Properties

Label 289.4.a.b.1.1
Level $289$
Weight $4$
Character 289.1
Self dual yes
Analytic conductor $17.052$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 289 = 17^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 289.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(17.0515519917\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.2636.1
Defining polynomial: \( x^{3} - 14x - 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 17)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-3.58966\) of defining polynomial
Character \(\chi\) \(=\) 289.1

$q$-expansion

\(f(q)\) \(=\) \(q-5.03251 q^{2} -8.47535 q^{3} +17.3261 q^{4} -0.885690 q^{5} +42.6523 q^{6} -3.81828 q^{7} -46.9339 q^{8} +44.8316 q^{9} +O(q^{10})\) \(q-5.03251 q^{2} -8.47535 q^{3} +17.3261 q^{4} -0.885690 q^{5} +42.6523 q^{6} -3.81828 q^{7} -46.9339 q^{8} +44.8316 q^{9} +4.45724 q^{10} +52.3720 q^{11} -146.845 q^{12} -8.06025 q^{13} +19.2156 q^{14} +7.50653 q^{15} +97.5862 q^{16} -225.616 q^{18} -66.5154 q^{19} -15.3456 q^{20} +32.3613 q^{21} -263.563 q^{22} -180.226 q^{23} +397.782 q^{24} -124.216 q^{25} +40.5633 q^{26} -151.129 q^{27} -66.1562 q^{28} +41.2800 q^{29} -37.7767 q^{30} +34.9114 q^{31} -115.632 q^{32} -443.871 q^{33} +3.38182 q^{35} +776.759 q^{36} -130.368 q^{37} +334.739 q^{38} +68.3134 q^{39} +41.5689 q^{40} +17.9081 q^{41} -162.859 q^{42} +277.620 q^{43} +907.405 q^{44} -39.7069 q^{45} +906.987 q^{46} +463.789 q^{47} -827.078 q^{48} -328.421 q^{49} +625.116 q^{50} -139.653 q^{52} -329.944 q^{53} +760.560 q^{54} -46.3853 q^{55} +179.207 q^{56} +563.741 q^{57} -207.742 q^{58} +678.656 q^{59} +130.059 q^{60} -340.280 q^{61} -175.692 q^{62} -171.180 q^{63} -198.770 q^{64} +7.13888 q^{65} +2233.79 q^{66} +15.3925 q^{67} +1527.48 q^{69} -17.0190 q^{70} +670.203 q^{71} -2104.12 q^{72} -193.480 q^{73} +656.080 q^{74} +1052.77 q^{75} -1152.46 q^{76} -199.971 q^{77} -343.788 q^{78} -1080.15 q^{79} -86.4311 q^{80} +70.4207 q^{81} -90.1229 q^{82} -865.668 q^{83} +560.697 q^{84} -1397.13 q^{86} -349.863 q^{87} -2458.02 q^{88} +1129.46 q^{89} +199.825 q^{90} +30.7763 q^{91} -3122.61 q^{92} -295.886 q^{93} -2334.02 q^{94} +58.9120 q^{95} +980.023 q^{96} +379.412 q^{97} +1652.78 q^{98} +2347.92 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + q^{2} - 4 q^{3} + 25 q^{4} + 8 q^{5} + 74 q^{6} - 22 q^{7} - 39 q^{8} + 59 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q + q^{2} - 4 q^{3} + 25 q^{4} + 8 q^{5} + 74 q^{6} - 22 q^{7} - 39 q^{8} + 59 q^{9} + 56 q^{10} + 28 q^{11} - 22 q^{12} + 30 q^{13} - 92 q^{14} + 108 q^{15} + 137 q^{16} - 103 q^{18} + 80 q^{19} + 168 q^{20} - 192 q^{21} - 286 q^{22} - 142 q^{23} + 666 q^{24} - 223 q^{25} + 26 q^{26} + 20 q^{27} - 476 q^{28} + 456 q^{29} + 400 q^{30} - 230 q^{31} - 71 q^{32} - 332 q^{33} - 332 q^{35} + 1313 q^{36} - 356 q^{37} + 724 q^{38} - 268 q^{39} + 424 q^{40} + 294 q^{41} - 1128 q^{42} + 556 q^{43} + 1122 q^{44} + 384 q^{45} + 704 q^{46} + 640 q^{47} - 774 q^{48} - 269 q^{49} + 547 q^{50} - 774 q^{52} + 302 q^{53} + 1100 q^{54} + 76 q^{55} - 684 q^{56} + 720 q^{57} + 1304 q^{58} + 636 q^{59} + 1328 q^{60} + 84 q^{61} - 508 q^{62} - 1122 q^{63} - 919 q^{64} - 408 q^{65} + 2468 q^{66} + 1008 q^{67} + 576 q^{69} - 1504 q^{70} + 402 q^{71} - 927 q^{72} - 838 q^{73} - 836 q^{74} + 1548 q^{75} - 908 q^{76} - 504 q^{77} - 1308 q^{78} + 594 q^{79} + 40 q^{80} - 505 q^{81} - 358 q^{82} - 2396 q^{83} - 2040 q^{84} - 1264 q^{86} + 1428 q^{87} - 1838 q^{88} - 170 q^{89} + 2008 q^{90} + 1016 q^{91} - 4896 q^{92} + 632 q^{93} - 2016 q^{94} + 472 q^{95} - 678 q^{96} + 270 q^{97} + 2857 q^{98} + 2920 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.03251 −1.77926 −0.889630 0.456681i \(-0.849038\pi\)
−0.889630 + 0.456681i \(0.849038\pi\)
\(3\) −8.47535 −1.63108 −0.815541 0.578699i \(-0.803561\pi\)
−0.815541 + 0.578699i \(0.803561\pi\)
\(4\) 17.3261 2.16577
\(5\) −0.885690 −0.0792185 −0.0396092 0.999215i \(-0.512611\pi\)
−0.0396092 + 0.999215i \(0.512611\pi\)
\(6\) 42.6523 2.90212
\(7\) −3.81828 −0.206168 −0.103084 0.994673i \(-0.532871\pi\)
−0.103084 + 0.994673i \(0.532871\pi\)
\(8\) −46.9339 −2.07421
\(9\) 44.8316 1.66043
\(10\) 4.45724 0.140950
\(11\) 52.3720 1.43552 0.717761 0.696289i \(-0.245167\pi\)
0.717761 + 0.696289i \(0.245167\pi\)
\(12\) −146.845 −3.53255
\(13\) −8.06025 −0.171962 −0.0859811 0.996297i \(-0.527402\pi\)
−0.0859811 + 0.996297i \(0.527402\pi\)
\(14\) 19.2156 0.366827
\(15\) 7.50653 0.129212
\(16\) 97.5862 1.52478
\(17\) 0 0
\(18\) −225.616 −2.95434
\(19\) −66.5154 −0.803141 −0.401570 0.915828i \(-0.631535\pi\)
−0.401570 + 0.915828i \(0.631535\pi\)
\(20\) −15.3456 −0.171569
\(21\) 32.3613 0.336277
\(22\) −263.563 −2.55417
\(23\) −180.226 −1.63390 −0.816948 0.576711i \(-0.804336\pi\)
−0.816948 + 0.576711i \(0.804336\pi\)
\(24\) 397.782 3.38320
\(25\) −124.216 −0.993724
\(26\) 40.5633 0.305966
\(27\) −151.129 −1.07722
\(28\) −66.1562 −0.446512
\(29\) 41.2800 0.264328 0.132164 0.991228i \(-0.457807\pi\)
0.132164 + 0.991228i \(0.457807\pi\)
\(30\) −37.7767 −0.229902
\(31\) 34.9114 0.202267 0.101133 0.994873i \(-0.467753\pi\)
0.101133 + 0.994873i \(0.467753\pi\)
\(32\) −115.632 −0.638783
\(33\) −443.871 −2.34146
\(34\) 0 0
\(35\) 3.38182 0.0163323
\(36\) 776.759 3.59611
