Properties

Label 177.4.a.c.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: \(x^{8} - 2 x^{7} - 49 x^{6} + 89 x^{5} + 648 x^{4} - 1023 x^{3} - 1476 x^{2} + 1940 x - 384\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-1.67303\) of defining polynomial
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.67303 q^{2} -3.00000 q^{3} -5.20096 q^{4} -6.76323 q^{5} +5.01910 q^{6} -19.0526 q^{7} +22.0856 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q-1.67303 q^{2} -3.00000 q^{3} -5.20096 q^{4} -6.76323 q^{5} +5.01910 q^{6} -19.0526 q^{7} +22.0856 q^{8} +9.00000 q^{9} +11.3151 q^{10} -65.4248 q^{11} +15.6029 q^{12} -46.8971 q^{13} +31.8757 q^{14} +20.2897 q^{15} +4.65770 q^{16} +48.0195 q^{17} -15.0573 q^{18} +147.256 q^{19} +35.1753 q^{20} +57.1579 q^{21} +109.458 q^{22} +33.1371 q^{23} -66.2569 q^{24} -79.2587 q^{25} +78.4604 q^{26} -27.0000 q^{27} +99.0919 q^{28} -73.6497 q^{29} -33.9453 q^{30} +142.529 q^{31} -184.478 q^{32} +196.274 q^{33} -80.3382 q^{34} +128.857 q^{35} -46.8087 q^{36} +397.714 q^{37} -246.363 q^{38} +140.691 q^{39} -149.370 q^{40} -100.625 q^{41} -95.6270 q^{42} +388.024 q^{43} +340.272 q^{44} -60.8691 q^{45} -55.4395 q^{46} -138.226 q^{47} -13.9731 q^{48} +20.0023 q^{49} +132.602 q^{50} -144.059 q^{51} +243.910 q^{52} -439.471 q^{53} +45.1719 q^{54} +442.483 q^{55} -420.789 q^{56} -441.767 q^{57} +123.218 q^{58} -59.0000 q^{59} -105.526 q^{60} -602.884 q^{61} -238.455 q^{62} -171.474 q^{63} +271.375 q^{64} +317.176 q^{65} -328.374 q^{66} -154.728 q^{67} -249.748 q^{68} -99.4113 q^{69} -215.582 q^{70} +552.436 q^{71} +198.771 q^{72} -107.785 q^{73} -665.389 q^{74} +237.776 q^{75} -765.871 q^{76} +1246.51 q^{77} -235.381 q^{78} +989.162 q^{79} -31.5011 q^{80} +81.0000 q^{81} +168.349 q^{82} -730.585 q^{83} -297.276 q^{84} -324.767 q^{85} -649.177 q^{86} +220.949 q^{87} -1444.95 q^{88} -1375.89 q^{89} +101.836 q^{90} +893.513 q^{91} -172.345 q^{92} -427.586 q^{93} +231.257 q^{94} -995.923 q^{95} +553.433 q^{96} -268.232 q^{97} -33.4645 q^{98} -588.823 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 2q^{2} - 24q^{3} + 38q^{4} - 12q^{5} - 6q^{6} + 53q^{7} + 3q^{8} + 72q^{9} + O(q^{10}) \) \( 8q + 2q^{2} - 24q^{3} + 38q^{4} - 12q^{5} - 6q^{6} + 53q^{7} + 3q^{8} + 72q^{9} + 29q^{10} - 27q^{11} - 114q^{12} + 89q^{13} - 37q^{14} + 36q^{15} + 362q^{16} + 79q^{17} + 18q^{18} + 288q^{19} + 457q^{20} - 159q^{21} + 596q^{22} + 202q^{23} - 9q^{24} + 264q^{25} + 270q^{26} - 216q^{27} + 702q^{28} - 114q^{29} - 87q^{30} + 538q^{31} + 316q^{32} + 81q^{33} + 498q^{34} - 196q^{35} + 342q^{36} + 395q^{37} + 397q^{38} - 267q^{39} + 918q^{40} - 39q^{41} + 111q^{42} + 527q^{43} + 64q^{44} - 108q^{45} - 539q^{46} + 860q^{47} - 1086q^{48} + 347q^{49} - 591q^{50} - 237q^{51} - 644q^{52} - 812q^{53} - 54q^{54} + 536q^{55} - 2218q^{56} - 864q^{57} - 1154q^{58} - 472q^{59} - 1371q^{60} - 460q^{61} - 2014q^{62} + 477q^{63} - 451q^{64} - 986q^{65} - 1788q^{66} + 1934q^{67} - 69q^{68} - 606q^{69} - 1028q^{70} - 1687q^{71} + 27q^{72} + 1980q^{73} - 2400q^{74} - 792q^{75} - 940q^{76} - 821q^{77} - 810q^{78} + 3319q^{79} - 2119q^{80} + 648q^{81} + 429q^{82} + 2057q^{83} - 2106q^{84} + 566q^{85} - 6690q^{86} + 342q^{87} + 1189q^{88} + 1668q^{89} + 261q^{90} + 2427q^{91} - 980q^{92} - 1614q^{93} + 332q^{94} + 2146q^{95} - 948q^{96} + 1956q^{97} - 2026q^{98} - 243q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.67303 −0.591506 −0.295753 0.955264i \(-0.595571\pi\)
