Properties

Label 177.4.a.a.1.5
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: \(x^{7} - x^{6} - 34 x^{5} + 25 x^{4} + 315 x^{3} - 146 x^{2} - 736 x + 512\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(-2.29817\) of defining polynomial
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.29817 q^{2} +3.00000 q^{3} -6.31476 q^{4} +7.05496 q^{5} +3.89451 q^{6} -33.4497 q^{7} -18.5830 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q+1.29817 q^{2} +3.00000 q^{3} -6.31476 q^{4} +7.05496 q^{5} +3.89451 q^{6} -33.4497 q^{7} -18.5830 q^{8} +9.00000 q^{9} +9.15853 q^{10} -27.5842 q^{11} -18.9443 q^{12} -55.6756 q^{13} -43.4234 q^{14} +21.1649 q^{15} +26.3942 q^{16} +108.437 q^{17} +11.6835 q^{18} -141.505 q^{19} -44.5504 q^{20} -100.349 q^{21} -35.8089 q^{22} +142.351 q^{23} -55.7489 q^{24} -75.2276 q^{25} -72.2763 q^{26} +27.0000 q^{27} +211.227 q^{28} -97.2883 q^{29} +27.4756 q^{30} -221.538 q^{31} +182.928 q^{32} -82.7525 q^{33} +140.770 q^{34} -235.987 q^{35} -56.8328 q^{36} +339.976 q^{37} -183.698 q^{38} -167.027 q^{39} -131.102 q^{40} -266.877 q^{41} -130.270 q^{42} -67.2505 q^{43} +174.187 q^{44} +63.4946 q^{45} +184.795 q^{46} -262.017 q^{47} +79.1827 q^{48} +775.886 q^{49} -97.6581 q^{50} +325.311 q^{51} +351.578 q^{52} +380.876 q^{53} +35.0506 q^{54} -194.605 q^{55} +621.596 q^{56} -424.516 q^{57} -126.297 q^{58} -59.0000 q^{59} -133.651 q^{60} -15.4226 q^{61} -287.593 q^{62} -301.048 q^{63} +26.3175 q^{64} -392.789 q^{65} -107.427 q^{66} -172.954 q^{67} -684.753 q^{68} +427.052 q^{69} -306.350 q^{70} -616.313 q^{71} -167.247 q^{72} -210.965 q^{73} +441.346 q^{74} -225.683 q^{75} +893.572 q^{76} +922.684 q^{77} -216.829 q^{78} +543.689 q^{79} +186.210 q^{80} +81.0000 q^{81} -346.452 q^{82} +350.751 q^{83} +633.681 q^{84} +765.019 q^{85} -87.3025 q^{86} -291.865 q^{87} +512.596 q^{88} +1447.29 q^{89} +82.4267 q^{90} +1862.34 q^{91} -898.911 q^{92} -664.613 q^{93} -340.143 q^{94} -998.315 q^{95} +548.784 q^{96} -625.674 q^{97} +1007.23 q^{98} -248.258 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q - 8q^{2} + 21q^{3} + 22q^{4} - 28q^{5} - 24q^{6} - 59q^{7} - 117q^{8} + 63q^{9} + O(q^{10}) \) \( 7q - 8q^{2} + 21q^{3} + 22q^{4} - 28q^{5} - 24q^{6} - 59q^{7} - 117q^{8} + 63q^{9} - 79q^{10} - 131q^{11} + 66q^{12} - 123q^{13} - 117q^{14} - 84q^{15} + 202q^{16} - 235q^{17} - 72q^{18} - 80q^{19} + 61q^{20} - 177q^{21} + 688q^{22} - 274q^{23} - 351q^{24} + 193q^{25} - 180q^{26} + 189q^{27} - 118q^{28} - 406q^{29} - 237q^{30} - 346q^{31} - 854q^{32} - 393q^{33} + 178q^{34} - 424q^{35} + 198q^{36} - 157q^{37} - 129q^{38} - 369q^{39} - 590q^{40} - 825q^{41} - 351q^{42} - 815q^{43} - 1690q^{44} - 252q^{45} + 1457q^{46} - 1196q^{47} + 606q^{48} + 914q^{49} + 713q^{50} - 705q^{51} + 1030q^{52} - 900q^{53} - 216q^{54} - 1044q^{55} + 2172q^{56} - 240q^{57} + 1242q^{58} - 413q^{59} + 183q^{60} + 420q^{61} + 646q^{62} - 531q^{63} + 3541q^{64} + 190q^{65} + 2064q^{66} + 1316q^{67} - 611q^{68} - 822q^{69} + 4658q^{70} - 173q^{71} - 1053q^{72} - 418q^{73} + 660q^{74} + 579q^{75} + 1540q^{76} - 753q^{77} - 540q^{78} + 2635q^{79} + 6155q^{80} + 567q^{81} - 125q^{82} + 457q^{83} - 354q^{84} + 1270q^{85} + 3482q^{86} - 1218q^{87} + 7685q^{88} + 592q^{89} - 711q^{90} + 3179q^{91} - 3500q^{92} - 1038q^{93} + 2064q^{94} - 2250q^{95} - 2562q^{96} - 1906q^{97} + 2994q^{98} - 1179q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.29817 0.458972 0.229486 0.973312i \(-0.426295\pi\)
0.229486 + 0.973312i \(0.426295\pi\)
\(3\) 3.00000 0.577350
\(4\) −6.31476 −0.789345
\(5\) 7.05496 0.631015 0.315507 0.948923i \(-0.397825\pi\)
0.315507 + 0.948923i \(0.397825\pi\)
\(6\) 3.89451 0.264988
\(7\) −33.4497 −1.80612 −0.903058 0.429518i \(-0.858684\pi\)
−0.903058 + 0.429518i \(0.858684\pi\)
\(8\) −18.5830 −0.821259
\(9\) 9.00000 0.333333
\(10\) 9.15853 0.289618
\(11\) −27.5842 −0.756086 −0.378043 0.925788i \(-0.623403\pi\)
−0.378043 + 0.925788i \(0.623403\pi\)
\(12\) −18.9443 −0.455728
\(13\) −55.6756 −1.18782 −0.593909 0.804532i \(-0.702416\pi\)
−0.593909 + 0.804532i \(0.702416\pi\)
\(14\) −43.4234 −0.828957
\(15\) 21.1649 0.364317
\(16\) 26.3942 0.412410
\(17\) 108.437 1.54705 0.773525 0.633766i \(-0.218492\pi\)
0.773525 + 0.633766i \(0.218492\pi\)
\(18\) 11.6835 0.152991
\(19\) −141.505 −1.70861 −0.854304 0.519773i \(-0.826017\pi\)
−0.854304 + 0.519773i \(0.826017\pi\)
\(20\) −44.5504 −0.498088
\(21\) −100.349 −1.04276
\(22\) −35.8089 −0.347022
\(23\) 142.351 1.29053 0.645265 0.763959i \(-0.276747\pi\)
0.645265 + 0.763959i \(0.276747\pi\)
\(24\) −55.7489 −0.474154
\(25\) −75.2276 −0.601820
\(26\) −72.2763 −0.545175
\(27\) 27.0000 0.192450
\(28\) 211.227 1.42565
\(29\) −97.2883 −0.622965 −0.311482 0.950252i \(-0.600825\pi\)
−0.311482 + 0.950252i \(0.600825\pi\)
\(30\) 27.4756 0.167211
\(31\) −221.538 −1.28353 −0.641763 0.766903i \(-0.721797\pi\)
−0.641763 + 0.766903i \(0.721797\pi\)
\(32\) 182.928 1.01054
\(33\) −82.7525 −0.436526
\(34\) 140.770 0.710052
\(35\) −235.987 −1.13969
\(36\) −56.8328 −0.263115
\(37\) 339.976 1.51059 0.755293 0.655387i \(-0.227494\pi\)
0.755293 + 0.655387i \(0.227494\pi\)
\(38\) −183.698 −0.784204
\(39\) −167.027 −0.685787
\(40\) −131.102 −0.518227
\(41\) −266.877 −1.01657 −0.508283 0.861190i \(-0.669720\pi\)
