Properties

Label 289.4.b.b.288.5
Level $289$
Weight $4$
Character 289.288
Analytic conductor $17.052$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 289 = 17^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 289.b (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(17.0515519917\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.27793984.1
Defining polynomial: \( x^{6} - 2x^{3} + 49x^{2} - 14x + 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{5} \)
Twist minimal: no (minimal twist has level 17)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 288.5
Root \(1.79483 + 1.79483i\) of defining polynomial
Character \(\chi\) \(=\) 289.288
Dual form 289.4.b.b.288.6

$q$-expansion

\(f(q)\) \(=\) \(q+5.03251 q^{2} -8.47535i q^{3} +17.3261 q^{4} -0.885690i q^{5} -42.6523i q^{6} +3.81828i q^{7} +46.9339 q^{8} -44.8316 q^{9} +O(q^{10})\) \(q+5.03251 q^{2} -8.47535i q^{3} +17.3261 q^{4} -0.885690i q^{5} -42.6523i q^{6} +3.81828i q^{7} +46.9339 q^{8} -44.8316 q^{9} -4.45724i q^{10} -52.3720i q^{11} -146.845i q^{12} -8.06025 q^{13} +19.2156i q^{14} -7.50653 q^{15} +97.5862 q^{16} -225.616 q^{18} +66.5154 q^{19} -15.3456i q^{20} +32.3613 q^{21} -263.563i q^{22} +180.226i q^{23} -397.782i q^{24} +124.216 q^{25} -40.5633 q^{26} +151.129i q^{27} +66.1562i q^{28} +41.2800i q^{29} -37.7767 q^{30} +34.9114i q^{31} +115.632 q^{32} -443.871 q^{33} +3.38182 q^{35} -776.759 q^{36} -130.368i q^{37} +334.739 q^{38} +68.3134i q^{39} -41.5689i q^{40} -17.9081i q^{41} +162.859 q^{42} -277.620 q^{43} -907.405i q^{44} +39.7069i q^{45} +906.987i q^{46} +463.789 q^{47} -827.078i q^{48} +328.421 q^{49} +625.116 q^{50} -139.653 q^{52} +329.944 q^{53} +760.560i q^{54} -46.3853 q^{55} +179.207i q^{56} -563.741i q^{57} +207.742i q^{58} -678.656 q^{59} -130.059 q^{60} +340.280i q^{61} +175.692i q^{62} -171.180i q^{63} -198.770 q^{64} +7.13888i q^{65} -2233.79 q^{66} +15.3925 q^{67} +1527.48 q^{69} +17.0190 q^{70} +670.203i q^{71} -2104.12 q^{72} -193.480i q^{73} -656.080i q^{74} -1052.77i q^{75} +1152.46 q^{76} +199.971 q^{77} +343.788i q^{78} +1080.15i q^{79} -86.4311i q^{80} +70.4207 q^{81} -90.1229i q^{82} +865.668 q^{83} +560.697 q^{84} -1397.13 q^{86} +349.863 q^{87} -2458.02i q^{88} +1129.46 q^{89} +199.825i q^{90} -30.7763i q^{91} +3122.61i q^{92} +295.886 q^{93} +2334.02 q^{94} -58.9120i q^{95} -980.023i q^{96} +379.412i q^{97} +1652.78 q^{98} +2347.92i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 2 q^{2} + 50 q^{4} + 78 q^{8} - 118 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 2 q^{2} + 50 q^{4} + 78 q^{8} - 118 q^{9} + 60 q^{13} - 216 q^{15} + 274 q^{16} - 206 q^{18} - 160 q^{19} - 384 q^{21} + 446 q^{25} - 52 q^{26} + 800 q^{30} + 142 q^{32} - 664 q^{33} - 664 q^{35} - 2626 q^{36} + 1448 q^{38} + 2256 q^{42} - 1112 q^{43} + 1280 q^{47} + 538 q^{49} + 1094 q^{50} - 1548 q^{52} - 604 q^{53} + 152 q^{55} - 1272 q^{59} - 2656 q^{60} - 1838 q^{64} - 4936 q^{66} + 2016 q^{67} + 1152 q^{69} + 3008 q^{70} - 1854 q^{72} + 1816 q^{76} + 1008 q^{77} - 1010 q^{81} + 4792 q^{83} - 4080 q^{84} - 2528 q^{86} - 2856 q^{87} - 340 q^{89} - 1264 q^{93} + 4032 q^{94} + 5714 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/289\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(-1\)

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 \(-0.150962\pi\)
0.889630 + 0.456681i \(0.150962\pi\)
\(3\) − 8.47535i − 1.63108i −0.578699 0.815541i \(-0.696439\pi\)
0.578699 0.815541i \(-0.303561\pi\)
\(4\) 17.3261 2.16577
\(5\) − 0.885690i − 0.0792185i −0.999215 0.0396092i \(-0.987389\pi\)
0.999215 0.0396092i \(-0.0126113\pi\)
\(6\) − 42.6523i − 2.90212i
\(7\) 3.81828i 0.206168i 0.994673 + 0.103084i \(0.0328711\pi\)
−0.994673 + 0.103084i \(0.967129\pi\)
\(8\) 46.9339 2.07421
\(9\) −44.8316 −1.66043
\(10\) − 4.45724i − 0.140950i
\(11\) − 52.3720i − 1.43552i −0.696289 0.717761i \(-0.745167\pi\)
0.696289 0.717761i \(-0.254833\pi\)
\(12\) − 146.845i − 3.53255i
\(13\) −8.06025 −0.171962 −0.0859811 0.996297i \(-0.527402\pi\)
−0.0859811 + 0.996297i \(0.527402\pi\)
\(14\) 19.2156i 0.366827i
\(15\) −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 \(-0.368465\pi\)
0.401570 + 0.915828i \(0.368465\pi\)
\(20\) − 15.3456i − 0.171569i
\(21\) 32.3613 0.336277
\(22\) − 263.563i − 2.55417i
\(23\) 180.226i 1.63390i 0.576711 + 0.816948i \(0.304336\pi\)
−0.576711 + 0.816948i \(0.695664\pi\)
\(24\) − 397.782i − 3.38320i
\(25\) 124.216 0.993724
\(26\) −40.5633 −0.305966
\(27\) 151.129i 1.07722i
\(28\) 66.1562i 0.446512i
\(29\) 41.2800i 0.264328i 0.991228 + 0.132164i \(0.0421925\pi\)
−0.991228 + 0.132164i \(0.957807\pi\)
\(30\) −37.7767 −0.229902
\(31\) 34.9114i 0.202267i 0.994873 + 0.101133i \(0.0322469\pi\)
−0.994873 + 0.101133i \(0.967753\pi\)
\(32\) 115.632 0.638783
\(33\) −443.871 −2.34146
\(34\) 0 0
\(35\) 3.38182 0.0163323
\(36\) −776.759 −3.59611
\(37\) − 130.368i − 0.579255i −0.957139 0.289627i \(-0.906469\pi\)
0.957139 0.289627i \(-0.0935314\pi\)
\(38\) 334.739 1.42900
\(39\) 68.3134i 0.280485i
\(40\) − 41.5689i − 0.164315i
