Properties

Label 289.4.b.b.288.6
Level $289$
Weight $4$
Character 289.288
Analytic conductor $17.052$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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

$q$-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 \(0.303561\pi\)
−0.578699 + 0.815541i \(0.696439\pi\)
\(4\) 17.3261 2.16577
\(5\) 0.885690i 0.0792185i 0.999215 + 0.0396092i \(0.0126113\pi\)
−0.999215 + 0.0396092i \(0.987389\pi\)
\(6\) 42.6523i 2.90212i
\(7\) − 3.81828i − 0.206168i −0.994673 0.103084i \(-0.967129\pi\)
0.994673 0.103084i \(-0.0328711\pi\)
\(8\) 46.9339 2.07421
\(9\) −44.8316 −1.66043
\(10\) 4.45724i 0.140950i
\(11\) 52.3720i 1.43552i 0.696289 + 0.717761i \(0.254833\pi\)
−0.696289 + 0.717761i \(0.745167\pi\)
\(12\) 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 \(-0.695664\pi\)
0.576711 0.816948i \(-0.304336\pi\)
\(24\) 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 \(-0.957807\pi\)
0.991228 0.132164i \(-0.0421925\pi\)
\(30\) −37.7767 −0.229902
\(31\) − 34.9114i − 0.202267i −0.994873 0.101133i \(-0.967753\pi\)
0.994873 0.101133i \(-0.0322469\pi\)
\(32\) 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 \(0.0935314\pi\)
−0.957139 + 0.289627i \(0.906469\pi\)
\(38\) 334.739 1.42900
\(39\) − 68.3134i − 0.280485i
\(40\) 41.5689i 0.164315i
\(41\) 17.9081i 0.0682142i 0.999418 + 0.0341071i \(0.0108587\pi\)
−0.999418 + 0.0341071i \(0.989141\pi\)
\(42\) 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 \(-0.883759\pi\)
0.934059 0.357118i \(-0.116241\pi\)
\(62\) − 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 \(-0.810751\pi\)
0.828405 0.560130i \(-0.189249\pi\)
\(72\) −2104.12 −3.44408
\(73\) 193.480i 0.310207i 0.987898 + 0.155103i \(0.0495711\pi\)
−0.987898 + 0.155103i \(0.950429\pi\)
\(74\) 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 \(-0.720677\pi\)
0.639061 0.769156i \(-0.279323\pi\)
\(80\) 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 \(-0.936369\pi\)
0.980086 0.198574i \(-0.0636311\pi\)
\(98\) 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 \(-0.929667\pi\)
0.975688 0.219163i \(-0.0703327\pi\)
\(108\) − 2618.49i − 2.33300i
\(109\) 1255.12i 1.10292i 0.834201 + 0.551460i \(0.185929\pi\)
−0.834201 + 0.551460i \(0.814071\pi\)
\(110\) −233.435 −0.202337
\(111\) −1104.92 −0.944812
\(112\) − 372.612i − 0.314362i
\(113\) 1013.35i 0.843612i 0.906686 + 0.421806i \(0.138604\pi\)
−0.906686 + 0.421806i \(0.861396\pi\)
\(114\) 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 \(-0.956692\pi\)
0.990759 0.135637i \(-0.0433081\pi\)
\(132\) −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 \(0.218030\pi\)
−0.774443 + 0.632644i \(0.781970\pi\)
\(140\) 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 \(0.112860\pi\)
−0.937800 + 0.347177i \(0.887140\pi\)
\(164\) 310.279i 0.147736i
\(165\) − 393.132i − 0.185487i
\(166\) 4356.48 2.03692
\(167\) − 501.565i − 0.232409i −0.993225 0.116204i \(-0.962927\pi\)
0.993225 0.116204i \(-0.0370728\pi\)
\(168\) 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 \(-0.807274\pi\)
0.822237 0.569146i \(-0.192726\pi\)
\(174\) 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 \(0.129385\pi\)
−0.918520 + 0.395375i \(0.870615\pi\)
\(182\) 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 \(-0.861636\pi\)
0.907004 0.421123i \(-0.138364\pi\)
\(194\) − 1909.39i − 0.706631i
\(195\) 60.5045 0.0222196
\(196\) 5690.27 2.07371
\(197\) 1270.70i 0.459560i 0.973243 + 0.229780i \(0.0738007\pi\)
−0.973243 + 0.229780i \(0.926199\pi\)
\(198\) − 11815.9i − 4.24102i
\(199\) − 4794.36i − 1.70786i −0.520392 0.853928i \(-0.674214\pi\)
0.520392 0.853928i \(-0.325786\pi\)
\(200\) 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 \(0.151405\pi\)
−0.888994 + 0.457918i \(0.848595\pi\)
\(212\) 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 \(0.0654096\pi\)
−0.978961 + 0.204047i \(0.934590\pi\)
\(228\) 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 \(0.0537814\pi\)
−0.985760 + 0.168156i \(0.946219\pi\)
\(234\) 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 \(-0.646625\pi\)
0.444518 0.895770i \(-0.353375\pi\)
\(242\) −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 \(0.227683\pi\)
