Properties

Label 177.4.a.d.1.3
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 1.3
Root \(2.26905\) of defining polynomial
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.26905 q^{2} +3.00000 q^{3} -6.38952 q^{4} +14.8820 q^{5} -3.80714 q^{6} +22.4903 q^{7} +18.2610 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q-1.26905 q^{2} +3.00000 q^{3} -6.38952 q^{4} +14.8820 q^{5} -3.80714 q^{6} +22.4903 q^{7} +18.2610 q^{8} +9.00000 q^{9} -18.8859 q^{10} -70.2303 q^{11} -19.1686 q^{12} -0.125351 q^{13} -28.5413 q^{14} +44.6459 q^{15} +27.9422 q^{16} +57.2801 q^{17} -11.4214 q^{18} +40.8191 q^{19} -95.0887 q^{20} +67.4710 q^{21} +89.1255 q^{22} +190.065 q^{23} +54.7829 q^{24} +96.4733 q^{25} +0.159076 q^{26} +27.0000 q^{27} -143.702 q^{28} +133.399 q^{29} -56.6578 q^{30} +129.061 q^{31} -181.548 q^{32} -210.691 q^{33} -72.6911 q^{34} +334.701 q^{35} -57.5057 q^{36} -364.329 q^{37} -51.8013 q^{38} -0.376052 q^{39} +271.759 q^{40} +195.632 q^{41} -85.6238 q^{42} +31.6882 q^{43} +448.738 q^{44} +133.938 q^{45} -241.201 q^{46} +479.330 q^{47} +83.8265 q^{48} +162.815 q^{49} -122.429 q^{50} +171.840 q^{51} +0.800930 q^{52} -402.892 q^{53} -34.2642 q^{54} -1045.17 q^{55} +410.695 q^{56} +122.457 q^{57} -169.290 q^{58} +59.0000 q^{59} -285.266 q^{60} -209.849 q^{61} -163.785 q^{62} +202.413 q^{63} +6.85497 q^{64} -1.86547 q^{65} +267.376 q^{66} -455.024 q^{67} -365.992 q^{68} +570.195 q^{69} -424.750 q^{70} +203.497 q^{71} +164.349 q^{72} -177.712 q^{73} +462.350 q^{74} +289.420 q^{75} -260.815 q^{76} -1579.50 q^{77} +0.477227 q^{78} -491.575 q^{79} +415.835 q^{80} +81.0000 q^{81} -248.266 q^{82} -717.862 q^{83} -431.107 q^{84} +852.441 q^{85} -40.2137 q^{86} +400.197 q^{87} -1282.47 q^{88} +1306.23 q^{89} -169.973 q^{90} -2.81918 q^{91} -1214.42 q^{92} +387.184 q^{93} -608.291 q^{94} +607.469 q^{95} -544.643 q^{96} +538.879 q^{97} -206.620 q^{98} -632.073 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 6q^{2} + 24q^{3} + 34q^{4} + 42q^{5} + 18q^{6} + 53q^{7} + 51q^{8} + 72q^{9} + O(q^{10}) \) \( 8q + 6q^{2} + 24q^{3} + 34q^{4} + 42q^{5} + 18q^{6} + 53q^{7} + 51q^{8} + 72q^{9} + 21q^{10} + 67q^{11} + 102q^{12} + 33q^{13} + 79q^{14} + 126q^{15} - 30q^{16} + 139q^{17} + 54q^{18} + 64q^{19} + 117q^{20} + 159q^{21} - 84q^{22} + 226q^{23} + 153q^{24} + 96q^{25} + 24q^{26} + 216q^{27} + 34q^{28} + 456q^{29} + 63q^{30} + 124q^{31} + 174q^{32} + 201q^{33} - 114q^{34} + 556q^{35} + 306q^{36} + 127q^{37} + 237q^{38} + 99q^{39} - 188q^{40} + 425q^{41} + 237q^{42} - 115q^{43} + 510q^{44} + 378q^{45} - 711q^{46} + 420q^{47} - 90q^{48} + 171q^{49} - 137q^{50} + 417q^{51} - 922q^{52} + 98q^{53} + 162q^{54} - 616q^{55} - 412q^{56} + 192q^{57} - 1548q^{58} + 472q^{59} + 351q^{60} - 1254q^{61} - 766q^{62} + 477q^{63} - 2019q^{64} - 734q^{65} - 252q^{66} - 1010q^{67} - 503q^{68} + 678q^{69} - 2956q^{70} - 17q^{71} + 459q^{72} - 1180q^{73} - 1228q^{74} + 288q^{75} - 2008q^{76} + 441q^{77} + 72q^{78} - 873q^{79} - 865q^{80} + 648q^{81} - 3645q^{82} + 759q^{83} + 102q^{84} - 850q^{85} - 1226q^{86} + 1368q^{87} - 3047q^{88} + 988q^{89} + 189q^{90} - 2111q^{91} - 1062q^{92} + 372q^{93} - 2240q^{94} + 1822q^{95} + 522q^{96} - 668q^{97} - 1368q^{98} + 603q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.26905 −0.448676 −0.224338 0.974511i \(-0.572022\pi\)
−0.224338 + 0.974511i \(0.572022\pi\)
\(3\) 3.00000 0.577350
\(4\) −6.38952 −0.798690
\(5\) 14.8820 1.33108 0.665542 0.746360i \(-0.268200\pi\)
0.665542 + 0.746360i \(0.268200\pi\)
\(6\) −3.80714 −0.259043
\(7\) 22.4903 1.21436 0.607182 0.794563i \(-0.292300\pi\)
0.607182 + 0.794563i \(0.292300\pi\)
\(8\) 18.2610 0.807028
\(9\) 9.00000 0.333333
\(10\) −18.8859 −0.597225
\(11\) −70.2303 −1.92502 −0.962510 0.271244i \(-0.912565\pi\)
−0.962510 + 0.271244i \(0.912565\pi\)
\(12\) −19.1686 −0.461124
\(13\) −0.125351 −0.00267431 −0.00133715 0.999999i \(-0.500426\pi\)
−0.00133715 + 0.999999i \(0.500426\pi\)
\(14\) −28.5413 −0.544855
\(15\) 44.6459 0.768502
\(16\) 27.9422 0.436596
\(17\) 57.2801 0.817203 0.408602 0.912713i \(-0.366017\pi\)
0.408602 + 0.912713i \(0.366017\pi\)
\(18\) −11.4214 −0.149559
\(19\) 40.8191 0.492871 0.246435 0.969159i \(-0.420741\pi\)
0.246435 + 0.969159i \(0.420741\pi\)
\(20\) −95.0887 −1.06312
\(21\) 67.4710 0.701113
\(22\) 89.1255 0.863710
\(23\) 190.065 1.72310 0.861550 0.507673i \(-0.169494\pi\)
0.861550 + 0.507673i \(0.169494\pi\)
\(24\) 54.7829 0.465938
\(25\) 96.4733 0.771787
\(26\) 0.159076 0.00119990
\(27\) 27.0000 0.192450
\(28\) −143.702 −0.969900
\(29\) 133.399 0.854193 0.427096 0.904206i \(-0.359537\pi\)
0.427096 + 0.904206i \(0.359537\pi\)
\(30\) −56.6578 −0.344808
\(31\) 129.061 0.747745 0.373872 0.927480i \(-0.378030\pi\)
0.373872 + 0.927480i \(0.378030\pi\)
\(32\) −181.548 −1.00292
\(33\) −210.691 −1.11141
\(34\) −72.6911 −0.366659
\(35\) 334.701 1.61642
\(36\) −57.5057 −0.266230
\(37\) −364.329 −1.61879 −0.809396 0.587263i \(-0.800205\pi\)
−0.809396 + 0.587263i \(0.800205\pi\)
\(38\) −51.8013 −0.221139
\(39\) −0.376052 −0.00154401
\(40\) 271.759 1.07422
\(41\) 195.632 0.745184 0.372592 0.927995i \(-0.378469\pi\)
0.372592 + 0.927995i \(0.378469\pi\)
\(42\) −85.6238 −0.314572
\(43\) 31.6882 0.112381 0.0561907 0.998420i \(-0.482105\pi\)