\(41\) − 17.9081i − 0.0682142i −0.999418 0.0341071i \(-0.989141\pi\)
0.999418 0.0341071i \(-0.0108587\pi\)
\(42\) 162.859 0.598325
\(43\) −277.620 −0.984573 −0.492287 0.870433i \(-0.663839\pi\)
−0.492287 + 0.870433i \(0.663839\pi\)
\(44\) − 907.405i − 3.10901i
\(45\) 39.7069i 0.131537i
\(46\) 906.987i 2.90713i
\(47\) 463.789 1.43937 0.719687 0.694299i \(-0.244285\pi\)
0.719687 + 0.694299i \(0.244285\pi\)
\(48\) − 827.078i − 2.48705i
\(49\) 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 \(-0.359374\pi\)
0.427559 + 0.903987i \(0.359374\pi\)
\(54\) 760.560i 1.91665i
\(55\) −46.3853 −0.113720
\(56\) 179.207i 0.427635i
\(57\) − 563.741i − 1.30999i
\(58\) 207.742i 0.470308i
\(59\) −678.656 −1.49752 −0.748759 0.662843i \(-0.769350\pi\)
−0.748759 + 0.662843i \(0.769350\pi\)
\(60\) −130.059 −0.279843
\(61\) 340.280i 0.714237i 0.934059 + 0.357118i \(0.116241\pi\)
−0.934059 + 0.357118i \(0.883759\pi\)
\(62\) 175.692i 0.359885i
\(63\) − 171.180i − 0.342328i
\(64\) −198.770 −0.388223
\(65\) 7.13888i 0.0136226i
\(66\) −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
\(71\) 670.203i 1.12026i 0.828405 + 0.560130i \(0.189249\pi\)
−0.828405 + 0.560130i \(0.810751\pi\)
\(72\) −2104.12 −3.44408
\(73\) − 193.480i − 0.310207i −0.987898 0.155103i \(-0.950429\pi\)
0.987898 0.155103i \(-0.0495711\pi\)
\(74\) − 656.080i − 1.03065i
\(75\) − 1052.77i − 1.62085i
\(76\) 1152.46 1.73942
\(77\) 199.971 0.295959
\(78\) 343.788i 0.499055i
\(79\) 1080.15i 1.53831i 0.639061 + 0.769156i \(0.279323\pi\)
−0.639061 + 0.769156i \(0.720677\pi\)
\(80\) − 86.4311i − 0.120791i
\(81\) 70.4207 0.0965990
\(82\) − 90.1229i − 0.121371i
\(83\) 865.668 1.14481 0.572406 0.819970i \(-0.306010\pi\)
0.572406 + 0.819970i \(0.306010\pi\)
\(84\) 560.697 0.728298
\(85\) 0 0
\(86\) −1397.13 −1.75181
\(87\) 349.863 0.431141
\(88\) − 2458.02i − 2.97757i
\(89\) 1129.46 1.34520 0.672599 0.740008i \(-0.265178\pi\)
0.672599 + 0.740008i \(0.265178\pi\)
\(90\) 199.825i 0.234038i
\(91\) − 30.7763i − 0.0354531i
\(92\) 3122.61i 3.53864i
\(93\) 295.886 0.329914
\(94\) 2334.02 2.56102
\(95\) − 58.9120i − 0.0636236i
\(96\) − 980.023i − 1.04191i
\(97\) 379.412i 0.397149i 0.980086 + 0.198574i \(0.0636311\pi\)
−0.980086 + 0.198574i \(0.936369\pi\)
\(98\) 1652.78 1.70363
\(99\) 2347.92i 2.38359i
\(100\) 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
\(105\) − 28.6621i − 0.0266394i
\(106\) 1660.45 1.52148
\(107\) 485.147i 0.438326i 0.975688 + 0.219163i \(0.0703327\pi\)
−0.975688 + 0.219163i \(0.929667\pi\)
\(108\) 2618.49i 2.33300i
\(109\) − 1255.12i − 1.10292i −0.834201 0.551460i \(-0.814071\pi\)
0.834201 0.551460i \(-0.185929\pi\)
\(110\) −233.435 −0.202337
\(111\) −1104.92 −0.944812
\(112\) 372.612i 0.314362i
\(113\) − 1013.35i − 0.843612i −0.906686 0.421806i \(-0.861396\pi\)
0.906686 0.421806i \(-0.138604\pi\)
\(114\) − 2837.03i − 2.33081i
\(115\) 159.624 0.129435
\(116\) 715.224i 0.572473i
\(117\) 361.354 0.285531
\(118\) −3415.34 −2.66447
\(119\) 0 0
\(120\) −352.311 −0.268012
\(121\) −1411.83 −1.06073
\(122\) 1712.46i 1.27081i
\(123\) −151.778 −0.111263
\(124\) 604.880i 0.438063i
\(125\) − 220.728i − 0.157940i
\(126\) − 861.464i − 0.609090i
\(127\) −1927.72 −1.34691 −0.673456 0.739227i \(-0.735191\pi\)
−0.673456 + 0.739227i \(0.735191\pi\)
\(128\) −1925.37 −1.32953
\(129\) 2352.93i 1.60592i
\(130\) 35.9265i 0.0242381i
\(131\) 406.738i 0.271274i 0.990759 + 0.135637i \(0.0433081\pi\)
−0.990759 + 0.135637i \(0.956692\pi\)
\(132\) −7690.58 −5.07105
\(133\) 253.975i 0.165582i
\(134\) 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
\(139\) − 2073.54i − 1.26529i −0.774443 0.632644i \(-0.781970\pi\)
0.774443 0.632644i \(-0.218030\pi\)
\(140\) 58.5938 0.0353720
\(141\) − 3930.78i − 2.34774i
\(142\) 3372.80i 1.99323i
\(143\) 422.131i 0.246856i
\(144\) −4374.95 −2.53180
\(145\) 36.5613 0.0209397
\(146\) − 973.689i − 0.551939i
\(147\) − 2783.48i − 1.56175i
\(148\) − 2258.78i − 1.25453i
\(149\) −1852.73 −1.01867 −0.509334 0.860569i \(-0.670108\pi\)
−0.509334 + 0.860569i \(0.670108\pi\)
\(150\) − 5298.08i − 2.88391i
\(151\) −2050.86 −1.10527 −0.552637 0.833422i \(-0.686378\pi\)
−0.552637 + 0.833422i \(0.686378\pi\)
\(152\) 3121.83 1.66588
\(153\) 0 0
\(154\) 1006.36 0.526588
\(155\) 30.9207 0.0160233
\(156\) 1183.61i 0.607465i
\(157\) −262.991 −0.133688 −0.0668438 0.997763i \(-0.521293\pi\)
−0.0668438 + 0.997763i \(0.521293\pi\)
\(158\) 5435.88i 2.73706i
\(159\) − 2796.39i − 1.39477i
\(160\) − 102.414i − 0.0506035i
\(161\) −688.152 −0.336857
\(162\) 354.393 0.171875
\(163\) − 1444.98i − 0.694354i −0.937800 0.347177i \(-0.887140\pi\)
0.937800 0.347177i \(-0.112860\pi\)
\(164\) − 310.279i − 0.147736i
\(165\) 393.132i 0.185487i
\(166\) 4356.48 2.03692
\(167\) 501.565i 0.232409i 0.993225 + 0.116204i \(0.0370728\pi\)
−0.993225 + 0.116204i \(0.962927\pi\)
\(168\) 1518.84 0.697508
\(169\) −2132.03 −0.970429
\(170\) 0 0
\(171\) −2981.99 −1.33356
\(172\) −4810.08 −2.13236
\(173\) 2590.14i 1.13829i 0.822237 + 0.569146i \(0.192726\pi\)
−0.822237 + 0.569146i \(0.807274\pi\)
\(174\) 1760.69 0.767112
