Properties

Label 177.4.a.d.1.8
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 1.8
Root \(-4.15242\) of defining polynomial
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+5.15242 q^{2} +3.00000 q^{3} +18.5474 q^{4} +1.69104 q^{5} +15.4573 q^{6} -11.0943 q^{7} +54.3449 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q+5.15242 q^{2} +3.00000 q^{3} +18.5474 q^{4} +1.69104 q^{5} +15.4573 q^{6} -11.0943 q^{7} +54.3449 q^{8} +9.00000 q^{9} +8.71294 q^{10} -10.1415 q^{11} +55.6423 q^{12} +29.5495 q^{13} -57.1625 q^{14} +5.07312 q^{15} +131.628 q^{16} -29.3698 q^{17} +46.3718 q^{18} -46.9309 q^{19} +31.3645 q^{20} -33.2829 q^{21} -52.2532 q^{22} +22.2505 q^{23} +163.035 q^{24} -122.140 q^{25} +152.252 q^{26} +27.0000 q^{27} -205.771 q^{28} -103.959 q^{29} +26.1388 q^{30} -52.5878 q^{31} +243.445 q^{32} -30.4245 q^{33} -151.326 q^{34} -18.7609 q^{35} +166.927 q^{36} +5.51956 q^{37} -241.808 q^{38} +88.6485 q^{39} +91.8993 q^{40} +201.493 q^{41} -171.487 q^{42} +479.341 q^{43} -188.099 q^{44} +15.2193 q^{45} +114.644 q^{46} -133.168 q^{47} +394.885 q^{48} -219.917 q^{49} -629.319 q^{50} -88.1094 q^{51} +548.068 q^{52} -484.443 q^{53} +139.115 q^{54} -17.1497 q^{55} -602.918 q^{56} -140.793 q^{57} -535.639 q^{58} +59.0000 q^{59} +94.0934 q^{60} +578.161 q^{61} -270.954 q^{62} -99.8486 q^{63} +201.305 q^{64} +49.9694 q^{65} -156.760 q^{66} +52.3009 q^{67} -544.735 q^{68} +66.7516 q^{69} -96.6639 q^{70} +399.262 q^{71} +489.104 q^{72} -1045.81 q^{73} +28.4391 q^{74} -366.421 q^{75} -870.449 q^{76} +112.513 q^{77} +456.755 q^{78} +269.263 q^{79} +222.588 q^{80} +81.0000 q^{81} +1038.18 q^{82} +174.118 q^{83} -617.312 q^{84} -49.6655 q^{85} +2469.77 q^{86} -311.876 q^{87} -551.138 q^{88} +1380.40 q^{89} +78.4165 q^{90} -327.831 q^{91} +412.691 q^{92} -157.763 q^{93} -686.140 q^{94} -79.3620 q^{95} +730.335 q^{96} +628.773 q^{97} -1133.10 q^{98} -91.2734 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 6q^{2} + 24q^{3} + 34q^{4} + 42q^{5} + 18q^{6} + 53q^{7} + 51q^{8} + 72q^{9} + O(q^{10}) \) \( 8q + 6q^{2} + 24q^{3} + 34q^{4} + 42q^{5} + 18q^{6} + 53q^{7} + 51q^{8} + 72q^{9} + 21q^{10} + 67q^{11} + 102q^{12} + 33q^{13} + 79q^{14} + 126q^{15} - 30q^{16} + 139q^{17} + 54q^{18} + 64q^{19} + 117q^{20} + 159q^{21} - 84q^{22} + 226q^{23} + 153q^{24} + 96q^{25} + 24q^{26} + 216q^{27} + 34q^{28} + 456q^{29} + 63q^{30} + 124q^{31} + 174q^{32} + 201q^{33} - 114q^{34} + 556q^{35} + 306q^{36} + 127q^{37} + 237q^{38} + 99q^{39} - 188q^{40} + 425q^{41} + 237q^{42} - 115q^{43} + 510q^{44} + 378q^{45} - 711q^{46} + 420q^{47} - 90q^{48} + 171q^{49} - 137q^{50} + 417q^{51} - 922q^{52} + 98q^{53} + 162q^{54} - 616q^{55} - 412q^{56} + 192q^{57} - 1548q^{58} + 472q^{59} + 351q^{60} - 1254q^{61} - 766q^{62} + 477q^{63} - 2019q^{64} - 734q^{65} - 252q^{66} - 1010q^{67} - 503q^{68} + 678q^{69} - 2956q^{70} - 17q^{71} + 459q^{72} - 1180q^{73} - 1228q^{74} + 288q^{75} - 2008q^{76} + 441q^{77} + 72q^{78} - 873q^{79} - 865q^{80} + 648q^{81} - 3645q^{82} + 759q^{83} + 102q^{84} - 850q^{85} - 1226q^{86} + 1368q^{87} - 3047q^{88} + 988q^{89} + 189q^{90} - 2111q^{91} - 1062q^{92} + 372q^{93} - 2240q^{94} + 1822q^{95} + 522q^{96} - 668q^{97} - 1368q^{98} + 603q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.15242 1.82166 0.910828 0.412786i \(-0.135444\pi\)
0.910828 + 0.412786i \(0.135444\pi\)
\(3\) 3.00000 0.577350
\(4\) 18.5474 2.31843
\(5\) 1.69104 0.151251 0.0756256 0.997136i \(-0.475905\pi\)
0.0756256 + 0.997136i \(0.475905\pi\)
\(6\) 15.4573 1.05173
\(7\) −11.0943 −0.599035 −0.299518 0.954091i \(-0.596826\pi\)
−0.299518 + 0.954091i \(0.596826\pi\)
\(8\) 54.3449 2.40173
\(9\) 9.00000 0.333333
\(10\) 8.71294 0.275528
\(11\) −10.1415 −0.277980 −0.138990 0.990294i \(-0.544386\pi\)
−0.138990 + 0.990294i \(0.544386\pi\)
\(12\) 55.6423 1.33855
\(13\) 29.5495 0.630428 0.315214 0.949021i \(-0.397924\pi\)
0.315214 + 0.949021i \(0.397924\pi\)
\(14\) −57.1625 −1.09124
\(15\) 5.07312 0.0873249
\(16\) 131.628 2.05669
\(17\) −29.3698 −0.419013 −0.209507 0.977807i \(-0.567186\pi\)
−0.209507 + 0.977807i \(0.567186\pi\)
\(18\) 46.3718 0.607219
\(19\) −46.9309 −0.566668 −0.283334 0.959021i \(-0.591441\pi\)
−0.283334 + 0.959021i \(0.591441\pi\)
\(20\) 31.3645 0.350665
\(21\) −33.2829 −0.345853
\(22\) −52.2532 −0.506383
\(23\) 22.2505 0.201720 0.100860 0.994901i \(-0.467841\pi\)
0.100860 + 0.994901i \(0.467841\pi\)
\(24\) 163.035 1.38664
\(25\) −122.140 −0.977123
\(26\) 152.252 1.14842
\(27\) 27.0000 0.192450
\(28\) −205.771 −1.38882
\(29\) −103.959 −0.665677 −0.332838 0.942984i \(-0.608006\pi\)
−0.332838 + 0.942984i \(0.608006\pi\)
\(30\) 26.1388 0.159076
\(31\) −52.5878 −0.304679 −0.152339 0.988328i \(-0.548681\pi\)
−0.152339 + 0.988328i \(0.548681\pi\)
\(32\) 243.445 1.34486
\(33\) −30.4245 −0.160492
\(34\) −151.326 −0.763298
\(35\) −18.7609 −0.0906048
\(36\) 166.927 0.772810
\(37\) 5.51956 0.0245246 0.0122623 0.999925i \(-0.496097\pi\)
0.0122623 + 0.999925i \(0.496097\pi\)
\(38\) −241.808 −1.03227
\(39\) 88.6485 0.363978
\(40\) 91.8993 0.363264
\(41\) 201.493 0.767512 0.383756 0.923435i \(-0.374630\pi\)
0.383756 + 0.923435i \(0.374630\pi\)
\(42\) −171.487 −0.630026
\(43\) 479.341 1.69997 0.849987 0.526804i \(-0.176610\pi\)
