Properties

Label 177.4.a.d.1.7
Level $177$
Weight $4$
Character 177.1
Self dual yes
Analytic conductor $10.443$
Analytic rank $0$
Dimension $8$
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: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Defining polynomial: \(x^{8} - 2 x^{7} - 45 x^{6} + 47 x^{5} + 654 x^{4} - 157 x^{3} - 2898 x^{2} + 96 x + 2432\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(-3.08481\) of defining polynomial
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+4.08481 q^{2} +3.00000 q^{3} +8.68564 q^{4} -7.45529 q^{5} +12.2544 q^{6} +34.0237 q^{7} +2.80073 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q+4.08481 q^{2} +3.00000 q^{3} +8.68564 q^{4} -7.45529 q^{5} +12.2544 q^{6} +34.0237 q^{7} +2.80073 q^{8} +9.00000 q^{9} -30.4534 q^{10} +30.1014 q^{11} +26.0569 q^{12} -5.30717 q^{13} +138.980 q^{14} -22.3659 q^{15} -58.0447 q^{16} +63.2506 q^{17} +36.7633 q^{18} -86.0442 q^{19} -64.7540 q^{20} +102.071 q^{21} +122.958 q^{22} +83.0398 q^{23} +8.40218 q^{24} -69.4186 q^{25} -21.6788 q^{26} +27.0000 q^{27} +295.518 q^{28} -27.8076 q^{29} -91.3603 q^{30} -48.3051 q^{31} -259.507 q^{32} +90.3042 q^{33} +258.366 q^{34} -253.657 q^{35} +78.1708 q^{36} -358.130 q^{37} -351.474 q^{38} -15.9215 q^{39} -20.8802 q^{40} -139.953 q^{41} +416.941 q^{42} -366.669 q^{43} +261.450 q^{44} -67.0976 q^{45} +339.202 q^{46} -130.162 q^{47} -174.134 q^{48} +814.613 q^{49} -283.562 q^{50} +189.752 q^{51} -46.0962 q^{52} +608.850 q^{53} +110.290 q^{54} -224.415 q^{55} +95.2911 q^{56} -258.133 q^{57} -113.588 q^{58} +59.0000 q^{59} -194.262 q^{60} -361.223 q^{61} -197.317 q^{62} +306.213 q^{63} -595.679 q^{64} +39.5665 q^{65} +368.875 q^{66} -519.397 q^{67} +549.372 q^{68} +249.120 q^{69} -1036.14 q^{70} -733.270 q^{71} +25.2065 q^{72} +1132.20 q^{73} -1462.89 q^{74} -208.256 q^{75} -747.349 q^{76} +1024.16 q^{77} -65.0363 q^{78} +280.538 q^{79} +432.740 q^{80} +81.0000 q^{81} -571.680 q^{82} +239.288 q^{83} +886.554 q^{84} -471.552 q^{85} -1497.77 q^{86} -83.4227 q^{87} +84.3058 q^{88} +1214.72 q^{89} -274.081 q^{90} -180.570 q^{91} +721.255 q^{92} -144.915 q^{93} -531.686 q^{94} +641.485 q^{95} -778.522 q^{96} +149.047 q^{97} +3327.54 q^{98} +270.913 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 6q^{2} + 24q^{3} + 34q^{4} + 42q^{5} + 18q^{6} + 53q^{7} + 51q^{8} + 72q^{9} + O(q^{10}) \) \( 8q + 6q^{2} + 24q^{3} + 34q^{4} + 42q^{5} + 18q^{6} + 53q^{7} + 51q^{8} + 72q^{9} + 21q^{10} + 67q^{11} + 102q^{12} + 33q^{13} + 79q^{14} + 126q^{15} - 30q^{16} + 139q^{17} + 54q^{18} + 64q^{19} + 117q^{20} + 159q^{21} - 84q^{22} + 226q^{23} + 153q^{24} + 96q^{25} + 24q^{26} + 216q^{27} + 34q^{28} + 456q^{29} + 63q^{30} + 124q^{31} + 174q^{32} + 201q^{33} - 114q^{34} + 556q^{35} + 306q^{36} + 127q^{37} + 237q^{38} + 99q^{39} - 188q^{40} + 425q^{41} + 237q^{42} - 115q^{43} + 510q^{44} + 378q^{45} - 711q^{46} + 420q^{47} - 90q^{48} + 171q^{49} - 137q^{50} + 417q^{51} - 922q^{52} + 98q^{53} + 162q^{54} - 616q^{55} - 412q^{56} + 192q^{57} - 1548q^{58} + 472q^{59} + 351q^{60} - 1254q^{61} - 766q^{62} + 477q^{63} - 2019q^{64} - 734q^{65} - 252q^{66} - 1010q^{67} - 503q^{68} + 678q^{69} - 2956q^{70} - 17q^{71} + 459q^{72} - 1180q^{73} - 1228q^{74} + 288q^{75} - 2008q^{76} + 441q^{77} + 72q^{78} - 873q^{79} - 865q^{80} + 648q^{81} - 3645q^{82} + 759q^{83} + 102q^{84} - 850q^{85} - 1226q^{86} + 1368q^{87} - 3047q^{88} + 988q^{89} + 189q^{90} - 2111q^{91} - 1062q^{92} + 372q^{93} - 2240q^{94} + 1822q^{95} + 522q^{96} - 668q^{97} - 1368q^{98} + 603q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.08481 1.44420 0.722099 0.691790i \(-0.243178\pi\)
0.722099 + 0.691790i \(0.243178\pi\)
\(3\) 3.00000 0.577350
\(4\) 8.68564 1.08571
\(5\) −7.45529 −0.666822 −0.333411 0.942782i \(-0.608200\pi\)
−0.333411 + 0.942782i \(0.608200\pi\)
\(6\) 12.2544 0.833808
\(7\) 34.0237 1.83711 0.918554 0.395296i \(-0.129358\pi\)
0.918554 + 0.395296i \(0.129358\pi\)
\(8\) 2.80073 0.123776
\(9\) 9.00000 0.333333
\(10\) −30.4534 −0.963022
\(11\) 30.1014 0.825083 0.412542 0.910939i \(-0.364641\pi\)
0.412542 + 0.910939i \(0.364641\pi\)
\(12\) 26.0569 0.626832
\(13\) −5.30717 −0.113226 −0.0566132 0.998396i \(-0.518030\pi\)
−0.0566132 + 0.998396i \(0.518030\pi\)
\(14\) 138.980 2.65315
\(15\) −22.3659 −0.384990
\(16\) −58.0447 −0.906949
\(17\) 63.2506 0.902384 0.451192 0.892427i \(-0.350999\pi\)
0.451192 + 0.892427i \(0.350999\pi\)
\(18\) 36.7633 0.481399
\(19\) −86.0442 −1.03894 −0.519471 0.854488i \(-0.673871\pi\)
−0.519471 + 0.854488i \(0.673871\pi\)
\(20\) −64.7540 −0.723972
\(21\) 102.071 1.06065
\(22\) 122.958 1.19158
\(23\) 83.0398 0.752826 0.376413 0.926452i \(-0.377157\pi\)
0.376413 + 0.926452i \(0.377157\pi\)
\(24\) 8.40218 0.0714620
\(25\) −69.4186 −0.555349
\(26\) −21.6788 −0.163521
\(27\) 27.0000 0.192450
\(28\) 295.518 1.99456
\(29\) −27.8076 −0.178060 −0.0890299 0.996029i \(-0.528377\pi\)
−0.0890299 + 0.996029i \(0.528377\pi\)
\(30\) −91.3603 −0.556001
\(31\) −48.3051 −0.279866 −0.139933 0.990161i \(-0.544689\pi\)
−0.139933 + 0.990161i \(0.544689\pi\)
\(32\) −259.507 −1.43359
\(33\) 90.3042 0.476362
\(34\) 258.366 1.30322
\(35\) −253.657 −1.22502
\(36\) 78.1708 0.361902
\(37\) −358.130 −1.59125 −0.795625 0.605789i \(-0.792857\pi\)