\(175\) 474.290i 0.204874i
\(176\) − 5110.79i − 2.18886i
\(177\) 5751.85i 2.44257i
\(178\) 5684.02 2.39346
\(179\) −2165.65 −0.904294 −0.452147 0.891943i \(-0.649342\pi\)
−0.452147 + 0.891943i \(0.649342\pi\)
\(180\) 687.968i 0.284878i
\(181\) − 1925.56i − 0.790750i −0.918520 0.395375i \(-0.870615\pi\)
0.918520 0.395375i \(-0.129385\pi\)
\(182\) − 154.882i − 0.0630803i
\(183\) 2884.00 1.16498
\(184\) 8458.69i 3.38904i
\(185\) −115.466 −0.0458877
\(186\) 1489.05 0.587003
\(187\) 0 0
\(188\) 8035.68 3.11735
\(189\) −577.055 −0.222088
\(190\) − 296.475i − 0.113203i
\(191\) −2783.52 −1.05449 −0.527247 0.849712i \(-0.676776\pi\)
−0.527247 + 0.849712i \(0.676776\pi\)
\(192\) 1684.65i 0.633223i
\(193\) 2258.27i 0.842246i 0.907004 + 0.421123i \(0.138364\pi\)
−0.907004 + 0.421123i \(0.861636\pi\)
\(194\) 1909.39i 0.706631i
\(195\) 60.5045 0.0222196
\(196\) 5690.27 2.07371
\(197\) − 1270.70i − 0.459560i −0.973243 0.229780i \(-0.926199\pi\)
0.973243 0.229780i \(-0.0738007\pi\)
\(198\) 11815.9i 4.24102i
\(199\) 4794.36i 1.70786i 0.520392 + 0.853928i \(0.325786\pi\)
−0.520392 + 0.853928i \(0.674214\pi\)
\(200\) 5829.92 2.06119
\(201\) − 130.457i − 0.0457798i
\(202\) 662.942 0.230913
\(203\) −157.619 −0.0544960
\(204\) 0 0
\(205\) −15.8611 −0.00540383
\(206\) 986.313 0.333591
\(207\) − 8079.80i − 2.71297i
\(208\) −786.569 −0.262205
\(209\) − 3483.54i − 1.15293i
\(210\) − 144.242i − 0.0473984i
\(211\) − 2807.00i − 0.915837i −0.888994 0.457918i \(-0.848595\pi\)
0.888994 0.457918i \(-0.151405\pi\)
\(212\) 5716.66 1.85199
\(213\) 5680.21 1.82724
\(214\) 2441.50i 0.779896i
\(215\) 245.885i 0.0779964i
\(216\) 7093.09i 2.23437i
\(217\) −133.302 −0.0417009
\(218\) − 6316.38i − 1.96238i
\(219\) −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 \(-0.748303\pi\)
−0.703327 + 0.710866i \(0.748303\pi\)
\(224\) 441.516i 0.131697i
\(225\) −5568.79 −1.65001
\(226\) − 5099.70i − 1.50101i
\(227\) − 1395.72i − 0.408095i −0.978961 0.204047i \(-0.934590\pi\)
0.978961 0.204047i \(-0.0654096\pi\)
\(228\) − 9767.47i − 2.83713i
\(229\) −894.638 −0.258163 −0.129082 0.991634i \(-0.541203\pi\)
−0.129082 + 0.991634i \(0.541203\pi\)
\(230\) 803.309 0.230298
\(231\) − 1694.83i − 0.482733i
\(232\) 1937.43i 0.548270i
\(233\) − 1196.13i − 0.336313i −0.985760 0.168156i \(-0.946219\pi\)
0.985760 0.168156i \(-0.0537814\pi\)
\(234\) 1818.52 0.508035
\(235\) − 410.773i − 0.114025i
\(236\) −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
\(241\) 6702.73i 1.79154i 0.444518 + 0.895770i \(0.353375\pi\)
−0.444518 + 0.895770i \(0.646625\pi\)
\(242\) −7105.03 −1.88731
\(243\) 3483.65i 0.919656i
\(244\) 5895.75i 1.54687i
\(245\) − 290.879i − 0.0758513i
\(246\) −763.824 −0.197966
\(247\) −536.130 −0.138110
\(248\) 1638.53i 0.419543i
\(249\) − 7336.85i − 1.86728i
\(250\) − 1110.81i − 0.281016i
\(251\) −4756.08 −1.19602 −0.598010 0.801489i \(-0.704042\pi\)
−0.598010 + 0.801489i \(0.704042\pi\)
\(252\) − 2965.89i − 0.741402i
\(253\) 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 \(-0.614183\pi\)
−0.351071 + 0.936349i \(0.614183\pi\)
\(258\) 11841.1i 2.85735i
\(259\) 497.784 0.119424
\(260\) 123.689i 0.0295034i
\(261\) − 1850.65i − 0.438898i
\(262\) 2046.92i 0.482667i
\(263\) −5415.48 −1.26971 −0.634853 0.772633i \(-0.718939\pi\)
−0.634853 + 0.772633i \(0.718939\pi\)
\(264\) −20832.6 −4.85666
\(265\) − 292.228i − 0.0677412i
\(266\) 1278.13i 0.294613i
\(267\) − 9572.58i − 2.19413i
\(268\) 266.693 0.0607869
\(269\) − 5787.00i − 1.31167i −0.754904 0.655835i \(-0.772317\pi\)
0.754904 0.655835i \(-0.227683\pi\)
\(270\) 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
\(275\) − 6505.42i − 1.42651i
\(276\) 26465.3 5.77182
\(277\) 1207.65i 0.261952i 0.991386 + 0.130976i \(0.0418111\pi\)
−0.991386 + 0.130976i \(0.958189\pi\)
\(278\) − 10435.1i − 2.25128i
\(279\) − 1565.13i − 0.335850i
\(280\) 158.722 0.0338766
\(281\) 1197.18 0.254155 0.127077 0.991893i \(-0.459440\pi\)
0.127077 + 0.991893i \(0.459440\pi\)
\(282\) − 19781.7i − 4.17724i
\(283\) 3164.73i 0.664748i 0.943148 + 0.332374i \(0.107850\pi\)
−0.943148 + 0.332374i \(0.892150\pi\)
\(284\) 11612.0i 2.42622i
\(285\) −499.300 −0.103775
\(286\) 2124.38i 0.439221i
\(287\) 68.3784 0.0140636
\(288\) −5183.98 −1.06066
\(289\) 0 0
\(290\) 183.995 0.0372571
\(291\) 3215.65 0.647782
\(292\) − 3352.26i − 0.671836i
\(293\) 7456.21 1.48668 0.743339 0.668915i \(-0.233241\pi\)
0.743339 + 0.668915i \(0.233241\pi\)
\(294\) − 14007.9i − 2.77877i
\(295\) 601.079i 0.118631i
\(296\) − 6118.70i − 1.20149i
\(297\) 7914.94 1.54637
\(298\) −9323.89 −1.81248
\(299\) − 1452.66i − 0.280969i
\(300\) − 18240.5i − 3.51038i
\(301\) − 1060.03i − 0.202988i
\(302\) −10321.0 −1.96657
\(303\) − 1116.47i − 0.211683i
\(304\) 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
\(309\) − 1661.07i − 0.305809i
\(310\) 155.608 0.0285096
\(311\) 8935.89i 1.62928i 0.579963 + 0.814642i \(0.303067\pi\)
−0.579963 + 0.814642i \(0.696933\pi\)
\(312\) 3206.22i 0.581783i
\(313\) − 2628.71i − 0.474707i −0.971423 0.237353i \(-0.923720\pi\)
0.971423 0.237353i \(-0.0762799\pi\)
