.3 0.700010
\(778\) 11117.8 0.512332
\(779\) 0 0
\(780\) −1339.10 −0.0614712
\(781\) −3090.53 −0.141598
\(782\) −2563.55 −0.117228
\(783\) 5598.65 0.255529
\(784\) 5000.43 0.227789
\(785\) −49734.0 −2.26125
\(786\) 4933.66 0.223890
\(787\) −42901.7 −1.94318 −0.971588 0.236680i \(-0.923941\pi\)
−0.971588 + 0.236680i \(0.923941\pi\)
\(788\) −4945.92 −0.223593
\(789\) −7467.49 −0.336945
\(790\) 9596.59 0.432192
\(791\) 7606.67 0.341924
\(792\) −1927.63 −0.0864840
\(793\) 4373.67 0.195856
\(794\) −18783.3 −0.839540
\(795\) −7922.77 −0.353449
\(796\) −18036.0 −0.803103
\(797\) 5540.21 0.246229 0.123114 0.992392i \(-0.460712\pi\)
0.123114 + 0.992392i \(0.460712\pi\)
\(798\) 0 0
\(799\) −2993.97 −0.132564
\(800\) −1398.35 −0.0617989
\(801\) 549.669 0.0242467
\(802\) −19064.3 −0.839379
\(803\) −22292.8 −0.979695
\(804\) 3008.63 0.131973
\(805\) 52176.4 2.28444
\(806\) 1624.16 0.0709784
\(807\) 18543.8 0.808890
\(808\) 6768.09 0.294679
\(809\) 20817.8 0.904715 0.452357 0.891837i \(-0.350583\pi\)
0.452357 + 0.891837i \(0.350583\pi\)
\(810\) 2104.12 0.0912731
\(811\) −20667.9 −0.894882 −0.447441 0.894313i \(-0.647665\pi\)
−0.447441 + 0.894313i \(0.647665\pi\)
\(812\) 21236.1 0.917784
\(813\) −18098.1 −0.780725
\(814\) −10569.2 −0.455097
\(815\) 12423.4 0.533952
\(816\) −392.129 −0.0168226
\(817\) 0 0
\(818\) −13159.0 −0.562461
\(819\) 1979.77 0.0844673
\(820\) 19572.9 0.833554
\(821\) −7501.01 −0.318864 −0.159432 0.987209i \(-0.550966\pi\)
−0.159432 + 0.987209i \(0.550966\pi\)
\(822\) −14671.3 −0.622532
\(823\) −362.296 −0.0153449 −0.00767244 0.999971i \(-0.502442\pi\)
−0.00767244 + 0.999971i \(0.502442\pi\)
\(824\) 11380.4 0.481135
\(825\) −3509.76 −0.148114
\(826\) 30324.7 1.27740
\(827\) −8779.02 −0.369137 −0.184568 0.982820i \(-0.559089\pi\)
−0.184568 + 0.982820i \(0.559089\pi\)
\(828\) 5648.41 0.237072
\(829\) 11789.0 0.493909 0.246954 0.969027i \(-0.420570\pi\)
0.246954 + 0.969027i \(0.420570\pi\)
\(830\) −33465.5 −1.39952
\(831\) −2738.15 −0.114303
\(832\) −549.866 −0.0229125
\(833\) 2553.14 0.106196
\(834\) 9026.05 0.374756
\(835\) 36104.7 1.49635
\(836\) 0 0
\(837\) −2552.03 −0.105390
\(838\) −8272.85 −0.341027
\(839\) −10761.2 −0.442811 −0.221405 0.975182i \(-0.571064\pi\)
−0.221405 + 0.975182i \(0.571064\pi\)
\(840\) 7981.08 0.327826
\(841\) 18608.1 0.762969
\(842\) −15584.9 −0.637876
\(843\) 1004.66 0.0410466
\(844\) −7.61879 −0.000310722 0
\(845\) 27576.7 1.12269
\(846\) 6596.77 0.268087
\(847\) 15726.2 0.637968
\(848\) −3253.27 −0.131743
\(849\) 8330.81 0.336764
\(850\) −713.976 −0.0288108
\(851\) 30970.1 1.24752
\(852\) 1385.23 0.0557011
\(853\) 4890.26 0.196294 0.0981472 0.995172i \(-0.468708\pi\)
0.0981472 + 0.995172i \(0.468708\pi\)
\(854\) −26067.2 −1.04450
\(855\) 0 0
\(856\) −2289.91 −0.0914342
\(857\) −30324.4 −1.20871 −0.604353 0.796717i \(-0.706568\pi\)
