Properties

Label 177.4.a.a.1.7
Level $177$
Weight $4$
Character 177.1
Self dual yes
Analytic conductor $10.443$
Analytic rank $1$
Dimension $7$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(10.4433380710\)
Analytic rank: \(1\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
Defining polynomial: \(x^{7} - x^{6} - 34 x^{5} + 25 x^{4} + 315 x^{3} - 146 x^{2} - 736 x + 512\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(-4.44426\) of defining polynomial
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+3.44426 q^{2} +3.00000 q^{3} +3.86292 q^{4} -20.9057 q^{5} +10.3328 q^{6} -30.0572 q^{7} -14.2492 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q+3.44426 q^{2} +3.00000 q^{3} +3.86292 q^{4} -20.9057 q^{5} +10.3328 q^{6} -30.0572 q^{7} -14.2492 q^{8} +9.00000 q^{9} -72.0046 q^{10} +51.2171 q^{11} +11.5888 q^{12} -22.3086 q^{13} -103.525 q^{14} -62.7171 q^{15} -79.9812 q^{16} -89.1524 q^{17} +30.9983 q^{18} +96.6448 q^{19} -80.7571 q^{20} -90.1715 q^{21} +176.405 q^{22} +76.1937 q^{23} -42.7475 q^{24} +312.048 q^{25} -76.8365 q^{26} +27.0000 q^{27} -116.108 q^{28} -71.5601 q^{29} -216.014 q^{30} -129.288 q^{31} -161.483 q^{32} +153.651 q^{33} -307.064 q^{34} +628.366 q^{35} +34.7663 q^{36} -108.382 q^{37} +332.870 q^{38} -66.9257 q^{39} +297.889 q^{40} -357.190 q^{41} -310.574 q^{42} -237.327 q^{43} +197.848 q^{44} -188.151 q^{45} +262.431 q^{46} +97.2732 q^{47} -239.944 q^{48} +560.433 q^{49} +1074.77 q^{50} -267.457 q^{51} -86.1763 q^{52} -705.515 q^{53} +92.9950 q^{54} -1070.73 q^{55} +428.290 q^{56} +289.934 q^{57} -246.471 q^{58} -59.0000 q^{59} -242.271 q^{60} -549.755 q^{61} -445.302 q^{62} -270.514 q^{63} +83.6615 q^{64} +466.376 q^{65} +529.215 q^{66} +652.131 q^{67} -344.389 q^{68} +228.581 q^{69} +2164.25 q^{70} -37.3589 q^{71} -128.243 q^{72} -600.093 q^{73} -373.297 q^{74} +936.144 q^{75} +373.331 q^{76} -1539.44 q^{77} -230.510 q^{78} +1221.13 q^{79} +1672.06 q^{80} +81.0000 q^{81} -1230.26 q^{82} -577.079 q^{83} -348.325 q^{84} +1863.79 q^{85} -817.417 q^{86} -214.680 q^{87} -729.802 q^{88} -375.999 q^{89} -648.042 q^{90} +670.532 q^{91} +294.330 q^{92} -387.864 q^{93} +335.034 q^{94} -2020.43 q^{95} -484.448 q^{96} +322.400 q^{97} +1930.28 q^{98} +460.954 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q - 8q^{2} + 21q^{3} + 22q^{4} - 28q^{5} - 24q^{6} - 59q^{7} - 117q^{8} + 63q^{9} + O(q^{10}) \) \( 7q - 8q^{2} + 21q^{3} + 22q^{4} - 28q^{5} - 24q^{6} - 59q^{7} - 117q^{8} + 63q^{9} - 79q^{10} - 131q^{11} + 66q^{12} - 123q^{13} - 117q^{14} - 84q^{15} + 202q^{16} - 235q^{17} - 72q^{18} - 80q^{19} + 61q^{20} - 177q^{21} + 688q^{22} - 274q^{23} - 351q^{24} + 193q^{25} - 180q^{26} + 189q^{27} - 118q^{28} - 406q^{29} - 237q^{30} - 346q^{31} - 854q^{32} - 393q^{33} + 178q^{34} - 424q^{35} + 198q^{36} - 157q^{37} - 129q^{38} - 369q^{39} - 590q^{40} - 825q^{41} - 351q^{42} - 815q^{43} - 1690q^{44} - 252q^{45} + 1457q^{46} - 1196q^{47} + 606q^{48} + 914q^{49} + 713q^{50} - 705q^{51} + 1030q^{52} - 900q^{53} - 216q^{54} - 1044q^{55} + 2172q^{56} - 240q^{57} + 1242q^{58} - 413q^{59} + 183q^{60} + 420q^{61} + 646q^{62} - 531q^{63} + 3541q^{64} + 190q^{65} + 2064q^{66} + 1316q^{67} - 611q^{68} - 822q^{69} + 4658q^{70} - 173q^{71} - 1053q^{72} - 418q^{73} + 660q^{74} + 579q^{75} + 1540q^{76} - 753q^{77} - 540q^{78} + 2635q^{79} + 6155q^{80} + 567q^{81} - 125q^{82} + 457q^{83} - 354q^{84} + 1270q^{85} + 3482q^{86} - 1218q^{87} + 7685q^{88} + 592q^{89} - 711q^{90} + 3179q^{91} - 3500q^{92} - 1038q^{93} + 2064q^{94} - 2250q^{95} - 2562q^{96} - 1906q^{97} + 2994q^{98} - 1179q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.44426 1.21773 0.608865 0.793274i \(-0.291625\pi\)
0.608865 + 0.793274i \(0.291625\pi\)
\(3\) 3.00000 0.577350
\(4\) 3.86292 0.482865
\(5\) −20.9057 −1.86986 −0.934931 0.354830i \(-0.884539\pi\)
−0.934931 + 0.354830i \(0.884539\pi\)
\(6\) 10.3328 0.703056
\(7\) −30.0572 −1.62293 −0.811467 0.584398i \(-0.801331\pi\)
−0.811467 + 0.584398i \(0.801331\pi\)
\(8\) −14.2492 −0.629730
\(9\) 9.00000 0.333333
\(10\) −72.0046 −2.27699
\(11\) 51.2171 1.40387 0.701934 0.712242i \(-0.252320\pi\)
0.701934 + 0.712242i \(0.252320\pi\)
\(12\) 11.5888 0.278782
\(13\) −22.3086 −0.475945 −0.237973 0.971272i \(-0.576483\pi\)
−0.237973 + 0.971272i \(0.576483\pi\)
\(14\) −103.525 −1.97629
\(15\) −62.7171 −1.07957
\(16\) −79.9812 −1.24971
\(17\) −89.1524 −1.27192 −0.635960 0.771722i \(-0.719395\pi\)
−0.635960 + 0.771722i \(0.719395\pi\)
\(18\) 30.9983 0.405910
\(19\) 96.6448 1.16694 0.583469 0.812135i \(-0.301695\pi\)
0.583469 + 0.812135i \(0.301695\pi\)
\(20\) −80.7571 −0.902891
\(21\) −90.1715 −0.937001
\(22\) 176.405 1.70953
\(23\) 76.1937 0.690760 0.345380 0.938463i \(-0.387750\pi\)
0.345380 + 0.938463i \(0.387750\pi\)
\(24\) −42.7475 −0.363575
\(25\) 312.048 2.49638
\(26\) −76.8365 −0.579572
\(27\) 27.0000 0.192450
\(28\) −116.108 −0.783658
\(29\) −71.5601 −0.458220 −0.229110 0.973401i \(-0.573581\pi\)
−0.229110 + 0.973401i \(0.573581\pi\)
\(30\) −216.014 −1.31462
\(31\) −129.288 −0.749059 −0.374530 0.927215i \(-0.622196\pi\)
−0.374530 + 0.927215i \(0.622196\pi\)
\(32\) −161.483 −0.892074
\(33\) 153.651 0.810524
\(34\) −307.064 −1.54885
\(35\) 628.366 3.03466
\(36\) 34.7663 0.160955