\(37\) −130.368 −0.579255 −0.289627 0.957139i \(-0.593531\pi\)
−0.289627 + 0.957139i \(0.593531\pi\)
\(38\) 334.739 1.42900
\(39\) 68.3134 0.280485
\(40\) 41.5689 0.164315
\(41\) 17.9081 0.0682142 0.0341071 0.999418i \(-0.489141\pi\)
0.0341071 + 0.999418i \(0.489141\pi\)
\(42\) −162.859 −0.598325
\(43\) 277.620 0.984573 0.492287 0.870433i \(-0.336161\pi\)
0.492287 + 0.870433i \(0.336161\pi\)
\(44\) 907.405 3.10901
\(45\) −39.7069 −0.131537
\(46\) 906.987 2.90713
\(47\) 463.789 1.43937 0.719687 0.694299i \(-0.244285\pi\)
0.719687 + 0.694299i \(0.244285\pi\)
\(48\) −827.078 −2.48705
\(49\) −328.421 −0.957495
\(50\) 625.116 1.76809
\(51\) 0 0
\(52\) −139.653 −0.372431
\(53\) −329.944 −0.855118 −0.427559 0.903987i \(-0.640626\pi\)
−0.427559 + 0.903987i \(0.640626\pi\)
\(54\) 760.560 1.91665
\(55\) −46.3853 −0.113720
\(56\) 179.207 0.427635
\(57\) 563.741 1.30999
\(58\) −207.742 −0.470308
\(59\) 678.656 1.49752 0.748759 0.662843i \(-0.230650\pi\)
0.748759 + 0.662843i \(0.230650\pi\)
\(60\) 130.059 0.279843
\(61\) −340.280 −0.714237 −0.357118 0.934059i \(-0.616241\pi\)
−0.357118 + 0.934059i \(0.616241\pi\)
\(62\) −175.692 −0.359885
\(63\) −171.180 −0.342328
\(64\) −198.770 −0.388223
\(65\) 7.13888 0.0136226
\(66\) 2233.79 4.16606
\(67\) 15.3925 0.0280671 0.0140336 0.999902i \(-0.495533\pi\)
0.0140336 + 0.999902i \(0.495533\pi\)
\(68\) 0 0
\(69\) 1527.48 2.66502
\(70\) −17.0190 −0.0290595
\(71\) 670.203 1.12026 0.560130 0.828405i \(-0.310751\pi\)
0.560130 + 0.828405i \(0.310751\pi\)
\(72\) −2104.12 −3.44408
\(73\) −193.480 −0.310207 −0.155103 0.987898i \(-0.549571\pi\)
−0.155103 + 0.987898i \(0.549571\pi\)
\(74\) 656.080 1.03065
\(75\) 1052.77 1.62085
\(76\) −1152.46 −1.73942
\(77\) −199.971 −0.295959
\(78\) −343.788 −0.499055
\(79\) −1080.15 −1.53831 −0.769156 0.639061i \(-0.779323\pi\)
−0.769156 + 0.639061i \(0.779323\pi\)
\(80\) −86.4311 −0.120791
\(81\) 70.4207 0.0965990
\(82\) −90.1229 −0.121371
\(83\) −865.668 −1.14481 −0.572406 0.819970i \(-0.693990\pi\)
−0.572406 + 0.819970i \(0.693990\pi\)
\(84\) 560.697 0.728298
\(85\) 0 0
\(86\) −1397.13 −1.75181
\(87\) −349.863 −0.431141
\(88\) −2458.02 −2.97757
\(89\) 1129.46 1.34520 0.672599 0.740008i \(-0.265178\pi\)
0.672599 + 0.740008i \(0.265178\pi\)
\(90\) 199.825 0.234038
\(91\) 30.7763 0.0354531
\(92\) −3122.61 −3.53864
\(93\) −295.886 −0.329914
\(94\) −2334.02 −2.56102
\(95\) 58.9120 0.0636236
\(96\) 980.023 1.04191
\(97\) 379.412 0.397149 0.198574 0.980086i \(-0.436369\pi\)
0.198574 + 0.980086i \(0.436369\pi\)
\(98\) 1652.78 1.70363
\(99\) 2347.92 2.38359
\(100\) −2152.18 −2.15218
\(101\) 131.732 0.129780 0.0648902 0.997892i \(-0.479330\pi\)
0.0648902 + 0.997892i \(0.479330\pi\)
\(102\) 0 0
\(103\) 195.988 0.187488 0.0937442 0.995596i \(-0.470116\pi\)
0.0937442 + 0.995596i \(0.470116\pi\)
\(104\) 378.299 0.356685
\(105\) −28.6621 −0.0266394
\(106\) 1660.45 1.52148
\(107\) 485.147 0.438326 0.219163 0.975688i \(-0.429667\pi\)
0.219163 + 0.975688i \(0.429667\pi\)
\(108\) −2618.49 −2.33300
\(109\) 1255.12 1.10292 0.551460 0.834201i \(-0.314071\pi\)
0.551460 + 0.834201i \(0.314071\pi\)
\(110\) 233.435 0.202337
\(111\) 1104.92 0.944812
\(112\) −372.612 −0.314362
\(113\) 1013.35 0.843612 0.421806 0.906686i \(-0.361396\pi\)
0.421806 + 0.906686i \(0.361396\pi\)
\(114\) −2837.03 −2.33081
\(115\) 159.624 0.129435
\(116\) 715.224 0.572473
\(117\) −361.354 −0.285531
\(118\) −3415.34 −2.66447
\(119\) 0 0
\(120\) −352.311 −0.268012
\(121\) 1411.83 1.06073
\(122\) 1712.46 1.27081
\(123\) −151.778 −0.111263
\(124\) 604.880 0.438063
\(125\) 220.728 0.157940
\(126\) 861.464 0.609090
\(127\) 1927.72 1.34691 0.673456 0.739227i \(-0.264809\pi\)
0.673456 + 0.739227i \(0.264809\pi\)
\(128\) 1925.37 1.32953
\(129\) −2352.93 −1.60592
\(130\) −35.9265 −0.0242381
\(131\) 406.738 0.271274 0.135637 0.990759i \(-0.456692\pi\)
0.135637 + 0.990759i \(0.456692\pi\)
\(132\) −7690.58 −5.07105
\(133\) 253.975 0.165582
\(134\) −77.4631 −0.0499387
\(135\) 133.854 0.0853355
\(136\) 0 0
\(137\) −130.552 −0.0814149 −0.0407074 0.999171i \(-0.512961\pi\)
−0.0407074 + 0.999171i \(0.512961\pi\)
\(138\) −7687.03 −4.74177
\(139\) −2073.54 −1.26529 −0.632644 0.774443i \(-0.718030\pi\)
−0.632644 + 0.774443i \(0.718030\pi\)
\(140\) 58.5938 0.0353720
\(141\) −3930.78 −2.34774
\(142\) −3372.80 −1.99323
\(143\) −422.131 −0.246856
\(144\) 4374.95 2.53180
\(145\) −36.5613 −0.0209397
\(146\) 973.689 0.551939
\(147\) 2783.48 1.56175
\(148\) −2258.78 −1.25453
\(149\) −1852.73 −1.01867 −0.509334 0.860569i \(-0.670108\pi\)
−0.509334 + 0.860569i \(0.670108\pi\)
\(150\) −5298.08 −2.88391
\(151\) 2050.86 1.10527 0.552637 0.833422i \(-0.313622\pi\)
0.552637 + 0.833422i \(0.313622\pi\)
\(152\) 3121.83 1.66588
\(153\) 0 0
\(154\) 1006.36 0.526588
\(155\) −30.9207 −0.0160233
\(156\) 1183.61 0.607465
\(157\) −262.991 −0.133688 −0.0668438 0.997763i \(-0.521293\pi\)
−0.0668438 + 0.997763i \(0.521293\pi\)
\(158\) 5435.88 2.73706
\(159\) 2796.39 1.39477
\(160\) 102.414 0.0506035
\(161\) 688.152 0.336857
\(162\) −354.393 −0.171875
\(163\) 1444.98 0.694354 0.347177 0.937800i \(-0.387140\pi\)
0.347177 + 0.937800i \(0.387140\pi\)
\(164\) 310.279 0.147736
\(165\) 393.132 0.185487
\(166\) 4356.48 2.03692
\(167\) 501.565 0.232409 0.116204 0.993225i \(-0.462927\pi\)