−0.795625 + 0.605789i \(0.792857\pi\)
\(38\) −351.474 −1.50044
\(39\) −15.9215 −0.0653713
\(40\) −20.8802 −0.0825363
\(41\) −139.953 −0.533096 −0.266548 0.963822i \(-0.585883\pi\)
−0.266548 + 0.963822i \(0.585883\pi\)
\(42\) 416.941 1.53179
\(43\) −366.669 −1.30038 −0.650192 0.759770i \(-0.725312\pi\)
−0.650192 + 0.759770i \(0.725312\pi\)
\(44\) 261.450 0.895797
\(45\) −67.0976 −0.222274
\(46\) 339.202 1.08723
\(47\) −130.162 −0.403959 −0.201979 0.979390i \(-0.564737\pi\)
−0.201979 + 0.979390i \(0.564737\pi\)
\(48\) −174.134 −0.523627
\(49\) 814.613 2.37497
\(50\) −283.562 −0.802034
\(51\) 189.752 0.520992
\(52\) −46.0962 −0.122931
\(53\) 608.850 1.57796 0.788982 0.614417i \(-0.210609\pi\)
0.788982 + 0.614417i \(0.210609\pi\)
\(54\) 110.290 0.277936
\(55\) −224.415 −0.550183
\(56\) 95.2911 0.227389
\(57\) −258.133 −0.599833
\(58\) −113.588 −0.257153
\(59\) 59.0000 0.130189
\(60\) −194.262 −0.417985
\(61\) −361.223 −0.758194 −0.379097 0.925357i \(-0.623765\pi\)
−0.379097 + 0.925357i \(0.623765\pi\)
\(62\) −197.317 −0.404182
\(63\) 306.213 0.612369
\(64\) −595.679 −1.16344
\(65\) 39.5665 0.0755018
\(66\) 368.875 0.687961
\(67\) −519.397 −0.947082 −0.473541 0.880772i \(-0.657024\pi\)
−0.473541 + 0.880772i \(0.657024\pi\)
\(68\) 549.372 0.979723
\(69\) 249.120 0.434644
\(70\) −1036.14 −1.76917
\(71\) −733.270 −1.22568 −0.612839 0.790208i \(-0.709973\pi\)
−0.612839 + 0.790208i \(0.709973\pi\)
\(72\) 25.2065 0.0412586
\(73\) 1132.20 1.81525 0.907626 0.419779i \(-0.137893\pi\)
0.907626 + 0.419779i \(0.137893\pi\)
\(74\) −1462.89 −2.29808
\(75\) −208.256 −0.320631
\(76\) −747.349 −1.12798
\(77\) 1024.16 1.51577
\(78\) −65.0363 −0.0944091
\(79\) 280.538 0.399532 0.199766 0.979844i \(-0.435982\pi\)
0.199766 + 0.979844i \(0.435982\pi\)
\(80\) 432.740 0.604773
\(81\) 81.0000 0.111111
\(82\) −571.680 −0.769896
\(83\) 239.288 0.316450 0.158225 0.987403i \(-0.449423\pi\)
0.158225 + 0.987403i \(0.449423\pi\)
\(84\) 886.554 1.15156
\(85\) −471.552 −0.601729
\(86\) −1497.77 −1.87801
\(87\) −83.4227 −0.102803
\(88\) 84.3058 0.102125
\(89\) 1214.72 1.44674 0.723372 0.690459i \(-0.242591\pi\)
0.723372 + 0.690459i \(0.242591\pi\)
\(90\) −274.081 −0.321007
\(91\) −180.570 −0.208009
\(92\) 721.255 0.817348
\(93\) −144.915 −0.161581
\(94\) −531.686 −0.583396
\(95\) 641.485 0.692789
\(96\) −778.522 −0.827683
\(97\) 149.047 0.156015 0.0780074 0.996953i \(-0.475144\pi\)
0.0780074 + 0.996953i \(0.475144\pi\)
\(98\) 3327.54 3.42992
\(99\) 270.913 0.275028
\(100\) −602.946 −0.602946
\(101\) −491.208 −0.483931 −0.241965 0.970285i \(-0.577792\pi\)
−0.241965 + 0.970285i \(0.577792\pi\)
\(102\) 775.099 0.752415
\(103\) −1710.99 −1.63679 −0.818393 0.574658i \(-0.805135\pi\)
−0.818393 + 0.574658i \(0.805135\pi\)
\(104\) −14.8639 −0.0140147
\(105\) −760.970 −0.707267
\(106\) 2487.04 2.27889
\(107\) 19.6195 0.0177261 0.00886304 0.999961i \(-0.497179\pi\)
0.00886304 + 0.999961i \(0.497179\pi\)
\(108\) 234.512 0.208944
\(109\) 227.070 0.199535 0.0997677 0.995011i \(-0.468190\pi\)
0.0997677 + 0.995011i \(0.468190\pi\)
\(110\) −916.691 −0.794573
\(111\) −1074.39 −0.918709
\(112\) −1974.90 −1.66616
\(113\) −406.168 −0.338134 −0.169067 0.985605i \(-0.554075\pi\)
−0.169067 + 0.985605i \(0.554075\pi\)
\(114\) −1054.42 −0.866278
\(115\) −619.086 −0.502001
\(116\) −241.527 −0.193320
\(117\) −47.7645 −0.0377421
\(118\) 241.004 0.188018
\(119\) 2152.02 1.65778
\(120\) −62.6407 −0.0476524
\(121\) −424.905 −0.319238
\(122\) −1475.52 −1.09498
\(123\) −419.858 −0.307783
\(124\) −419.561 −0.303852
\(125\) 1449.45 1.03714
\(126\) 1250.82 0.884382
\(127\) 1305.00 0.911810 0.455905 0.890028i \(-0.349316\pi\)
0.455905 + 0.890028i \(0.349316\pi\)
\(128\) −357.176 −0.246642
\(129\) −1100.01 −0.750777
\(130\) 161.621 0.109040
\(131\) 1256.06 0.837727 0.418863 0.908049i \(-0.362429\pi\)
0.418863 + 0.908049i \(0.362429\pi\)
\(132\) 784.350 0.517189
\(133\) −2927.54 −1.90865
\(134\) −2121.64 −1.36777
\(135\) −201.293 −0.128330
\(136\) 177.148 0.111693
\(137\) −1061.86 −0.662198 −0.331099 0.943596i \(-0.607419\pi\)
−0.331099 + 0.943596i \(0.607419\pi\)
\(138\) 1017.61 0.627712
\(139\) −1006.82 −0.614368 −0.307184 0.951650i \(-0.599387\pi\)
−0.307184 + 0.951650i \(0.599387\pi\)
\(140\) −2203.17 −1.33001
\(141\) −390.485 −0.233226
\(142\) −2995.27 −1.77012
\(143\) −159.753 −0.0934212
\(144\) −522.403 −0.302316
\(145\) 207.313 0.118734
\(146\) 4624.80 2.62158
\(147\) 2443.84 1.37119
\(148\) −3110.59 −1.72763
\(149\) 971.154 0.533960 0.266980 0.963702i \(-0.413974\pi\)
0.266980 + 0.963702i \(0.413974\pi\)
\(150\) −850.685 −0.463054
\(151\) 3599.13 1.93969 0.969843 0.243729i \(-0.0783708\pi\)
0.969843 + 0.243729i \(0.0783708\pi\)
\(152\) −240.986 −0.128596
\(153\) 569.255 0.300795
\(154\) 4183.50 2.18907
\(155\) 360.129 0.186621
\(156\) −138.289 −0.0709740
\(157\) 1208.64 0.614393 0.307197 0.951646i \(-0.400609\pi\)
0.307197 + 0.951646i \(0.400609\pi\)
\(158\) 1145.94 0.577003
\(159\) 1826.55 0.911037
\(160\) 1934.70 0.955948
\(161\) 2825.32 1.38302
\(162\) 330.869 0.160466
\(163\) 686.989 0.330118 0.165059 0.986284i \(-0.447219\pi\)
0.165059 + 0.986284i \(0.447219\pi\)
\(164\) −1215.58 −0.578785
\(165\) −673.244 −0.317648
\(166\) 977.447 0.457016
\(167\) 3111.46 1.44175 0.720874 0.693066i \(-0.243740\pi\)