\(37\) −108.382 −0.481567 −0.240783 0.970579i \(-0.577404\pi\)
−0.240783 + 0.970579i \(0.577404\pi\)
\(38\) 332.870 1.42102
\(39\) −66.9257 −0.274787
\(40\) 297.889 1.17751
\(41\) −357.190 −1.36058 −0.680290 0.732943i \(-0.738146\pi\)
−0.680290 + 0.732943i \(0.738146\pi\)
\(42\) −310.574 −1.14101
\(43\) −237.327 −0.841676 −0.420838 0.907136i \(-0.638264\pi\)
−0.420838 + 0.907136i \(0.638264\pi\)
\(44\) 197.848 0.677879
\(45\) −188.151 −0.623287
\(46\) 262.431 0.841159
\(47\) 97.2732 0.301889 0.150944 0.988542i \(-0.451769\pi\)
0.150944 + 0.988542i \(0.451769\pi\)
\(48\) −239.944 −0.721518
\(49\) 560.433 1.63392
\(50\) 1074.77 3.03992
\(51\) −267.457 −0.734343
\(52\) −86.1763 −0.229817
\(53\) −705.515 −1.82849 −0.914245 0.405162i \(-0.867215\pi\)
−0.914245 + 0.405162i \(0.867215\pi\)
\(54\) 92.9950 0.234352
\(55\) −1070.73 −2.62504
\(56\) 428.290 1.02201
\(57\) 289.934 0.673733
\(58\) −246.471 −0.557988
\(59\) −59.0000 −0.130189
\(60\) −242.271 −0.521285
\(61\) −549.755 −1.15392 −0.576958 0.816774i \(-0.695760\pi\)
−0.576958 + 0.816774i \(0.695760\pi\)
\(62\) −445.302 −0.912152
\(63\) −270.514 −0.540978
\(64\) 83.6615 0.163401
\(65\) 466.376 0.889951
\(66\) 529.215 0.986999
\(67\) 652.131 1.18911 0.594555 0.804055i \(-0.297328\pi\)
0.594555 + 0.804055i \(0.297328\pi\)
\(68\) −344.389 −0.614166
\(69\) 228.581 0.398811
\(70\) 2164.25 3.69540
\(71\) −37.3589 −0.0624463 −0.0312232 0.999512i \(-0.509940\pi\)
−0.0312232 + 0.999512i \(0.509940\pi\)
\(72\) −128.243 −0.209910
\(73\) −600.093 −0.962131 −0.481066 0.876685i \(-0.659750\pi\)
−0.481066 + 0.876685i \(0.659750\pi\)
\(74\) −373.297 −0.586418
\(75\) 936.144 1.44129
\(76\) 373.331 0.563474
\(77\) −1539.44 −2.27839
\(78\) −230.510 −0.334616
\(79\) 1221.13 1.73909 0.869546 0.493851i \(-0.164411\pi\)
0.869546 + 0.493851i \(0.164411\pi\)
\(80\) 1672.06 2.33678
\(81\) 81.0000 0.111111
\(82\) −1230.26 −1.65682
\(83\) −577.079 −0.763164 −0.381582 0.924335i \(-0.624621\pi\)
−0.381582 + 0.924335i \(0.624621\pi\)
\(84\) −348.325 −0.452445
\(85\) 1863.79 2.37831
\(86\) −817.417 −1.02493
\(87\) −214.680 −0.264553
\(88\) −729.802 −0.884058
\(89\) −375.999 −0.447818 −0.223909 0.974610i \(-0.571882\pi\)
−0.223909 + 0.974610i \(0.571882\pi\)
\(90\) −648.042 −0.758995
\(91\) 670.532 0.772427
\(92\) 294.330 0.333544
\(93\) −387.864 −0.432470
\(94\) 335.034 0.367619
\(95\) −2020.43 −2.18201
\(96\) −484.448 −0.515039
\(97\) 322.400 0.337472 0.168736 0.985661i \(-0.446032\pi\)
0.168736 + 0.985661i \(0.446032\pi\)
\(98\) 1930.28 1.98967
\(99\) 460.954 0.467956
\(100\) 1205.42 1.20542
\(101\) 657.772 0.648027 0.324014 0.946052i \(-0.394968\pi\)
0.324014 + 0.946052i \(0.394968\pi\)
\(102\) −921.192 −0.894231
\(103\) 1003.17 0.959667 0.479834 0.877359i \(-0.340697\pi\)
0.479834 + 0.877359i \(0.340697\pi\)
\(104\) 317.879 0.299717
\(105\) 1885.10 1.75206
\(106\) −2429.98 −2.22661
\(107\) −882.607 −0.797428 −0.398714 0.917075i \(-0.630543\pi\)
−0.398714 + 0.917075i \(0.630543\pi\)
\(108\) 104.299 0.0929275
\(109\) 608.066 0.534332 0.267166 0.963651i \(-0.413913\pi\)
0.267166 + 0.963651i \(0.413913\pi\)
\(110\) −3687.87 −3.19659
\(111\) −325.147 −0.278033
\(112\) 2404.01 2.02819
\(113\) 373.130 0.310629 0.155315 0.987865i \(-0.450361\pi\)
0.155315 + 0.987865i \(0.450361\pi\)
\(114\) 998.609 0.820424
\(115\) −1592.88 −1.29163
\(116\) −276.431 −0.221258
\(117\) −200.777 −0.158648
\(118\) −203.211 −0.158535
\(119\) 2679.67 2.06424
\(120\) 893.666 0.679835
\(121\) 1292.20 0.970846
\(122\) −1893.50 −1.40516
\(123\) −1071.57 −0.785531
\(124\) −499.430 −0.361695
\(125\) −3910.37 −2.79803
\(126\) −931.722 −0.658765
\(127\) 626.337 0.437625 0.218813 0.975767i \(-0.429782\pi\)
0.218813 + 0.975767i \(0.429782\pi\)
\(128\) 1580.01 1.09105
\(129\) −711.982 −0.485942
\(130\) 1606.32 1.08372
\(131\) 1191.46 0.794641 0.397320 0.917680i \(-0.369940\pi\)
0.397320 + 0.917680i \(0.369940\pi\)
\(132\) 593.543 0.391374
\(133\) −2904.87 −1.89387
\(134\) 2246.11 1.44802
\(135\) −564.454 −0.359855
\(136\) 1270.35 0.800966
\(137\) −487.325 −0.303905 −0.151952 0.988388i \(-0.548556\pi\)
−0.151952 + 0.988388i \(0.548556\pi\)
\(138\) 787.293 0.485644
\(139\) 552.716 0.337272 0.168636 0.985678i \(-0.446064\pi\)
0.168636 + 0.985678i \(0.446064\pi\)
\(140\) 2427.33 1.46533
\(141\) 291.820 0.174295
\(142\) −128.674 −0.0760427
\(143\) −1142.58 −0.668164
\(144\) −719.831 −0.416569
\(145\) 1496.01 0.856807
\(146\) −2066.88 −1.17162
\(147\) 1681.30 0.943341
\(148\) −418.673 −0.232532
\(149\) −3509.24 −1.92945 −0.964725 0.263260i \(-0.915202\pi\)
−0.964725 + 0.263260i \(0.915202\pi\)
\(150\) 3224.32 1.75510
\(151\) 3175.51 1.71138 0.855692 0.517485i \(-0.173132\pi\)
0.855692 + 0.517485i \(0.173132\pi\)
\(152\) −1377.11 −0.734857
\(153\) −802.371 −0.423973
\(154\) −5302.24 −2.77446
\(155\) 2702.86 1.40064
\(156\) −258.529 −0.132685
\(157\) 719.754 0.365877 0.182938 0.983124i \(-0.441439\pi\)
0.182938 + 0.983124i \(0.441439\pi\)
\(158\) 4205.90 2.11774
\(159\) −2116.55 −1.05568
\(160\) 3375.91 1.66806
\(161\) −2290.17 −1.12106
\(162\) 278.985 0.135303
\(163\) −1106.29 −0.531602 −0.265801 0.964028i \(-0.585636\pi\)
−0.265801 + 0.964028i \(0.585636\pi\)
\(164\) −1379.80 −0.656977
\(165\) −3212.19 −1.51557
\(166\) −1987.61 −0.929327