0.116204 + 0.993225i \(0.462927\pi\)
\(168\) −1518.84 −0.697508
\(169\) −2132.03 −0.970429
\(170\) 0 0
\(171\) −2981.99 −1.33356
\(172\) 4810.08 2.13236
\(173\) 2590.14 1.13829 0.569146 0.822237i \(-0.307274\pi\)
0.569146 + 0.822237i \(0.307274\pi\)
\(174\) 1760.69 0.767112
\(175\) 474.290 0.204874
\(176\) 5110.79 2.18886
\(177\) −5751.85 −2.44257
\(178\) −5684.02 −2.39346
\(179\) 2165.65 0.904294 0.452147 0.891943i \(-0.350658\pi\)
0.452147 + 0.891943i \(0.350658\pi\)
\(180\) −687.968 −0.284878
\(181\) 1925.56 0.790750 0.395375 0.918520i \(-0.370615\pi\)
0.395375 + 0.918520i \(0.370615\pi\)
\(182\) −154.882 −0.0630803
\(183\) 2884.00 1.16498
\(184\) 8458.69 3.38904
\(185\) 115.466 0.0458877
\(186\) 1489.05 0.587003
\(187\) 0 0
\(188\) 8035.68 3.11735
\(189\) 577.055 0.222088
\(190\) −296.475 −0.113203
\(191\) −2783.52 −1.05449 −0.527247 0.849712i \(-0.676776\pi\)
−0.527247 + 0.849712i \(0.676776\pi\)
\(192\) 1684.65 0.633223
\(193\) −2258.27 −0.842246 −0.421123 0.907004i \(-0.638364\pi\)
−0.421123 + 0.907004i \(0.638364\pi\)
\(194\) −1909.39 −0.706631
\(195\) −60.5045 −0.0222196
\(196\) −5690.27 −2.07371
\(197\) 1270.70 0.459560 0.229780 0.973243i \(-0.426199\pi\)
0.229780 + 0.973243i \(0.426199\pi\)
\(198\) −11815.9 −4.24102
\(199\) 4794.36 1.70786 0.853928 0.520392i \(-0.174214\pi\)
0.853928 + 0.520392i \(0.174214\pi\)
\(200\) 5829.92 2.06119
\(201\) −130.457 −0.0457798
\(202\) −662.942 −0.230913
\(203\) −157.619 −0.0544960
\(204\) 0 0
\(205\) −15.8611 −0.00540383
\(206\) −986.313 −0.333591
\(207\) −8079.80 −2.71297
\(208\) −786.569 −0.262205
\(209\) −3483.54 −1.15293
\(210\) 144.242 0.0473984
\(211\) 2807.00 0.915837 0.457918 0.888994i \(-0.348595\pi\)
0.457918 + 0.888994i \(0.348595\pi\)
\(212\) −5716.66 −1.85199
\(213\) −5680.21 −1.82724
\(214\) −2441.50 −0.779896
\(215\) −245.885 −0.0779964
\(216\) 7093.09 2.23437
\(217\) −133.302 −0.0417009
\(218\) −6316.38 −1.96238
\(219\) 1639.81 0.505973
\(220\) −803.679 −0.246291
\(221\) 0 0
\(222\) −5560.51 −1.68107
\(223\) 4684.30 1.40665 0.703327 0.710866i \(-0.251697\pi\)
0.703327 + 0.710866i \(0.251697\pi\)
\(224\) 441.516 0.131697
\(225\) −5568.79 −1.65001
\(226\) −5099.70 −1.50101
\(227\) 1395.72 0.408095 0.204047 0.978961i \(-0.434590\pi\)
0.204047 + 0.978961i \(0.434590\pi\)
\(228\) 9767.47 2.83713
\(229\) 894.638 0.258163 0.129082 0.991634i \(-0.458797\pi\)
0.129082 + 0.991634i \(0.458797\pi\)
\(230\) −803.309 −0.230298
\(231\) 1694.83 0.482733
\(232\) −1937.43 −0.548270
\(233\) −1196.13 −0.336313 −0.168156 0.985760i \(-0.553781\pi\)
−0.168156 + 0.985760i \(0.553781\pi\)
\(234\) 1818.52 0.508035
\(235\) −410.773 −0.114025
\(236\) 11758.5 3.24328
\(237\) 9154.67 2.50911
\(238\) 0 0
\(239\) 4948.82 1.33938 0.669691 0.742639i \(-0.266426\pi\)
0.669691 + 0.742639i \(0.266426\pi\)
\(240\) 732.534 0.197020
\(241\) 6702.73 1.79154 0.895770 0.444518i \(-0.146625\pi\)
0.895770 + 0.444518i \(0.146625\pi\)
\(242\) −7105.03 −1.88731
\(243\) 3483.65 0.919656
\(244\) −5895.75 −1.54687
\(245\) 290.879 0.0758513
\(246\) 763.824 0.197966
\(247\) 536.130 0.138110
\(248\) −1638.53 −0.419543
\(249\) 7336.85 1.86728
\(250\) −1110.81 −0.281016
\(251\) −4756.08 −1.19602 −0.598010 0.801489i \(-0.704042\pi\)
−0.598010 + 0.801489i \(0.704042\pi\)
\(252\) −2965.89 −0.741402
\(253\) −9438.77 −2.34550
\(254\) −9701.29 −2.39651
\(255\) 0 0
\(256\) −8099.28 −1.97736
\(257\) 2892.84 0.702143 0.351071 0.936349i \(-0.385817\pi\)
0.351071 + 0.936349i \(0.385817\pi\)
\(258\) 11841.1 2.85735
\(259\) 497.784 0.119424
\(260\) 123.689 0.0295034
\(261\) 1850.65 0.438898
\(262\) −2046.92 −0.482667
\(263\) 5415.48 1.26971 0.634853 0.772633i \(-0.281061\pi\)
0.634853 + 0.772633i \(0.281061\pi\)
\(264\) 20832.6 4.85666
\(265\) 292.228 0.0677412
\(266\) −1278.13 −0.294613
\(267\) −9572.58 −2.19413
\(268\) 266.693 0.0607869
\(269\) −5787.00 −1.31167 −0.655835 0.754904i \(-0.727683\pi\)
−0.655835 + 0.754904i \(0.727683\pi\)
\(270\) −673.620 −0.151834
\(271\) 5465.13 1.22503 0.612515 0.790459i \(-0.290158\pi\)
0.612515 + 0.790459i \(0.290158\pi\)
\(272\) 0 0
\(273\) −260.840 −0.0578270
\(274\) 657.006 0.144858
\(275\) −6505.42 −1.42651
\(276\) 26465.3 5.77182
\(277\) 1207.65 0.261952 0.130976 0.991386i \(-0.458189\pi\)
0.130976 + 0.991386i \(0.458189\pi\)
\(278\) 10435.1 2.25128
\(279\) 1565.13 0.335850
\(280\) −158.722 −0.0338766
\(281\) −1197.18 −0.254155 −0.127077 0.991893i \(-0.540560\pi\)
−0.127077 + 0.991893i \(0.540560\pi\)
\(282\) 19781.7 4.17724
\(283\) −3164.73 −0.664748 −0.332374 0.943148i \(-0.607850\pi\)
−0.332374 + 0.943148i \(0.607850\pi\)
\(284\) 11612.0 2.42622
\(285\) −499.300 −0.103775
\(286\) 2124.38 0.439221
\(287\) −68.3784 −0.0140636
\(288\) −5183.98 −1.06066
\(289\) 0 0
\(290\) 183.995 0.0372571
\(291\) −3215.65 −0.647782
\(292\) −3352.26 −0.671836
\(293\) 7456.21 1.48668 0.743339 0.668915i \(-0.233241\pi\)
0.743339 + 0.668915i \(0.233241\pi\)
\(294\) −14007.9 −2.77877
\(295\) −601.079 −0.118631
\(296\) 6118.70 1.20149
\(297\) −7914.94 −1.54637
\(298\) 9323.89 1.81248
\(299\) 1452.66 0.280969
\(300\) 18240.5 3.51038
\(301\) −1060.03 −0.202988
\(302\) −10321.0 −1.96657
\(303\) −1116.47 −0.211683
\(304\) −6490.98 −1.22462
\(305\) 301.383 0.0565808
\(306\) 0 0
\(307\) −6535.48 −1.21498 −0.607491 0.794327i \(-0.707824\pi\)