−0.295753 + 0.955264i \(0.595571\pi\)
\(3\) −3.00000 −0.577350
\(4\) −5.20096 −0.650120
\(5\) −6.76323 −0.604922 −0.302461 0.953162i \(-0.597808\pi\)
−0.302461 + 0.953162i \(0.597808\pi\)
\(6\) 5.01910 0.341506
\(7\) −19.0526 −1.02874 −0.514372 0.857567i \(-0.671975\pi\)
−0.514372 + 0.857567i \(0.671975\pi\)
\(8\) 22.0856 0.976057
\(9\) 9.00000 0.333333
\(10\) 11.3151 0.357815
\(11\) −65.4248 −1.79330 −0.896651 0.442737i \(-0.854007\pi\)
−0.896651 + 0.442737i \(0.854007\pi\)
\(12\) 15.6029 0.375347
\(13\) −46.8971 −1.00053 −0.500266 0.865872i \(-0.666764\pi\)
−0.500266 + 0.865872i \(0.666764\pi\)
\(14\) 31.8757 0.608509
\(15\) 20.2897 0.349252
\(16\) 4.65770 0.0727766
\(17\) 48.0195 0.685085 0.342542 0.939502i \(-0.388712\pi\)
0.342542 + 0.939502i \(0.388712\pi\)
\(18\) −15.0573 −0.197169
\(19\) 147.256 1.77804 0.889020 0.457869i \(-0.151387\pi\)
0.889020 + 0.457869i \(0.151387\pi\)
\(20\) 35.1753 0.393272
\(21\) 57.1579 0.593946
\(22\) 109.458 1.06075
\(23\) 33.1371 0.300416 0.150208 0.988654i \(-0.452006\pi\)
0.150208 + 0.988654i \(0.452006\pi\)
\(24\) −66.2569 −0.563527
\(25\) −79.2587 −0.634070
\(26\) 78.4604 0.591821
\(27\) −27.0000 −0.192450
\(28\) 99.0919 0.668808
\(29\) −73.6497 −0.471600 −0.235800 0.971802i \(-0.575771\pi\)
−0.235800 + 0.971802i \(0.575771\pi\)
\(30\) −33.9453 −0.206585
\(31\) 142.529 0.825771 0.412886 0.910783i \(-0.364521\pi\)
0.412886 + 0.910783i \(0.364521\pi\)
\(32\) −184.478 −1.01910
\(33\) 196.274 1.03536
\(34\) −80.3382 −0.405232
\(35\) 128.857 0.622310
\(36\) −46.8087 −0.216707
\(37\) 397.714 1.76713 0.883565 0.468308i \(-0.155136\pi\)
0.883565 + 0.468308i \(0.155136\pi\)
\(38\) −246.363 −1.05172
\(39\) 140.691 0.577658
\(40\) −149.370 −0.590438
\(41\) −100.625 −0.383293 −0.191646 0.981464i \(-0.561383\pi\)
−0.191646 + 0.981464i \(0.561383\pi\)
\(42\) −95.6270 −0.351323
\(43\) 388.024 1.37612 0.688060 0.725654i \(-0.258463\pi\)
0.688060 + 0.725654i \(0.258463\pi\)
\(44\) 340.272 1.16586
\(45\) −60.8691 −0.201641
\(46\) −55.4395 −0.177698
\(47\) −138.226 −0.428987 −0.214493 0.976725i \(-0.568810\pi\)
−0.214493 + 0.976725i \(0.568810\pi\)
\(48\) −13.9731 −0.0420176
\(49\) 20.0023 0.0583158
\(50\) 132.602 0.375056
\(51\) −144.059 −0.395534
\(52\) 243.910 0.650466
\(53\) −439.471 −1.13898 −0.569491 0.821998i \(-0.692859\pi\)
−0.569491 + 0.821998i \(0.692859\pi\)
\(54\) 45.1719 0.113835
\(55\) 442.483 1.08481
\(56\) −420.789 −1.00411
\(57\) −441.767 −1.02655
\(58\) 123.218 0.278954
\(59\) −59.0000 −0.130189
\(60\) −105.526 −0.227056
\(61\) −602.884 −1.26543 −0.632716 0.774384i \(-0.718060\pi\)
−0.632716 + 0.774384i \(0.718060\pi\)
