Properties

Label 29.4.a.a.1.2
Level $29$
Weight $4$
Character 29.1
Self dual yes
Analytic conductor $1.711$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 29 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 29.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(1.71105539017\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{8})^+\)
Defining polynomial: \(x^{2} - 2\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(1.41421\) of defining polynomial
Character \(\chi\) \(=\) 29.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.414214 q^{2} -9.24264 q^{3} -7.82843 q^{4} +0.656854 q^{5} -3.82843 q^{6} +6.14214 q^{7} -6.55635 q^{8} +58.4264 q^{9} +O(q^{10})\) \(q+0.414214 q^{2} -9.24264 q^{3} -7.82843 q^{4} +0.656854 q^{5} -3.82843 q^{6} +6.14214 q^{7} -6.55635 q^{8} +58.4264 q^{9} +0.272078 q^{10} -65.3259 q^{11} +72.3553 q^{12} -49.7696 q^{13} +2.54416 q^{14} -6.07107 q^{15} +59.9117 q^{16} +55.4558 q^{17} +24.2010 q^{18} -64.7452 q^{19} -5.14214 q^{20} -56.7696 q^{21} -27.0589 q^{22} +93.8823 q^{23} +60.5980 q^{24} -124.569 q^{25} -20.6152 q^{26} -290.463 q^{27} -48.0833 q^{28} +29.0000 q^{29} -2.51472 q^{30} -236.095 q^{31} +77.2670 q^{32} +603.784 q^{33} +22.9706 q^{34} +4.03449 q^{35} -457.387 q^{36} +76.8040 q^{37} -26.8183 q^{38} +460.002 q^{39} -4.30657 q^{40} +215.161 q^{41} -23.5147 q^{42} +80.8305 q^{43} +511.399 q^{44} +38.3776 q^{45} +38.8873 q^{46} -357.742 q^{47} -553.742 q^{48} -305.274 q^{49} -51.5980 q^{50} -512.558 q^{51} +389.617 q^{52} +328.466 q^{53} -120.314 q^{54} -42.9096 q^{55} -40.2700 q^{56} +598.416 q^{57} +12.0122 q^{58} -99.2750 q^{59} +47.5269 q^{60} -725.730 q^{61} -97.7939 q^{62} +358.863 q^{63} -447.288 q^{64} -32.6913 q^{65} +250.095 q^{66} +844.479 q^{67} -434.132 q^{68} -867.720 q^{69} +1.67114 q^{70} -378.083 q^{71} -383.064 q^{72} -581.097 q^{73} +31.8133 q^{74} +1151.34 q^{75} +506.853 q^{76} -401.241 q^{77} +190.539 q^{78} -353.247 q^{79} +39.3532 q^{80} +1107.13 q^{81} +89.1228 q^{82} +696.510 q^{83} +444.416 q^{84} +36.4264 q^{85} +33.4811 q^{86} -268.037 q^{87} +428.299 q^{88} +1118.22 q^{89} +15.8965 q^{90} -305.691 q^{91} -734.950 q^{92} +2182.15 q^{93} -148.182 q^{94} -42.5281 q^{95} -714.151 q^{96} -805.415 q^{97} -126.449 q^{98} -3816.76 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 2q^{2} - 10q^{3} - 10q^{4} - 10q^{5} - 2q^{6} - 16q^{7} + 18q^{8} + 32q^{9} + O(q^{10}) \) \( 2q - 2q^{2} - 10q^{3} - 10q^{4} - 10q^{5} - 2q^{6} - 16q^{7} + 18q^{8} + 32q^{9} + 26q^{10} - 26q^{11} + 74q^{12} - 26q^{13} + 56q^{14} + 2q^{15} + 18q^{16} + 60q^{17} + 88q^{18} - 220q^{19} + 18q^{20} - 40q^{21} - 122q^{22} + 52q^{23} + 42q^{24} - 136q^{25} - 78q^{26} - 250q^{27} + 58q^{29} - 22q^{30} - 294q^{31} - 18q^{32} + 574q^{33} + 12q^{34} + 240q^{35} - 400q^{36} + 312q^{37} + 348q^{38} + 442q^{39} - 266q^{40} + 40q^{41} - 64q^{42} - 322q^{43} + 426q^{44} + 320q^{45} + 140q^{46} - 130q^{47} - 522q^{48} - 158q^{49} - 24q^{50} - 516q^{51} + 338q^{52} + 1002q^{53} - 218q^{54} - 462q^{55} - 584q^{56} + 716q^{57} - 58q^{58} - 900q^{59} + 30q^{60} - 948q^{61} + 42q^{62} + 944q^{63} + 118q^{64} - 286q^{65} + 322q^{66} + 320q^{67} - 444q^{68} - 836q^{69} - 568q^{70} - 660q^{71} - 1032q^{72} + 648q^{73} - 536q^{74} + 1160q^{75} + 844q^{76} - 1272q^{77} + 234q^{78} + 258q^{79} + 486q^{80} + 1790q^{81} + 512q^{82} + 1212q^{83} + 408q^{84} - 12q^{85} + 1006q^{86} - 290q^{87} + 1394q^{88} + 760q^{89} - 664q^{90} - 832q^{91} - 644q^{92} + 2226q^{93} - 698q^{94} + 1612q^{95} - 642q^{96} + 24q^{97} - 482q^{98} - 4856q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.414214 0.146447 0.0732233 0.997316i \(-0.476671\pi\)
0.0732233 + 0.997316i \(0.476671\pi\)
\(3\) −9.24264 −1.77875 −0.889374 0.457181i \(-0.848859\pi\)
−0.889374 + 0.457181i \(0.848859\pi\)
\(4\) −7.82843 −0.978553
\(5\) 0.656854 0.0587508 0.0293754 0.999568i \(-0.490648\pi\)
0.0293754 + 0.999568i \(0.490648\pi\)
\(6\) −3.82843 −0.260491
\(7\) 6.14214 0.331644 0.165822 0.986156i \(-0.446972\pi\)
0.165822 + 0.986156i \(0.446972\pi\)
\(8\) −6.55635 −0.289752
\(9\) 58.4264 2.16394
\(10\) 0.272078 0.00860386
\(11\) −65.3259 −1.79059 −0.895295 0.445473i \(-0.853036\pi\)
−0.895295 + 0.445473i \(0.853036\pi\)
\(12\) 72.3553 1.74060
\(13\) −49.7696 −1.06181 −0.530907 0.847430i \(-0.678149\pi\)
−0.530907 + 0.847430i \(0.678149\pi\)
\(14\) 2.54416 0.0485682
\(15\) −6.07107 −0.104503
\(16\) 59.9117 0.936120
\(17\) 55.4558 0.791178 0.395589 0.918428i \(-0.370541\pi\)
0.395589 + 0.918428i \(0.370541\pi\)
\(18\) 24.2010 0.316902
\(19\) −64.7452 −0.781766 −0.390883 0.920440i \(-0.627830\pi\)
−0.390883 + 0.920440i \(0.627830\pi\)
\(20\) −5.14214 −0.0574908
\(21\) −56.7696 −0.589911
\(22\) −27.0589 −0.262226
\(23\) 93.8823 0.851122 0.425561 0.904930i \(-0.360077\pi\)
0.425561 + 0.904930i \(0.360077\pi\)
\(24\) 60.5980 0.515396
\(25\) −124.569 −0.996548
\(26\) −20.6152 −0.155499
\(27\) −290.463 −2.07036
\(28\) −48.0833 −0.324532
\(29\) 29.0000 0.185695
\(30\) −2.51472 −0.0153041
\(31\) −236.095 −1.36787 −0.683935 0.729543i \(-0.739733\pi\)
−0.683935 + 0.729543i \(0.739733\pi\)
\(32\) 77.2670 0.426844
\(33\) 603.784 3.18501
\(34\) 22.9706 0.115865
\(35\) 4.03449 0.0194844
\(36\) −457.387 −2.11753
\(37\) 76.8040 0.341257 0.170628 0.985335i \(-0.445420\pi\)
0.170628 + 0.985335i \(0.445420\pi\)
\(38\) −26.8183 −0.114487