0.849987 + 0.526804i \(0.176610\pi\)
\(44\) −188.099 −0.644476
\(45\) 15.2193 0.0504170
\(46\) 114.644 0.367464
\(47\) −133.168 −0.413290 −0.206645 0.978416i \(-0.566254\pi\)
−0.206645 + 0.978416i \(0.566254\pi\)
\(48\) 394.885 1.18743
\(49\) −219.917 −0.641157
\(50\) −629.319 −1.77998
\(51\) −88.1094 −0.241917
\(52\) 548.068 1.46160
\(53\) −484.443 −1.25553 −0.627767 0.778401i \(-0.716031\pi\)
−0.627767 + 0.778401i \(0.716031\pi\)
\(54\) 139.115 0.350578
\(55\) −17.1497 −0.0420447
\(56\) −602.918 −1.43872
\(57\) −140.793 −0.327166
\(58\) −535.639 −1.21263
\(59\) 59.0000 0.130189
\(60\) 94.0934 0.202457
\(61\) 578.161 1.21354 0.606770 0.794877i \(-0.292465\pi\)
0.606770 + 0.794877i \(0.292465\pi\)
\(62\) −270.954 −0.555020
\(63\) −99.8486 −0.199678
\(64\) 201.305 0.393174
\(65\) 49.9694 0.0953529
\(66\) −156.760 −0.292360
\(67\) 52.3009 0.0953668 0.0476834 0.998862i \(-0.484816\pi\)
0.0476834 + 0.998862i \(0.484816\pi\)
\(68\) −544.735 −0.971453
\(69\) 66.7516 0.116463
\(70\) −96.6639 −0.165051
\(71\) 399.262 0.667375 0.333687 0.942684i \(-0.391707\pi\)
0.333687 + 0.942684i \(0.391707\pi\)
\(72\) 489.104 0.800576
\(73\) −1045.81 −1.67675 −0.838374 0.545096i \(-0.816493\pi\)
−0.838374 + 0.545096i \(0.816493\pi\)
\(74\) 28.4391 0.0446754
\(75\) −366.421 −0.564142
\(76\) −870.449 −1.31378
\(77\) 112.513 0.166520
\(78\) 456.755 0.663042
\(79\) 269.263 0.383474 0.191737 0.981446i \(-0.438588\pi\)
0.191737 + 0.981446i \(0.438588\pi\)
\(80\) 222.588 0.311077
\(81\) 81.0000 0.111111
\(82\) 1038.18 1.39814
\(83\) 174.118 0.230265 0.115132 0.993350i \(-0.463271\pi\)
0.115132 + 0.993350i \(0.463271\pi\)
\(84\) −617.312 −0.801837
\(85\) −49.6655 −0.0633762
\(86\) 2469.77 3.09677
\(87\) −311.876 −0.384329
\(88\) −551.138 −0.667631
\(89\) 1380.40 1.64407 0.822036 0.569435i \(-0.192838\pi\)
0.822036 + 0.569435i \(0.192838\pi\)
\(90\) 78.4165 0.0918425
\(91\) −327.831 −0.377648
\(92\) 412.691 0.467674
\(93\) −157.763 −0.175906
\(94\) −686.140 −0.752871
\(95\) −79.3620 −0.0857092
\(96\) 730.335 0.776453
\(97\) 628.773 0.658167 0.329084 0.944301i \(-0.393260\pi\)
0.329084 + 0.944301i \(0.393260\pi\)
\(98\) −1133.10 −1.16797
\(99\) −91.2734 −0.0926598
\(100\) −2265.39 −2.26539
\(101\) 553.980 0.545773 0.272887 0.962046i \(-0.412022\pi\)
0.272887 + 0.962046i \(0.412022\pi\)
\(102\) −453.977 −0.440690
\(103\) 401.263 0.383861 0.191930 0.981409i \(-0.438525\pi\)
0.191930 + 0.981409i \(0.438525\pi\)
\(104\) 1605.86 1.51412
\(105\) −56.2826 −0.0523107
\(106\) −2496.05 −2.28715
\(107\) −129.942 −0.117401 −0.0587007 0.998276i \(-0.518696\pi\)
−0.0587007 + 0.998276i \(0.518696\pi\)
\(108\) 500.781 0.446182
\(109\) −1248.43 −1.09705 −0.548524 0.836135i \(-0.684810\pi\)
−0.548524 + 0.836135i \(0.684810\pi\)
\(110\) −88.3623 −0.0765910
\(111\) 16.5587 0.0141593
\(112\) −1460.32 −1.23203
\(113\) 1175.90 0.978933 0.489466 0.872022i \(-0.337192\pi\)
0.489466 + 0.872022i \(0.337192\pi\)
\(114\) −725.424 −0.595984
\(115\) 37.6265 0.0305104
\(116\) −1928.17 −1.54333
\(117\) 265.946 0.210143
\(118\) 303.993 0.237159
\(119\) 325.837 0.251004
\(120\) 275.698 0.209731
\(121\) −1228.15 −0.922727
\(122\) 2978.93 2.21065
\(123\) 604.480 0.443123
\(124\) −975.369 −0.706377
\(125\) −417.924 −0.299042
\(126\) −514.462 −0.363745
\(127\) −1993.40 −1.39280 −0.696399 0.717654i \(-0.745216\pi\)
−0.696399 + 0.717654i \(0.745216\pi\)
\(128\) −910.351 −0.628629
\(129\) 1438.02 0.981480
\(130\) 257.463 0.173700
\(131\) 1519.30 1.01330 0.506650 0.862152i \(-0.330884\pi\)
0.506650 + 0.862152i \(0.330884\pi\)
\(132\) −564.296 −0.372089
\(133\) 520.665 0.339454
\(134\) 269.476 0.173726
\(135\) 45.6580 0.0291083
\(136\) −1596.10 −1.00636
\(137\) 1596.83 0.995812 0.497906 0.867231i \(-0.334102\pi\)
0.497906 + 0.867231i \(0.334102\pi\)
\(138\) 343.933 0.212156
\(139\) 666.080 0.406447 0.203224 0.979132i \(-0.434858\pi\)
0.203224 + 0.979132i \(0.434858\pi\)
\(140\) −347.966 −0.210061
\(141\) −399.505 −0.238613
\(142\) 2057.16 1.21573
\(143\) −299.676 −0.175246
\(144\) 1184.65 0.685564
\(145\) −175.798 −0.100684
\(146\) −5388.44 −3.05446
\(147\) −659.750 −0.370172
\(148\) 102.374 0.0568586
\(149\) 1767.90 0.972029 0.486014 0.873951i \(-0.338450\pi\)
0.486014 + 0.873951i \(0.338450\pi\)
\(150\) −1887.96 −1.02767
\(151\) −1053.25 −0.567633 −0.283817 0.958879i \(-0.591601\pi\)
−0.283817 + 0.958879i \(0.591601\pi\)
\(152\) −2550.46 −1.36098
\(153\) −264.328 −0.139671
\(154\) 579.713 0.303341
\(155\) −88.9280 −0.0460830
\(156\) 1644.20 0.843857
\(157\) −47.5287 −0.0241605 −0.0120803 0.999927i \(-0.503845\pi\)
−0.0120803 + 0.999927i \(0.503845\pi\)
\(158\) 1387.36 0.698558
\(159\) −1453.33 −0.724883
\(160\) 411.675 0.203411
\(161\) −246.854 −0.120837
\(162\) 417.346 0.202406
\(163\) 3084.59 1.48223 0.741115 0.671378i \(-0.234297\pi\)
0.741115 + 0.671378i \(0.234297\pi\)
\(164\) 3737.19 1.77942
\(165\) −51.4490 −0.0242745
\(166\) 897.132 0.419463
\(167\) 3685.43 1.70771 0.853854 0.520513i \(-0.174259\pi\)
0.853854 + 0.520513i \(0.174259\pi\)
\(168\) −1808.75 −0.830645
\(169\) −1323.83 −0.602561
\(170\) −255.898 −0.115450
\(171\) −422.378 −0.188889
\(172\) 8890.56 3.94127
\(173\) 504.194 0.221579 0.110790 0.993844i \(-0.464662\pi\)
0.110790 + 0.993844i \(0.464662\pi\)