−0.508283 + 0.861190i \(0.669720\pi\)
\(42\) −130.270 −0.478599
\(43\) −67.2505 −0.238503 −0.119251 0.992864i \(-0.538049\pi\)
−0.119251 + 0.992864i \(0.538049\pi\)
\(44\) 174.187 0.596812
\(45\) 63.4946 0.210338
\(46\) 184.795 0.592317
\(47\) −262.017 −0.813174 −0.406587 0.913612i \(-0.633281\pi\)
−0.406587 + 0.913612i \(0.633281\pi\)
\(48\) 79.1827 0.238105
\(49\) 775.886 2.26206
\(50\) −97.6581 −0.276219
\(51\) 325.311 0.893189
\(52\) 351.578 0.937598
\(53\) 380.876 0.987121 0.493560 0.869712i \(-0.335695\pi\)
0.493560 + 0.869712i \(0.335695\pi\)
\(54\) 35.0506 0.0883292
\(55\) −194.605 −0.477101
\(56\) 621.596 1.48329
\(57\) −424.516 −0.986466
\(58\) −126.297 −0.285923
\(59\) −59.0000 −0.130189
\(60\) −133.651 −0.287571
\(61\) −15.4226 −0.0323715 −0.0161857 0.999869i \(-0.505152\pi\)
−0.0161857 + 0.999869i \(0.505152\pi\)
\(62\) −287.593 −0.589103
\(63\) −301.048 −0.602039
\(64\) 26.3175 0.0514014
\(65\) −392.789 −0.749531
\(66\) −107.427 −0.200353
\(67\) −172.954 −0.315369 −0.157685 0.987490i \(-0.550403\pi\)
−0.157685 + 0.987490i \(0.550403\pi\)
\(68\) −684.753 −1.22116
\(69\) 427.052 0.745088
\(70\) −306.350 −0.523084
\(71\) −616.313 −1.03018 −0.515091 0.857136i \(-0.672242\pi\)
−0.515091 + 0.857136i \(0.672242\pi\)
\(72\) −167.247 −0.273753
\(73\) −210.965 −0.338242 −0.169121 0.985595i \(-0.554093\pi\)
−0.169121 + 0.985595i \(0.554093\pi\)
\(74\) 441.346 0.693317
\(75\) −225.683 −0.347461
\(76\) 893.572 1.34868
\(77\) 922.684 1.36558
\(78\) −216.829 −0.314757
\(79\) 543.689 0.774302 0.387151 0.922016i \(-0.373459\pi\)
0.387151 + 0.922016i \(0.373459\pi\)
\(80\) 186.210 0.260237
\(81\) 81.0000 0.111111
\(82\) −346.452 −0.466575
\(83\) 350.751 0.463855 0.231927 0.972733i \(-0.425497\pi\)
0.231927 + 0.972733i \(0.425497\pi\)
\(84\) 633.681 0.823099
\(85\) 765.019 0.976211
\(86\) −87.3025 −0.109466
\(87\) −291.865 −0.359669
\(88\) 512.596 0.620942
\(89\) 1447.29 1.72373 0.861867 0.507135i \(-0.169295\pi\)
0.861867 + 0.507135i \(0.169295\pi\)
\(90\) 82.4267 0.0965394
\(91\) 1862.34 2.14534
\(92\) −898.911 −1.01867
\(93\) −664.613 −0.741044
\(94\) −340.143 −0.373224
\(95\) −998.315 −1.07816
\(96\) 548.784 0.583438
\(97\) −625.674 −0.654924 −0.327462 0.944864i \(-0.606193\pi\)
−0.327462 + 0.944864i \(0.606193\pi\)
\(98\) 1007.23 1.03822
\(99\) −248.258 −0.252029
\(100\) 475.044 0.475044
\(101\) −902.589 −0.889218 −0.444609 0.895725i \(-0.646657\pi\)
−0.444609 + 0.895725i \(0.646657\pi\)
\(102\) 422.309 0.409949
\(103\) 700.033 0.669673 0.334836 0.942276i \(-0.391319\pi\)
0.334836 + 0.942276i \(0.391319\pi\)
\(104\) 1034.62 0.975507
\(105\) −707.960 −0.657998
\(106\) 494.442 0.453061
\(107\) 1645.87 1.48703 0.743513 0.668721i \(-0.233158\pi\)
0.743513 + 0.668721i \(0.233158\pi\)
\(108\) −170.498 −0.151909
\(109\) −253.521 −0.222779 −0.111390 0.993777i \(-0.535530\pi\)
−0.111390 + 0.993777i \(0.535530\pi\)
\(110\) −252.630 −0.218976
\(111\) 1019.93 0.872138
\(112\) −882.880 −0.744860
\(113\) −947.504 −0.788793 −0.394397 0.918940i \(-0.629046\pi\)
−0.394397 + 0.918940i \(0.629046\pi\)
\(114\) −551.094 −0.452760
\(115\) 1004.28 0.814343
\(116\) 614.352 0.491734
\(117\) −501.081 −0.395939
\(118\) −76.5920 −0.0597531
\(119\) −3627.19 −2.79415
\(120\) −393.306 −0.299198
\(121\) −570.113 −0.428335
\(122\) −20.0211 −0.0148576
\(123\) −800.631 −0.586915
\(124\) 1398.96 1.01314
\(125\) −1412.60 −1.01077
\(126\) −390.811 −0.276319
\(127\) −2655.70 −1.85555 −0.927775 0.373139i \(-0.878281\pi\)
−0.927775 + 0.373139i \(0.878281\pi\)
\(128\) −1429.26 −0.986952
\(129\) −201.752 −0.137700
\(130\) −509.907 −0.344014
\(131\) −1677.06 −1.11851 −0.559256 0.828995i \(-0.688913\pi\)
−0.559256 + 0.828995i \(0.688913\pi\)
\(132\) 522.562 0.344570
\(133\) 4733.32 3.08595
\(134\) −224.524 −0.144746
\(135\) 190.484 0.121439
\(136\) −2015.08 −1.27053
\(137\) 687.255 0.428585 0.214293 0.976769i \(-0.431255\pi\)
0.214293 + 0.976769i \(0.431255\pi\)
\(138\) 554.386 0.341974
\(139\) −149.695 −0.0913451 −0.0456726 0.998956i \(-0.514543\pi\)
−0.0456726 + 0.998956i \(0.514543\pi\)
\(140\) 1490.20 0.899605
\(141\) −786.052 −0.469486
\(142\) −800.078 −0.472825
\(143\) 1535.77 0.898092
\(144\) 237.548 0.137470
\(145\) −686.365 −0.393100
\(146\) −273.869 −0.155243
\(147\) 2327.66 1.30600
\(148\) −2146.87 −1.19237
\(149\) 221.901 0.122005 0.0610027 0.998138i \(-0.480570\pi\)
0.0610027 + 0.998138i \(0.480570\pi\)
\(150\) −292.974 −0.159475
\(151\) −1262.38 −0.680340 −0.340170 0.940364i \(-0.610485\pi\)
−0.340170 + 0.940364i \(0.610485\pi\)
\(152\) 2629.59 1.40321
\(153\) 975.933 0.515683
\(154\) 1197.80 0.626762
\(155\) −1562.94 −0.809924
\(156\) 1054.73 0.541323
\(157\) −3446.33 −1.75189 −0.875947 0.482407i \(-0.839763\pi\)
−0.875947 + 0.482407i \(0.839763\pi\)
\(158\) 705.801 0.355383
\(159\) 1142.63 0.569914
\(160\) 1290.55 0.637668
\(161\) −4761.60 −2.33085
\(162\) 105.152 0.0509969
\(163\) −1915.37 −0.920388 −0.460194 0.887818i \(-0.652220\pi\)
−0.460194 + 0.887818i \(0.652220\pi\)
\(164\) 1685.26 0.802421
\(165\) −583.816 −0.275454
\(166\) 455.334 0.212896
\(167\) −3013.60 −1.39640 −0.698201 0.715902i \(-0.746016\pi\)
−0.698201 + 0.715902i \(0.746016\pi\)
\(168\) 1864.79 0.856378
\(169\) 902.774 0.410912
\(170\) 993.123 0.448053
\(171\) −1273.55 −0.569536
