Properties

Label 177.4.a.d.1.1
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 1.1
Root \(5.26439\) of defining polynomial
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-4.26439 q^{2} +3.00000 q^{3} +10.1850 q^{4} +13.9771 q^{5} -12.7932 q^{6} +21.4669 q^{7} -9.31764 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q-4.26439 q^{2} +3.00000 q^{3} +10.1850 q^{4} +13.9771 q^{5} -12.7932 q^{6} +21.4669 q^{7} -9.31764 q^{8} +9.00000 q^{9} -59.6039 q^{10} +50.2623 q^{11} +30.5550 q^{12} -31.1995 q^{13} -91.5433 q^{14} +41.9314 q^{15} -41.7459 q^{16} +2.00676 q^{17} -38.3795 q^{18} -59.2842 q^{19} +142.357 q^{20} +64.4008 q^{21} -214.338 q^{22} -28.6724 q^{23} -27.9529 q^{24} +70.3601 q^{25} +133.047 q^{26} +27.0000 q^{27} +218.640 q^{28} +92.9707 q^{29} -178.812 q^{30} -88.6315 q^{31} +252.562 q^{32} +150.787 q^{33} -8.55761 q^{34} +300.046 q^{35} +91.6649 q^{36} +231.603 q^{37} +252.811 q^{38} -93.5986 q^{39} -130.234 q^{40} +237.954 q^{41} -274.630 q^{42} +29.7378 q^{43} +511.921 q^{44} +125.794 q^{45} +122.270 q^{46} -433.646 q^{47} -125.238 q^{48} +117.829 q^{49} -300.042 q^{50} +6.02029 q^{51} -317.767 q^{52} +464.489 q^{53} -115.138 q^{54} +702.522 q^{55} -200.021 q^{56} -177.853 q^{57} -396.463 q^{58} +59.0000 q^{59} +427.071 q^{60} -328.206 q^{61} +377.959 q^{62} +193.202 q^{63} -743.054 q^{64} -436.080 q^{65} -643.013 q^{66} -841.628 q^{67} +20.4388 q^{68} -86.0172 q^{69} -1279.51 q^{70} +46.3476 q^{71} -83.8588 q^{72} -738.776 q^{73} -987.644 q^{74} +211.080 q^{75} -603.809 q^{76} +1078.98 q^{77} +399.140 q^{78} +734.298 q^{79} -583.488 q^{80} +81.0000 q^{81} -1014.73 q^{82} +353.300 q^{83} +655.921 q^{84} +28.0488 q^{85} -126.813 q^{86} +278.912 q^{87} -468.326 q^{88} -704.085 q^{89} -536.435 q^{90} -669.758 q^{91} -292.028 q^{92} -265.894 q^{93} +1849.23 q^{94} -828.623 q^{95} +757.685 q^{96} +1479.12 q^{97} -502.468 q^{98} +452.360 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 6q^{2} + 24q^{3} + 34q^{4} + 42q^{5} + 18q^{6} + 53q^{7} + 51q^{8} + 72q^{9} + O(q^{10}) \) \( 8q + 6q^{2} + 24q^{3} + 34q^{4} + 42q^{5} + 18q^{6} + 53q^{7} + 51q^{8} + 72q^{9} + 21q^{10} + 67q^{11} + 102q^{12} + 33q^{13} + 79q^{14} + 126q^{15} - 30q^{16} + 139q^{17} + 54q^{18} + 64q^{19} + 117q^{20} + 159q^{21} - 84q^{22} + 226q^{23} + 153q^{24} + 96q^{25} + 24q^{26} + 216q^{27} + 34q^{28} + 456q^{29} + 63q^{30} + 124q^{31} + 174q^{32} + 201q^{33} - 114q^{34} + 556q^{35} + 306q^{36} + 127q^{37} + 237q^{38} + 99q^{39} - 188q^{40} + 425q^{41} + 237q^{42} - 115q^{43} + 510q^{44} + 378q^{45} - 711q^{46} + 420q^{47} - 90q^{48} + 171q^{49} - 137q^{50} + 417q^{51} - 922q^{52} + 98q^{53} + 162q^{54} - 616q^{55} - 412q^{56} + 192q^{57} - 1548q^{58} + 472q^{59} + 351q^{60} - 1254q^{61} - 766q^{62} + 477q^{63} - 2019q^{64} - 734q^{65} - 252q^{66} - 1010q^{67} - 503q^{68} + 678q^{69} - 2956q^{70} - 17q^{71} + 459q^{72} - 1180q^{73} - 1228q^{74} + 288q^{75} - 2008q^{76} + 441q^{77} + 72q^{78} - 873q^{79} - 865q^{80} + 648q^{81} - 3645q^{82} + 759q^{83} + 102q^{84} - 850q^{85} - 1226q^{86} + 1368q^{87} - 3047q^{88} + 988q^{89} + 189q^{90} - 2111q^{91} - 1062q^{92} + 372q^{93} - 2240q^{94} + 1822q^{95} + 522q^{96} - 668q^{97} - 1368q^{98} + 603q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.26439 −1.50769 −0.753844 0.657053i \(-0.771803\pi\)
−0.753844 + 0.657053i \(0.771803\pi\)
\(3\) 3.00000 0.577350
\(4\) 10.1850 1.27312
\(5\) 13.9771 1.25015 0.625076 0.780564i \(-0.285068\pi\)
0.625076 + 0.780564i \(0.285068\pi\)
\(6\) −12.7932 −0.870464
\(7\) 21.4669 1.15910 0.579552 0.814935i \(-0.303227\pi\)
0.579552 + 0.814935i \(0.303227\pi\)
\(8\) −9.31764 −0.411785
\(9\) 9.00000 0.333333
\(10\) −59.6039 −1.88484
\(11\) 50.2623 1.37769 0.688847 0.724907i \(-0.258117\pi\)
0.688847 + 0.724907i \(0.258117\pi\)
\(12\) 30.5550 0.735038
\(13\) −31.1995 −0.665630 −0.332815 0.942992i \(-0.607998\pi\)
−0.332815 + 0.942992i \(0.607998\pi\)
\(14\) −91.5433 −1.74757
\(15\) 41.9314 0.721776
\(16\) −41.7459 −0.652280
\(17\) 2.00676 0.0286301 0.0143150 0.999898i \(-0.495443\pi\)
0.0143150 + 0.999898i \(0.495443\pi\)
\(18\) −38.3795 −0.502563
\(19\) −59.2842 −0.715828 −0.357914 0.933755i \(-0.616512\pi\)
−0.357914 + 0.933755i \(0.616512\pi\)
\(20\) 142.357 1.59160
\(21\) 64.4008 0.669210
\(22\) −214.338 −2.07713
\(23\) −28.6724 −0.259939 −0.129970 0.991518i \(-0.541488\pi\)
−0.129970 + 0.991518i \(0.541488\pi\)
\(24\) −27.9529 −0.237744
\(25\) 70.3601 0.562881
\(26\) 133.047 1.00356
\(27\) 27.0000 0.192450
\(28\) 218.640 1.47568
\(29\) 92.9707 0.595318 0.297659 0.954672i \(-0.403794\pi\)
0.297659 + 0.954672i \(0.403794\pi\)
\(30\) −178.812 −1.08821
\(31\) −88.6315 −0.513506 −0.256753 0.966477i \(-0.582653\pi\)
−0.256753 + 0.966477i \(0.582653\pi\)
\(32\) 252.562 1.39522
\(33\) 150.787 0.795412
\(34\) −8.55761 −0.0431652
\(35\) 300.046 1.44906
\(36\) 91.6649 0.424375
\(37\) 231.603 1.02906 0.514531 0.857472i \(-0.327966\pi\)
0.514531 + 0.857472i \(0.327966\pi\)
\(38\) 252.811 1.07925
\(39\) −93.5986 −0.384302
\(40\) −130.234 −0.514794
\(41\) 237.954 0.906393 0.453196 0.891411i \(-0.350284\pi\)
0.453196 + 0.891411i \(0.350284\pi\)
\(42\) −274.630 −1.00896
\(43\) 29.7378 0.105464 0.0527322 0.998609i \(-0.483207\pi\)