\(167\) −821.206 −0.380520 −0.190260 0.981734i \(-0.560933\pi\)
−0.190260 + 0.981734i \(0.560933\pi\)
\(168\) 1284.87 0.590058
\(169\) −1699.33 −0.773476
\(170\) 6419.38 2.89614
\(171\) 869.803 0.388980
\(172\) −916.777 −0.406416
\(173\) −4010.92 −1.76269 −0.881343 0.472476i \(-0.843360\pi\)
−0.881343 + 0.472476i \(0.843360\pi\)
\(174\) −739.414 −0.322154
\(175\) −9379.28 −4.05147
\(176\) −4096.41 −1.75442
\(177\) −177.000 −0.0751646
\(178\) −1295.04 −0.545321
\(179\) −716.188 −0.299053 −0.149526 0.988758i \(-0.547775\pi\)
−0.149526 + 0.988758i \(0.547775\pi\)
\(180\) −726.814 −0.300964
\(181\) 1786.44 0.733619 0.366809 0.930296i \(-0.380450\pi\)
0.366809 + 0.930296i \(0.380450\pi\)
\(182\) 2309.49 0.940608
\(183\) −1649.26 −0.666214
\(184\) −1085.70 −0.434993
\(185\) 2265.81 0.900463
\(186\) −1335.91 −0.526631
\(187\) −4566.13 −1.78561
\(188\) 375.759 0.145771
\(189\) −811.543 −0.312334
\(190\) −6958.87 −2.65710
\(191\) 853.280 0.323252 0.161626 0.986852i \(-0.448326\pi\)
0.161626 + 0.986852i \(0.448326\pi\)
\(192\) 250.985 0.0943398
\(193\) −3478.84 −1.29747 −0.648737 0.761013i \(-0.724702\pi\)
−0.648737 + 0.761013i \(0.724702\pi\)
\(194\) 1110.43 0.410949
\(195\) 1399.13 0.513814
\(196\) 2164.91 0.788961
\(197\) −337.299 −0.121988 −0.0609938 0.998138i \(-0.519427\pi\)
−0.0609938 + 0.998138i \(0.519427\pi\)
\(198\) 1587.65 0.569844
\(199\) −2613.64 −0.931035 −0.465518 0.885039i \(-0.654132\pi\)
−0.465518 + 0.885039i \(0.654132\pi\)
\(200\) −4446.42 −1.57205
\(201\) 1956.39 0.686533
\(202\) 2265.54 0.789122
\(203\) 2150.89 0.743660
\(204\) −1033.17 −0.354589
\(205\) 7467.31 2.54410
\(206\) 3455.19 1.16862
\(207\) 685.744 0.230253
\(208\) 1784.27 0.594792
\(209\) 4949.87 1.63823
\(210\) 6492.76 2.13354
\(211\) 4988.17 1.62749 0.813743 0.581224i \(-0.197426\pi\)
0.813743 + 0.581224i \(0.197426\pi\)
\(212\) −2725.35 −0.882914
\(213\) −112.077 −0.0360534
\(214\) −3039.93 −0.971052
\(215\) 4961.49 1.57382
\(216\) −384.728 −0.121192
\(217\) 3886.04 1.21567
\(218\) 2094.34 0.650672
\(219\) −1800.28 −0.555487
\(220\) −4136.15 −1.26754
\(221\) 1988.86 0.605364
\(222\) −1119.89 −0.338569
\(223\) 1752.62 0.526296 0.263148 0.964755i \(-0.415239\pi\)
0.263148 + 0.964755i \(0.415239\pi\)
\(224\) 4853.71 1.44778
\(225\) 2808.43 0.832128
\(226\) 1285.16 0.378262
\(227\) −2983.27 −0.872276 −0.436138 0.899880i \(-0.643654\pi\)
−0.436138 + 0.899880i \(0.643654\pi\)
\(228\) 1119.99 0.325322
\(229\) 1672.34 0.482583 0.241292 0.970453i \(-0.422429\pi\)
0.241292 + 0.970453i \(0.422429\pi\)
\(230\) −5486.30 −1.57285
\(231\) −4618.33 −1.31543
\(232\) 1019.67 0.288555
\(233\) 508.127 0.142869 0.0714345 0.997445i \(-0.477242\pi\)
0.0714345 + 0.997445i \(0.477242\pi\)
\(234\) −691.529 −0.193191
\(235\) −2033.56 −0.564490
\(236\) −227.912 −0.0628637
\(237\) 3663.40 1.00407
\(238\) 9229.47 2.51369
\(239\) −2497.08 −0.675828 −0.337914 0.941177i \(-0.609721\pi\)
−0.337914 + 0.941177i \(0.609721\pi\)
\(240\) 5016.19 1.34914
\(241\) −4476.15 −1.19641 −0.598204 0.801344i \(-0.704119\pi\)
−0.598204 + 0.801344i \(0.704119\pi\)
\(242\) 4450.66 1.18223
\(243\) 243.000 0.0641500
\(244\) −2123.66 −0.557186
\(245\) −11716.2 −3.05520
\(246\) −3690.77 −0.956564
\(247\) −2156.01 −0.555399
\(248\) 1842.25 0.471705
\(249\) −1731.24 −0.440613
\(250\) −13468.3 −3.40724
\(251\) −5524.04 −1.38914 −0.694571 0.719425i \(-0.744406\pi\)
−0.694571 + 0.719425i \(0.744406\pi\)
\(252\) −1044.98 −0.261219
\(253\) 3902.43 0.969737
\(254\) 2157.27 0.532909
\(255\) 5591.38 1.37312
\(256\) 4772.68 1.16521
\(257\) 7709.96 1.87134 0.935669 0.352879i \(-0.114797\pi\)
0.935669 + 0.352879i \(0.114797\pi\)
\(258\) −2452.25 −0.591746
\(259\) 3257.67 0.781551
\(260\) 1801.57 0.429727
\(261\) −644.041 −0.152740
\(262\) 4103.68 0.967657
\(263\) −2619.57 −0.614181 −0.307091 0.951680i \(-0.599356\pi\)
−0.307091 + 0.951680i \(0.599356\pi\)
\(264\) −2189.41 −0.510411
\(265\) 14749.3 3.41902
\(266\) −10005.1 −2.30622
\(267\) −1128.00 −0.258548
\(268\) 2519.13 0.574180
\(269\) 3075.82 0.697160 0.348580 0.937279i \(-0.386664\pi\)
0.348580 + 0.937279i \(0.386664\pi\)
\(270\) −1944.12 −0.438206
\(271\) −4028.15 −0.902926 −0.451463 0.892290i \(-0.649098\pi\)
−0.451463 + 0.892290i \(0.649098\pi\)
\(272\) 7130.51 1.58953
\(273\) 2011.60 0.445961
\(274\) −1678.47 −0.370074
\(275\) 15982.2 3.50459
\(276\) 882.991 0.192572
\(277\) −3905.75 −0.847197 −0.423599 0.905850i \(-0.639233\pi\)
−0.423599 + 0.905850i \(0.639233\pi\)
\(278\) 1903.70 0.410706
\(279\) −1163.59 −0.249686
\(280\) −8953.69 −1.91102
\(281\) −3502.01 −0.743461 −0.371730 0.928341i \(-0.621235\pi\)
−0.371730 + 0.928341i \(0.621235\pi\)
\(282\) 1005.10 0.212245
\(283\) −6544.11 −1.37458 −0.687291 0.726382i \(-0.741200\pi\)
−0.687291 + 0.726382i \(0.741200\pi\)
\(284\) −144.315 −0.0301532
\(285\) −6061.28 −1.25979
\(286\) −3935.35 −0.813643
\(287\) 10736.1 2.20813
\(288\) −1453.34 −0.297358
\(289\) 3035.14 0.617778
\(290\) 5152.65 1.04336
\(291\) 967.200 0.194839
\(292\) −2318.11 −0.464580
\(293\) 6261.31 1.24843 0.624215 0.781253i \(-0.285419\pi\)
0.624215 + 0.781253i \(0.285419\pi\)
\(294\) 5790.83 1.14873
\(295\) 1233.44 0.243435
\(296\) 1544.36 0.303257
\(297\) 1382.86 0.270175
\(298\) −12086.7 −2.34955
\(299\) −1699.77 −0.328764
\(300\) 3616.25 0.695948