\(172\) 424.671 0.188261
\(173\) −1913.98 −0.841138 −0.420569 0.907261i \(-0.638170\pi\)
−0.420569 + 0.907261i \(0.638170\pi\)
\(174\) −378.890 −0.165078
\(175\) 2516.34 1.08696
\(176\) −728.063 −0.311817
\(177\) −177.000 −0.0751646
\(178\) 1878.83 0.791146
\(179\) 1507.53 0.629485 0.314742 0.949177i \(-0.398082\pi\)
0.314742 + 0.949177i \(0.398082\pi\)
\(180\) −400.953 −0.166029
\(181\) −1970.30 −0.809123 −0.404562 0.914511i \(-0.632576\pi\)
−0.404562 + 0.914511i \(0.632576\pi\)
\(182\) 2417.63 0.984650
\(183\) −46.2678 −0.0186897
\(184\) −2645.30 −1.05986
\(185\) 2398.52 0.953202
\(186\) −862.779 −0.340119
\(187\) −2991.15 −1.16970
\(188\) 1654.58 0.641874
\(189\) −903.143 −0.347587
\(190\) −1295.98 −0.494844
\(191\) −2132.62 −0.807911 −0.403955 0.914779i \(-0.632365\pi\)
−0.403955 + 0.914779i \(0.632365\pi\)
\(192\) 78.9526 0.0296766
\(193\) 1319.47 0.492112 0.246056 0.969256i \(-0.420865\pi\)
0.246056 + 0.969256i \(0.420865\pi\)
\(194\) −812.231 −0.300592
\(195\) −1178.37 −0.432742
\(196\) −4899.53 −1.78554
\(197\) 187.057 0.0676511 0.0338255 0.999428i \(-0.489231\pi\)
0.0338255 + 0.999428i \(0.489231\pi\)
\(198\) −322.280 −0.115674
\(199\) 3324.89 1.18440 0.592200 0.805791i \(-0.298260\pi\)
0.592200 + 0.805791i \(0.298260\pi\)
\(200\) 1397.95 0.494251
\(201\) −518.863 −0.182078
\(202\) −1171.71 −0.408126
\(203\) 3254.27 1.12515
\(204\) −2054.26 −0.705034
\(205\) −1882.81 −0.641468
\(206\) 908.761 0.307361
\(207\) 1281.16 0.430177
\(208\) −1469.51 −0.489868
\(209\) 3903.31 1.29185
\(210\) −919.051 −0.302003
\(211\) 4844.60 1.58065 0.790323 0.612691i \(-0.209913\pi\)
0.790323 + 0.612691i \(0.209913\pi\)
\(212\) −2405.14 −0.779179
\(213\) −1848.94 −0.594776
\(214\) 2136.61 0.682504
\(215\) −474.450 −0.150499
\(216\) −501.740 −0.158051
\(217\) 7410.38 2.31820
\(218\) −329.114 −0.102249
\(219\) −632.896 −0.195284
\(220\) 1228.88 0.376597
\(221\) −6037.30 −1.83761
\(222\) 1324.04 0.400287
\(223\) −4223.02 −1.26814 −0.634068 0.773277i \(-0.718616\pi\)
−0.634068 + 0.773277i \(0.718616\pi\)
\(224\) −6118.89 −1.82516
\(225\) −677.048 −0.200607
\(226\) −1230.02 −0.362034
\(227\) 6199.87 1.81277 0.906387 0.422448i \(-0.138829\pi\)
0.906387 + 0.422448i \(0.138829\pi\)
\(228\) 2680.72 0.778662
\(229\) −2502.28 −0.722075 −0.361037 0.932551i \(-0.617577\pi\)
−0.361037 + 0.932551i \(0.617577\pi\)
\(230\) 1303.72 0.373761
\(231\) 2768.05 0.788417
\(232\) 1807.91 0.511615
\(233\) −5317.19 −1.49503 −0.747513 0.664247i \(-0.768752\pi\)
−0.747513 + 0.664247i \(0.768752\pi\)
\(234\) −650.487 −0.181725
\(235\) −1848.52 −0.513125
\(236\) 372.571 0.102764
\(237\) 1631.07 0.447043
\(238\) −4708.71 −1.28244
\(239\) 6431.88 1.74077 0.870385 0.492372i \(-0.163870\pi\)
0.870385 + 0.492372i \(0.163870\pi\)
\(240\) 558.631 0.150248
\(241\) 2651.24 0.708638 0.354319 0.935125i \(-0.384713\pi\)
0.354319 + 0.935125i \(0.384713\pi\)
\(242\) −740.103 −0.196594
\(243\) 243.000 0.0641500
\(244\) 97.3899 0.0255522
\(245\) 5473.84 1.42739
\(246\) −1039.35 −0.269377
\(247\) 7878.40 2.02952
\(248\) 4116.83 1.05411
\(249\) 1052.25 0.267807
\(250\) −1833.79 −0.463916
\(251\) 3189.73 0.802126 0.401063 0.916050i \(-0.368641\pi\)
0.401063 + 0.916050i \(0.368641\pi\)
\(252\) 1901.04 0.475216
\(253\) −3926.63 −0.975751
\(254\) −3447.54 −0.851646
\(255\) 2295.06 0.563616
\(256\) −2065.96 −0.504385
\(257\) 6997.92 1.69851 0.849257 0.527980i \(-0.177050\pi\)
0.849257 + 0.527980i \(0.177050\pi\)
\(258\) −261.908 −0.0632002
\(259\) −11372.1 −2.72830
\(260\) 2480.37 0.591638
\(261\) −875.594 −0.207655
\(262\) −2177.10 −0.513366
\(263\) −4833.10 −1.13316 −0.566582 0.824006i \(-0.691734\pi\)
−0.566582 + 0.824006i \(0.691734\pi\)
\(264\) 1537.79 0.358501
\(265\) 2687.07 0.622888
\(266\) 6144.65 1.41636
\(267\) 4341.87 0.995198
\(268\) 1092.16 0.248935
\(269\) 4142.13 0.938849 0.469424 0.882973i \(-0.344461\pi\)
0.469424 + 0.882973i \(0.344461\pi\)
\(270\) 247.280 0.0557370
\(271\) −3931.65 −0.881295 −0.440648 0.897680i \(-0.645251\pi\)
−0.440648 + 0.897680i \(0.645251\pi\)
\(272\) 2862.11 0.638018
\(273\) 5587.01 1.23861
\(274\) 892.173 0.196709
\(275\) 2075.09 0.455028
\(276\) −2696.73 −0.588131
\(277\) −2635.02 −0.571564 −0.285782 0.958295i \(-0.592253\pi\)
−0.285782 + 0.958295i \(0.592253\pi\)
\(278\) −194.329 −0.0419248
\(279\) −1993.84 −0.427842
\(280\) 4385.33 0.935978
\(281\) −2791.96 −0.592721 −0.296360 0.955076i \(-0.595773\pi\)
−0.296360 + 0.955076i \(0.595773\pi\)
\(282\) −1020.43 −0.215481
\(283\) −915.281 −0.192254 −0.0961268 0.995369i \(-0.530645\pi\)
−0.0961268 + 0.995369i \(0.530645\pi\)
\(284\) 3891.87 0.813169
\(285\) −2994.94 −0.622474
\(286\) 1993.68 0.412199
\(287\) 8926.97 1.83604
\(288\) 1646.35 0.336848
\(289\) 6845.59 1.39336
\(290\) −891.017 −0.180422
\(291\) −1877.02 −0.378120
\(292\) 1332.20 0.266989
\(293\) 2631.82 0.524752 0.262376 0.964966i \(-0.415494\pi\)
0.262376 + 0.964966i \(0.415494\pi\)
\(294\) 3021.69 0.599417
\(295\) −416.243 −0.0821511
\(296\) −6317.76 −1.24058
\(297\) −744.773 −0.145509
\(298\) 288.065 0.0559971
\(299\) −7925.47 −1.53291
\(300\) 1425.13 0.274267
\(301\) 2249.51 0.430763
\(302\) −1638.79 −0.312257
\(303\) −2707.77 −0.513390
\(304\) −3734.93 −0.704647
\(305\) −108.806 −0.0204269
\(306\) 1266.93 0.236684