0.0527322 + 0.998609i \(0.483207\pi\)
\(44\) 511.921 1.75398
\(45\) 125.794 0.416717
\(46\) 122.270 0.391908
\(47\) −433.646 −1.34582 −0.672912 0.739722i \(-0.734957\pi\)
−0.672912 + 0.739722i \(0.734957\pi\)
\(48\) −125.238 −0.376594
\(49\) 117.829 0.343524
\(50\) −300.042 −0.848648
\(51\) 6.02029 0.0165296
\(52\) −317.767 −0.847429
\(53\) 464.489 1.20382 0.601910 0.798564i \(-0.294406\pi\)
0.601910 + 0.798564i \(0.294406\pi\)
\(54\) −115.138 −0.290155
\(55\) 702.522 1.72233
\(56\) −200.021 −0.477302
\(57\) −177.853 −0.413284
\(58\) −396.463 −0.897554
\(59\) 59.0000 0.130189
\(60\) 427.071 0.918910
\(61\) −328.206 −0.688894 −0.344447 0.938806i \(-0.611934\pi\)
−0.344447 + 0.938806i \(0.611934\pi\)
\(62\) 377.959 0.774207
\(63\) 193.202 0.386368
\(64\) −743.054 −1.45128
\(65\) −436.080 −0.832139
\(66\) −643.013 −1.19923
\(67\) −841.628 −1.53464 −0.767322 0.641261i \(-0.778411\pi\)
−0.767322 + 0.641261i \(0.778411\pi\)
\(68\) 20.4388 0.0364496
\(69\) −86.0172 −0.150076
\(70\) −1279.51 −2.18473
\(71\) 46.3476 0.0774711 0.0387355 0.999249i \(-0.487667\pi\)
0.0387355 + 0.999249i \(0.487667\pi\)
\(72\) −83.8588 −0.137262
\(73\) −738.776 −1.18448 −0.592241 0.805761i \(-0.701757\pi\)
−0.592241 + 0.805761i \(0.701757\pi\)
\(74\) −987.644 −1.55150
\(75\) 211.080 0.324979
\(76\) −603.809 −0.911338
\(77\) 1078.98 1.59689
\(78\) 399.140 0.579407
\(79\) 734.298 1.04576 0.522880 0.852407i \(-0.324858\pi\)
0.522880 + 0.852407i \(0.324858\pi\)
\(80\) −583.488 −0.815449
\(81\) 81.0000 0.111111
\(82\) −1014.73 −1.36656
\(83\) 353.300 0.467225 0.233613 0.972330i \(-0.424945\pi\)
0.233613 + 0.972330i \(0.424945\pi\)
\(84\) 655.921 0.851987
\(85\) 28.0488 0.0357920
\(86\) −126.813 −0.159008
\(87\) 278.912 0.343707
\(88\) −468.326 −0.567314
\(89\) −704.085 −0.838572 −0.419286 0.907854i \(-0.637720\pi\)
−0.419286 + 0.907854i \(0.637720\pi\)
\(90\) −536.435 −0.628280
\(91\) −669.758 −0.771535
\(92\) −292.028 −0.330935
\(93\) −265.894 −0.296473
\(94\) 1849.23 2.02908
\(95\) −828.623 −0.894894
\(96\) 757.685 0.805531
\(97\) 1479.12 1.54826 0.774132 0.633024i \(-0.218186\pi\)
0.774132 + 0.633024i \(0.218186\pi\)
\(98\) −502.468 −0.517928
\(99\) 452.360 0.459231
\(100\) 716.617 0.716617
\(101\) −1542.67 −1.51982 −0.759910 0.650028i \(-0.774757\pi\)
−0.759910 + 0.650028i \(0.774757\pi\)
\(102\) −25.6728 −0.0249215
\(103\) 1588.52 1.51963 0.759813 0.650141i \(-0.225290\pi\)
0.759813 + 0.650141i \(0.225290\pi\)
\(104\) 290.706 0.274097
\(105\) 900.138 0.836614
\(106\) −1980.76 −1.81499
\(107\) 813.279 0.734791 0.367395 0.930065i \(-0.380250\pi\)
0.367395 + 0.930065i \(0.380250\pi\)
\(108\) 274.995 0.245013
\(109\) 179.016 0.157309 0.0786544 0.996902i \(-0.474938\pi\)
0.0786544 + 0.996902i \(0.474938\pi\)
\(110\) −2995.82 −2.59673
\(111\) 694.808 0.594129
\(112\) −896.156 −0.756061
\(113\) −2091.75 −1.74137 −0.870686 0.491839i \(-0.836325\pi\)
−0.870686 + 0.491839i \(0.836325\pi\)
\(114\) 758.433 0.623103
\(115\) −400.758 −0.324964
\(116\) 946.906 0.757914
\(117\) −280.796 −0.221877
\(118\) −251.599 −0.196284
\(119\) 43.0790 0.0331853
\(120\) −390.701 −0.297217
\(121\) 1195.29 0.898042
\(122\) 1399.60 1.03864
\(123\) 713.861 0.523306
\(124\) −902.711 −0.653757
\(125\) −763.709 −0.546466
\(126\) −823.889 −0.582523
\(127\) −232.320 −0.162324 −0.0811618 0.996701i \(-0.525863\pi\)
−0.0811618 + 0.996701i \(0.525863\pi\)
\(128\) 1148.17 0.792853
\(129\) 89.2134 0.0608899
\(130\) 1859.61 1.25461
\(131\) 2481.08 1.65475 0.827377 0.561647i \(-0.189832\pi\)
0.827377 + 0.561647i \(0.189832\pi\)
\(132\) 1535.76 1.01266
\(133\) −1272.65 −0.829720
\(134\) 3589.03 2.31377
\(135\) 377.382 0.240592
\(136\) −18.6983 −0.0117894
\(137\) 1729.83 1.07875 0.539377 0.842064i \(-0.318660\pi\)
0.539377 + 0.842064i \(0.318660\pi\)
\(138\) 366.810 0.226268
\(139\) 3180.68 1.94088 0.970439 0.241346i \(-0.0775888\pi\)
0.970439 + 0.241346i \(0.0775888\pi\)
\(140\) 3055.96 1.84483
\(141\) −1300.94 −0.777012
\(142\) −197.644 −0.116802
\(143\) −1568.16 −0.917035
\(144\) −375.713 −0.217427
\(145\) 1299.46 0.744238
\(146\) 3150.42 1.78583
\(147\) 353.487 0.198334
\(148\) 2358.87 1.31012
\(149\) −2741.73 −1.50746 −0.753729 0.657185i \(-0.771747\pi\)
−0.753729 + 0.657185i \(0.771747\pi\)
\(150\) −900.127 −0.489967
\(151\) −3325.09 −1.79200 −0.896000 0.444054i \(-0.853540\pi\)
−0.896000 + 0.444054i \(0.853540\pi\)
\(152\) 552.389 0.294768
\(153\) 18.0609 0.00954336
\(154\) −4601.17 −2.40762
\(155\) −1238.81 −0.641961
\(156\) −953.300 −0.489264
\(157\) 2216.16 1.12656 0.563278 0.826268i \(-0.309540\pi\)
0.563278 + 0.826268i \(0.309540\pi\)
\(158\) −3131.33 −1.57668
\(159\) 1393.47 0.695026
\(160\) 3530.09 1.74424
\(161\) −615.508 −0.301297
\(162\) −345.415 −0.167521
\(163\) −3322.16 −1.59639 −0.798196 0.602397i \(-0.794212\pi\)
−0.798196 + 0.602397i \(0.794212\pi\)
\(164\) 2423.56 1.15395
\(165\) 2107.57 0.994386
\(166\) −1506.61 −0.704430
\(167\) 3401.05 1.57593 0.787967 0.615717i \(-0.211134\pi\)
0.787967 + 0.615717i \(0.211134\pi\)
\(168\) −600.063 −0.275571
\(169\) −1223.59 −0.556937
\(170\) −119.611 −0.0539631
\(171\) −533.558 −0.238609
\(172\) 302.879 0.134269
\(173\) −2335.37 −1.02633 −0.513164 0.858290i \(-0.671527\pi\)