−0.607491 + 0.794327i \(0.707824\pi\)
\(308\) −3464.73 −0.640978
\(309\) −1661.07 −0.305809
\(310\) 155.608 0.0285096
\(311\) 8935.89 1.62928 0.814642 0.579963i \(-0.196933\pi\)
0.814642 + 0.579963i \(0.196933\pi\)
\(312\) −3206.22 −0.581783
\(313\) 2628.71 0.474707 0.237353 0.971423i \(-0.423720\pi\)
0.237353 + 0.971423i \(0.423720\pi\)
\(314\) 1323.50 0.237865
\(315\) 151.612 0.0271187
\(316\) −18714.9 −3.33163
\(317\) −4268.54 −0.756293 −0.378147 0.925746i \(-0.623438\pi\)
−0.378147 + 0.925746i \(0.623438\pi\)
\(318\) −14072.9 −2.48166
\(319\) 2161.92 0.379449
\(320\) 176.048 0.0307544
\(321\) −4111.79 −0.714946
\(322\) −3463.13 −0.599357
\(323\) 0 0
\(324\) 1220.12 0.209211
\(325\) 1001.21 0.170883
\(326\) −7271.89 −1.23544
\(327\) −10637.5 −1.79895
\(328\) −840.500 −0.141490
\(329\) −1770.88 −0.296753
\(330\) −1978.44 −0.330029
\(331\) 992.298 0.164778 0.0823892 0.996600i \(-0.473745\pi\)
0.0823892 + 0.996600i \(0.473745\pi\)
\(332\) −14998.7 −2.47940
\(333\) −5844.63 −0.961812
\(334\) −2524.13 −0.413516
\(335\) −13.6330 −0.00222344
\(336\) 3158.02 0.512750
\(337\) −8042.26 −1.29997 −0.649985 0.759947i \(-0.725225\pi\)
−0.649985 + 0.759947i \(0.725225\pi\)
\(338\) 10729.5 1.72665
\(339\) −8588.52 −1.37600
\(340\) 0 0
\(341\) 1828.38 0.290359
\(342\) 15006.9 2.37275
\(343\) 2563.68 0.403573
\(344\) −13029.8 −2.04221
\(345\) −1352.87 −0.211119
\(346\) −13034.9 −2.02532
\(347\) 7414.16 1.14701 0.573506 0.819202i \(-0.305583\pi\)
0.573506 + 0.819202i \(0.305583\pi\)
\(348\) −6061.78 −0.933751
\(349\) −859.194 −0.131781 −0.0658905 0.997827i \(-0.520989\pi\)
−0.0658905 + 0.997827i \(0.520989\pi\)
\(350\) −2386.87 −0.364525
\(351\) 1218.14 0.185241
\(352\) −6055.89 −0.916988
\(353\) 569.084 0.0858053 0.0429027 0.999079i \(-0.486339\pi\)
0.0429027 + 0.999079i \(0.486339\pi\)
\(354\) 28946.3 4.34598
\(355\) −593.592 −0.0887453
\(356\) 19569.2 2.91339
\(357\) 0 0
\(358\) −10898.7 −1.60897
\(359\) −5005.21 −0.735835 −0.367918 0.929858i \(-0.619929\pi\)
−0.367918 + 0.929858i \(0.619929\pi\)
\(360\) 1863.60 0.272834
\(361\) −2434.71 −0.354965
\(362\) −9690.40 −1.40695
\(363\) −11965.7 −1.73013
\(364\) 533.235 0.0767833
\(365\) 171.363 0.0245741
\(366\) −14513.7 −2.07280
\(367\) 10975.3 1.56105 0.780523 0.625127i \(-0.214953\pi\)
0.780523 + 0.625127i \(0.214953\pi\)
\(368\) −17587.5 −2.49134
\(369\) 802.851 0.113265
\(370\) −581.083 −0.0816462
\(371\) 1259.82 0.176298
\(372\) −5126.57 −0.714517
\(373\) −3211.72 −0.445835 −0.222918 0.974837i \(-0.571558\pi\)
−0.222918 + 0.974837i \(0.571558\pi\)
\(374\) 0 0
\(375\) −1870.74 −0.257613
\(376\) −21767.4 −2.98556
\(377\) −332.727 −0.0454544
\(378\) −2904.03 −0.395152
\(379\) −8051.48 −1.09123 −0.545616 0.838035i \(-0.683704\pi\)
−0.545616 + 0.838035i \(0.683704\pi\)
\(380\) 1020.72 0.137794
\(381\) −16338.1 −2.19692
\(382\) 14008.1 1.87622
\(383\) −2584.16 −0.344763 −0.172382 0.985030i \(-0.555146\pi\)
−0.172382 + 0.985030i \(0.555146\pi\)
\(384\) −16318.2 −2.16858
\(385\) 177.112 0.0234454
\(386\) 11364.7 1.49858
\(387\) 12446.2 1.63482
\(388\) 6573.74 0.860132
\(389\) −5174.31 −0.674417 −0.337208 0.941430i \(-0.609483\pi\)
−0.337208 + 0.941430i \(0.609483\pi\)
\(390\) 304.489 0.0395344
\(391\) 0 0
\(392\) 15414.1 1.98604
\(393\) −3447.25 −0.442470
\(394\) −6394.79 −0.817677
\(395\) 956.680 0.121863
\(396\) 40680.4 5.16230
\(397\) 5149.36 0.650980 0.325490 0.945545i \(-0.394471\pi\)
0.325490 + 0.945545i \(0.394471\pi\)
\(398\) −24127.7 −3.03872
\(399\) −2152.53 −0.270078
\(400\) −12121.7 −1.51522
\(401\) −8700.49 −1.08350 −0.541748 0.840541i \(-0.682237\pi\)
−0.541748 + 0.840541i \(0.682237\pi\)
\(402\) 656.527 0.0814542
\(403\) −281.394 −0.0347823
\(404\) 2282.41 0.281074
\(405\) −62.3709 −0.00765243
\(406\) 793.219 0.0969625
\(407\) −6827.65 −0.831533
\(408\) 0 0
\(409\) 12346.0 1.49260 0.746299 0.665611i \(-0.231829\pi\)
0.746299 + 0.665611i \(0.231829\pi\)
\(410\) 79.8209 0.00961482
\(411\) 1106.48 0.132794
\(412\) 3395.72 0.406056
\(413\) −2591.30 −0.308740
\(414\) 40661.7 4.82708
\(415\) 766.713 0.0906903
\(416\) 932.023 0.109847
\(417\) 17574.0 2.06379
\(418\) 17531.0 2.05136
\(419\) 5763.33 0.671974 0.335987 0.941867i \(-0.390930\pi\)
0.335987 + 0.941867i \(0.390930\pi\)
\(420\) −496.604 −0.0576947
\(421\) −1876.12 −0.217188 −0.108594 0.994086i \(-0.534635\pi\)
−0.108594 + 0.994086i \(0.534635\pi\)
\(422\) −14126.2 −1.62951
\(423\) 20792.4 2.38998
\(424\) 15485.6 1.77369
\(425\) 0 0
\(426\) 28585.7 3.25113
\(427\) 1299.29 0.147253
\(428\) 8405.72 0.949313
\(429\) 3577.71 0.402642
\(430\) 1237.42 0.138776
\(431\) −83.9299 −0.00937996 −0.00468998 0.999989i \(-0.501493\pi\)
−0.00468998 + 0.999989i \(0.501493\pi\)
\(432\) −14748.1 −1.64252
\(433\) −15345.0 −1.70308 −0.851539 0.524291i \(-0.824331\pi\)
−0.851539 + 0.524291i \(0.824331\pi\)
\(434\) 670.842 0.0741968
\(435\) 309.870 0.0341543
\(436\) 21746.3 2.38867
\(437\) 11987.8 1.31225
\(438\) −8252.36 −0.900258
\(439\) −3064.74 −0.333194 −0.166597 0.986025i \(-0.553278\pi\)
−0.166597 + 0.986025i \(0.553278\pi\)
\(440\) 2177.05 0.235879
\(441\) −14723.6 −1.58985
\(442\) 0 0
\(443\) −1792.97 −0.192295 −0.0961474 0.995367i \(-0.530652\pi\)
−0.0961474 + 0.995367i \(0.530652\pi\)
\(444\) 19144.0 2.04624
\(445\) −1000.35 −0.106564