0.0561907 + 0.998420i \(0.482105\pi\)
\(44\) 448.738 1.53750
\(45\) 133.938 0.443695
\(46\) −241.201 −0.773113
\(47\) 479.330 1.48760 0.743802 0.668400i \(-0.233020\pi\)
0.743802 + 0.668400i \(0.233020\pi\)
\(48\) 83.8265 0.252069
\(49\) 162.815 0.474679
\(50\) −122.429 −0.346282
\(51\) 171.840 0.471813
\(52\) 0.800930 0.00213594
\(53\) −402.892 −1.04418 −0.522090 0.852891i \(-0.674847\pi\)
−0.522090 + 0.852891i \(0.674847\pi\)
\(54\) −34.2642 −0.0863476
\(55\) −1045.17 −2.56237
\(56\) 410.695 0.980026
\(57\) 122.457 0.284559
\(58\) −169.290 −0.383255
\(59\) 59.0000 0.130189
\(60\) −285.266 −0.613795
\(61\) −209.849 −0.440465 −0.220232 0.975447i \(-0.570682\pi\)
−0.220232 + 0.975447i \(0.570682\pi\)
\(62\) −163.785 −0.335495
\(63\) 202.413 0.404788
\(64\) 6.85497 0.0133886
\(65\) −1.86547 −0.00355973
\(66\) 267.376 0.498663
\(67\) −455.024 −0.829702 −0.414851 0.909889i \(-0.636166\pi\)
−0.414851 + 0.909889i \(0.636166\pi\)
\(68\) −365.992 −0.652692
\(69\) 570.195 0.994832
\(70\) −424.750 −0.725248
\(71\) 203.497 0.340151 0.170075 0.985431i \(-0.445599\pi\)
0.170075 + 0.985431i \(0.445599\pi\)
\(72\) 164.349 0.269009
\(73\) −177.712 −0.284927 −0.142463 0.989800i \(-0.545502\pi\)
−0.142463 + 0.989800i \(0.545502\pi\)
\(74\) 462.350 0.726313
\(75\) 289.420 0.445591
\(76\) −260.815 −0.393651
\(77\) −1579.50 −2.33768
\(78\) 0.477227 0.000692761 0
\(79\) −491.575 −0.700082 −0.350041 0.936734i \(-0.613832\pi\)
−0.350041 + 0.936734i \(0.613832\pi\)
\(80\) 415.835 0.581147
\(81\) 81.0000 0.111111
\(82\) −248.266 −0.334346
\(83\) −717.862 −0.949345 −0.474673 0.880162i \(-0.657433\pi\)
−0.474673 + 0.880162i \(0.657433\pi\)
\(84\) −431.107 −0.559972
\(85\) 852.441 1.08777
\(86\) −40.2137 −0.0504228
\(87\) 400.197 0.493168
\(88\) −1282.47 −1.55355
\(89\) 1306.23 1.55573 0.777865 0.628431i \(-0.216303\pi\)
0.777865 + 0.628431i \(0.216303\pi\)
\(90\) −169.973 −0.199075
\(91\) −2.81918 −0.00324758
\(92\) −1214.42 −1.37622
\(93\) 387.184 0.431711
\(94\) −608.291 −0.667452
\(95\) 607.469 0.656053
\(96\) −544.643 −0.579035
\(97\) 538.879 0.564071 0.282036 0.959404i \(-0.408990\pi\)
0.282036 + 0.959404i \(0.408990\pi\)
\(98\) −206.620 −0.212977
\(99\) −632.073 −0.641674
\(100\) −616.419 −0.616419
\(101\) −1585.19 −1.56171 −0.780854 0.624714i \(-0.785216\pi\)
−0.780854 + 0.624714i \(0.785216\pi\)
\(102\) −218.073 −0.211691
\(103\) −512.174 −0.489961 −0.244980 0.969528i \(-0.578782\pi\)
−0.244980 + 0.969528i \(0.578782\pi\)
\(104\) −2.28902 −0.00215824
\(105\) 1004.10 0.933241
\(106\) 511.289 0.468498
\(107\) 90.3234 0.0816065 0.0408033 0.999167i \(-0.487008\pi\)
0.0408033 + 0.999167i \(0.487008\pi\)
\(108\) −172.517 −0.153708
\(109\) −2241.55 −1.96974 −0.984870 0.173297i \(-0.944558\pi\)
−0.984870 + 0.173297i \(0.944558\pi\)
\(110\) 1326.36 1.14967
\(111\) −1092.99 −0.934610
\(112\) 628.428 0.530187
\(113\) −1538.31 −1.28064 −0.640319 0.768109i \(-0.721198\pi\)
−0.640319 + 0.768109i \(0.721198\pi\)
\(114\) −155.404 −0.127675
\(115\) 2828.54 2.29359
\(116\) −852.356 −0.682235
\(117\) −1.12816 −0.000891436 0
\(118\) −74.8737 −0.0584126
\(119\) 1288.25 0.992382
\(120\) 815.278 0.620203
\(121\) 3601.29 2.70571
\(122\) 266.308 0.197626
\(123\) 586.896 0.430232
\(124\) −824.640 −0.597216
\(125\) −424.533 −0.303771
\(126\) −256.871 −0.181618
\(127\) 1230.53 0.859780 0.429890 0.902881i \(-0.358552\pi\)
0.429890 + 0.902881i \(0.358552\pi\)
\(128\) 1443.68 0.996911
\(129\) 95.0645 0.0648834
\(130\) 2.36736 0.00159716
\(131\) 972.455 0.648578 0.324289 0.945958i \(-0.394875\pi\)
0.324289 + 0.945958i \(0.394875\pi\)
\(132\) 1346.21 0.887673
\(133\) 918.035 0.598525
\(134\) 577.447 0.372267
\(135\) 401.813 0.256167
\(136\) 1045.99 0.659506
\(137\) −335.709 −0.209355 −0.104677 0.994506i \(-0.533381\pi\)
−0.104677 + 0.994506i \(0.533381\pi\)
\(138\) −723.604 −0.446357
\(139\) −2222.42 −1.35614 −0.678068 0.734999i \(-0.737183\pi\)
−0.678068 + 0.734999i \(0.737183\pi\)
\(140\) −2138.58 −1.29102
\(141\) 1437.99 0.858869
\(142\) −258.248 −0.152617
\(143\) 8.80341 0.00514810
\(144\) 251.480 0.145532
\(145\) 1985.24 1.13700
\(146\) 225.525 0.127840
\(147\) 488.444 0.274056
\(148\) 2327.89 1.29291
\(149\) 1467.58 0.806906 0.403453 0.915000i \(-0.367810\pi\)
0.403453 + 0.915000i \(0.367810\pi\)
\(150\) −367.287 −0.199926
\(151\) −2400.31 −1.29361 −0.646804 0.762656i \(-0.723895\pi\)
−0.646804 + 0.762656i \(0.723895\pi\)
\(152\) 745.397 0.397761
\(153\) 515.521 0.272401
\(154\) 2004.46 1.04886
\(155\) 1920.69 0.995312
\(156\) 2.40279 0.00123319
\(157\) −3571.25 −1.81539 −0.907697 0.419627i \(-0.862161\pi\)
−0.907697 + 0.419627i \(0.862161\pi\)
\(158\) 623.831 0.314110
\(159\) −1208.68 −0.602857
\(160\) −2701.79 −1.33497
\(161\) 4274.62 2.09247
\(162\) −102.793 −0.0498528
\(163\) −1305.57 −0.627365 −0.313683 0.949528i \(-0.601563\pi\)
−0.313683 + 0.949528i \(0.601563\pi\)
\(164\) −1249.99 −0.595172
\(165\) −3135.50 −1.47938
\(166\) 911.000 0.425948
\(167\) 156.555 0.0725423 0.0362711 0.999342i \(-0.488452\pi\)
0.0362711 + 0.999342i \(0.488452\pi\)
\(168\) 1232.09 0.565818
\(169\) −2196.98 −0.999993
\(170\) −1081.79 −0.488054
\(171\) 367.372 0.164290
\(172\) −202.472 −0.0897579
\(173\) 357.266 0.157008 0.0785042 0.996914i \(-0.474986\pi\)
0.0785042 + 0.996914i \(0.474986\pi\)