−0.513164 + 0.858290i \(0.671527\pi\)
\(174\) −1189.39 −0.518203
\(175\) 1510.41 0.652438
\(176\) −2098.24 −0.898642
\(177\) 177.000 0.0751646
\(178\) 3002.49 1.26430
\(179\) −3089.58 −1.29009 −0.645044 0.764145i \(-0.723161\pi\)
−0.645044 + 0.764145i \(0.723161\pi\)
\(180\) 1281.21 0.530533
\(181\) −968.584 −0.397758 −0.198879 0.980024i \(-0.563730\pi\)
−0.198879 + 0.980024i \(0.563730\pi\)
\(182\) 2856.11 1.16323
\(183\) −984.619 −0.397733
\(184\) 267.159 0.107039
\(185\) 3237.14 1.28648
\(186\) 1133.88 0.446989
\(187\) 100.864 0.0394435
\(188\) −4416.68 −1.71340
\(189\) 579.607 0.223070
\(190\) 3533.57 1.34922
\(191\) −3777.44 −1.43102 −0.715512 0.698600i \(-0.753807\pi\)
−0.715512 + 0.698600i \(0.753807\pi\)
\(192\) −2229.16 −0.837895
\(193\) −1579.07 −0.588933 −0.294466 0.955662i \(-0.595142\pi\)
−0.294466 + 0.955662i \(0.595142\pi\)
\(194\) −6307.53 −2.33430
\(195\) −1308.24 −0.480436
\(196\) 1200.09 0.437349
\(197\) 1937.93 0.700871 0.350435 0.936587i \(-0.386034\pi\)
0.350435 + 0.936587i \(0.386034\pi\)
\(198\) −1929.04 −0.692378
\(199\) −4431.22 −1.57850 −0.789248 0.614075i \(-0.789529\pi\)
−0.789248 + 0.614075i \(0.789529\pi\)
\(200\) −655.590 −0.231786
\(201\) −2524.88 −0.886028
\(202\) 6578.56 2.29142
\(203\) 1995.80 0.690036
\(204\) 61.3165 0.0210442
\(205\) 3325.91 1.13313
\(206\) −6774.06 −2.29112
\(207\) −258.052 −0.0866465
\(208\) 1302.45 0.434177
\(209\) −2979.76 −0.986193
\(210\) −3838.54 −1.26135
\(211\) 453.497 0.147962 0.0739810 0.997260i \(-0.476430\pi\)
0.0739810 + 0.997260i \(0.476430\pi\)
\(212\) 4730.82 1.53261
\(213\) 139.043 0.0447279
\(214\) −3468.13 −1.10784
\(215\) 415.649 0.131847
\(216\) −251.576 −0.0792481
\(217\) −1902.65 −0.595207
\(218\) −763.395 −0.237173
\(219\) −2216.33 −0.683861
\(220\) 7155.18 2.19274
\(221\) −62.6100 −0.0190570
\(222\) −2962.93 −0.895761
\(223\) 551.465 0.165600 0.0828001 0.996566i \(-0.473614\pi\)
0.0828001 + 0.996566i \(0.473614\pi\)
\(224\) 5421.72 1.61721
\(225\) 633.241 0.187627
\(226\) 8920.02 2.62545
\(227\) 5742.83 1.67914 0.839570 0.543252i \(-0.182807\pi\)
0.839570 + 0.543252i \(0.182807\pi\)
\(228\) −1811.43 −0.526161
\(229\) −5428.07 −1.56636 −0.783181 0.621794i \(-0.786404\pi\)
−0.783181 + 0.621794i \(0.786404\pi\)
\(230\) 1708.99 0.489944
\(231\) 3236.93 0.921966
\(232\) −866.268 −0.245143
\(233\) 1383.05 0.388869 0.194435 0.980915i \(-0.437713\pi\)
0.194435 + 0.980915i \(0.437713\pi\)
\(234\) 1197.42 0.334521
\(235\) −6061.12 −1.68249
\(236\) 600.914 0.165747
\(237\) 2202.89 0.603769
\(238\) −183.706 −0.0500330
\(239\) −380.199 −0.102900 −0.0514499 0.998676i \(-0.516384\pi\)
−0.0514499 + 0.998676i \(0.516384\pi\)
\(240\) −1750.46 −0.470800
\(241\) −178.971 −0.0478362 −0.0239181 0.999714i \(-0.507614\pi\)
−0.0239181 + 0.999714i \(0.507614\pi\)
\(242\) −5097.20 −1.35397
\(243\) 243.000 0.0641500
\(244\) −3342.78 −0.877047
\(245\) 1646.91 0.429458
\(246\) −3044.18 −0.788983
\(247\) 1849.64 0.476477
\(248\) 825.836 0.211454
\(249\) 1059.90 0.269753
\(250\) 3256.75 0.823900
\(251\) 1119.05 0.281409 0.140704 0.990052i \(-0.455063\pi\)
0.140704 + 0.990052i \(0.455063\pi\)
\(252\) 1967.76 0.491895
\(253\) −1441.14 −0.358117
\(254\) 990.703 0.244733
\(255\) 84.1463 0.0206645
\(256\) 1048.17 0.255902
\(257\) −2474.60 −0.600627 −0.300314 0.953841i \(-0.597091\pi\)
−0.300314 + 0.953841i \(0.597091\pi\)
\(258\) −380.440 −0.0918030
\(259\) 4971.80 1.19279
\(260\) −4441.47 −1.05942
\(261\) 836.736 0.198439
\(262\) −10580.3 −2.49485
\(263\) 4863.06 1.14019 0.570093 0.821580i \(-0.306907\pi\)
0.570093 + 0.821580i \(0.306907\pi\)
\(264\) −1404.98 −0.327539
\(265\) 6492.22 1.50496
\(266\) 5427.07 1.25096
\(267\) −2112.26 −0.484150
\(268\) −8571.97 −1.95379
\(269\) 4289.91 0.972345 0.486172 0.873863i \(-0.338393\pi\)
0.486172 + 0.873863i \(0.338393\pi\)
\(270\) −1609.30 −0.362738
\(271\) −2447.41 −0.548596 −0.274298 0.961645i \(-0.588445\pi\)
−0.274298 + 0.961645i \(0.588445\pi\)
\(272\) −83.7741 −0.0186748
\(273\) −2009.27 −0.445446
\(274\) −7376.66 −1.62643
\(275\) 3536.46 0.775477
\(276\) −876.084 −0.191065
\(277\) −505.181 −0.109579 −0.0547895 0.998498i \(-0.517449\pi\)
−0.0547895 + 0.998498i \(0.517449\pi\)
\(278\) −13563.7 −2.92624
\(279\) −797.683 −0.171169
\(280\) −2795.72 −0.596701
\(281\) −2909.81 −0.617738 −0.308869 0.951105i \(-0.599951\pi\)
−0.308869 + 0.951105i \(0.599951\pi\)
\(282\) 5547.70 1.17149
\(283\) 978.711 0.205577 0.102789 0.994703i \(-0.467224\pi\)
0.102789 + 0.994703i \(0.467224\pi\)
\(284\) 472.050 0.0986303
\(285\) −2485.87 −0.516667
\(286\) 6687.23 1.38260
\(287\) 5108.13 1.05060
\(288\) 2273.06 0.465073
\(289\) −4908.97 −0.999180
\(290\) −5541.41 −1.12208
\(291\) 4437.35 0.893891
\(292\) −7524.42 −1.50799
\(293\) 4827.48 0.962541 0.481271 0.876572i \(-0.340175\pi\)
0.481271 + 0.876572i \(0.340175\pi\)
\(294\) −1507.40 −0.299026
\(295\) 824.650 0.162756
\(296\) −2157.99 −0.423752
\(297\) 1357.08 0.265137
\(298\) 11691.8 2.27278
\(299\) 894.565 0.173024
\(300\) 2149.85 0.413739
\(301\) 638.379 0.122244
\(302\) 14179.5 2.70178
\(303\) −4628.02 −0.877469
\(304\) 2474.87 0.466920
\(305\) −4587.38 −0.861222
\(306\) −77.0185 −0.0143884
\(307\) −1687.14 −0.313649 −0.156825 0.987626i \(-0.550126\pi\)
−0.156825 + 0.987626i \(0.550126\pi\)
