Properties

Label 177.4.a.b.1.1
Level $177$
Weight $4$
Character 177.1
Self dual yes
Analytic conductor $10.443$
Analytic rank $1$
Dimension $7$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(10.4433380710\)
Analytic rank: \(1\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
Defining polynomial: \(x^{7} - 41 x^{5} - 7 x^{4} + 484 x^{3} + 63 x^{2} - 1736 x - 44\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(5.07078\) of defining polynomial
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-5.07078 q^{2} -3.00000 q^{3} +17.7128 q^{4} +5.77165 q^{5} +15.2123 q^{6} -31.1296 q^{7} -49.2517 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q-5.07078 q^{2} -3.00000 q^{3} +17.7128 q^{4} +5.77165 q^{5} +15.2123 q^{6} -31.1296 q^{7} -49.2517 q^{8} +9.00000 q^{9} -29.2668 q^{10} +52.2494 q^{11} -53.1385 q^{12} -16.2393 q^{13} +157.851 q^{14} -17.3150 q^{15} +108.042 q^{16} +102.687 q^{17} -45.6370 q^{18} +46.2494 q^{19} +102.232 q^{20} +93.3888 q^{21} -264.945 q^{22} -99.1068 q^{23} +147.755 q^{24} -91.6880 q^{25} +82.3459 q^{26} -27.0000 q^{27} -551.394 q^{28} -119.005 q^{29} +87.8004 q^{30} +20.2372 q^{31} -153.844 q^{32} -156.748 q^{33} -520.703 q^{34} -179.669 q^{35} +159.416 q^{36} +117.880 q^{37} -234.521 q^{38} +48.7179 q^{39} -284.264 q^{40} -278.005 q^{41} -473.554 q^{42} -484.571 q^{43} +925.485 q^{44} +51.9449 q^{45} +502.549 q^{46} -347.541 q^{47} -324.126 q^{48} +626.051 q^{49} +464.930 q^{50} -308.061 q^{51} -287.644 q^{52} +161.039 q^{53} +136.911 q^{54} +301.565 q^{55} +1533.19 q^{56} -138.748 q^{57} +603.449 q^{58} +59.0000 q^{59} -306.697 q^{60} -845.543 q^{61} -102.618 q^{62} -280.166 q^{63} -84.2264 q^{64} -93.7275 q^{65} +794.836 q^{66} -740.885 q^{67} +1818.88 q^{68} +297.320 q^{69} +911.063 q^{70} -738.136 q^{71} -443.265 q^{72} +539.769 q^{73} -597.743 q^{74} +275.064 q^{75} +819.208 q^{76} -1626.50 q^{77} -247.038 q^{78} -412.312 q^{79} +623.581 q^{80} +81.0000 q^{81} +1409.70 q^{82} -75.5904 q^{83} +1654.18 q^{84} +592.673 q^{85} +2457.15 q^{86} +357.016 q^{87} -2573.37 q^{88} +163.421 q^{89} -263.401 q^{90} +505.523 q^{91} -1755.46 q^{92} -60.7116 q^{93} +1762.31 q^{94} +266.935 q^{95} +461.532 q^{96} +857.136 q^{97} -3174.57 q^{98} +470.244 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q - 21q^{3} + 26q^{4} - 2q^{5} - 59q^{7} - 21q^{8} + 63q^{9} + O(q^{10}) \) \( 7q - 21q^{3} + 26q^{4} - 2q^{5} - 59q^{7} - 21q^{8} + 63q^{9} - 71q^{10} - 5q^{11} - 78q^{12} - 67q^{13} - 65q^{14} + 6q^{15} - 94q^{16} - 23q^{17} - 176q^{19} - 207q^{20} + 177q^{21} - 704q^{22} - 218q^{23} + 63q^{24} - 183q^{25} + 58q^{26} - 189q^{27} - 938q^{28} + 168q^{29} + 213q^{30} - 604q^{31} - 448q^{32} + 15q^{33} - 610q^{34} - 336q^{35} + 234q^{36} - 505q^{37} - 453q^{38} + 201q^{39} - 1080q^{40} - 265q^{41} + 195q^{42} - 493q^{43} + 504q^{44} - 18q^{45} + 381q^{46} - 244q^{47} + 282q^{48} + 770q^{49} + 1639q^{50} + 69q^{51} + 160q^{52} + 686q^{53} - 116q^{55} + 2190q^{56} + 528q^{57} + 1584q^{58} + 413q^{59} + 621q^{60} - 838q^{61} + 286q^{62} - 531q^{63} + 205q^{64} + 490q^{65} + 2112q^{66} - 1504q^{67} + 3047q^{68} + 654q^{69} + 1530q^{70} - 1267q^{71} - 189q^{72} - 666q^{73} + 528q^{74} + 549q^{75} - 64q^{76} + 1109q^{77} - 174q^{78} - 2741q^{79} + 1213q^{80} + 567q^{81} + 953q^{82} - 2025q^{83} + 2814q^{84} - 1274q^{85} + 4394q^{86} - 504q^{87} - 1639q^{88} + 616q^{89} - 639q^{90} - 2415q^{91} + 218q^{92} + 1812q^{93} + 900q^{94} + 2554q^{95} + 1344q^{96} - 1298q^{97} - 172q^{98} - 45q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.07078 −1.79279 −0.896396 0.443253i \(-0.853824\pi\)
−0.896396 + 0.443253i \(0.853824\pi\)
\(3\) −3.00000 −0.577350
\(4\) 17.7128 2.21411
\(5\) 5.77165 0.516232 0.258116 0.966114i \(-0.416898\pi\)
0.258116 + 0.966114i \(0.416898\pi\)
\(6\) 15.2123 1.03507
\(7\) −31.1296 −1.68084 −0.840420 0.541936i \(-0.817692\pi\)
−0.840420 + 0.541936i \(0.817692\pi\)
\(8\) −49.2517 −2.17664
\(9\) 9.00000 0.333333
\(10\) −29.2668 −0.925497
\(11\) 52.2494 1.43216 0.716081 0.698018i \(-0.245934\pi\)
0.716081 + 0.698018i \(0.245934\pi\)
\(12\) −53.1385 −1.27831
\(13\) −16.2393 −0.346459 −0.173230 0.984881i \(-0.555420\pi\)
−0.173230 + 0.984881i \(0.555420\pi\)
\(14\) 157.851 3.01340
\(15\) −17.3150 −0.298047
\(16\) 108.042 1.68816
\(17\) 102.687 1.46501 0.732507 0.680760i \(-0.238350\pi\)
0.732507 + 0.680760i \(0.238350\pi\)
\(18\) −45.6370 −0.597598
\(19\) 46.2494 0.558439 0.279219 0.960227i \(-0.409924\pi\)
0.279219 + 0.960227i \(0.409924\pi\)
\(20\) 102.232 1.14299
\(21\) 93.3888 0.970433
\(22\) −264.945 −2.56757
\(23\) −99.1068 −0.898487 −0.449243 0.893409i \(-0.648306\pi\)
−0.449243 + 0.893409i \(0.648306\pi\)
\(24\) 147.755 1.25668
\(25\) −91.6880 −0.733504
\(26\) 82.3459 0.621129
\(27\) −27.0000 −0.192450
\(28\) −551.394 −3.72156
\(29\) −119.005 −0.762024 −0.381012 0.924570i \(-0.624424\pi\)
−0.381012 + 0.924570i \(0.624424\pi\)
\(30\) 87.8004 0.534336
\(31\) 20.2372 0.117249 0.0586243 0.998280i \(-0.481329\pi\)
0.0586243 + 0.998280i \(0.481329\pi\)
\(32\) −153.844 −0.849877
\(33\) −156.748 −0.826859
\(34\) −520.703 −2.62647
\(35\) −179.669 −0.867704
\(36\) 159.416 0.738035
\(37\) 117.880 0.523766 0.261883 0.965100i \(-0.415657\pi\)
0.261883 + 0.965100i \(0.415657\pi\)