\(174\) −507.869 −0.221273
\(175\) 2169.72 0.937230
\(176\) −1962.39 −0.840457
\(177\) 177.000 0.0751646
\(178\) −1657.66 −0.698018
\(179\) 1581.04 0.660183 0.330092 0.943949i \(-0.392920\pi\)
0.330092 + 0.943949i \(0.392920\pi\)
\(180\) −855.799 −0.354375
\(181\) 1674.78 0.687766 0.343883 0.939012i \(-0.388258\pi\)
0.343883 + 0.939012i \(0.388258\pi\)
\(182\) 3.57766 0.00145711
\(183\) −629.546 −0.254303
\(184\) 3470.77 1.39059
\(185\) −5421.94 −2.15475
\(186\) −491.354 −0.193698
\(187\) −4022.80 −1.57313
\(188\) −3062.69 −1.18814
\(189\) 607.239 0.233704
\(190\) −770.907 −0.294355
\(191\) 5015.44 1.90002 0.950011 0.312217i \(-0.101071\pi\)
0.950011 + 0.312217i \(0.101071\pi\)
\(192\) 20.5649 0.00772992
\(193\) 1296.37 0.483496 0.241748 0.970339i \(-0.422279\pi\)
0.241748 + 0.970339i \(0.422279\pi\)
\(194\) −683.863 −0.253085
\(195\) −5.59640 −0.00205521
\(196\) −1040.31 −0.379121
\(197\) −2894.70 −1.04690 −0.523449 0.852057i \(-0.675355\pi\)
−0.523449 + 0.852057i \(0.675355\pi\)
\(198\) 802.129 0.287903
\(199\) −2835.15 −1.00994 −0.504971 0.863136i \(-0.668497\pi\)
−0.504971 + 0.863136i \(0.668497\pi\)
\(200\) 1761.70 0.622854
\(201\) −1365.07 −0.479029
\(202\) 2011.68 0.700700
\(203\) 3000.19 1.03730
\(204\) −1097.98 −0.376832
\(205\) 2911.39 0.991904
\(206\) 649.972 0.219833
\(207\) 1710.58 0.574366
\(208\) −3.50257 −0.00116759
\(209\) −2866.74 −0.948787
\(210\) −1274.25 −0.418722
\(211\) 894.249 0.291766 0.145883 0.989302i \(-0.453398\pi\)
0.145883 + 0.989302i \(0.453398\pi\)
\(212\) 2574.29 0.833976
\(213\) 610.492 0.196386
\(214\) −114.625 −0.0366148
\(215\) 471.583 0.149589
\(216\) 493.046 0.155313
\(217\) 2902.63 0.908034
\(218\) 2844.63 0.883774
\(219\) −533.137 −0.164503
\(220\) 6678.11 2.04654
\(221\) −7.18009 −0.00218545
\(222\) 1387.05 0.419337
\(223\) 2418.78 0.726338 0.363169 0.931723i \(-0.381695\pi\)
0.363169 + 0.931723i \(0.381695\pi\)
\(224\) −4083.07 −1.21791
\(225\) 868.260 0.257262
\(226\) 1952.19 0.574591
\(227\) −1116.89 −0.326565 −0.163283 0.986579i \(-0.552208\pi\)
−0.163283 + 0.986579i \(0.552208\pi\)
\(228\) −782.444 −0.227275
\(229\) −4003.70 −1.15534 −0.577668 0.816272i \(-0.696037\pi\)
−0.577668 + 0.816272i \(0.696037\pi\)
\(230\) −3589.55 −1.02908
\(231\) −4738.51 −1.34966
\(232\) 2436.00 0.689358
\(233\) −3831.54 −1.07731 −0.538654 0.842527i \(-0.681067\pi\)
−0.538654 + 0.842527i \(0.681067\pi\)
\(234\) 1.43168 0.000399966 0
\(235\) 7133.37 1.98013
\(236\) −376.982 −0.103981
\(237\) −1474.72 −0.404193
\(238\) −1634.85 −0.445258
\(239\) −665.336 −0.180071 −0.0900356 0.995939i \(-0.528698\pi\)
−0.0900356 + 0.995939i \(0.528698\pi\)
\(240\) 1247.50 0.335525
\(241\) 6021.52 1.60946 0.804730 0.593640i \(-0.202310\pi\)
0.804730 + 0.593640i \(0.202310\pi\)
\(242\) −4570.21 −1.21398
\(243\) 243.000 0.0641500
\(244\) 1340.83 0.351795
\(245\) 2423.01 0.631838
\(246\) −744.797 −0.193035
\(247\) −5.11670 −0.00131809
\(248\) 2356.78 0.603451
\(249\) −2153.59 −0.548105
\(250\) 538.752 0.136295
\(251\) −1854.47 −0.466347 −0.233173 0.972435i \(-0.574911\pi\)
−0.233173 + 0.972435i \(0.574911\pi\)
\(252\) −1293.32 −0.323300
\(253\) −13348.3 −3.31700
\(254\) −1561.60 −0.385762
\(255\) 2557.32 0.628023
\(256\) −1886.94 −0.460678
\(257\) −3407.16 −0.826976 −0.413488 0.910510i \(-0.635690\pi\)
−0.413488 + 0.910510i \(0.635690\pi\)
\(258\) −120.641 −0.0291116
\(259\) −8193.88 −1.96580
\(260\) 11.9194 0.00284312
\(261\) 1200.59 0.284731
\(262\) −1234.09 −0.291001
\(263\) −2085.60 −0.488986 −0.244493 0.969651i \(-0.578622\pi\)
−0.244493 + 0.969651i \(0.578622\pi\)
\(264\) −3847.42 −0.896940
\(265\) −5995.83 −1.38989
\(266\) −1165.03 −0.268543
\(267\) 3918.69 0.898201
\(268\) 2907.39 0.662675
\(269\) −6495.06 −1.47216 −0.736080 0.676895i \(-0.763325\pi\)
−0.736080 + 0.676895i \(0.763325\pi\)
\(270\) −509.920 −0.114936
\(271\) −3252.61 −0.729085 −0.364543 0.931187i \(-0.618775\pi\)
−0.364543 + 0.931187i \(0.618775\pi\)
\(272\) 1600.53 0.356788
\(273\) −8.45753 −0.00187499
\(274\) 426.031 0.0939323
\(275\) −6775.35 −1.48571
\(276\) −3643.27 −0.794562
\(277\) 5905.21 1.28090 0.640451 0.767999i \(-0.278747\pi\)
0.640451 + 0.767999i \(0.278747\pi\)
\(278\) 2820.35 0.608465
\(279\) 1161.55 0.249248
\(280\) 6111.96 1.30450
\(281\) 6504.05 1.38078 0.690390 0.723437i \(-0.257439\pi\)
0.690390 + 0.723437i \(0.257439\pi\)
\(282\) −1824.87 −0.385353
\(283\) 6587.83 1.38377 0.691883 0.722010i \(-0.256782\pi\)
0.691883 + 0.722010i \(0.256782\pi\)
\(284\) −1300.25 −0.271675
\(285\) 1822.41 0.378772
\(286\) −11.1719 −0.00230983
\(287\) 4399.82 0.904925
\(288\) −1633.93 −0.334306
\(289\) −1631.99 −0.332179
\(290\) −2519.36 −0.510145
\(291\) 1616.64 0.325667
\(292\) 1135.50 0.227568
\(293\) 4655.68 0.928285 0.464142 0.885761i \(-0.346363\pi\)
0.464142 + 0.885761i \(0.346363\pi\)
\(294\) −619.859 −0.122962
\(295\) 878.037 0.173292
\(296\) −6653.00 −1.30641
\(297\) −1896.22 −0.370470
\(298\) −1862.43 −0.362039
\(299\) −23.8248 −0.00460810
\(300\) −1849.26 −0.355889
\(301\) 712.677 0.136472
\(302\) 3046.11 0.580410
\(303\) −4755.58 −0.901652
\(304\) 1140.57 0.215186
\(305\) −3122.96 −0.586296
\(306\) −654.219 −0.122220
\(307\) −1381.12 −0.256758 −0.128379 0.991725i \(-0.540977\pi\)
−0.128379 + 0.991725i \(0.540977\pi\)