\(308\) 10989.4 2.03304
\(309\) 4765.56 0.877357
\(310\) 5282.78 0.967876
\(311\) −6570.44 −1.19799 −0.598996 0.800752i \(-0.704433\pi\)
−0.598996 + 0.800752i \(0.704433\pi\)
\(312\) 872.118 0.158250
\(313\) 2380.42 0.429871 0.214935 0.976628i \(-0.431046\pi\)
0.214935 + 0.976628i \(0.431046\pi\)
\(314\) −9450.58 −1.69849
\(315\) 2700.41 0.483019
\(316\) 7478.82 1.33138
\(317\) −1913.91 −0.339104 −0.169552 0.985521i \(-0.554232\pi\)
−0.169552 + 0.985521i \(0.554232\pi\)
\(318\) −5942.28 −1.04788
\(319\) 4672.92 0.820167
\(320\) −10385.8 −1.81432
\(321\) 2439.84 0.424232
\(322\) 2624.76 0.454262
\(323\) −118.969 −0.0204942
\(324\) 824.984 0.141458
\(325\) −2195.20 −0.374670
\(326\) 14167.0 2.40686
\(327\) 537.049 0.0908223
\(328\) −2217.17 −0.373239
\(329\) −9309.04 −1.55995
\(330\) −8987.47 −1.49922
\(331\) −5860.84 −0.973236 −0.486618 0.873615i \(-0.661770\pi\)
−0.486618 + 0.873615i \(0.661770\pi\)
\(332\) 3598.35 0.594835
\(333\) 2084.43 0.343020
\(334\) −14503.4 −2.37602
\(335\) −11763.5 −1.91854
\(336\) −2688.47 −0.436512
\(337\) −9890.58 −1.59874 −0.799368 0.600841i \(-0.794832\pi\)
−0.799368 + 0.600841i \(0.794832\pi\)
\(338\) 5217.86 0.839687
\(339\) −6275.24 −1.00538
\(340\) 285.676 0.0455676
\(341\) −4454.82 −0.707454
\(342\) 2275.30 0.359749
\(343\) −4833.73 −0.760924
\(344\) −277.086 −0.0434287
\(345\) −1202.27 −0.187618
\(346\) 9958.92 1.54738
\(347\) 12225.3 1.89132 0.945658 0.325164i \(-0.105420\pi\)
0.945658 + 0.325164i \(0.105420\pi\)
\(348\) 2840.72 0.437582
\(349\) −6380.04 −0.978555 −0.489278 0.872128i \(-0.662740\pi\)
−0.489278 + 0.872128i \(0.662740\pi\)
\(350\) −6440.99 −0.983672
\(351\) −842.387 −0.128101
\(352\) 12694.3 1.92219
\(353\) −9132.68 −1.37701 −0.688503 0.725233i \(-0.741732\pi\)
−0.688503 + 0.725233i \(0.741732\pi\)
\(354\) −754.796 −0.113325
\(355\) 647.806 0.0968506
\(356\) −7171.10 −1.06761
\(357\) 129.237 0.0191595
\(358\) 13175.1 1.94505
\(359\) 40.7954 0.00599749 0.00299875 0.999996i \(-0.499045\pi\)
0.00299875 + 0.999996i \(0.499045\pi\)
\(360\) −1172.10 −0.171598
\(361\) −3344.38 −0.487590
\(362\) 4130.42 0.599696
\(363\) 3585.88 0.518485
\(364\) −6821.48 −0.982260
\(365\) −10326.0 −1.48078
\(366\) 4198.80 0.599658
\(367\) 11214.7 1.59510 0.797552 0.603250i \(-0.206128\pi\)
0.797552 + 0.603250i \(0.206128\pi\)
\(368\) 1196.95 0.169553
\(369\) 2141.58 0.302131
\(370\) −13804.4 −1.93962
\(371\) 9971.15 1.39535
\(372\) −2708.13 −0.377447
\(373\) −2620.02 −0.363698 −0.181849 0.983326i \(-0.558208\pi\)
−0.181849 + 0.983326i \(0.558208\pi\)
\(374\) −430.125 −0.0594685
\(375\) −2291.13 −0.315502
\(376\) 4040.56 0.554191
\(377\) −2900.64 −0.396262
\(378\) −2471.67 −0.336320
\(379\) 405.076 0.0549007 0.0274503 0.999623i \(-0.491261\pi\)
0.0274503 + 0.999623i \(0.491261\pi\)
\(380\) −8439.52 −1.13931
\(381\) −696.961 −0.0937175
\(382\) 16108.4 2.15754
\(383\) −382.637 −0.0510492 −0.0255246 0.999674i \(-0.508126\pi\)
−0.0255246 + 0.999674i \(0.508126\pi\)
\(384\) 3444.52 0.457754
\(385\) 15081.0 1.99636
\(386\) 6733.77 0.887927
\(387\) 267.640 0.0351548
\(388\) 15064.8 1.97113
\(389\) −6688.89 −0.871826 −0.435913 0.899989i \(-0.643574\pi\)
−0.435913 + 0.899989i \(0.643574\pi\)
\(390\) 5578.84 0.724347
\(391\) −57.5387 −0.00744209
\(392\) −1097.89 −0.141458
\(393\) 7443.23 0.955372
\(394\) −8264.06 −1.05669
\(395\) 10263.4 1.30736
\(396\) 4607.28 0.584659
\(397\) 920.669 0.116391 0.0581953 0.998305i \(-0.481465\pi\)
0.0581953 + 0.998305i \(0.481465\pi\)
\(398\) 18896.4 2.37988
\(399\) −3817.95 −0.479039
\(400\) −2937.24 −0.367156
\(401\) 9189.09 1.14434 0.572171 0.820134i \(-0.306101\pi\)
0.572171 + 0.820134i \(0.306101\pi\)
\(402\) 10767.1 1.33585
\(403\) 2765.26 0.341805
\(404\) −15712.1 −1.93492
\(405\) 1132.15 0.138906
\(406\) −8510.84 −1.04036
\(407\) 11640.9 1.41773
\(408\) −56.0949 −0.00680664
\(409\) 15208.0 1.83860 0.919302 0.393553i \(-0.128754\pi\)
0.919302 + 0.393553i \(0.128754\pi\)
\(410\) −14183.0 −1.70841
\(411\) 5189.49 0.622819
\(412\) 16179.1 1.93467
\(413\) 1266.55 0.150903
\(414\) 1100.43 0.130636
\(415\) 4938.12 0.584103
\(416\) −7879.81 −0.928700
\(417\) 9542.05 1.12057
\(418\) 12706.8 1.48687
\(419\) −13021.4 −1.51822 −0.759111 0.650962i \(-0.774366\pi\)
−0.759111 + 0.650962i \(0.774366\pi\)
\(420\) 9167.89 1.06511
\(421\) −3275.96 −0.379242 −0.189621 0.981857i \(-0.560726\pi\)
−0.189621 + 0.981857i \(0.560726\pi\)
\(422\) −1933.88 −0.223081
\(423\) −3902.81 −0.448608
\(424\) −4327.94 −0.495716
\(425\) 141.196 0.0161153
\(426\) −592.932 −0.0674358
\(427\) −7045.58 −0.798500
\(428\) 8283.23 0.935479
\(429\) −4704.47 −0.529450
\(430\) −1772.49 −0.198784
\(431\) 7674.36 0.857682 0.428841 0.903380i \(-0.358922\pi\)
0.428841 + 0.903380i \(0.358922\pi\)
\(432\) −1127.14 −0.125531
\(433\) −12802.6 −1.42091 −0.710456 0.703741i \(-0.751511\pi\)
−0.710456 + 0.703741i \(0.751511\pi\)
\(434\) 8113.62 0.897387
\(435\) 3898.39 0.429686
\(436\) 1823.28 0.200274
\(437\) 1699.82 0.186072
\(438\) 9451.27 1.03105
\(439\) −1638.69 −0.178156 −0.0890781 0.996025i \(-0.528392\pi\)
−0.0890781 + 0.996025i \(0.528392\pi\)
\(440\) −6545.85 −0.709229
\(441\) 1060.46 0.114508
\(442\) 266.993 0.0287321
\(443\) −7210.63 −0.773335 −0.386667 0.922219i \(-0.626374\pi\)