\(39\) 460.002 1.88870
\(40\) −4.30657 −0.0170232
\(41\) 215.161 0.819575 0.409788 0.912181i \(-0.365603\pi\)
0.409788 + 0.912181i \(0.365603\pi\)
\(42\) −23.5147 −0.0863905
\(43\) 80.8305 0.286664 0.143332 0.989675i \(-0.454218\pi\)
0.143332 + 0.989675i \(0.454218\pi\)
\(44\) 511.399 1.75219
\(45\) 38.3776 0.127133
\(46\) 38.8873 0.124644
\(47\) −357.742 −1.11026 −0.555128 0.831765i \(-0.687331\pi\)
−0.555128 + 0.831765i \(0.687331\pi\)
\(48\) −553.742 −1.66512
\(49\) −305.274 −0.890012
\(50\) −51.5980 −0.145941
\(51\) −512.558 −1.40730
\(52\) 389.617 1.03904
\(53\) 328.466 0.851288 0.425644 0.904891i \(-0.360048\pi\)
0.425644 + 0.904891i \(0.360048\pi\)
\(54\) −120.314 −0.303197
\(55\) −42.9096 −0.105199
\(56\) −40.2700 −0.0960947
\(57\) 598.416 1.39056
\(58\) 12.0122 0.0271945
\(59\) −99.2750 −0.219059 −0.109530 0.993984i \(-0.534934\pi\)
−0.109530 + 0.993984i \(0.534934\pi\)
\(60\) 47.5269 0.102262
\(61\) −725.730 −1.52328 −0.761641 0.647999i \(-0.775606\pi\)
−0.761641 + 0.647999i \(0.775606\pi\)
\(62\) −97.7939 −0.200320
\(63\) 358.863 0.717658
\(64\) −447.288 −0.873610
\(65\) −32.6913 −0.0623825
\(66\) 250.095 0.466434
\(67\) 844.479 1.53984 0.769922 0.638138i \(-0.220295\pi\)
0.769922 + 0.638138i \(0.220295\pi\)
\(68\) −434.132 −0.774209
\(69\) −867.720 −1.51393
\(70\) 1.67114 0.00285342
\(71\) −378.083 −0.631975 −0.315988 0.948763i \(-0.602336\pi\)
−0.315988 + 0.948763i \(0.602336\pi\)
\(72\) −383.064 −0.627007
\(73\) −581.097 −0.931674 −0.465837 0.884870i \(-0.654247\pi\)
−0.465837 + 0.884870i \(0.654247\pi\)
\(74\) 31.8133 0.0499759
\(75\) 1151.34 1.77261
\(76\) 506.853 0.765000
\(77\) −401.241 −0.593839
\(78\) 190.539 0.276594
\(79\) −353.247 −0.503081 −0.251540 0.967847i \(-0.580937\pi\)
−0.251540 + 0.967847i \(0.580937\pi\)
\(80\) 39.3532 0.0549978
\(81\) 1107.13 1.51870
\(82\) 89.1228 0.120024
\(83\) 696.510 0.921107 0.460553 0.887632i \(-0.347651\pi\)
0.460553 + 0.887632i \(0.347651\pi\)
\(84\) 444.416 0.577259
\(85\) 36.4264 0.0464823
\(86\) 33.4811 0.0419809
\(87\) −268.037 −0.330305
\(88\) 428.299 0.518828
\(89\) 1118.22 1.33181 0.665905 0.746037i \(-0.268046\pi\)
0.665905 + 0.746037i \(0.268046\pi\)
\(90\) 15.8965 0.0186182
\(91\) −305.691 −0.352145
\(92\) −734.950 −0.832868
\(93\) 2182.15 2.43310
\(94\) −148.182 −0.162593
\(95\) −42.5281 −0.0459294
\(96\) −714.151 −0.759248
\(97\) −805.415 −0.843068 −0.421534 0.906813i \(-0.638508\pi\)
−0.421534 + 0.906813i \(0.638508\pi\)
\(98\) −126.449 −0.130339
\(99\) −3816.76 −3.87473
\(100\) 975.176 0.975176
\(101\) −1373.99 −1.35363 −0.676817 0.736151i \(-0.736641\pi\)
−0.676817 + 0.736151i \(0.736641\pi\)
\(102\) −212.309 −0.206095
\(103\) −634.672 −0.607147 −0.303573 0.952808i \(-0.598180\pi\)
−0.303573 + 0.952808i \(0.598180\pi\)
\(104\) 326.307 0.307663
\(105\) −37.2893 −0.0346578
\(106\) 136.055 0.124668
\(107\) −180.956 −0.163493 −0.0817463 0.996653i \(-0.526050\pi\)
−0.0817463 + 0.996653i \(0.526050\pi\)
\(108\) 2273.87 2.02595
\(109\) 1038.14 0.912251 0.456125 0.889916i \(-0.349237\pi\)
0.456125 + 0.889916i \(0.349237\pi\)
\(110\) −17.7737 −0.0154060
\(111\) −709.872 −0.607010
\(112\) 367.986 0.310459
\(113\) −184.765 −0.153816 −0.0769082 0.997038i \(-0.524505\pi\)
−0.0769082 + 0.997038i \(0.524505\pi\)
\(114\) 247.872 0.203643
\(115\) 61.6670 0.0500041
\(116\) −227.024 −0.181713
\(117\) −2907.86 −2.29770
\(118\) −41.1211 −0.0320805
\(119\) 340.617 0.262389
\(120\) 39.8040 0.0302800
\(121\) 2936.47 2.20622
\(122\) −300.607 −0.223079
\(123\) −1988.66 −1.45782
\(124\) 1848.26 1.33853
\(125\) −163.930 −0.117299
\(126\) 148.646 0.105099
\(127\) 1999.58 1.39712 0.698558 0.715554i \(-0.253825\pi\)
0.698558 + 0.715554i \(0.253825\pi\)
\(128\) −803.409 −0.554781
\(129\) −747.087 −0.509902
\(130\) −13.5412 −0.00913570
\(131\) 561.468 0.374471 0.187236 0.982315i \(-0.440047\pi\)
0.187236 + 0.982315i \(0.440047\pi\)
\(132\) −4726.68 −3.11670
\(133\) −397.674 −0.259268
\(134\) 349.795 0.225505
\(135\) −190.792 −0.121635
\(136\) −363.588 −0.229246
\(137\) −250.489 −0.156210 −0.0781050 0.996945i \(-0.524887\pi\)
−0.0781050 + 0.996945i \(0.524887\pi\)
\(138\) −359.421 −0.221710
\(139\) −242.244 −0.147819 −0.0739096 0.997265i \(-0.523548\pi\)
−0.0739096 + 0.997265i \(0.523548\pi\)
\(140\) −31.5837 −0.0190665
\(141\) 3306.48 1.97487
\(142\) −156.607 −0.0925506
\(143\) 3251.24 1.90128
\(144\) 3500.42 2.02571
\(145\) 19.0488 0.0109098
\(146\) −240.698 −0.136441
\(147\) 2821.54 1.58311
\(148\) −601.255 −0.333938
\(149\) −1632.63 −0.897652 −0.448826 0.893619i \(-0.648158\pi\)
−0.448826 + 0.893619i \(0.648158\pi\)
\(150\) 476.902 0.259592
\(151\) −121.582 −0.0655245 −0.0327623 0.999463i \(-0.510430\pi\)
−0.0327623 + 0.999463i \(0.510430\pi\)
\(152\) 424.492 0.226519
\(153\) 3240.09 1.71206
\(154\) −166.199 −0.0869657
\(155\) −155.080 −0.0803635
\(156\) −3601.09 −1.84819
\(157\) −753.163 −0.382860 −0.191430 0.981506i \(-0.561312\pi\)
−0.191430 + 0.981506i \(0.561312\pi\)
\(158\) −146.320 −0.0736745
\(159\) −3035.89 −1.51423
\(160\) 50.7532 0.0250774
\(161\) 576.638 0.282270
\(162\) 458.589 0.222408
\(163\) 537.917 0.258484 0.129242 0.991613i \(-0.458746\pi\)
0.129242 + 0.991613i \(0.458746\pi\)
\(164\) −1684.38 −0.801998
\(165\) 396.598 0.187122
\(166\) 288.504 0.134893
\(167\) 484.613 0.224554 0.112277 0.993677i \(-0.464186\pi\)
0.112277 + 0.993677i \(0.464186\pi\)