\(301\) 7133.38 1.36598
\(302\) 10937.3 2.08400
\(303\) 1973.32 0.374139
\(304\) −7729.77 −1.45833
\(305\) 11493.0 2.15766
\(306\) −2763.57 −0.516284
\(307\) −3929.77 −0.730566 −0.365283 0.930896i \(-0.619028\pi\)
−0.365283 + 0.930896i \(0.619028\pi\)
\(308\) −5946.74 −1.10015
\(309\) 3009.52 0.554064
\(310\) 9309.35 1.70560
\(311\) −6515.56 −1.18798 −0.593992 0.804471i \(-0.702449\pi\)
−0.593992 + 0.804471i \(0.702449\pi\)
\(312\) 953.636 0.173042
\(313\) −61.8440 −0.0111681 −0.00558407 0.999984i \(-0.501777\pi\)
−0.00558407 + 0.999984i \(0.501777\pi\)
\(314\) 2479.02 0.445539
\(315\) 5655.29 1.01155
\(316\) 4717.15 0.839747
\(317\) 4490.24 0.795574 0.397787 0.917478i \(-0.369778\pi\)
0.397787 + 0.917478i \(0.369778\pi\)
\(318\) −7289.93 −1.28553
\(319\) −3665.10 −0.643280
\(320\) −1749.00 −0.305538
\(321\) −2647.82 −0.460395
\(322\) −7887.93 −1.36515
\(323\) −8616.11 −1.48425
\(324\) 312.897 0.0536517
\(325\) −6961.35 −1.18814
\(326\) −3810.34 −0.647348
\(327\) 1824.20 0.308497
\(328\) 5089.67 0.856798
\(329\) −2923.76 −0.489945
\(330\) −11063.6 −1.84555
\(331\) 7049.54 1.17063 0.585314 0.810807i \(-0.300971\pi\)
0.585314 + 0.810807i \(0.300971\pi\)
\(332\) −2229.21 −0.368505
\(333\) −975.442 −0.160522
\(334\) −2828.45 −0.463371
\(335\) −13633.2 −2.22347
\(336\) 7212.02 1.17098
\(337\) 4495.19 0.726613 0.363307 0.931670i \(-0.381648\pi\)
0.363307 + 0.931670i \(0.381648\pi\)
\(338\) −5852.92 −0.941885
\(339\) 1119.39 0.179342
\(340\) 7199.68 1.14840
\(341\) −6621.77 −1.05158
\(342\) 2995.83 0.473672
\(343\) −6535.42 −1.02880
\(344\) 3381.72 0.530029
\(345\) −4778.65 −0.745721
\(346\) −13814.7 −2.14648
\(347\) 9082.61 1.40513 0.702565 0.711620i \(-0.252038\pi\)
0.702565 + 0.711620i \(0.252038\pi\)
\(348\) −829.293 −0.127744
\(349\) 12020.9 1.84374 0.921870 0.387498i \(-0.126661\pi\)
0.921870 + 0.387498i \(0.126661\pi\)
\(350\) −32304.7 −4.93359
\(351\) −602.332 −0.0915957
\(352\) −8270.68 −1.25235
\(353\) −5538.86 −0.835138 −0.417569 0.908645i \(-0.637118\pi\)
−0.417569 + 0.908645i \(0.637118\pi\)
\(354\) −609.634 −0.0915302
\(355\) 781.014 0.116766
\(356\) −1452.45 −0.216236
\(357\) 8039.00 1.19179
\(358\) −2466.74 −0.364165
\(359\) −10116.0 −1.48719 −0.743595 0.668630i \(-0.766881\pi\)
−0.743595 + 0.668630i \(0.766881\pi\)
\(360\) 2681.00 0.392503
\(361\) 2481.22 0.361747
\(362\) 6152.96 0.893349
\(363\) 3876.59 0.560518
\(364\) 2590.21 0.372978
\(365\) 12545.4 1.79905
\(366\) −5680.49 −0.811268
\(367\) −5324.58 −0.757332 −0.378666 0.925533i \(-0.623617\pi\)
−0.378666 + 0.925533i \(0.623617\pi\)
\(368\) −6094.07 −0.863248
\(369\) −3214.71 −0.453527
\(370\) 7804.04 1.09652
\(371\) 21205.8 2.96752
\(372\) −1498.29 −0.208825
\(373\) −7097.68 −0.985266 −0.492633 0.870237i \(-0.663965\pi\)
−0.492633 + 0.870237i \(0.663965\pi\)
\(374\) −15726.9 −2.17439
\(375\) −11731.1 −1.61544
\(376\) −1386.06 −0.190108
\(377\) 1596.40 0.218087
\(378\) −2795.17 −0.380338
\(379\) −8367.60 −1.13408 −0.567038 0.823692i \(-0.691911\pi\)
−0.567038 + 0.823692i \(0.691911\pi\)
\(380\) −7804.75 −1.05362
\(381\) 1879.01 0.252663
\(382\) 2938.92 0.393634
\(383\) −10657.5 −1.42186 −0.710928 0.703265i \(-0.751725\pi\)
−0.710928 + 0.703265i \(0.751725\pi\)
\(384\) 4740.04 0.629920
\(385\) 32183.1 4.26027
\(386\) −11982.0 −1.57997
\(387\) −2135.95 −0.280559
\(388\) 1245.41 0.162953
\(389\) 1280.56 0.166907 0.0834534 0.996512i \(-0.473405\pi\)
0.0834534 + 0.996512i \(0.473405\pi\)
\(390\) 4818.96 0.625686
\(391\) −6792.85 −0.878591
\(392\) −7985.70 −1.02893
\(393\) 3574.37 0.458786
\(394\) −1161.75 −0.148548
\(395\) −25528.7 −3.25186
\(396\) 1780.63 0.225960
\(397\) 831.103 0.105068 0.0525338 0.998619i \(-0.483270\pi\)
0.0525338 + 0.998619i \(0.483270\pi\)
\(398\) −9002.05 −1.13375
\(399\) −8714.61 −1.09342
\(400\) −24958.0 −3.11975
\(401\) 4713.15 0.586941 0.293471 0.955968i \(-0.405190\pi\)
0.293471 + 0.955968i \(0.405190\pi\)
\(402\) 6738.32 0.836012
\(403\) 2884.23 0.356511
\(404\) 2540.92 0.312910
\(405\) −1693.36 −0.207762
\(406\) 7408.23 0.905577
\(407\) −5551.04 −0.676056
\(408\) 3811.04 0.462438
\(409\) 10700.4 1.29364 0.646820 0.762643i \(-0.276098\pi\)
0.646820 + 0.762643i \(0.276098\pi\)
\(410\) 25719.4 3.09802
\(411\) −1461.97 −0.175460
\(412\) 3875.19 0.463390
\(413\) 1773.37 0.211288
\(414\) 2361.88 0.280386
\(415\) 12064.2 1.42701
\(416\) 3602.45 0.424578
\(417\) 1658.15 0.194724
\(418\) 17048.6 1.99492
\(419\) 3995.59 0.465864 0.232932 0.972493i \(-0.425168\pi\)
0.232932 + 0.972493i \(0.425168\pi\)
\(420\) 7281.98 0.846010
\(421\) 5484.63 0.634928 0.317464 0.948270i \(-0.397169\pi\)
0.317464 + 0.948270i \(0.397169\pi\)
\(422\) 17180.5 1.98184
\(423\) 875.459 0.100630
\(424\) 10053.0 1.15146
\(425\) −27819.8 −3.17520
\(426\) −386.021 −0.0439033
\(427\) 16524.1 1.87273
\(428\) −3409.44 −0.385050
\(429\) −3427.74 −0.385765
\(430\) 17088.7 1.91648
\(431\) −9116.24 −1.01883 −0.509413 0.860522i \(-0.670137\pi\)
−0.509413 + 0.860522i \(0.670137\pi\)
\(432\) −2159.49 −0.240506
\(433\) −13162.3 −1.46083 −0.730415 0.683004i \(-0.760673\pi\)
−0.730415 + 0.683004i \(0.760673\pi\)
\(434\) 13384.5 1.48036
\(435\) 4488.04 0.494678
\(436\) 2348.91 0.258010
\(437\) 7363.73 0.806075
\(438\) −6200.63 −0.676433
\(439\) −2279.58 −0.247833 −0.123916 0.992293i \(-0.539545\pi\)