0.720874 + 0.693066i \(0.243740\pi\)
\(168\) 285.873 0.131283
\(169\) −2168.83 −0.987180
\(170\) −1926.20 −0.869015
\(171\) −774.398 −0.346314
\(172\) −3184.76 −1.41183
\(173\) 574.070 0.252288 0.126144 0.992012i \(-0.459740\pi\)
0.126144 + 0.992012i \(0.459740\pi\)
\(174\) −340.765 −0.148468
\(175\) −2361.88 −1.02024
\(176\) −1747.23 −0.748308
\(177\) 177.000 0.0751646
\(178\) 4961.90 2.08938
\(179\) 3296.00 1.37628 0.688142 0.725576i \(-0.258426\pi\)
0.688142 + 0.725576i \(0.258426\pi\)
\(180\) −582.786 −0.241324
\(181\) 2022.64 0.830616 0.415308 0.909681i \(-0.363674\pi\)
0.415308 + 0.909681i \(0.363674\pi\)
\(182\) −737.592 −0.300406
\(183\) −1083.67 −0.437743
\(184\) 232.572 0.0931816
\(185\) 2669.97 1.06108
\(186\) −591.951 −0.233355
\(187\) 1903.93 0.744542
\(188\) −1130.54 −0.438580
\(189\) 918.640 0.353552
\(190\) 2620.34 1.00052
\(191\) −3437.29 −1.30216 −0.651082 0.759007i \(-0.725685\pi\)
−0.651082 + 0.759007i \(0.725685\pi\)
\(192\) −1787.04 −0.671710
\(193\) 4382.77 1.63460 0.817301 0.576210i \(-0.195469\pi\)
0.817301 + 0.576210i \(0.195469\pi\)
\(194\) 608.828 0.225316
\(195\) 118.699 0.0435910
\(196\) 7075.44 2.57851
\(197\) −5031.35 −1.81964 −0.909819 0.415004i \(-0.863780\pi\)
−0.909819 + 0.415004i \(0.863780\pi\)
\(198\) 1106.63 0.397194
\(199\) 4357.76 1.55233 0.776164 0.630532i \(-0.217163\pi\)
0.776164 + 0.630532i \(0.217163\pi\)
\(200\) −194.423 −0.0687387
\(201\) −1558.19 −0.546798
\(202\) −2006.49 −0.698891
\(203\) −946.116 −0.327115
\(204\) 1648.12 0.565643
\(205\) 1043.39 0.355480
\(206\) −6989.07 −2.36384
\(207\) 747.359 0.250942
\(208\) 308.053 0.102691
\(209\) −2590.05 −0.857213
\(210\) −3108.42 −1.02143
\(211\) −4436.30 −1.44743 −0.723715 0.690099i \(-0.757567\pi\)
−0.723715 + 0.690099i \(0.757567\pi\)
\(212\) 5288.26 1.71320
\(213\) −2199.81 −0.707645
\(214\) 80.1420 0.0256000
\(215\) 2733.63 0.867124
\(216\) 75.6196 0.0238207
\(217\) −1643.52 −0.514144
\(218\) 927.536 0.288168
\(219\) 3396.59 1.04804
\(220\) −1949.19 −0.597337
\(221\) −335.682 −0.102174
\(222\) −4388.68 −1.32680
\(223\) −518.147 −0.155595 −0.0777975 0.996969i \(-0.524789\pi\)
−0.0777975 + 0.996969i \(0.524789\pi\)
\(224\) −8829.40 −2.63366
\(225\) −624.768 −0.185116
\(226\) −1659.12 −0.488332
\(227\) −5358.31 −1.56671 −0.783355 0.621574i \(-0.786493\pi\)
−0.783355 + 0.621574i \(0.786493\pi\)
\(228\) −2242.05 −0.651242
\(229\) 2805.75 0.809647 0.404823 0.914395i \(-0.367333\pi\)
0.404823 + 0.914395i \(0.367333\pi\)
\(230\) −2528.85 −0.724988
\(231\) 3072.48 0.875128
\(232\) −77.8813 −0.0220395
\(233\) −4221.06 −1.18683 −0.593414 0.804897i \(-0.702220\pi\)
−0.593414 + 0.804897i \(0.702220\pi\)
\(234\) −195.109 −0.0545071
\(235\) 970.394 0.269368
\(236\) 512.453 0.141347
\(237\) 841.614 0.230670
\(238\) 8790.59 2.39416
\(239\) 5412.00 1.46474 0.732371 0.680905i \(-0.238414\pi\)
0.732371 + 0.680905i \(0.238414\pi\)
\(240\) 1298.22 0.349166
\(241\) −3003.56 −0.802806 −0.401403 0.915902i \(-0.631477\pi\)
−0.401403 + 0.915902i \(0.631477\pi\)
\(242\) −1735.66 −0.461042
\(243\) 243.000 0.0641500
\(244\) −3137.45 −0.823175
\(245\) −6073.18 −1.58368
\(246\) −1715.04 −0.444500
\(247\) 456.651 0.117636
\(248\) −135.289 −0.0346407
\(249\) 717.865 0.182702
\(250\) 5920.71 1.49784
\(251\) −900.091 −0.226348 −0.113174 0.993575i \(-0.536102\pi\)
−0.113174 + 0.993575i \(0.536102\pi\)
\(252\) 2659.66 0.664853
\(253\) 2499.62 0.621144
\(254\) 5330.67 1.31683
\(255\) −1414.66 −0.347408
\(256\) 3306.44 0.807236
\(257\) 3419.24 0.829907 0.414953 0.909843i \(-0.363798\pi\)
0.414953 + 0.909843i \(0.363798\pi\)
\(258\) −4493.32 −1.08427
\(259\) −12184.9 −2.92330
\(260\) 343.660 0.0819727
\(261\) −250.268 −0.0593533
\(262\) 5130.75 1.20984
\(263\) 1273.15 0.298501 0.149250 0.988799i \(-0.452314\pi\)
0.149250 + 0.988799i \(0.452314\pi\)
\(264\) 252.917 0.0589621
\(265\) −4539.16 −1.05222
\(266\) −11958.4 −2.75646
\(267\) 3644.16 0.835278
\(268\) −4511.30 −1.02825
\(269\) 3437.51 0.779141 0.389570 0.920997i \(-0.372624\pi\)
0.389570 + 0.920997i \(0.372624\pi\)
\(270\) −822.242 −0.185334
\(271\) −2409.95 −0.540199 −0.270100 0.962832i \(-0.587057\pi\)
−0.270100 + 0.962832i \(0.587057\pi\)
\(272\) −3671.36 −0.818416
\(273\) −541.709 −0.120094
\(274\) −4337.51 −0.956344
\(275\) −2089.60 −0.458209
\(276\) 2163.76 0.471896
\(277\) −7279.05 −1.57890 −0.789450 0.613814i \(-0.789634\pi\)
−0.789450 + 0.613814i \(0.789634\pi\)
\(278\) −4112.66 −0.887269
\(279\) −434.746 −0.0932887
\(280\) −710.423 −0.151628
\(281\) 6298.57 1.33716 0.668579 0.743641i \(-0.266903\pi\)
0.668579 + 0.743641i \(0.266903\pi\)
\(282\) −1595.06 −0.336824
\(283\) −3561.67 −0.748124 −0.374062 0.927404i \(-0.622035\pi\)
−0.374062 + 0.927404i \(0.622035\pi\)
\(284\) −6368.92 −1.33072
\(285\) 1924.45 0.399982
\(286\) −652.561 −0.134919
\(287\) −4761.71 −0.979355
\(288\) −2335.57 −0.477863
\(289\) −912.361 −0.185703
\(290\) 846.835 0.171475
\(291\) 447.141 0.0900752
\(292\) 9833.84 1.97083
\(293\) −4374.10 −0.872142 −0.436071 0.899912i \(-0.643630\pi\)
−0.436071 + 0.899912i \(0.643630\pi\)
\(294\) 9982.61 1.98026
\(295\) −439.862 −0.0868128
\(296\) −1003.02 −0.196958
\(297\) 812.738 0.158787
\(298\) 3966.98 0.771144
\(299\) −440.706 −0.0852398
\(300\) −1808.84 −0.348111
\(301\) −12475.4 −2.38895