\(38\) −234.521 −1.00117
\(39\) 48.7179 0.200028
\(40\) −284.264 −1.12365
\(41\) −278.005 −1.05895 −0.529476 0.848325i \(-0.677611\pi\)
−0.529476 + 0.848325i \(0.677611\pi\)
\(42\) −473.554 −1.73979
\(43\) −484.571 −1.71852 −0.859260 0.511539i \(-0.829076\pi\)
−0.859260 + 0.511539i \(0.829076\pi\)
\(44\) 925.485 3.17096
\(45\) 51.9449 0.172077
\(46\) 502.549 1.61080
\(47\) −347.541 −1.07860 −0.539299 0.842114i \(-0.681311\pi\)
−0.539299 + 0.842114i \(0.681311\pi\)
\(48\) −324.126 −0.974658
\(49\) 626.051 1.82522
\(50\) 464.930 1.31502
\(51\) −308.061 −0.845826
\(52\) −287.644 −0.767097
\(53\) 161.039 0.417367 0.208684 0.977983i \(-0.433082\pi\)
0.208684 + 0.977983i \(0.433082\pi\)
\(54\) 136.911 0.345023
\(55\) 301.565 0.739328
\(56\) 1533.19 3.65858
\(57\) −138.748 −0.322415
\(58\) 603.449 1.36615
\(59\) 59.0000 0.130189
\(60\) −306.697 −0.659907
\(61\) −845.543 −1.77477 −0.887383 0.461033i \(-0.847479\pi\)
−0.887383 + 0.461033i \(0.847479\pi\)
\(62\) −102.618 −0.210203
\(63\) −280.166 −0.560280
\(64\) −84.2264 −0.164505
\(65\) −93.7275 −0.178853
\(66\) 794.836 1.48239
\(67\) −740.885 −1.35095 −0.675474 0.737384i \(-0.736061\pi\)
−0.675474 + 0.737384i \(0.736061\pi\)
\(68\) 1818.88 3.24369
\(69\) 297.320 0.518742
\(70\) 911.063 1.55561
\(71\) −738.136 −1.23381 −0.616906 0.787037i \(-0.711614\pi\)
−0.616906 + 0.787037i \(0.711614\pi\)
\(72\) −443.265 −0.725546
\(73\) 539.769 0.865413 0.432706 0.901535i \(-0.357559\pi\)
0.432706 + 0.901535i \(0.357559\pi\)
\(74\) −597.743 −0.939003
\(75\) 275.064 0.423489
\(76\) 819.208 1.23644
\(77\) −1626.50 −2.40723
\(78\) −247.038 −0.358609
\(79\) −412.312 −0.587199 −0.293599 0.955929i \(-0.594853\pi\)
−0.293599 + 0.955929i \(0.594853\pi\)
\(80\) 623.581 0.871481
\(81\) 81.0000 0.111111
\(82\) 1409.70 1.89848
\(83\) −75.5904 −0.0999654 −0.0499827 0.998750i \(-0.515917\pi\)
−0.0499827 + 0.998750i \(0.515917\pi\)
\(84\) 1654.18 2.14864
\(85\) 592.673 0.756287
\(86\) 2457.15 3.08095
\(87\) 357.016 0.439955
\(88\) −2573.37 −3.11730
\(89\) 163.421 0.194635 0.0973177 0.995253i \(-0.468974\pi\)
0.0973177 + 0.995253i \(0.468974\pi\)
\(90\) −263.401 −0.308499
\(91\) 505.523 0.582342
\(92\) −1755.46 −1.98934
\(93\) −60.7116 −0.0676936
\(94\) 1762.31 1.93370
\(95\) 266.935 0.288284
\(96\) 461.532 0.490676
\(97\) 857.136 0.897205 0.448603 0.893731i \(-0.351922\pi\)
0.448603 + 0.893731i \(0.351922\pi\)
\(98\) −3174.57 −3.27225
\(99\) 470.244 0.477387
\(100\) −1624.06 −1.62406
\(101\) 1635.06 1.61083 0.805417 0.592708i \(-0.201941\pi\)
0.805417 + 0.592708i \(0.201941\pi\)
\(102\) 1562.11 1.51639
\(103\) −127.175 −0.121659 −0.0608296 0.998148i \(-0.519375\pi\)
−0.0608296 + 0.998148i \(0.519375\pi\)
\(104\) 799.813 0.754117
\(105\) 539.008 0.500969
\(106\) −816.596 −0.748253
\(107\) −1769.35 −1.59859 −0.799296 0.600938i \(-0.794794\pi\)
−0.799296 + 0.600938i \(0.794794\pi\)
\(108\) −478.247 −0.426105
\(109\) −1862.08 −1.63628 −0.818140 0.575019i \(-0.804995\pi\)
−0.818140 + 0.575019i \(0.804995\pi\)
\(110\) −1529.17 −1.32546
\(111\) −353.640 −0.302396
\(112\) −3363.31 −2.83752
\(113\) 2135.01 1.77739 0.888694 0.458501i \(-0.151614\pi\)
0.888694 + 0.458501i \(0.151614\pi\)
\(114\) 703.562 0.578023
\(115\) −572.010 −0.463828
\(116\) −2107.92 −1.68720
\(117\) −146.154 −0.115486
\(118\) −299.176 −0.233402
\(119\) −3196.60 −2.46245
\(120\) 852.791 0.648740
\(121\) 1399.00 1.05109
\(122\) 4287.57 3.18179
\(123\) 834.014 0.611386
\(124\) 358.458 0.259601
\(125\) −1250.65 −0.894891
\(126\) 1420.66 1.00447
\(127\) 487.180 0.340396 0.170198 0.985410i \(-0.445559\pi\)
0.170198 + 0.985410i \(0.445559\pi\)
\(128\) 1657.85 1.14480
\(129\) 1453.71 0.992188
\(130\) 475.272 0.320647
\(131\) 1162.04 0.775022 0.387511 0.921865i \(-0.373335\pi\)
0.387511 + 0.921865i \(0.373335\pi\)
\(132\) −2776.45 −1.83075
\(133\) −1439.72 −0.938647
\(134\) 3756.87 2.42197
\(135\) −155.835 −0.0993489
\(136\) −5057.51 −3.18881
\(137\) 47.9021 0.0298727 0.0149363 0.999888i \(-0.495245\pi\)
0.0149363 + 0.999888i \(0.495245\pi\)
\(138\) −1507.65 −0.929996
\(139\) −2217.52 −1.35315 −0.676573 0.736375i \(-0.736536\pi\)
−0.676573 + 0.736375i \(0.736536\pi\)
\(140\) −3182.45 −1.92119
\(141\) 1042.62 0.622729
\(142\) 3742.93 2.21197
\(143\) −848.493 −0.496185
\(144\) 972.379 0.562719
\(145\) −686.856 −0.393382
\(146\) −2737.05 −1.55151
\(147\) −1878.15 −1.05379
\(148\) 2087.99 1.15967
\(149\) −830.176 −0.456448 −0.228224 0.973609i \(-0.573292\pi\)
−0.228224 + 0.973609i \(0.573292\pi\)
\(150\) −1394.79 −0.759228
\(151\) −2874.89 −1.54937 −0.774685 0.632347i \(-0.782092\pi\)
−0.774685 + 0.632347i \(0.782092\pi\)
\(152\) −2277.86 −1.21552
\(153\) 924.182 0.488338
\(154\) 8247.64 4.31567
\(155\) 116.802 0.0605275
\(156\) 862.932 0.442884
\(157\) −341.385 −0.173538 −0.0867691 0.996228i \(-0.527654\pi\)
−0.0867691 + 0.996228i \(0.527654\pi\)
\(158\) 2090.74 1.05273
\(159\) −483.118 −0.240967
\(160\) −887.935 −0.438734
\(161\) 3085.15 1.51021
\(162\) −410.733 −0.199199
\(163\) 3435.09 1.65065 0.825327 0.564655i \(-0.190991\pi\)
0.825327 + 0.564655i \(0.190991\pi\)
\(164\) −4924.25 −2.34463
\(165\) −904.695 −0.426851
\(166\) 383.303 0.179217
\(167\) −2320.44 −1.07522 −0.537608 0.843195i \(-0.680672\pi\)