−0.123916 + 0.992293i \(0.539545\pi\)
\(440\) 15257.0 1.65307
\(441\) 5043.90 0.544638
\(442\) 6850.16 0.737169
\(443\) 13194.2 1.41507 0.707536 0.706678i \(-0.249807\pi\)
0.707536 + 0.706678i \(0.249807\pi\)
\(444\) −1256.02 −0.134252
\(445\) 7860.51 0.837357
\(446\) 6036.47 0.640886
\(447\) −10527.7 −1.11397
\(448\) −2514.63 −0.265190
\(449\) 3287.96 0.345587 0.172794 0.984958i \(-0.444721\pi\)
0.172794 + 0.984958i \(0.444721\pi\)
\(450\) 9672.97 1.01331
\(451\) −18294.3 −1.91007
\(452\) 1441.37 0.149992
\(453\) 9526.52 0.988068
\(454\) −10275.2 −1.06220
\(455\) −14017.9 −1.44433
\(456\) −4131.32 −0.424270
\(457\) −14476.7 −1.48182 −0.740908 0.671606i \(-0.765605\pi\)
−0.740908 + 0.671606i \(0.765605\pi\)
\(458\) 5759.99 0.587656
\(459\) −2407.11 −0.244781
\(460\) −6153.18 −0.623682
\(461\) −4765.61 −0.481468 −0.240734 0.970591i \(-0.577388\pi\)
−0.240734 + 0.970591i \(0.577388\pi\)
\(462\) −15906.7 −1.60183
\(463\) 6286.30 0.630992 0.315496 0.948927i \(-0.397829\pi\)
0.315496 + 0.948927i \(0.397829\pi\)
\(464\) 5723.46 0.572640
\(465\) 8108.58 0.808658
\(466\) 1750.12 0.173976
\(467\) 5623.77 0.557253 0.278626 0.960400i \(-0.410121\pi\)
0.278626 + 0.960400i \(0.410121\pi\)
\(468\) −775.587 −0.0766058
\(469\) −19601.2 −1.92985
\(470\) −7004.12 −0.687396
\(471\) 2159.26 0.211239
\(472\) 840.701 0.0819839
\(473\) −12155.2 −1.18160
\(474\) 12617.7 1.22268
\(475\) 30157.8 2.91313
\(476\) 10351.3 0.996750
\(477\) −6349.64 −0.609497
\(478\) −8600.61 −0.822976
\(479\) 10680.0 1.01875 0.509376 0.860544i \(-0.329876\pi\)
0.509376 + 0.860544i \(0.329876\pi\)
\(480\) 10127.7 0.963052
\(481\) 2417.86 0.229199
\(482\) −15417.0 −1.45690
\(483\) −6870.50 −0.647244
\(484\) 4991.65 0.468788
\(485\) −6739.99 −0.631025
\(486\) 836.955 0.0781174
\(487\) 8071.47 0.751034 0.375517 0.926816i \(-0.377465\pi\)
0.375517 + 0.926816i \(0.377465\pi\)
\(488\) 7833.55 0.726656
\(489\) −3318.86 −0.306921
\(490\) −40353.8 −3.72040
\(491\) −11495.5 −1.05659 −0.528295 0.849061i \(-0.677168\pi\)
−0.528295 + 0.849061i \(0.677168\pi\)
\(492\) −4139.40 −0.379306
\(493\) 6379.75 0.582818
\(494\) −7425.85 −0.676326
\(495\) −9636.57 −0.875013
\(496\) 10340.6 0.936104
\(497\) 1122.90 0.101346
\(498\) −5962.83 −0.536547
\(499\) −340.307 −0.0305295 −0.0152648 0.999883i \(-0.504859\pi\)
−0.0152648 + 0.999883i \(0.504859\pi\)
\(500\) −15105.4 −1.35107
\(501\) −2463.62 −0.219693
\(502\) −19026.2 −1.69160
\(503\) −6818.69 −0.604434 −0.302217 0.953239i \(-0.597727\pi\)
−0.302217 + 0.953239i \(0.597727\pi\)
\(504\) 3854.61 0.340670
\(505\) −13751.2 −1.21172
\(506\) 13441.0 1.18088
\(507\) −5097.98 −0.446567
\(508\) 2419.49 0.211314
\(509\) 19771.2 1.72170 0.860849 0.508860i \(-0.169933\pi\)
0.860849 + 0.508860i \(0.169933\pi\)
\(510\) 19258.1 1.67209
\(511\) 18037.1 1.56148
\(512\) 3798.25 0.327853
\(513\) 2609.41 0.224578
\(514\) 26555.1 2.27878
\(515\) −20972.1 −1.79445
\(516\) −2750.33 −0.234644
\(517\) 4982.06 0.423812
\(518\) 11220.3 0.951718
\(519\) −12032.8 −1.01769
\(520\) −6645.47 −0.560429
\(521\) 20826.6 1.75130 0.875652 0.482943i \(-0.160432\pi\)
0.875652 + 0.482943i \(0.160432\pi\)
\(522\) −2218.24 −0.185996
\(523\) 5693.85 0.476051 0.238026 0.971259i \(-0.423500\pi\)
0.238026 + 0.971259i \(0.423500\pi\)
\(524\) 4602.50 0.383704
\(525\) −28137.8 −2.33912
\(526\) −9022.49 −0.747907
\(527\) 11526.3 0.952743
\(528\) −12289.2 −1.01292
\(529\) −6361.52 −0.522850
\(530\) 50800.4 4.16345
\(531\) −531.000 −0.0433963
\(532\) −11221.3 −0.914482
\(533\) 7968.41 0.647561
\(534\) −3885.11 −0.314841
\(535\) 18451.5 1.49108
\(536\) −9292.32 −0.748819
\(537\) −2148.56 −0.172658
\(538\) 10593.9 0.848952
\(539\) 28703.8 2.29380
\(540\) −2180.44 −0.173762
\(541\) 1565.72 0.124428 0.0622140 0.998063i \(-0.480184\pi\)
0.0622140 + 0.998063i \(0.480184\pi\)
\(542\) −13874.0 −1.09952
\(543\) 5359.32 0.423555
\(544\) 14396.6 1.13465
\(545\) −12712.0 −0.999127
\(546\) 6928.46 0.543060
\(547\) 2599.10 0.203162 0.101581 0.994827i \(-0.467610\pi\)
0.101581 + 0.994827i \(0.467610\pi\)
\(548\) −1882.50 −0.146745
\(549\) −4947.79 −0.384639
\(550\) 55046.9 4.26765
\(551\) −6915.91 −0.534714
\(552\) −3257.09 −0.251143
\(553\) −36703.8 −2.82243
\(554\) −13452.4 −1.03166
\(555\) 6797.43 0.519883
\(556\) 2135.10 0.162857
\(557\) 14567.3 1.10814 0.554072 0.832469i \(-0.313073\pi\)
0.554072 + 0.832469i \(0.313073\pi\)
\(558\) −4007.72 −0.304051
\(559\) 5294.43 0.400591
\(560\) −50257.5 −3.79244
\(561\) −13698.4 −1.03092
\(562\) −12061.8 −0.905334
\(563\) 11318.1 0.847251 0.423626 0.905837i \(-0.360757\pi\)
0.423626 + 0.905837i \(0.360757\pi\)
\(564\) 1127.28 0.0841612
\(565\) −7800.54 −0.580834
\(566\) −22539.6 −1.67387
\(567\) −2434.63 −0.180326
\(568\) 532.334 0.0393243
\(569\) −16128.1 −1.18827 −0.594134 0.804366i \(-0.702505\pi\)
−0.594134 + 0.804366i \(0.702505\pi\)
\(570\) −20876.6 −1.53408
\(571\) −13301.5 −0.974867 −0.487433 0.873160i \(-0.662067\pi\)
−0.487433 + 0.873160i \(0.662067\pi\)
\(572\) −4413.70 −0.322633
\(573\) 2559.84 0.186630
\(574\) 36978.0 2.68891
\(575\) 23776.1 1.72440
\(576\) 752.954 0.0544671
\(577\) −19302.8 −1.39270 −0.696348 0.717704i \(-0.745193\pi\)
−0.696348 + 0.717704i \(0.745193\pi\)
\(578\) 10453.8 0.752287
\(579\) −10436.5 −0.749096