\(314\) −1323.50 −0.237865
\(315\) −151.612 −0.0271187
\(316\) 18714.9i 3.33163i
\(317\) 4268.54i 0.756293i 0.925746 + 0.378147i \(0.123438\pi\)
−0.925746 + 0.378147i \(0.876562\pi\)
\(318\) − 14072.9i − 2.48166i
\(319\) 2161.92 0.379449
\(320\) 176.048i 0.0307544i
\(321\) 4111.79 0.714946
\(322\) −3463.13 −0.599357
\(323\) 0 0
\(324\) 1220.12 0.209211
\(325\) −1001.21 −0.170883
\(326\) − 7271.89i − 1.23544i
\(327\) −10637.5 −1.79895
\(328\) − 840.500i − 0.141490i
\(329\) 1770.88i 0.296753i
\(330\) 1978.44i 0.330029i
\(331\) −992.298 −0.164778 −0.0823892 0.996600i \(-0.526255\pi\)
−0.0823892 + 0.996600i \(0.526255\pi\)
\(332\) 14998.7 2.47940
\(333\) 5844.63i 0.961812i
\(334\) 2524.13i 0.413516i
\(335\) − 13.6330i − 0.00222344i
\(336\) 3158.02 0.512750
\(337\) − 8042.26i − 1.29997i −0.759947 0.649985i \(-0.774775\pi\)
0.759947 0.649985i \(-0.225225\pi\)
\(338\) −10729.5 −1.72665
\(339\) −8588.52 −1.37600
\(340\) 0 0
\(341\) 1828.38 0.290359
\(342\) −15006.9 −2.37275
\(343\) 2563.68i 0.403573i
\(344\) −13029.8 −2.04221
\(345\) − 1352.87i − 0.211119i
\(346\) 13034.9i 2.02532i
\(347\) − 7414.16i − 1.14701i −0.819202 0.573506i \(-0.805583\pi\)
0.819202 0.573506i \(-0.194417\pi\)
\(348\) 6061.78 0.933751
\(349\) 859.194 0.131781 0.0658905 0.997827i \(-0.479011\pi\)
0.0658905 + 0.997827i \(0.479011\pi\)
\(350\) 2386.87i 0.364525i
\(351\) − 1218.14i − 0.185241i
\(352\) − 6055.89i − 0.916988i
\(353\) 569.084 0.0858053 0.0429027 0.999079i \(-0.486339\pi\)
0.0429027 + 0.999079i \(0.486339\pi\)
\(354\) 28946.3i 4.34598i
\(355\) 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 \(-0.380071\pi\)
0.367918 + 0.929858i \(0.380071\pi\)
\(360\) 1863.60i 0.272834i
\(361\) −2434.71 −0.354965
\(362\) − 9690.40i − 1.40695i
\(363\) 11965.7i 1.73013i
\(364\) − 533.235i − 0.0767833i
\(365\) −171.363 −0.0245741
\(366\) 14513.7 2.07280
\(367\) − 10975.3i − 1.56105i −0.625127 0.780523i \(-0.714953\pi\)
0.625127 0.780523i \(-0.285047\pi\)
\(368\) 17587.5i 2.49134i
\(369\) 802.851i 0.113265i
\(370\) −581.083 −0.0816462
\(371\) 1259.82i 0.176298i
\(372\) 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
\(377\) − 332.727i − 0.0454544i
\(378\) −2904.03 −0.395152
\(379\) − 8051.48i − 1.09123i −0.838035 0.545616i \(-0.816296\pi\)
0.838035 0.545616i \(-0.183704\pi\)
\(380\) − 1020.72i − 0.137794i
\(381\) 16338.1i 2.19692i
\(382\) −14008.1 −1.87622
\(383\) 2584.16 0.344763 0.172382 0.985030i \(-0.444854\pi\)
0.172382 + 0.985030i \(0.444854\pi\)
\(384\) 16318.2i 2.16858i
\(385\) − 177.112i − 0.0234454i
\(386\) 11364.7i 1.49858i
\(387\) 12446.2 1.63482
\(388\) 6573.74i 0.860132i
\(389\) 5174.31 0.674417 0.337208 0.941430i \(-0.390517\pi\)
0.337208 + 0.941430i \(0.390517\pi\)
\(390\) 304.489 0.0395344
\(391\) 0 0
\(392\) 15414.1 1.98604
\(393\) 3447.25 0.442470
\(394\) − 6394.79i − 0.817677i
\(395\) 956.680 0.121863
\(396\) 40680.4i 5.16230i
\(397\) − 5149.36i − 0.650980i −0.945545 0.325490i \(-0.894471\pi\)
0.945545 0.325490i \(-0.105529\pi\)
\(398\) 24127.7i 3.03872i
\(399\) 2152.53 0.270078
\(400\) 12121.7 1.51522
\(401\) 8700.49i 1.08350i 0.840541 + 0.541748i \(0.182237\pi\)
−0.840541 + 0.541748i \(0.817763\pi\)
\(402\) − 656.527i − 0.0814542i
\(403\) − 281.394i − 0.0347823i
\(404\) 2282.41 0.281074
\(405\) − 62.3709i − 0.00765243i
\(406\) −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
\(411\) 1106.48i 0.132794i
\(412\) 3395.72 0.406056
\(413\) − 2591.30i − 0.308740i
\(414\) − 40661.7i − 4.82708i
\(415\) − 766.713i − 0.0906903i
\(416\) −932.023 −0.109847
\(417\) −17574.0 −2.06379
\(418\) − 17531.0i − 2.05136i
\(419\) − 5763.33i − 0.671974i −0.941867 0.335987i \(-0.890930\pi\)
0.941867 0.335987i \(-0.109070\pi\)
\(420\) − 496.604i − 0.0576947i
\(421\) −1876.12 −0.217188 −0.108594 0.994086i \(-0.534635\pi\)
−0.108594 + 0.994086i \(0.534635\pi\)
\(422\) − 14126.2i − 1.62951i
\(423\) −20792.4 −2.38998
\(424\) 15485.6 1.77369
\(425\) 0 0
\(426\) 28585.7 3.25113
\(427\) −1299.29 −0.147253
\(428\) 8405.72i 0.949313i
\(429\) 3577.71 0.402642
\(430\) 1237.42i 0.138776i
\(431\) 83.9299i 0.00937996i 0.999989 + 0.00468998i \(0.00149287\pi\)
−0.999989 + 0.00468998i \(0.998507\pi\)
\(432\) 14748.1i 1.64252i
\(433\) 15345.0 1.70308 0.851539 0.524291i \(-0.175669\pi\)
0.851539 + 0.524291i \(0.175669\pi\)
\(434\) −670.842 −0.0741968
\(435\) − 309.870i − 0.0341543i
\(436\) − 21746.3i − 2.38867i
\(437\) 11987.8i 1.31225i
\(438\) −8252.36 −0.900258
\(439\) − 3064.74i − 0.333194i −0.986025 0.166597i \(-0.946722\pi\)
0.986025 0.166597i \(-0.0532778\pi\)
\(440\) −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
\(445\) − 1000.35i − 0.106564i
\(446\) −23573.8 −2.50281
\(447\) 15702.6i 1.66153i
\(448\) − 758.960i − 0.0800391i
\(449\) 2499.19i 0.262681i 0.991337 + 0.131341i \(0.0419282\pi\)
−0.991337 + 0.131341i \(0.958072\pi\)
\(450\) −28025.0 −2.93580
\(451\) −937.885 −0.0979231
\(452\) − 17557.5i − 1.82707i
\(453\) 17381.7i 1.80279i
\(454\) − 7024.00i − 0.726107i
\(455\) −27.2583 −0.00280854
\(456\) − 26458.6i − 2.71719i
\(457\) −14784.4 −1.51331 −0.756656 0.653813i \(-0.773168\pi\)