\(308\) 10092.3 1.86708
\(309\) −1536.52 −0.282879
\(310\) −2437.44 −0.446572
\(311\) 2269.90 0.413873 0.206936 0.978354i \(-0.433651\pi\)
0.206936 + 0.978354i \(0.433651\pi\)
\(312\) −6.86707 −0.00124606
\(313\) −487.625 −0.0880581 −0.0440290 0.999030i \(-0.514019\pi\)
−0.0440290 + 0.999030i \(0.514019\pi\)
\(314\) 4532.08 0.814523
\(315\) 3012.31 0.538807
\(316\) 3140.93 0.559149
\(317\) 8517.00 1.50903 0.754515 0.656283i \(-0.227872\pi\)
0.754515 + 0.656283i \(0.227872\pi\)
\(318\) 1533.87 0.270487
\(319\) −9368.66 −1.64434
\(320\) 102.015 0.0178214
\(321\) 270.970 0.0471155
\(322\) −5424.69 −0.938840
\(323\) 2338.12 0.402776
\(324\) −517.551 −0.0887434
\(325\) −12.0930 −0.00206400
\(326\) 1656.83 0.281483
\(327\) −6724.65 −1.13723
\(328\) 3572.43 0.601385
\(329\) 10780.3 1.80649
\(330\) 3979.09 0.663763
\(331\) 10338.9 1.71685 0.858423 0.512942i \(-0.171444\pi\)
0.858423 + 0.512942i \(0.171444\pi\)
\(332\) 4586.80 0.758233
\(333\) −3278.96 −0.539597
\(334\) −198.675 −0.0325480
\(335\) −6771.66 −1.10440
\(336\) 1885.29 0.306103
\(337\) −344.378 −0.0556660 −0.0278330 0.999613i \(-0.508861\pi\)
−0.0278330 + 0.999613i \(0.508861\pi\)
\(338\) 2788.07 0.448672
\(339\) −4614.94 −0.739377
\(340\) −5446.69 −0.868789
\(341\) −9064.01 −1.43942
\(342\) −466.212 −0.0737131
\(343\) −4052.42 −0.637931
\(344\) 578.656 0.0906949
\(345\) 8485.63 1.32421
\(346\) −453.387 −0.0704458
\(347\) 4032.71 0.623883 0.311942 0.950101i \(-0.399021\pi\)
0.311942 + 0.950101i \(0.399021\pi\)
\(348\) −2557.07 −0.393889
\(349\) 6299.32 0.966175 0.483087 0.875572i \(-0.339515\pi\)
0.483087 + 0.875572i \(0.339515\pi\)
\(350\) −2753.47 −0.420512
\(351\) −3.38447 −0.000514671 0
\(352\) 12750.1 1.93064
\(353\) −8240.96 −1.24256 −0.621278 0.783590i \(-0.713386\pi\)
−0.621278 + 0.783590i \(0.713386\pi\)
\(354\) −224.621 −0.0337245
\(355\) 3028.44 0.452769
\(356\) −8346.18 −1.24255
\(357\) 3864.74 0.572952
\(358\) −2006.42 −0.296208
\(359\) −6605.66 −0.971124 −0.485562 0.874202i \(-0.661385\pi\)
−0.485562 + 0.874202i \(0.661385\pi\)
\(360\) 2445.83 0.358074
\(361\) −5192.80 −0.757078
\(362\) −2125.38 −0.308584
\(363\) 10803.9 1.56214
\(364\) 18.0132 0.00259381
\(365\) −2644.71 −0.379262
\(366\) 798.923 0.114099
\(367\) 10563.8 1.50253 0.751263 0.660003i \(-0.229445\pi\)
0.751263 + 0.660003i \(0.229445\pi\)
\(368\) 5310.83 0.752299
\(369\) 1760.69 0.248395
\(370\) 6880.69 0.966784
\(371\) −9061.18 −1.26801
\(372\) −2473.92 −0.344803
\(373\) −9588.55 −1.33104 −0.665518 0.746382i \(-0.731789\pi\)
−0.665518 + 0.746382i \(0.731789\pi\)
\(374\) 5105.11 0.705827
\(375\) −1273.60 −0.175382
\(376\) 8753.02 1.20054
\(377\) −16.7217 −0.00228437
\(378\) −770.614 −0.104857
\(379\) 8045.04 1.09036 0.545180 0.838319i \(-0.316461\pi\)
0.545180 + 0.838319i \(0.316461\pi\)
\(380\) −3881.44 −0.523983
\(381\) 3691.59 0.496394
\(382\) −6364.82 −0.852493
\(383\) −13181.7 −1.75863 −0.879314 0.476242i \(-0.841999\pi\)
−0.879314 + 0.476242i \(0.841999\pi\)
\(384\) 4331.05 0.575567
\(385\) −23506.1 −3.11164
\(386\) −1645.15 −0.216933
\(387\) 285.193 0.0374605
\(388\) −3443.18 −0.450518
\(389\) 1629.56 0.212396 0.106198 0.994345i \(-0.466132\pi\)
0.106198 + 0.994345i \(0.466132\pi\)
\(390\) 7.10208 0.000922123 0
\(391\) 10886.9 1.40812
\(392\) 2973.16 0.383079
\(393\) 2917.36 0.374457
\(394\) 3673.51 0.469718
\(395\) −7315.61 −0.931869
\(396\) 4038.64 0.512498
\(397\) 2405.86 0.304148 0.152074 0.988369i \(-0.451405\pi\)
0.152074 + 0.988369i \(0.451405\pi\)
\(398\) 3597.94 0.453136
\(399\) 2754.11 0.345558
\(400\) 2695.67 0.336959
\(401\) 4383.33 0.545868 0.272934 0.962033i \(-0.412006\pi\)
0.272934 + 0.962033i \(0.412006\pi\)
\(402\) 1732.34 0.214928
\(403\) −16.1779 −0.00199970
\(404\) 10128.6 1.24732
\(405\) 1205.44 0.147898
\(406\) −3807.38 −0.465411
\(407\) 25586.9 3.11621
\(408\) 3137.97 0.380766
\(409\) −8567.44 −1.03578 −0.517888 0.855448i \(-0.673282\pi\)
−0.517888 + 0.855448i \(0.673282\pi\)
\(410\) −3694.69 −0.445043
\(411\) −1007.13 −0.120871
\(412\) 3272.54 0.391327
\(413\) 1326.93 0.158097
\(414\) −2170.81 −0.257704
\(415\) −10683.2 −1.26366
\(416\) 22.7571 0.00268211
\(417\) −6667.25 −0.782966
\(418\) 3638.02 0.425698
\(419\) 7908.61 0.922102 0.461051 0.887374i \(-0.347472\pi\)
0.461051 + 0.887374i \(0.347472\pi\)
\(420\) −6415.73 −0.745370
\(421\) 4262.15 0.493407 0.246703 0.969091i \(-0.420653\pi\)
0.246703 + 0.969091i \(0.420653\pi\)
\(422\) −1134.84 −0.130908
\(423\) 4313.97 0.495868
\(424\) −7357.20 −0.842682
\(425\) 5526.00 0.630707
\(426\) −774.743 −0.0881136
\(427\) −4719.56 −0.534885
\(428\) −577.124 −0.0651783
\(429\) 26.4102 0.00297226
\(430\) −598.460 −0.0671170
\(431\) 12851.4 1.43627 0.718134 0.695905i \(-0.244997\pi\)
0.718134 + 0.695905i \(0.244997\pi\)
\(432\) 754.439 0.0840230
\(433\) −10952.4 −1.21556 −0.607782 0.794104i \(-0.707940\pi\)
−0.607782 + 0.794104i \(0.707940\pi\)
\(434\) −3683.57 −0.407413
\(435\) 5955.73 0.656449
\(436\) 14322.4 1.57321
\(437\) 7758.28 0.849266
\(438\) 676.576 0.0738083
\(439\) −12153.2 −1.32128 −0.660638 0.750705i \(-0.729714\pi\)
−0.660638 + 0.750705i \(0.729714\pi\)
\(440\) −19085.7 −2.06790
\(441\) 1465.33 0.158226
\(442\) 9.11187 0.000980560 0
\(443\) 11624.3 1.24670 0.623348 0.781944i \(-0.285772\pi\)