−0.537608 + 0.843195i \(0.680672\pi\)
\(168\) −4599.56 −2.11228
\(169\) −1933.29 −0.879966
\(170\) −3005.32 −1.35587
\(171\) 416.245 0.186146
\(172\) −8583.13 −3.80498
\(173\) −2665.42 −1.17138 −0.585689 0.810536i \(-0.699176\pi\)
−0.585689 + 0.810536i \(0.699176\pi\)
\(174\) −1810.35 −0.788748
\(175\) 2854.21 1.23290
\(176\) 5645.13 2.41771
\(177\) −177.000 −0.0751646
\(178\) −828.670 −0.348941
\(179\) 771.425 0.322117 0.161059 0.986945i \(-0.448509\pi\)
0.161059 + 0.986945i \(0.448509\pi\)
\(180\) 920.091 0.380998
\(181\) 1057.15 0.434129 0.217065 0.976157i \(-0.430352\pi\)
0.217065 + 0.976157i \(0.430352\pi\)
\(182\) −2563.40 −1.04402
\(183\) 2536.63 1.02466
\(184\) 4881.18 1.95568
\(185\) 680.362 0.270385
\(186\) 307.855 0.121360
\(187\) 5365.32 2.09814
\(188\) −6155.95 −2.38813
\(189\) 840.499 0.323478
\(190\) −1353.57 −0.516834
\(191\) 2555.11 0.967966 0.483983 0.875078i \(-0.339190\pi\)
0.483983 + 0.875078i \(0.339190\pi\)
\(192\) 252.679 0.0949768
\(193\) −2038.27 −0.760197 −0.380098 0.924946i \(-0.624110\pi\)
−0.380098 + 0.924946i \(0.624110\pi\)
\(194\) −4346.35 −1.60850
\(195\) 281.183 0.103261
\(196\) 11089.2 4.04124
\(197\) 1204.93 0.435776 0.217888 0.975974i \(-0.430083\pi\)
0.217888 + 0.975974i \(0.430083\pi\)
\(198\) −2384.51 −0.855856
\(199\) 3829.73 1.36423 0.682116 0.731244i \(-0.261060\pi\)
0.682116 + 0.731244i \(0.261060\pi\)
\(200\) 4515.79 1.59657
\(201\) 2222.65 0.779970
\(202\) −8291.02 −2.88789
\(203\) 3704.58 1.28084
\(204\) −5456.63 −1.87275
\(205\) −1604.55 −0.546665
\(206\) 644.876 0.218110
\(207\) −891.961 −0.299496
\(208\) −1754.53 −0.584878
\(209\) 2416.50 0.799775
\(210\) −2733.19 −0.898134
\(211\) 3285.19 1.07186 0.535929 0.844263i \(-0.319961\pi\)
0.535929 + 0.844263i \(0.319961\pi\)
\(212\) 2852.46 0.924095
\(213\) 2214.41 0.712342
\(214\) 8971.98 2.86594
\(215\) −2796.77 −0.887155
\(216\) 1329.80 0.418894
\(217\) −629.976 −0.197076
\(218\) 9442.19 2.93351
\(219\) −1619.31 −0.499646
\(220\) 5341.58 1.63695
\(221\) −1667.56 −0.507567
\(222\) 1793.23 0.542134
\(223\) 426.083 0.127949 0.0639745 0.997952i \(-0.479622\pi\)
0.0639745 + 0.997952i \(0.479622\pi\)
\(224\) 4789.10 1.42851
\(225\) −825.192 −0.244501
\(226\) −10826.2 −3.18649
\(227\) −4529.34 −1.32433 −0.662164 0.749359i \(-0.730362\pi\)
−0.662164 + 0.749359i \(0.730362\pi\)
\(228\) −2457.63 −0.713861
\(229\) 2137.81 0.616900 0.308450 0.951241i \(-0.400190\pi\)
0.308450 + 0.951241i \(0.400190\pi\)
\(230\) 2900.54 0.831547
\(231\) 4879.50 1.38982
\(232\) 5861.21 1.65865
\(233\) 5634.00 1.58410 0.792051 0.610455i \(-0.209013\pi\)
0.792051 + 0.610455i \(0.209013\pi\)
\(234\) 741.113 0.207043
\(235\) −2005.89 −0.556807
\(236\) 1045.06 0.288252
\(237\) 1236.93 0.339019
\(238\) 16209.3 4.41467
\(239\) −4143.54 −1.12144 −0.560718 0.828007i \(-0.689475\pi\)
−0.560718 + 0.828007i \(0.689475\pi\)
\(240\) −1870.74 −0.503150
\(241\) −5880.72 −1.57183 −0.785914 0.618335i \(-0.787807\pi\)
−0.785914 + 0.618335i \(0.787807\pi\)
\(242\) −7094.00 −1.88438
\(243\) −243.000 −0.0641500
\(244\) −14977.0 −3.92952
\(245\) 3613.35 0.942239
\(246\) −4229.10 −1.09609
\(247\) −751.057 −0.193476
\(248\) −996.717 −0.255208
\(249\) 226.771 0.0577150
\(250\) 6341.76 1.60435
\(251\) −2345.45 −0.589814 −0.294907 0.955526i \(-0.595289\pi\)
−0.294907 + 0.955526i \(0.595289\pi\)
\(252\) −4962.54 −1.24052
\(253\) −5178.27 −1.28678
\(254\) −2470.38 −0.610259
\(255\) −1778.02 −0.436643
\(256\) −7732.77 −1.88788
\(257\) −4401.18 −1.06824 −0.534120 0.845409i \(-0.679357\pi\)
−0.534120 + 0.845409i \(0.679357\pi\)
\(258\) −7371.46 −1.77879
\(259\) −3669.55 −0.880366
\(260\) −1660.18 −0.396000
\(261\) −1071.05 −0.254008
\(262\) −5892.45 −1.38945
\(263\) 6751.11 1.58286 0.791428 0.611262i \(-0.209338\pi\)
0.791428 + 0.611262i \(0.209338\pi\)
\(264\) 7720.11 1.79977
\(265\) 929.463 0.215458
\(266\) 7300.53 1.68280
\(267\) −490.262 −0.112373
\(268\) −13123.2 −2.99114
\(269\) 2097.51 0.475419 0.237709 0.971336i \(-0.423603\pi\)
0.237709 + 0.971336i \(0.423603\pi\)
\(270\) 790.204 0.178112
\(271\) −5765.27 −1.29231 −0.646153 0.763208i \(-0.723623\pi\)
−0.646153 + 0.763208i \(0.723623\pi\)
\(272\) 11094.5 2.47317
\(273\) −1516.57 −0.336216
\(274\) −242.901 −0.0535555
\(275\) −4790.64 −1.05050
\(276\) 5266.39 1.14855
\(277\) −3383.35 −0.733884 −0.366942 0.930244i \(-0.619595\pi\)
−0.366942 + 0.930244i \(0.619595\pi\)
\(278\) 11244.5 2.42591
\(279\) 182.135 0.0390829
\(280\) 8849.02 1.88868
\(281\) −2239.18 −0.475368 −0.237684 0.971343i \(-0.576388\pi\)
−0.237684 + 0.971343i \(0.576388\pi\)
\(282\) −5286.92 −1.11642
\(283\) −4303.21 −0.903884 −0.451942 0.892047i \(-0.649269\pi\)
−0.451942 + 0.892047i \(0.649269\pi\)
\(284\) −13074.5 −2.73179
\(285\) −800.806 −0.166441
\(286\) 4302.52 0.889558
\(287\) 8654.17 1.77993
\(288\) −1384.60 −0.283292
\(289\) 5631.60 1.14626
\(290\) 3482.90 0.705252
\(291\) −2571.41 −0.518002
\(292\) 9560.83 1.91611
\(293\) −3649.23 −0.727612 −0.363806 0.931475i \(-0.618523\pi\)
−0.363806 + 0.931475i \(0.618523\pi\)
\(294\) 9523.71 1.88923
\(295\) 340.527 0.0672077
\(296\) −5805.79 −1.14005
\(297\) −1410.73 −0.275620
\(298\) 4209.64 0.818316
\(299\) 1609.42 0.311289
\(300\) 4872.17 0.937649
\(301\) 15084.5 2.88856
\(302\) 14577.9 2.77770