−0.386667 + 0.922219i \(0.626374\pi\)
\(444\) 7076.62 0.756399
\(445\) −9841.09 −1.04834
\(446\) −2351.66 −0.249674
\(447\) −8225.19 −0.870331
\(448\) −15951.1 −1.68218
\(449\) −1210.22 −0.127202 −0.0636012 0.997975i \(-0.520259\pi\)
−0.0636012 + 0.997975i \(0.520259\pi\)
\(450\) −2700.38 −0.282883
\(451\) 11960.1 1.24873
\(452\) −21304.4 −2.21698
\(453\) −9975.27 −1.03461
\(454\) −24489.6 −2.53162
\(455\) −9361.29 −0.964536
\(456\) 1657.17 0.170184
\(457\) −14691.6 −1.50382 −0.751908 0.659268i \(-0.770866\pi\)
−0.751908 + 0.659268i \(0.770866\pi\)
\(458\) 23147.4 2.36158
\(459\) 54.1826 0.00550986
\(460\) −4081.71 −0.413719
\(461\) 1906.98 0.192662 0.0963309 0.995349i \(-0.469289\pi\)
0.0963309 + 0.995349i \(0.469289\pi\)
\(462\) −13803.5 −1.39004
\(463\) −2607.30 −0.261710 −0.130855 0.991402i \(-0.541772\pi\)
−0.130855 + 0.991402i \(0.541772\pi\)
\(464\) −3881.15 −0.388314
\(465\) −3716.44 −0.370636
\(466\) −5897.85 −0.586293
\(467\) 9821.65 0.973216 0.486608 0.873621i \(-0.338234\pi\)
0.486608 + 0.873621i \(0.338234\pi\)
\(468\) −2859.90 −0.282476
\(469\) −18067.2 −1.77881
\(470\) 25847.0 2.53666
\(471\) 6648.49 0.650417
\(472\) −549.741 −0.0536099
\(473\) 1494.69 0.145298
\(474\) −9393.99 −0.910296
\(475\) −4171.24 −0.402926
\(476\) 438.759 0.0422489
\(477\) 4180.40 0.401273
\(478\) 1621.32 0.155141
\(479\) −3910.32 −0.373000 −0.186500 0.982455i \(-0.559714\pi\)
−0.186500 + 0.982455i \(0.559714\pi\)
\(480\) 10590.3 1.00704
\(481\) −7225.90 −0.684974
\(482\) 763.201 0.0721221
\(483\) −1846.52 −0.173954
\(484\) 12174.1 1.14332
\(485\) 20673.8 1.93557
\(486\) −1036.25 −0.0967182
\(487\) 17045.3 1.58603 0.793016 0.609200i \(-0.208509\pi\)
0.793016 + 0.609200i \(0.208509\pi\)
\(488\) 3058.11 0.283676
\(489\) −9966.49 −0.921678
\(490\) −7023.06 −0.647488
\(491\) −15162.2 −1.39361 −0.696804 0.717262i \(-0.745395\pi\)
−0.696804 + 0.717262i \(0.745395\pi\)
\(492\) 7270.67 0.666234
\(493\) 186.570 0.0170440
\(494\) −7887.58 −0.718378
\(495\) 6322.70 0.574109
\(496\) 3700.00 0.334950
\(497\) 994.940 0.0897971
\(498\) −4519.82 −0.406703
\(499\) 18914.2 1.69682 0.848411 0.529339i \(-0.177560\pi\)
0.848411 + 0.529339i \(0.177560\pi\)
\(500\) −7778.37 −0.695719
\(501\) 10203.1 0.909866
\(502\) −4772.04 −0.424276
\(503\) 10331.8 0.915849 0.457924 0.888991i \(-0.348593\pi\)
0.457924 + 0.888991i \(0.348593\pi\)
\(504\) −1800.19 −0.159101
\(505\) −21562.2 −1.90001
\(506\) 6145.57 0.539929
\(507\) −3670.77 −0.321548
\(508\) −2366.18 −0.206658
\(509\) 15683.4 1.36573 0.682864 0.730546i \(-0.260734\pi\)
0.682864 + 0.730546i \(0.260734\pi\)
\(510\) −358.832 −0.0311556
\(511\) −15859.2 −1.37294
\(512\) −13655.2 −1.17867
\(513\) −1600.67 −0.137761
\(514\) 10552.6 0.905558
\(515\) 22202.9 1.89976
\(516\) 908.637 0.0775204
\(517\) −21796.0 −1.85413
\(518\) −21201.7 −1.79836
\(519\) −7006.11 −0.592551
\(520\) 4063.23 0.342663
\(521\) −7550.71 −0.634938 −0.317469 0.948269i \(-0.602833\pi\)
−0.317469 + 0.948269i \(0.602833\pi\)
\(522\) −3568.17 −0.299185
\(523\) −12867.2 −1.07580 −0.537901 0.843008i \(-0.680783\pi\)
−0.537901 + 0.843008i \(0.680783\pi\)
\(524\) 25269.7 2.10671
\(525\) 4531.24 0.376685
\(526\) −20738.0 −1.71905
\(527\) −177.862 −0.0147017
\(528\) −6294.73 −0.518831
\(529\) −11344.9 −0.932431
\(530\) −27685.3 −2.26901
\(531\) 531.000 0.0433963
\(532\) −12961.9 −1.05634
\(533\) −7424.04 −0.603322
\(534\) 9007.48 0.729947
\(535\) 11367.3 0.918600
\(536\) 7841.99 0.631944
\(537\) −9268.73 −0.744833
\(538\) −18293.9 −1.46599
\(539\) 5922.34 0.473272
\(540\) 3843.64 0.306303
\(541\) −6294.73 −0.500243 −0.250121 0.968214i \(-0.580471\pi\)
−0.250121 + 0.968214i \(0.580471\pi\)
\(542\) 10436.7 0.827111
\(543\) −2905.75 −0.229646
\(544\) 506.831 0.0399452
\(545\) 2502.13 0.196660
\(546\) 8568.32 0.671594
\(547\) −17015.5 −1.33003 −0.665017 0.746828i \(-0.731576\pi\)
−0.665017 + 0.746828i \(0.731576\pi\)
\(548\) 17618.3 1.37339
\(549\) −2953.86 −0.229631
\(550\) −15080.8 −1.16918
\(551\) −5511.70 −0.426146
\(552\) 801.477 0.0617991
\(553\) 15763.1 1.21214
\(554\) 2154.29 0.165211
\(555\) 9711.43 0.742751
\(556\) 32395.2 2.47098
\(557\) 425.562 0.0323728 0.0161864 0.999869i \(-0.494847\pi\)
0.0161864 + 0.999869i \(0.494847\pi\)
\(558\) 3401.63 0.258069
\(559\) −927.805 −0.0702003
\(560\) −12525.7 −0.945191
\(561\) 302.593 0.0227727
\(562\) 12408.5 0.931357
\(563\) 22080.6 1.65291 0.826454 0.563004i \(-0.190354\pi\)
0.826454 + 0.563004i \(0.190354\pi\)
\(564\) −13250.0 −0.989233
\(565\) −29236.6 −2.17698
\(566\) −4173.60 −0.309946
\(567\) 1738.82 0.128789
\(568\) −431.850 −0.0319015
\(569\) 14807.4 1.09096 0.545482 0.838123i \(-0.316347\pi\)
0.545482 + 0.838123i \(0.316347\pi\)
\(570\) 10600.7 0.778973
\(571\) 8320.22 0.609790 0.304895 0.952386i \(-0.401379\pi\)
0.304895 + 0.952386i \(0.401379\pi\)
\(572\) −15971.7 −1.16750
\(573\) −11332.3 −0.826202
\(574\) −21783.0 −1.58398
\(575\) −2017.39 −0.146315
\(576\) −6687.48 −0.483759
\(577\) 6428.58 0.463822 0.231911 0.972737i \(-0.425502\pi\)
0.231911 + 0.972737i \(0.425502\pi\)
\(578\) 20933.8 1.50645
\(579\) −4737.21 −0.340020
\(580\) 13235.0 0.947508
\(581\) 7584.26 0.541563
\(582\) −18922.6 −1.34771
\(583\) 23346.3 1.65850