\(580\) 5778.98 0.413723
\(581\) 17345.3 1.23857
\(582\) 3331.29 0.237262
\(583\) −36134.5 −2.56696
\(584\) 8550.83 0.605883
\(585\) 4197.39 0.296650
\(586\) 21565.6 1.52025
\(587\) 17933.2 1.26096 0.630480 0.776205i \(-0.282858\pi\)
0.630480 + 0.776205i \(0.282858\pi\)
\(588\) 6494.73 0.455507
\(589\) −12495.0 −0.874107
\(590\) 4248.27 0.296438
\(591\) −1011.90 −0.0704296
\(592\) 8668.56 0.601817
\(593\) −26500.4 −1.83515 −0.917573 0.397567i \(-0.869855\pi\)
−0.917573 + 0.397567i \(0.869855\pi\)
\(594\) 4762.94 0.329000
\(595\) −56020.3 −3.85985
\(596\) −13555.9 −0.931664
\(597\) −7840.92 −0.537533
\(598\) −5854.46 −0.400346
\(599\) 14006.2 0.955388 0.477694 0.878526i \(-0.341473\pi\)
0.477694 + 0.878526i \(0.341473\pi\)
\(600\) −13339.3 −0.907623
\(601\) 8209.99 0.557225 0.278613 0.960404i \(-0.410125\pi\)
0.278613 + 0.960404i \(0.410125\pi\)
\(602\) 24569.2 1.66340
\(603\) 5869.17 0.396370
\(604\) 12266.7 0.826368
\(605\) −27014.2 −1.81535
\(606\) 6796.61 0.455600
\(607\) 150.423 0.0100585 0.00502924 0.999987i \(-0.498399\pi\)
0.00502924 + 0.999987i \(0.498399\pi\)
\(608\) −15606.5 −1.04100
\(609\) 6452.68 0.429352
\(610\) 39584.9 2.62745
\(611\) −2170.03 −0.143682
\(612\) −3099.50 −0.204722
\(613\) 1790.10 0.117947 0.0589734 0.998260i \(-0.481217\pi\)
0.0589734 + 0.998260i \(0.481217\pi\)
\(614\) −13535.1 −0.889632
\(615\) 22401.9 1.46883
\(616\) 21935.8 1.43477
\(617\) 12232.0 0.798122 0.399061 0.916924i \(-0.369336\pi\)
0.399061 + 0.916924i \(0.369336\pi\)
\(618\) 10365.6 0.674700
\(619\) −5439.47 −0.353200 −0.176600 0.984283i \(-0.556510\pi\)
−0.176600 + 0.984283i \(0.556510\pi\)
\(620\) 10440.9 0.676319
\(621\) 2057.23 0.132937
\(622\) −22441.3 −1.44664
\(623\) 11301.5 0.726779
\(624\) 5352.80 0.343403
\(625\) 42742.9 2.73555
\(626\) −213.007 −0.0135998
\(627\) 14849.6 0.945832
\(628\) 2780.35 0.176669
\(629\) 9662.56 0.612514
\(630\) 19478.3 1.23180
\(631\) 12962.2 0.817776 0.408888 0.912585i \(-0.365917\pi\)
0.408888 + 0.912585i \(0.365917\pi\)
\(632\) −17400.1 −1.09516
\(633\) 14964.5 0.939630
\(634\) 15465.5 0.968794
\(635\) −13094.0 −0.818299
\(636\) −8176.05 −0.509751
\(637\) −12502.5 −0.777654
\(638\) −12623.6 −0.783341
\(639\) −336.230 −0.0208154
\(640\) −33031.3 −2.04012
\(641\) −13358.5 −0.823131 −0.411566 0.911380i \(-0.635018\pi\)
−0.411566 + 0.911380i \(0.635018\pi\)
\(642\) −9119.78 −0.560637
\(643\) −23023.9 −1.41209 −0.706046 0.708166i \(-0.749523\pi\)
−0.706046 + 0.708166i \(0.749523\pi\)
\(644\) −8846.74 −0.541320
\(645\) 14884.5 0.908644
\(646\) −29676.1 −1.80742
\(647\) 29405.1 1.78676 0.893379 0.449303i \(-0.148328\pi\)
0.893379 + 0.449303i \(0.148328\pi\)
\(648\) −1154.18 −0.0699700
\(649\) −3021.81 −0.182768
\(650\) −23976.7 −1.44683
\(651\) 11658.1 0.701870
\(652\) −4273.50 −0.256692
\(653\) 16468.8 0.986944 0.493472 0.869762i \(-0.335728\pi\)
0.493472 + 0.869762i \(0.335728\pi\)
\(654\) 6283.01 0.375666
\(655\) −24908.2 −1.48587
\(656\) 28568.5 1.70033
\(657\) −5400.84 −0.320710
\(658\) −10070.2 −0.596621
\(659\) −377.335 −0.0223048 −0.0111524 0.999938i \(-0.503550\pi\)
−0.0111524 + 0.999938i \(0.503550\pi\)
\(660\) −12408.4 −0.731815
\(661\) −15474.3 −0.910559 −0.455280 0.890348i \(-0.650461\pi\)
−0.455280 + 0.890348i \(0.650461\pi\)
\(662\) 24280.4 1.42551
\(663\) 5966.59 0.349507
\(664\) 8222.89 0.480588
\(665\) 60728.3 3.54127
\(666\) −3359.68 −0.195473
\(667\) −5452.43 −0.316520
\(668\) −3172.26 −0.183740
\(669\) 5257.86 0.303857
\(670\) −46956.4 −2.70759
\(671\) −28156.9 −1.61995
\(672\) 14561.1 0.835875
\(673\) 15634.5 0.895490 0.447745 0.894161i \(-0.352227\pi\)
0.447745 + 0.894161i \(0.352227\pi\)
\(674\) 15482.6 0.884818
\(675\) 8425.29 0.480429
\(676\) −6564.37 −0.373485
\(677\) −26000.2 −1.47603 −0.738014 0.674786i \(-0.764236\pi\)
−0.738014 + 0.674786i \(0.764236\pi\)
\(678\) 3855.47 0.218390
\(679\) −9690.42 −0.547694
\(680\) −26557.5 −1.49770
\(681\) −8949.81 −0.503609
\(682\) −22807.1 −1.28054
\(683\) −19549.4 −1.09522 −0.547612 0.836733i \(-0.684463\pi\)
−0.547612 + 0.836733i \(0.684463\pi\)
\(684\) 3359.98 0.187825
\(685\) 10187.9 0.568260
\(686\) −22509.7 −1.25280
\(687\) 5017.03 0.278620
\(688\) 18981.7 1.05185
\(689\) 15739.0 0.870261
\(690\) −16458.9 −0.908087
\(691\) −28184.4 −1.55164 −0.775821 0.630952i \(-0.782664\pi\)
−0.775821 + 0.630952i \(0.782664\pi\)
\(692\) −15493.9 −0.851140
\(693\) −13855.0 −0.759462
\(694\) 31282.9 1.71107
\(695\) −11554.9 −0.630652
\(696\) 3059.01 0.166597
\(697\) 31844.4 1.73055
\(698\) 41403.2 2.24518
\(699\) 1524.38 0.0824855
\(700\) −36231.4 −1.95631
\(701\) 2313.19 0.124633 0.0623167 0.998056i \(-0.480151\pi\)
0.0623167 + 0.998056i \(0.480151\pi\)
\(702\) −2074.59 −0.111539
\(703\) −10474.6 −0.561959
\(704\) 4284.90 0.229394
\(705\) −6100.69 −0.325908
\(706\) −19077.3 −1.01697
\(707\) −19770.8 −1.05171
\(708\) −683.737 −0.0362944
\(709\) −16383.6 −0.867841 −0.433920 0.900951i \(-0.642870\pi\)
−0.433920 + 0.900951i \(0.642870\pi\)
\(710\) 2690.02 0.142189
\(711\) 10990.2 0.579698
\(712\) 5357.67 0.282004
\(713\) −9850.95 −0.517421
\(714\) 27688.4 1.45128
\(715\) 23886.5 1.24937
\(716\) −2766.58 −0.144402
\(717\) −7491.25 −0.390190
\(718\) −34842.1 −1.81100
\(719\) −30186.8 −1.56575 −0.782876 0.622177i \(-0.786248\pi\)