−0.756656 + 0.653813i \(0.773168\pi\)
\(458\) −4502.28 −0.459340
\(459\) 0 0
\(460\) 2765.67 0.280326
\(461\) 17746.9 1.79297 0.896483 0.443078i \(-0.146113\pi\)
0.896483 + 0.443078i \(0.146113\pi\)
\(462\) − 8529.23i − 0.858909i
\(463\) 18486.4 1.85559 0.927793 0.373096i \(-0.121704\pi\)
0.927793 + 0.373096i \(0.121704\pi\)
\(464\) 4028.36i 0.403043i
\(465\) − 262.064i − 0.0261353i
\(466\) − 6019.52i − 0.598388i
\(467\) −7406.57 −0.733908 −0.366954 0.930239i \(-0.619599\pi\)
−0.366954 + 0.930239i \(0.619599\pi\)
\(468\) 6260.87 0.618395
\(469\) 58.7731i 0.00578655i
\(470\) − 2067.22i − 0.202880i
\(471\) 2228.94i 0.218055i
\(472\) −31852.0 −3.10616
\(473\) 14539.5i 1.41338i
\(474\) 46071.0 4.46437
\(475\) 8262.24 0.798101
\(476\) 0 0
\(477\) −14791.9 −1.41986
\(478\) 24905.0 2.38311
\(479\) 18550.9i 1.76955i 0.466019 + 0.884775i \(0.345688\pi\)
−0.466019 + 0.884775i \(0.654312\pi\)
\(480\) −867.997 −0.0825384
\(481\) 1050.80i 0.0996100i
\(482\) 33731.6i 3.18762i
\(483\) 5832.34i 0.549442i
\(484\) −24461.5 −2.29729
\(485\) 336.041 0.0314615
\(486\) 17531.5i 1.63631i
\(487\) 10203.4i 0.949406i 0.880146 + 0.474703i \(0.157444\pi\)
−0.880146 + 0.474703i \(0.842556\pi\)
\(488\) 15970.7i 1.48147i
\(489\) −12246.7 −1.13255
\(490\) − 1463.85i − 0.134959i
\(491\) 1247.46 0.114658 0.0573290 0.998355i \(-0.481742\pi\)
0.0573290 + 0.998355i \(0.481742\pi\)
\(492\) −2629.73 −0.240970
\(493\) 0 0
\(494\) −2698.08 −0.245734
\(495\) 2079.53 0.188824
\(496\) 3406.87i 0.308413i
\(497\) −2559.03 −0.230962
\(498\) − 36922.7i − 3.32238i
\(499\) 70.0303i 0.00628254i 0.999995 + 0.00314127i \(0.000999898\pi\)
−0.999995 + 0.00314127i \(0.999000\pi\)
\(500\) − 3824.36i − 0.342061i
\(501\) 4250.94 0.379078
\(502\) −23935.0 −2.12803
\(503\) 1444.29i 0.128028i 0.997949 + 0.0640138i \(0.0203902\pi\)
−0.997949 + 0.0640138i \(0.979610\pi\)
\(504\) − 8034.15i − 0.710058i
\(505\) − 116.674i − 0.0102810i
\(506\) 47500.7 4.17325
\(507\) 18069.7i 1.58285i
\(508\) −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
\(513\) 10052.4i 0.865157i
\(514\) −14558.3 −1.24929
\(515\) − 173.585i − 0.0148525i
\(516\) 40767.2i 3.47805i
\(517\) − 24289.6i − 2.06625i
\(518\) 2505.10 0.212486
\(519\) 21952.3 1.85665
\(520\) 335.055i 0.0282561i
\(521\) 14874.0i 1.25075i 0.780324 + 0.625376i \(0.215054\pi\)
−0.780324 + 0.625376i \(0.784946\pi\)
\(522\) − 9313.42i − 0.780914i
\(523\) −8142.90 −0.680811 −0.340406 0.940279i \(-0.610564\pi\)
−0.340406 + 0.940279i \(0.610564\pi\)
\(524\) 7047.21i 0.587517i
\(525\) 4019.78 0.334167
\(526\) −27253.4 −2.25914
\(527\) 0 0
\(528\) −43315.7 −3.57022
\(529\) −20314.2 −1.66962
\(530\) − 1470.64i − 0.120529i
\(531\) 30425.3 2.48652
\(532\) 4400.40i 0.358612i
\(533\) 144.344i 0.0117303i
\(534\) − 48174.1i − 3.90393i
\(535\) 429.689 0.0347235
\(536\) 722.432 0.0582170
\(537\) 18354.7i 1.47498i
\(538\) − 29123.1i − 2.33380i
\(539\) − 17200.0i − 1.37451i
\(540\) 2319.17 0.184817
\(541\) − 3179.67i − 0.252689i −0.991986 0.126344i \(-0.959676\pi\)
0.991986 0.126344i \(-0.0403244\pi\)
\(542\) 27503.3 2.17965
\(543\) −16319.8 −1.28978
\(544\) 0 0
\(545\) −1111.64 −0.0873716
\(546\) −1312.68 −0.102889
\(547\) − 2107.07i − 0.164702i −0.996603 0.0823509i \(-0.973757\pi\)
0.996603 0.0823509i \(-0.0262428\pi\)
\(548\) −2261.97 −0.176326
\(549\) − 15255.3i − 1.18594i
\(550\) − 32738.6i − 2.53814i
\(551\) 2745.76i 0.212292i
\(552\) 71690.4 5.52780
\(553\) −4124.33 −0.317151
\(554\) 6077.51i 0.466081i
\(555\) 978.614i 0.0748466i
\(556\) − 35926.4i − 2.74032i
\(557\) 467.382 0.0355540 0.0177770 0.999842i \(-0.494341\pi\)
0.0177770 + 0.999842i \(0.494341\pi\)
\(558\) − 7876.55i − 0.597565i
\(559\) 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 \(-0.684206\pi\)
−0.546935 + 0.837175i \(0.684206\pi\)
\(564\) − 68105.2i − 5.08466i
\(565\) −897.515 −0.0668297
\(566\) 15926.5i 1.18276i
\(567\) 268.886i 0.0199156i
\(568\) 31455.3i 2.32365i
\(569\) −11602.3 −0.854821 −0.427410 0.904058i \(-0.640574\pi\)
−0.427410 + 0.904058i \(0.640574\pi\)
\(570\) −2512.73 −0.184643
\(571\) − 10534.9i − 0.772104i −0.922477 0.386052i \(-0.873839\pi\)
0.922477 0.386052i \(-0.126161\pi\)
\(572\) 7313.91i 0.534633i
\(573\) 23591.3i 1.71997i
\(574\) 344.115 0.0250228
\(575\) 22386.8i 1.62364i
\(576\) 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
\(581\) 3305.37i 0.236024i
\(582\) 16182.8 1.15257
\(583\) − 17279.8i − 1.22754i
\(584\) − 9080.77i − 0.643433i
\(585\) − 320.047i − 0.0226194i
\(586\) 37523.5 2.64519
\(587\) 11004.9 0.773799 0.386900 0.922122i \(-0.373546\pi\)
0.386900 + 0.922122i \(0.373546\pi\)
\(588\) − 48227.0i − 3.38240i
\(589\) 2322.14i 0.162449i
\(590\) 3024.94i 0.211076i
\(591\) −10769.6 −0.749581
\(592\) − 12722.2i − 0.883239i
\(593\) −1853.59 −0.128361 −0.0641804 0.997938i \(-0.520443\pi\)
−0.0641804 + 0.997938i \(0.520443\pi\)
\(594\) 39832.0 2.75139
\(595\) 0 0
\(596\) −32100.7 −2.20620
\(597\) 40633.9 2.78565
\(598\) − 7310.53i − 0.499916i
\(599\) 19074.7 1.30112 0.650559 0.759456i \(-0.274535\pi\)