\(584\) 6883.65 0.487752
\(585\) −3924.72 −0.277380
\(586\) −20586.3 −1.45121
\(587\) 9120.74 0.641318 0.320659 0.947195i \(-0.396096\pi\)
0.320659 + 0.947195i \(0.396096\pi\)
\(588\) 3600.26 0.252504
\(589\) 5254.45 0.367582
\(590\) −3516.63 −0.245385
\(591\) 5813.78 0.404648
\(592\) −9668.47 −0.671236
\(593\) −21233.1 −1.47038 −0.735192 0.677859i \(-0.762908\pi\)
−0.735192 + 0.677859i \(0.762908\pi\)
\(594\) −5787.12 −0.399745
\(595\) 602.121 0.0414866
\(596\) −27924.5 −1.91918
\(597\) −13293.7 −0.911345
\(598\) −3814.77 −0.260866
\(599\) −2232.18 −0.152261 −0.0761305 0.997098i \(-0.524257\pi\)
−0.0761305 + 0.997098i \(0.524257\pi\)
\(600\) −1966.77 −0.133822
\(601\) 8970.12 0.608817 0.304408 0.952542i \(-0.401541\pi\)
0.304408 + 0.952542i \(0.401541\pi\)
\(602\) −2722.29 −0.184306
\(603\) −7574.65 −0.511548
\(604\) −33866.0 −2.28144
\(605\) 16706.8 1.12269
\(606\) 19735.7 1.32295
\(607\) 14005.7 0.936531 0.468265 0.883588i \(-0.344879\pi\)
0.468265 + 0.883588i \(0.344879\pi\)
\(608\) −14972.9 −0.998738
\(609\) 5987.39 0.398393
\(610\) 19562.4 1.29845
\(611\) 13529.5 0.895821
\(612\) 183.950 0.0121499
\(613\) 10352.6 0.682119 0.341059 0.940042i \(-0.389214\pi\)
0.341059 + 0.940042i \(0.389214\pi\)
\(614\) 7194.63 0.472885
\(615\) 9977.72 0.654212
\(616\) −10053.5 −0.657577
\(617\) 17951.3 1.17130 0.585649 0.810564i \(-0.300840\pi\)
0.585649 + 0.810564i \(0.300840\pi\)
\(618\) −20322.2 −1.32278
\(619\) 11187.1 0.726406 0.363203 0.931710i \(-0.381683\pi\)
0.363203 + 0.931710i \(0.381683\pi\)
\(620\) −12617.3 −0.817295
\(621\) −774.155 −0.0500254
\(622\) 28018.9 1.80620
\(623\) −15114.5 −0.971993
\(624\) 3907.36 0.250672
\(625\) −19469.5 −1.24605
\(626\) −10151.1 −0.648111
\(627\) −8939.28 −0.569379
\(628\) 22571.6 1.43424
\(629\) 464.772 0.0294621
\(630\) −11515.6 −0.728242
\(631\) −5810.20 −0.366562 −0.183281 0.983061i \(-0.558672\pi\)
−0.183281 + 0.983061i \(0.558672\pi\)
\(632\) −6841.92 −0.430628
\(633\) 1360.49 0.0854259
\(634\) 8161.67 0.511264
\(635\) −3247.17 −0.202929
\(636\) 14192.5 0.884854
\(637\) −3676.20 −0.228660
\(638\) −19927.1 −1.23656
\(639\) 417.128 0.0258237
\(640\) 16048.2 0.991187
\(641\) 13147.8 0.810152 0.405076 0.914283i \(-0.367245\pi\)
0.405076 + 0.914283i \(0.367245\pi\)
\(642\) −10404.4 −0.639609
\(643\) 15035.7 0.922162 0.461081 0.887358i \(-0.347462\pi\)
0.461081 + 0.887358i \(0.347462\pi\)
\(644\) −6268.94 −0.383588
\(645\) 1246.95 0.0761217
\(646\) 507.331 0.0308989
\(647\) −14522.4 −0.882435 −0.441217 0.897400i \(-0.645453\pi\)
−0.441217 + 0.897400i \(0.645453\pi\)
\(648\) −754.729 −0.0457539
\(649\) 2965.47 0.179361
\(650\) 9361.18 0.564886
\(651\) −5707.94 −0.343643
\(652\) −33836.2 −2.03241
\(653\) −7321.61 −0.438770 −0.219385 0.975638i \(-0.570405\pi\)
−0.219385 + 0.975638i \(0.570405\pi\)
\(654\) −2290.18 −0.136932
\(655\) 34678.3 2.06869
\(656\) −9933.59 −0.591222
\(657\) −6648.98 −0.394827
\(658\) 39697.4 2.35192
\(659\) 18730.0 1.10716 0.553580 0.832796i \(-0.313261\pi\)
0.553580 + 0.832796i \(0.313261\pi\)
\(660\) 21465.5 1.26598
\(661\) 23121.7 1.36056 0.680281 0.732952i \(-0.261858\pi\)
0.680281 + 0.732952i \(0.261858\pi\)
\(662\) 24992.9 1.46734
\(663\) −187.830 −0.0110026
\(664\) −3291.92 −0.192396
\(665\) −17788.0 −1.03728
\(666\) −8888.79 −0.517168
\(667\) −2665.69 −0.154747
\(668\) 34639.7 2.00636
\(669\) 1654.40 0.0956093
\(670\) 50164.3 2.89256
\(671\) −16496.4 −0.949085
\(672\) 16265.2 0.933694
\(673\) −9783.94 −0.560391 −0.280195 0.959943i \(-0.590399\pi\)
−0.280195 + 0.959943i \(0.590399\pi\)
\(674\) 42177.2 2.41040
\(675\) 1899.72 0.108326
\(676\) −12462.2 −0.709049
\(677\) −7309.79 −0.414975 −0.207487 0.978238i \(-0.566529\pi\)
−0.207487 + 0.978238i \(0.566529\pi\)
\(678\) 26760.1 1.51580
\(679\) 31752.1 1.79460
\(680\) −261.348 −0.0147386
\(681\) 17228.5 0.969452
\(682\) 18997.1 1.06662
\(683\) −26062.1 −1.46009 −0.730043 0.683401i \(-0.760500\pi\)
−0.730043 + 0.683401i \(0.760500\pi\)
\(684\) −5434.28 −0.303779
\(685\) 24178.1 1.34861
\(686\) 20612.9 1.14724
\(687\) −16284.2 −0.904339
\(688\) −1241.43 −0.0687923
\(689\) −14491.8 −0.801299
\(690\) 5126.96 0.282869
\(691\) −5703.45 −0.313993 −0.156997 0.987599i \(-0.550181\pi\)
−0.156997 + 0.987599i \(0.550181\pi\)
\(692\) −23785.7 −1.30664
\(693\) 9710.78 0.532298
\(694\) −52133.2 −2.85151
\(695\) 44456.8 2.42639
\(696\) −2598.80 −0.141534
\(697\) 477.516 0.0259501
\(698\) 27207.0 1.47536
\(699\) 4149.14 0.224514
\(700\) 15383.6 0.830634
\(701\) 29032.2 1.56424 0.782120 0.623127i \(-0.214138\pi\)
0.782120 + 0.623127i \(0.214138\pi\)
\(702\) 3592.26 0.193136
\(703\) −13730.4 −0.736631
\(704\) −37347.6 −1.99942
\(705\) −18183.4 −0.971383
\(706\) 38945.3 2.07610
\(707\) −33116.5 −1.76163
\(708\) 1802.74 0.0956938
\(709\) 14314.4 0.758235 0.379117 0.925349i \(-0.376228\pi\)
0.379117 + 0.925349i \(0.376228\pi\)
\(710\) −2762.50 −0.146021
\(711\) 6608.68 0.348586
\(712\) 6560.41 0.345312
\(713\) 2541.28 0.133480
\(714\) −551.117 −0.0288866
\(715\) −21918.3 −1.14643
\(716\) −31467.3 −1.64244
\(717\) −1140.60 −0.0594092
\(718\) −173.967 −0.00904235
\(719\) 19598.6 1.01656 0.508278 0.861193i \(-0.330282\pi\)
0.508278 + 0.861193i \(0.330282\pi\)
\(720\) −5251.39 −0.271816
\(721\) 34100.6 1.76141