−0.782876 + 0.622177i \(0.786248\pi\)
\(720\) 15048.6 0.778926
\(721\) −30152.6 −1.55748
\(722\) 8545.96 0.440510
\(723\) −13428.5 −0.690746
\(724\) 6900.88 0.354239
\(725\) −22330.2 −1.14389
\(726\) 13352.0 0.682559
\(727\) 16487.2 0.841095 0.420547 0.907271i \(-0.361838\pi\)
0.420547 + 0.907271i \(0.361838\pi\)
\(728\) −9554.53 −0.486421
\(729\) 729.000 0.0370370
\(730\) 43209.5 2.19076
\(731\) 21158.3 1.07054
\(732\) −6370.98 −0.321691
\(733\) −13859.4 −0.698372 −0.349186 0.937053i \(-0.613542\pi\)
−0.349186 + 0.937053i \(0.613542\pi\)
\(734\) −18339.2 −0.922226
\(735\) −35148.7 −1.76392
\(736\) −12304.0 −0.616210
\(737\) 33400.3 1.66935
\(738\) −11072.3 −0.552273
\(739\) 36238.9 1.80388 0.901942 0.431856i \(-0.142141\pi\)
0.901942 + 0.431856i \(0.142141\pi\)
\(740\) 8752.65 0.434803
\(741\) −6468.02 −0.320660
\(742\) 73038.2 3.61364
\(743\) 11663.4 0.575893 0.287946 0.957647i \(-0.407028\pi\)
0.287946 + 0.957647i \(0.407028\pi\)
\(744\) 5526.75 0.272339
\(745\) 73363.1 3.60780
\(746\) −24446.3 −1.19979
\(747\) −5193.71 −0.254388
\(748\) −17638.6 −0.862207
\(749\) 26528.6 1.29417
\(750\) −40405.0 −1.96717
\(751\) 4619.42 0.224454 0.112227 0.993683i \(-0.464202\pi\)
0.112227 + 0.993683i \(0.464202\pi\)
\(752\) −7780.03 −0.377272
\(753\) −16572.1 −0.802021
\(754\) 5498.43 0.265571
\(755\) −66386.2 −3.20005
\(756\) −3134.93 −0.150815
\(757\) −17625.2 −0.846233 −0.423116 0.906075i \(-0.639064\pi\)
−0.423116 + 0.906075i \(0.639064\pi\)
\(758\) −28820.2 −1.38100
\(759\) 11707.3 0.559878
\(760\) 28789.4 1.37408
\(761\) −3247.66 −0.154701 −0.0773506 0.997004i \(-0.524646\pi\)
−0.0773506 + 0.997004i \(0.524646\pi\)
\(762\) 6471.80 0.307675
\(763\) −18276.7 −0.867185
\(764\) 3296.16 0.156087
\(765\) 16774.1 0.792771
\(766\) −36707.1 −1.73144
\(767\) 1316.21 0.0619628
\(768\) 14318.0 0.672732
\(769\) −3993.05 −0.187247 −0.0936236 0.995608i \(-0.529845\pi\)
−0.0936236 + 0.995608i \(0.529845\pi\)
\(770\) 110847. 5.18785
\(771\) 23129.9 1.08042
\(772\) −13438.5 −0.626505
\(773\) 9486.90 0.441423 0.220712 0.975339i \(-0.429162\pi\)
0.220712 + 0.975339i \(0.429162\pi\)
\(774\) −7356.75 −0.341645
\(775\) −40344.1 −1.86994
\(776\) −4593.93 −0.212516
\(777\) 9773.01 0.451229
\(778\) 4410.57 0.203247
\(779\) −34520.6 −1.58771
\(780\) 5404.72 0.248103
\(781\) −1913.42 −0.0876664
\(782\) −23396.3 −1.06989
\(783\) −1932.12 −0.0881844
\(784\) −44824.1 −2.04191
\(785\) −15047.0 −0.684139
\(786\) 12311.0 0.558677
\(787\) 9310.51 0.421708 0.210854 0.977518i \(-0.432376\pi\)
0.210854 + 0.977518i \(0.432376\pi\)
\(788\) −1302.96 −0.0589036
\(789\) −7858.72 −0.354598
\(790\) −87927.3 −3.95989
\(791\) −11215.2 −0.504131
\(792\) −6568.22 −0.294686
\(793\) 12264.2 0.549200
\(794\) 2862.53 0.127944
\(795\) 44247.9 1.97397
\(796\) −10096.3 −0.449565
\(797\) 1402.21 0.0623196 0.0311598 0.999514i \(-0.490080\pi\)
0.0311598 + 0.999514i \(0.490080\pi\)
\(798\) −30015.4 −1.33149
\(799\) −8672.14 −0.383978
\(800\) −50390.3 −2.22696
\(801\) −3383.99 −0.149273
\(802\) 16233.3 0.714735
\(803\) −30735.1 −1.35071
\(804\) 7557.39 0.331503
\(805\) 47877.5 2.09623
\(806\) 9934.05 0.434134
\(807\) 9227.45 0.402505
\(808\) −9372.71 −0.408082
\(809\) 33015.3 1.43480 0.717402 0.696659i \(-0.245331\pi\)
0.717402 + 0.696659i \(0.245331\pi\)
\(810\) −5832.37 −0.252998
\(811\) 35812.1 1.55060 0.775298 0.631596i \(-0.217600\pi\)
0.775298 + 0.631596i \(0.217600\pi\)
\(812\) 8308.73 0.359088
\(813\) −12084.5 −0.521304
\(814\) −19119.2 −0.823254
\(815\) 23127.7 0.994023
\(816\) 21391.5 0.917713
\(817\) −22936.4 −0.982184
\(818\) 36854.8 1.57530
\(819\) 6034.79 0.257476
\(820\) 28845.6 1.22846
\(821\) −1940.92 −0.0825076 −0.0412538 0.999149i \(-0.513135\pi\)
−0.0412538 + 0.999149i \(0.513135\pi\)
\(822\) −5035.42 −0.213662
\(823\) −1861.48 −0.0788424 −0.0394212 0.999223i \(-0.512551\pi\)
−0.0394212 + 0.999223i \(0.512551\pi\)
\(824\) −14294.4 −0.604332
\(825\) 47946.6 2.02338
\(826\) 6107.95 0.257292
\(827\) −7336.67 −0.308490 −0.154245 0.988033i \(-0.549294\pi\)
−0.154245 + 0.988033i \(0.549294\pi\)
\(828\) 2648.97 0.111181
\(829\) 30106.6 1.26133 0.630667 0.776053i \(-0.282781\pi\)
0.630667 + 0.776053i \(0.282781\pi\)
\(830\) 41552.3 1.73771
\(831\) −11717.2 −0.489130
\(832\) −1866.37 −0.0777701
\(833\) −49963.9 −2.07821
\(834\) 5711.09 0.237121
\(835\) 17167.9 0.711520
\(836\) 19121.0 0.791044
\(837\) −3490.78 −0.144157
\(838\) 13761.8 0.567297
\(839\) −27636.8 −1.13722 −0.568611 0.822607i \(-0.692519\pi\)
−0.568611 + 0.822607i \(0.692519\pi\)
\(840\) −26861.1 −1.10333
\(841\) −19268.2 −0.790035
\(842\) 18890.5 0.773170
\(843\) −10506.0 −0.429237
\(844\) 19268.9 0.785857
\(845\) 35525.6 1.44629
\(846\) 3015.31 0.122540
\(847\) −38839.7 −1.57562
\(848\) 56428.0 2.28508
\(849\) −19632.3 −0.793615
\(850\) −95818.7 −3.86653
\(851\) −8258.07 −0.332647
\(852\) −432.944 −0.0174089
\(853\) −23055.8 −0.925457 −0.462728 0.886500i \(-0.653129\pi\)
−0.462728 + 0.886500i \(0.653129\pi\)
\(854\) 56913.1 2.28048
\(855\) −18183.8 −0.727338
\(856\) 12576.4 0.502165
\(857\) −44339.3 −1.76733 −0.883665 0.468119i \(-0.844932\pi\)
−0.883665 + 0.468119i \(0.844932\pi\)
\(858\) −11806.0 −0.469757
\(859\) −5864.49 −0.232938 −0.116469 0.993194i \(-0.537158\pi\)
−0.116469 + 0.993194i \(0.537158\pi\)