\(446\) −23573.8 −2.50281
\(447\) 15702.6 1.66153
\(448\) 758.960 0.0800391
\(449\) −2499.19 −0.262681 −0.131341 0.991337i \(-0.541928\pi\)
−0.131341 + 0.991337i \(0.541928\pi\)
\(450\) 28025.0 2.93580
\(451\) 937.885 0.0979231
\(452\) 17557.5 1.82707
\(453\) −17381.7 −1.80279
\(454\) −7024.00 −0.726107
\(455\) −27.2583 −0.00280854
\(456\) −26458.6 −2.71719
\(457\) 14784.4 1.51331 0.756656 0.653813i \(-0.226832\pi\)
0.756656 + 0.653813i \(0.226832\pi\)
\(458\) −4502.28 −0.459340
\(459\) 0 0
\(460\) 2765.67 0.280326
\(461\) −17746.9 −1.79297 −0.896483 0.443078i \(-0.853887\pi\)
−0.896483 + 0.443078i \(0.853887\pi\)
\(462\) −8529.23 −0.858909
\(463\) 18486.4 1.85559 0.927793 0.373096i \(-0.121704\pi\)
0.927793 + 0.373096i \(0.121704\pi\)
\(464\) 4028.36 0.403043
\(465\) 262.064 0.0261353
\(466\) 6019.52 0.598388
\(467\) 7406.57 0.733908 0.366954 0.930239i \(-0.380401\pi\)
0.366954 + 0.930239i \(0.380401\pi\)
\(468\) −6260.87 −0.618395
\(469\) −58.7731 −0.00578655
\(470\) 2067.22 0.202880
\(471\) 2228.94 0.218055
\(472\) −31852.0 −3.10616
\(473\) 14539.5 1.41338
\(474\) −46071.0 −4.46437
\(475\) 8262.24 0.798101
\(476\) 0 0
\(477\) −14791.9 −1.41986
\(478\) −24905.0 −2.38311
\(479\) 18550.9 1.76955 0.884775 0.466019i \(-0.154312\pi\)
0.884775 + 0.466019i \(0.154312\pi\)
\(480\) −867.997 −0.0825384
\(481\) 1050.80 0.0996100
\(482\) −33731.6 −3.18762
\(483\) −5832.34 −0.549442
\(484\) 24461.5 2.29729
\(485\) −336.041 −0.0314615
\(486\) −17531.5 −1.63631
\(487\) −10203.4 −0.949406 −0.474703 0.880146i \(-0.657444\pi\)
−0.474703 + 0.880146i \(0.657444\pi\)
\(488\) 15970.7 1.48147
\(489\) −12246.7 −1.13255
\(490\) −1463.85 −0.134959
\(491\) −1247.46 −0.114658 −0.0573290 0.998355i \(-0.518258\pi\)
−0.0573290 + 0.998355i \(0.518258\pi\)
\(492\) −2629.73 −0.240970
\(493\) 0 0
\(494\) −2698.08 −0.245734
\(495\) −2079.53 −0.188824
\(496\) 3406.87 0.308413
\(497\) −2559.03 −0.230962
\(498\) −36922.7 −3.32238
\(499\) −70.0303 −0.00628254 −0.00314127 0.999995i \(-0.501000\pi\)
−0.00314127 + 0.999995i \(0.501000\pi\)
\(500\) 3824.36 0.342061
\(501\) −4250.94 −0.379078
\(502\) 23935.0 2.12803
\(503\) −1444.29 −0.128028 −0.0640138 0.997949i \(-0.520390\pi\)
−0.0640138 + 0.997949i \(0.520390\pi\)
\(504\) 8034.15 0.710058
\(505\) −116.674 −0.0102810
\(506\) 47500.7 4.17325
\(507\) 18069.7 1.58285
\(508\) 33400.0 2.91710
\(509\) 14272.8 1.24289 0.621445 0.783458i \(-0.286546\pi\)
0.621445 + 0.783458i \(0.286546\pi\)
\(510\) 0 0
\(511\) 738.761 0.0639547
\(512\) 25356.7 2.18871
\(513\) 10052.4 0.865157
\(514\) −14558.3 −1.24929
\(515\) −173.585 −0.0148525
\(516\) −40767.2 −3.47805
\(517\) 24289.6 2.06625
\(518\) −2505.10 −0.212486
\(519\) −21952.3 −1.85665
\(520\) −335.055 −0.0282561
\(521\) −14874.0 −1.25075 −0.625376 0.780324i \(-0.715054\pi\)
−0.625376 + 0.780324i \(0.715054\pi\)
\(522\) −9313.42 −0.780914
\(523\) −8142.90 −0.680811 −0.340406 0.940279i \(-0.610564\pi\)
−0.340406 + 0.940279i \(0.610564\pi\)
\(524\) 7047.21 0.587517
\(525\) −4019.78 −0.334167
\(526\) −27253.4 −2.25914
\(527\) 0 0
\(528\) −43315.7 −3.57022
\(529\) 20314.2 1.66962
\(530\) −1470.64 −0.120529
\(531\) 30425.3 2.48652
\(532\) 4400.40 0.358612
\(533\) −144.344 −0.0117303
\(534\) 48174.1 3.90393
\(535\) −429.689 −0.0347235
\(536\) −722.432 −0.0582170
\(537\) −18354.7 −1.47498
\(538\) 29123.1 2.33380
\(539\) −17200.0 −1.37451
\(540\) 2319.17 0.184817
\(541\) −3179.67 −0.252689 −0.126344 0.991986i \(-0.540324\pi\)
−0.126344 + 0.991986i \(0.540324\pi\)
\(542\) −27503.3 −2.17965
\(543\) −16319.8 −1.28978
\(544\) 0 0
\(545\) −1111.64 −0.0873716
\(546\) 1312.68 0.102889
\(547\) −2107.07 −0.164702 −0.0823509 0.996603i \(-0.526243\pi\)
−0.0823509 + 0.996603i \(0.526243\pi\)
\(548\) −2261.97 −0.176326
\(549\) −15255.3 −1.18594
\(550\) 32738.6 2.53814
\(551\) −2745.76 −0.212292
\(552\) −71690.4 −5.52780
\(553\) 4124.33 0.317151
\(554\) −6077.51 −0.466081
\(555\) −978.614 −0.0748466
\(556\) −35926.4 −2.74032
\(557\) 467.382 0.0355540 0.0177770 0.999842i \(-0.494341\pi\)
0.0177770 + 0.999842i \(0.494341\pi\)
\(558\) −7876.55 −0.597565
\(559\) −2237.69 −0.169309
\(560\) 330.019 0.0249033
\(561\) 0 0
\(562\) 6024.80 0.452208
\(563\) 14612.6 1.09387 0.546935 0.837175i \(-0.315794\pi\)
0.546935 + 0.837175i \(0.315794\pi\)
\(564\) −68105.2 −5.08466
\(565\) −897.515 −0.0668297
\(566\) 15926.5 1.18276
\(567\) −268.886 −0.0199156
\(568\) −31455.3 −2.32365
\(569\) 11602.3 0.854821 0.427410 0.904058i \(-0.359426\pi\)
0.427410 + 0.904058i \(0.359426\pi\)
\(570\) 2512.73 0.184643
\(571\) 10534.9 0.772104 0.386052 0.922477i \(-0.373839\pi\)
0.386052 + 0.922477i \(0.373839\pi\)
\(572\) −7313.91 −0.534633
\(573\) 23591.3 1.71997
\(574\) 344.115 0.0250228
\(575\) 22386.8 1.62364
\(576\) −8911.18 −0.644617
\(577\) 14404.7 1.03930 0.519650 0.854379i \(-0.326062\pi\)
0.519650 + 0.854379i \(0.326062\pi\)
\(578\) 0 0
\(579\) 19139.6 1.37377
\(580\) −633.466 −0.0453504
\(581\) 3305.37 0.236024
\(582\) 16182.8 1.15257
\(583\) −17279.8 −1.22754
\(584\) 9080.77 0.643433
\(585\) 320.047 0.0226194
\(586\) −37523.5 −2.64519
\(587\) −11004.9 −0.773799 −0.386900 0.922122i \(-0.626454\pi\)
−0.386900 + 0.922122i \(0.626454\pi\)
\(588\) 48227.0 3.38240
\(589\) −2322.14 −0.162449
\(590\) 3024.94 0.211076