0.650559 + 0.759456i \(0.274535\pi\)
\(600\) − 49410.7i − 3.36197i
\(601\) − 27776.0i − 1.88520i −0.333923 0.942600i \(-0.608373\pi\)
0.333923 0.942600i \(-0.391627\pi\)
\(602\) − 5334.62i − 0.361168i
\(603\) −690.073 −0.0466035
\(604\) −35533.4 −2.39377
\(605\) 1250.44i 0.0840291i
\(606\) − 5618.67i − 0.376638i
\(607\) − 18728.3i − 1.25232i −0.779695 0.626159i \(-0.784626\pi\)
0.779695 0.626159i \(-0.215374\pi\)
\(608\) 7691.32 0.513033
\(609\) 1335.88i 0.0888874i
\(610\) 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
\(615\) 134.428i 0.00881409i
\(616\) 9385.43 0.613880
\(617\) 22516.4i 1.46917i 0.678518 + 0.734584i \(0.262623\pi\)
−0.678518 + 0.734584i \(0.737377\pi\)
\(618\) − 8359.35i − 0.544114i
\(619\) − 5146.53i − 0.334179i −0.985942 0.167089i \(-0.946563\pi\)
0.985942 0.167089i \(-0.0534369\pi\)
\(620\) 535.736 0.0347027
\(621\) −27237.4 −1.76006
\(622\) 44969.9i 2.89892i
\(623\) 4312.60i 0.277337i
\(624\) 6666.45i 0.427679i
\(625\) 15331.4 0.981213
\(626\) − 13229.0i − 0.844627i
\(627\) −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 \(-0.461158\pi\)
0.121724 + 0.992564i \(0.461158\pi\)
\(632\) 50695.8i 3.19078i
\(633\) −23790.3 −1.49381
\(634\) 21481.5i 1.34564i
\(635\) 1707.36i 0.106700i
\(636\) − 48450.7i − 3.02075i
\(637\) −2647.15 −0.164653
\(638\) 10879.9 0.675138
\(639\) − 30046.3i − 1.86011i
\(640\) 1705.28i 0.105324i
\(641\) − 18689.3i − 1.15161i −0.817587 0.575805i \(-0.804689\pi\)
0.817587 0.575805i \(-0.195311\pi\)
\(642\) 20692.6 1.27208
\(643\) − 26473.5i − 1.62366i −0.583893 0.811831i \(-0.698471\pi\)
0.583893 0.811831i \(-0.301529\pi\)
\(644\) −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
\(649\) 35542.6i 2.14972i
\(650\) −5038.59 −0.304046
\(651\) 1129.78i 0.0680177i
\(652\) − 25036.0i − 1.50381i
\(653\) 20939.5i 1.25486i 0.778672 + 0.627431i \(0.215893\pi\)
−0.778672 + 0.627431i \(0.784107\pi\)
\(654\) −53533.6 −3.20081
\(655\) 360.244 0.0214899
\(656\) − 1747.59i − 0.104012i
\(657\) 8674.02i 0.515077i
\(658\) 8911.96i 0.528001i
\(659\) 4031.76 0.238323 0.119162 0.992875i \(-0.461979\pi\)
0.119162 + 0.992875i \(0.461979\pi\)
\(660\) 6811.47i 0.401721i
\(661\) −6691.52 −0.393752 −0.196876 0.980428i \(-0.563080\pi\)
−0.196876 + 0.980428i \(0.563080\pi\)
\(662\) −4993.75 −0.293184
\(663\) 0 0
\(664\) 40629.2 2.37458
\(665\) 224.943 0.0131171
\(666\) 29413.1i 1.71131i
\(667\) −7439.71 −0.431884
\(668\) 8690.19i 0.503344i
\(669\) 39701.1i 2.29437i
\(670\) − 68.6083i − 0.00395607i
\(671\) 17821.2 1.02530
\(672\) 3742.01 0.214808
\(673\) 10319.2i 0.591048i 0.955335 + 0.295524i \(0.0954942\pi\)
−0.955335 + 0.295524i \(0.904506\pi\)
\(674\) − 40472.7i − 2.31298i
\(675\) 18772.6i 1.07046i
\(676\) −36939.9 −2.10172
\(677\) 19813.3i 1.12480i 0.826866 + 0.562398i \(0.190121\pi\)
−0.826866 + 0.562398i \(0.809879\pi\)
\(678\) −43221.8 −2.44826
\(679\) −1448.70 −0.0818793
\(680\) 0 0
\(681\) −11829.3 −0.665636
\(682\) 9201.33 0.516624
\(683\) − 5924.61i − 0.331916i −0.986133 0.165958i \(-0.946928\pi\)
0.986133 0.165958i \(-0.0530717\pi\)
\(684\) −51666.4 −2.88818
\(685\) 115.629i 0.00644957i
\(686\) 12901.7i 0.718061i
\(687\) 7582.38i 0.421085i
\(688\) −27091.9 −1.50126
\(689\) −2659.43 −0.147048
\(690\) − 6808.33i − 0.375636i
\(691\) 1973.16i 0.108629i 0.998524 + 0.0543143i \(0.0172973\pi\)
−0.998524 + 0.0543143i \(0.982703\pi\)
\(692\) 44877.1i 2.46528i
\(693\) −8965.03 −0.491419
\(694\) − 37311.8i − 2.04083i
\(695\) −1836.51 −0.100234
\(696\) 16420.4 0.894274
\(697\) 0 0
\(698\) 4323.90 0.234473
\(699\) −10137.6 −0.548554
\(700\) 8217.63i 0.443710i
\(701\) −12840.1 −0.691815 −0.345907 0.938269i \(-0.612429\pi\)
−0.345907 + 0.938269i \(0.612429\pi\)
\(702\) − 6130.30i − 0.329591i
\(703\) − 8671.50i − 0.465223i
\(704\) 10410.0i 0.557302i
\(705\) −3481.45 −0.185984
\(706\) 2863.92 0.152670
\(707\) 502.990i 0.0267566i
\(708\) 99657.5i 5.29005i
\(709\) 27749.7i 1.46990i 0.678119 + 0.734952i \(0.262796\pi\)
−0.678119 + 0.734952i \(0.737204\pi\)
\(710\) 2987.26 0.157901
\(711\) − 48425.0i − 2.55426i
\(712\) 53010.0 2.79022
\(713\) −6291.92 −0.330483
\(714\) 0 0
\(715\) 373.877 0.0195555
\(716\) −37522.4 −1.95849
\(717\) − 41943.0i − 2.18464i
\(718\) 25188.8 1.30924
\(719\) − 16888.3i − 0.875979i −0.898980 0.437989i \(-0.855691\pi\)
0.898980 0.437989i \(-0.144309\pi\)
\(720\) 3874.85i 0.200565i
\(721\) 748.339i 0.0386541i
\(722\) −12252.7 −0.631575
\(723\) 56808.0 2.92215
\(724\) − 33362.6i − 1.71258i
\(725\) 5127.62i 0.262669i
\(726\) 60217.6i 3.07835i
\(727\) 2135.25 0.108930 0.0544649 0.998516i \(-0.482655\pi\)
0.0544649 + 0.998516i \(0.482655\pi\)
\(728\) − 1444.45i − 0.0735371i
\(729\) 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 \(-0.538551\pi\)
−0.120817 + 0.992675i \(0.538551\pi\)
\(734\) − 55233.1i − 2.77751i
\(735\) −2465.30 −0.123720
\(736\) 20839.9i 1.04371i
\(737\) − 806.138i − 0.0402910i
\(738\) 4040.36i 0.201528i
\(739\) 32747.6 1.63010 0.815048 0.579393i \(-0.196710\pi\)
0.815048 + 0.579393i \(0.196710\pi\)
\(740\) −2000.58 −0.0993821
\(741\) 4543.89i 0.225269i
\(742\) 6340.05i 0.313680i