\(174\) −1606.92 −0.700115
\(175\) 1355.06 0.585331
\(176\) −1334.91 −0.571718
\(177\) 177.000 0.0751646
\(178\) 7112.42 2.99494
\(179\) 2931.88 1.22424 0.612120 0.790765i \(-0.290317\pi\)
0.612120 + 0.790765i \(0.290317\pi\)
\(180\) 282.280 0.116888
\(181\) 4335.05 1.78023 0.890116 0.455734i \(-0.150623\pi\)
0.890116 + 0.455734i \(0.150623\pi\)
\(182\) −1689.12 −0.687946
\(183\) 1734.48 0.700638
\(184\) 1209.20 0.484476
\(185\) 9.33380 0.00370937
\(186\) −812.863 −0.320441
\(187\) 297.854 0.116477
\(188\) −2469.93 −0.958183
\(189\) −299.546 −0.115284
\(190\) −408.907 −0.156133
\(191\) 2286.00 0.866016 0.433008 0.901390i \(-0.357452\pi\)
0.433008 + 0.901390i \(0.357452\pi\)
\(192\) 603.915 0.226999
\(193\) −1685.13 −0.628487 −0.314244 0.949342i \(-0.601751\pi\)
−0.314244 + 0.949342i \(0.601751\pi\)
\(194\) 3239.70 1.19895
\(195\) 149.908 0.0550520
\(196\) −4078.89 −1.48648
\(197\) 690.913 0.249876 0.124938 0.992165i \(-0.460127\pi\)
0.124938 + 0.992165i \(0.460127\pi\)
\(198\) −470.279 −0.168794
\(199\) −1448.24 −0.515894 −0.257947 0.966159i \(-0.583046\pi\)
−0.257947 + 0.966159i \(0.583046\pi\)
\(200\) −6637.71 −2.34678
\(201\) 156.903 0.0550601
\(202\) 2854.34 0.994211
\(203\) 1153.35 0.398764
\(204\) −1634.21 −0.560869
\(205\) 340.733 0.116087
\(206\) 2067.48 0.699262
\(207\) 200.255 0.0672400
\(208\) 3889.55 1.29659
\(209\) 475.950 0.157522
\(210\) −289.992 −0.0952921
\(211\) −5007.79 −1.63389 −0.816944 0.576717i \(-0.804333\pi\)
−0.816944 + 0.576717i \(0.804333\pi\)
\(212\) −8985.18 −2.91087
\(213\) 1197.78 0.385309
\(214\) −669.515 −0.213865
\(215\) 810.585 0.257123
\(216\) 1467.31 0.462213
\(217\) 583.424 0.182513
\(218\) −6432.46 −1.99844
\(219\) −3137.42 −0.968071
\(220\) −318.082 −0.0974778
\(221\) −867.864 −0.264158
\(222\) 85.3173 0.0257934
\(223\) 1275.24 0.382943 0.191471 0.981498i \(-0.438674\pi\)
0.191471 + 0.981498i \(0.438674\pi\)
\(224\) −2700.85 −0.805616
\(225\) −1099.26 −0.325708
\(226\) 6058.73 1.78328
\(227\) −1302.24 −0.380760 −0.190380 0.981711i \(-0.560972\pi\)
−0.190380 + 0.981711i \(0.560972\pi\)
\(228\) −2611.35 −0.758512
\(229\) −3359.40 −0.969413 −0.484706 0.874677i \(-0.661073\pi\)
−0.484706 + 0.874677i \(0.661073\pi\)
\(230\) 193.868 0.0555794
\(231\) 337.538 0.0961401
\(232\) −5649.62 −1.59877
\(233\) −2610.02 −0.733855 −0.366927 0.930250i \(-0.619590\pi\)
−0.366927 + 0.930250i \(0.619590\pi\)
\(234\) 1370.26 0.382807
\(235\) −225.193 −0.0625105
\(236\) 1094.30 0.301834
\(237\) 807.789 0.221399
\(238\) 1678.85 0.457243
\(239\) −4236.99 −1.14673 −0.573364 0.819301i \(-0.694362\pi\)
−0.573364 + 0.819301i \(0.694362\pi\)
\(240\) 667.765 0.179600
\(241\) −3164.38 −0.845792 −0.422896 0.906178i \(-0.638986\pi\)
−0.422896 + 0.906178i \(0.638986\pi\)
\(242\) −6327.95 −1.68089
\(243\) 243.000 0.0641500
\(244\) 10723.4 2.81351
\(245\) −371.888 −0.0969756
\(246\) 3114.54 0.807218
\(247\) −1386.79 −0.357243
\(248\) −2857.88 −0.731756
\(249\) 522.355 0.132943
\(250\) −2153.32 −0.544752
\(251\) −6495.46 −1.63343 −0.816713 0.577044i \(-0.804206\pi\)
−0.816713 + 0.577044i \(0.804206\pi\)
\(252\) −1851.94 −0.462941
\(253\) −225.654 −0.0560740
\(254\) −10270.8 −2.53720
\(255\) −148.996 −0.0365903
\(256\) −6300.95 −1.53832
\(257\) −4426.51 −1.07439 −0.537195 0.843458i \(-0.680516\pi\)
−0.537195 + 0.843458i \(0.680516\pi\)
\(258\) 7409.30 1.78792
\(259\) −61.2356 −0.0146911
\(260\) 926.804 0.221069
\(261\) −935.627 −0.221892
\(262\) 7828.10 1.84588
\(263\) 6798.01 1.59385 0.796927 0.604076i \(-0.206458\pi\)
0.796927 + 0.604076i \(0.206458\pi\)
\(264\) −1653.41 −0.385457
\(265\) −819.212 −0.189901
\(266\) 2682.69 0.618369
\(267\) 4141.21 0.949206
\(268\) 970.049 0.221101
\(269\) 6894.51 1.56270 0.781349 0.624095i \(-0.214532\pi\)
0.781349 + 0.624095i \(0.214532\pi\)
\(270\) 235.250 0.0530253
\(271\) 2936.35 0.658195 0.329097 0.944296i \(-0.393256\pi\)
0.329097 + 0.944296i \(0.393256\pi\)
\(272\) −3865.90 −0.861781
\(273\) −983.493 −0.218035
\(274\) 8227.53 1.81403
\(275\) 1238.69 0.271620
\(276\) 1238.07 0.270012
\(277\) −7457.80 −1.61767 −0.808837 0.588033i \(-0.799902\pi\)
−0.808837 + 0.588033i \(0.799902\pi\)
\(278\) 3431.92 0.740407
\(279\) −473.290 −0.101560
\(280\) −1019.56 −0.217608
\(281\) −5450.35 −1.15708 −0.578542 0.815652i \(-0.696378\pi\)
−0.578542 + 0.815652i \(0.696378\pi\)
\(282\) −2058.42 −0.434671
\(283\) 2984.42 0.626873 0.313437 0.949609i \(-0.398520\pi\)
0.313437 + 0.949609i \(0.398520\pi\)
\(284\) 7405.28 1.54726
\(285\) −238.086 −0.0494842
\(286\) −1544.06 −0.319238
\(287\) −2235.43 −0.459767
\(288\) 2191.00 0.448285
\(289\) −4050.41 −0.824428
\(290\) −905.786 −0.183412
\(291\) 1886.32 0.379993
\(292\) −19397.1 −3.88742
\(293\) 2189.77 0.436613 0.218307 0.975880i \(-0.429947\pi\)
0.218307 + 0.975880i \(0.429947\pi\)
\(294\) −3399.31 −0.674326
\(295\) 99.7713 0.0196912
\(296\) 299.960 0.0589014
\(297\) −273.820 −0.0534972
\(298\) 9108.98 1.77070
\(299\) 657.493 0.127170
\(300\) −6796.18 −1.30792
\(301\) −5317.95 −1.01834
\(302\) −5426.81 −1.03403
\(303\) 1661.94 0.315102
\(304\) −6177.43 −1.16546
\(305\) 977.693 0.183549
\(306\) −1361.93 −0.254433
\(307\) −8606.40 −1.59998 −0.799989 0.600014i \(-0.795162\pi\)
−0.799989 + 0.600014i \(0.795162\pi\)
\(308\) 2086.82 0.386064