\(168\) 372.201 0.170928
\(169\) 280.008 0.127450
\(170\) 15.0883 0.00680718
\(171\) −3782.83 −1.69170
\(172\) −632.776 −0.280516
\(173\) −3269.70 −1.43694 −0.718469 0.695559i \(-0.755157\pi\)
−0.718469 + 0.695559i \(0.755157\pi\)
\(174\) −111.024 −0.0483721
\(175\) −765.117 −0.330499
\(176\) −3913.79 −1.67621
\(177\) 917.563 0.389651
\(178\) 463.182 0.195039
\(179\) −562.267 −0.234781 −0.117390 0.993086i \(-0.537453\pi\)
−0.117390 + 0.993086i \(0.537453\pi\)
\(180\) −300.437 −0.124407
\(181\) −1507.32 −0.618998 −0.309499 0.950900i \(-0.600161\pi\)
−0.309499 + 0.950900i \(0.600161\pi\)
\(182\) −126.621 −0.0515704
\(183\) 6707.66 2.70953
\(184\) −615.525 −0.246615
\(185\) 50.4491 0.0200491
\(186\) 903.874 0.356319
\(187\) −3622.70 −1.41668
\(188\) 2800.56 1.08645
\(189\) −1784.06 −0.686622
\(190\) −17.6157 −0.00672621
\(191\) 4532.00 1.71688 0.858439 0.512915i \(-0.171434\pi\)
0.858439 + 0.512915i \(0.171434\pi\)
\(192\) 4134.13 1.55393
\(193\) −2935.17 −1.09471 −0.547353 0.836902i \(-0.684364\pi\)
−0.547353 + 0.836902i \(0.684364\pi\)
\(194\) −333.614 −0.123464
\(195\) 302.154 0.110963
\(196\) 2389.82 0.870924
\(197\) 2682.20 0.970043 0.485022 0.874502i \(-0.338812\pi\)
0.485022 + 0.874502i \(0.338812\pi\)
\(198\) −1580.95 −0.567442
\(199\) −648.376 −0.230966 −0.115483 0.993309i \(-0.536842\pi\)
−0.115483 + 0.993309i \(0.536842\pi\)
\(200\) 816.715 0.288752
\(201\) −7805.22 −2.73899
\(202\) −569.125 −0.198235
\(203\) 178.122 0.0615848
\(204\) 4012.53 1.37712
\(205\) 141.330 0.0481507
\(206\) −262.890 −0.0889145
\(207\) 5485.20 1.84178
\(208\) −2981.78 −0.993986
\(209\) 4229.54 1.39982
\(210\) −15.4457 −0.00507551
\(211\) −4949.57 −1.61489 −0.807446 0.589941i \(-0.799151\pi\)
−0.807446 + 0.589941i \(0.799151\pi\)
\(212\) −2571.37 −0.833031
\(213\) 3494.49 1.12412
\(214\) −74.9545 −0.0239429
\(215\) 53.0939 0.0168417
\(216\) 1904.38 0.599891
\(217\) −1450.13 −0.453646
\(218\) 430.010 0.133596
\(219\) 5370.87 1.65721
\(220\) 335.915 0.102943
\(221\) −2760.01 −0.840084
\(222\) −294.039 −0.0888945
\(223\) 2216.94 0.665729 0.332864 0.942975i \(-0.391985\pi\)
0.332864 + 0.942975i \(0.391985\pi\)
\(224\) 474.585 0.141560
\(225\) −7278.09 −2.15647
\(226\) −76.5323 −0.0225259
\(227\) 4546.09 1.32923 0.664613 0.747187i \(-0.268596\pi\)
0.664613 + 0.747187i \(0.268596\pi\)
\(228\) −4684.66 −1.36074
\(229\) 3339.05 0.963539 0.481770 0.876298i \(-0.339994\pi\)
0.481770 + 0.876298i \(0.339994\pi\)
\(230\) 25.5433 0.00732293
\(231\) 3708.52 1.05629
\(232\) −190.134 −0.0538057
\(233\) −3995.35 −1.12336 −0.561682 0.827353i \(-0.689846\pi\)
−0.561682 + 0.827353i \(0.689846\pi\)
\(234\) −1204.47 −0.336491
\(235\) −234.984 −0.0652285
\(236\) 777.167 0.214361
\(237\) 3264.93 0.894853
\(238\) 141.088 0.0384260
\(239\) −1400.04 −0.378915 −0.189458 0.981889i \(-0.560673\pi\)
−0.189458 + 0.981889i \(0.560673\pi\)
\(240\) −363.728 −0.0978272
\(241\) −2040.94 −0.545513 −0.272756 0.962083i \(-0.587935\pi\)
−0.272756 + 0.962083i \(0.587935\pi\)
\(242\) 1216.33 0.323093
\(243\) −2390.32 −0.631026
\(244\) 5681.32 1.49061
\(245\) −200.521 −0.0522890
\(246\) −823.730 −0.213492
\(247\) 3222.34 0.830091
\(248\) 1547.92 0.396344
\(249\) −6437.59 −1.63842
\(250\) −67.9021 −0.0171780
\(251\) 802.648 0.201843 0.100922 0.994894i \(-0.467821\pi\)
0.100922 + 0.994894i \(0.467821\pi\)
\(252\) −2809.33 −0.702267
\(253\) −6132.94 −1.52401
\(254\) 828.252 0.204603
\(255\) −336.676 −0.0826803
\(256\) 3245.52 0.792364
\(257\) −4464.10 −1.08351 −0.541756 0.840536i \(-0.682240\pi\)
−0.541756 + 0.840536i \(0.682240\pi\)
\(258\) −309.454 −0.0746734
\(259\) 471.741 0.113176
\(260\) 255.922 0.0610446
\(261\) 1694.37 0.401834
\(262\) 232.568 0.0548400
\(263\) −3815.21 −0.894509 −0.447255 0.894407i \(-0.647598\pi\)
−0.447255 + 0.894407i \(0.647598\pi\)
\(264\) −3958.62 −0.922864
\(265\) 215.754 0.0500139
\(266\) −164.722 −0.0379690
\(267\) −10335.3 −2.36895
\(268\) −6610.95 −1.50682
\(269\) 4523.98 1.02540 0.512699 0.858569i \(-0.328646\pi\)
0.512699 + 0.858569i \(0.328646\pi\)
\(270\) −79.0286 −0.0178131
\(271\) 3962.65 0.888242 0.444121 0.895967i \(-0.353516\pi\)
0.444121 + 0.895967i \(0.353516\pi\)
\(272\) 3322.45 0.740637
\(273\) 2825.40 0.626376
\(274\) −103.756 −0.0228764
\(275\) 8137.55 1.78441
\(276\) 6792.88 1.48146
\(277\) 2217.59 0.481019 0.240509 0.970647i \(-0.422685\pi\)
0.240509 + 0.970647i \(0.422685\pi\)
\(278\) −100.341 −0.0216476
\(279\) −13794.2 −2.95999
\(280\) −26.4515 −0.00564564
\(281\) −2562.96 −0.544105 −0.272053 0.962282i \(-0.587702\pi\)
−0.272053 + 0.962282i \(0.587702\pi\)
\(282\) 1369.59 0.289212
\(283\) −3869.29 −0.812741 −0.406370 0.913708i \(-0.633206\pi\)
−0.406370 + 0.913708i \(0.633206\pi\)
\(284\) 2959.80 0.618421
\(285\) 393.072 0.0816968
\(286\) 1346.71 0.278435
\(287\) 1321.55 0.271807
\(288\) 4514.43 0.923665
\(289\) −1837.65 −0.374038
\(290\) 7.89026 0.00159770
\(291\) 7444.17 1.49960
\(292\) 4549.07 0.911693
\(293\) −3883.83 −0.774388 −0.387194 0.921998i \(-0.626556\pi\)
−0.387194 + 0.921998i \(0.626556\pi\)
\(294\) 1168.72 0.231841
\(295\) −65.2092 −0.0128699
\(296\) −503.554 −0.0988800
\(297\) 18974.8 3.70716
\(298\) −676.257 −0.131458
\(299\) −4672.48 −0.903734
\(300\) −9013.20 −1.73459
\(301\) 496.472 0.0950703
\(302\) −50.3609 −0.00959584
\(303\) 12699.3 2.40777
\(304\) −3878.99 −0.731827