\(302\) 14701.7 2.80129
\(303\) −1473.62 −0.279397
\(304\) 4994.41 0.942267
\(305\) 2693.02 0.505580
\(306\) 2325.30 0.434407
\(307\) 5264.64 0.978726 0.489363 0.872080i \(-0.337229\pi\)
0.489363 + 0.872080i \(0.337229\pi\)
\(308\) 8895.50 1.64568
\(309\) −5132.98 −0.944999
\(310\) 1471.06 0.269517
\(311\) 3889.00 0.709083 0.354542 0.935040i \(-0.384637\pi\)
0.354542 + 0.935040i \(0.384637\pi\)
\(312\) −44.5918 −0.00809138
\(313\) −8815.40 −1.59194 −0.795968 0.605339i \(-0.793038\pi\)
−0.795968 + 0.605339i \(0.793038\pi\)
\(314\) 4937.05 0.887305
\(315\) −2282.91 −0.408341
\(316\) 2436.65 0.433774
\(317\) −10172.7 −1.80239 −0.901196 0.433412i \(-0.857309\pi\)
−0.901196 + 0.433412i \(0.857309\pi\)
\(318\) 7461.11 1.31572
\(319\) −837.047 −0.146914
\(320\) 4440.96 0.775804
\(321\) 58.8586 0.0102342
\(322\) 11540.9 1.99736
\(323\) −5442.35 −0.937524
\(324\) 703.537 0.120634
\(325\) 368.416 0.0628802
\(326\) 2806.22 0.476755
\(327\) 681.210 0.115202
\(328\) −391.969 −0.0659844
\(329\) −4428.59 −0.742115
\(330\) −2750.07 −0.458747
\(331\) −2899.09 −0.481415 −0.240707 0.970598i \(-0.577379\pi\)
−0.240707 + 0.970598i \(0.577379\pi\)
\(332\) 2078.37 0.343571
\(333\) −3223.17 −0.530417
\(334\) 12709.7 2.08217
\(335\) 3872.26 0.631534
\(336\) −5924.69 −0.961960
\(337\) −11201.0 −1.81055 −0.905277 0.424821i \(-0.860337\pi\)
−0.905277 + 0.424821i \(0.860337\pi\)
\(338\) −8859.27 −1.42568
\(339\) −1218.51 −0.195222
\(340\) −4095.73 −0.653300
\(341\) −1454.05 −0.230913
\(342\) −3163.27 −0.500146
\(343\) 16046.0 2.52596
\(344\) −1026.94 −0.160956
\(345\) −1857.26 −0.289830
\(346\) 2344.97 0.364353
\(347\) 9034.82 1.39774 0.698868 0.715251i \(-0.253687\pi\)
0.698868 + 0.715251i \(0.253687\pi\)
\(348\) −724.580 −0.111614
\(349\) 2985.35 0.457886 0.228943 0.973440i \(-0.426473\pi\)
0.228943 + 0.973440i \(0.426473\pi\)
\(350\) −9647.82 −1.47342
\(351\) −143.294 −0.0217904
\(352\) −7811.54 −1.18283
\(353\) 10272.8 1.54892 0.774458 0.632626i \(-0.218023\pi\)
0.774458 + 0.632626i \(0.218023\pi\)
\(354\) 723.011 0.108553
\(355\) 5466.74 0.817308
\(356\) 10550.6 1.57074
\(357\) 6456.06 0.957118
\(358\) 13463.5 1.98763
\(359\) −4648.82 −0.683442 −0.341721 0.939802i \(-0.611010\pi\)
−0.341721 + 0.939802i \(0.611010\pi\)
\(360\) −187.922 −0.0275121
\(361\) 544.604 0.0793999
\(362\) 8262.08 1.19957
\(363\) −1274.72 −0.184312
\(364\) −1568.36 −0.225837
\(365\) −8440.84 −1.21045
\(366\) −4426.57 −0.632188
\(367\) −1646.71 −0.234216 −0.117108 0.993119i \(-0.537362\pi\)
−0.117108 + 0.993119i \(0.537362\pi\)
\(368\) −4820.03 −0.682775
\(369\) −1259.57 −0.177699
\(370\) 10906.3 1.53241
\(371\) 20715.4 2.89889
\(372\) −1258.68 −0.175429
\(373\) 6528.88 0.906307 0.453154 0.891432i \(-0.350299\pi\)
0.453154 + 0.891432i \(0.350299\pi\)
\(374\) 7777.19 1.07527
\(375\) 4348.34 0.598793
\(376\) −364.548 −0.0500003
\(377\) 147.579 0.0201611
\(378\) 3752.47 0.510598
\(379\) 6421.70 0.870344 0.435172 0.900347i \(-0.356688\pi\)
0.435172 + 0.900347i \(0.356688\pi\)
\(380\) 5571.71 0.752165
\(381\) 3915.00 0.526434
\(382\) −14040.7 −1.88058
\(383\) −3048.13 −0.406663 −0.203332 0.979110i \(-0.565177\pi\)
−0.203332 + 0.979110i \(0.565177\pi\)
\(384\) −1071.53 −0.142399
\(385\) −7635.42 −1.01075
\(386\) 17902.7 2.36069
\(387\) −3300.02 −0.433461
\(388\) 1294.57 0.169386
\(389\) 8129.80 1.05963 0.529816 0.848112i \(-0.322261\pi\)
0.529816 + 0.848112i \(0.322261\pi\)
\(390\) 484.864 0.0629540
\(391\) 5252.32 0.679338
\(392\) 2281.51 0.293963
\(393\) 3768.17 0.483662
\(394\) −20552.1 −2.62792
\(395\) −2091.49 −0.266416
\(396\) 2353.05 0.298599
\(397\) −5072.35 −0.641244 −0.320622 0.947207i \(-0.603892\pi\)
−0.320622 + 0.947207i \(0.603892\pi\)
\(398\) 17800.6 2.24187
\(399\) −8782.63 −1.10196
\(400\) 4029.39 0.503673
\(401\) 9539.59 1.18799 0.593996 0.804468i \(-0.297550\pi\)
0.593996 + 0.804468i \(0.297550\pi\)
\(402\) −6364.91 −0.789684
\(403\) 256.363 0.0316883
\(404\) −4266.46 −0.525406
\(405\) −603.879 −0.0740913
\(406\) −3864.70 −0.472419
\(407\) −10780.2 −1.31291
\(408\) 531.443 0.0644861
\(409\) 10696.8 1.29321 0.646605 0.762825i \(-0.276188\pi\)
0.646605 + 0.762825i \(0.276188\pi\)
\(410\) 4262.04 0.513383
\(411\) −3185.59 −0.382320
\(412\) −14861.1 −1.77707
\(413\) 2007.40 0.239171
\(414\) 3052.82 0.362410
\(415\) −1783.96 −0.211015
\(416\) 1377.25 0.162320
\(417\) −3020.45 −0.354706
\(418\) −10579.9 −1.23799
\(419\) −2134.24 −0.248841 −0.124421 0.992230i \(-0.539707\pi\)
−0.124421 + 0.992230i \(0.539707\pi\)
\(420\) −6609.52 −0.767884
\(421\) 6780.72 0.784970 0.392485 0.919758i \(-0.371616\pi\)
0.392485 + 0.919758i \(0.371616\pi\)
\(422\) −18121.4 −2.09037
\(423\) −1171.46 −0.134653
\(424\) 1705.22 0.195314
\(425\) −4390.77 −0.501138
\(426\) −8985.80 −1.02198
\(427\) −12290.1 −1.39288
\(428\) 170.408 0.0192453
\(429\) −479.260 −0.0539368
\(430\) 11166.3 1.25230
\(431\) −16691.4 −1.86542 −0.932708 0.360633i \(-0.882561\pi\)
−0.932708 + 0.360633i \(0.882561\pi\)
\(432\) −1567.21 −0.174542
\(433\) −2902.98 −0.322190 −0.161095 0.986939i \(-0.551503\pi\)
−0.161095 + 0.986939i \(0.551503\pi\)
\(434\) −6713.46 −0.742526
\(435\) 621.940 0.0685512
\(436\) 1972.25 0.216637
\(437\) −7145.10 −0.782143
\(438\) 13874.4 1.51357
\(439\) 8526.93 0.927034 0.463517 0.886088i \(-0.346587\pi\)