\(722\) 14261.7 0.735134
\(723\) −536.913 −0.0276183
\(724\) −9865.02 −0.506396
\(725\) 6541.43 0.335093
\(726\) −15291.6 −0.781713
\(727\) 25217.2 1.28646 0.643228 0.765675i \(-0.277595\pi\)
0.643228 + 0.765675i \(0.277595\pi\)
\(728\) 6240.56 0.317707
\(729\) 729.000 0.0370370
\(730\) 44033.9 2.23256
\(731\) 59.6767 0.00301946
\(732\) −10028.3 −0.506363
\(733\) −14826.4 −0.747101 −0.373550 0.927610i \(-0.621860\pi\)
−0.373550 + 0.927610i \(0.621860\pi\)
\(734\) −47823.9 −2.40492
\(735\) 4940.73 0.247948
\(736\) −7241.55 −0.362673
\(737\) −42302.1 −2.11427
\(738\) −9132.53 −0.455519
\(739\) −29860.2 −1.48637 −0.743184 0.669087i \(-0.766686\pi\)
−0.743184 + 0.669087i \(0.766686\pi\)
\(740\) 32970.3 1.63785
\(741\) 5548.92 0.275094
\(742\) −42520.8 −2.10376
\(743\) 12908.8 0.637388 0.318694 0.947858i \(-0.396756\pi\)
0.318694 + 0.947858i \(0.396756\pi\)
\(744\) 2477.51 0.122083
\(745\) −38321.5 −1.88455
\(746\) 11172.8 0.548344
\(747\) 3179.70 0.155742
\(748\) 1027.30 0.0502164
\(749\) 17458.6 0.851700
\(750\) 9770.25 0.475679
\(751\) 6544.75 0.318005 0.159002 0.987278i \(-0.449172\pi\)
0.159002 + 0.987278i \(0.449172\pi\)
\(752\) 18102.9 0.877854
\(753\) 3357.14 0.162471
\(754\) 12369.5 0.597439
\(755\) −46475.2 −2.24027
\(756\) 5903.29 0.283996
\(757\) −4239.81 −0.203565 −0.101782 0.994807i \(-0.532455\pi\)
−0.101782 + 0.994807i \(0.532455\pi\)
\(758\) −1727.40 −0.0827731
\(759\) −4323.42 −0.206759
\(760\) 7720.81 0.368504
\(761\) 16068.6 0.765421 0.382711 0.923868i \(-0.374991\pi\)
0.382711 + 0.923868i \(0.374991\pi\)
\(762\) 2972.11 0.141297
\(763\) 3842.93 0.182337
\(764\) −38473.1 −1.82187
\(765\) 252.439 0.0119307
\(766\) 1631.71 0.0769663
\(767\) −1840.77 −0.0866577
\(768\) 3144.52 0.147745
\(769\) −12692.7 −0.595201 −0.297601 0.954690i \(-0.596186\pi\)
−0.297601 + 0.954690i \(0.596186\pi\)
\(770\) −64311.1 −3.00989
\(771\) −7423.79 −0.346772
\(772\) −16082.8 −0.749784
\(773\) 5663.38 0.263515 0.131758 0.991282i \(-0.457938\pi\)
0.131758 + 0.991282i \(0.457938\pi\)
\(774\) −1141.32 −0.0530025
\(775\) −6236.12 −0.289043
\(776\) −13781.9 −0.637553
\(777\) 14915.4 0.688658
\(778\) 28524.0 1.31444
\(779\) −14106.9 −0.648822
\(780\) −13324.4 −0.611654
\(781\) 2329.53 0.106731
\(782\) 245.367 0.0112203
\(783\) 2510.21 0.114569
\(784\) −4918.87 −0.224074
\(785\) 30975.6 1.40837
\(786\) −31740.8 −1.44040
\(787\) −2659.15 −0.120443 −0.0602214 0.998185i \(-0.519181\pi\)
−0.0602214 + 0.998185i \(0.519181\pi\)
\(788\) 19737.8 0.892295
\(789\) 14589.2 0.658287
\(790\) −43767.0 −1.97109
\(791\) −44903.4 −2.01843
\(792\) −4214.93 −0.189105
\(793\) 10239.9 0.458549
\(794\) −3926.09 −0.175481
\(795\) 19476.7 0.868888
\(796\) −45131.9 −2.00962
\(797\) 22767.0 1.01186 0.505928 0.862576i \(-0.331150\pi\)
0.505928 + 0.862576i \(0.331150\pi\)
\(798\) 16281.2 0.722242
\(799\) −870.224 −0.0385311
\(800\) 17770.3 0.785342
\(801\) −6336.77 −0.279524
\(802\) −39185.8 −1.72531
\(803\) −37132.5 −1.63185
\(804\) −25715.9 −1.12802
\(805\) −8603.03 −0.376667
\(806\) −11792.1 −0.515335
\(807\) 12869.7 0.561383
\(808\) 14374.1 0.625840
\(809\) 32981.9 1.43335 0.716676 0.697406i \(-0.245662\pi\)
0.716676 + 0.697406i \(0.245662\pi\)
\(810\) −4827.91 −0.209427
\(811\) 20038.8 0.867642 0.433821 0.900999i \(-0.357165\pi\)
0.433821 + 0.900999i \(0.357165\pi\)
\(812\) 20327.2 0.878502
\(813\) −7342.23 −0.316732
\(814\) −49641.2 −2.13750
\(815\) −46434.3 −1.99573
\(816\) −251.322 −0.0107819
\(817\) −1762.98 −0.0754944
\(818\) −64852.9 −2.77204
\(819\) −6027.82 −0.257178
\(820\) 33874.3 1.44261
\(821\) −16024.0 −0.681172 −0.340586 0.940213i \(-0.610626\pi\)
−0.340586 + 0.940213i \(0.610626\pi\)
\(822\) −22130.0 −0.939017
\(823\) 25375.3 1.07476 0.537379 0.843341i \(-0.319414\pi\)
0.537379 + 0.843341i \(0.319414\pi\)
\(824\) −14801.3 −0.625760
\(825\) 10609.4 0.447722
\(826\) −5401.05 −0.227514
\(827\) 15790.0 0.663931 0.331966 0.943291i \(-0.392288\pi\)
0.331966 + 0.943291i \(0.392288\pi\)
\(828\) −2628.25 −0.110312
\(829\) 26581.6 1.11365 0.556826 0.830629i \(-0.312019\pi\)
0.556826 + 0.830629i \(0.312019\pi\)
\(830\) −21058.0 −0.880645
\(831\) −1515.54 −0.0632655
\(832\) 23182.9 0.966013
\(833\) 236.454 0.00983513
\(834\) −40691.0 −1.68947
\(835\) 47536.9 1.97016
\(836\) −30348.8 −1.25555
\(837\) −2393.05 −0.0988243
\(838\) 55528.1 2.28900
\(839\) −8481.14 −0.348989 −0.174494 0.984658i \(-0.555829\pi\)
−0.174494 + 0.984658i \(0.555829\pi\)
\(840\) −8387.16 −0.344505
\(841\) −15745.4 −0.645596
\(842\) 13970.0 0.571778
\(843\) −8729.42 −0.356651
\(844\) 4618.86 0.188374
\(845\) −17102.3 −0.696256
\(846\) 16643.1 0.676361
\(847\) 25659.3 1.04093
\(848\) −19390.5 −0.785228
\(849\) 2936.13 0.118690
\(850\) −602.114 −0.0242969
\(851\) −6640.61 −0.267494
\(852\) 1416.15 0.0569442
\(853\) 1049.74 0.0421366 0.0210683 0.999778i \(-0.493293\pi\)
0.0210683 + 0.999778i \(0.493293\pi\)
\(854\) 30045.1 1.20389
\(855\) −7457.61 −0.298298
\(856\) −7577.84 −0.302576
\(857\) 13685.0 0.545472 0.272736 0.962089i \(-0.412071\pi\)
0.272736 + 0.962089i \(0.412071\pi\)
\(858\) 20061.7 0.798246
\(859\) 2391.73 0.0949998 0.0474999 0.998871i \(-0.484875\pi\)
0.0474999 + 0.998871i \(0.484875\pi\)
\(860\) 4233.38 0.167857
\(861\) 15324.4 0.606567