\(305\) −476.699 −0.0894941
\(306\) 1342.09 0.250726
\(307\) −403.210 −0.0749590 −0.0374795 0.999297i \(-0.511933\pi\)
−0.0374795 + 0.999297i \(0.511933\pi\)
\(308\) 3141.08 0.581103
\(309\) 5866.05 1.07996
\(310\) −64.2364 −0.0117690
\(311\) −4838.71 −0.882244 −0.441122 0.897447i \(-0.645419\pi\)
−0.441122 + 0.897447i \(0.645419\pi\)
\(312\) −3015.93 −0.547255
\(313\) −8544.28 −1.54298 −0.771488 0.636244i \(-0.780487\pi\)
−0.771488 + 0.636244i \(0.780487\pi\)
\(314\) −311.970 −0.0560685
\(315\) 235.721 0.0421630
\(316\) 2765.37 0.492291
\(317\) −1773.06 −0.314148 −0.157074 0.987587i \(-0.550206\pi\)
−0.157074 + 0.987587i \(0.550206\pi\)
\(318\) −1257.51 −0.221753
\(319\) −1894.45 −0.332504
\(320\) −293.803 −0.0513253
\(321\) 1672.51 0.290812
\(322\) 238.851 0.0413374
\(323\) −3590.50 −0.618516
\(324\) −8667.10 −1.48613
\(325\) 6199.72 1.05815
\(326\) 222.813 0.0378541
\(327\) −9595.11 −1.62266
\(328\) −1410.67 −0.237474
\(329\) −2197.30 −0.368210
\(330\) 164.276 0.0274034
\(331\) 801.875 0.133157 0.0665786 0.997781i \(-0.478792\pi\)
0.0665786 + 0.997781i \(0.478792\pi\)
\(332\) −5452.58 −0.901352
\(333\) 4487.38 0.738460
\(334\) 200.733 0.0328851
\(335\) 554.700 0.0904671
\(336\) −3401.16 −0.552228
\(337\) 8193.23 1.32437 0.662186 0.749339i \(-0.269629\pi\)
0.662186 + 0.749339i \(0.269629\pi\)
\(338\) 115.983 0.0186647
\(339\) 1707.72 0.273601
\(340\) −285.161 −0.0454854
\(341\) 15423.1 2.44930
\(342\) −1566.90 −0.247743
\(343\) −3981.79 −0.626811
\(344\) −529.953 −0.0830615
\(345\) −569.966 −0.0889447
\(346\) −1354.35 −0.210435
\(347\) −10914.9 −1.68860 −0.844301 0.535869i \(-0.819984\pi\)
−0.844301 + 0.535869i \(0.819984\pi\)
\(348\) 2098.30 0.323221
\(349\) 6697.83 1.02730 0.513649 0.858001i \(-0.328294\pi\)
0.513649 + 0.858001i \(0.328294\pi\)
\(350\) −316.922 −0.0484005
\(351\) 14456.2 2.19833
\(352\) −5047.54 −0.764303
\(353\) −3764.83 −0.567654 −0.283827 0.958875i \(-0.591604\pi\)
−0.283827 + 0.958875i \(0.591604\pi\)
\(354\) 380.067 0.0570631
\(355\) −248.346 −0.0371291
\(356\) −8753.90 −1.30325
\(357\) −3148.20 −0.466724
\(358\) −232.898 −0.0343829
\(359\) 6577.13 0.966930 0.483465 0.875364i \(-0.339378\pi\)
0.483465 + 0.875364i \(0.339378\pi\)
\(360\) −251.617 −0.0368372
\(361\) −2667.06 −0.388841
\(362\) −624.354 −0.0906501
\(363\) −27140.8 −3.92430
\(364\) 2393.08 0.344592
\(365\) −381.696 −0.0547366
\(366\) 2778.40 0.396802
\(367\) 2274.27 0.323477 0.161738 0.986834i \(-0.448290\pi\)
0.161738 + 0.986834i \(0.448290\pi\)
\(368\) 5624.64 0.796752
\(369\) 12571.1 1.77351
\(370\) 20.8967 0.00293613
\(371\) 2017.48 0.282325
\(372\) −17082.8 −2.38091
\(373\) 1284.94 0.178369 0.0891844 0.996015i \(-0.471574\pi\)
0.0891844 + 0.996015i \(0.471574\pi\)
\(374\) −1500.57 −0.207467
\(375\) 1515.15 0.208645
\(376\) 2345.48 0.321700
\(377\) −1443.32 −0.197174
\(378\) −738.983 −0.100553
\(379\) 174.785 0.0236890 0.0118445 0.999930i \(-0.496230\pi\)
0.0118445 + 0.999930i \(0.496230\pi\)
\(380\) 332.928 0.0449444
\(381\) −18481.4 −2.48512
\(382\) 1877.22 0.251431
\(383\) −5558.62 −0.741599 −0.370799 0.928713i \(-0.620916\pi\)
−0.370799 + 0.928713i \(0.620916\pi\)
\(384\) 7425.62 0.986816
\(385\) −263.557 −0.0348885
\(386\) −1215.79 −0.160316
\(387\) 4722.64 0.620323
\(388\) 6305.14 0.824987
\(389\) −2556.05 −0.333154 −0.166577 0.986028i \(-0.553271\pi\)
−0.166577 + 0.986028i \(0.553271\pi\)
\(390\) 125.156 0.0162501
\(391\) 5206.32 0.673388
\(392\) 2001.48 0.257883
\(393\) −5189.45 −0.666089
\(394\) 1111.00 0.142060
\(395\) −232.032 −0.0295564
\(396\) 29879.2 3.79163
\(397\) 5927.27 0.749323 0.374662 0.927162i \(-0.377759\pi\)
0.374662 + 0.927162i \(0.377759\pi\)
\(398\) −268.566 −0.0338241
\(399\) 3675.55 0.461173
\(400\) −7463.11 −0.932889
\(401\) 4747.99 0.591280 0.295640 0.955299i \(-0.404467\pi\)
0.295640 + 0.955299i \(0.404467\pi\)
\(402\) −3233.03 −0.401116
\(403\) 11750.4 1.45243
\(404\) 10756.2 1.32460
\(405\) 727.224 0.0892249
\(406\) 73.7805 0.00901888
\(407\) −5017.29 −0.611052
\(408\) 3360.51 0.407770
\(409\) 5200.19 0.628686 0.314343 0.949309i \(-0.398216\pi\)
0.314343 + 0.949309i \(0.398216\pi\)
\(410\) 58.5407 0.00705151
\(411\) 2315.18 0.277858
\(412\) 4968.48 0.594125
\(413\) −609.761 −0.0726498
\(414\) 2272.05 0.269722
\(415\) 457.505 0.0541158
\(416\) −3845.55 −0.453229
\(417\) 2238.97 0.262933
\(418\) 1751.93 0.204999
\(419\) −6425.59 −0.749189 −0.374595 0.927189i \(-0.622218\pi\)
−0.374595 + 0.927189i \(0.622218\pi\)
\(420\) 291.917 0.0339145
\(421\) 10037.6 1.16201 0.581003 0.813902i \(-0.302661\pi\)
0.581003 + 0.813902i \(0.302661\pi\)
\(422\) −2050.18 −0.236496
\(423\) −20901.6 −2.40253
\(424\) −2153.54 −0.246663
\(425\) −6908.05 −0.788447
\(426\) 1447.46 0.164624
\(427\) −4457.53 −0.505188
\(428\) 1416.60 0.159986
\(429\) −30050.1 −3.38189
\(430\) 21.9922 0.00246641
\(431\) 16646.8 1.86044 0.930218 0.367006i \(-0.119617\pi\)
0.930218 + 0.367006i \(0.119617\pi\)
\(432\) −17402.1 −1.93810
\(433\) 15089.1 1.67468 0.837340 0.546682i \(-0.184109\pi\)
0.837340 + 0.546682i \(0.184109\pi\)
\(434\) −600.664 −0.0664350
\(435\) −176.061 −0.0194057
\(436\) −8126.97 −0.892686
\(437\) −6078.42 −0.665378
\(438\) 2224.69 0.242693
\(439\) −3777.24 −0.410656 −0.205328 0.978693i \(-0.565826\pi\)
−0.205328 + 0.978693i \(0.565826\pi\)
\(440\) 281.330 0.0304816
\(441\) −17836.1 −1.92593
\(442\) −1143.23 −0.123027