\(307\) −6778.17 −1.26010 −0.630050 0.776555i \(-0.716965\pi\)
−0.630050 + 0.776555i \(0.716965\pi\)
\(308\) −5826.52 −1.07791
\(309\) 2100.10 0.386636
\(310\) −2028.96 −0.371732
\(311\) 5915.03 1.07849 0.539245 0.842149i \(-0.318710\pi\)
0.539245 + 0.842149i \(0.318710\pi\)
\(312\) 3103.86 0.563209
\(313\) 6150.93 1.11077 0.555385 0.831593i \(-0.312571\pi\)
0.555385 + 0.831593i \(0.312571\pi\)
\(314\) −4473.92 −0.804070
\(315\) −2123.88 −0.379895
\(316\) −3433.27 −0.611191
\(317\) −3992.23 −0.707337 −0.353669 0.935371i \(-0.615066\pi\)
−0.353669 + 0.935371i \(0.615066\pi\)
\(318\) 1483.33 0.261575
\(319\) 2683.62 0.471015
\(320\) 185.669 0.0324350
\(321\) 4937.60 0.858535
\(322\) −6181.36 −1.06979
\(323\) −15344.4 −2.64330
\(324\) −511.495 −0.0877050
\(325\) 4188.34 0.714853
\(326\) −2486.47 −0.422432
\(327\) −760.564 −0.128622
\(328\) 4959.37 0.834864
\(329\) 8764.42 1.46869
\(330\) −757.891 −0.126426
\(331\) −4224.03 −0.701431 −0.350715 0.936482i \(-0.614062\pi\)
−0.350715 + 0.936482i \(0.614062\pi\)
\(332\) −2214.91 −0.366141
\(333\) 3059.78 0.503529
\(334\) −3912.16 −0.640909
\(335\) −1220.19 −0.199003
\(336\) −2648.64 −0.430045
\(337\) 2266.93 0.366431 0.183216 0.983073i \(-0.441349\pi\)
0.183216 + 0.983073i \(0.441349\pi\)
\(338\) 1171.95 0.188597
\(339\) −2842.51 −0.455410
\(340\) −4830.91 −0.770567
\(341\) 6110.93 0.970456
\(342\) −1653.28 −0.261401
\(343\) −14479.9 −2.27942
\(344\) 1249.71 0.195872
\(345\) 3012.84 0.470161
\(346\) −2484.66 −0.386059
\(347\) −270.565 −0.0418579 −0.0209290 0.999781i \(-0.506662\pi\)
−0.0209290 + 0.999781i \(0.506662\pi\)
\(348\) 1843.06 0.283903
\(349\) 2623.43 0.402375 0.201188 0.979553i \(-0.435520\pi\)
0.201188 + 0.979553i \(0.435520\pi\)
\(350\) 3266.64 0.498883
\(351\) −1503.24 −0.228596
\(352\) −5045.92 −0.764058
\(353\) −4779.31 −0.720615 −0.360307 0.932834i \(-0.617328\pi\)
−0.360307 + 0.932834i \(0.617328\pi\)
\(354\) −229.776 −0.0344984
\(355\) −4348.06 −0.650060
\(356\) −9139.28 −1.36062
\(357\) −10881.6 −1.61320
\(358\) 1957.02 0.288916
\(359\) −5676.39 −0.834509 −0.417254 0.908790i \(-0.637008\pi\)
−0.417254 + 0.908790i \(0.637008\pi\)
\(360\) −1179.92 −0.172742
\(361\) 13164.8 1.91934
\(362\) −2557.78 −0.371365
\(363\) −1710.34 −0.247299
\(364\) −11760.2 −1.69341
\(365\) −1488.35 −0.213435
\(366\) −60.0634 −0.00857804
\(367\) 4096.80 0.582701 0.291350 0.956616i \(-0.405895\pi\)
0.291350 + 0.956616i \(0.405895\pi\)
\(368\) 3757.24 0.532227
\(369\) −2401.89 −0.338855
\(370\) 3113.68 0.437493
\(371\) −12740.2 −1.78286
\(372\) 4196.87 0.584939
\(373\) 11745.0 1.63038 0.815190 0.579194i \(-0.196633\pi\)
0.815190 + 0.579194i \(0.196633\pi\)
\(374\) −3883.01 −0.536860
\(375\) −4237.79 −0.583570
\(376\) 4869.06 0.667826
\(377\) 5416.58 0.739969
\(378\) −1172.43 −0.159533
\(379\) −973.770 −0.131977 −0.0659884 0.997820i \(-0.521020\pi\)
−0.0659884 + 0.997820i \(0.521020\pi\)
\(380\) 6304.12 0.851038
\(381\) −7967.09 −1.07130
\(382\) −2768.50 −0.370808
\(383\) −3020.77 −0.403013 −0.201506 0.979487i \(-0.564584\pi\)
−0.201506 + 0.979487i \(0.564584\pi\)
\(384\) −4287.78 −0.569817
\(385\) 6509.50 0.861700
\(386\) 1712.90 0.225865
\(387\) −605.255 −0.0795008
\(388\) 3950.98 0.516961
\(389\) −327.769 −0.0427213 −0.0213606 0.999772i \(-0.506800\pi\)
−0.0213606 + 0.999772i \(0.506800\pi\)
\(390\) −1529.72 −0.198616
\(391\) 15436.1 1.99651
\(392\) −14418.3 −1.85774
\(393\) −5031.17 −0.645774
\(394\) 242.832 0.0310499
\(395\) 3835.71 0.488596
\(396\) 1567.69 0.198937
\(397\) 5076.62 0.641785 0.320892 0.947116i \(-0.396017\pi\)
0.320892 + 0.947116i \(0.396017\pi\)
\(398\) 4316.27 0.543606
\(399\) 14200.0 1.78167
\(400\) −1985.57 −0.248197
\(401\) 6277.21 0.781718 0.390859 0.920450i \(-0.372178\pi\)
0.390859 + 0.920450i \(0.372178\pi\)
\(402\) −673.572 −0.0835689
\(403\) 12334.2 1.52460
\(404\) 5699.63 0.701899
\(405\) 571.452 0.0701127
\(406\) 4224.59 0.516411
\(407\) −9377.96 −1.14213
\(408\) −6045.25 −0.733540
\(409\) −6562.26 −0.793357 −0.396679 0.917958i \(-0.629837\pi\)
−0.396679 + 0.917958i \(0.629837\pi\)
\(410\) −2444.20 −0.294416
\(411\) 2061.77 0.247444
\(412\) −4420.54 −0.528603
\(413\) 1973.54 0.235136
\(414\) 1663.16 0.197439
\(415\) 2474.54 0.292699
\(416\) −10184.6 −1.20034
\(417\) −449.085 −0.0527381
\(418\) 5067.16 0.592925
\(419\) 10923.8 1.27365 0.636827 0.771006i \(-0.280246\pi\)
0.636827 + 0.771006i \(0.280246\pi\)
\(420\) 4470.59 0.519387
\(421\) 1049.00 0.121437 0.0607187 0.998155i \(-0.480661\pi\)
0.0607187 + 0.998155i \(0.480661\pi\)
\(422\) 6289.11 0.725472
\(423\) −2358.16 −0.271058
\(424\) −7077.82 −0.810682
\(425\) −8157.45 −0.931046
\(426\) −2400.24 −0.272985
\(427\) 515.882 0.0584667
\(428\) −10393.2 −1.17378
\(429\) 4607.30 0.518514
\(430\) −615.916 −0.0690746
\(431\) −8997.43 −1.00555 −0.502774 0.864418i \(-0.667687\pi\)
−0.502774 + 0.864418i \(0.667687\pi\)
\(432\) 712.644 0.0793683
\(433\) −7942.35 −0.881490 −0.440745 0.897632i \(-0.645286\pi\)
−0.440745 + 0.897632i \(0.645286\pi\)
\(434\) 9619.92 1.06399
\(435\) −2059.09 −0.226956
\(436\) 1600.93 0.175850
\(437\) −20143.4 −2.20501
\(438\) −821.606 −0.0896298
\(439\) −3365.40 −0.365881 −0.182941 0.983124i \(-0.558562\pi\)
−0.182941 + 0.983124i \(0.558562\pi\)
\(440\) 3616.34 0.391824
\(441\) 6982.97 0.754019