\(591\) −10769.6 −0.749581
\(592\) −12722.2 −0.883239
\(593\) 1853.59 0.128361 0.0641804 0.997938i \(-0.479557\pi\)
0.0641804 + 0.997938i \(0.479557\pi\)
\(594\) 39832.0 2.75139
\(595\) 0 0
\(596\) −32100.7 −2.20620
\(597\) −40633.9 −2.78565
\(598\) −7310.53 −0.499916
\(599\) 19074.7 1.30112 0.650559 0.759456i \(-0.274535\pi\)
0.650559 + 0.759456i \(0.274535\pi\)
\(600\) −49410.7 −3.36197
\(601\) 27776.0 1.88520 0.942600 0.333923i \(-0.108373\pi\)
0.942600 + 0.333923i \(0.108373\pi\)
\(602\) 5334.62 0.361168
\(603\) 690.073 0.0466035
\(604\) 35533.4 2.39377
\(605\) −1250.44 −0.0840291
\(606\) 5618.67 0.376638
\(607\) −18728.3 −1.25232 −0.626159 0.779695i \(-0.715374\pi\)
−0.626159 + 0.779695i \(0.715374\pi\)
\(608\) 7691.32 0.513033
\(609\) 1335.88 0.0888874
\(610\) −1516.71 −0.100672
\(611\) −3738.25 −0.247518
\(612\) 0 0
\(613\) −24405.3 −1.60802 −0.804012 0.594613i \(-0.797305\pi\)
−0.804012 + 0.594613i \(0.797305\pi\)
\(614\) 32889.8 2.16177
\(615\) 134.428 0.00881409
\(616\) 9385.43 0.613880
\(617\) 22516.4 1.46917 0.734584 0.678518i \(-0.237377\pi\)
0.734584 + 0.678518i \(0.237377\pi\)
\(618\) 8359.35 0.544114
\(619\) 5146.53 0.334179 0.167089 0.985942i \(-0.446563\pi\)
0.167089 + 0.985942i \(0.446563\pi\)
\(620\) −535.736 −0.0347027
\(621\) 27237.4 1.76006
\(622\) −44969.9 −2.89892
\(623\) −4312.60 −0.277337
\(624\) 6666.45 0.427679
\(625\) 15331.4 0.981213
\(626\) −13229.0 −0.844627
\(627\) 29524.3 1.88052
\(628\) −4556.62 −0.289536
\(629\) 0 0
\(630\) −762.990 −0.0482512
\(631\) −3858.77 −0.243447 −0.121724 0.992564i \(-0.538842\pi\)
−0.121724 + 0.992564i \(0.538842\pi\)
\(632\) 50695.8 3.19078
\(633\) −23790.3 −1.49381
\(634\) 21481.5 1.34564
\(635\) −1707.36 −0.106700
\(636\) 48450.7 3.02075
\(637\) 2647.15 0.164653
\(638\) −10879.9 −0.675138
\(639\) 30046.3 1.86011
\(640\) −1705.28 −0.105324
\(641\) −18689.3 −1.15161 −0.575805 0.817587i \(-0.695311\pi\)
−0.575805 + 0.817587i \(0.695311\pi\)
\(642\) 20692.6 1.27208
\(643\) −26473.5 −1.62366 −0.811831 0.583893i \(-0.801529\pi\)
−0.811831 + 0.583893i \(0.801529\pi\)
\(644\) 11923.0 0.729555
\(645\) 2083.96 0.127219
\(646\) 0 0
\(647\) 14397.7 0.874855 0.437427 0.899254i \(-0.355890\pi\)
0.437427 + 0.899254i \(0.355890\pi\)
\(648\) −3305.12 −0.200366
\(649\) 35542.6 2.14972
\(650\) −5038.59 −0.304046
\(651\) 1129.78 0.0680177
\(652\) 25036.0 1.50381
\(653\) −20939.5 −1.25486 −0.627431 0.778672i \(-0.715893\pi\)
−0.627431 + 0.778672i \(0.715893\pi\)
\(654\) 53533.6 3.20081
\(655\) −360.244 −0.0214899
\(656\) 1747.59 0.104012
\(657\) −8674.02 −0.515077
\(658\) 8911.96 0.528001
\(659\) 4031.76 0.238323 0.119162 0.992875i \(-0.461979\pi\)
0.119162 + 0.992875i \(0.461979\pi\)
\(660\) 6811.47 0.401721
\(661\) 6691.52 0.393752 0.196876 0.980428i \(-0.436920\pi\)
0.196876 + 0.980428i \(0.436920\pi\)
\(662\) −4993.75 −0.293184
\(663\) 0 0
\(664\) 40629.2 2.37458
\(665\) −224.943 −0.0131171
\(666\) 29413.1 1.71131
\(667\) −7439.71 −0.431884
\(668\) 8690.19 0.503344
\(669\) −39701.1 −2.29437
\(670\) 68.6083 0.00395607
\(671\) −17821.2 −1.02530
\(672\) −3742.01 −0.214808
\(673\) −10319.2 −0.591048 −0.295524 0.955335i \(-0.595494\pi\)
−0.295524 + 0.955335i \(0.595494\pi\)
\(674\) 40472.7 2.31298
\(675\) 18772.6 1.07046
\(676\) −36939.9 −2.10172
\(677\) 19813.3 1.12480 0.562398 0.826866i \(-0.309879\pi\)
0.562398 + 0.826866i \(0.309879\pi\)
\(678\) 43221.8 2.44826
\(679\) −1448.70 −0.0818793
\(680\) 0 0
\(681\) −11829.3 −0.665636
\(682\) −9201.33 −0.516624
\(683\) −5924.61 −0.331916 −0.165958 0.986133i \(-0.553072\pi\)
−0.165958 + 0.986133i \(0.553072\pi\)
\(684\) −51666.4 −2.88818
\(685\) 115.629 0.00644957
\(686\) −12901.7 −0.718061
\(687\) −7582.38 −0.421085
\(688\) 27091.9 1.50126
\(689\) 2659.43 0.147048
\(690\) 6808.33 0.375636
\(691\) −1973.16 −0.108629 −0.0543143 0.998524i \(-0.517297\pi\)
−0.0543143 + 0.998524i \(0.517297\pi\)
\(692\) 44877.1 2.46528
\(693\) −8965.03 −0.491419
\(694\) −37311.8 −2.04083
\(695\) 1836.51 0.100234
\(696\) 16420.4 0.894274
\(697\) 0 0
\(698\) 4323.90 0.234473
\(699\) 10137.6 0.548554
\(700\) 8217.63 0.443710
\(701\) −12840.1 −0.691815 −0.345907 0.938269i \(-0.612429\pi\)
−0.345907 + 0.938269i \(0.612429\pi\)
\(702\) −6130.30 −0.329591
\(703\) 8671.50 0.465223
\(704\) −10410.0 −0.557302
\(705\) 3481.45 0.185984
\(706\) −2863.92 −0.152670
\(707\) −502.990 −0.0267566
\(708\) −99657.5 −5.29005
\(709\) 27749.7 1.46990 0.734952 0.678119i \(-0.237204\pi\)
0.734952 + 0.678119i \(0.237204\pi\)
\(710\) 2987.26 0.157901
\(711\) −48425.0 −2.55426
\(712\) −53010.0 −2.79022
\(713\) −6291.92 −0.330483
\(714\) 0 0
\(715\) 373.877 0.0195555
\(716\) 37522.4 1.95849
\(717\) −41943.0 −2.18464
\(718\) 25188.8 1.30924
\(719\) −16888.3 −0.875979 −0.437989 0.898980i \(-0.644309\pi\)
−0.437989 + 0.898980i \(0.644309\pi\)
\(720\) −3874.85 −0.200565
\(721\) −748.339 −0.0386541
\(722\) 12252.7 0.631575
\(723\) −56808.0 −2.92215
\(724\) 33362.6 1.71258
\(725\) −5127.62 −0.262669
\(726\) 60217.6 3.07835
\(727\) 2135.25 0.108930 0.0544649 0.998516i \(-0.482655\pi\)
0.0544649 + 0.998516i \(0.482655\pi\)
\(728\) −1444.45 −0.0735371
\(729\) −31426.5 −1.59663
\(730\) −862.386 −0.0437238
\(731\) 0 0
\(732\) 49968.6 2.52308
\(733\) 4795.27 0.241633 0.120817 0.992675i \(-0.461449\pi\)