−0.754904 + 0.655835i \(0.772317\pi\)
\(270\) 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 \(-0.958189\pi\)
0.991386 0.130976i \(-0.0418111\pi\)
\(278\) 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 \(-0.892150\pi\)
0.943148 0.332374i \(-0.107850\pi\)
\(284\) − 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 \(-0.696933\pi\)
0.579963 0.814642i \(-0.303067\pi\)
\(312\) − 3206.22i − 0.581783i
\(313\) 2628.71i 0.474707i 0.971423 + 0.237353i \(0.0762799\pi\)
−0.971423 + 0.237353i \(0.923720\pi\)
\(314\) −1323.50 −0.237865
\(315\) −151.612 −0.0271187
\(316\) − 18714.9i − 3.33163i
\(317\) − 4268.54i − 0.756293i −0.925746 0.378147i \(-0.876562\pi\)
0.925746 0.378147i \(-0.123438\pi\)
\(318\) 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 \(0.225225\pi\)
−0.759947 + 0.649985i \(0.774775\pi\)
\(338\) −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 \(0.194417\pi\)
−0.819202 + 0.573506i \(0.805583\pi\)
\(348\) 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 \(0.285047\pi\)
−0.625127 + 0.780523i \(0.714953\pi\)
\(368\) − 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 \(0.183704\pi\)
−0.838035 + 0.545616i \(0.816296\pi\)
\(380\) 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 \(0.105529\pi\)
−0.945545 + 0.325490i \(0.894471\pi\)
\(398\) − 24127.7i − 3.03872i
\(399\) 2152.53 0.270078
\(400\) 12121.7 1.51522
\(401\) − 8700.49i − 1.08350i −0.840541 0.541748i \(-0.817763\pi\)
0.840541 0.541748i \(-0.182237\pi\)
\(402\) 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 \(0.109070\pi\)
−0.941867 + 0.335987i \(0.890930\pi\)
\(420\) 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 \(-0.998507\pi\)
0.999989 0.00468998i \(-0.00149287\pi\)
\(432\) − 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 \(0.0532778\pi\)
−0.986025 + 0.166597i \(0.946722\pi\)
\(440\) −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 \(-0.958072\pi\)
0.991337 0.131341i \(-0.0419282\pi\)
\(450\) −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 \(-0.654312\pi\)
0.466019 0.884775i \(-0.345688\pi\)
\(480\) −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 \(-0.842556\pi\)
0.880146 0.474703i \(-0.157444\pi\)
\(488\) − 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 \(-0.999000\pi\)
0.999995 0.00314127i \(-0.000999898\pi\)
\(500\) 3824.36i 0.342061i
\(501\) 4250.94 0.379078
\(502\) −23935.0 −2.12803
\(503\) − 1444.29i − 0.128028i −0.997949 0.0640138i \(-0.979610\pi\)
0.997949 0.0640138i \(-0.0203902\pi\)
\(504\) 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 \(-0.784946\pi\)
0.780324 0.625376i \(-0.215054\pi\)
\(522\) 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 \(0.0403244\pi\)
−0.991986 + 0.126344i \(0.959676\pi\)
\(542\) 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 \(0.0262428\pi\)
−0.996603 + 0.0823509i \(0.973757\pi\)
\(548\) −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 \(0.126161\pi\)
−0.922477 + 0.386052i \(0.873839\pi\)
\(572\) − 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 \(0.391627\pi\)
−0.333923 + 0.942600i \(0.608373\pi\)
\(602\) 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 \(0.215374\pi\)
−0.779695 + 0.626159i \(0.784626\pi\)
\(608\) 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 \(-0.737377\pi\)
0.678518 0.734584i \(-0.262623\pi\)
\(618\) 8359.35i 0.544114i
\(619\) 5146.53i 0.334179i 0.985942 + 0.167089i \(0.0534369\pi\)
−0.985942 + 0.167089i \(0.946563\pi\)
\(620\) 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 \(0.195311\pi\)
−0.817587 + 0.575805i \(0.804689\pi\)
\(642\) 20692.6 1.27208
\(643\) 26473.5i 1.62366i 0.583893 + 0.811831i \(0.301529\pi\)
−0.583893 + 0.811831i \(0.698471\pi\)
\(644\) −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 \(-0.784107\pi\)
0.778672 0.627431i \(-0.215893\pi\)
\(654\) −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 \(-0.904506\pi\)
0.955335 0.295524i \(-0.0954942\pi\)
\(674\) 40472.7i 2.31298i
\(675\) − 18772.6i − 1.07046i
\(676\) −36939.9 −2.10172
\(677\) − 19813.3i − 1.12480i −0.826866 0.562398i \(-0.809879\pi\)
0.826866 0.562398i \(-0.190121\pi\)
\(678\) −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 \(0.0530717\pi\)