\(442\) −7837.43 −0.843413
\(443\) −4056.81 −0.435090 −0.217545 0.976050i \(-0.569805\pi\)
−0.217545 + 0.976050i \(0.569805\pi\)
\(444\) −6440.60 −0.688417
\(445\) 10210.6 1.08770
\(446\) −5482.19 −0.582039
\(447\) 665.702 0.0704399
\(448\) −880.315 −0.0928370
\(449\) 10892.7 1.14490 0.572449 0.819940i \(-0.305993\pi\)
0.572449 + 0.819940i \(0.305993\pi\)
\(450\) −878.923 −0.0920729
\(451\) 7361.58 0.768611
\(452\) 5983.26 0.622630
\(453\) −3787.15 −0.392794
\(454\) 8048.48 0.832013
\(455\) 13138.7 1.35374
\(456\) 7888.77 0.810144
\(457\) 9685.62 0.991409 0.495705 0.868491i \(-0.334910\pi\)
0.495705 + 0.868491i \(0.334910\pi\)
\(458\) −3248.38 −0.331412
\(459\) 2927.80 0.297730
\(460\) −6341.78 −0.642798
\(461\) 145.044 0.0146538 0.00732689 0.999973i \(-0.497668\pi\)
0.00732689 + 0.999973i \(0.497668\pi\)
\(462\) 3593.40 0.361861
\(463\) −12516.4 −1.25634 −0.628169 0.778077i \(-0.716195\pi\)
−0.628169 + 0.778077i \(0.716195\pi\)
\(464\) −2567.85 −0.256917
\(465\) −4688.81 −0.467610
\(466\) −6902.62 −0.686175
\(467\) 2625.49 0.260156 0.130078 0.991504i \(-0.458477\pi\)
0.130078 + 0.991504i \(0.458477\pi\)
\(468\) 3164.20 0.312533
\(469\) 5785.28 0.569593
\(470\) −2399.69 −0.235510
\(471\) −10339.0 −1.01146
\(472\) 1096.40 0.106919
\(473\) 1855.05 0.180328
\(474\) 2117.40 0.205180
\(475\) 10645.1 1.02828
\(476\) 22904.8 2.20555
\(477\) 3427.89 0.329040
\(478\) 8349.67 0.798964
\(479\) −16253.8 −1.55043 −0.775216 0.631697i \(-0.782359\pi\)
−0.775216 + 0.631697i \(0.782359\pi\)
\(480\) 3871.65 0.368158
\(481\) −18928.4 −1.79430
\(482\) 3441.76 0.325245
\(483\) −14284.8 −1.34572
\(484\) 3600.13 0.338104
\(485\) −4414.11 −0.413266
\(486\) 315.455 0.0294431
\(487\) −1328.98 −0.123659 −0.0618296 0.998087i \(-0.519694\pi\)
−0.0618296 + 0.998087i \(0.519694\pi\)
\(488\) 286.597 0.0265854
\(489\) −5746.11 −0.531386
\(490\) 7105.97 0.655133
\(491\) 14197.4 1.30493 0.652463 0.757820i \(-0.273736\pi\)
0.652463 + 0.757820i \(0.273736\pi\)
\(492\) 5055.79 0.463278
\(493\) −10549.6 −0.963757
\(494\) 10227.5 0.931491
\(495\) −1751.45 −0.159034
\(496\) −5847.31 −0.529339
\(497\) 20615.5 1.86063
\(498\) 1366.00 0.122916
\(499\) −7543.06 −0.676701 −0.338350 0.941020i \(-0.609869\pi\)
−0.338350 + 0.941020i \(0.609869\pi\)
\(500\) 8920.21 0.797848
\(501\) −9040.79 −0.806213
\(502\) 4140.80 0.368154
\(503\) −8035.31 −0.712280 −0.356140 0.934433i \(-0.615907\pi\)
−0.356140 + 0.934433i \(0.615907\pi\)
\(504\) 5594.36 0.494430
\(505\) −6367.73 −0.561109
\(506\) −5097.43 −0.447842
\(507\) 2708.32 0.237240
\(508\) 16770.1 1.46467
\(509\) −2243.76 −0.195389 −0.0976946 0.995216i \(-0.531147\pi\)
−0.0976946 + 0.995216i \(0.531147\pi\)
\(510\) 2979.37 0.258684
\(511\) 7056.74 0.610904
\(512\) 8752.11 0.755453
\(513\) −3820.65 −0.328822
\(514\) 9084.48 0.779570
\(515\) 4938.70 0.422573
\(516\) 1274.01 0.108692
\(517\) 7227.53 0.614829
\(518\) −14762.9 −1.25221
\(519\) −5741.93 −0.485631
\(520\) 7299.19 0.615559
\(521\) 5397.02 0.453834 0.226917 0.973914i \(-0.427135\pi\)
0.226917 + 0.973914i \(0.427135\pi\)
\(522\) −1136.67 −0.0953078
\(523\) −229.273 −0.0191690 −0.00958451 0.999954i \(-0.503051\pi\)
−0.00958451 + 0.999954i \(0.503051\pi\)
\(524\) 10590.2 0.882892
\(525\) 7549.03 0.627555
\(526\) −6274.19 −0.520090
\(527\) −24022.9 −1.98568
\(528\) −2184.19 −0.180028
\(529\) 8096.74 0.665467
\(530\) 3488.27 0.285888
\(531\) −531.000 −0.0433963
\(532\) −29889.8 −2.43588
\(533\) 14858.5 1.20750
\(534\) 5636.48 0.456768
\(535\) 11611.5 0.938336
\(536\) 3214.01 0.259000
\(537\) 4522.58 0.363433
\(538\) 5377.19 0.430905
\(539\) −21402.2 −1.71031
\(540\) −1202.86 −0.0958571
\(541\) 21118.4 1.67829 0.839143 0.543911i \(-0.183057\pi\)
0.839143 + 0.543911i \(0.183057\pi\)
\(542\) −5103.95 −0.404490
\(543\) −5910.90 −0.467147
\(544\) 19836.2 1.56336
\(545\) −1788.58 −0.140577
\(546\) 7252.88 0.568488
\(547\) 700.599 0.0547632 0.0273816 0.999625i \(-0.491283\pi\)
0.0273816 + 0.999625i \(0.491283\pi\)
\(548\) −4339.85 −0.338302
\(549\) −138.803 −0.0107905
\(550\) 2693.82 0.208845
\(551\) 13766.8 1.06440
\(552\) −7935.90 −0.611910
\(553\) −18186.3 −1.39848
\(554\) −3420.70 −0.262332
\(555\) 7195.55 0.550332
\(556\) 945.288 0.0721028
\(557\) 13.7365 0.00104495 0.000522474 1.00000i \(-0.499834\pi\)
0.000522474 1.00000i \(0.499834\pi\)
\(558\) −2588.34 −0.196368
\(559\) 3744.21 0.283298
\(560\) −6228.68 −0.470018
\(561\) −8973.44 −0.675328
\(562\) −3624.44 −0.272042
\(563\) −20483.4 −1.53334 −0.766672 0.642039i \(-0.778089\pi\)
−0.766672 + 0.642039i \(0.778089\pi\)
\(564\) 4963.73 0.370586
\(565\) −6684.60 −0.497740
\(566\) −1188.19 −0.0882390
\(567\) −2709.43 −0.200680
\(568\) 11452.9 0.846046
\(569\) −16699.3 −1.23035 −0.615175 0.788390i \(-0.710915\pi\)
−0.615175 + 0.788390i \(0.710915\pi\)
\(570\) −3887.94 −0.285698
\(571\) −2261.27 −0.165729 −0.0828643 0.996561i \(-0.526407\pi\)
−0.0828643 + 0.996561i \(0.526407\pi\)
\(572\) −9697.99 −0.708904
\(573\) −6397.86 −0.466448
\(574\) 11588.7 0.842689
\(575\) −10708.7 −0.776667
\(576\) 236.858 0.0171338
\(577\) −12365.4 −0.892160 −0.446080 0.894993i \(-0.647180\pi\)
−0.446080 + 0.894993i \(0.647180\pi\)
\(578\) 8886.73 0.639514
\(579\) 3958.41 0.284121
\(580\) 4334.23 0.310291
\(581\) −11732.5 −0.837776
\(582\) −2436.69 −0.173547