\(309\) 1203.79 0.221622
\(310\) −458.195 −0.0839474
\(311\) 757.395 0.138096 0.0690482 0.997613i \(-0.478004\pi\)
0.0690482 + 0.997613i \(0.478004\pi\)
\(312\) 4817.59 0.874175
\(313\) −2172.72 −0.392363 −0.196182 0.980568i \(-0.562854\pi\)
−0.196182 + 0.980568i \(0.562854\pi\)
\(314\) −244.888 −0.0440122
\(315\) −168.848 −0.0302016
\(316\) 4994.14 0.889058
\(317\) −6786.82 −1.20248 −0.601239 0.799069i \(-0.705326\pi\)
−0.601239 + 0.799069i \(0.705326\pi\)
\(318\) −7488.16 −1.32049
\(319\) 1054.30 0.185045
\(320\) 340.414 0.0594679
\(321\) −389.825 −0.0677817
\(322\) −1271.90 −0.220124
\(323\) 1378.35 0.237441
\(324\) 1502.34 0.257603
\(325\) −3609.19 −0.616005
\(326\) 15893.1 2.70011
\(327\) −3745.30 −0.633381
\(328\) 10950.1 1.84335
\(329\) 1477.41 0.247575
\(330\) −265.087 −0.0442198
\(331\) −2842.29 −0.471984 −0.235992 0.971755i \(-0.575834\pi\)
−0.235992 + 0.971755i \(0.575834\pi\)
\(332\) 3229.45 0.533853
\(333\) 49.6761 0.00817487
\(334\) 18988.9 3.11086
\(335\) 88.4429 0.0144243
\(336\) −4380.96 −0.711313
\(337\) −6547.58 −1.05837 −0.529183 0.848508i \(-0.677501\pi\)
−0.529183 + 0.848508i \(0.677501\pi\)
\(338\) −6820.91 −1.09766
\(339\) 3527.70 0.565187
\(340\) −921.168 −0.146933
\(341\) 533.319 0.0846945
\(342\) −2176.27 −0.344091
\(343\) 6245.16 0.983111
\(344\) 26049.7 4.08287
\(345\) 112.880 0.0176152
\(346\) 2597.82 0.403641
\(347\) −35.2935 −0.00546010 −0.00273005 0.999996i \(-0.500869\pi\)
−0.00273005 + 0.999996i \(0.500869\pi\)
\(348\) −5784.50 −0.891040
\(349\) 10692.0 1.63991 0.819956 0.572427i \(-0.193998\pi\)
0.819956 + 0.572427i \(0.193998\pi\)
\(350\) 6981.85 1.06627
\(351\) 797.837 0.121326
\(352\) −2468.89 −0.373842
\(353\) −8661.89 −1.30602 −0.653011 0.757348i \(-0.726495\pi\)
−0.653011 + 0.757348i \(0.726495\pi\)
\(354\) 911.979 0.136924
\(355\) 675.167 0.100941
\(356\) 25603.0 3.81167
\(357\) 977.512 0.144917
\(358\) 15106.3 2.23014
\(359\) −5422.56 −0.797192 −0.398596 0.917127i \(-0.630502\pi\)
−0.398596 + 0.917127i \(0.630502\pi\)
\(360\) 827.094 0.121088
\(361\) −4656.49 −0.678887
\(362\) 22336.0 3.24297
\(363\) −3684.45 −0.532737
\(364\) −6080.43 −0.875552
\(365\) −1768.50 −0.253610
\(366\) 8936.79 1.27632
\(367\) −1346.75 −0.191552 −0.0957762 0.995403i \(-0.530533\pi\)
−0.0957762 + 0.995403i \(0.530533\pi\)
\(368\) 2928.80 0.414876
\(369\) 1813.44 0.255837
\(370\) 48.0916 0.00675720
\(371\) 5374.55 0.752110
\(372\) −2926.11 −0.407827
\(373\) −4622.11 −0.641618 −0.320809 0.947144i \(-0.603955\pi\)
−0.320809 + 0.947144i \(0.603955\pi\)
\(374\) 1534.67 0.212181
\(375\) −1253.77 −0.172652
\(376\) −7237.02 −0.992609
\(377\) −3071.93 −0.419661
\(378\) −1543.39 −0.210009
\(379\) 8654.75 1.17299 0.586497 0.809952i \(-0.300507\pi\)
0.586497 + 0.809952i \(0.300507\pi\)
\(380\) −1471.96 −0.198711
\(381\) −5980.19 −0.804133
\(382\) 11778.4 1.57758
\(383\) −2461.00 −0.328333 −0.164166 0.986433i \(-0.552493\pi\)
−0.164166 + 0.986433i \(0.552493\pi\)
\(384\) −2731.05 −0.362939
\(385\) 190.263 0.0251863
\(386\) −8682.48 −1.14489
\(387\) 4314.07 0.566658
\(388\) 11662.1 1.52592
\(389\) −8258.56 −1.07642 −0.538208 0.842812i \(-0.680898\pi\)
−0.538208 + 0.842812i \(0.680898\pi\)
\(390\) 772.390 0.100286
\(391\) −653.494 −0.0845234
\(392\) −11951.3 −1.53988
\(393\) 4557.91 0.585029
\(394\) 3559.87 0.455187
\(395\) 455.334 0.0580009
\(396\) −1692.89 −0.214825
\(397\) −4331.00 −0.547523 −0.273761 0.961798i \(-0.588268\pi\)
−0.273761 + 0.961798i \(0.588268\pi\)
\(398\) −7461.94 −0.939781
\(399\) 1562.00 0.195984
\(400\) −16077.1 −2.00964
\(401\) −2292.26 −0.285461 −0.142731 0.989762i \(-0.545588\pi\)
−0.142731 + 0.989762i \(0.545588\pi\)
\(402\) 808.429 0.100300
\(403\) −1553.94 −0.192078
\(404\) 10274.9 1.26534
\(405\) 136.974 0.0168057
\(406\) 5942.53 0.726411
\(407\) −55.9766 −0.00681734
\(408\) −4788.30 −0.581020
\(409\) −13032.9 −1.57563 −0.787817 0.615909i \(-0.788789\pi\)
−0.787817 + 0.615909i \(0.788789\pi\)
\(410\) 1755.60 0.211471
\(411\) 4790.49 0.574932
\(412\) 7442.41 0.889954
\(413\) −654.563 −0.0779878
\(414\) 1031.80 0.122488
\(415\) 294.441 0.0348278
\(416\) 7193.68 0.847834
\(417\) 1998.24 0.234662
\(418\) 2452.29 0.286951
\(419\) −3919.78 −0.457026 −0.228513 0.973541i \(-0.573386\pi\)
−0.228513 + 0.973541i \(0.573386\pi\)
\(420\) −1043.90 −0.121279
\(421\) 4905.30 0.567862 0.283931 0.958845i \(-0.408361\pi\)
0.283931 + 0.958845i \(0.408361\pi\)
\(422\) −25802.2 −2.97638
\(423\) −1198.52 −0.137763
\(424\) −26327.0 −3.01545
\(425\) 3587.24 0.409428
\(426\) 6171.49 0.701901
\(427\) −6414.29 −0.726954
\(428\) −2410.09 −0.272187
\(429\) −899.028 −0.101178
\(430\) 4176.47 0.468389
\(431\) 13528.1 1.51189 0.755947 0.654633i \(-0.227177\pi\)
0.755947 + 0.654633i \(0.227177\pi\)
\(432\) 3553.96 0.395810
\(433\) 15378.7 1.70683 0.853413 0.521236i \(-0.174529\pi\)
0.853413 + 0.521236i \(0.174529\pi\)
\(434\) 3006.05 0.332477
\(435\) −527.394 −0.0581301
\(436\) −23155.3 −2.54343
\(437\) −1044.24 −0.114308
\(438\) −16165.3 −1.76349
\(439\) 2929.73 0.318515 0.159258 0.987237i \(-0.449090\pi\)
0.159258 + 0.987237i \(0.449090\pi\)
\(440\) −931.996 −0.100980
\(441\) −1979.25 −0.213719
\(442\) −4471.60 −0.481204
\(443\) −5825.07 −0.624734 −0.312367 0.949961i \(-0.601122\pi\)