\(303\) −4905.17 −0.930016
\(304\) 4996.88 0.942733
\(305\) −4880.18 −0.916192
\(306\) −4686.33 −0.875488
\(307\) −4242.25 −0.788658 −0.394329 0.918969i \(-0.629023\pi\)
−0.394329 + 0.918969i \(0.629023\pi\)
\(308\) −28810.0 −5.32987
\(309\) 381.524 0.0702400
\(310\) −592.278 −0.108513
\(311\) −292.249 −0.0532859 −0.0266430 0.999645i \(-0.508482\pi\)
−0.0266430 + 0.999645i \(0.508482\pi\)
\(312\) −2399.44 −0.435389
\(313\) 5053.05 0.912509 0.456254 0.889849i \(-0.349191\pi\)
0.456254 + 0.889849i \(0.349191\pi\)
\(314\) 1731.09 0.311118
\(315\) −1617.02 −0.289235
\(316\) −7303.21 −1.30012
\(317\) −7858.38 −1.39234 −0.696168 0.717879i \(-0.745113\pi\)
−0.696168 + 0.717879i \(0.745113\pi\)
\(318\) 2449.79 0.432004
\(319\) −6217.94 −1.09134
\(320\) −486.126 −0.0849226
\(321\) 5308.04 0.922947
\(322\) −15644.2 −2.70750
\(323\) 4749.21 0.818121
\(324\) 1434.74 0.246012
\(325\) 1488.95 0.254129
\(326\) −17418.6 −2.95928
\(327\) 5586.23 0.944707
\(328\) 13692.2 2.30496
\(329\) 10818.8 1.81295
\(330\) 4587.51 0.765256
\(331\) 6703.97 1.11324 0.556622 0.830766i \(-0.312097\pi\)
0.556622 + 0.830766i \(0.312097\pi\)
\(332\) −1338.92 −0.221334
\(333\) 1060.92 0.174589
\(334\) 11766.4 1.92764
\(335\) −4276.13 −0.697403
\(336\) 10089.9 1.63824
\(337\) −1034.27 −0.167182 −0.0835910 0.996500i \(-0.526639\pi\)
−0.0835910 + 0.996500i \(0.526639\pi\)
\(338\) 9803.27 1.57760
\(339\) −6405.03 −1.02618
\(340\) 10497.9 1.67450
\(341\) 1057.38 0.167919
\(342\) −2110.69 −0.333722
\(343\) −8811.28 −1.38707
\(344\) 23865.9 3.74060
\(345\) 1716.03 0.267791
\(346\) 13515.8 2.10004
\(347\) −2414.72 −0.373571 −0.186785 0.982401i \(-0.559807\pi\)
−0.186785 + 0.982401i \(0.559807\pi\)
\(348\) 6323.76 0.974107
\(349\) 1429.79 0.219298 0.109649 0.993970i \(-0.465027\pi\)
0.109649 + 0.993970i \(0.465027\pi\)
\(350\) −14473.1 −2.21034
\(351\) 438.461 0.0666761
\(352\) −8038.26 −1.21716
\(353\) 9657.60 1.45615 0.728077 0.685496i \(-0.240415\pi\)
0.728077 + 0.685496i \(0.240415\pi\)
\(354\) 897.529 0.134755
\(355\) −4260.27 −0.636934
\(356\) 2894.64 0.430943
\(357\) 9589.80 1.42170
\(358\) −3911.73 −0.577490
\(359\) 1728.23 0.254074 0.127037 0.991898i \(-0.459453\pi\)
0.127037 + 0.991898i \(0.459453\pi\)
\(360\) −2558.37 −0.374550
\(361\) −4719.99 −0.688146
\(362\) −5360.58 −0.778304
\(363\) −4196.99 −0.606845
\(364\) 8954.24 1.28937
\(365\) 3115.36 0.446754
\(366\) −12862.7 −1.83701
\(367\) −2452.53 −0.348831 −0.174416 0.984672i \(-0.555804\pi\)
−0.174416 + 0.984672i \(0.555804\pi\)
\(368\) −10707.7 −1.51679
\(369\) −2502.04 −0.352984
\(370\) −3449.97 −0.484744
\(371\) −5013.09 −0.701527
\(372\) −1075.38 −0.149881
\(373\) 8584.89 1.19171 0.595856 0.803091i \(-0.296813\pi\)
0.595856 + 0.803091i \(0.296813\pi\)
\(374\) −27206.4 −3.76152
\(375\) 3751.94 0.516665
\(376\) 17117.0 2.34772
\(377\) 1932.56 0.264010
\(378\) −4261.99 −0.579929
\(379\) −6441.28 −0.872998 −0.436499 0.899705i \(-0.643782\pi\)
−0.436499 + 0.899705i \(0.643782\pi\)
\(380\) 4728.19 0.638292
\(381\) −1461.54 −0.196527
\(382\) −12956.4 −1.73536
\(383\) −10167.8 −1.35653 −0.678264 0.734818i \(-0.737268\pi\)
−0.678264 + 0.734818i \(0.737268\pi\)
\(384\) −4973.54 −0.660950
\(385\) −9387.60 −1.24269
\(386\) 10335.6 1.36288
\(387\) −4361.14 −0.572840
\(388\) 15182.3 1.98651
\(389\) 3426.40 0.446595 0.223297 0.974750i \(-0.428318\pi\)
0.223297 + 0.974750i \(0.428318\pi\)
\(390\) −1425.82 −0.185126
\(391\) −10177.0 −1.31630
\(392\) −30834.1 −3.97285
\(393\) −3486.12 −0.447459
\(394\) −6109.95 −0.781256
\(395\) −2379.72 −0.303131
\(396\) 8329.36 1.05699
\(397\) −8161.03 −1.03171 −0.515857 0.856675i \(-0.672526\pi\)
−0.515857 + 0.856675i \(0.672526\pi\)
\(398\) −19419.7 −2.44578
\(399\) 4319.17 0.541928
\(400\) −9906.16 −1.23827
\(401\) 8303.40 1.03404 0.517022 0.855972i \(-0.327040\pi\)
0.517022 + 0.855972i \(0.327040\pi\)
\(402\) −11270.6 −1.39832
\(403\) −328.638 −0.0406219
\(404\) 28961.5 3.56656
\(405\) 467.504 0.0573591
\(406\) −18785.1 −2.29628
\(407\) 6159.15 0.750117
\(408\) 15172.5 1.84106
\(409\) −1611.03 −0.194769 −0.0973844 0.995247i \(-0.531048\pi\)
−0.0973844 + 0.995247i \(0.531048\pi\)
\(410\) 8136.31 0.980057
\(411\) −143.706 −0.0172470
\(412\) −2252.63 −0.269366
\(413\) −1836.65 −0.218827
\(414\) 4522.94 0.536934
\(415\) −436.282 −0.0516053
\(416\) 2498.32 0.294448
\(417\) 6652.55 0.781239
\(418\) −12253.6 −1.43383
\(419\) 12278.0 1.43155 0.715776 0.698330i \(-0.246073\pi\)
0.715776 + 0.698330i \(0.246073\pi\)
\(420\) 9547.36 1.10920
\(421\) −2402.19 −0.278089 −0.139045 0.990286i \(-0.544403\pi\)
−0.139045 + 0.990286i \(0.544403\pi\)
\(422\) −16658.5 −1.92162
\(423\) −3127.87 −0.359533
\(424\) −7931.46 −0.908457
\(425\) −9415.16 −1.07459
\(426\) −11228.8 −1.27708
\(427\) 26321.4 2.98310
\(428\) −31340.2 −3.53945
\(429\) 2545.48 0.286473
\(430\) 14181.8 1.59049
\(431\) 7294.64 0.815245 0.407622 0.913151i \(-0.366358\pi\)
0.407622 + 0.913151i \(0.366358\pi\)
\(432\) −2917.14 −0.324886
\(433\) 13340.5 1.48060 0.740302 0.672275i \(-0.234683\pi\)
0.740302 + 0.672275i \(0.234683\pi\)
\(434\) 3194.47 0.353317
\(435\) 2060.57 0.227119
\(436\) −32982.7 −3.62290
\(437\) −4583.63 −0.501750
\(438\) 8211.15 0.895762
\(439\) 7920.79 0.861136 0.430568 0.902558i \(-0.358313\pi\)