\(443\) 7992.65 0.857206 0.428603 0.903493i \(-0.359006\pi\)
0.428603 + 0.903493i \(0.359006\pi\)
\(444\) 5557.18 0.593991
\(445\) 734.507 0.0782449
\(446\) 918.288 0.0974937
\(447\) 15089.8 1.59670
\(448\) −2747.31 −0.289728
\(449\) 6433.54 0.676209 0.338104 0.941109i \(-0.390214\pi\)
0.338104 + 0.941109i \(0.390214\pi\)
\(450\) −3014.68 −0.315808
\(451\) −14055.6 −1.46752
\(452\) 1446.42 0.150518
\(453\) 1123.74 0.116552
\(454\) 1883.05 0.194661
\(455\) −200.795 −0.0206888
\(456\) −3923.43 −0.402919
\(457\) 6975.18 0.713972 0.356986 0.934110i \(-0.383804\pi\)
0.356986 + 0.934110i \(0.383804\pi\)
\(458\) 1383.08 0.141107
\(459\) −16107.9 −1.63802
\(460\) −482.755 −0.0489317
\(461\) −14758.9 −1.49109 −0.745543 0.666458i \(-0.767810\pi\)
−0.745543 + 0.666458i \(0.767810\pi\)
\(462\) 1536.12 0.154690
\(463\) −18951.2 −1.90224 −0.951121 0.308818i \(-0.900067\pi\)
−0.951121 + 0.308818i \(0.900067\pi\)
\(464\) 1737.44 0.173833
\(465\) 1433.35 0.142946
\(466\) −1654.93 −0.164513
\(467\) 12442.4 1.23290 0.616449 0.787395i \(-0.288571\pi\)
0.616449 + 0.787395i \(0.288571\pi\)
\(468\) 22763.9 2.24843
\(469\) 5186.91 0.510680
\(470\) −97.3338 −0.00955249
\(471\) 6961.22 0.681010
\(472\) 650.882 0.0634730
\(473\) −5280.33 −0.513297
\(474\) 1352.38 0.131048
\(475\) 8065.21 0.779068
\(476\) −2666.50 −0.256762
\(477\) 19191.1 1.84214
\(478\) −579.914 −0.0554909
\(479\) 12947.5 1.23504 0.617522 0.786554i \(-0.288137\pi\)
0.617522 + 0.786554i \(0.288137\pi\)
\(480\) −469.093 −0.0446064
\(481\) −3822.50 −0.362352
\(482\) −845.385 −0.0798885
\(483\) −5329.65 −0.502086
\(484\) −22988.0 −2.15890
\(485\) −529.041 −0.0495309
\(486\) −990.104 −0.0924116
\(487\) 9844.72 0.916030 0.458015 0.888944i \(-0.348561\pi\)
0.458015 + 0.888944i \(0.348561\pi\)
\(488\) 4758.14 0.441375
\(489\) −4971.77 −0.459778
\(490\) −83.0584 −0.00765754
\(491\) −6809.50 −0.625883 −0.312941 0.949772i \(-0.601314\pi\)
−0.312941 + 0.949772i \(0.601314\pi\)
\(492\) 15568.1 1.42655
\(493\) 1608.22 0.146918
\(494\) 1334.74 0.121564
\(495\) −2507.05 −0.227644
\(496\) −14144.9 −1.28049
\(497\) −2322.24 −0.209591
\(498\) −2666.54 −0.239940
\(499\) −15953.8 −1.43124 −0.715622 0.698488i \(-0.753857\pi\)
−0.715622 + 0.698488i \(0.753857\pi\)
\(500\) 1283.32 0.114783
\(501\) −4479.11 −0.399424
\(502\) 332.468 0.0295593
\(503\) −14582.7 −1.29267 −0.646334 0.763054i \(-0.723699\pi\)
−0.646334 + 0.763054i \(0.723699\pi\)
\(504\) −2352.83 −0.207943
\(505\) −902.511 −0.0795272
\(506\) −2540.35 −0.223186
\(507\) −2588.02 −0.226702
\(508\) −15653.5 −1.36715
\(509\) 20906.4 1.82055 0.910273 0.414008i \(-0.135871\pi\)
0.910273 + 0.414008i \(0.135871\pi\)
\(510\) −139.456 −0.0121083
\(511\) −3569.17 −0.308984
\(512\) 7771.61 0.670820
\(513\) 18806.1 1.61854
\(514\) −1849.09 −0.158677
\(515\) −416.887 −0.0356704
\(516\) 5848.52 0.498967
\(517\) 23369.8 1.98802
\(518\) 195.401 0.0165742
\(519\) 30220.6 2.55595
\(520\) 214.336 0.0180755
\(521\) −15131.7 −1.27242 −0.636212 0.771515i \(-0.719500\pi\)
−0.636212 + 0.771515i \(0.719500\pi\)
\(522\) 701.829 0.0588472
\(523\) 12146.9 1.01558 0.507790 0.861481i \(-0.330463\pi\)
0.507790 + 0.861481i \(0.330463\pi\)
\(524\) −4395.41 −0.366440
\(525\) 7071.70 0.587875
\(526\) −1580.31 −0.130998
\(527\) −13092.9 −1.08223
\(528\) 36173.7 2.98155
\(529\) −3353.12 −0.275592
\(530\) 89.3683 0.00732436
\(531\) −5800.28 −0.474032
\(532\) 3113.16 0.253708
\(533\) −10708.5 −0.870237
\(534\) −4281.02 −0.346925
\(535\) −118.862 −0.00960532
\(536\) −5536.70 −0.446174
\(537\) 5196.83 0.417616
\(538\) 1873.89 0.150166
\(539\) 19942.3 1.59365
\(540\) 1493.60 0.119027
\(541\) −22291.8 −1.77153 −0.885767 0.464130i \(-0.846367\pi\)
−0.885767 + 0.464130i \(0.846367\pi\)
\(542\) 1641.38 0.130080
\(543\) 13931.7 1.10104
\(544\) 4284.91 0.337709
\(545\) 681.904 0.0535955
\(546\) 1170.32 0.0917307
\(547\) −15439.4 −1.20684 −0.603421 0.797423i \(-0.706196\pi\)
−0.603421 + 0.797423i \(0.706196\pi\)
\(548\) 1960.94 0.152860
\(549\) −42401.8 −3.29629
\(550\) 3370.68 0.261321
\(551\) −1877.61 −0.145170
\(552\) 5689.07 0.438665
\(553\) −2169.69 −0.166844
\(554\) 918.557 0.0704436
\(555\) −466.283 −0.0356623
\(556\) 1896.39 0.144649
\(557\) 2336.99 0.177776 0.0888881 0.996042i \(-0.471669\pi\)
0.0888881 + 0.996042i \(0.471669\pi\)
\(558\) −5713.75 −0.433481
\(559\) −4022.90 −0.304384
\(560\) 241.713 0.0182397
\(561\) 33483.3 2.51991
\(562\) −1061.61 −0.0796824
\(563\) 19833.3 1.48468 0.742340 0.670023i \(-0.233716\pi\)
0.742340 + 0.670023i \(0.233716\pi\)
\(564\) −25884.6 −1.93251
\(565\) −121.364 −0.00903685
\(566\) −1602.71 −0.119023
\(567\) 6800.16 0.503668
\(568\) 2478.85 0.183116
\(569\) 11063.7 0.815141 0.407571 0.913174i \(-0.366376\pi\)
0.407571 + 0.913174i \(0.366376\pi\)
\(570\) 162.816 0.0119642
\(571\) −665.827 −0.0487986 −0.0243993 0.999702i \(-0.507767\pi\)
−0.0243993 + 0.999702i \(0.507767\pi\)
\(572\) −25452.1 −1.86050
\(573\) −41887.6 −3.05389
\(574\) 547.404 0.0398053
\(575\) −11694.8 −0.848184
\(576\) −26133.5 −1.89044
\(577\) −7165.21 −0.516970 −0.258485 0.966015i \(-0.583223\pi\)
−0.258485 + 0.966015i \(0.583223\pi\)
\(578\) −761.179 −0.0547766
\(579\) 27128.7 1.94720
\(580\) −149.122 −0.0106758
\(581\) 4278.06 0.305480
\(582\) 3083.47 0.219612
\(583\) −21457.3 −1.52431
\(584\) 3809.87 0.269955
\(585\) −1910.04 −0.134992
\(586\) −1608.73 −0.113406