0.463517 + 0.886088i \(0.346587\pi\)
\(440\) −628.524 −0.0680993
\(441\) 7331.52 0.791655
\(442\) −1371.19 −0.147559
\(443\) −3174.04 −0.340413 −0.170207 0.985408i \(-0.554444\pi\)
−0.170207 + 0.985408i \(0.554444\pi\)
\(444\) −9331.78 −0.997447
\(445\) −9056.10 −0.964720
\(446\) −2116.53 −0.224710
\(447\) 2913.46 0.308282
\(448\) −20267.2 −2.13736
\(449\) −2111.09 −0.221889 −0.110945 0.993827i \(-0.535388\pi\)
−0.110945 + 0.993827i \(0.535388\pi\)
\(450\) −2552.06 −0.267345
\(451\) −4212.77 −0.439849
\(452\) −3527.83 −0.367114
\(453\) 10797.4 1.11988
\(454\) −21887.6 −2.26264
\(455\) 1346.20 0.138705
\(456\) −722.959 −0.0742448
\(457\) −6995.71 −0.716074 −0.358037 0.933707i \(-0.616554\pi\)
−0.358037 + 0.933707i \(0.616554\pi\)
\(458\) 11460.9 1.16929
\(459\) 1707.77 0.173664
\(460\) −5377.16 −0.545025
\(461\) 426.893 0.0431288 0.0215644 0.999767i \(-0.493135\pi\)
0.0215644 + 0.999767i \(0.493135\pi\)
\(462\) 12550.5 1.26386
\(463\) 2901.91 0.291281 0.145641 0.989338i \(-0.453476\pi\)
0.145641 + 0.989338i \(0.453476\pi\)
\(464\) 1614.08 0.161491
\(465\) 1080.39 0.107746
\(466\) −17242.2 −1.71401
\(467\) 8424.34 0.834758 0.417379 0.908733i \(-0.362949\pi\)
0.417379 + 0.908733i \(0.362949\pi\)
\(468\) −414.866 −0.0409769
\(469\) −17671.8 −1.73989
\(470\) 3963.87 0.389021
\(471\) 3625.91 0.354720
\(472\) 165.243 0.0161142
\(473\) −11037.3 −1.07293
\(474\) 3437.83 0.333133
\(475\) 5973.07 0.576975
\(476\) 18691.7 1.79986
\(477\) 5479.65 0.525988
\(478\) 22107.0 2.11538
\(479\) −10436.0 −0.995476 −0.497738 0.867327i \(-0.665836\pi\)
−0.497738 + 0.867327i \(0.665836\pi\)
\(480\) 5804.11 0.551917
\(481\) 1900.66 0.180172
\(482\) −12269.0 −1.15941
\(483\) 8475.97 0.798489
\(484\) −3690.58 −0.346598
\(485\) −1111.19 −0.104034
\(486\) 992.608 0.0926453
\(487\) 6183.28 0.575341 0.287671 0.957729i \(-0.407119\pi\)
0.287671 + 0.957729i \(0.407119\pi\)
\(488\) −1011.69 −0.0938460
\(489\) 2060.97 0.190593
\(490\) −24807.8 −2.28714
\(491\) −4039.61 −0.371293 −0.185647 0.982617i \(-0.559438\pi\)
−0.185647 + 0.982617i \(0.559438\pi\)
\(492\) −3646.74 −0.334162
\(493\) −1758.84 −0.160678
\(494\) 1865.33 0.169889
\(495\) −2019.73 −0.183394
\(496\) 2803.86 0.253824
\(497\) −24948.6 −2.25170
\(498\) 2932.34 0.263858
\(499\) −17134.6 −1.53718 −0.768589 0.639743i \(-0.779041\pi\)
−0.768589 + 0.639743i \(0.779041\pi\)
\(500\) 12589.4 1.12603
\(501\) 9334.38 0.832394
\(502\) −3676.70 −0.326890
\(503\) 19616.1 1.73884 0.869422 0.494069i \(-0.164491\pi\)
0.869422 + 0.494069i \(0.164491\pi\)
\(504\) 857.620 0.0757965
\(505\) 3662.10 0.322695
\(506\) 10210.4 0.897055
\(507\) −6506.50 −0.569949
\(508\) 11334.8 0.989957
\(509\) 15281.4 1.33072 0.665358 0.746524i \(-0.268279\pi\)
0.665358 + 0.746524i \(0.268279\pi\)
\(510\) −5778.59 −0.501726
\(511\) 38521.5 3.33481
\(512\) 16363.6 1.41245
\(513\) −2323.19 −0.199944
\(514\) 13966.9 1.19855
\(515\) 12755.9 1.09144
\(516\) −9554.28 −0.815123
\(517\) −3918.05 −0.333299
\(518\) −49773.1 −4.22182
\(519\) 1722.21 0.145658
\(520\) 110.815 0.00934530
\(521\) 20973.2 1.76363 0.881816 0.471593i \(-0.156321\pi\)
0.881816 + 0.471593i \(0.156321\pi\)
\(522\) −1022.30 −0.0857178
\(523\) 7587.00 0.634334 0.317167 0.948370i \(-0.397268\pi\)
0.317167 + 0.948370i \(0.397268\pi\)
\(524\) 10909.7 0.909525
\(525\) −7085.64 −0.589034
\(526\) 5200.57 0.431094
\(527\) −3055.33 −0.252547
\(528\) −5241.68 −0.432036
\(529\) −5271.39 −0.433253
\(530\) −18541.6 −1.51961
\(531\) 531.000 0.0433963
\(532\) −25427.6 −2.07223
\(533\) 742.753 0.0603606
\(534\) 14885.7 1.20631
\(535\) −146.269 −0.0118201
\(536\) −1454.69 −0.117226
\(537\) 9888.01 0.794598
\(538\) 14041.6 1.12523
\(539\) 24521.0 1.95954
\(540\) −1748.36 −0.139328
\(541\) 1078.04 0.0856721 0.0428360 0.999082i \(-0.486361\pi\)
0.0428360 + 0.999082i \(0.486361\pi\)
\(542\) −9844.18 −0.780154
\(543\) 6067.91 0.479556
\(544\) −16414.0 −1.29365
\(545\) −1692.87 −0.133054
\(546\) −2212.78 −0.173440
\(547\) −318.365 −0.0248854 −0.0124427 0.999923i \(-0.503961\pi\)
−0.0124427 + 0.999923i \(0.503961\pi\)
\(548\) −9222.97 −0.718952
\(549\) −3251.00 −0.252731
\(550\) −8535.61 −0.661744
\(551\) 2392.68 0.184994
\(552\) 697.715 0.0537984
\(553\) 9544.95 0.733983
\(554\) −29733.5 −2.28024
\(555\) 8009.90 0.612615
\(556\) −8744.87 −0.667023
\(557\) −7357.32 −0.559676 −0.279838 0.960047i \(-0.590281\pi\)
−0.279838 + 0.960047i \(0.590281\pi\)
\(558\) −1775.85 −0.134727
\(559\) 1945.98 0.147238
\(560\) 14723.4 1.11103
\(561\) 5711.80 0.429861
\(562\) 25728.5 1.93112
\(563\) −10907.4 −0.816505 −0.408253 0.912869i \(-0.633862\pi\)
−0.408253 + 0.912869i \(0.633862\pi\)
\(564\) −3391.62 −0.253214
\(565\) 3028.10 0.225475
\(566\) −14548.7 −1.08044
\(567\) 2755.92 0.204123
\(568\) −2053.69 −0.151709
\(569\) −8712.06 −0.641878 −0.320939 0.947100i \(-0.603998\pi\)
−0.320939 + 0.947100i \(0.603998\pi\)
\(570\) 7861.02 0.577653
\(571\) 120.132 0.00880446 0.00440223 0.999990i \(-0.498599\pi\)
0.00440223 + 0.999990i \(0.498599\pi\)
\(572\) −1387.56 −0.101428
\(573\) −10311.9 −0.751805
\(574\) −19450.7 −1.41438
\(575\) −5764.51 −0.418081
\(576\) −5361.11 −0.387812
\(577\) 2169.26 0.156512 0.0782560 0.996933i \(-0.475065\pi\)
0.0782560 + 0.996933i \(0.475065\pi\)
\(578\) −3726.82 −0.268192
\(579\) 13148.3 0.943738