0.430568 + 0.902558i \(0.358313\pi\)
\(440\) −14852.6 −1.60925
\(441\) 5634.46 0.608408
\(442\) 8455.85 0.909963
\(443\) 776.340 0.0832619 0.0416310 0.999133i \(-0.486745\pi\)
0.0416310 + 0.999133i \(0.486745\pi\)
\(444\) −6263.96 −0.669537
\(445\) 943.207 0.100477
\(446\) −2160.57 −0.229386
\(447\) 2490.53 0.263530
\(448\) 2621.93 0.276506
\(449\) 2796.54 0.293935 0.146968 0.989141i \(-0.453049\pi\)
0.146968 + 0.989141i \(0.453049\pi\)
\(450\) 4184.37 0.438340
\(451\) −14525.6 −1.51659
\(452\) 37817.1 3.93532
\(453\) 8624.66 0.894529
\(454\) 22967.3 2.37425
\(455\) 2917.70 0.300624
\(456\) 6833.59 0.701781
\(457\) −3189.75 −0.326499 −0.163250 0.986585i \(-0.552198\pi\)
−0.163250 + 0.986585i \(0.552198\pi\)
\(458\) −10840.3 −1.10597
\(459\) −2772.55 −0.281942
\(460\) −10131.9 −1.02696
\(461\) 11072.8 1.11868 0.559339 0.828939i \(-0.311055\pi\)
0.559339 + 0.828939i \(0.311055\pi\)
\(462\) −24742.9 −2.49165
\(463\) 15208.6 1.52658 0.763288 0.646059i \(-0.223584\pi\)
0.763288 + 0.646059i \(0.223584\pi\)
\(464\) −12857.6 −1.28642
\(465\) −350.406 −0.0349456
\(466\) −28568.8 −2.83997
\(467\) −2666.62 −0.264233 −0.132116 0.991234i \(-0.542177\pi\)
−0.132116 + 0.991234i \(0.542177\pi\)
\(468\) −2588.80 −0.255699
\(469\) 23063.4 2.27073
\(470\) 10171.4 0.998240
\(471\) 1024.16 0.100192
\(472\) −2905.85 −0.283374
\(473\) −25318.5 −2.46120
\(474\) −6272.23 −0.607791
\(475\) −4240.52 −0.409617
\(476\) −56620.9 −5.45213
\(477\) 1449.35 0.139122
\(478\) 21011.0 2.01050
\(479\) −1470.72 −0.140290 −0.0701451 0.997537i \(-0.522346\pi\)
−0.0701451 + 0.997537i \(0.522346\pi\)
\(480\) 2663.80 0.253303
\(481\) −1914.29 −0.181463
\(482\) 29819.9 2.81796
\(483\) −9255.46 −0.871922
\(484\) 24780.2 2.32722
\(485\) 4947.09 0.463166
\(486\) 1232.20 0.115008
\(487\) −10466.9 −0.973921 −0.486960 0.873424i \(-0.661894\pi\)
−0.486960 + 0.873424i \(0.661894\pi\)
\(488\) 41644.5 3.86303
\(489\) −10305.3 −0.953006
\(490\) −18322.5 −1.68924
\(491\) 8125.93 0.746880 0.373440 0.927654i \(-0.378178\pi\)
0.373440 + 0.927654i \(0.378178\pi\)
\(492\) 14772.8 1.35367
\(493\) −12220.3 −1.11638
\(494\) 3808.45 0.346863
\(495\) 2714.09 0.246443
\(496\) 2186.47 0.197934
\(497\) 22977.9 2.07384
\(498\) −1149.91 −0.103471
\(499\) −14989.0 −1.34469 −0.672344 0.740239i \(-0.734712\pi\)
−0.672344 + 0.740239i \(0.734712\pi\)
\(500\) −22152.5 −1.98138
\(501\) 6961.32 0.620776
\(502\) 11893.2 1.05741
\(503\) −5526.27 −0.489869 −0.244935 0.969540i \(-0.578766\pi\)
−0.244935 + 0.969540i \(0.578766\pi\)
\(504\) 13798.7 1.21953
\(505\) 9436.98 0.831565
\(506\) 26257.9 2.30693
\(507\) 5799.86 0.508049
\(508\) 8629.34 0.753672
\(509\) 16053.1 1.39792 0.698962 0.715159i \(-0.253646\pi\)
0.698962 + 0.715159i \(0.253646\pi\)
\(510\) 9015.95 0.782810
\(511\) −16802.8 −1.45462
\(512\) 25948.4 2.23978
\(513\) −1248.73 −0.107472
\(514\) 22317.4 1.91513
\(515\) −734.008 −0.0628044
\(516\) 25749.4 2.19681
\(517\) −18158.8 −1.54473
\(518\) 18607.5 1.57831
\(519\) 7996.26 0.676295
\(520\) 4616.24 0.389299
\(521\) −16059.8 −1.35047 −0.675234 0.737604i \(-0.735957\pi\)
−0.675234 + 0.737604i \(0.735957\pi\)
\(522\) 5431.05 0.455384
\(523\) −18602.9 −1.55535 −0.777675 0.628666i \(-0.783601\pi\)
−0.777675 + 0.628666i \(0.783601\pi\)
\(524\) 20583.0 1.71598
\(525\) −8562.63 −0.711817
\(526\) −34233.4 −2.83773
\(527\) 2078.10 0.171771
\(528\) −16935.4 −1.39587
\(529\) −2344.84 −0.192721
\(530\) −4713.11 −0.386272
\(531\) 531.000 0.0433963
\(532\) −25501.6 −2.07826
\(533\) 4514.60 0.366884
\(534\) 2486.01 0.201461
\(535\) −10212.1 −0.825245
\(536\) 36489.9 2.94053
\(537\) −2314.27 −0.185975
\(538\) −10636.0 −0.852327
\(539\) 32710.8 2.61401
\(540\) −2760.27 −0.219969
\(541\) −21283.9 −1.69144 −0.845718 0.533630i \(-0.820827\pi\)
−0.845718 + 0.533630i \(0.820827\pi\)
\(542\) 29234.4 2.31684
\(543\) −3171.45 −0.250645
\(544\) −15797.8 −1.24508
\(545\) −10747.3 −0.844701
\(546\) 7690.19 0.602765
\(547\) 17983.2 1.40568 0.702839 0.711349i \(-0.251915\pi\)
0.702839 + 0.711349i \(0.251915\pi\)
\(548\) 848.483 0.0661412
\(549\) −7609.89 −0.591589
\(550\) 24292.3 1.88332
\(551\) −5503.92 −0.425544
\(552\) −14643.5 −1.12911
\(553\) 12835.1 0.986987
\(554\) 17156.2 1.31570
\(555\) −2041.08 −0.156107
\(556\) −39278.5 −2.99601
\(557\) 22854.0 1.73852 0.869261 0.494354i \(-0.164595\pi\)
0.869261 + 0.494354i \(0.164595\pi\)
\(558\) −923.566 −0.0700675
\(559\) 7869.09 0.595397
\(560\) −19411.8 −1.46482
\(561\) −16096.0 −1.21136
\(562\) 11354.4 0.852236
\(563\) −9314.59 −0.697271 −0.348635 0.937258i \(-0.613355\pi\)
−0.348635 + 0.937258i \(0.613355\pi\)
\(564\) 18467.8 1.37879
\(565\) 12322.5 0.917545
\(566\) 21820.6 1.62048
\(567\) −2521.50 −0.186760
\(568\) 36354.5 2.68556
\(569\) 13990.2 1.03075 0.515376 0.856964i \(-0.327652\pi\)
0.515376 + 0.856964i \(0.327652\pi\)
\(570\) 4060.72 0.298394
\(571\) 19287.1 1.41355 0.706777 0.707437i \(-0.250149\pi\)
0.706777 + 0.707437i \(0.250149\pi\)
\(572\) −15029.2 −1.09861
\(573\) −7665.34 −0.558855
\(574\) −43883.4 −3.19104
\(575\) 9086.91 0.659044
\(576\) −758.038 −0.0548349
\(577\) −23173.6 −1.67197 −0.835986 0.548750i \(-0.815104\pi\)
−0.835986 + 0.548750i \(0.815104\pi\)
\(578\) −28556.6 −2.05501
\(579\) 6114.81 0.438900