0.623348 + 0.781944i \(0.285772\pi\)
\(444\) 6983.66 0.746464
\(445\) 19439.3 2.07081
\(446\) −3069.54 −0.325890
\(447\) 4402.75 0.465867
\(448\) 154.170 0.0162586
\(449\) −9152.69 −0.962009 −0.481005 0.876718i \(-0.659728\pi\)
−0.481005 + 0.876718i \(0.659728\pi\)
\(450\) −1101.86 −0.115427
\(451\) −13739.3 −1.43450
\(452\) 9829.08 1.02283
\(453\) −7200.94 −0.746865
\(454\) 1417.38 0.146522
\(455\) −41.9549 −0.00432281
\(456\) 2236.19 0.229647
\(457\) −1864.25 −0.190822 −0.0954112 0.995438i \(-0.530417\pi\)
−0.0954112 + 0.995438i \(0.530417\pi\)
\(458\) 5080.88 0.518371
\(459\) 1546.56 0.157271
\(460\) −18073.0 −1.83187
\(461\) −19215.7 −1.94136 −0.970679 0.240377i \(-0.922729\pi\)
−0.970679 + 0.240377i \(0.922729\pi\)
\(462\) 6013.38 0.605558
\(463\) 7787.00 0.781626 0.390813 0.920470i \(-0.372194\pi\)
0.390813 + 0.920470i \(0.372194\pi\)
\(464\) 3727.46 0.372937
\(465\) 5762.06 0.574643
\(466\) 4862.41 0.483362
\(467\) −9537.66 −0.945076 −0.472538 0.881310i \(-0.656662\pi\)
−0.472538 + 0.881310i \(0.656662\pi\)
\(468\) 7.20837 0.000711981 0
\(469\) −10233.6 −1.00756
\(470\) −9052.58 −0.888435
\(471\) −10713.7 −1.04812
\(472\) 1077.40 0.105066
\(473\) −2225.47 −0.216336
\(474\) 1871.49 0.181351
\(475\) 3937.96 0.380391
\(476\) −8231.29 −0.792606
\(477\) −3626.03 −0.348060
\(478\) 844.343 0.0807936
\(479\) −2560.30 −0.244223 −0.122112 0.992516i \(-0.538967\pi\)
−0.122112 + 0.992516i \(0.538967\pi\)
\(480\) −8105.36 −0.770745
\(481\) 45.6689 0.00432915
\(482\) −7641.58 −0.722126
\(483\) 12823.9 1.20809
\(484\) −23010.5 −2.16102
\(485\) 8019.59 0.750827
\(486\) −308.378 −0.0287825
\(487\) 4855.22 0.451768 0.225884 0.974154i \(-0.427473\pi\)
0.225884 + 0.974154i \(0.427473\pi\)
\(488\) −3832.04 −0.355468
\(489\) −3916.72 −0.362209
\(490\) −3074.91 −0.283490
\(491\) 18773.3 1.72551 0.862755 0.505622i \(-0.168737\pi\)
0.862755 + 0.505622i \(0.168737\pi\)
\(492\) −3749.98 −0.343622
\(493\) 7641.11 0.698049
\(494\) 6.49333 0.000591394 0
\(495\) −9406.49 −0.854122
\(496\) 3606.25 0.326463
\(497\) 4576.72 0.413067
\(498\) 2733.00 0.245921
\(499\) −8138.08 −0.730081 −0.365040 0.930992i \(-0.618945\pi\)
−0.365040 + 0.930992i \(0.618945\pi\)
\(500\) 2712.56 0.242619
\(501\) 469.664 0.0418823
\(502\) 2353.41 0.209238
\(503\) 7732.32 0.685422 0.342711 0.939441i \(-0.388655\pi\)
0.342711 + 0.939441i \(0.388655\pi\)
\(504\) 3696.26 0.326675
\(505\) −23590.8 −2.07877
\(506\) 16939.6 1.48826
\(507\) −6590.95 −0.577346
\(508\) −7862.51 −0.686698
\(509\) 1365.77 0.118933 0.0594665 0.998230i \(-0.481060\pi\)
0.0594665 + 0.998230i \(0.481060\pi\)
\(510\) −3245.36 −0.281778
\(511\) −3996.81 −0.346005
\(512\) −9154.84 −0.790216
\(513\) 1102.12 0.0948531
\(514\) 4323.84 0.371044
\(515\) −7622.16 −0.652179
\(516\) −607.417 −0.0518217
\(517\) −33663.5 −2.86367
\(518\) 10398.4 0.882008
\(519\) 1071.80 0.0906488
\(520\) −34.0652 −0.00287280
\(521\) −5123.71 −0.430852 −0.215426 0.976520i \(-0.569114\pi\)
−0.215426 + 0.976520i \(0.569114\pi\)
\(522\) −1523.61 −0.127752
\(523\) 20522.1 1.71581 0.857907 0.513805i \(-0.171765\pi\)
0.857907 + 0.513805i \(0.171765\pi\)
\(524\) −6213.52 −0.518013
\(525\) 6509.15 0.541110
\(526\) 2646.72 0.219396
\(527\) 7392.64 0.611060
\(528\) −5887.16 −0.485238
\(529\) 23957.7 1.96907
\(530\) 7608.99 0.623610
\(531\) 531.000 0.0433963
\(532\) −5865.81 −0.478036
\(533\) −24.5226 −0.00199285
\(534\) −4972.99 −0.403001
\(535\) 1344.19 0.108625
\(536\) −8309.18 −0.669593
\(537\) 4743.13 0.381157
\(538\) 8242.53 0.660522
\(539\) −11434.5 −0.913767
\(540\) −2567.40 −0.204598
\(541\) −17106.3 −1.35944 −0.679720 0.733471i \(-0.737899\pi\)
−0.679720 + 0.733471i \(0.737899\pi\)
\(542\) 4127.71 0.327123
\(543\) 5024.35 0.397082
\(544\) −10399.1 −0.819588
\(545\) −33358.7 −2.62189
\(546\) 10.7330 0.000841263 0
\(547\) 4023.62 0.314511 0.157255 0.987558i \(-0.449735\pi\)
0.157255 + 0.987558i \(0.449735\pi\)
\(548\) 2145.02 0.167209
\(549\) −1888.64 −0.146822
\(550\) 8598.23 0.666600
\(551\) 5445.23 0.421007
\(552\) 10412.3 0.802857
\(553\) −11055.7 −0.850154
\(554\) −7493.99 −0.574709
\(555\) −16265.8 −1.24405
\(556\) 14200.2 1.08313
\(557\) 18019.0 1.37072 0.685360 0.728204i \(-0.259645\pi\)
0.685360 + 0.728204i \(0.259645\pi\)
\(558\) −1474.06 −0.111832
\(559\) −3.97213 −0.000300542 0
\(560\) 9352.26 0.705723
\(561\) −12068.4 −0.908249
\(562\) −8253.94 −0.619522
\(563\) 25706.0 1.92430 0.962148 0.272526i \(-0.0878591\pi\)
0.962148 + 0.272526i \(0.0878591\pi\)
\(564\) −9188.06 −0.685970
\(565\) −22893.1 −1.70464
\(566\) −8360.25 −0.620862
\(567\) 1821.72 0.134929
\(568\) 3716.06 0.274511
\(569\) −3090.70 −0.227713 −0.113857 0.993497i \(-0.536320\pi\)
−0.113857 + 0.993497i \(0.536320\pi\)
\(570\) −2312.72 −0.169946
\(571\) 7296.29 0.534746 0.267373 0.963593i \(-0.413844\pi\)
0.267373 + 0.963593i \(0.413844\pi\)
\(572\) −56.2496 −0.00411174
\(573\) 15046.3 1.09698
\(574\) −5583.58 −0.406018
\(575\) 18336.2 1.32987
\(576\) 61.6947 0.00446287
\(577\) −1681.44 −0.121316 −0.0606579 0.998159i \(-0.519320\pi\)
−0.0606579 + 0.998159i \(0.519320\pi\)
\(578\) 2071.07 0.149040
\(579\) 3889.11 0.279147
\(580\) −12684.7 −0.908113
\(581\) −16145.0 −1.15285
\(582\) −2051.59 −0.146119
\(583\) 28295.2 2.01007
\(584\) −3245.20 −0.229944