\(587\) −10375.2 −0.729525 −0.364763 0.931101i \(-0.618850\pi\)
−0.364763 + 0.931101i \(0.618850\pi\)
\(588\) −22088.2 −1.54915
\(589\) 15286.0 1.06936
\(590\) −27.0105 −0.00188476
\(591\) −24790.6 −1.72546
\(592\) 4601.46 0.319457
\(593\) 18931.5 1.31100 0.655501 0.755194i \(-0.272458\pi\)
0.655501 + 0.755194i \(0.272458\pi\)
\(594\) 7859.60 0.542901
\(595\) 223.736 0.0154156
\(596\) 12780.9 0.878401
\(597\) 5992.71 0.410829
\(598\) −1935.40 −0.132349
\(599\) −12244.2 −0.835199 −0.417600 0.908631i \(-0.637129\pi\)
−0.417600 + 0.908631i \(0.637129\pi\)
\(600\) −7548.60 −0.513617
\(601\) 15596.9 1.05859 0.529293 0.848439i \(-0.322457\pi\)
0.529293 + 0.848439i \(0.322457\pi\)
\(602\) 205.645 0.0139227
\(603\) 49339.9 3.33213
\(604\) 951.796 0.0641192
\(605\) 1928.84 0.129617
\(606\) 5260.22 0.352610
\(607\) −10155.5 −0.679076 −0.339538 0.940592i \(-0.610271\pi\)
−0.339538 + 0.940592i \(0.610271\pi\)
\(608\) −5002.67 −0.333692
\(609\) −1646.32 −0.109544
\(610\) −197.455 −0.0131061
\(611\) 17804.7 1.17889
\(612\) −25364.8 −1.67534
\(613\) −6227.67 −0.410331 −0.205166 0.978727i \(-0.565773\pi\)
−0.205166 + 0.978727i \(0.565773\pi\)
\(614\) −167.015 −0.0109775
\(615\) −1306.26 −0.0856479
\(616\) 2630.67 0.172066
\(617\) 14357.5 0.936808 0.468404 0.883514i \(-0.344829\pi\)
0.468404 + 0.883514i \(0.344829\pi\)
\(618\) 2429.80 0.158156
\(619\) −13220.6 −0.858453 −0.429227 0.903197i \(-0.641214\pi\)
−0.429227 + 0.903197i \(0.641214\pi\)
\(620\) 1214.03 0.0786400
\(621\) −27269.3 −1.76213
\(622\) −2004.26 −0.129202
\(623\) 6868.26 0.441687
\(624\) 27559.5 1.76805
\(625\) 15463.4 0.989657
\(626\) −3539.16 −0.225963
\(627\) −39092.1 −2.48993
\(628\) 5896.08 0.374649
\(629\) 4259.23 0.269995
\(630\) 97.6387 0.00617463
\(631\) 1828.97 0.115389 0.0576943 0.998334i \(-0.481625\pi\)
0.0576943 + 0.998334i \(0.481625\pi\)
\(632\) 2316.01 0.145769
\(633\) 45747.1 2.87249
\(634\) −734.426 −0.0460059
\(635\) 1313.43 0.0820817
\(636\) 23766.3 1.48175
\(637\) 15193.4 0.945028
\(638\) −784.707 −0.0486941
\(639\) −22090.0 −1.36756
\(640\) −527.723 −0.0325939
\(641\) −22644.1 −1.39530 −0.697651 0.716437i \(-0.745772\pi\)
−0.697651 + 0.716437i \(0.745772\pi\)
\(642\) 692.778 0.0425884
\(643\) 22728.4 1.39397 0.696983 0.717088i \(-0.254525\pi\)
0.696983 + 0.717088i \(0.254525\pi\)
\(644\) −4514.16 −0.276216
\(645\) −490.728 −0.0299572
\(646\) −1487.23 −0.0905796
\(647\) −5844.85 −0.355154 −0.177577 0.984107i \(-0.556826\pi\)
−0.177577 + 0.984107i \(0.556826\pi\)
\(648\) −7258.74 −0.440047
\(649\) 6485.23 0.392246
\(650\) 2568.01 0.154962
\(651\) 13403.0 0.806922
\(652\) −4211.04 −0.252941
\(653\) 15174.1 0.909355 0.454677 0.890656i \(-0.349755\pi\)
0.454677 + 0.890656i \(0.349755\pi\)
\(654\) −3974.43 −0.237634
\(655\) 368.803 0.0220005
\(656\) 12890.7 0.767221
\(657\) −33951.4 −2.01609
\(658\) −910.152 −0.0539231
\(659\) −27857.0 −1.64667 −0.823333 0.567558i \(-0.807888\pi\)
−0.823333 + 0.567558i \(0.807888\pi\)
\(660\) −3104.74 −0.183109
\(661\) −4966.64 −0.292254 −0.146127 0.989266i \(-0.546681\pi\)
−0.146127 + 0.989266i \(0.546681\pi\)
\(662\) 332.148 0.0195004
\(663\) 25509.8 1.49430
\(664\) −4566.56 −0.266893
\(665\) −261.214 −0.0152322
\(666\) 1858.74 0.108145
\(667\) 2722.59 0.158049
\(668\) −3793.76 −0.219738
\(669\) −20490.4 −1.18416
\(670\) 229.764 0.0132486
\(671\) 47409.0 2.72758
\(672\) −4386.41 −0.251800
\(673\) −2338.02 −0.133914 −0.0669569 0.997756i \(-0.521329\pi\)
−0.0669569 + 0.997756i \(0.521329\pi\)
\(674\) 3393.75 0.193950
\(675\) 36182.6 2.06321
\(676\) −2192.03 −0.124717
\(677\) 6342.30 0.360051 0.180025 0.983662i \(-0.442382\pi\)
0.180025 + 0.983662i \(0.442382\pi\)
\(678\) 707.361 0.0400679
\(679\) −4946.97 −0.279598
\(680\) −238.824 −0.0134684
\(681\) −42017.9 −2.36436
\(682\) 6388.48 0.358691
\(683\) −30366.6 −1.70124 −0.850620 0.525780i \(-0.823773\pi\)
−0.850620 + 0.525780i \(0.823773\pi\)
\(684\) 29613.6 1.65542
\(685\) −164.535 −0.00917746
\(686\) −1649.31 −0.0917944
\(687\) −30861.6 −1.71389
\(688\) 4842.69 0.268352
\(689\) −16347.6 −0.903910
\(690\) −236.087 −0.0130256
\(691\) −11826.5 −0.651089 −0.325545 0.945527i \(-0.605548\pi\)
−0.325545 + 0.945527i \(0.605548\pi\)
\(692\) 25596.6 1.40612
\(693\) −23443.0 −1.28503
\(694\) −4521.12 −0.247290
\(695\) −159.119 −0.00868450
\(696\) 1757.34 0.0957067
\(697\) 11932.0 0.648429
\(698\) 2774.33 0.150444
\(699\) 36927.6 1.99818
\(700\) 5989.66 0.323411
\(701\) −2776.33 −0.149587 −0.0747936 0.997199i \(-0.523830\pi\)
−0.0747936 + 0.997199i \(0.523830\pi\)
\(702\) 5987.96 0.321939
\(703\) −4972.69 −0.266783
\(704\) 29219.5 1.56428
\(705\) 2171.88 0.116025
\(706\) −1559.45 −0.0831310
\(707\) −8439.23 −0.448925
\(708\) −7183.08 −0.381295
\(709\) −15962.7 −0.845543 −0.422772 0.906236i \(-0.638943\pi\)
−0.422772 + 0.906236i \(0.638943\pi\)
\(710\) −102.868 −0.00543742
\(711\) −20638.9 −1.08864
\(712\) −7331.44 −0.385895
\(713\) −22165.2 −1.16422
\(714\) −1304.03 −0.0683502
\(715\) 2135.59 0.111702
\(716\) 4401.66 0.229746
\(717\) 12940.0 0.673994
\(718\) 2724.34 0.141604
\(719\) −20832.9 −1.08058 −0.540289 0.841480i \(-0.681685\pi\)
−0.540289 + 0.841480i \(0.681685\pi\)
\(720\) 2299.27 0.119012
\(721\) −3898.24 −0.201357
\(722\) −1104.73 −0.0569445
\(723\) 18863.7 0.970329
\(724\) 11800.0 0.605722
\(725\) −3612.49 −0.185054
\(726\) −11242.1 −0.574700