\(580\) −12166.2 −0.870988
\(581\) 2353.10 0.168026
\(582\) 13039.0 0.928670
\(583\) 8414.20 0.597737
\(584\) −26584.5 −1.88369
\(585\) −843.548 −0.0596178
\(586\) 18504.5 1.30446
\(587\) 26048.4 1.83157 0.915787 0.401663i \(-0.131568\pi\)
0.915787 + 0.401663i \(0.131568\pi\)
\(588\) −33267.5 −2.33321
\(589\) 935.958 0.0654762
\(590\) −1726.74 −0.120489
\(591\) −3614.80 −0.251595
\(592\) 12736.0 0.884199
\(593\) −54.2397 −0.00375609 −0.00187804 0.999998i \(-0.500598\pi\)
−0.00187804 + 0.999998i \(0.500598\pi\)
\(594\) 7153.52 0.494129
\(595\) −18449.7 −1.27120
\(596\) −14704.8 −1.01062
\(597\) −11489.2 −0.787640
\(598\) −8161.04 −0.558077
\(599\) −7953.75 −0.542540 −0.271270 0.962503i \(-0.587444\pi\)
−0.271270 + 0.962503i \(0.587444\pi\)
\(600\) −13547.4 −0.921782
\(601\) 10456.8 0.709720 0.354860 0.934919i \(-0.384528\pi\)
0.354860 + 0.934919i \(0.384528\pi\)
\(602\) −76490.2 −5.17858
\(603\) −6667.96 −0.450316
\(604\) −50922.4 −3.43047
\(605\) 8074.52 0.542605
\(606\) 24873.1 1.66733
\(607\) 6233.80 0.416840 0.208420 0.978039i \(-0.433168\pi\)
0.208420 + 0.978039i \(0.433168\pi\)
\(608\) −7115.20 −0.474604
\(609\) −11113.7 −0.739494
\(610\) 24746.3 1.64254
\(611\) 5643.83 0.373690
\(612\) 16369.9 1.08123
\(613\) −12563.6 −0.827794 −0.413897 0.910324i \(-0.635833\pi\)
−0.413897 + 0.910324i \(0.635833\pi\)
\(614\) 21511.5 1.41390
\(615\) 4813.64 0.315617
\(616\) 80108.0 5.23968
\(617\) −14795.6 −0.965396 −0.482698 0.875787i \(-0.660343\pi\)
−0.482698 + 0.875787i \(0.660343\pi\)
\(618\) −1934.63 −0.125926
\(619\) −1136.52 −0.0737976 −0.0368988 0.999319i \(-0.511748\pi\)
−0.0368988 + 0.999319i \(0.511748\pi\)
\(620\) 2068.90 0.134014
\(621\) 2675.88 0.172914
\(622\) 1481.93 0.0955306
\(623\) −5087.22 −0.327151
\(624\) 5263.58 0.337679
\(625\) 4242.70 0.271533
\(626\) −25622.9 −1.63594
\(627\) −7249.50 −0.461750
\(628\) −6046.90 −0.384232
\(629\) 12104.7 0.767324
\(630\) 8199.57 0.518538
\(631\) −8230.74 −0.519272 −0.259636 0.965707i \(-0.583603\pi\)
−0.259636 + 0.965707i \(0.583603\pi\)
\(632\) 20307.1 1.27812
\(633\) −9855.58 −0.618838
\(634\) 39848.1 2.49617
\(635\) 2811.83 0.175723
\(636\) −8557.39 −0.533526
\(637\) −10166.6 −0.632365
\(638\) 31529.8 1.95655
\(639\) −6643.23 −0.411271
\(640\) 9568.51 0.590982
\(641\) −20600.4 −1.26937 −0.634685 0.772771i \(-0.718870\pi\)
−0.634685 + 0.772771i \(0.718870\pi\)
\(642\) −26915.9 −1.65465
\(643\) 8955.01 0.549224 0.274612 0.961555i \(-0.411451\pi\)
0.274612 + 0.961555i \(0.411451\pi\)
\(644\) 54646.9 3.34377
\(645\) 8390.32 0.512199
\(646\) −24082.2 −1.46672
\(647\) −19489.8 −1.18427 −0.592136 0.805838i \(-0.701715\pi\)
−0.592136 + 0.805838i \(0.701715\pi\)
\(648\) −3989.39 −0.241849
\(649\) 3082.71 0.186452
\(650\) −7550.14 −0.455601
\(651\) 1889.93 0.113782
\(652\) 60845.1 3.65472
\(653\) 24922.7 1.49357 0.746784 0.665067i \(-0.231597\pi\)
0.746784 + 0.665067i \(0.231597\pi\)
\(654\) −28326.6 −1.69366
\(655\) 6706.89 0.400092
\(656\) −30036.2 −1.78768
\(657\) 4857.92 0.288471
\(658\) −54859.9 −3.25025
\(659\) −29532.0 −1.74568 −0.872839 0.488008i \(-0.837724\pi\)
−0.872839 + 0.488008i \(0.837724\pi\)
\(660\) −16024.7 −0.945093
\(661\) 23688.8 1.39393 0.696965 0.717105i \(-0.254533\pi\)
0.696965 + 0.717105i \(0.254533\pi\)
\(662\) −33994.4 −1.99581
\(663\) 5002.69 0.293044
\(664\) 3722.96 0.217589
\(665\) −8309.59 −0.484560
\(666\) −5379.69 −0.313001
\(667\) 11794.2 0.684669
\(668\) −41101.6 −2.38064
\(669\) −1278.25 −0.0738714
\(670\) 21683.3 1.25030
\(671\) −44179.1 −2.54175
\(672\) −14367.3 −0.824749
\(673\) 11534.1 0.660636 0.330318 0.943870i \(-0.392844\pi\)
0.330318 + 0.943870i \(0.392844\pi\)
\(674\) 5244.56 0.299723
\(675\) 2475.58 0.141163
\(676\) −34244.0 −1.94834
\(677\) 3710.82 0.210662 0.105331 0.994437i \(-0.466410\pi\)
0.105331 + 0.994437i \(0.466410\pi\)
\(678\) 32478.5 1.83972
\(679\) −26682.3 −1.50806
\(680\) −29190.2 −1.64616
\(681\) 13588.0 0.764601
\(682\) −5361.75 −0.301044
\(683\) −8278.65 −0.463797 −0.231899 0.972740i \(-0.574494\pi\)
−0.231899 + 0.972740i \(0.574494\pi\)
\(684\) 7372.88 0.412148
\(685\) 276.474 0.0154212
\(686\) 44680.1 2.48672
\(687\) −6413.42 −0.356167
\(688\) −52354.0 −2.90113
\(689\) −2615.16 −0.144601
\(690\) −8701.62 −0.480094
\(691\) 19296.8 1.06235 0.531176 0.847261i \(-0.321750\pi\)
0.531176 + 0.847261i \(0.321750\pi\)
\(692\) −47212.2 −2.59355
\(693\) −14638.5 −0.802411
\(694\) 12244.5 0.669735
\(695\) −12798.7 −0.698538
\(696\) −17583.6 −0.957623
\(697\) −28547.4 −1.55138
\(698\) −7250.17 −0.393156
\(699\) −16902.0 −0.914582
\(700\) 50556.2 2.72978
\(701\) 1826.74 0.0984237 0.0492119 0.998788i \(-0.484329\pi\)
0.0492119 + 0.998788i \(0.484329\pi\)
\(702\) −2223.34 −0.119536
\(703\) 5451.87 0.292491
\(704\) −4400.78 −0.235597
\(705\) 6017.66 0.321473
\(706\) −48971.6 −2.61058
\(707\) −50898.7 −2.70756
\(708\) −3135.17 −0.166422
\(709\) −10531.6 −0.557862 −0.278931 0.960311i \(-0.589980\pi\)
−0.278931 + 0.960311i \(0.589980\pi\)
\(710\) 21602.9 1.14189
\(711\) −3710.80 −0.195733
\(712\) −8048.75 −0.423651
\(713\) −2005.64 −0.105346
\(714\) −48627.8 −2.54881
\(715\) −4897.20 −0.256147
\(716\) 13664.1 0.713202
\(717\) 12430.6 0.647462
\(718\) −8763.47 −0.455501
\(719\) 20954.3 1.08688 0.543438 0.839449i \(-0.317122\pi\)