\(583\) −10506.2 −0.746348
\(584\) 3920.36 0.277784
\(585\) −3535.10 −0.249844
\(586\) 3416.54 0.240847
\(587\) 17739.0 1.24730 0.623651 0.781703i \(-0.285649\pi\)
0.623651 + 0.781703i \(0.285649\pi\)
\(588\) −14698.6 −1.03088
\(589\) 31348.8 2.19304
\(590\) −540.353 −0.0377051
\(591\) 561.171 0.0390584
\(592\) 8973.40 0.622981
\(593\) 24070.9 1.66690 0.833451 0.552594i \(-0.186362\pi\)
0.833451 + 0.552594i \(0.186362\pi\)
\(594\) −966.841 −0.0667844
\(595\) −25589.7 −1.76315
\(596\) −1401.25 −0.0963044
\(597\) 9974.68 0.683813
\(598\) −10288.6 −0.703565
\(599\) 28779.3 1.96309 0.981544 0.191238i \(-0.0612501\pi\)
0.981544 + 0.191238i \(0.0612501\pi\)
\(600\) 4193.85 0.285356
\(601\) −11612.0 −0.788128 −0.394064 0.919083i \(-0.628931\pi\)
−0.394064 + 0.919083i \(0.628931\pi\)
\(602\) 2920.25 0.197708
\(603\) −1556.59 −0.105123
\(604\) 7971.65 0.537023
\(605\) −4022.13 −0.270285
\(606\) −3515.14 −0.235632
\(607\) −821.129 −0.0549071 −0.0274535 0.999623i \(-0.508740\pi\)
−0.0274535 + 0.999623i \(0.508740\pi\)
\(608\) −25885.3 −1.72662
\(609\) 9762.80 0.649604
\(610\) −141.248 −0.00937536
\(611\) 14588.0 0.965903
\(612\) −6162.78 −0.407052
\(613\) 7705.99 0.507736 0.253868 0.967239i \(-0.418297\pi\)
0.253868 + 0.967239i \(0.418297\pi\)
\(614\) −8799.21 −0.578350
\(615\) −5648.42 −0.370352
\(616\) −17146.2 −1.12149
\(617\) −447.613 −0.0292062 −0.0146031 0.999893i \(-0.504648\pi\)
−0.0146031 + 0.999893i \(0.504648\pi\)
\(618\) 2726.28 0.177455
\(619\) −5073.90 −0.329462 −0.164731 0.986339i \(-0.552676\pi\)
−0.164731 + 0.986339i \(0.552676\pi\)
\(620\) 9869.58 0.639309
\(621\) 3843.47 0.248363
\(622\) 7678.70 0.494997
\(623\) −48411.4 −3.11326
\(624\) −4408.54 −0.282825
\(625\) −562.371 −0.0359917
\(626\) 7984.94 0.509812
\(627\) 11709.9 0.745853
\(628\) 21762.8 1.38285
\(629\) 36866.0 2.33695
\(630\) −2757.15 −0.174361
\(631\) 20851.5 1.31551 0.657753 0.753234i \(-0.271507\pi\)
0.657753 + 0.753234i \(0.271507\pi\)
\(632\) −10103.4 −0.635902
\(633\) 14533.8 0.912586
\(634\) −5182.59 −0.324648
\(635\) −18735.8 −1.17088
\(636\) −7215.43 −0.449859
\(637\) −43197.9 −2.68691
\(638\) 3483.79 0.216183
\(639\) −5546.82 −0.343394
\(640\) −10083.4 −0.622781
\(641\) −5938.37 −0.365915 −0.182957 0.983121i \(-0.558567\pi\)
−0.182957 + 0.983121i \(0.558567\pi\)
\(642\) 6409.84 0.394044
\(643\) 943.102 0.0578418 0.0289209 0.999582i \(-0.490793\pi\)
0.0289209 + 0.999582i \(0.490793\pi\)
\(644\) 30068.3 1.83984
\(645\) −1423.35 −0.0868904
\(646\) −19919.7 −1.21320
\(647\) 14236.8 0.865082 0.432541 0.901614i \(-0.357617\pi\)
0.432541 + 0.901614i \(0.357617\pi\)
\(648\) −1505.22 −0.0912510
\(649\) 1627.47 0.0984340
\(650\) 5437.17 0.328098
\(651\) 22231.1 1.33841
\(652\) 12095.1 0.726503
\(653\) 8903.59 0.533575 0.266788 0.963755i \(-0.414038\pi\)
0.266788 + 0.963755i \(0.414038\pi\)
\(654\) −987.341 −0.0590338
\(655\) −11831.6 −0.705798
\(656\) −7044.01 −0.419242
\(657\) −1898.69 −0.112747
\(658\) 11377.7 0.674086
\(659\) −4548.25 −0.268854 −0.134427 0.990924i \(-0.542919\pi\)
−0.134427 + 0.990924i \(0.542919\pi\)
\(660\) 3686.65 0.217429
\(661\) −3357.62 −0.197574 −0.0987870 0.995109i \(-0.531496\pi\)
−0.0987870 + 0.995109i \(0.531496\pi\)
\(662\) −5483.50 −0.321937
\(663\) −18111.9 −1.06095
\(664\) −6518.00 −0.380945
\(665\) 33393.4 1.94728
\(666\) 3972.12 0.231106
\(667\) −13849.1 −0.803955
\(668\) 19030.1 1.10224
\(669\) −12669.1 −0.732159
\(670\) −1584.01 −0.0913366
\(671\) 425.419 0.0244756
\(672\) −18356.7 −1.05376
\(673\) −14707.2 −0.842382 −0.421191 0.906972i \(-0.638388\pi\)
−0.421191 + 0.906972i \(0.638388\pi\)
\(674\) 2942.85 0.168182
\(675\) −2031.14 −0.115820
\(676\) −5700.80 −0.324351
\(677\) −7070.52 −0.401392 −0.200696 0.979654i \(-0.564320\pi\)
−0.200696 + 0.979654i \(0.564320\pi\)
\(678\) −3690.06 −0.209020
\(679\) 20928.6 1.18287
\(680\) −14216.3 −0.801722
\(681\) 18599.6 1.04661
\(682\) 7933.02 0.445412
\(683\) 16587.9 0.929308 0.464654 0.885492i \(-0.346179\pi\)
0.464654 + 0.885492i \(0.346179\pi\)
\(684\) 8042.15 0.449560
\(685\) 4848.56 0.270444
\(686\) −18797.4 −1.04619
\(687\) −7506.83 −0.416890
\(688\) −1775.03 −0.0983608
\(689\) −21205.5 −1.17252
\(690\) 3911.17 0.215791
\(691\) −32722.2 −1.80147 −0.900733 0.434373i \(-0.856970\pi\)
−0.900733 + 0.434373i \(0.856970\pi\)
\(692\) 12086.3 0.663948
\(693\) 8304.15 0.455193
\(694\) −351.239 −0.0192116
\(695\) −1056.09 −0.0576401
\(696\) 5423.72 0.295381
\(697\) −28939.4 −1.57268
\(698\) 3405.65 0.184679
\(699\) −15951.6 −0.863154
\(700\) −15890.1 −0.857984
\(701\) −24968.5 −1.34529 −0.672645 0.739965i \(-0.734842\pi\)
−0.672645 + 0.739965i \(0.734842\pi\)
\(702\) −1951.46 −0.104919
\(703\) −48108.4 −2.58100
\(704\) −725.947 −0.0388639
\(705\) −5545.57 −0.296253
\(706\) −6204.35 −0.330742
\(707\) 30191.4 1.60603
\(708\) 1117.71 0.0593308
\(709\) 33965.7 1.79916 0.899582 0.436752i \(-0.143871\pi\)
0.899582 + 0.436752i \(0.143871\pi\)
\(710\) −5644.52 −0.298359
\(711\) 4893.20 0.258101
\(712\) −26894.9 −1.41563
\(713\) −31536.0 −1.65643
\(714\) −14126.1 −0.740416
\(715\) 10834.8 0.566709
\(716\) −9519.66 −0.496880
\(717\) 19295.6 1.00503
\(718\) −7368.92 −0.383016
\(719\) 14477.7 0.750941 0.375470 0.926834i \(-0.377481\pi\)
0.375470 + 0.926834i \(0.377481\pi\)