\(580\) 1800.65 0.128910
\(581\) 8141.48 0.581352
\(582\) 1826.48 0.130086
\(583\) 18327.3 1.30195
\(584\) 3170.97 0.224684
\(585\) 356.098 0.0251673
\(586\) −17867.3 −1.25954
\(587\) −1300.42 −0.0914378 −0.0457189 0.998954i \(-0.514558\pi\)
−0.0457189 + 0.998954i \(0.514558\pi\)
\(588\) 21226.3 1.48871
\(589\) 4156.37 0.290765
\(590\) −1796.75 −0.125375
\(591\) −15094.1 −1.05057
\(592\) 20787.6 1.44318
\(593\) −13449.8 −0.931395 −0.465698 0.884944i \(-0.654197\pi\)
−0.465698 + 0.884944i \(0.654197\pi\)
\(594\) 3319.88 0.229320
\(595\) −16043.9 −1.10544
\(596\) 8435.10 0.579724
\(597\) 13073.3 0.896237
\(598\) −1800.20 −0.123103
\(599\) −11679.1 −0.796652 −0.398326 0.917244i \(-0.630409\pi\)
−0.398326 + 0.917244i \(0.630409\pi\)
\(600\) −583.268 −0.0396863
\(601\) −7992.33 −0.542452 −0.271226 0.962516i \(-0.587429\pi\)
−0.271226 + 0.962516i \(0.587429\pi\)
\(602\) −50959.8 −3.45011
\(603\) −4674.57 −0.315694
\(604\) 31260.7 2.10593
\(605\) 3167.79 0.212875
\(606\) −6019.46 −0.403505
\(607\) 9263.57 0.619434 0.309717 0.950829i \(-0.399766\pi\)
0.309717 + 0.950829i \(0.399766\pi\)
\(608\) 22329.1 1.48942
\(609\) −2838.35 −0.188860
\(610\) 11000.5 0.730157
\(611\) 690.791 0.0457388
\(612\) 4944.35 0.326574
\(613\) −11447.6 −0.754267 −0.377134 0.926159i \(-0.623090\pi\)
−0.377134 + 0.926159i \(0.623090\pi\)
\(614\) 21505.0 1.41347
\(615\) 3130.16 0.205236
\(616\) 2868.40 0.187615
\(617\) −27000.2 −1.76173 −0.880863 0.473371i \(-0.843037\pi\)
−0.880863 + 0.473371i \(0.843037\pi\)
\(618\) −20967.2 −1.36477
\(619\) 22497.9 1.46085 0.730425 0.682993i \(-0.239322\pi\)
0.730425 + 0.682993i \(0.239322\pi\)
\(620\) 3127.95 0.202615
\(621\) 2242.08 0.144881
\(622\) 15885.8 1.02406
\(623\) 41329.3 2.65782
\(624\) 924.160 0.0592884
\(625\) −2128.72 −0.136238
\(626\) −36009.2 −2.29907
\(627\) −7770.15 −0.494912
\(628\) 10497.8 0.667050
\(629\) −22652.0 −1.43592
\(630\) −9325.25 −0.589725
\(631\) 20510.4 1.29399 0.646994 0.762495i \(-0.276026\pi\)
0.646994 + 0.762495i \(0.276026\pi\)
\(632\) 785.710 0.0494523
\(633\) −13308.9 −0.835674
\(634\) −41553.7 −2.60301
\(635\) −9729.14 −0.608015
\(636\) 15864.8 0.989118
\(637\) −4323.29 −0.268909
\(638\) −3419.17 −0.212173
\(639\) −6599.43 −0.408559
\(640\) 2662.85 0.164466
\(641\) 9877.54 0.608642 0.304321 0.952570i \(-0.401570\pi\)
0.304321 + 0.952570i \(0.401570\pi\)
\(642\) 240.426 0.0147801
\(643\) 9789.87 0.600427 0.300214 0.953872i \(-0.402942\pi\)
0.300214 + 0.953872i \(0.402942\pi\)
\(644\) 24539.8 1.50156
\(645\) 8200.88 0.500634
\(646\) −22230.9 −1.35397
\(647\) −9704.28 −0.589667 −0.294834 0.955549i \(-0.595264\pi\)
−0.294834 + 0.955549i \(0.595264\pi\)
\(648\) 226.859 0.0137529
\(649\) 1775.98 0.107417
\(650\) 1504.91 0.0908114
\(651\) −4930.56 −0.296841
\(652\) 5966.95 0.358410
\(653\) 19355.5 1.15994 0.579970 0.814638i \(-0.303064\pi\)
0.579970 + 0.814638i \(0.303064\pi\)
\(654\) 2782.61 0.166374
\(655\) −9364.27 −0.558614
\(656\) 8123.52 0.483491
\(657\) 10189.8 0.605084
\(658\) −18089.9 −1.07176
\(659\) −9598.00 −0.567352 −0.283676 0.958920i \(-0.591554\pi\)
−0.283676 + 0.958920i \(0.591554\pi\)
\(660\) −5847.56 −0.344873
\(661\) −30099.9 −1.77118 −0.885591 0.464465i \(-0.846247\pi\)
−0.885591 + 0.464465i \(0.846247\pi\)
\(662\) −11842.2 −0.695258
\(663\) −1007.04 −0.0589900
\(664\) 670.181 0.0391688
\(665\) 21825.7 1.27273
\(666\) −13166.0 −0.766026
\(667\) −2309.14 −0.134048
\(668\) 27025.0 1.56531
\(669\) −1554.44 −0.0898328
\(670\) 15817.4 0.912060
\(671\) −10873.3 −0.625573
\(672\) −26488.2 −1.52054
\(673\) 4334.61 0.248272 0.124136 0.992265i \(-0.460384\pi\)
0.124136 + 0.992265i \(0.460384\pi\)
\(674\) −45753.9 −2.61480
\(675\) −1874.30 −0.106877
\(676\) −18837.7 −1.07179
\(677\) 26966.0 1.53085 0.765427 0.643523i \(-0.222528\pi\)
0.765427 + 0.643523i \(0.222528\pi\)
\(678\) −4977.36 −0.281938
\(679\) 5071.13 0.286616
\(680\) −1320.69 −0.0744795
\(681\) −16074.9 −0.904541
\(682\) −5939.52 −0.333484
\(683\) 4741.14 0.265615 0.132807 0.991142i \(-0.457601\pi\)
0.132807 + 0.991142i \(0.457601\pi\)
\(684\) −6726.14 −0.375995
\(685\) 7916.50 0.441568
\(686\) 65544.9 3.64798
\(687\) 8417.25 0.467450
\(688\) 21283.2 1.17938
\(689\) −3231.27 −0.178667
\(690\) −7586.54 −0.418572
\(691\) 7335.54 0.403845 0.201923 0.979401i \(-0.435281\pi\)
0.201923 + 0.979401i \(0.435281\pi\)
\(692\) 4986.17 0.273910
\(693\) 9217.45 0.505256
\(694\) 36905.5 2.01861
\(695\) 7506.12 0.409674
\(696\) −233.644 −0.0127245
\(697\) −8852.09 −0.481057
\(698\) 12194.6 0.661277
\(699\) −12663.2 −0.685216
\(700\) −20514.4 −1.10768
\(701\) 8441.52 0.454824 0.227412 0.973799i \(-0.426974\pi\)
0.227412 + 0.973799i \(0.426974\pi\)
\(702\) −585.326 −0.0314697
\(703\) 30815.0 1.65322
\(704\) −17930.8 −0.959932
\(705\) 2911.18 0.155520
\(706\) 41962.5 2.23694
\(707\) −16712.7 −0.889033
\(708\) 1537.36 0.0816066
\(709\) 9530.08 0.504809 0.252405 0.967622i \(-0.418779\pi\)
0.252405 + 0.967622i \(0.418779\pi\)
\(710\) 22330.6 1.18035
\(711\) 2524.84 0.133177
\(712\) 3402.10 0.179072
\(713\) −4011.25 −0.210691
\(714\) 26371.8 1.38227
\(715\) 1191.01 0.0622953
\(716\) 28627.9 1.49424
\(717\) 16236.0 0.845670
\(718\) −18989.5 −0.987024
\(719\) −8740.89 −0.453380 −0.226690 0.973967i \(-0.572790\pi\)
−0.226690 + 0.973967i \(0.572790\pi\)