0.120817 + 0.992675i \(0.461449\pi\)
\(734\) −55233.1 −2.77751
\(735\) −2465.30 −0.123720
\(736\) 20839.9 1.04371
\(737\) 806.138 0.0402910
\(738\) −4040.36 −0.201528
\(739\) −32747.6 −1.63010 −0.815048 0.579393i \(-0.803290\pi\)
−0.815048 + 0.579393i \(0.803290\pi\)
\(740\) 2000.58 0.0993821
\(741\) −4543.89 −0.225269
\(742\) −6340.05 −0.313680
\(743\) −12299.4 −0.607298 −0.303649 0.952784i \(-0.598205\pi\)
−0.303649 + 0.952784i \(0.598205\pi\)
\(744\) 13887.1 0.684309
\(745\) 1640.94 0.0806974
\(746\) 16163.0 0.793257
\(747\) −38809.3 −1.90088
\(748\) 0 0
\(749\) −1852.43 −0.0903688
\(750\) 9414.54 0.458361
\(751\) −30102.6 −1.46266 −0.731332 0.682021i \(-0.761101\pi\)
−0.731332 + 0.682021i \(0.761101\pi\)
\(752\) 45259.4 2.19474
\(753\) 40309.4 1.95081
\(754\) 1674.45 0.0808753
\(755\) −1816.42 −0.0875581
\(756\) 9998.14 0.480990
\(757\) 38826.3 1.86416 0.932078 0.362257i \(-0.117994\pi\)
0.932078 + 0.362257i \(0.117994\pi\)
\(758\) 40519.2 1.94159
\(759\) 79996.9 3.82570
\(760\) −2764.97 −0.131968
\(761\) 19981.6 0.951815 0.475907 0.879495i \(-0.342120\pi\)
0.475907 + 0.879495i \(0.342120\pi\)
\(762\) 82221.8 3.90890
\(763\) −4792.39 −0.227387
\(764\) −48227.7 −2.28379
\(765\) 0 0
\(766\) 13004.8 0.613424
\(767\) −5470.14 −0.257517
\(768\) 68644.2 3.22524
\(769\) −22407.7 −1.05077 −0.525384 0.850865i \(-0.676078\pi\)
−0.525384 + 0.850865i \(0.676078\pi\)
\(770\) −891.320 −0.0417155
\(771\) −24517.9 −1.14525
\(772\) −39127.0 −1.82411
\(773\) −6902.77 −0.321184 −0.160592 0.987021i \(-0.551340\pi\)
−0.160592 + 0.987021i \(0.551340\pi\)
\(774\) −62635.4 −2.90876
\(775\) −4336.54 −0.200997
\(776\) −17807.3 −0.823768
\(777\) −4218.89 −0.194790
\(778\) 26039.8 1.19996
\(779\) −1191.17 −0.0547856
\(780\) −1048.31 −0.0481225
\(781\) 35099.9 1.60816
\(782\) 0 0
\(783\) −6238.62 −0.284738
\(784\) −32049.3 −1.45997
\(785\) 232.928 0.0105905
\(786\) 17348.3 0.787270
\(787\) 22185.9 1.00488 0.502442 0.864611i \(-0.332435\pi\)
0.502442 + 0.864611i \(0.332435\pi\)
\(788\) 22016.3 0.995301
\(789\) −45898.1 −2.07099
\(790\) −4814.50 −0.216826
\(791\) −3869.27 −0.173926
\(792\) −110197. −4.94405
\(793\) 2742.74 0.122822
\(794\) −25914.2 −1.15826
\(795\) −2476.73 −0.110491
\(796\) 83067.8 3.69882
\(797\) −16291.1 −0.724040 −0.362020 0.932170i \(-0.617913\pi\)
−0.362020 + 0.932170i \(0.617913\pi\)
\(798\) 10832.6 0.480539
\(799\) 0 0
\(800\) 14363.3 0.634775
\(801\) 50635.5 2.23361
\(802\) 43785.3 1.92782
\(803\) −10132.9 −0.445309
\(804\) −2260.32 −0.0991485
\(805\) −609.489 −0.0266853
\(806\) 1416.12 0.0618867
\(807\) 49046.8 2.13944
\(808\) −6182.70 −0.269191
\(809\) −17696.8 −0.769082 −0.384541 0.923108i \(-0.625640\pi\)
−0.384541 + 0.923108i \(0.625640\pi\)
\(810\) 313.882 0.0136157
\(811\) 3095.34 0.134022 0.0670111 0.997752i \(-0.478654\pi\)
0.0670111 + 0.997752i \(0.478654\pi\)
\(812\) −2730.93 −0.118026
\(813\) −46318.9 −1.99812
\(814\) 34360.2 1.47951
\(815\) −1279.81 −0.0550057
\(816\) 0 0
\(817\) −18466.0 −0.790751
\(818\) −62131.5 −2.65572
\(819\) 1379.75 0.0588674
\(820\) −274.811 −0.0117034
\(821\) −12323.5 −0.523864 −0.261932 0.965086i \(-0.584360\pi\)
−0.261932 + 0.965086i \(0.584360\pi\)
\(822\) −5568.36 −0.236276
\(823\) 34436.5 1.45854 0.729271 0.684225i \(-0.239860\pi\)
0.729271 + 0.684225i \(0.239860\pi\)
\(824\) −9198.50 −0.388889
\(825\) 55135.7 2.32676
\(826\) 13040.8 0.549329
\(827\) −18761.6 −0.788880 −0.394440 0.918922i \(-0.629061\pi\)
−0.394440 + 0.918922i \(0.629061\pi\)
\(828\) −139992. −5.87567
\(829\) 22423.8 0.939457 0.469728 0.882811i \(-0.344352\pi\)
0.469728 + 0.882811i \(0.344352\pi\)
\(830\) −3858.49 −0.161362
\(831\) −10235.3 −0.427265
\(832\) 1602.13 0.0667596
\(833\) 0 0
\(834\) −88441.1 −3.67202
\(835\) −444.231 −0.0184111
\(836\) −60356.4 −2.49697
\(837\) −5276.13 −0.217885
\(838\) −29004.0 −1.19562
\(839\) −9128.63 −0.375632 −0.187816 0.982204i \(-0.560141\pi\)
−0.187816 + 0.982204i \(0.560141\pi\)
\(840\) 1345.22 0.0552555
\(841\) −22685.0 −0.930131
\(842\) 9441.58 0.386435
\(843\) 10146.5 0.414547
\(844\) 48634.4 1.98349
\(845\) 1888.32 0.0768759
\(846\) −104638. −4.25240
\(847\) −5390.75 −0.218688
\(848\) −32198.0 −1.30387
\(849\) 26822.2 1.08426
\(850\) 0 0
\(851\) 23495.7 0.946442
\(852\) −98416.1 −3.95737
\(853\) −27204.8 −1.09200 −0.545999 0.837786i \(-0.683850\pi\)
−0.545999 + 0.837786i \(0.683850\pi\)
\(854\) −6538.68 −0.262001
\(855\) 2641.12 0.105643
\(856\) −22769.8 −0.909179
\(857\) 38060.0 1.51704 0.758520 0.651649i \(-0.225923\pi\)
0.758520 + 0.651649i \(0.225923\pi\)
\(858\) −18004.9 −0.716405
\(859\) −33326.2 −1.32372 −0.661860 0.749627i \(-0.730233\pi\)
−0.661860 + 0.749627i \(0.730233\pi\)
\(860\) −4260.24 −0.168922
\(861\) 579.531 0.0229389
\(862\) 422.378 0.0166894
\(863\) −41724.2 −1.64578 −0.822890 0.568201i \(-0.807640\pi\)
−0.822890 + 0.568201i \(0.807640\pi\)
\(864\) 17475.4 0.688108
\(865\) −2294.06 −0.0901737
\(866\) 77223.8 3.03022
\(867\) 0 0
\(868\) −2309.60 −0.0903146
\(869\) −56569.7 −2.20828
\(870\) −1559.42 −0.0607694
\(871\) −124.068 −0.00482649
\(872\) −58907.5 −2.28768
\(873\) 17009.6 0.659438
\(874\) −60328.6 −2.33483
\(875\) −842.801 −0.0325621
\(876\) 28411.6 1.09582
\(877\) 49337.3 1.89966 0.949830 0.312767i \(-0.101256\pi\)
0.949830 + 0.312767i \(0.101256\pi\)