0.543438 + 0.839449i \(0.317122\pi\)
\(720\) 5612.23 0.290494
\(721\) 3958.90 0.204490
\(722\) 23934.1 1.23370
\(723\) 17642.2 0.907496
\(724\) 18725.2 0.961208
\(725\) 10911.4 0.558948
\(726\) 21282.0 1.08795
\(727\) 12108.1 0.617697 0.308849 0.951111i \(-0.400056\pi\)
0.308849 + 0.951111i \(0.400056\pi\)
\(728\) −24897.9 −1.26755
\(729\) 729.000 0.0370370
\(730\) −15797.3 −0.800937
\(731\) −49759.1 −2.51765
\(732\) 44930.9 2.26871
\(733\) 11182.5 0.563486 0.281743 0.959490i \(-0.409087\pi\)
0.281743 + 0.959490i \(0.409087\pi\)
\(734\) 12436.3 0.625382
\(735\) −10840.1 −0.544002
\(736\) 15247.0 0.763603
\(737\) −38710.8 −1.93477
\(738\) 12687.3 0.632827
\(739\) −9024.78 −0.449231 −0.224616 0.974447i \(-0.572113\pi\)
−0.224616 + 0.974447i \(0.572113\pi\)
\(740\) 12051.1 0.598660
\(741\) 2253.17 0.111704
\(742\) 25420.3 1.25769
\(743\) 17214.3 0.849974 0.424987 0.905200i \(-0.360279\pi\)
0.424987 + 0.905200i \(0.360279\pi\)
\(744\) 2990.15 0.147344
\(745\) −4791.49 −0.235633
\(746\) −43532.1 −2.13649
\(747\) −680.314 −0.0333218
\(748\) 95035.1 4.64549
\(749\) 55079.1 2.68698
\(750\) −19025.3 −0.926274
\(751\) −10115.7 −0.491517 −0.245758 0.969331i \(-0.579037\pi\)
−0.245758 + 0.969331i \(0.579037\pi\)
\(752\) −37549.1 −1.82084
\(753\) 7036.34 0.340529
\(754\) −9799.59 −0.473316
\(755\) −16592.8 −0.799835
\(756\) 14887.6 0.716214
\(757\) 21416.7 1.02827 0.514137 0.857708i \(-0.328112\pi\)
0.514137 + 0.857708i \(0.328112\pi\)
\(758\) 32662.3 1.56510
\(759\) 15534.8 0.742922
\(760\) −13147.0 −0.627491
\(761\) −26539.8 −1.26421 −0.632107 0.774881i \(-0.717810\pi\)
−0.632107 + 0.774881i \(0.717810\pi\)
\(762\) 7411.15 0.352333
\(763\) 57965.7 2.75033
\(764\) 45258.3 2.14318
\(765\) 5334.06 0.252096
\(766\) 51558.7 2.43197
\(767\) −958.118 −0.0451051
\(768\) 23198.3 1.08997
\(769\) −8581.69 −0.402423 −0.201212 0.979548i \(-0.564488\pi\)
−0.201212 + 0.979548i \(0.564488\pi\)
\(770\) 47602.5 2.22789
\(771\) 13203.5 0.616749
\(772\) −36103.6 −1.68316
\(773\) −9126.70 −0.424663 −0.212331 0.977198i \(-0.568106\pi\)
−0.212331 + 0.977198i \(0.568106\pi\)
\(774\) 22114.4 1.02698
\(775\) −1855.51 −0.0860024
\(776\) −42215.4 −1.95289
\(777\) 11008.7 0.508280
\(778\) −17374.5 −0.800652
\(779\) −12857.5 −0.591360
\(780\) 4980.54 0.228631
\(781\) −38567.2 −1.76702
\(782\) 51605.2 2.35984
\(783\) 3213.14 0.146652
\(784\) 67639.9 3.08126
\(785\) −1970.36 −0.0895860
\(786\) 17677.4 0.802202
\(787\) 29121.3 1.31901 0.659507 0.751699i \(-0.270765\pi\)
0.659507 + 0.751699i \(0.270765\pi\)
\(788\) 21342.8 0.964854
\(789\) −20253.3 −0.913863
\(790\) 12067.0 0.543451
\(791\) −66462.0 −2.98750
\(792\) −23160.3 −1.03910
\(793\) 13731.0 0.614884
\(794\) 41382.8 1.84965
\(795\) −2788.39 −0.124395
\(796\) 67835.4 3.02055
\(797\) −29979.5 −1.33241 −0.666204 0.745770i \(-0.732082\pi\)
−0.666204 + 0.745770i \(0.732082\pi\)
\(798\) −21901.6 −0.971564
\(799\) −35687.9 −1.58016
\(800\) 14105.7 0.623388
\(801\) 1470.79 0.0648785
\(802\) −42104.7 −1.85383
\(803\) 28202.6 1.23941
\(804\) 39369.5 1.72694
\(805\) 17806.4 0.779621
\(806\) 1666.45 0.0728266
\(807\) −6292.54 −0.274483
\(808\) −80529.4 −3.50621
\(809\) 14674.6 0.637739 0.318870 0.947799i \(-0.396697\pi\)
0.318870 + 0.947799i \(0.396697\pi\)
\(810\) −2370.61 −0.102833
\(811\) 23037.9 0.997496 0.498748 0.866747i \(-0.333793\pi\)
0.498748 + 0.866747i \(0.333793\pi\)
\(812\) 65618.7 2.83592
\(813\) 17295.8 0.746114
\(814\) −31231.7 −1.34480
\(815\) 19826.1 0.852121
\(816\) −33283.5 −1.42789
\(817\) −22411.1 −0.959689
\(818\) 8169.20 0.349180
\(819\) 4549.70 0.194114
\(820\) −28421.1 −1.21037
\(821\) 22136.0 0.940987 0.470494 0.882403i \(-0.344076\pi\)
0.470494 + 0.882403i \(0.344076\pi\)
\(822\) 728.704 0.0309203
\(823\) −31318.9 −1.32650 −0.663249 0.748399i \(-0.730823\pi\)
−0.663249 + 0.748399i \(0.730823\pi\)
\(824\) 6263.58 0.264808
\(825\) 14371.9 0.606504
\(826\) 9313.23 0.392311
\(827\) 17055.7 0.717151 0.358576 0.933501i \(-0.383262\pi\)
0.358576 + 0.933501i \(0.383262\pi\)
\(828\) −15799.2 −0.663115
\(829\) −23830.8 −0.998406 −0.499203 0.866485i \(-0.666374\pi\)
−0.499203 + 0.866485i \(0.666374\pi\)
\(830\) 2212.29 0.0925177
\(831\) 10150.0 0.423708
\(832\) 1367.78 0.0569942
\(833\) 64287.3 2.67398
\(834\) −33733.6 −1.40060
\(835\) −13392.8 −0.555061
\(836\) 42803.1 1.77079
\(837\) −546.404 −0.0225645
\(838\) −62259.2 −2.56648
\(839\) −6153.41 −0.253205 −0.126603 0.991954i \(-0.540407\pi\)
−0.126603 + 0.991954i \(0.540407\pi\)
\(840\) −26547.0 −1.09043
\(841\) −10226.8 −0.419319
\(842\) 12181.0 0.498556
\(843\) 6717.55 0.274454
\(844\) 58190.1 2.37321
\(845\) −11158.3 −0.454267
\(846\) 15860.8 0.644568
\(847\) −43550.2 −1.76671
\(848\) 17399.0 0.704581
\(849\) 12909.6 0.521858
\(850\) 47742.2 1.92652
\(851\) −11682.7 −0.470597
\(852\) 39223.5 1.57720
\(853\) 23127.0 0.928318 0.464159 0.885752i \(-0.346357\pi\)
0.464159 + 0.885752i \(0.346357\pi\)
\(854\) −133470. −5.34808
\(855\) 2402.42 0.0960947
\(856\) 87143.4 3.47956
\(857\) 9069.34 0.361497 0.180748 0.983529i \(-0.442148\pi\)
0.180748 + 0.983529i \(0.442148\pi\)
\(858\) −12907.6 −0.513586
\(859\) 5101.91 0.202649 0.101324 0.994853i \(-0.467692\pi\)
0.101324 + 0.994853i \(0.467692\pi\)
\(860\) −49538.8 −1.96426