\(720\) 3894.66 0.201591
\(721\) −58214.3 −3.00695
\(722\) 2224.60 0.114669
\(723\) −9010.68 −0.463500
\(724\) 17567.9 0.901804
\(725\) 1930.36 0.0988853
\(726\) −5206.97 −0.266183
\(727\) 19162.5 0.977575 0.488788 0.872403i \(-0.337439\pi\)
0.488788 + 0.872403i \(0.337439\pi\)
\(728\) −505.726 −0.0257465
\(729\) 729.000 0.0370370
\(730\) −34479.2 −1.74813
\(731\) −23192.0 −1.17345
\(732\) −9412.35 −0.475260
\(733\) 14807.2 0.746134 0.373067 0.927804i \(-0.378306\pi\)
0.373067 + 0.927804i \(0.378306\pi\)
\(734\) −6726.48 −0.338255
\(735\) −18219.5 −0.914337
\(736\) −21549.4 −1.07924
\(737\) −15634.6 −0.781421
\(738\) −5145.12 −0.256632
\(739\) −22838.8 −1.13686 −0.568430 0.822732i \(-0.692449\pi\)
−0.568430 + 0.822732i \(0.692449\pi\)
\(740\) 23190.4 1.15202
\(741\) 1369.95 0.0679170
\(742\) 84618.2 4.18657
\(743\) −2638.81 −0.130294 −0.0651472 0.997876i \(-0.520752\pi\)
−0.0651472 + 0.997876i \(0.520752\pi\)
\(744\) −405.868 −0.0199998
\(745\) −7240.24 −0.356056
\(746\) 26669.2 1.30889
\(747\) 2153.60 0.105483
\(748\) 16536.9 0.808353
\(749\) 667.529 0.0325647
\(750\) 17762.1 0.864775
\(751\) −6880.34 −0.334311 −0.167155 0.985931i \(-0.553458\pi\)
−0.167155 + 0.985931i \(0.553458\pi\)
\(752\) 7555.21 0.366370
\(753\) −2700.27 −0.130682
\(754\) 602.833 0.0291166
\(755\) −26832.5 −1.29342
\(756\) 7978.98 0.383853
\(757\) 41277.3 1.98183 0.990916 0.134479i \(-0.0429359\pi\)
0.990916 + 0.134479i \(0.0429359\pi\)
\(758\) 26231.4 1.25695
\(759\) 7498.85 0.358618
\(760\) 1796.62 0.0857504
\(761\) 16764.5 0.798570 0.399285 0.916827i \(-0.369258\pi\)
0.399285 + 0.916827i \(0.369258\pi\)
\(762\) 15992.0 0.760274
\(763\) 7725.76 0.366568
\(764\) −29855.1 −1.41377
\(765\) −4243.97 −0.200576
\(766\) −12451.0 −0.587302
\(767\) −313.123 −0.0147408
\(768\) 9919.32 0.466058
\(769\) −29667.0 −1.39118 −0.695591 0.718438i \(-0.744858\pi\)
−0.695591 + 0.718438i \(0.744858\pi\)
\(770\) −31189.2 −1.45972
\(771\) 10257.7 0.479147
\(772\) 38067.1 1.77470
\(773\) −1557.94 −0.0724904 −0.0362452 0.999343i \(-0.511540\pi\)
−0.0362452 + 0.999343i \(0.511540\pi\)
\(774\) −13480.0 −0.626004
\(775\) 3353.27 0.155423
\(776\) 417.440 0.0193108
\(777\) −36554.8 −1.68777
\(778\) 33208.7 1.53032
\(779\) 12042.1 0.553856
\(780\) 1030.98 0.0473270
\(781\) −22072.5 −1.01129
\(782\) 21454.7 0.981098
\(783\) −750.804 −0.0342676
\(784\) −47284.0 −2.15397
\(785\) −9010.74 −0.409691
\(786\) 15392.2 0.698503
\(787\) 8898.56 0.403049 0.201524 0.979483i \(-0.435410\pi\)
0.201524 + 0.979483i \(0.435410\pi\)
\(788\) −43700.5 −1.97559
\(789\) 3819.45 0.172340
\(790\) −8543.35 −0.384758
\(791\) −13819.4 −0.621188
\(792\) 758.752 0.0340418
\(793\) 1917.07 0.0858476
\(794\) −20719.6 −0.926083
\(795\) −13617.5 −0.607499
\(796\) 37849.9 1.68537
\(797\) 25724.7 1.14331 0.571654 0.820495i \(-0.306302\pi\)
0.571654 + 0.820495i \(0.306302\pi\)
\(798\) −35875.3 −1.59145
\(799\) −8232.81 −0.364526
\(800\) 18014.6 0.796142
\(801\) 10932.5 0.482248
\(802\) 38967.4 1.71569
\(803\) 34080.7 1.49773
\(804\) −13533.9 −0.593661
\(805\) −21063.6 −0.922229
\(806\) 1047.19 0.0457641
\(807\) 10312.5 0.449837
\(808\) −1375.74 −0.0598989
\(809\) −25187.9 −1.09463 −0.547317 0.836926i \(-0.684351\pi\)
−0.547317 + 0.836926i \(0.684351\pi\)
\(810\) −2466.73 −0.107002
\(811\) −1555.98 −0.0673709 −0.0336854 0.999432i \(-0.510724\pi\)
−0.0336854 + 0.999432i \(0.510724\pi\)
\(812\) −8217.63 −0.355151
\(813\) −7229.85 −0.311884
\(814\) −44035.1 −1.89611
\(815\) −5121.71 −0.220129
\(816\) −11014.1 −0.472513
\(817\) 31549.8 1.35102
\(818\) 43694.3 1.86765
\(819\) −1625.13 −0.0693364
\(820\) 9062.50 0.385947
\(821\) −10402.0 −0.442182 −0.221091 0.975253i \(-0.570962\pi\)
−0.221091 + 0.975253i \(0.570962\pi\)
\(822\) −13012.5 −0.552146
\(823\) −3211.80 −0.136035 −0.0680173 0.997684i \(-0.521667\pi\)
−0.0680173 + 0.997684i \(0.521667\pi\)
\(824\) −4792.02 −0.202595
\(825\) −6268.80 −0.264547
\(826\) 8199.84 0.345410
\(827\) −14355.4 −0.603612 −0.301806 0.953369i \(-0.597589\pi\)
−0.301806 + 0.953369i \(0.597589\pi\)
\(828\) 6491.29 0.272449
\(829\) 40266.3 1.68698 0.843490 0.537145i \(-0.180497\pi\)
0.843490 + 0.537145i \(0.180497\pi\)
\(830\) −7287.15 −0.304748
\(831\) −21837.1 −0.911579
\(832\) 3161.37 0.131732
\(833\) 51524.8 2.14313
\(834\) −12338.0 −0.512265
\(835\) −23196.8 −0.961389
\(836\) −22496.3 −0.930681
\(837\) −1304.24 −0.0538603
\(838\) −8717.96 −0.359376
\(839\) −32142.4 −1.32262 −0.661310 0.750113i \(-0.729999\pi\)
−0.661310 + 0.750113i \(0.729999\pi\)
\(840\) −2131.27 −0.0875426
\(841\) −23615.7 −0.968295
\(842\) 27697.9 1.13365
\(843\) 18895.7 0.772008
\(844\) −38532.2 −1.57148
\(845\) 16169.3 0.658273
\(846\) −4785.17 −0.194465
\(847\) −14456.9 −0.586474
\(848\) −35340.6 −1.43113
\(849\) −10685.0 −0.431930
\(850\) −17935.4 −0.723742
\(851\) −29739.1 −1.19793
\(852\) −19106.8 −0.768294
\(853\) 3961.96 0.159033 0.0795164 0.996834i \(-0.474662\pi\)
0.0795164 + 0.996834i \(0.474662\pi\)
\(854\) −50202.8 −2.01160
\(855\) 5773.36 0.230930
\(856\) 54.9489 0.00219406
\(857\) −38708.1 −1.54287 −0.771437 0.636306i \(-0.780462\pi\)
−0.771437 + 0.636306i \(0.780462\pi\)
\(858\) −1957.68 −0.0778953
\(859\) −6725.04 −0.267119 −0.133560 0.991041i \(-0.542641\pi\)
−0.133560 + 0.991041i \(0.542641\pi\)