−0.312367 + 0.949961i \(0.601122\pi\)
\(444\) 307.121 0.0328273
\(445\) 2334.32 0.248668
\(446\) 6570.56 0.697590
\(447\) 5303.71 0.561201
\(448\) −2233.33 −0.235525
\(449\) −9997.96 −1.05085 −0.525426 0.850839i \(-0.676094\pi\)
−0.525426 + 0.850839i \(0.676094\pi\)
\(450\) −5663.87 −0.593327
\(451\) −2043.44 −0.213353
\(452\) 21810.0 2.26959
\(453\) −3159.76 −0.327723
\(454\) −6709.67 −0.693613
\(455\) −554.375 −0.0571198
\(456\) −7651.37 −0.785763
\(457\) −11063.7 −1.13246 −0.566232 0.824246i \(-0.691599\pi\)
−0.566232 + 0.824246i \(0.691599\pi\)
\(458\) −17309.0 −1.76594
\(459\) −792.985 −0.0806392
\(460\) 697.876 0.0707362
\(461\) 9657.22 0.975665 0.487832 0.872937i \(-0.337788\pi\)
0.487832 + 0.872937i \(0.337788\pi\)
\(462\) 1739.14 0.175134
\(463\) 2678.74 0.268880 0.134440 0.990922i \(-0.457076\pi\)
0.134440 + 0.990922i \(0.457076\pi\)
\(464\) −13683.9 −1.36909
\(465\) −266.784 −0.0266060
\(466\) −13447.9 −1.33683
\(467\) −1146.00 −0.113556 −0.0567781 0.998387i \(-0.518083\pi\)
−0.0567781 + 0.998387i \(0.518083\pi\)
\(468\) 4932.61 0.487201
\(469\) −580.242 −0.0571281
\(470\) −1160.29 −0.113873
\(471\) −142.586 −0.0139491
\(472\) 3206.35 0.312678
\(473\) −4861.24 −0.472558
\(474\) 4162.07 0.403313
\(475\) 5732.16 0.553704
\(476\) 6043.45 0.581935
\(477\) −4359.99 −0.418512
\(478\) −21830.7 −2.08894
\(479\) 18182.6 1.73441 0.867207 0.497948i \(-0.165913\pi\)
0.867207 + 0.497948i \(0.165913\pi\)
\(480\) 1235.02 0.117439
\(481\) 163.100 0.0154610
\(482\) −16304.2 −1.54074
\(483\) −740.562 −0.0697655
\(484\) −22779.0 −2.13928
\(485\) 1063.28 0.0995485
\(486\) 1252.04 0.116859
\(487\) 3231.33 0.300668 0.150334 0.988635i \(-0.451965\pi\)
0.150334 + 0.988635i \(0.451965\pi\)
\(488\) 31420.1 2.91459
\(489\) 9253.76 0.855766
\(490\) −1916.12 −0.176656
\(491\) 6518.84 0.599168 0.299584 0.954070i \(-0.403152\pi\)
0.299584 + 0.954070i \(0.403152\pi\)
\(492\) 11211.6 1.02735
\(493\) 3053.25 0.278927
\(494\) −7145.31 −0.650774
\(495\) −154.347 −0.0140149
\(496\) −6922.04 −0.626630
\(497\) −4429.52 −0.399781
\(498\) 2691.39 0.242177
\(499\) 14603.3 1.31009 0.655045 0.755590i \(-0.272650\pi\)
0.655045 + 0.755590i \(0.272650\pi\)
\(500\) −7751.42 −0.693308
\(501\) 11056.3 0.985945
\(502\) −33467.4 −2.97554
\(503\) −1522.39 −0.134950 −0.0674751 0.997721i \(-0.521494\pi\)
−0.0674751 + 0.997721i \(0.521494\pi\)
\(504\) −5426.26 −0.479573
\(505\) 936.802 0.0825488
\(506\) −1162.66 −0.102148
\(507\) −3971.48 −0.347889
\(508\) −36972.4 −3.22911
\(509\) 33.4888 0.00291624 0.00145812 0.999999i \(-0.499536\pi\)
0.00145812 + 0.999999i \(0.499536\pi\)
\(510\) −767.693 −0.0666549
\(511\) 11602.5 1.00443
\(512\) −25182.4 −2.17366
\(513\) −1267.14 −0.109055
\(514\) −22807.3 −1.95717
\(515\) 678.552 0.0580593
\(516\) 26671.7 2.27549
\(517\) 1350.53 0.114886
\(518\) −315.512 −0.0267622
\(519\) 1512.58 0.127929
\(520\) 2715.58 0.229012
\(521\) 12883.7 1.08339 0.541694 0.840576i \(-0.317783\pi\)
0.541694 + 0.840576i \(0.317783\pi\)
\(522\) −4820.75 −0.404211
\(523\) 14819.1 1.23899 0.619497 0.784999i \(-0.287337\pi\)
0.619497 + 0.784999i \(0.287337\pi\)
\(524\) 28179.2 2.34927
\(525\) 4065.18 0.337941
\(526\) 35026.2 2.90345
\(527\) 1544.49 0.127665
\(528\) −4004.72 −0.330081
\(529\) −11671.9 −0.959309
\(530\) −4220.92 −0.345934
\(531\) 531.000 0.0433963
\(532\) 9657.01 0.787001
\(533\) 5954.03 0.483861
\(534\) 21337.3 1.72913
\(535\) −219.737 −0.0177571
\(536\) 2842.29 0.229045
\(537\) 8795.64 0.706815
\(538\) 35523.4 2.84670
\(539\) 2230.28 0.178228
\(540\) 846.840 0.0674856
\(541\) −14334.6 −1.13917 −0.569585 0.821932i \(-0.692896\pi\)
−0.569585 + 0.821932i \(0.692896\pi\)
\(542\) 15129.3 1.19900
\(543\) 13005.2 1.02782
\(544\) −7149.93 −0.563512
\(545\) −2111.15 −0.165930
\(546\) −5067.37 −0.397186
\(547\) 23516.6 1.83820 0.919102 0.394019i \(-0.128915\pi\)
0.919102 + 0.394019i \(0.128915\pi\)
\(548\) 29617.1 2.30872
\(549\) 5203.45 0.404514
\(550\) 6382.23 0.494799
\(551\) 4878.87 0.377218
\(552\) 3627.61 0.279713
\(553\) −2987.28 −0.229715
\(554\) −38425.7 −2.94685
\(555\) 28.0014 0.00214161
\(556\) 12354.1 0.942320
\(557\) −2834.56 −0.215627 −0.107813 0.994171i \(-0.534385\pi\)
−0.107813 + 0.994171i \(0.534385\pi\)
\(558\) −2438.59 −0.185007
\(559\) 14164.3 1.07171
\(560\) −2469.46 −0.186346
\(561\) 893.561 0.0672481
\(562\) −28082.5 −2.10781
\(563\) −15215.1 −1.13897 −0.569484 0.822002i \(-0.692857\pi\)
−0.569484 + 0.822002i \(0.692857\pi\)
\(564\) −7409.80 −0.553207
\(565\) 1988.49 0.148065
\(566\) 15377.0 1.14195
\(567\) −898.638 −0.0665595
\(568\) 21697.8 1.60285
\(569\) −18473.2 −1.36105 −0.680526 0.732724i \(-0.738249\pi\)
−0.680526 + 0.732724i \(0.738249\pi\)
\(570\) −1226.72 −0.0901432
\(571\) 2472.87 0.181237 0.0906185 0.995886i \(-0.471116\pi\)
0.0906185 + 0.995886i \(0.471116\pi\)
\(572\) −5558.23 −0.406296
\(573\) 6858.00 0.499995
\(574\) −11517.9 −0.837537
\(575\) −2717.69 −0.197105
\(576\) 1811.74 0.131058
\(577\) 1987.70 0.143413 0.0717064 0.997426i \(-0.477156\pi\)
0.0717064 + 0.997426i \(0.477156\pi\)
\(578\) −20869.4 −1.50182
\(579\) −5055.38 −0.362857
\(580\) −3260.60 −0.233430
\(581\) −1931.72 −0.137937
\(582\) 9719.11 0.692217
\(583\) 4912.97 0.349013
\(584\) −56834.3 −4.02709
\(585\) 449.724 0.0317843