\(720\) 1675.89 0.0867456
\(721\) −23415.9 −1.20951
\(722\) 17090.1 0.880925
\(723\) 7953.73 0.409132
\(724\) 12442.0 0.638677
\(725\) 7318.76 0.374913
\(726\) −2220.31 −0.113503
\(727\) 18345.6 0.935900 0.467950 0.883755i \(-0.344993\pi\)
0.467950 + 0.883755i \(0.344993\pi\)
\(728\) −34607.7 −1.76188
\(729\) 729.000 0.0370370
\(730\) −1932.13 −0.0979609
\(731\) −7292.45 −0.368975
\(732\) 292.170 0.0147526
\(733\) −24879.5 −1.25368 −0.626839 0.779149i \(-0.715652\pi\)
−0.626839 + 0.779149i \(0.715652\pi\)
\(734\) 5318.34 0.267443
\(735\) 16421.5 0.824105
\(736\) 26039.9 1.30414
\(737\) 4770.80 0.238446
\(738\) −3118.06 −0.155525
\(739\) 522.214 0.0259945 0.0129973 0.999916i \(-0.495863\pi\)
0.0129973 + 0.999916i \(0.495863\pi\)
\(740\) −15146.1 −0.752405
\(741\) 23635.2 1.17174
\(742\) −16539.0 −0.818281
\(743\) −1698.03 −0.0838422 −0.0419211 0.999121i \(-0.513348\pi\)
−0.0419211 + 0.999121i \(0.513348\pi\)
\(744\) 12350.5 0.608589
\(745\) 1565.50 0.0769872
\(746\) 15247.0 0.748299
\(747\) 3156.76 0.154618
\(748\) 18888.4 0.923298
\(749\) −55053.8 −2.68574
\(750\) −5501.37 −0.267842
\(751\) −21329.8 −1.03640 −0.518199 0.855260i \(-0.673397\pi\)
−0.518199 + 0.855260i \(0.673397\pi\)
\(752\) −6915.75 −0.335361
\(753\) 9569.18 0.463108
\(754\) 7031.64 0.339625
\(755\) −8906.06 −0.429304
\(756\) 5703.13 0.274366
\(757\) −2570.95 −0.123438 −0.0617192 0.998094i \(-0.519658\pi\)
−0.0617192 + 0.998094i \(0.519658\pi\)
\(758\) −1264.12 −0.0605736
\(759\) −11779.9 −0.563350
\(760\) 18551.7 0.885447
\(761\) −16345.4 −0.778606 −0.389303 0.921110i \(-0.627284\pi\)
−0.389303 + 0.921110i \(0.627284\pi\)
\(762\) −10342.6 −0.491698
\(763\) 8480.23 0.402365
\(764\) 13467.0 0.637720
\(765\) 6885.17 0.325404
\(766\) −3921.47 −0.184972
\(767\) 3284.86 0.154641
\(768\) −6197.88 −0.291207
\(769\) 35378.7 1.65902 0.829512 0.558489i \(-0.188619\pi\)
0.829512 + 0.558489i \(0.188619\pi\)
\(770\) 8450.42 0.395496
\(771\) 20993.7 0.980637
\(772\) −8332.13 −0.388446
\(773\) −8622.56 −0.401206 −0.200603 0.979673i \(-0.564290\pi\)
−0.200603 + 0.979673i \(0.564290\pi\)
\(774\) −785.723 −0.0364887
\(775\) 16665.7 0.772452
\(776\) 11626.9 0.537862
\(777\) −34116.3 −1.57518
\(778\) −425.500 −0.0196079
\(779\) 37764.6 1.73691
\(780\) 7441.11 0.341582
\(781\) 17000.5 0.778906
\(782\) 20038.7 0.916344
\(783\) −2626.78 −0.119890
\(784\) 20478.9 0.932895
\(785\) −24313.7 −1.10547
\(786\) −6531.31 −0.296392
\(787\) 18664.1 0.845366 0.422683 0.906278i \(-0.361088\pi\)
0.422683 + 0.906278i \(0.361088\pi\)
\(788\) −1181.22 −0.0534000
\(789\) −14499.3 −0.654232
\(790\) 4979.39 0.224252
\(791\) 31693.8 1.42465
\(792\) 4613.36 0.206981
\(793\) 858.662 0.0384514
\(794\) 6590.32 0.294561
\(795\) 8061.20 0.359624
\(796\) −20995.9 −0.934900
\(797\) −41335.9 −1.83713 −0.918564 0.395272i \(-0.870650\pi\)
−0.918564 + 0.395272i \(0.870650\pi\)
\(798\) 18433.9 0.817738
\(799\) −28412.4 −1.25802
\(800\) −13761.2 −0.608166
\(801\) 13025.6 0.574578
\(802\) 8148.88 0.358787
\(803\) 5819.31 0.255740
\(804\) 3276.49 0.143723
\(805\) −33592.9 −1.47080
\(806\) 16011.9 0.699747
\(807\) 12426.4 0.542045
\(808\) 16772.8 0.730278
\(809\) 19310.4 0.839206 0.419603 0.907708i \(-0.362169\pi\)
0.419603 + 0.907708i \(0.362169\pi\)
\(810\) 741.841 0.0321798
\(811\) 6287.79 0.272249 0.136125 0.990692i \(-0.456535\pi\)
0.136125 + 0.990692i \(0.456535\pi\)
\(812\) −20549.9 −0.888129
\(813\) −11795.0 −0.508816
\(814\) −12174.2 −0.524207
\(815\) −13512.8 −0.580778
\(816\) 8586.33 0.368360
\(817\) 9516.31 0.407508
\(818\) −8518.93 −0.364129
\(819\) 16761.0 0.715113
\(820\) 11889.5 0.506339
\(821\) −10235.6 −0.435109 −0.217554 0.976048i \(-0.569808\pi\)
−0.217554 + 0.976048i \(0.569808\pi\)
\(822\) 2676.52 0.113570
\(823\) −7825.03 −0.331426 −0.165713 0.986174i \(-0.552992\pi\)
−0.165713 + 0.986174i \(0.552992\pi\)
\(824\) −13008.7 −0.549975
\(825\) 6225.27 0.262710
\(826\) 2561.98 0.107921
\(827\) 15916.1 0.669233 0.334617 0.942354i \(-0.391393\pi\)
0.334617 + 0.942354i \(0.391393\pi\)
\(828\) −8090.20 −0.339558
\(829\) −26623.7 −1.11541 −0.557707 0.830038i \(-0.688319\pi\)
−0.557707 + 0.830038i \(0.688319\pi\)
\(830\) 3212.36 0.134341
\(831\) −7905.07 −0.329993
\(832\) −1465.24 −0.0610555
\(833\) 84134.7 3.49951
\(834\) −582.988 −0.0242053
\(835\) −21260.8 −0.881150
\(836\) −24648.5 −1.01972
\(837\) −5981.51 −0.247015
\(838\) 14180.9 0.584572
\(839\) −19230.4 −0.791307 −0.395653 0.918400i \(-0.629482\pi\)
−0.395653 + 0.918400i \(0.629482\pi\)
\(840\) 13156.0 0.540387
\(841\) −14924.0 −0.611915
\(842\) 1361.78 0.0557363
\(843\) −8375.89 −0.342207
\(844\) −30592.5 −1.24767
\(845\) 6369.04 0.259292
\(846\) −3061.29 −0.124408
\(847\) 19070.1 0.773622
\(848\) 10052.9 0.407098
\(849\) −2745.84 −0.110998
\(850\) −10589.7 −0.427324
\(851\) 48395.8 1.94946
\(852\) 11675.6 0.469483
\(853\) 21069.1 0.845710 0.422855 0.906197i \(-0.361028\pi\)
0.422855 + 0.906197i \(0.361028\pi\)
\(854\) 669.701 0.0268346
\(855\) −8984.83 −0.359386
\(856\) −30585.1 −1.22123
\(857\) −8066.10 −0.321508 −0.160754 0.986994i \(-0.551393\pi\)
−0.160754 + 0.986994i \(0.551393\pi\)
\(858\) 5981.05 0.237983
\(859\) −17890.8 −0.710625 −0.355313 0.934748i \(-0.615626\pi\)
−0.355313 + 0.934748i \(0.615626\pi\)
\(860\) 2996.03 0.118795