\(860\) 23743.3 0.941442
\(861\) −14285.1 −0.565431
\(862\) −68180.9 −2.69403
\(863\) 22856.4 0.901554 0.450777 0.892637i \(-0.351147\pi\)
0.450777 + 0.892637i \(0.351147\pi\)
\(864\) −7006.70 −0.275894
\(865\) −4279.86 −0.168231
\(866\) −11858.1 −0.465306
\(867\) −2737.08 −0.107216
\(868\) −14275.0 −0.558209
\(869\) 8444.59 0.329647
\(870\) 2540.51 0.0990014
\(871\) 2756.53 0.107235
\(872\) 635.960 0.0246976
\(873\) 1341.42 0.0520049
\(874\) −29186.3 −1.12957
\(875\) 49315.6 1.90534
\(876\) 29501.5 1.13786
\(877\) 25523.5 0.982744 0.491372 0.870950i \(-0.336496\pi\)
0.491372 + 0.870950i \(0.336496\pi\)
\(878\) 34830.8 1.33882
\(879\) −13122.3 −0.503531
\(880\) 13026.1 0.498988
\(881\) 37925.5 1.45033 0.725166 0.688574i \(-0.241763\pi\)
0.725166 + 0.688574i \(0.241763\pi\)
\(882\) 29947.8 1.14331
\(883\) −44752.5 −1.70560 −0.852798 0.522241i \(-0.825096\pi\)
−0.852798 + 0.522241i \(0.825096\pi\)
\(884\) −2915.61 −0.110931
\(885\) −1319.59 −0.0501214
\(886\) −12965.3 −0.491624
\(887\) 27284.8 1.03285 0.516423 0.856334i \(-0.327263\pi\)
0.516423 + 0.856334i \(0.327263\pi\)
\(888\) −3009.07 −0.113714
\(889\) 44400.9 1.67509
\(890\) −36992.4 −1.39325
\(891\) 2438.21 0.0916759
\(892\) −4500.44 −0.168930
\(893\) 11199.7 0.419689
\(894\) 11900.9 0.445220
\(895\) −24572.7 −0.917736
\(896\) −12152.5 −0.453109
\(897\) −1322.12 −0.0492132
\(898\) −8623.38 −0.320452
\(899\) 1343.25 0.0498329
\(900\) −5426.51 −0.200982
\(901\) 38510.2 1.42393
\(902\) −17208.4 −0.635228
\(903\) −37426.3 −1.37926
\(904\) −1137.57 −0.0418528
\(905\) −15079.4 −0.553873
\(906\) 44105.2 1.61733
\(907\) 22037.7 0.806779 0.403390 0.915028i \(-0.367832\pi\)
0.403390 + 0.915028i \(0.367832\pi\)
\(908\) −46540.3 −1.70099
\(909\) −4420.87 −0.161310
\(910\) 5498.96 0.200317
\(911\) 53768.1 1.95545 0.977726 0.209884i \(-0.0673087\pi\)
0.977726 + 0.209884i \(0.0673087\pi\)
\(912\) 14983.2 0.544018
\(913\) 7202.92 0.261097
\(914\) −28576.1 −1.03415
\(915\) 8079.06 0.291897
\(916\) 24369.7 0.879038
\(917\) 42735.7 1.53899
\(918\) 6975.90 0.250805
\(919\) 12821.6 0.460224 0.230112 0.973164i \(-0.426091\pi\)
0.230112 + 0.973164i \(0.426091\pi\)
\(920\) −1733.89 −0.0621355
\(921\) 15793.9 0.565068
\(922\) 1743.77 0.0622865
\(923\) 3891.59 0.138779
\(924\) 26686.5 0.950132
\(925\) 24860.9 0.883699
\(926\) 11853.7 0.420667
\(927\) −15398.9 −0.545596
\(928\) 7216.26 0.255265
\(929\) −20227.5 −0.714361 −0.357181 0.934035i \(-0.616262\pi\)
−0.357181 + 0.934035i \(0.616262\pi\)
\(930\) 4413.17 0.155606
\(931\) −70092.7 −2.46745
\(932\) −36662.7 −1.28855
\(933\) 11667.0 0.409389
\(934\) 34411.8 1.20555
\(935\) −14194.4 −0.496476
\(936\) −133.775 −0.00467156
\(937\) −43813.7 −1.52757 −0.763784 0.645471i \(-0.776661\pi\)
−0.763784 + 0.645471i \(0.776661\pi\)
\(938\) −72186.0 −2.51275
\(939\) −26446.2 −0.919104
\(940\) 8428.50 0.292455
\(941\) 36622.2 1.26870 0.634351 0.773045i \(-0.281267\pi\)
0.634351 + 0.773045i \(0.281267\pi\)
\(942\) 14811.1 0.512286
\(943\) −11621.7 −0.401329
\(944\) −3424.64 −0.118075
\(945\) −6848.73 −0.235756
\(946\) −45085.1 −1.54952
\(947\) −15181.8 −0.520952 −0.260476 0.965480i \(-0.583879\pi\)
−0.260476 + 0.965480i \(0.583879\pi\)
\(948\) 7309.96 0.250439
\(949\) −6008.75 −0.205535
\(950\) 24398.8 0.833266
\(951\) −30518.2 −1.04061
\(952\) 6027.22 0.205193
\(953\) −17530.8 −0.595885 −0.297942 0.954584i \(-0.596300\pi\)
−0.297942 + 0.954584i \(0.596300\pi\)
\(954\) 22383.3 0.759630
\(955\) 25626.0 0.868311
\(956\) 47006.7 1.59028
\(957\) −2511.14 −0.0848209
\(958\) −42629.0 −1.43766
\(959\) −36128.5 −1.21653
\(960\) 13322.9 0.447911
\(961\) −27457.6 −0.921675
\(962\) 7763.82 0.260203
\(963\) 176.576 0.00590869
\(964\) −26087.9 −0.871611
\(965\) −32674.8 −1.08999
\(966\) 34622.7 1.15318
\(967\) 50857.1 1.69127 0.845633 0.533765i \(-0.179223\pi\)
0.845633 + 0.533765i \(0.179223\pi\)
\(968\) −1190.04 −0.0395139
\(969\) −16327.0 −0.541280
\(970\) −4538.99 −0.150246
\(971\) −24239.2 −0.801105 −0.400553 0.916274i \(-0.631182\pi\)
−0.400553 + 0.916274i \(0.631182\pi\)
\(972\) 2110.61 0.0696480
\(973\) −34255.7 −1.12866
\(974\) 25257.5 0.830906
\(975\) 1105.25 0.0363039
\(976\) 20967.1 0.687643
\(977\) −52188.5 −1.70896 −0.854482 0.519481i \(-0.826125\pi\)
−0.854482 + 0.519481i \(0.826125\pi\)
\(978\) 8418.66 0.275255
\(979\) 36564.8 1.19368
\(980\) −52749.5 −1.71941
\(981\) 2043.63 0.0665118
\(982\) −16501.0 −0.536221
\(983\) −6206.63 −0.201384 −0.100692 0.994918i \(-0.532106\pi\)
−0.100692 + 0.994918i \(0.532106\pi\)
\(984\) −1175.91 −0.0380961
\(985\) 37510.2 1.21337
\(986\) −7184.54 −0.232051
\(987\) −13285.8 −0.428460
\(988\) 3966.31 0.127718
\(989\) −30448.2 −0.978964
\(990\) −8250.22 −0.264858
\(991\) 11627.8 0.372724 0.186362 0.982481i \(-0.440330\pi\)
0.186362 + 0.982481i \(0.440330\pi\)
\(992\) 12535.5 0.401213
\(993\) −8697.27 −0.277945
\(994\) −101910. −3.25190
\(995\) −32488.3 −1.03513
\(996\) 6235.12 0.198361
\(997\) 27404.9 0.870533 0.435266 0.900302i \(-0.356654\pi\)
0.435266 + 0.900302i \(0.356654\pi\)
\(998\) −69991.7 −2.21999
\(999\) −9669.52 −0.306236
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.d.1.7 8
3.2 odd 2 531.4.a.e.1.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.4.a.d.1.7 8 1.1 even 1 trivial
531.4.a.e.1.2 8 3.2 odd 2