\(862\) −32726.5 −1.29312
\(863\) −16019.6 −0.631883 −0.315942 0.948779i \(-0.602320\pi\)
−0.315942 + 0.948779i \(0.602320\pi\)
\(864\) 6819.17 0.268510
\(865\) −32641.8 −1.28307
\(866\) 54595.4 2.14229
\(867\) −14726.9 −0.576877
\(868\) −19378.4 −0.757773
\(869\) 36907.5 1.44074
\(870\) −16624.2 −0.647833
\(871\) 26258.4 1.02151
\(872\) −1668.01 −0.0647774
\(873\) 13312.1 0.516088
\(874\) −7248.69 −0.280539
\(875\) −16394.5 −0.633411
\(876\) −22573.3 −0.870639
\(877\) 21231.4 0.817483 0.408742 0.912650i \(-0.365968\pi\)
0.408742 + 0.912650i \(0.365968\pi\)
\(878\) 6988.03 0.268604
\(879\) 14482.5 0.555724
\(880\) −29327.4 −1.12344
\(881\) −40809.0 −1.56060 −0.780301 0.625405i \(-0.784934\pi\)
−0.780301 + 0.625405i \(0.784934\pi\)
\(882\) −4522.21 −0.172643
\(883\) −24840.7 −0.946723 −0.473361 0.880868i \(-0.656960\pi\)
−0.473361 + 0.880868i \(0.656960\pi\)
\(884\) −637.682 −0.0242620
\(885\) 2473.95 0.0939672
\(886\) 30748.9 1.16595
\(887\) −7368.83 −0.278942 −0.139471 0.990226i \(-0.544540\pi\)
−0.139471 + 0.990226i \(0.544540\pi\)
\(888\) −6473.97 −0.244654
\(889\) −4987.20 −0.188150
\(890\) 41966.2 1.58057
\(891\) 4071.24 0.153077
\(892\) 5616.67 0.210830
\(893\) 25708.4 0.963379
\(894\) 35075.4 1.31219
\(895\) −43183.4 −1.61281
\(896\) 24647.8 0.919000
\(897\) 2683.69 0.0998952
\(898\) 5160.85 0.191782
\(899\) −8240.13 −0.305699
\(900\) 6449.55 0.238872
\(901\) 932.119 0.0344655
\(902\) −51002.4 −1.88270
\(903\) 1915.14 0.0705778
\(904\) 19490.2 0.717072
\(905\) −13538.0 −0.497259
\(906\) 42538.4 1.55987
\(907\) 13529.1 0.495289 0.247645 0.968851i \(-0.420343\pi\)
0.247645 + 0.968851i \(0.420343\pi\)
\(908\) 58490.6 2.13775
\(909\) −13884.1 −0.506607
\(910\) 39920.2 1.45422
\(911\) −12796.3 −0.465380 −0.232690 0.972551i \(-0.574753\pi\)
−0.232690 + 0.972551i \(0.574753\pi\)
\(912\) 7424.62 0.269577
\(913\) 17757.6 0.643694
\(914\) 62650.7 2.26729
\(915\) −13762.2 −0.497227
\(916\) −55284.8 −1.99417
\(917\) 53261.1 1.91803
\(918\) −231.055 −0.00830715
\(919\) 1229.33 0.0441259 0.0220629 0.999757i \(-0.492977\pi\)
0.0220629 + 0.999757i \(0.492977\pi\)
\(920\) 3734.12 0.133815
\(921\) −5061.43 −0.181085
\(922\) −8132.12 −0.290474
\(923\) −1446.02 −0.0515671
\(924\) 32968.1 1.17378
\(925\) 16295.6 0.579239
\(926\) 11118.5 0.394577
\(927\) 14296.7 0.506542
\(928\) 23480.8 0.830600
\(929\) −40507.0 −1.43056 −0.715280 0.698838i \(-0.753701\pi\)
−0.715280 + 0.698838i \(0.753701\pi\)
\(930\) 15848.3 0.558804
\(931\) −6985.39 −0.245904
\(932\) 14086.3 0.495078
\(933\) −19711.3 −0.691661
\(934\) −41883.3 −1.46731
\(935\) 1409.79 0.0493104
\(936\) 2616.35 0.0913656
\(937\) 46898.8 1.63513 0.817565 0.575837i \(-0.195324\pi\)
0.817565 + 0.575837i \(0.195324\pi\)
\(938\) 77045.4 2.68190
\(939\) 7141.27 0.248186
\(940\) −61732.5 −2.14201
\(941\) −10886.3 −0.377134 −0.188567 0.982060i \(-0.560384\pi\)
−0.188567 + 0.982060i \(0.560384\pi\)
\(942\) −28351.7 −0.980626
\(943\) −6822.70 −0.235607
\(944\) −2463.01 −0.0849196
\(945\) 8101.24 0.278871
\(946\) −6373.93 −0.219064
\(947\) −33388.0 −1.14569 −0.572843 0.819665i \(-0.694159\pi\)
−0.572843 + 0.819665i \(0.694159\pi\)
\(948\) 22436.5 0.768673
\(949\) 23049.4 0.788426
\(950\) 17787.8 0.607486
\(951\) −5741.74 −0.195782
\(952\) −401.395 −0.0136652
\(953\) −25026.7 −0.850676 −0.425338 0.905035i \(-0.639845\pi\)
−0.425338 + 0.905035i \(0.639845\pi\)
\(954\) −17826.8 −0.604995
\(955\) −52797.7 −1.78900
\(956\) −3872.32 −0.131004
\(957\) 14018.8 0.473523
\(958\) 16675.1 0.562368
\(959\) 37134.1 1.25039
\(960\) −31157.3 −1.04750
\(961\) −21935.5 −0.736312
\(962\) 30814.0 1.03273
\(963\) 7319.51 0.244930
\(964\) −1822.82 −0.0609014
\(965\) −22070.9 −0.736255
\(966\) 7874.29 0.262268
\(967\) 15589.4 0.518430 0.259215 0.965820i \(-0.416536\pi\)
0.259215 + 0.965820i \(0.416536\pi\)
\(968\) −11137.3 −0.369801
\(969\) −356.908 −0.0118323
\(970\) −88161.2 −2.91823
\(971\) −55818.4 −1.84480 −0.922398 0.386240i \(-0.873774\pi\)
−0.922398 + 0.386240i \(0.873774\pi\)
\(972\) 2474.95 0.0816709
\(973\) 68279.5 2.24968
\(974\) −72687.9 −2.39124
\(975\) −6585.60 −0.216316
\(976\) 13701.3 0.449352
\(977\) 11417.4 0.373873 0.186936 0.982372i \(-0.440144\pi\)
0.186936 + 0.982372i \(0.440144\pi\)
\(978\) 42501.0 1.38960
\(979\) −35388.9 −1.15530
\(980\) 16773.7 0.546753
\(981\) 1611.15 0.0524363
\(982\) 64657.6 2.10113
\(983\) 13517.3 0.438593 0.219296 0.975658i \(-0.429624\pi\)
0.219296 + 0.975658i \(0.429624\pi\)
\(984\) −6651.50 −0.215490
\(985\) 27086.6 0.876195
\(986\) −795.607 −0.0256970
\(987\) −27927.1 −0.900639
\(988\) 18838.6 0.606614
\(989\) −852.654 −0.0274144
\(990\) −26962.4 −0.865578
\(991\) 20867.5 0.668897 0.334448 0.942414i \(-0.391450\pi\)
0.334448 + 0.942414i \(0.391450\pi\)
\(992\) −22384.9 −0.716454
\(993\) −17582.5 −0.561898
\(994\) −4242.81 −0.135386
\(995\) −61935.7 −1.97336
\(996\) 10795.1 0.343428
\(997\) −22265.9 −0.707290 −0.353645 0.935380i \(-0.615058\pi\)
−0.353645 + 0.935380i \(0.615058\pi\)
\(998\) −80657.2 −2.55828
\(999\) 6253.28 0.198043
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.1.1 8
3.2 odd 2 531.4.a.e.1.8 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.4.a.d.1.1 8 1.1 even 1 trivial
531.4.a.e.1.8 8 3.2 odd 2