\(586\) 11282.6 0.795359
\(587\) 1325.75 0.0932192 0.0466096 0.998913i \(-0.485158\pi\)
0.0466096 + 0.998913i \(0.485158\pi\)
\(588\) −12236.7 −0.858218
\(589\) 2467.99 0.172652
\(590\) 514.064 0.0358706
\(591\) 2072.74 0.144266
\(592\) 726.530 0.0504395
\(593\) 23945.6 1.65822 0.829112 0.559083i \(-0.188847\pi\)
0.829112 + 0.559083i \(0.188847\pi\)
\(594\) −1410.84 −0.0974535
\(595\) 551.004 0.0379646
\(596\) 32790.1 2.25358
\(597\) −4344.72 −0.297852
\(598\) 3387.68 0.231660
\(599\) −21924.8 −1.49553 −0.747766 0.663962i \(-0.768874\pi\)
−0.747766 + 0.663962i \(0.768874\pi\)
\(600\) −19913.1 −1.35492
\(601\) −6361.22 −0.431746 −0.215873 0.976421i \(-0.569260\pi\)
−0.215873 + 0.976421i \(0.569260\pi\)
\(602\) −27400.3 −1.85507
\(603\) 470.708 0.0317889
\(604\) −19535.2 −1.31602
\(605\) −2076.85 −0.139564
\(606\) 8563.02 0.574008
\(607\) −4019.17 −0.268753 −0.134376 0.990930i \(-0.542903\pi\)
−0.134376 + 0.990930i \(0.542903\pi\)
\(608\) −11425.1 −0.762087
\(609\) 3460.04 0.230227
\(610\) 5037.49 0.334364
\(611\) −3935.06 −0.260549
\(612\) −4902.62 −0.323818
\(613\) 7840.19 0.516578 0.258289 0.966068i \(-0.416841\pi\)
0.258289 + 0.966068i \(0.416841\pi\)
\(614\) −44343.8 −2.91461
\(615\) 1022.20 0.0670229
\(616\) 6114.49 0.399935
\(617\) 1831.09 0.119476 0.0597382 0.998214i \(-0.480973\pi\)
0.0597382 + 0.998214i \(0.480973\pi\)
\(618\) 6202.43 0.403719
\(619\) 7868.38 0.510916 0.255458 0.966820i \(-0.417774\pi\)
0.255458 + 0.966820i \(0.417774\pi\)
\(620\) −1649.39 −0.106840
\(621\) 600.765 0.0388210
\(622\) 3902.42 0.251564
\(623\) −15314.6 −0.984858
\(624\) 11668.6 0.748589
\(625\) 14560.8 0.931893
\(626\) −11194.8 −0.714751
\(627\) 1427.85 0.0909454
\(628\) −881.536 −0.0560145
\(629\) −162.109 −0.0102761
\(630\) −869.975 −0.0550169
\(631\) −4830.13 −0.304730 −0.152365 0.988324i \(-0.548689\pi\)
−0.152365 + 0.988324i \(0.548689\pi\)
\(632\) 14633.1 0.921000
\(633\) −15023.4 −0.943325
\(634\) −34968.5 −2.19050
\(635\) −3370.91 −0.210662
\(636\) −26955.5 −1.68059
\(637\) −6498.43 −0.404203
\(638\) 5432.17 0.337088
\(639\) 3593.35 0.222458
\(640\) −1539.44 −0.0950808
\(641\) 5637.67 0.347386 0.173693 0.984800i \(-0.444430\pi\)
0.173693 + 0.984800i \(0.444430\pi\)
\(642\) −2008.54 −0.123475
\(643\) −16485.8 −1.01110 −0.505548 0.862798i \(-0.668710\pi\)
−0.505548 + 0.862798i \(0.668710\pi\)
\(644\) −4578.51 −0.280153
\(645\) 2431.75 0.148450
\(646\) 7101.85 0.432537
\(647\) 9709.68 0.589995 0.294998 0.955498i \(-0.404681\pi\)
0.294998 + 0.955498i \(0.404681\pi\)
\(648\) 4401.94 0.266859
\(649\) −598.348 −0.0361899
\(650\) −18596.1 −1.12215
\(651\) 1750.27 0.105374
\(652\) 57211.2 3.43645
\(653\) −21099.7 −1.26446 −0.632231 0.774780i \(-0.717861\pi\)
−0.632231 + 0.774780i \(0.717861\pi\)
\(654\) −19297.4 −1.15380
\(655\) 2569.20 0.153263
\(656\) 26522.2 1.57853
\(657\) −9412.27 −0.558916
\(658\) 7612.23 0.450997
\(659\) 18800.6 1.11133 0.555665 0.831407i \(-0.312464\pi\)
0.555665 + 0.831407i \(0.312464\pi\)
\(660\) −954.247 −0.0562788
\(661\) −11341.7 −0.667384 −0.333692 0.942682i \(-0.608295\pi\)
−0.333692 + 0.942682i \(0.608295\pi\)
\(662\) −14644.7 −0.859792
\(663\) −2603.59 −0.152511
\(664\) 9462.45 0.553033
\(665\) 880.465 0.0513428
\(666\) 255.952 0.0148918
\(667\) −2313.14 −0.134280
\(668\) 68355.3 3.95920
\(669\) 3825.71 0.221092
\(670\) 455.695 0.0262762
\(671\) −5863.42 −0.337339
\(672\) −8102.54 −0.465123
\(673\) 29906.1 1.71292 0.856460 0.516214i \(-0.172659\pi\)
0.856460 + 0.516214i \(0.172659\pi\)
\(674\) −33735.9 −1.92798
\(675\) −3297.79 −0.188047
\(676\) −24553.6 −1.39700
\(677\) 7445.33 0.422670 0.211335 0.977414i \(-0.432219\pi\)
0.211335 + 0.977414i \(0.432219\pi\)
\(678\) 18176.2 1.02958
\(679\) −6975.79 −0.394266
\(680\) −2699.07 −0.152212
\(681\) −3906.71 −0.219832
\(682\) 2747.88 0.154284
\(683\) −6445.33 −0.361089 −0.180544 0.983567i \(-0.557786\pi\)
−0.180544 + 0.983567i \(0.557786\pi\)
\(684\) −7834.04 −0.437927
\(685\) 2700.30 0.150618
\(686\) 32177.7 1.79089
\(687\) −10078.2 −0.559691
\(688\) 63094.8 3.49632
\(689\) −14315.1 −0.791524
\(690\) 581.603 0.0320888
\(691\) −3347.76 −0.184305 −0.0921525 0.995745i \(-0.529375\pi\)
−0.0921525 + 0.995745i \(0.529375\pi\)
\(692\) 9351.52 0.513716
\(693\) 1012.61 0.0555065
\(694\) −181.847 −0.00994643
\(695\) 1126.37 0.0614756
\(696\) −16948.9 −0.923053
\(697\) −5917.82 −0.321598
\(698\) 55089.6 2.98735
\(699\) −7830.06 −0.423691
\(700\) 25132.9 1.35705
\(701\) −4893.37 −0.263652 −0.131826 0.991273i \(-0.542084\pi\)
−0.131826 + 0.991273i \(0.542084\pi\)
\(702\) 4110.79 0.221014
\(703\) −259.038 −0.0138973
\(704\) −2041.53 −0.109294
\(705\) −675.579 −0.0360905
\(706\) −44629.7 −2.37912
\(707\) −6146.02 −0.326938
\(708\) 3282.90 0.174264
\(709\) 11964.9 0.633782 0.316891 0.948462i \(-0.397361\pi\)
0.316891 + 0.948462i \(0.397361\pi\)
\(710\) 3478.74 0.183880
\(711\) 2423.37 0.127825
\(712\) 75017.9 3.94861
\(713\) −1170.11 −0.0614598
\(714\) 5036.55 0.263989
\(715\) −506.764 −0.0265061
\(716\) 54378.9 2.83831
\(717\) −12711.0 −0.662063
\(718\) −27939.3 −1.45221
\(719\) 25587.9 1.32722 0.663608 0.748081i \(-0.269024\pi\)
0.663608 + 0.748081i \(0.269024\pi\)
\(720\) 2003.30 0.103692
\(721\) −4451.73 −0.229946
\(722\) −23992.2 −1.23670