\(585\) −16.7892 −0.00118658
\(586\) −5908.27 −0.416499
\(587\) −6885.79 −0.484169 −0.242084 0.970255i \(-0.577831\pi\)
−0.242084 + 0.970255i \(0.577831\pi\)
\(588\) −3120.93 −0.218886
\(589\) 5268.17 0.368542
\(590\) −1114.27 −0.0777521
\(591\) −8684.11 −0.604427
\(592\) −10180.1 −0.706759
\(593\) −24880.0 −1.72293 −0.861467 0.507813i \(-0.830454\pi\)
−0.861467 + 0.507813i \(0.830454\pi\)
\(594\) 2406.39 0.166221
\(595\) 19171.7 1.32094
\(596\) −9377.15 −0.644468
\(597\) −8505.45 −0.583090
\(598\) 30.2347 0.00206754
\(599\) 5068.39 0.345724 0.172862 0.984946i \(-0.444698\pi\)
0.172862 + 0.984946i \(0.444698\pi\)
\(600\) 5285.09 0.359605
\(601\) −5800.47 −0.393687 −0.196844 0.980435i \(-0.563069\pi\)
−0.196844 + 0.980435i \(0.563069\pi\)
\(602\) −904.420 −0.0612316
\(603\) −4095.22 −0.276567
\(604\) 15336.9 1.03319
\(605\) 53594.4 3.60152
\(606\) 6035.05 0.404549
\(607\) 8659.84 0.579064 0.289532 0.957168i \(-0.406500\pi\)
0.289532 + 0.957168i \(0.406500\pi\)
\(608\) −7410.61 −0.494309
\(609\) 9000.57 0.598886
\(610\) 3963.18 0.263057
\(611\) −60.0843 −0.00397831
\(612\) −3293.93 −0.217564
\(613\) −3303.27 −0.217647 −0.108824 0.994061i \(-0.534708\pi\)
−0.108824 + 0.994061i \(0.534708\pi\)
\(614\) 1752.70 0.115201
\(615\) 8734.17 0.572676
\(616\) −28843.2 −1.88657
\(617\) −9356.43 −0.610495 −0.305248 0.952273i \(-0.598739\pi\)
−0.305248 + 0.952273i \(0.598739\pi\)
\(618\) 1949.92 0.126921
\(619\) 1106.92 0.0718756 0.0359378 0.999354i \(-0.488558\pi\)
0.0359378 + 0.999354i \(0.488558\pi\)
\(620\) −12272.3 −0.794946
\(621\) 5131.75 0.331611
\(622\) −2880.61 −0.185695
\(623\) 29377.5 1.88922
\(624\) −10.5077 −0.000674110 0
\(625\) −18377.1 −1.17613
\(626\) 618.818 0.0395095
\(627\) −8600.22 −0.547782
\(628\) 22818.6 1.44994
\(629\) −20868.8 −1.32288
\(630\) −3822.75 −0.241749
\(631\) 23600.6 1.48895 0.744473 0.667653i \(-0.232701\pi\)
0.744473 + 0.667653i \(0.232701\pi\)
\(632\) −8976.63 −0.564986
\(633\) 2682.75 0.168451
\(634\) −10808.5 −0.677065
\(635\) 18312.7 1.14444
\(636\) 7722.87 0.481496
\(637\) −20.4089 −0.00126944
\(638\) 11889.3 0.737774
\(639\) 1831.48 0.113384
\(640\) 21484.8 1.32697
\(641\) −3922.67 −0.241710 −0.120855 0.992670i \(-0.538564\pi\)
−0.120855 + 0.992670i \(0.538564\pi\)
\(642\) −343.874 −0.0211396
\(643\) −11078.8 −0.679482 −0.339741 0.940519i \(-0.610339\pi\)
−0.339741 + 0.940519i \(0.610339\pi\)
\(644\) −27312.8 −1.67123
\(645\) 1414.75 0.0863653
\(646\) −2967.18 −0.180716
\(647\) −18371.0 −1.11629 −0.558143 0.829745i \(-0.688486\pi\)
−0.558143 + 0.829745i \(0.688486\pi\)
\(648\) 1479.14 0.0896698
\(649\) −4143.59 −0.250616
\(650\) 15.3466 0.000926064 0
\(651\) 8707.89 0.524254
\(652\) 8342.00 0.501070
\(653\) 12179.0 0.729862 0.364931 0.931035i \(-0.381093\pi\)
0.364931 + 0.931035i \(0.381093\pi\)
\(654\) 8533.89 0.510247
\(655\) 14472.1 0.863313
\(656\) 5466.38 0.325345
\(657\) −1599.41 −0.0949757
\(658\) −13680.7 −0.810529
\(659\) −18245.7 −1.07853 −0.539266 0.842135i \(-0.681298\pi\)
−0.539266 + 0.842135i \(0.681298\pi\)
\(660\) 20034.3 1.18157
\(661\) 20360.6 1.19809 0.599043 0.800717i \(-0.295548\pi\)
0.599043 + 0.800717i \(0.295548\pi\)
\(662\) −13120.5 −0.770307
\(663\) −21.5403 −0.00126177
\(664\) −13108.9 −0.766148
\(665\) 13662.2 0.796687
\(666\) 4161.15 0.242104
\(667\) 25354.5 1.47186
\(668\) −1000.31 −0.0579388
\(669\) 7256.33 0.419351
\(670\) 8593.55 0.495519
\(671\) 14737.7 0.847904
\(672\) −12249.2 −0.703159
\(673\) −3894.49 −0.223063 −0.111531 0.993761i \(-0.535576\pi\)
−0.111531 + 0.993761i \(0.535576\pi\)
\(674\) 437.031 0.0249760
\(675\) 2604.78 0.148530
\(676\) 14037.7 0.798685
\(677\) 23571.6 1.33815 0.669077 0.743194i \(-0.266690\pi\)
0.669077 + 0.743194i \(0.266690\pi\)
\(678\) 5856.57 0.331740
\(679\) 12119.6 0.684987
\(680\) 15566.4 0.877859
\(681\) −3350.66 −0.188542
\(682\) 11502.6 0.645834
\(683\) −7789.31 −0.436383 −0.218192 0.975906i \(-0.570016\pi\)
−0.218192 + 0.975906i \(0.570016\pi\)
\(684\) −2347.33 −0.131217
\(685\) −4996.02 −0.278669
\(686\) 5142.71 0.286224
\(687\) −12011.1 −0.667034
\(688\) 885.436 0.0490653
\(689\) 50.5028 0.00279246
\(690\) −10768.7 −0.594139
\(691\) −8889.84 −0.489414 −0.244707 0.969597i \(-0.578692\pi\)
−0.244707 + 0.969597i \(0.578692\pi\)
\(692\) −2282.76 −0.125401
\(693\) −14215.5 −0.779225
\(694\) −5117.70 −0.279921
\(695\) −33074.0 −1.80513
\(696\) 7307.99 0.398001
\(697\) 11205.8 0.608967
\(698\) −7994.13 −0.433499
\(699\) −11494.6 −0.621984
\(700\) −13863.5 −0.748556
\(701\) 32472.7 1.74961 0.874804 0.484477i \(-0.160990\pi\)
0.874804 + 0.484477i \(0.160990\pi\)
\(702\) 4.29504 0.000230920 0
\(703\) −14871.6 −0.797856
\(704\) −481.426 −0.0257734
\(705\) 21400.1 1.14323
\(706\) 10458.2 0.557504
\(707\) −35651.5 −1.89648
\(708\) −1130.95 −0.0600332
\(709\) 4596.06 0.243454 0.121727 0.992564i \(-0.461157\pi\)
0.121727 + 0.992564i \(0.461157\pi\)
\(710\) −3843.24 −0.203147
\(711\) −4424.17 −0.233361
\(712\) 23853.0 1.25552
\(713\) 24530.0 1.28844
\(714\) −4904.54 −0.257070
\(715\) 131.012 0.00685256
\(716\) −10102.1 −0.527282
\(717\) −1996.01 −0.103964
\(718\) 8382.89 0.435720
\(719\) −81.6045 −0.00423273 −0.00211637 0.999998i \(-0.500674\pi\)
−0.00211637 + 0.999998i \(0.500674\pi\)
\(720\) 3742.51 0.193716
\(721\) −11519.0 −0.594991