\(743\) − 12299.4i − 0.607298i −0.952784 0.303649i \(-0.901795\pi\)
0.952784 0.303649i \(-0.0982050\pi\)
\(744\) 13887.1 0.684309
\(745\) 1640.94i 0.0806974i
\(746\) −16163.0 −0.793257
\(747\) −38809.3 −1.90088
\(748\) 0 0
\(749\) −1852.43 −0.0903688
\(750\) −9414.54 −0.458361
\(751\) − 30102.6i − 1.46266i −0.682021 0.731332i \(-0.738899\pi\)
0.682021 0.731332i \(-0.261101\pi\)
\(752\) 45259.4 2.19474
\(753\) 40309.4i 1.95081i
\(754\) − 1674.45i − 0.0808753i
\(755\) 1816.42i 0.0875581i
\(756\) −9998.14 −0.480990
\(757\) −38826.3 −1.86416 −0.932078 0.362257i \(-0.882006\pi\)
−0.932078 + 0.362257i \(0.882006\pi\)
\(758\) − 40519.2i − 1.94159i
\(759\) − 79996.9i − 3.82570i
\(760\) − 2764.97i − 0.131968i
\(761\) 19981.6 0.951815 0.475907 0.879495i \(-0.342120\pi\)
0.475907 + 0.879495i \(0.342120\pi\)
\(762\) 82221.8i 3.90890i
\(763\) 4792.39 0.227387
\(764\) −48227.7 −2.28379
\(765\) 0 0
\(766\) 13004.8 0.613424
\(767\) 5470.14 0.257517
\(768\) 68644.2i 3.22524i
\(769\) −22407.7 −1.05077 −0.525384 0.850865i \(-0.676078\pi\)
−0.525384 + 0.850865i \(0.676078\pi\)
\(770\) − 891.320i − 0.0417155i
\(771\) 24517.9i 1.14525i
\(772\) 39127.0i 1.82411i
\(773\) 6902.77 0.321184 0.160592 0.987021i \(-0.448660\pi\)
0.160592 + 0.987021i \(0.448660\pi\)
\(774\) 62635.4 2.90876
\(775\) 4336.54i 0.200997i
\(776\) 17807.3i 0.823768i
\(777\) − 4218.89i − 0.194790i
\(778\) 26039.8 1.19996
\(779\) − 1191.17i − 0.0547856i
\(780\) 1048.31 0.0481225
\(781\) 35099.9 1.60816
\(782\) 0 0
\(783\) −6238.62 −0.284738
\(784\) 32049.3 1.45997
\(785\) 232.928i 0.0105905i
\(786\) 17348.3 0.787270
\(787\) 22185.9i 1.00488i 0.864611 + 0.502442i \(0.167565\pi\)
−0.864611 + 0.502442i \(0.832435\pi\)
\(788\) − 22016.3i − 0.995301i
\(789\) 45898.1i 2.07099i
\(790\) 4814.50 0.216826
\(791\) 3869.27 0.173926
\(792\) 110197.i 4.94405i
\(793\) − 2742.74i − 0.122822i
\(794\) − 25914.2i − 1.15826i
\(795\) −2476.73 −0.110491
\(796\) 83067.8i 3.69882i
\(797\) 16291.1 0.724040 0.362020 0.932170i \(-0.382087\pi\)
0.362020 + 0.932170i \(0.382087\pi\)
\(798\) 10832.6 0.480539
\(799\) 0 0
\(800\) 14363.3 0.634775
\(801\) −50635.5 −2.23361
\(802\) 43785.3i 1.92782i
\(803\) −10132.9 −0.445309
\(804\) − 2260.32i − 0.0991485i
\(805\) 609.489i 0.0266853i
\(806\) − 1416.12i − 0.0618867i
\(807\) −49046.8 −2.13944
\(808\) 6182.70 0.269191
\(809\) 17696.8i 0.769082i 0.923108 + 0.384541i \(0.125640\pi\)
−0.923108 + 0.384541i \(0.874360\pi\)
\(810\) − 313.882i − 0.0136157i
\(811\) 3095.34i 0.134022i 0.997752 + 0.0670111i \(0.0213463\pi\)
−0.997752 + 0.0670111i \(0.978654\pi\)
\(812\) −2730.93 −0.118026
\(813\) − 46318.9i − 1.99812i
\(814\) −34360.2 −1.47951
\(815\) −1279.81 −0.0550057
\(816\) 0 0
\(817\) −18466.0 −0.790751
\(818\) 62131.5 2.65572
\(819\) 1379.75i 0.0588674i
\(820\) −274.811 −0.0117034
\(821\) − 12323.5i − 0.523864i −0.965086 0.261932i \(-0.915640\pi\)
0.965086 0.261932i \(-0.0843597\pi\)
\(822\) 5568.36i 0.236276i
\(823\) − 34436.5i − 1.45854i −0.684225 0.729271i \(-0.739860\pi\)
0.684225 0.729271i \(-0.260140\pi\)
\(824\) 9198.50 0.388889
\(825\) −55135.7 −2.32676
\(826\) − 13040.8i − 0.549329i
\(827\) 18761.6i 0.788880i 0.918922 + 0.394440i \(0.129061\pi\)
−0.918922 + 0.394440i \(0.870939\pi\)
\(828\) − 139992.i − 5.87567i
\(829\) 22423.8 0.939457 0.469728 0.882811i \(-0.344352\pi\)
0.469728 + 0.882811i \(0.344352\pi\)
\(830\) − 3858.49i − 0.161362i
\(831\) 10235.3 0.427265
\(832\) 1602.13 0.0667596
\(833\) 0 0
\(834\) −88441.1 −3.67202
\(835\) 444.231 0.0184111
\(836\) − 60356.4i − 2.49697i
\(837\) −5276.13 −0.217885
\(838\) − 29004.0i − 1.19562i
\(839\) 9128.63i 0.375632i 0.982204 + 0.187816i \(0.0601409\pi\)
−0.982204 + 0.187816i \(0.939859\pi\)
\(840\) − 1345.22i − 0.0552555i
\(841\) 22685.0 0.930131
\(842\) −9441.58 −0.386435
\(843\) − 10146.5i − 0.414547i
\(844\) − 48634.4i − 1.98349i
\(845\) 1888.32i 0.0768759i
\(846\) −104638. −4.25240
\(847\) − 5390.75i − 0.218688i
\(848\) 32198.0 1.30387
\(849\) 26822.2 1.08426
\(850\) 0 0
\(851\) 23495.7 0.946442
\(852\) 98416.1 3.95737
\(853\) − 27204.8i − 1.09200i −0.837786 0.545999i \(-0.816150\pi\)
0.837786 0.545999i \(-0.183850\pi\)
\(854\) −6538.68 −0.262001
\(855\) 2641.12i 0.105643i
\(856\) 22769.8i 0.909179i
\(857\) − 38060.0i − 1.51704i −0.651649 0.758520i \(-0.725923\pi\)
0.651649 0.758520i \(-0.274077\pi\)
\(858\) 18004.9 0.716405
\(859\) 33326.2 1.32372 0.661860 0.749627i \(-0.269767\pi\)
0.661860 + 0.749627i \(0.269767\pi\)
\(860\) 4260.24i 0.168922i
\(861\) − 579.531i − 0.0229389i
\(862\) 422.378i 0.0166894i
\(863\) −41724.2 −1.64578 −0.822890 0.568201i \(-0.807640\pi\)
−0.822890 + 0.568201i \(0.807640\pi\)
\(864\) 17475.4i 0.688108i
\(865\) 2294.06 0.0901737
\(866\) 77223.8 3.03022
\(867\) 0 0
\(868\) −2309.60 −0.0903146
\(869\) 56569.7 2.20828
\(870\) − 1559.42i − 0.0607694i
\(871\) −124.068 −0.00482649
\(872\) − 58907.5i − 2.28768i
\(873\) − 17009.6i − 0.659438i
\(874\) 60328.6i 2.33483i
\(875\) 842.801 0.0325621
\(876\) −28411.6 −1.09582
\(877\) − 49337.3i − 1.89966i −0.312767 0.949830i \(-0.601256\pi\)