\(727\) 4452.04 0.227121 0.113561 0.993531i \(-0.463774\pi\)
0.113561 + 0.993531i \(0.463774\pi\)
\(728\) 2004.22 0.102035
\(729\) −7799.67 −0.396264
\(730\) −158.104 −0.00801599
\(731\) 4482.52 0.226802
\(732\) −52510.4 −2.65142
\(733\) −12107.2 −0.610082 −0.305041 0.952339i \(-0.598670\pi\)
−0.305041 + 0.952339i \(0.598670\pi\)
\(734\) 942.034 0.0473721
\(735\) 1853.34 0.0930088
\(736\) 7254.00 0.363296
\(737\) −55166.4 −2.75723
\(738\) 5207.12 0.259725
\(739\) −4506.27 −0.224311 −0.112156 0.993691i \(-0.535775\pi\)
−0.112156 + 0.993691i \(0.535775\pi\)
\(740\) −394.937 −0.0196191
\(741\) −29782.9 −1.47652
\(742\) 835.669 0.0413455
\(743\) 1177.19 0.0581253 0.0290626 0.999578i \(-0.490748\pi\)
0.0290626 + 0.999578i \(0.490748\pi\)
\(744\) −14306.9 −0.704996
\(745\) −1072.40 −0.0527378
\(746\) 532.239 0.0261215
\(747\) 40694.6 1.99322
\(748\) 28360.1 1.38629
\(749\) −1111.46 −0.0542214
\(750\) 627.595 0.0305554
\(751\) 27631.6 1.34260 0.671300 0.741186i \(-0.265736\pi\)
0.671300 + 0.741186i \(0.265736\pi\)
\(752\) −21432.9 −1.03933
\(753\) −7418.59 −0.359028
\(754\) −597.841 −0.0288755
\(755\) −79.8616 −0.00384962
\(756\) 13966.4 0.671896
\(757\) 11336.6 0.544300 0.272150 0.962255i \(-0.412265\pi\)
0.272150 + 0.962255i \(0.412265\pi\)
\(758\) 72.3984 0.00346917
\(759\) 56684.6 2.71083
\(760\) 278.829 0.0133082
\(761\) 4356.58 0.207524 0.103762 0.994602i \(-0.466912\pi\)
0.103762 + 0.994602i \(0.466912\pi\)
\(762\) −7655.23 −0.363937
\(763\) 6376.37 0.302543
\(764\) −35478.4 −1.68006
\(765\) 2128.26 0.100585
\(766\) −2302.46 −0.108605
\(767\) 4940.87 0.232601
\(768\) −29997.2 −1.40942
\(769\) −21718.1 −1.01843 −0.509217 0.860638i \(-0.670065\pi\)
−0.509217 + 0.860638i \(0.670065\pi\)
\(770\) −109.169 −0.00510931
\(771\) 41260.0 1.92729
\(772\) 22977.8 1.07123
\(773\) 22688.4 1.05568 0.527842 0.849343i \(-0.323001\pi\)
0.527842 + 0.849343i \(0.323001\pi\)
\(774\) 1956.18 0.0908442
\(775\) 29410.1 1.36315
\(776\) 5280.58 0.244281
\(777\) −4360.13 −0.201311
\(778\) −1058.75 −0.0487893
\(779\) −13930.7 −0.640716
\(780\) −2365.39 −0.108583
\(781\) 24698.6 1.13161
\(782\) 2156.53 0.0986155
\(783\) −8423.43 −0.384456
\(784\) −18289.5 −0.833158
\(785\) −494.718 −0.0224933
\(786\) −2149.54 −0.0975465
\(787\) −32890.9 −1.48975 −0.744875 0.667204i \(-0.767491\pi\)
−0.744875 + 0.667204i \(0.767491\pi\)
\(788\) −20997.4 −0.949239
\(789\) 35262.6 1.59111
\(790\) −96.1107 −0.00432844
\(791\) −1134.85 −0.0510123
\(792\) 25024.0 1.12271
\(793\) 36119.3 1.61744
\(794\) 2455.16 0.109736
\(795\) −1994.14 −0.0889620
\(796\) 5075.76 0.226012
\(797\) 30404.1 1.35128 0.675638 0.737233i \(-0.263868\pi\)
0.675638 + 0.737233i \(0.263868\pi\)
\(798\) 1522.46 0.0675372
\(799\) −19838.9 −0.878410
\(800\) −9625.04 −0.425371
\(801\) 65333.5 2.88196
\(802\) 1966.68 0.0865909
\(803\) 37960.7 1.66825
\(804\) 61102.6 2.68025
\(805\) 378.767 0.0165836
\(806\) 4867.16 0.212703
\(807\) −41813.5 −1.82392
\(808\) 9008.36 0.392219
\(809\) −37889.3 −1.64662 −0.823311 0.567591i \(-0.807876\pi\)
−0.823311 + 0.567591i \(0.807876\pi\)
\(810\) 301.226 0.0130667
\(811\) −8123.23 −0.351720 −0.175860 0.984415i \(-0.556271\pi\)
−0.175860 + 0.984415i \(0.556271\pi\)
\(812\) −1394.41 −0.0602640
\(813\) −36625.3 −1.57996
\(814\) −2078.23 −0.0894864
\(815\) 353.333 0.0151862
\(816\) −30708.2 −1.31741
\(817\) −5233.39 −0.224104
\(818\) 2153.99 0.0920690
\(819\) −17860.4 −0.762020
\(820\) −1106.39 −0.0471180
\(821\) 13226.8 0.562264 0.281132 0.959669i \(-0.409290\pi\)
0.281132 + 0.959669i \(0.409290\pi\)
\(822\) 958.981 0.0406914
\(823\) −29575.2 −1.25265 −0.626323 0.779563i \(-0.715441\pi\)
−0.626323 + 0.779563i \(0.715441\pi\)
\(824\) 4161.13 0.175922
\(825\) −75212.5 −3.17401
\(826\) −252.571 −0.0106393
\(827\) −36661.2 −1.54152 −0.770758 0.637128i \(-0.780122\pi\)
−0.770758 + 0.637128i \(0.780122\pi\)
\(828\) −42940.5 −1.80228
\(829\) 11277.0 0.472455 0.236228 0.971698i \(-0.424089\pi\)
0.236228 + 0.971698i \(0.424089\pi\)
\(830\) 189.505 0.00792507
\(831\) −20496.4 −0.855611
\(832\) 22261.3 0.927612
\(833\) −16929.2 −0.704158
\(834\) 927.413 0.0385056
\(835\) 318.320 0.0131927
\(836\) −33110.6 −1.36980
\(837\) 68577.0 2.83198
\(838\) −2661.56 −0.109716
\(839\) −18965.7 −0.780417 −0.390208 0.920727i \(-0.627597\pi\)
−0.390208 + 0.920727i \(0.627597\pi\)
\(840\) 244.482 0.0100422
\(841\) 841.000 0.0344828
\(842\) 4157.72 0.170172
\(843\) 23688.5 0.967825
\(844\) 38747.3 1.58026
\(845\) 183.925 0.00748781
\(846\) −8657.72 −0.351842
\(847\) 18036.2 0.731679
\(848\) 19678.9 0.796908
\(849\) 35762.5 1.44566
\(850\) −2861.41 −0.115465
\(851\) 7210.54 0.290451
\(852\) −27356.3 −1.10002
\(853\) 8067.23 0.323818 0.161909 0.986806i \(-0.448235\pi\)
0.161909 + 0.986806i \(0.448235\pi\)
\(854\) −1846.37 −0.0739830
\(855\) −2484.77 −0.0993886
\(856\) 1186.41 0.0473724
\(857\) 15281.7 0.609118 0.304559 0.952493i \(-0.401491\pi\)
0.304559 + 0.952493i \(0.401491\pi\)
\(858\) −12447.1 −0.495266
\(859\) −36789.1 −1.46127 −0.730634 0.682770i \(-0.760775\pi\)
−0.730634 + 0.682770i \(0.760775\pi\)
\(860\) −415.641 −0.0164805
\(861\) −12214.6 −0.483476
\(862\) 6895.33 0.272455
\(863\) 40907.8 1.61358 0.806788 0.590840i \(-0.201204\pi\)
0.806788 + 0.590840i \(0.201204\pi\)
\(864\) −22443.2 −0.883719
\(865\) −2147.71 −0.0844213
\(866\) 6250.12 0.245251
\(867\) 16984.7 0.665319