\(722\) 6589.90 0.339682
\(723\) 18064.6 0.929223
\(724\) −10701.1 −0.549312
\(725\) 12869.5 0.659254
\(726\) −13710.6 −0.700894
\(727\) −5240.27 −0.267333 −0.133666 0.991026i \(-0.542675\pi\)
−0.133666 + 0.991026i \(0.542675\pi\)
\(728\) −51.4809 −0.00262089
\(729\) 729.000 0.0370370
\(730\) 3356.26 0.170166
\(731\) 1815.10 0.0918384
\(732\) 4022.50 0.203109
\(733\) 27362.1 1.37877 0.689386 0.724394i \(-0.257880\pi\)
0.689386 + 0.724394i \(0.257880\pi\)
\(734\) −13406.0 −0.674147
\(735\) 7269.02 0.364792
\(736\) −34505.8 −1.72813
\(737\) 31956.5 1.59719
\(738\) −2234.39 −0.111449
\(739\) 15458.7 0.769497 0.384748 0.923021i \(-0.374288\pi\)
0.384748 + 0.923021i \(0.374288\pi\)
\(740\) 34643.6 1.72098
\(741\) −15.3501 −0.000760999 0
\(742\) 11499.1 0.568927
\(743\) −33376.7 −1.64801 −0.824006 0.566581i \(-0.808266\pi\)
−0.824006 + 0.566581i \(0.808266\pi\)
\(744\) 7070.35 0.348403
\(745\) 21840.5 1.07406
\(746\) 12168.3 0.597203
\(747\) −6460.76 −0.316448
\(748\) 25703.7 1.25645
\(749\) 2031.40 0.0991000
\(750\) 1616.26 0.0786898
\(751\) −8832.20 −0.429150 −0.214575 0.976708i \(-0.568837\pi\)
−0.214575 + 0.976708i \(0.568837\pi\)
\(752\) 13393.5 0.649483
\(753\) −5563.41 −0.269245
\(754\) 21.2205 0.00102494
\(755\) −35721.4 −1.72190
\(756\) −3879.97 −0.186657
\(757\) −4971.26 −0.238684 −0.119342 0.992853i \(-0.538078\pi\)
−0.119342 + 0.992853i \(0.538078\pi\)
\(758\) −10209.5 −0.489218
\(759\) −40045.0 −1.91507
\(760\) 11093.0 0.529453
\(761\) 25414.3 1.21060 0.605300 0.795997i \(-0.293053\pi\)
0.605300 + 0.795997i \(0.293053\pi\)
\(762\) −4684.80 −0.222720
\(763\) −50413.2 −2.39198
\(764\) −32046.2 −1.51753
\(765\) 7671.97 0.362589
\(766\) 16728.2 0.789054
\(767\) −7.39569 −0.000348165 0
\(768\) −5660.82 −0.265973
\(769\) 30483.0 1.42945 0.714725 0.699406i \(-0.246552\pi\)
0.714725 + 0.699406i \(0.246552\pi\)
\(770\) 29830.4 1.39612
\(771\) −10221.5 −0.477455
\(772\) −8283.19 −0.386164
\(773\) 18113.2 0.842802 0.421401 0.906874i \(-0.361538\pi\)
0.421401 + 0.906874i \(0.361538\pi\)
\(774\) −361.924 −0.0168076
\(775\) 12451.0 0.577099
\(776\) 9840.46 0.455221
\(777\) −24581.6 −1.13496
\(778\) −2067.99 −0.0952969
\(779\) 7985.52 0.367280
\(780\) 35.7583 0.00164148
\(781\) −14291.7 −0.654797
\(782\) −13816.0 −0.631790
\(783\) 3601.77 0.164389
\(784\) 4549.40 0.207243
\(785\) −53147.3 −2.41644
\(786\) −3702.27 −0.168010
\(787\) 3681.38 0.166743 0.0833717 0.996519i \(-0.473431\pi\)
0.0833717 + 0.996519i \(0.473431\pi\)
\(788\) 18495.8 0.836148
\(789\) −6256.79 −0.282316
\(790\) 9283.84 0.418107
\(791\) −34597.1 −1.55516
\(792\) −11542.3 −0.517849
\(793\) 26.3046 0.00117794
\(794\) −3053.15 −0.136464
\(795\) −17987.5 −0.802454
\(796\) 18115.3 0.806631
\(797\) −40435.4 −1.79711 −0.898554 0.438863i \(-0.855381\pi\)
−0.898554 + 0.438863i \(0.855381\pi\)
\(798\) −3495.09 −0.155044
\(799\) 27456.0 1.21568
\(800\) −17514.5 −0.774039
\(801\) 11756.1 0.518577
\(802\) −5562.65 −0.244918
\(803\) 12480.8 0.548490
\(804\) 8722.16 0.382596
\(805\) 63614.9 2.78525
\(806\) 20.5305 0.000897216 0
\(807\) −19485.2 −0.849952
\(808\) −28947.1 −1.26034
\(809\) −36431.5 −1.58327 −0.791633 0.610997i \(-0.790769\pi\)
−0.791633 + 0.610997i \(0.790769\pi\)
\(810\) −1529.76 −0.0663584
\(811\) −30923.2 −1.33891 −0.669457 0.742851i \(-0.733473\pi\)
−0.669457 + 0.742851i \(0.733473\pi\)
\(812\) −19169.8 −0.828482
\(813\) −9757.84 −0.420938
\(814\) −32471.0 −1.39817
\(815\) −19429.5 −0.835076
\(816\) 4801.59 0.205992
\(817\) 1293.48 0.0553895
\(818\) 10872.5 0.464728
\(819\) −25.3726 −0.00108253
\(820\) −18602.4 −0.792224
\(821\) 3516.20 0.149472 0.0747359 0.997203i \(-0.476189\pi\)
0.0747359 + 0.997203i \(0.476189\pi\)
\(822\) 1278.09 0.0542318
\(823\) 39234.9 1.66178 0.830889 0.556439i \(-0.187833\pi\)
0.830889 + 0.556439i \(0.187833\pi\)
\(824\) −9352.78 −0.395412
\(825\) −20326.1 −0.857773
\(826\) −1683.93 −0.0709341
\(827\) 20321.9 0.854486 0.427243 0.904137i \(-0.359485\pi\)
0.427243 + 0.904137i \(0.359485\pi\)
\(828\) −10929.8 −0.458741
\(829\) −36098.3 −1.51236 −0.756180 0.654364i \(-0.772936\pi\)
−0.756180 + 0.654364i \(0.772936\pi\)
\(830\) 13557.5 0.566973
\(831\) 17715.6 0.739529
\(832\) −0.859274 −3.58053e−5 0
\(833\) 9326.04 0.387909
\(834\) 8461.05 0.351298
\(835\) 2329.84 0.0965600
\(836\) 18317.1 0.757787
\(837\) 3484.65 0.143904
\(838\) −10036.4 −0.413725
\(839\) 19751.4 0.812746 0.406373 0.913707i \(-0.366793\pi\)
0.406373 + 0.913707i \(0.366793\pi\)
\(840\) 18335.9 0.753152
\(841\) −6593.69 −0.270355
\(842\) −5408.86 −0.221380
\(843\) 19512.2 0.797194
\(844\) −5713.82 −0.233031
\(845\) −32695.5 −1.33108
\(846\) −5474.62 −0.222484
\(847\) 80994.3 3.28571
\(848\) −11257.7 −0.455885
\(849\) 19763.5 0.798917
\(850\) −7012.75 −0.282983
\(851\) −69246.2 −2.78934
\(852\) −3900.75 −0.156852
\(853\) 13812.9 0.554448 0.277224 0.960805i \(-0.410586\pi\)
0.277224 + 0.960805i \(0.410586\pi\)
\(854\) 5989.34 0.239990
\(855\) 5467.22 0.218684
\(856\) 1649.39 0.0658588
\(857\) 10194.0 0.406323 0.203162 0.979145i \(-0.434878\pi\)
0.203162 + 0.979145i \(0.434878\pi\)
\(858\) −33.5158 −0.00133358
\(859\) −11608.7 −0.461099 −0.230549 0.973061i \(-0.574052\pi\)
−0.230549 + 0.973061i \(0.574052\pi\)
\(860\) −3013.19 −0.119475
\(861\) 13199.5 0.522459