−0.986133 + 0.165958i \(0.946928\pi\)
\(684\) −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 \(-0.982703\pi\)
0.998524 0.0543143i \(-0.0172973\pi\)
\(692\) − 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 \(-0.737204\pi\)
0.678119 0.734952i \(-0.262796\pi\)
\(710\) 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 \(0.144309\pi\)
−0.898980 + 0.437989i \(0.855691\pi\)
\(720\) − 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 \(0.0982050\pi\)
−0.952784 + 0.303649i \(0.901795\pi\)
\(744\) 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 \(0.261101\pi\)
−0.682021 + 0.731332i \(0.738899\pi\)
\(752\) 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 \(-0.832435\pi\)
0.864611 0.502442i \(-0.167565\pi\)
\(788\) 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 \(-0.874360\pi\)
0.923108 0.384541i \(-0.125640\pi\)
\(810\) 313.882i 0.0136157i
\(811\) − 3095.34i − 0.134022i −0.997752 0.0670111i \(-0.978654\pi\)
0.997752 0.0670111i \(-0.0213463\pi\)
\(812\) −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 \(0.0843597\pi\)
−0.965086 + 0.261932i \(0.915640\pi\)
\(822\) − 5568.36i − 0.236276i
\(823\) 34436.5i 1.45854i 0.684225 + 0.729271i \(0.260140\pi\)
−0.684225 + 0.729271i \(0.739860\pi\)
\(824\) 9198.50 0.388889
\(825\) −55135.7 −2.32676
\(826\) 13040.8i 0.549329i
\(827\) − 18761.6i − 0.788880i −0.918922 0.394440i \(-0.870939\pi\)
0.918922 0.394440i \(-0.129061\pi\)
\(828\) 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 \(-0.939859\pi\)
0.982204 0.187816i \(-0.0601409\pi\)
\(840\) 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 \(0.183850\pi\)
−0.837786 + 0.545999i \(0.816150\pi\)
\(854\) −6538.68 −0.262001
\(855\) − 2641.12i − 0.105643i
\(856\) − 22769.8i − 0.909179i
\(857\) 38060.0i 1.51704i 0.651649 + 0.758520i \(0.274077\pi\)
−0.651649 + 0.758520i \(0.725923\pi\)
\(858\) 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 \(0.398744\pi\)
−0.312767 + 0.949830i \(0.601256\pi\)
\(878\) 15423.3i 0.592838i
\(879\) 63194.0i 2.42489i
\(880\) −4526.57 −0.173398
\(881\) 8845.46i 0.338265i 0.985593 + 0.169132i \(0.0540965\pi\)
−0.985593 + 0.169132i \(0.945903\pi\)
\(882\) −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 \(0.0233025\pi\)
−0.997322 + 0.0731415i \(0.976698\pi\)
\(888\) −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 \(0.00433162\pi\)
−0.999907 + 0.0136078i \(0.995668\pi\)
\(908\) 24182.5i 0.883839i
\(909\) −5905.76 −0.215491
\(910\) −137.177 −0.00499713
\(911\) − 16291.0i − 0.592475i −0.955114 0.296238i \(-0.904268\pi\)
0.955114 0.296238i \(-0.0957320\pi\)
\(912\) 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 \(0.188849\pi\)
−0.829108 + 0.559089i \(0.811151\pi\)
\(930\) 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 \(0.290079\pi\)
−0.612711 + 0.790307i \(0.709921\pi\)
\(942\) − 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 \(-0.879693\pi\)
0.929421 0.369022i \(-0.120307\pi\)
\(948\) 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 \(-0.881026\pi\)
0.930958 0.365126i \(-0.118974\pi\)
\(984\) −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 \(0.175560\pi\)
−0.851720 + 0.523997i \(0.824440\pi\)
\(992\) − 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 \(-0.906397\pi\)
0.957074 0.289843i \(-0.0936030\pi\)
\(998\) − 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.288.6 6
17.4 even 4 17.4.a.b.1.1 3
17.13 even 4 289.4.a.b.1.1 3
17.16 even 2 inner 289.4.b.b.288.5 6
51.38 odd 4 153.4.a.g.1.3 3
68.55 odd 4 272.4.a.h.1.1 3
85.4 even 4 425.4.a.g.1.3 3
85.38 odd 4 425.4.b.f.324.6 6
85.72 odd 4 425.4.b.f.324.1 6
119.55 odd 4 833.4.a.d.1.1 3
136.21 even 4 1088.4.a.v.1.1 3
136.123 odd 4 1088.4.a.x.1.3 3
187.21 odd 4 2057.4.a.e.1.3 3
204.191 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 17.4 even 4
153.4.a.g.1.3 3 51.38 odd 4
272.4.a.h.1.1 3 68.55 odd 4
289.4.a.b.1.1 3 17.13 even 4
289.4.b.b.288.5 6 17.16 even 2 inner
289.4.b.b.288.6 6 1.1 even 1 trivial
425.4.a.g.1.3 3 85.4 even 4
425.4.b.f.324.1 6 85.72 odd 4
425.4.b.f.324.6 6 85.38 odd 4
833.4.a.d.1.1 3 119.55 odd 4
1088.4.a.v.1.1 3 136.21 even 4
1088.4.a.x.1.3 3 136.123 odd 4
2057.4.a.e.1.3 3 187.21 odd 4
2448.4.a.bi.1.2 3 204.191 even 4