\(878\) 15423.3 0.592838
\(879\) −63194.0 −2.42489
\(880\) −4526.57 −0.173398
\(881\) −8845.46 −0.338265 −0.169132 0.985593i \(-0.554097\pi\)
−0.169132 + 0.985593i \(0.554097\pi\)
\(882\) 74096.8 2.82876
\(883\) 14724.2 0.561165 0.280582 0.959830i \(-0.409472\pi\)
0.280582 + 0.959830i \(0.409472\pi\)
\(884\) 0 0
\(885\) 5094.36 0.193497
\(886\) 9023.14 0.342143
\(887\) −3864.38 −0.146283 −0.0731415 0.997322i \(-0.523302\pi\)
−0.0731415 + 0.997322i \(0.523302\pi\)
\(888\) −51858.1 −1.95974
\(889\) −7360.60 −0.277690
\(890\) 5034.28 0.189606
\(891\) 3688.07 0.138670
\(892\) 81160.9 3.04649
\(893\) −30849.1 −1.15602
\(894\) −79023.2 −2.95630
\(895\) −1918.10 −0.0716368
\(896\) −7351.61 −0.274107
\(897\) −12311.8 −0.458283
\(898\) 12577.2 0.467379
\(899\) 1441.14 0.0534648
\(900\) −96485.6 −3.57354
\(901\) 0 0
\(902\) −4719.92 −0.174231
\(903\) 8984.15 0.331089
\(904\) −47560.6 −1.74982
\(905\) −1705.45 −0.0626421
\(906\) 87473.7 3.20764
\(907\) 743.409 0.0272155 0.0136078 0.999907i \(-0.495668\pi\)
0.0136078 + 0.999907i \(0.495668\pi\)
\(908\) 24182.5 0.883839
\(909\) 5905.76 0.215491
\(910\) 137.177 0.00499713
\(911\) −16291.0 −0.592475 −0.296238 0.955114i \(-0.595732\pi\)
−0.296238 + 0.955114i \(0.595732\pi\)
\(912\) 55013.4 1.99745
\(913\) −45336.8 −1.64340
\(914\) −74402.5 −2.69258
\(915\) −2554.33 −0.0922879
\(916\) 15500.6 0.559122
\(917\) −1553.04 −0.0559280
\(918\) 0 0
\(919\) −6188.99 −0.222150 −0.111075 0.993812i \(-0.535429\pi\)
−0.111075 + 0.993812i \(0.535429\pi\)
\(920\) −7491.78 −0.268474
\(921\) 55390.5 1.98174
\(922\) 89311.6 3.19015
\(923\) −5402.00 −0.192643
\(924\) 29364.8 1.04549
\(925\) 16193.8 0.575620
\(926\) −93033.0 −3.30157
\(927\) 8786.47 0.311311
\(928\) −4773.30 −0.168848
\(929\) 31661.7 1.11818 0.559089 0.829108i \(-0.311151\pi\)
0.559089 + 0.829108i \(0.311151\pi\)
\(930\) −1318.84 −0.0465015
\(931\) 21845.0 0.769003
\(932\) −20724.3 −0.728376
\(933\) −75734.8 −2.65750
\(934\) −37273.6 −1.30581
\(935\) 0 0
\(936\) 16959.8 0.592251
\(937\) 35010.5 1.22064 0.610322 0.792153i \(-0.291040\pi\)
0.610322 + 0.792153i \(0.291040\pi\)
\(938\) 295.776 0.0102958
\(939\) −22279.2 −0.774286
\(940\) −7117.12 −0.246952
\(941\) 45625.8 1.58061 0.790307 0.612711i \(-0.209921\pi\)
0.790307 + 0.612711i \(0.209921\pi\)
\(942\) −11217.2 −0.387977
\(943\) −3227.51 −0.111455
\(944\) 66227.5 2.28339
\(945\) −511.092 −0.0175934
\(946\) −73170.2 −2.51477
\(947\) 21508.4 0.738044 0.369022 0.929421i \(-0.379693\pi\)
0.369022 + 0.929421i \(0.379693\pi\)
\(948\) 158615. 5.43416
\(949\) 1559.50 0.0533439
\(950\) −41579.8 −1.42003
\(951\) 36177.4 1.23358
\(952\) 0 0
\(953\) 35686.7 1.21302 0.606509 0.795076i \(-0.292569\pi\)
0.606509 + 0.795076i \(0.292569\pi\)
\(954\) 74440.5 2.52631
\(955\) 2465.34 0.0835355
\(956\) 85744.0 2.90079
\(957\) −18323.0 −0.618912
\(958\) −93357.8 −3.14849
\(959\) 498.486 0.0167851
\(960\) −1492.07 −0.0501630
\(961\) −28572.2 −0.959088
\(962\) −5288.17 −0.177232
\(963\) 21749.9 0.727810
\(964\) 116133. 3.88006
\(965\) 2000.12 0.0667215
\(966\) 29351.3 0.977600
\(967\) −3731.33 −0.124086 −0.0620432 0.998073i \(-0.519762\pi\)
−0.0620432 + 0.998073i \(0.519762\pi\)
\(968\) −66262.5 −2.20016
\(969\) 0 0
\(970\) 1691.13 0.0559782
\(971\) 17645.1 0.583171 0.291585 0.956545i \(-0.405817\pi\)
0.291585 + 0.956545i \(0.405817\pi\)
\(972\) 60358.3 1.99176
\(973\) 7917.35 0.260862
\(974\) 51348.7 1.68924
\(975\) −8485.59 −0.278725
\(976\) −33206.7 −1.08906
\(977\) 24941.2 0.816723 0.408362 0.912820i \(-0.366100\pi\)
0.408362 + 0.912820i \(0.366100\pi\)
\(978\) 61631.8 2.01510
\(979\) 59152.1 1.93106
\(980\) 5039.81 0.164276
\(981\) 56268.9 1.83132
\(982\) 6277.85 0.204006
\(983\) 22506.2 0.730252 0.365126 0.930958i \(-0.381026\pi\)
0.365126 + 0.930958i \(0.381026\pi\)
\(984\) 7123.53 0.230782
\(985\) −1125.44 −0.0364057
\(986\) 0 0
\(987\) 15008.8 0.484029
\(988\) 9289.07 0.299114
\(989\) −50034.2 −1.60869
\(990\) 10465.3 0.335967
\(991\) −32694.1 −1.04799 −0.523997 0.851720i \(-0.675560\pi\)
−0.523997 + 0.851720i \(0.675560\pi\)
\(992\) −4036.88 −0.129205
\(993\) −8410.08 −0.268767
\(994\) 12878.3 0.410941
\(995\) −4246.32 −0.135294
\(996\) 127119. 4.04410
\(997\) −18248.8 −0.579686 −0.289843 0.957074i \(-0.593603\pi\)
−0.289843 + 0.957074i \(0.593603\pi\)
\(998\) 352.428 0.0111783
\(999\) 19702.5 0.623983
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 289.4.a.b.1.1 3
17.4 even 4 289.4.b.b.288.6 6
17.13 even 4 289.4.b.b.288.5 6
17.16 even 2 17.4.a.b.1.1 3
51.50 odd 2 153.4.a.g.1.3 3
68.67 odd 2 272.4.a.h.1.1 3
85.33 odd 4 425.4.b.f.324.6 6
85.67 odd 4 425.4.b.f.324.1 6
85.84 even 2 425.4.a.g.1.3 3
119.118 odd 2 833.4.a.d.1.1 3
136.67 odd 2 1088.4.a.x.1.3 3
136.101 even 2 1088.4.a.v.1.1 3
187.186 odd 2 2057.4.a.e.1.3 3
204.203 even 2 2448.4.a.bi.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
17.4.a.b.1.1 3 17.16 even 2
153.4.a.g.1.3 3 51.50 odd 2
272.4.a.h.1.1 3 68.67 odd 2
289.4.a.b.1.1 3 1.1 even 1 trivial
289.4.b.b.288.5 6 17.13 even 4
289.4.b.b.288.6 6 17.4 even 4
425.4.a.g.1.3 3 85.84 even 2
425.4.b.f.324.1 6 85.67 odd 4
425.4.b.f.324.6 6 85.33 odd 4
833.4.a.d.1.1 3 119.118 odd 2
1088.4.a.v.1.1 3 136.101 even 2
1088.4.a.x.1.3 3 136.67 odd 2
2057.4.a.e.1.3 3 187.186 odd 2
2448.4.a.bi.1.2 3 204.203 even 2