\(723\) −9493.15 −0.488318
\(724\) 80404.2 4.12734
\(725\) 12697.5 0.650448
\(726\) −18983.8 −0.970463
\(727\) −18321.4 −0.934667 −0.467334 0.884081i \(-0.654785\pi\)
−0.467334 + 0.884081i \(0.654785\pi\)
\(728\) −17815.9 −0.907009
\(729\) 729.000 0.0370370
\(730\) −9112.07 −0.461990
\(731\) −14078.2 −0.712312
\(732\) 32170.2 1.62438
\(733\) −11139.1 −0.561298 −0.280649 0.959810i \(-0.590550\pi\)
−0.280649 + 0.959810i \(0.590550\pi\)
\(734\) −6939.02 −0.348943
\(735\) −1115.66 −0.0559889
\(736\) 5416.78 0.271284
\(737\) −530.410 −0.0265100
\(738\) 9343.61 0.466047
\(739\) −16786.9 −0.835610 −0.417805 0.908537i \(-0.637200\pi\)
−0.417805 + 0.908537i \(0.637200\pi\)
\(740\) 173.118 0.00859993
\(741\) −4160.36 −0.206254
\(742\) 27692.0 1.37009
\(743\) 35364.4 1.74615 0.873077 0.487582i \(-0.162121\pi\)
0.873077 + 0.487582i \(0.162121\pi\)
\(744\) −8573.63 −0.422479
\(745\) 2989.59 0.147020
\(746\) −23815.0 −1.16881
\(747\) 1567.07 0.0767549
\(748\) 5524.43 0.270044
\(749\) 1441.61 0.0703276
\(750\) −6459.96 −0.314513
\(751\) −14920.5 −0.724977 −0.362488 0.931988i \(-0.618073\pi\)
−0.362488 + 0.931988i \(0.618073\pi\)
\(752\) −17528.7 −0.850009
\(753\) −19486.4 −0.943059
\(754\) −15827.9 −0.764478
\(755\) −1781.09 −0.0858551
\(756\) −5555.81 −0.267279
\(757\) −17934.5 −0.861083 −0.430541 0.902571i \(-0.641677\pi\)
−0.430541 + 0.902571i \(0.641677\pi\)
\(758\) 44592.9 2.13679
\(759\) −676.961 −0.0323744
\(760\) −4312.92 −0.205850
\(761\) −11900.1 −0.566858 −0.283429 0.958993i \(-0.591472\pi\)
−0.283429 + 0.958993i \(0.591472\pi\)
\(762\) −30812.5 −1.46485
\(763\) 13850.5 0.657171
\(764\) 42399.4 2.00780
\(765\) −446.989 −0.0211254
\(766\) −12680.1 −0.598109
\(767\) 1743.42 0.0820747
\(768\) −18902.9 −0.888149
\(769\) −3012.80 −0.141280 −0.0706400 0.997502i \(-0.522504\pi\)
−0.0706400 + 0.997502i \(0.522504\pi\)
\(770\) 980.317 0.0458807
\(771\) −13279.5 −0.620299
\(772\) −31254.8 −1.45710
\(773\) 24647.7 1.14685 0.573427 0.819257i \(-0.305614\pi\)
0.573427 + 0.819257i \(0.305614\pi\)
\(774\) 22227.9 1.03226
\(775\) 6423.09 0.297709
\(776\) 34170.6 1.58074
\(777\) −183.707 −0.00848192
\(778\) −42551.6 −1.96086
\(779\) −9456.27 −0.434924
\(780\) 2780.41 0.127634
\(781\) −4049.11 −0.185517
\(782\) −3367.08 −0.153973
\(783\) −2806.88 −0.128110
\(784\) −28947.2 −1.31866
\(785\) −80.3729 −0.00365431
\(786\) 23484.3 1.06572
\(787\) 16431.2 0.744230 0.372115 0.928187i \(-0.378633\pi\)
0.372115 + 0.928187i \(0.378633\pi\)
\(788\) 12814.7 0.579319
\(789\) 20394.0 0.920212
\(790\) 2346.07 0.105658
\(791\) −13045.8 −0.586415
\(792\) −4960.24 −0.222544
\(793\) 17084.4 0.765050
\(794\) −22315.1 −0.997398
\(795\) −2457.64 −0.109639
\(796\) −26861.1 −1.19606
\(797\) −2015.52 −0.0895776 −0.0447888 0.998996i \(-0.514261\pi\)
−0.0447888 + 0.998996i \(0.514261\pi\)
\(798\) 8048.06 0.357015
\(799\) 3911.13 0.173174
\(800\) −29734.4 −1.31409
\(801\) 12423.6 0.548024
\(802\) −11810.7 −0.520012
\(803\) 10606.1 0.466102
\(804\) 2910.15 0.127653
\(805\) −417.440 −0.0182768
\(806\) −8006.57 −0.349900
\(807\) 20683.5 0.902224
\(808\) 30106.0 1.31080
\(809\) 5483.10 0.238289 0.119144 0.992877i \(-0.461985\pi\)
0.119144 + 0.992877i \(0.461985\pi\)
\(810\) 705.749 0.0306142
\(811\) −12029.9 −0.520870 −0.260435 0.965491i \(-0.583866\pi\)
−0.260435 + 0.965491i \(0.583866\pi\)
\(812\) 21391.6 0.924507
\(813\) 8809.06 0.380009
\(814\) −288.415 −0.0124188
\(815\) 5216.15 0.224189
\(816\) −11597.7 −0.497549
\(817\) −22495.9 −0.963321
\(818\) −67150.9 −2.87026
\(819\) −2950.48 −0.125883
\(820\) 6319.73 0.269140
\(821\) 13978.8 0.594230 0.297115 0.954842i \(-0.403975\pi\)
0.297115 + 0.954842i \(0.403975\pi\)
\(822\) 24682.6 1.04733
\(823\) −7223.95 −0.305967 −0.152984 0.988229i \(-0.548888\pi\)
−0.152984 + 0.988229i \(0.548888\pi\)
\(824\) 21806.6 0.921928
\(825\) 3716.06 0.156820
\(826\) −3372.59 −0.142067
\(827\) −34864.4 −1.46597 −0.732983 0.680247i \(-0.761872\pi\)
−0.732983 + 0.680247i \(0.761872\pi\)
\(828\) 3714.22 0.155891
\(829\) −14737.1 −0.617420 −0.308710 0.951156i \(-0.599897\pi\)
−0.308710 + 0.951156i \(0.599897\pi\)
\(830\) 1517.08 0.0634443
\(831\) −22373.4 −0.933964
\(832\) 5948.46 0.247867
\(833\) 6458.91 0.268653
\(834\) 10295.8 0.427474
\(835\) 6232.20 0.258293
\(836\) 8827.65 0.365204
\(837\) −1419.87 −0.0586355
\(838\) −20196.4 −0.832544
\(839\) −33895.2 −1.39475 −0.697374 0.716708i \(-0.745648\pi\)
−0.697374 + 0.716708i \(0.745648\pi\)
\(840\) −3058.67 −0.125636
\(841\) −13581.6 −0.556874
\(842\) 25274.2 1.03445
\(843\) −16351.1 −0.668043
\(844\) −92881.7 −3.78806
\(845\) −2238.64 −0.0911380
\(846\) −6175.26 −0.250957
\(847\) 13625.5 0.552746
\(848\) −63766.4 −2.58225
\(849\) 8953.25 0.361926
\(850\) 18483.0 0.745836
\(851\) 122.813 0.00494710
\(852\) 22215.8 0.893313
\(853\) −36174.1 −1.45202 −0.726012 0.687682i \(-0.758629\pi\)
−0.726012 + 0.687682i \(0.758629\pi\)
\(854\) −33049.1 −1.32426
\(855\) −714.258 −0.0285697
\(856\) −7061.67 −0.281966
\(857\) 20528.3 0.818241 0.409120 0.912480i \(-0.365836\pi\)
0.409120 + 0.912480i \(0.365836\pi\)
\(858\) −4632.17 −0.184312
\(859\) 1704.21 0.0676912 0.0338456 0.999427i \(-0.489225\pi\)
0.0338456 + 0.999427i \(0.489225\pi\)
\(860\) 15034.3 0.596122
\(861\) −6706.28 −0.265446