\(860\) 19165.8 0.759942
\(861\) 32208.4 1.27487
\(862\) −31398.7 −1.24065
\(863\) 8819.67 0.347886 0.173943 0.984756i \(-0.444349\pi\)
0.173943 + 0.984756i \(0.444349\pi\)
\(864\) −4360.03 −0.171680
\(865\) 83851.1 3.29598
\(866\) −45334.3 −1.77890
\(867\) 9105.43 0.356674
\(868\) 15011.5 0.587007
\(869\) 62543.0 2.44146
\(870\) 15458.0 0.602384
\(871\) −14548.1 −0.565951
\(872\) −8664.44 −0.336485
\(873\) 2901.60 0.112491
\(874\) 25362.6 0.981582
\(875\) 117535. 4.54102
\(876\) −6954.34 −0.268225
\(877\) −16591.0 −0.638814 −0.319407 0.947618i \(-0.603484\pi\)
−0.319407 + 0.947618i \(0.603484\pi\)
\(878\) −7851.47 −0.301793
\(879\) 18783.9 0.720781
\(880\) 85638.3 3.28053
\(881\) −28452.1 −1.08806 −0.544028 0.839067i \(-0.683101\pi\)
−0.544028 + 0.839067i \(0.683101\pi\)
\(882\) 17372.5 0.663222
\(883\) −6177.75 −0.235445 −0.117722 0.993047i \(-0.537559\pi\)
−0.117722 + 0.993047i \(0.537559\pi\)
\(884\) 7682.82 0.292309
\(885\) 3700.31 0.140547
\(886\) 45444.3 1.72317
\(887\) −13155.6 −0.497996 −0.248998 0.968504i \(-0.580101\pi\)
−0.248998 + 0.968504i \(0.580101\pi\)
\(888\) 4633.08 0.175086
\(889\) −18825.9 −0.710237
\(890\) 27073.6 1.01967
\(891\) 4148.59 0.155985
\(892\) 6770.23 0.254130
\(893\) 9400.95 0.352285
\(894\) −36260.2 −1.35651
\(895\) 14972.4 0.559187
\(896\) −47490.7 −1.77071
\(897\) −5099.32 −0.189812
\(898\) 11324.6 0.420832
\(899\) 9251.87 0.343234
\(900\) 10848.8 0.401806
\(901\) 62898.4 2.32569
\(902\) −63010.2 −2.32595
\(903\) 21400.1 0.788652
\(904\) −5316.79 −0.195613
\(905\) −37346.8 −1.37177
\(906\) 32811.8 1.20320
\(907\) 11767.5 0.430796 0.215398 0.976526i \(-0.430895\pi\)
0.215398 + 0.976526i \(0.430895\pi\)
\(908\) −11524.1 −0.421192
\(909\) 5919.95 0.216009
\(910\) −48281.4 −1.75881
\(911\) 8944.57 0.325298 0.162649 0.986684i \(-0.447996\pi\)
0.162649 + 0.986684i \(0.447996\pi\)
\(912\) −23189.3 −0.841968
\(913\) −29556.3 −1.07138
\(914\) −49861.4 −1.80445
\(915\) 34479.0 1.24573
\(916\) 6460.14 0.233023
\(917\) −35811.8 −1.28965
\(918\) −8290.72 −0.298077
\(919\) 38367.6 1.37718 0.688591 0.725150i \(-0.258230\pi\)
0.688591 + 0.725150i \(0.258230\pi\)
\(920\) 22697.3 0.813376
\(921\) −11789.3 −0.421793
\(922\) −16414.0 −0.586298
\(923\) 833.424 0.0297210
\(924\) −17840.2 −0.635174
\(925\) −33820.5 −1.20218
\(926\) 21651.7 0.768378
\(927\) 9028.57 0.319889
\(928\) 11555.7 0.408766
\(929\) −47966.0 −1.69399 −0.846993 0.531604i \(-0.821590\pi\)
−0.846993 + 0.531604i \(0.821590\pi\)
\(930\) 27928.0 0.984727
\(931\) 54162.9 1.90668
\(932\) 1962.85 0.0689865
\(933\) −19546.7 −0.685883
\(934\) 19369.7 0.678583
\(935\) 95458.1 3.33884
\(936\) 2860.91 0.0999057
\(937\) 72.7929 0.00253793 0.00126896 0.999999i \(-0.499596\pi\)
0.00126896 + 0.999999i \(0.499596\pi\)
\(938\) −67511.6 −2.35003
\(939\) −185.532 −0.00644793
\(940\) −7855.50 −0.272573
\(941\) −1145.95 −0.0396992 −0.0198496 0.999803i \(-0.506319\pi\)
−0.0198496 + 0.999803i \(0.506319\pi\)
\(942\) 7437.06 0.257232
\(943\) −27215.7 −0.939835
\(944\) 4718.89 0.162698
\(945\) 16965.9 0.584021
\(946\) −41865.7 −1.43887
\(947\) −52363.7 −1.79682 −0.898412 0.439153i \(-0.855279\pi\)
−0.898412 + 0.439153i \(0.855279\pi\)
\(948\) 14151.4 0.484828
\(949\) 13387.2 0.457922
\(950\) 103871. 3.54740
\(951\) 13470.7 0.459325
\(952\) −38183.0 −1.29992
\(953\) −18197.6 −0.618549 −0.309274 0.950973i \(-0.600086\pi\)
−0.309274 + 0.950973i \(0.600086\pi\)
\(954\) −21869.8 −0.742202
\(955\) −17838.4 −0.604437
\(956\) −9646.04 −0.326334
\(957\) −10995.3 −0.371398
\(958\) 36784.7 1.24056
\(959\) 14647.6 0.493217
\(960\) −5247.00 −0.176402
\(961\) −13075.6 −0.438910
\(962\) 8327.73 0.279103
\(963\) −7943.46 −0.265809
\(964\) −17291.0 −0.577704
\(965\) 72727.5 2.42610
\(966\) −23663.8 −0.788168
\(967\) −15190.1 −0.505149 −0.252575 0.967577i \(-0.581277\pi\)
−0.252575 + 0.967577i \(0.581277\pi\)
\(968\) −18412.7 −0.611371
\(969\) −25848.3 −0.856933
\(970\) −23214.3 −0.768418
\(971\) −33558.7 −1.10911 −0.554557 0.832146i \(-0.687112\pi\)
−0.554557 + 0.832146i \(0.687112\pi\)
\(972\) 938.690 0.0309758
\(973\) −16613.1 −0.547370
\(974\) 27800.2 0.914556
\(975\) −20884.0 −0.685974
\(976\) 43970.0 1.44206
\(977\) 13843.4 0.453317 0.226658 0.973974i \(-0.427220\pi\)
0.226658 + 0.973974i \(0.427220\pi\)
\(978\) −11431.0 −0.373746
\(979\) −19257.6 −0.628677
\(980\) −45258.9 −1.47525
\(981\) 5472.60 0.178111
\(982\) −39593.5 −1.28664
\(983\) −10695.3 −0.347027 −0.173514 0.984831i \(-0.555512\pi\)
−0.173514 + 0.984831i \(0.555512\pi\)
\(984\) 15269.0 0.494673
\(985\) 7051.47 0.228100
\(986\) 21973.5 0.709715
\(987\) −8771.27 −0.282870
\(988\) −8328.49 −0.268183
\(989\) −18082.8 −0.581396
\(990\) −33190.8 −1.06553
\(991\) 14749.0 0.472773 0.236386 0.971659i \(-0.424037\pi\)
0.236386 + 0.971659i \(0.424037\pi\)
\(992\) 20877.8 0.668216
\(993\) 21148.6 0.675862
\(994\) 3867.57 0.123412
\(995\) 54640.0 1.74091
\(996\) −6687.63 −0.212757
\(997\) 30262.1 0.961294 0.480647 0.876914i \(-0.340402\pi\)
0.480647 + 0.876914i \(0.340402\pi\)
\(998\) −1172.11 −0.0371767
\(999\) −2926.33 −0.0926776
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 177.4.a.a.1.7 7
3.2 odd 2 531.4.a.d.1.1 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.4.a.a.1.7 7 1.1 even 1 trivial
531.4.a.d.1.1 7 3.2 odd 2