\(861\) 26780.9 1.06004
\(862\) −11680.2 −0.461518
\(863\) −17900.4 −0.706069 −0.353035 0.935610i \(-0.614850\pi\)
−0.353035 + 0.935610i \(0.614850\pi\)
\(864\) 4939.05 0.194479
\(865\) −13503.0 −0.530770
\(866\) −10310.5 −0.404579
\(867\) 20536.8 0.804458
\(868\) −46794.7 −1.82986
\(869\) −14997.2 −0.585438
\(870\) −2673.05 −0.104167
\(871\) 9629.34 0.374601
\(872\) 4711.18 0.182960
\(873\) −5631.07 −0.218308
\(874\) −26149.5 −1.01204
\(875\) 47251.0 1.82557
\(876\) 3996.59 0.154146
\(877\) 45119.0 1.73724 0.868620 0.495478i \(-0.165007\pi\)
0.868620 + 0.495478i \(0.165007\pi\)
\(878\) −4368.86 −0.167929
\(879\) 7895.45 0.302966
\(880\) −5136.45 −0.196761
\(881\) −43192.5 −1.65175 −0.825876 0.563852i \(-0.809319\pi\)
−0.825876 + 0.563852i \(0.809319\pi\)
\(882\) 9065.08 0.346074
\(883\) 36353.7 1.38550 0.692751 0.721177i \(-0.256399\pi\)
0.692751 + 0.721177i \(0.256399\pi\)
\(884\) 38124.1 1.45051
\(885\) −1248.73 −0.0474300
\(886\) −5266.43 −0.199694
\(887\) −4579.23 −0.173343 −0.0866717 0.996237i \(-0.527623\pi\)
−0.0866717 + 0.996237i \(0.527623\pi\)
\(888\) −18953.3 −0.716251
\(889\) 88832.4 3.35134
\(890\) 13255.0 0.499224
\(891\) −2234.32 −0.0840095
\(892\) 26667.3 1.00100
\(893\) 37076.9 1.38940
\(894\) 864.194 0.0323299
\(895\) 10635.5 0.397214
\(896\) 47808.4 1.78255
\(897\) −23776.4 −0.885029
\(898\) 14140.6 0.525476
\(899\) 21553.0 0.799592
\(900\) 4275.39 0.158348
\(901\) 41301.1 1.52712
\(902\) 9556.58 0.352771
\(903\) 6748.54 0.248701
\(904\) 17607.4 0.647804
\(905\) −13900.4 −0.510569
\(906\) −4916.36 −0.180282
\(907\) −47448.3 −1.73704 −0.868520 0.495654i \(-0.834929\pi\)
−0.868520 + 0.495654i \(0.834929\pi\)
\(908\) −39150.7 −1.43090
\(909\) −8123.30 −0.296406
\(910\) 17056.3 0.621329
\(911\) −25809.9 −0.938660 −0.469330 0.883023i \(-0.655505\pi\)
−0.469330 + 0.883023i \(0.655505\pi\)
\(912\) −11204.8 −0.406828
\(913\) −9675.18 −0.350714
\(914\) 12573.6 0.455029
\(915\) −326.417 −0.0117935
\(916\) 15801.3 0.569966
\(917\) 56097.2 2.02016
\(918\) 3800.78 0.136650
\(919\) 27429.5 0.984565 0.492283 0.870435i \(-0.336163\pi\)
0.492283 + 0.870435i \(0.336163\pi\)
\(920\) −18662.5 −0.668787
\(921\) −20334.5 −0.727519
\(922\) 188.292 0.00672567
\(923\) 34313.6 1.22367
\(924\) −17479.6 −0.622333
\(925\) −25575.6 −0.909102
\(926\) −16248.3 −0.576624
\(927\) 6300.30 0.223224
\(928\) −17796.7 −0.629533
\(929\) −15216.0 −0.537375 −0.268688 0.963227i \(-0.586590\pi\)
−0.268688 + 0.963227i \(0.586590\pi\)
\(930\) −6086.87 −0.214620
\(931\) −109792. −3.86497
\(932\) 33576.8 1.18009
\(933\) 17745.1 0.622666
\(934\) 3408.32 0.119404
\(935\) −21102.4 −0.738099
\(936\) 9311.57 0.325169
\(937\) 44431.6 1.54911 0.774556 0.632506i \(-0.217973\pi\)
0.774556 + 0.632506i \(0.217973\pi\)
\(938\) 7510.27 0.261427
\(939\) 18452.8 0.641303
\(940\) 11673.0 0.405032
\(941\) −5816.82 −0.201512 −0.100756 0.994911i \(-0.532126\pi\)
−0.100756 + 0.994911i \(0.532126\pi\)
\(942\) −13421.8 −0.464230
\(943\) −37990.2 −1.31191
\(944\) −1557.26 −0.0536912
\(945\) −6371.64 −0.219333
\(946\) 2408.17 0.0827657
\(947\) 19125.2 0.656267 0.328134 0.944631i \(-0.393580\pi\)
0.328134 + 0.944631i \(0.393580\pi\)
\(948\) −10299.8 −0.352871
\(949\) 11745.6 0.401769
\(950\) 13819.1 0.471950
\(951\) −11976.7 −0.408381
\(952\) 67404.0 2.29472
\(953\) 20408.0 0.693682 0.346841 0.937924i \(-0.387254\pi\)
0.346841 + 0.937924i \(0.387254\pi\)
\(954\) 4449.98 0.151020
\(955\) −15045.5 −0.509804
\(956\) −40615.8 −1.37407
\(957\) 8050.85 0.271940
\(958\) −21100.2 −0.711605
\(959\) −22988.5 −0.774075
\(960\) 557.007 0.0187264
\(961\) 19287.9 0.647440
\(962\) −24572.2 −0.823535
\(963\) 14812.8 0.495676
\(964\) −16742.0 −0.559359
\(965\) 9308.81 0.310530
\(966\) −18544.1 −0.617646
\(967\) −16417.9 −0.545981 −0.272991 0.962017i \(-0.588013\pi\)
−0.272991 + 0.962017i \(0.588013\pi\)
\(968\) 10594.4 0.351774
\(969\) −46033.3 −1.52611
\(970\) −5730.25 −0.189678
\(971\) −567.686 −0.0187620 −0.00938101 0.999956i \(-0.502986\pi\)
−0.00938101 + 0.999956i \(0.502986\pi\)
\(972\) −1534.49 −0.0506365
\(973\) 5007.26 0.164980
\(974\) −1725.25 −0.0567561
\(975\) 12565.0 0.412721
\(976\) −407.067 −0.0133503
\(977\) 906.220 0.0296751 0.0148375 0.999890i \(-0.495277\pi\)
0.0148375 + 0.999890i \(0.495277\pi\)
\(978\) −7459.41 −0.243891
\(979\) −39922.3 −1.30329
\(980\) −34566.0 −1.12670
\(981\) −2281.69 −0.0742598
\(982\) 18430.6 0.598925
\(983\) 54807.1 1.77831 0.889153 0.457609i \(-0.151294\pi\)
0.889153 + 0.457609i \(0.151294\pi\)
\(984\) 14878.1 0.482009
\(985\) 1319.68 0.0426888
\(986\) −13695.2 −0.442338
\(987\) 26293.3 0.847947
\(988\) −49750.2 −1.60199
\(989\) −9573.16 −0.307795
\(990\) −2273.67 −0.0729920
\(991\) −22970.2 −0.736298 −0.368149 0.929767i \(-0.620008\pi\)
−0.368149 + 0.929767i \(0.620008\pi\)
\(992\) −40525.4 −1.29706
\(993\) −12672.1 −0.404971
\(994\) 26762.4 0.853976
\(995\) 23457.0 0.747374
\(996\) −6644.73 −0.211392
\(997\) −41803.1 −1.32790 −0.663951 0.747776i \(-0.731122\pi\)
−0.663951 + 0.747776i \(0.731122\pi\)
\(998\) −9792.16 −0.310587
\(999\) 9179.35 0.290713
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.a.1.5 7
3.2 odd 2 531.4.a.d.1.3 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.4.a.a.1.5 7 1.1 even 1 trivial
531.4.a.d.1.3 7 3.2 odd 2