\(862\) −16309.0 −0.644418
\(863\) −45095.9 −1.77877 −0.889387 0.457155i \(-0.848868\pi\)
−0.889387 + 0.457155i \(0.848868\pi\)
\(864\) −4901.79 −0.193012
\(865\) 5316.83 0.208991
\(866\) 13899.1 0.545393
\(867\) −4895.98 −0.191783
\(868\) −18546.4 −0.725238
\(869\) 34523.5 1.34767
\(870\) −7558.09 −0.294533
\(871\) 57.0376 0.00221888
\(872\) −40932.9 −1.58964
\(873\) 4849.91 0.188024
\(874\) −9845.62 −0.381045
\(875\) −9547.89 −0.368889
\(876\) 3406.49 0.131387
\(877\) 38676.9 1.48920 0.744599 0.667512i \(-0.232641\pi\)
0.744599 + 0.667512i \(0.232641\pi\)
\(878\) 15423.0 0.592824
\(879\) 13967.0 0.535946
\(880\) −29204.2 −1.11872
\(881\) −34130.6 −1.30521 −0.652604 0.757699i \(-0.726323\pi\)
−0.652604 + 0.757699i \(0.726323\pi\)
\(882\) −1859.58 −0.0709923
\(883\) −39285.3 −1.49723 −0.748615 0.663005i \(-0.769281\pi\)
−0.748615 + 0.663005i \(0.769281\pi\)
\(884\) 45.8774 0.00174550
\(885\) 2634.11 0.100050
\(886\) −14751.8 −0.559362
\(887\) −27255.1 −1.03172 −0.515860 0.856673i \(-0.672528\pi\)
−0.515860 + 0.856673i \(0.672528\pi\)
\(888\) −19959.0 −0.754257
\(889\) 27675.1 1.04409
\(890\) −24669.3 −0.929121
\(891\) −5688.65 −0.213891
\(892\) −15454.8 −0.580119
\(893\) 19565.8 0.733197
\(894\) −5587.29 −0.209023
\(895\) 23529.1 0.878760
\(896\) 32468.9 1.21061
\(897\) −71.4743 −0.00266049
\(898\) 11615.2 0.431630
\(899\) 17216.6 0.638718
\(900\) −5547.77 −0.205473
\(901\) −23077.7 −0.853307
\(902\) 17435.8 0.643623
\(903\) 2138.03 0.0787920
\(904\) −28091.1 −1.03351
\(905\) 24924.1 0.915475
\(906\) 9138.33 0.335100
\(907\) −40763.1 −1.49230 −0.746151 0.665777i \(-0.768100\pi\)
−0.746151 + 0.665777i \(0.768100\pi\)
\(908\) 7136.36 0.260824
\(909\) −14266.7 −0.520569
\(910\) 53.2427 0.00193954
\(911\) 9175.77 0.333707 0.166853 0.985982i \(-0.446639\pi\)
0.166853 + 0.985982i \(0.446639\pi\)
\(912\) 3421.72 0.124238
\(913\) 50415.7 1.82751
\(914\) 2365.82 0.0856174
\(915\) −9368.89 −0.338498
\(916\) 25581.7 0.922756
\(917\) 21870.8 0.787610
\(918\) −1962.66 −0.0705636
\(919\) −33814.3 −1.21374 −0.606871 0.794800i \(-0.707576\pi\)
−0.606871 + 0.794800i \(0.707576\pi\)
\(920\) 51651.9 1.85099
\(921\) −4143.36 −0.148239
\(922\) 24385.7 0.871040
\(923\) −25.5085 −0.000909668 0
\(924\) 30276.8 1.07796
\(925\) −35148.0 −1.24936
\(926\) −9882.07 −0.350696
\(927\) −4609.56 −0.163320
\(928\) −24218.3 −0.856685
\(929\) 428.503 0.0151332 0.00756659 0.999971i \(-0.497591\pi\)
0.00756659 + 0.999971i \(0.497591\pi\)
\(930\) −7312.32 −0.257828
\(931\) 6645.96 0.233955
\(932\) 24481.7 0.860435
\(933\) 6809.71 0.238950
\(934\) 12103.7 0.424032
\(935\) −59867.2 −2.09397
\(936\) −20.6012 −0.000719414 0
\(937\) 32339.2 1.12751 0.563755 0.825942i \(-0.309356\pi\)
0.563755 + 0.825942i \(0.309356\pi\)
\(938\) 12987.0 0.452068
\(939\) −1462.87 −0.0508403
\(940\) −45578.8 −1.58151
\(941\) 3308.12 0.114603 0.0573016 0.998357i \(-0.481750\pi\)
0.0573016 + 0.998357i \(0.481750\pi\)
\(942\) 13596.2 0.470265
\(943\) 37182.8 1.28403
\(944\) 1648.59 0.0568400
\(945\) 9036.92 0.311080
\(946\) 2824.22 0.0970649
\(947\) 2319.50 0.0795921 0.0397961 0.999208i \(-0.487329\pi\)
0.0397961 + 0.999208i \(0.487329\pi\)
\(948\) 9422.79 0.322825
\(949\) 22.2764 0.000761982 0
\(950\) −4997.45 −0.170672
\(951\) 25551.0 0.871239
\(952\) 23524.6 0.800880
\(953\) 8790.44 0.298793 0.149397 0.988777i \(-0.452267\pi\)
0.149397 + 0.988777i \(0.452267\pi\)
\(954\) 4601.60 0.156166
\(955\) 74639.6 2.52909
\(956\) 4251.18 0.143821
\(957\) −28106.0 −0.949359
\(958\) 3249.13 0.109577
\(959\) −7550.21 −0.254233
\(960\) 306.046 0.0102892
\(961\) −13134.2 −0.440878
\(962\) −57.9559 −0.00194238
\(963\) 812.911 0.0272022
\(964\) −38474.6 −1.28546
\(965\) 19292.6 0.643575
\(966\) −16274.1 −0.542039
\(967\) −20867.5 −0.693953 −0.346976 0.937874i \(-0.612792\pi\)
−0.346976 + 0.937874i \(0.612792\pi\)
\(968\) 65763.1 2.18358
\(969\) 7014.37 0.232543
\(970\) −10177.2 −0.336877
\(971\) 2174.66 0.0718726 0.0359363 0.999354i \(-0.488559\pi\)
0.0359363 + 0.999354i \(0.488559\pi\)
\(972\) −1552.65 −0.0512360
\(973\) −49982.9 −1.64684
\(974\) −6161.49 −0.202697
\(975\) −36.2790 −0.00119165
\(976\) −5863.62 −0.192305
\(977\) −6656.04 −0.217959 −0.108979 0.994044i \(-0.534758\pi\)
−0.108979 + 0.994044i \(0.534758\pi\)
\(978\) 4970.50 0.162514
\(979\) −91736.8 −2.99481
\(980\) −15481.9 −0.504643
\(981\) −20174.0 −0.656580
\(982\) −23824.1 −0.774194
\(983\) 52028.5 1.68815 0.844075 0.536224i \(-0.180150\pi\)
0.844075 + 0.536224i \(0.180150\pi\)
\(984\) 10717.3 0.347210
\(985\) −43078.9 −1.39351
\(986\) −9696.92 −0.313198
\(987\) 32340.8 1.04298
\(988\) 32.6933 0.00105274
\(989\) 6022.81 0.193644
\(990\) 11937.3 0.383224
\(991\) 9152.99 0.293395 0.146697 0.989181i \(-0.453136\pi\)
0.146697 + 0.989181i \(0.453136\pi\)
\(992\) −23430.8 −0.749927
\(993\) 31016.6 0.991222
\(994\) −5808.07 −0.185333
\(995\) −42192.7 −1.34432
\(996\) 13760.4 0.437766
\(997\) −43711.9 −1.38854 −0.694268 0.719717i \(-0.744272\pi\)
−0.694268 + 0.719717i \(0.744272\pi\)
\(998\) 10327.6 0.327569
\(999\) −9836.88 −0.311537
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.1.3 8
3.2 odd 2 531.4.a.e.1.6 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.4.a.d.1.3 8 1.1 even 1 trivial
531.4.a.e.1.6 8 3.2 odd 2