−0.604353 + 0.796717i \(0.706568\pi\)
\(858\) −1380.13 −0.0549146
\(859\) −15071.6 −0.598644 −0.299322 0.954152i \(-0.596760\pi\)
−0.299322 + 0.954152i \(0.596760\pi\)
\(860\) 26405.1 1.04698
\(861\) −28937.1 −1.14538
\(862\) 14701.2 0.580887
\(863\) 283.180 0.0111698 0.00558490 0.999984i \(-0.498222\pi\)
0.00558490 + 0.999984i \(0.498222\pi\)
\(864\) 864.000 0.0340207
\(865\) 4020.58 0.158039
\(866\) −21385.2 −0.839145
\(867\) 14538.8 0.569508
\(868\) −9680.05 −0.378528
\(869\) 9890.59 0.386094
\(870\) 16159.4 0.629720
\(871\) 2154.09 0.0837986
\(872\) 258.283 0.0100305
\(873\) 2227.59 0.0863604
\(874\) 0 0
\(875\) −27036.4 −1.04457
\(876\) 9992.05 0.385388
\(877\) −2201.83 −0.0847782 −0.0423891 0.999101i \(-0.513497\pi\)
−0.0423891 + 0.999101i \(0.513497\pi\)
\(878\) 19239.3 0.739516
\(879\) 9203.55 0.353160
\(880\) −5563.73 −0.213129
\(881\) 21218.9 0.811443 0.405722 0.913997i \(-0.367020\pi\)
0.405722 + 0.913997i \(0.367020\pi\)
\(882\) −5625.48 −0.214762
\(883\) −8730.23 −0.332724 −0.166362 0.986065i \(-0.553202\pi\)
−0.166362 + 0.986065i \(0.553202\pi\)
\(884\) −280.753 −0.0106818
\(885\) 23075.3 0.876463
\(886\) −25208.9 −0.955880
\(887\) −11548.0 −0.437139 −0.218570 0.975821i \(-0.570139\pi\)
−0.218570 + 0.975821i \(0.570139\pi\)
\(888\) 4737.30 0.179024
\(889\) −68288.8 −2.57630
\(890\) 1586.52 0.0597529
\(891\) 2168.58 0.0815379
\(892\) −18640.9 −0.699713
\(893\) 0 0
\(894\) −4324.48 −0.161781
\(895\) −60399.8 −2.25580
\(896\) 3277.22 0.122192
\(897\) 4044.10 0.150533
\(898\) −29915.8 −1.11170
\(899\) −19599.4 −0.727113
\(900\) 1573.14 0.0582646
\(901\) −1661.07 −0.0614188
\(902\) 20172.5 0.744647
\(903\) −39038.1 −1.43866
\(904\) 2376.78 0.0874453
\(905\) 3503.34 0.128679
\(906\) 10807.5 0.396308
\(907\) −7282.96 −0.266622 −0.133311 0.991074i \(-0.542561\pi\)
−0.133311 + 0.991074i \(0.542561\pi\)
\(908\) −16180.6 −0.591380
\(909\) −7614.11 −0.277826
\(910\) 5714.22 0.208159
\(911\) 32720.6 1.18999 0.594995 0.803729i \(-0.297154\pi\)
0.594995 + 0.803729i \(0.297154\pi\)
\(912\) 0 0
\(913\) −34490.8 −1.25025
\(914\) 4007.00 0.145011
\(915\) −19835.6 −0.716662
\(916\) 20250.9 0.730468
\(917\) −21052.9 −0.758156
\(918\) 441.146 0.0158605
\(919\) 1970.84 0.0707421 0.0353710 0.999374i \(-0.488739\pi\)
0.0353710 + 0.999374i \(0.488739\pi\)
\(920\) 16303.1 0.584235
\(921\) 22463.4 0.803686
\(922\) 2269.31 0.0810585
\(923\) 991.786 0.0353684
\(924\) 8225.59 0.292859
\(925\) 8625.52 0.306600
\(926\) 5868.67 0.208268
\(927\) −12802.9 −0.453618
\(928\) 6635.43 0.234719
\(929\) 10757.5 0.379916 0.189958 0.981792i \(-0.439165\pi\)
0.189958 + 0.981792i \(0.439165\pi\)
\(930\) −7365.95 −0.259720
\(931\) 0 0
\(932\) 1732.36 0.0608854
\(933\) 20045.7 0.703392
\(934\) 1861.16 0.0652022
\(935\) −2840.76 −0.0993613
\(936\) 618.599 0.0216021