\(861\) −25962.5 −1.02764
\(862\) −36989.6 −1.46157
\(863\) −28547.6 −1.12604 −0.563020 0.826444i \(-0.690360\pi\)
−0.563020 + 0.826444i \(0.690360\pi\)
\(864\) 4153.79 0.163559
\(865\) −15383.9 −0.604703
\(866\) −67646.5 −2.65441
\(867\) −16894.8 −0.661796
\(868\) −11158.7 −0.436348
\(869\) −21543.0 −0.840963
\(870\) −10448.7 −0.407177
\(871\) 12031.4 0.468048
\(872\) 91710.5 3.56159
\(873\) 7714.22 0.299068
\(874\) 23242.6 0.899534
\(875\) 38932.2 1.50417
\(876\) −28682.5 −1.10627
\(877\) −810.103 −0.0311918 −0.0155959 0.999878i \(-0.504965\pi\)
−0.0155959 + 0.999878i \(0.504965\pi\)
\(878\) −40164.6 −1.54384
\(879\) 10947.7 0.420087
\(880\) 32581.7 1.24810
\(881\) −26009.1 −0.994630 −0.497315 0.867570i \(-0.665681\pi\)
−0.497315 + 0.867570i \(0.665681\pi\)
\(882\) −28571.1 −1.09075
\(883\) 19343.3 0.737208 0.368604 0.929586i \(-0.379836\pi\)
0.368604 + 0.929586i \(0.379836\pi\)
\(884\) −29537.3 −1.12381
\(885\) −1021.58 −0.0388024
\(886\) −3936.65 −0.149271
\(887\) 10442.1 0.395279 0.197639 0.980275i \(-0.436673\pi\)
0.197639 + 0.980275i \(0.436673\pi\)
\(888\) 17417.4 0.658208
\(889\) −15165.7 −0.572150
\(890\) −4782.80 −0.180135
\(891\) 4232.20 0.159129
\(892\) 7547.14 0.283293
\(893\) −16073.6 −0.602331
\(894\) −12628.9 −0.472455
\(895\) 4452.40 0.166287
\(896\) −51608.1 −1.92422
\(897\) −4828.27 −0.179723
\(898\) −14180.6 −0.526965
\(899\) −2408.33 −0.0893463
\(900\) −14616.5 −0.541352
\(901\) 16536.6 0.611448
\(902\) 73656.0 2.71893
\(903\) −45253.5 −1.66771
\(904\) −105153. −3.86873
\(905\) 6101.51 0.224112
\(906\) −43733.8 −1.60371
\(907\) 31550.6 1.15504 0.577519 0.816377i \(-0.304021\pi\)
0.577519 + 0.816377i \(0.304021\pi\)
\(908\) −80227.4 −2.93220
\(909\) 14715.5 0.536945
\(910\) −14795.0 −0.538956
\(911\) 7389.17 0.268731 0.134366 0.990932i \(-0.457100\pi\)
0.134366 + 0.990932i \(0.457100\pi\)
\(912\) −14990.6 −0.544287
\(913\) −3949.55 −0.143167
\(914\) 16174.5 0.585345
\(915\) 14640.5 0.528963
\(916\) 37866.6 1.36588
\(917\) −36173.8 −1.30269
\(918\) 14059.0 0.505463
\(919\) 25793.5 0.925842 0.462921 0.886399i \(-0.346801\pi\)
0.462921 + 0.886399i \(0.346801\pi\)
\(920\) 28172.5 1.00959
\(921\) 12726.7 0.455332
\(922\) −56147.6 −2.00556
\(923\) 11986.8 0.427466
\(924\) 86429.9 3.07720
\(925\) −10808.2 −0.384184
\(926\) −77119.6 −2.73683
\(927\) −1144.57 −0.0405531
\(928\) 18308.2 0.647627
\(929\) −29660.4 −1.04750 −0.523749 0.851872i \(-0.675467\pi\)
−0.523749 + 0.851872i \(0.675467\pi\)
\(930\) 1776.83 0.0626502
\(931\) 28954.5 1.01928
\(932\) 99794.2 3.50737
\(933\) 876.747 0.0307646
\(934\) 13521.9 0.473714
\(935\) 30966.8 1.08313
\(936\) 7198.32 0.251372
\(937\) 29585.3 1.03149 0.515747 0.856741i \(-0.327514\pi\)
0.515747 + 0.856741i \(0.327514\pi\)
\(938\) −116950. −4.07094
\(939\) −15159.1 −0.526837
\(940\) −35530.0 −1.23283
\(941\) 26146.0 0.905778 0.452889 0.891567i \(-0.350393\pi\)
0.452889 + 0.891567i \(0.350393\pi\)
\(942\) −5193.27 −0.179624
\(943\) 27552.2 0.951454
\(944\) 6374.48 0.219779
\(945\) 4851.07 0.166990
\(946\) 128385. 4.41242
\(947\) −22905.8 −0.785998 −0.392999 0.919539i \(-0.628562\pi\)
−0.392999 + 0.919539i \(0.628562\pi\)
\(948\) 21909.6 0.750624
\(949\) −8765.46 −0.299830
\(950\) 21502.7 0.734359
\(951\) 23575.1 0.803865
\(952\) 157438. 5.35987
\(953\) 2307.17 0.0784225 0.0392113 0.999231i \(-0.487515\pi\)
0.0392113 + 0.999231i \(0.487515\pi\)
\(954\) −7349.36 −0.249418
\(955\) 14747.2 0.499695
\(956\) −73393.9 −2.48298
\(957\) 18653.8 0.630086
\(958\) 7457.71 0.251511
\(959\) −1491.17 −0.0502112
\(960\) 1458.38 0.0490301
\(961\) −29381.5 −0.986253
\(962\) 9706.93 0.325326
\(963\) −15924.1 −0.532864
\(964\) −104164. −3.48019
\(965\) −11764.2 −0.392438
\(966\) 46932.5 1.56317
\(967\) 13468.7 0.447906 0.223953 0.974600i \(-0.428104\pi\)
0.223953 + 0.974600i \(0.428104\pi\)
\(968\) −68902.9 −2.28784
\(969\) −14247.6 −0.472342
\(970\) −25085.6 −0.830361
\(971\) 18009.0 0.595197 0.297598 0.954691i \(-0.403814\pi\)
0.297598 + 0.954691i \(0.403814\pi\)
\(972\) −4304.22 −0.142035
\(973\) 69030.4 2.27442
\(974\) 53075.3 1.74604
\(975\) −4466.85 −0.146722
\(976\) −91354.3 −2.99608
\(977\) 39514.9 1.29395 0.646977 0.762510i \(-0.276033\pi\)
0.646977 + 0.762510i \(0.276033\pi\)
\(978\) 52255.7 1.70854
\(979\) 8538.62 0.278749
\(980\) 64002.7 2.08622
\(981\) −16758.7 −0.545427
\(982\) −41204.8 −1.33900
\(983\) −2941.64 −0.0954464 −0.0477232 0.998861i \(-0.515197\pi\)
−0.0477232 + 0.998861i \(0.515197\pi\)
\(984\) −41076.6 −1.33077
\(985\) 6954.45 0.224962
\(986\) 61966.3 2.00143
\(987\) −32456.5 −1.04671
\(988\) −13303.4 −0.428377
\(989\) 48024.3 1.54407
\(990\) −13762.5 −0.441821
\(991\) 22197.7 0.711537 0.355769 0.934574i \(-0.384219\pi\)
0.355769 + 0.934574i \(0.384219\pi\)
\(992\) −3113.37 −0.0996469
\(993\) −20111.9 −0.642731
\(994\) −116516. −3.71797
\(995\) 22103.9 0.704261
\(996\) 4016.76 0.127787
\(997\) 2312.86 0.0734695 0.0367347 0.999325i \(-0.488304\pi\)
0.0367347 + 0.999325i \(0.488304\pi\)
\(998\) 76005.9 2.41074
\(999\) −3182.76 −0.100799
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 177.4.a.b.1.1 7
3.2 odd 2 531.4.a.c.1.7 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.4.a.b.1.1 7 1.1 even 1 trivial
531.4.a.c.1.7 7 3.2 odd 2