0.312767 0.949830i \(-0.398744\pi\)
\(878\) − 15423.3i − 0.592838i
\(879\) − 63194.0i − 2.42489i
\(880\) −4526.57 −0.173398
\(881\) − 8845.46i − 0.338265i −0.985593 0.169132i \(-0.945903\pi\)
0.985593 0.169132i \(-0.0540965\pi\)
\(882\) −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
\(887\) − 3864.38i − 0.146283i −0.997322 0.0731415i \(-0.976698\pi\)
0.997322 0.0731415i \(-0.0233025\pi\)
\(888\) −51858.1 −1.95974
\(889\) − 7360.60i − 0.277690i
\(890\) − 5034.28i − 0.189606i
\(891\) − 3688.07i − 0.138670i
\(892\) −81160.9 −3.04649
\(893\) 30849.1 1.15602
\(894\) 79023.2i 2.95630i
\(895\) 1918.10i 0.0716368i
\(896\) − 7351.61i − 0.274107i
\(897\) −12311.8 −0.458283
\(898\) 12577.2i 0.467379i
\(899\) −1441.14 −0.0534648
\(900\) −96485.6 −3.57354
\(901\) 0 0
\(902\) −4719.92 −0.174231
\(903\) −8984.15 −0.331089
\(904\) − 47560.6i − 1.74982i
\(905\) −1705.45 −0.0626421
\(906\) 87473.7i 3.20764i
\(907\) − 743.409i − 0.0272155i −0.999907 0.0136078i \(-0.995668\pi\)
0.999907 0.0136078i \(-0.00433162\pi\)
\(908\) − 24182.5i − 0.883839i
\(909\) −5905.76 −0.215491
\(910\) −137.177 −0.00499713
\(911\) 16291.0i 0.592475i 0.955114 + 0.296238i \(0.0957320\pi\)
−0.955114 + 0.296238i \(0.904268\pi\)
\(912\) − 55013.4i − 1.99745i
\(913\) − 45336.8i − 1.64340i
\(914\) −74402.5 −2.69258
\(915\) − 2554.33i − 0.0922879i
\(916\) −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
\(921\) 55390.5i 1.98174i
\(922\) 89311.6 3.19015
\(923\) − 5402.00i − 0.192643i
\(924\) − 29364.8i − 1.04549i
\(925\) − 16193.8i − 0.575620i
\(926\) 93033.0 3.30157
\(927\) −8786.47 −0.311311
\(928\) 4773.30i 0.168848i
\(929\) − 31661.7i − 1.11818i −0.829108 0.559089i \(-0.811151\pi\)
0.829108 0.559089i \(-0.188849\pi\)
\(930\) − 1318.84i − 0.0465015i
\(931\) 21845.0 0.769003
\(932\) − 20724.3i − 0.728376i
\(933\) 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 \(-0.708960\pi\)
−0.610322 + 0.792153i \(0.708960\pi\)
\(938\) 295.776i 0.0102958i
\(939\) −22279.2 −0.774286
\(940\) − 7117.12i − 0.246952i
\(941\) − 45625.8i − 1.58061i −0.612711 0.790307i \(-0.709921\pi\)
0.612711 0.790307i \(-0.290079\pi\)
\(942\) 11217.2i 0.387977i
\(943\) 3227.51 0.111455
\(944\) −66227.5 −2.28339
\(945\) 511.092i 0.0175934i
\(946\) 73170.2i 2.51477i
\(947\) 21508.4i 0.738044i 0.929421 + 0.369022i \(0.120307\pi\)
−0.929421 + 0.369022i \(0.879693\pi\)
\(948\) 158615. 5.43416
\(949\) 1559.50i 0.0533439i
\(950\) 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
\(955\) 2465.34i 0.0835355i
\(956\) 85744.0 2.90079
\(957\) − 18323.0i − 0.618912i
\(958\) 93357.8i 3.14849i
\(959\) − 498.486i − 0.0167851i
\(960\) 1492.07 0.0501630
\(961\) 28572.2 0.959088
\(962\) 5288.17i 0.177232i
\(963\) − 21749.9i − 0.727810i
\(964\) 116133.i 3.88006i
\(965\) 2000.12 0.0667215
\(966\) 29351.3i 0.977600i
\(967\) 3731.33 0.124086 0.0620432 0.998073i \(-0.480238\pi\)
0.0620432 + 0.998073i \(0.480238\pi\)
\(968\) −66262.5 −2.20016
\(969\) 0 0
\(970\) 1691.13 0.0559782
\(971\) −17645.1 −0.583171 −0.291585 0.956545i \(-0.594183\pi\)
−0.291585 + 0.956545i \(0.594183\pi\)
\(972\) 60358.3i 1.99176i
\(973\) 7917.35 0.260862
\(974\) 51348.7i 1.68924i
\(975\) 8485.59i 0.278725i
\(976\) 33206.7i 1.08906i
\(977\) −24941.2 −0.816723 −0.408362 0.912820i \(-0.633900\pi\)
−0.408362 + 0.912820i \(0.633900\pi\)
\(978\) −61631.8 −2.01510
\(979\) − 59152.1i − 1.93106i
\(980\) − 5039.81i − 0.164276i
\(981\) 56268.9i 1.83132i
\(982\) 6277.85 0.204006
\(983\) 22506.2i 0.730252i 0.930958 + 0.365126i \(0.118974\pi\)
−0.930958 + 0.365126i \(0.881026\pi\)
\(984\) −7123.53 −0.230782
\(985\) −1125.44 −0.0364057
\(986\) 0 0
\(987\) 15008.8 0.484029
\(988\) −9289.07 −0.299114
\(989\) − 50034.2i − 1.60869i
\(990\) 10465.3 0.335967
\(991\) − 32694.1i − 1.04799i −0.851720 0.523997i \(-0.824440\pi\)
0.851720 0.523997i \(-0.175560\pi\)
\(992\) 4036.88i 0.129205i
\(993\) 8410.08i 0.268767i
\(994\) −12878.3 −0.410941
\(995\) 4246.32 0.135294
\(996\) − 127119.i − 4.04410i
\(997\) 18248.8i 0.579686i 0.957074 + 0.289843i \(0.0936030\pi\)
−0.957074 + 0.289843i \(0.906397\pi\)
\(998\) 352.428i 0.0111783i
\(999\) 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.b.b.288.5 6
17.4 even 4 289.4.a.b.1.1 3
17.13 even 4 17.4.a.b.1.1 3
17.16 even 2 inner 289.4.b.b.288.6 6
51.47 odd 4 153.4.a.g.1.3 3
68.47 odd 4 272.4.a.h.1.1 3
85.13 odd 4 425.4.b.f.324.6 6
85.47 odd 4 425.4.b.f.324.1 6
85.64 even 4 425.4.a.g.1.3 3
119.13 odd 4 833.4.a.d.1.1 3
136.13 even 4 1088.4.a.v.1.1 3
136.115 odd 4 1088.4.a.x.1.3 3
187.98 odd 4 2057.4.a.e.1.3 3
204.47 even 4 2448.4.a.bi.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
17.4.a.b.1.1 3 17.13 even 4
153.4.a.g.1.3 3 51.47 odd 4
272.4.a.h.1.1 3 68.47 odd 4
289.4.a.b.1.1 3 17.4 even 4
289.4.b.b.288.5 6 1.1 even 1 trivial
289.4.b.b.288.6 6 17.16 even 2 inner
425.4.a.g.1.3 3 85.64 even 4
425.4.b.f.324.1 6 85.47 odd 4
425.4.b.f.324.6 6 85.13 odd 4
833.4.a.d.1.1 3 119.13 odd 4
1088.4.a.v.1.1 3 136.13 even 4
1088.4.a.x.1.3 3 136.115 odd 4
2057.4.a.e.1.3 3 187.98 odd 4
2448.4.a.bi.1.2 3 204.47 even 4