\(937\) 32578.3 1.13585 0.567923 0.823082i \(-0.307747\pi\)
0.567923 + 0.823082i \(0.307747\pi\)
\(938\) −12838.5 −0.446898
\(939\) −24486.1 −0.850982
\(940\) 19040.3 0.660667
\(941\) 45845.4 1.58822 0.794112 0.607772i \(-0.207936\pi\)
0.794112 + 0.607772i \(0.207936\pi\)
\(942\) 22974.7 0.794644
\(943\) −59110.3 −2.04125
\(944\) 9475.27 0.326688
\(945\) −8978.72 −0.309077
\(946\) 27214.0 0.935311
\(947\) −28244.0 −0.969172 −0.484586 0.874744i \(-0.661030\pi\)
−0.484586 + 0.874744i \(0.661030\pi\)
\(948\) −4433.15 −0.151880
\(949\) 7154.01 0.244709
\(950\) 0 0
\(951\) 8518.62 0.290468
\(952\) 1673.30 0.0569663
\(953\) −44693.4 −1.51916 −0.759582 0.650412i \(-0.774596\pi\)
−0.759582 + 0.650412i \(0.774596\pi\)
\(954\) 3659.93 0.124208
\(955\) 25326.9 0.858178
\(956\) −16660.9 −0.563652
\(957\) 16654.5 0.562553
\(958\) −31198.4 −1.05217
\(959\) 62605.7 2.10807
\(960\) 2493.77 0.0838397
\(961\) −20857.0 −0.700112
\(962\) 3391.77 0.113675
\(963\) 2576.15 0.0862050
\(964\) 16677.7 0.557212
\(965\) −38072.9 −1.27006
\(966\) −24102.9 −0.802794
\(967\) 45581.0 1.51581 0.757905 0.652365i \(-0.226223\pi\)
0.757905 + 0.652365i \(0.226223\pi\)
\(968\) 4913.82 0.163157
\(969\) 0 0
\(970\) 6429.53 0.212824
\(971\) −4735.96 −0.156523 −0.0782616 0.996933i \(-0.524937\pi\)
−0.0782616 + 0.996933i \(0.524937\pi\)
\(972\) −972.000 −0.0320750
\(973\) −38516.0 −1.26903
\(974\) −27160.2 −0.893498
\(975\) 1126.32 0.0369962
\(976\) −8144.96 −0.267125
\(977\) −57565.1 −1.88503 −0.942514 0.334167i \(-0.891545\pi\)
−0.942514 + 0.334167i \(0.891545\pi\)
\(978\) −5738.98 −0.187640
\(979\) 1635.12 0.0533796
\(980\) −16236.9 −0.529253
\(981\) −290.569 −0.00945682
\(982\) −1593.95 −0.0517975
\(983\) 34628.3 1.12357 0.561786 0.827282i \(-0.310114\pi\)
0.561786 + 0.827282i \(0.310114\pi\)
\(984\) −9041.71 −0.292926
\(985\) 16059.9 0.519503
\(986\) 3387.95 0.109426
\(987\) −28149.8 −0.907820
\(988\) 0 0
\(989\) −79743.5 −2.56390
\(990\) 6259.20 0.200940
\(991\) 31575.5 1.01214 0.506069 0.862493i \(-0.331098\pi\)
0.506069 + 0.862493i \(0.331098\pi\)
\(992\) −3024.63 −0.0968066
\(993\) −33168.7 −1.06000
\(994\) −5911.08 −0.188620
\(995\) 58564.8 1.86596
\(996\) 15459.4 0.491818
\(997\) 38723.3 1.23007 0.615035 0.788500i \(-0.289142\pi\)
0.615035 + 0.788500i \(0.289142\pi\)
\(998\) −17802.7 −0.564662
\(999\) −5329.46 −0.168785
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 2166.4.a.s.1.1 3
19.7 even 3 114.4.e.e.49.3 yes 6
19.11 even 3 114.4.e.e.7.3 6
19.18 odd 2 2166.4.a.w.1.1 3
57.11 odd 6 342.4.g.g.235.1 6
57.26 odd 6 342.4.g.g.163.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
114.4.e.e.7.3 6 19.11 even 3
114.4.e.e.49.3 yes 6 19.7 even 3
342.4.g.g.163.1 6 57.26 odd 6
342.4.g.g.235.1 6 57.11 odd 6
2166.4.a.s.1.1 3 1.1 even 1 trivial
2166.4.a.w.1.1 3 19.18 odd 2