\(862\) 69702.6 2.75415
\(863\) 39538.0 1.55955 0.779773 0.626063i \(-0.215335\pi\)
0.779773 + 0.626063i \(0.215335\pi\)
\(864\) 6573.01 0.258818
\(865\) 852.612 0.0335141
\(866\) 79237.8 3.10925
\(867\) −12151.2 −0.475984
\(868\) 10821.0 0.423145
\(869\) −2730.73 −0.106598
\(870\) −2717.36 −0.105893
\(871\) 1545.47 0.0601219
\(872\) −67846.0 −2.63481
\(873\) 5658.96 0.219389
\(874\) −5380.36 −0.208230
\(875\) 4636.57 0.179137
\(876\) −58191.2 −2.24441
\(877\) 25216.9 0.970938 0.485469 0.874254i \(-0.338649\pi\)
0.485469 + 0.874254i \(0.338649\pi\)
\(878\) 15095.2 0.580226
\(879\) 6569.31 0.252079
\(880\) −2257.38 −0.0864730
\(881\) −35122.3 −1.34313 −0.671567 0.740944i \(-0.734378\pi\)
−0.671567 + 0.740944i \(0.734378\pi\)
\(882\) −10197.9 −0.389322
\(883\) 20139.2 0.767539 0.383770 0.923429i \(-0.374626\pi\)
0.383770 + 0.923429i \(0.374626\pi\)
\(884\) −16096.7 −0.612431
\(885\) 299.314 0.0113687
\(886\) −30013.2 −1.13805
\(887\) 35541.7 1.34540 0.672702 0.739914i \(-0.265134\pi\)
0.672702 + 0.739914i \(0.265134\pi\)
\(888\) 899.880 0.0340068
\(889\) 22115.3 0.834336
\(890\) 12027.4 0.452987
\(891\) −821.461 −0.0308866
\(892\) 23652.4 0.887826
\(893\) 6249.72 0.234198
\(894\) 27326.9 1.02232
\(895\) 4957.92 0.185168
\(896\) 10099.7 0.376571
\(897\) 1972.48 0.0734216
\(898\) −51513.7 −1.91429
\(899\) 5466.95 0.202818
\(900\) −20388.5 −0.755131
\(901\) 14228.0 0.526086
\(902\) −10528.7 −0.388655
\(903\) −15953.9 −0.587941
\(904\) 63904.2 2.35113
\(905\) 7330.74 0.269262
\(906\) −16280.4 −0.596999
\(907\) −5257.49 −0.192472 −0.0962360 0.995359i \(-0.530680\pi\)
−0.0962360 + 0.995359i \(0.530680\pi\)
\(908\) −24153.1 −0.882765
\(909\) 4985.82 0.181924
\(910\) −2856.37 −0.104053
\(911\) −25638.3 −0.932419 −0.466210 0.884674i \(-0.654381\pi\)
−0.466210 + 0.884674i \(0.654381\pi\)
\(912\) −18532.3 −0.672879
\(913\) −1765.82 −0.0640089
\(914\) −57004.6 −2.06296
\(915\) 2933.08 0.105972
\(916\) −62308.3 −2.24752
\(917\) −16855.6 −0.607002
\(918\) −4085.79 −0.146897
\(919\) 40415.4 1.45069 0.725344 0.688387i \(-0.241681\pi\)
0.725344 + 0.688387i \(0.241681\pi\)
\(920\) 2044.81 0.0732776
\(921\) −25819.2 −0.923748
\(922\) 49758.1 1.77733
\(923\) 11798.0 0.420732
\(924\) 6260.47 0.222894
\(925\) −674.162 −0.0239636
\(926\) 13802.0 0.489807
\(927\) 3611.37 0.127954
\(928\) −25308.2 −0.895239
\(929\) 22855.5 0.807176 0.403588 0.914941i \(-0.367763\pi\)
0.403588 + 0.914941i \(0.367763\pi\)
\(930\) −1374.58 −0.0484671
\(931\) 10320.9 0.363323
\(932\) −48409.2 −1.70139
\(933\) 2272.19 0.0797299
\(934\) −5904.70 −0.206860
\(935\) 503.682 0.0176173
\(936\) 14452.8 0.504705
\(937\) −17288.6 −0.602770 −0.301385 0.953503i \(-0.597449\pi\)
−0.301385 + 0.953503i \(0.597449\pi\)
\(938\) −2989.65 −0.104068
\(939\) −6518.17 −0.226531
\(940\) −4176.75 −0.144926
\(941\) 31998.0 1.10851 0.554253 0.832348i \(-0.313004\pi\)
0.554253 + 0.832348i \(0.313004\pi\)
\(942\) −734.664 −0.0254104
\(943\) 4483.34 0.154822
\(944\) 7766.06 0.267758
\(945\) −506.544 −0.0174369
\(946\) −25047.1 −0.860838
\(947\) −13177.3 −0.452170 −0.226085 0.974108i \(-0.572593\pi\)
−0.226085 + 0.974108i \(0.572593\pi\)
\(948\) 14982.4 0.513298
\(949\) −30903.1 −1.05707
\(950\) 29534.5 1.00866
\(951\) −20360.5 −0.694251
\(952\) 17707.6 0.602843
\(953\) 35095.6 1.19292 0.596462 0.802641i \(-0.296573\pi\)
0.596462 + 0.802641i \(0.296573\pi\)
\(954\) −22464.5 −0.762384
\(955\) 3865.71 0.130986
\(956\) −78585.3 −2.65861
\(957\) 3162.89 0.106836
\(958\) 93684.4 3.15951
\(959\) −17715.7 −0.596527
\(960\) 1021.24 0.0343338
\(961\) −27025.5 −0.907171
\(962\) 840.362 0.0281646
\(963\) −1169.48 −0.0391338
\(964\) −58691.2 −1.96091
\(965\) −2849.61 −0.0950594
\(966\) −3815.69 −0.127089
\(967\) −556.001 −0.0184900 −0.00924498 0.999957i \(-0.502943\pi\)
−0.00924498 + 0.999957i \(0.502943\pi\)
\(968\) −66743.7 −2.21614
\(969\) 4135.06 0.137087
\(970\) 5478.47 0.181343
\(971\) −46251.0 −1.52859 −0.764297 0.644865i \(-0.776914\pi\)
−0.764297 + 0.644865i \(0.776914\pi\)
\(972\) 4507.03 0.148727
\(973\) −7389.68 −0.243476
\(974\) 16649.2 0.547714
\(975\) −10827.6 −0.355651
\(976\) 76102.3 2.49588
\(977\) 29081.6 0.952306 0.476153 0.879362i \(-0.342031\pi\)
0.476153 + 0.879362i \(0.342031\pi\)
\(978\) 47679.3 1.55891
\(979\) −13999.4 −0.457019
\(980\) −6897.57 −0.224831
\(981\) −11235.9 −0.365683
\(982\) 33587.8 1.09148
\(983\) −43019.6 −1.39584 −0.697920 0.716175i \(-0.745891\pi\)
−0.697920 + 0.716175i \(0.745891\pi\)
\(984\) 32850.4 1.06426
\(985\) 1168.36 0.0377940
\(986\) 15731.6 0.508110
\(987\) 4432.23 0.142938
\(988\) −25721.3 −0.828244
\(989\) 10665.6 0.342919
\(990\) −795.260 −0.0255303
\(991\) −19398.1 −0.621798 −0.310899 0.950443i \(-0.600630\pi\)
−0.310899 + 0.950443i \(0.600630\pi\)
\(992\) −12802.2 −0.409749
\(993\) −8526.88 −0.272500
\(994\) −22822.8 −0.728264
\(995\) −2449.03 −0.0780295
\(996\) 9688.36 0.308220
\(997\) 48069.8 1.52697 0.763484 0.645827i \(-0.223487\pi\)
0.763484 + 0.645827i \(0.223487\pi\)
\(998\) 75242.5 2.38653
\(999\) 149.028 0.00471976
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.1.8 8
3.2 odd 2 531.4.a.e.1.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.4.a.d.1.8 8 1.1 even 1 trivial
531.4.a.e.1.1 8 3.2 odd 2