\(868\) 11352.2 0.443917
\(869\) 23076.2 0.900812
\(870\) −72.9268 −0.00284190
\(871\) −42029.4 −1.63503
\(872\) −6806.38 −0.264327
\(873\) −47057.5 −1.82435
\(874\) −2517.76 −0.0974424
\(875\) −1006.88 −0.0389015
\(876\) −42045.4 −1.62167
\(877\) 2391.60 0.0920852 0.0460426 0.998939i \(-0.485339\pi\)
0.0460426 + 0.998939i \(0.485339\pi\)
\(878\) −1564.59 −0.0601392
\(879\) 35896.8 1.37744
\(880\) −2570.79 −0.0984786
\(881\) 5487.72 0.209859 0.104930 0.994480i \(-0.466538\pi\)
0.104930 + 0.994480i \(0.466538\pi\)
\(882\) −7387.94 −0.282046
\(883\) 170.008 0.00647931 0.00323966 0.999995i \(-0.498969\pi\)
0.00323966 + 0.999995i \(0.498969\pi\)
\(884\) 21606.6 0.822067
\(885\) 602.705 0.0228923
\(886\) 3310.66 0.125535
\(887\) 25867.3 0.979188 0.489594 0.871950i \(-0.337145\pi\)
0.489594 + 0.871950i \(0.337145\pi\)
\(888\) 4654.17 0.175883
\(889\) 12281.7 0.463345
\(890\) 304.243 0.0114587
\(891\) −72324.4 −2.71937
\(892\) −17355.2 −0.651451
\(893\) 23162.1 0.867961
\(894\) 6250.40 0.233831
\(895\) −369.327 −0.0137936
\(896\) −4934.65 −0.183990
\(897\) 43186.0 1.60751
\(898\) 2664.86 0.0990285
\(899\) −6846.77 −0.254007
\(900\) 56976.0 2.11022
\(901\) 18215.4 0.673520
\(902\) −5822.03 −0.214914
\(903\) −4588.71 −0.169106
\(904\) 1211.39 0.0445687
\(905\) −990.093 −0.0363666
\(906\) 465.468 0.0170686
\(907\) 11411.5 0.417765 0.208882 0.977941i \(-0.433017\pi\)
0.208882 + 0.977941i \(0.433017\pi\)
\(908\) −35588.7 −1.30072
\(909\) −80277.3 −2.92919
\(910\) −83.1719 −0.00302980
\(911\) −38718.5 −1.40813 −0.704063 0.710138i \(-0.748633\pi\)
−0.704063 + 0.710138i \(0.748633\pi\)
\(912\) 35852.1 1.30174
\(913\) −45500.1 −1.64933
\(914\) 2889.21 0.104559
\(915\) 4405.96 0.159187
\(916\) −26139.5 −0.942875
\(917\) 3448.62 0.124191
\(918\) −6672.10 −0.239882
\(919\) −48465.3 −1.73963 −0.869817 0.493374i \(-0.835763\pi\)
−0.869817 + 0.493374i \(0.835763\pi\)
\(920\) −404.310 −0.0144888
\(921\) 3726.72 0.133333
\(922\) −6113.34 −0.218364
\(923\) 18817.0 0.671040
\(924\) −29031.9 −1.03364
\(925\) −9567.37 −0.340079
\(926\) −7849.85 −0.278577
\(927\) −37081.6 −1.31383
\(928\) 2240.74 0.0792630
\(929\) 10560.1 0.372946 0.186473 0.982460i \(-0.440294\pi\)
0.186473 + 0.982460i \(0.440294\pi\)
\(930\) 593.714 0.0209340
\(931\) 19765.0 0.695782
\(932\) 31277.3 1.09927
\(933\) 44722.4 1.56929
\(934\) 5153.79 0.180554
\(935\) −2379.59 −0.0832309
\(936\) 19064.9 0.665765
\(937\) −23025.0 −0.802769 −0.401384 0.915910i \(-0.631471\pi\)
−0.401384 + 0.915910i \(0.631471\pi\)
\(938\) 2148.49 0.0747874
\(939\) 78971.7 2.74456
\(940\) 1839.56 0.0638296
\(941\) 40778.1 1.41268 0.706338 0.707874i \(-0.250346\pi\)
0.706338 + 0.707874i \(0.250346\pi\)
\(942\) 2883.43 0.0997317
\(943\) 20199.8 0.697558
\(944\) −5947.74 −0.205066
\(945\) −1171.87 −0.0403396
\(946\) −2187.18 −0.0751707
\(947\) 36129.8 1.23977 0.619884 0.784693i \(-0.287179\pi\)
0.619884 + 0.784693i \(0.287179\pi\)
\(948\) −25559.3 −0.875662
\(949\) 28920.9 0.989265
\(950\) 3340.72 0.114092
\(951\) 16387.8 0.558790
\(952\) −2233.21 −0.0760280
\(953\) 20831.4 0.708075 0.354037 0.935231i \(-0.384809\pi\)
0.354037 + 0.935231i \(0.384809\pi\)
\(954\) 7949.21 0.269775
\(955\) 2976.86 0.100868
\(956\) 10960.1 0.370789
\(957\) 17509.7 0.591441
\(958\) 5363.02 0.180868
\(959\) −1538.54 −0.0518061
\(960\) 2715.52 0.0912948
\(961\) 25950.1 0.871071
\(962\) −1583.33 −0.0530652
\(963\) −10572.6 −0.353788
\(964\) 15977.4 0.533813
\(965\) −1927.98 −0.0643149
\(966\) −2207.61 −0.0735288
\(967\) 49242.5 1.63757 0.818785 0.574100i \(-0.194648\pi\)
0.818785 + 0.574100i \(0.194648\pi\)
\(968\) −19252.5 −0.639256
\(969\) 33185.7 1.10018
\(970\) −219.136 −0.00725363
\(971\) −2352.05 −0.0777351 −0.0388675 0.999244i \(-0.512375\pi\)
−0.0388675 + 0.999244i \(0.512375\pi\)
\(972\) 18712.5 0.617493
\(973\) −1487.89 −0.0490233
\(974\) 4077.82 0.134150
\(975\) −57301.8 −1.88218
\(976\) −43479.7 −1.42598
\(977\) 18768.3 0.614588 0.307294 0.951615i \(-0.400577\pi\)
0.307294 + 0.951615i \(0.400577\pi\)
\(978\) −2059.38 −0.0673329
\(979\) −73048.7 −2.38473
\(980\) 1569.76 0.0511675
\(981\) 60654.5 1.97406
\(982\) −2820.59 −0.0916584
\(983\) −49014.5 −1.59036 −0.795179 0.606375i \(-0.792623\pi\)
−0.795179 + 0.606375i \(0.792623\pi\)
\(984\) 13038.4 0.422406
\(985\) 1761.81 0.0569908
\(986\) 666.146 0.0215156
\(987\) 20308.9 0.654953
\(988\) −25225.8 −0.812288
\(989\) 7588.55 0.243986
\(990\) −1038.46 −0.0333377
\(991\) −48860.6 −1.56620 −0.783102 0.621893i \(-0.786364\pi\)
−0.783102 + 0.621893i \(0.786364\pi\)
\(992\) −18242.4 −0.583868
\(993\) −7411.44 −0.236853
\(994\) −961.903 −0.0306939
\(995\) −425.888 −0.0135694
\(996\) 50396.2 1.60328
\(997\) 2934.57 0.0932184 0.0466092 0.998913i \(-0.485158\pi\)
0.0466092 + 0.998913i \(0.485158\pi\)
\(998\) −6608.29 −0.209601
\(999\) −22308.7 −0.706524
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 29.4.a.a.1.2 2
3.2 odd 2 261.4.a.b.1.1 2
4.3 odd 2 464.4.a.f.1.2 2
5.4 even 2 725.4.a.b.1.1 2
7.6 odd 2 1421.4.a.c.1.2 2
8.3 odd 2 1856.4.a.h.1.1 2
8.5 even 2 1856.4.a.n.1.2 2
29.28 even 2 841.4.a.a.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
29.4.a.a.1.2 2 1.1 even 1 trivial
261.4.a.b.1.1 2 3.2 odd 2
464.4.a.f.1.2 2 4.3 odd 2
725.4.a.b.1.1 2 5.4 even 2
841.4.a.a.1.1 2 29.28 even 2
1421.4.a.c.1.2 2 7.6 odd 2
1856.4.a.h.1.1 2 8.3 odd 2
1856.4.a.n.1.2 2 8.5 even 2