\(62\) −238.455 −0.488449
\(63\) −171.474 −0.342915
\(64\) 271.375 0.530030
\(65\) 317.176 0.605244
\(66\) −328.374 −0.612424
\(67\) −154.728 −0.282134 −0.141067 0.990000i \(-0.545053\pi\)
−0.141067 + 0.990000i \(0.545053\pi\)
\(68\) −249.748 −0.445388
\(69\) −99.4113 −0.173445
\(70\) −215.582 −0.368100
\(71\) 552.436 0.923410 0.461705 0.887033i \(-0.347238\pi\)
0.461705 + 0.887033i \(0.347238\pi\)
\(72\) 198.771 0.325352
\(73\) −107.785 −0.172812 −0.0864062 0.996260i \(-0.527538\pi\)
−0.0864062 + 0.996260i \(0.527538\pi\)
\(74\) −665.389 −1.04527
\(75\) 237.776 0.366080
\(76\) −765.871 −1.15594
\(77\) 1246.51 1.84485
\(78\) −235.381 −0.341688
\(79\) 989.162 1.40873 0.704363 0.709840i \(-0.251233\pi\)
0.704363 + 0.709840i \(0.251233\pi\)
\(80\) −31.5011 −0.0440241
\(81\) 81.0000 0.111111
\(82\) 168.349 0.226720
\(83\) −730.585 −0.966170 −0.483085 0.875573i \(-0.660484\pi\)
−0.483085 + 0.875573i \(0.660484\pi\)
\(84\) −297.276 −0.386136
\(85\) −324.767 −0.414423
\(86\) −649.177 −0.813983
\(87\) 220.949 0.272278
\(88\) −1444.95 −1.75036
\(89\) −1375.89 −1.63869 −0.819346 0.573300i \(-0.805663\pi\)
−0.819346 + 0.573300i \(0.805663\pi\)
\(90\) 101.836 0.119272
\(91\) 893.513 1.02929
\(92\) −172.345 −0.195306
\(93\) −427.586 −0.476759
\(94\) 231.257 0.253748
\(95\) −995.923 −1.07557
\(96\) 553.433 0.588380
\(97\) −268.232 −0.280772 −0.140386 0.990097i \(-0.544834\pi\)
−0.140386 + 0.990097i \(0.544834\pi\)
\(98\) −33.4645 −0.0344942
\(99\) −588.823 −0.597768
\(100\) 412.222 0.412222
\(101\) 198.697 0.195753 0.0978766 0.995199i \(-0.468795\pi\)
0.0978766 + 0.995199i \(0.468795\pi\)
\(102\) 241.015 0.233961
\(103\) 1107.72 1.05968 0.529838 0.848099i \(-0.322253\pi\)
0.529838 + 0.848099i \(0.322253\pi\)
\(104\) −1035.75 −0.976576
\(105\) −386.572 −0.359291
\(106\) 735.249 0.673715
\(107\) −562.412 −0.508134 −0.254067 0.967187i \(-0.581768\pi\)
−0.254067 + 0.967187i \(0.581768\pi\)
\(108\) 140.426 0.125116
\(109\) 1069.38 0.939711 0.469855 0.882743i \(-0.344306\pi\)
0.469855 + 0.882743i \(0.344306\pi\)
\(110\) −740.289 −0.641671
\(111\) −1193.14 −1.02025
\(112\) −88.7414 −0.0748685
\(113\) 1601.88 1.33356 0.666781 0.745254i \(-0.267672\pi\)
0.666781 + 0.745254i \(0.267672\pi\)
\(114\) 739.090 0.607212
\(115\) −224.114 −0.181728
\(116\) 383.049 0.306597
\(117\) −422.074 −0.333511
\(118\) 98.7089 0.0770076
\(119\) −914.898 −0.704778
\(120\) 448.111 0.340889
\(121\) 2949.41 2.21593
\(122\) 1008.64 0.748511
\(123\) 301.875 0.221294
\(124\) −741.286 −0.536850
\(125\) 1381.45 0.988484
\(126\) 286.881 0.202836
\(127\) −251.661 −0.175837 −0.0879184 0.996128i \(-0.528021\pi\)
−0.0879184 + 0.996128i \(0.528021\pi\)
\(128\) 1021.80 0.705588
\(129\) −1164.07 −0.794503
\(130\) −530.646 −0.358005
\(131\) 2491.36 1.66161 0.830806 0.556562i \(-0.187880\pi\)
0.830806 + 0.556562i \(0.187880\pi\)
\(132\) −1020.82 −0.673111
\(133\) −2805.60 −1.82915
\(134\) 258.864 0.166884
\(135\) 182.607 0.116417
\(136\) 1060.54 0.668682
\(137\) 2395.27 1.49374 0.746869 0.664971i \(-0.231556\pi\)
0.746869 + 0.664971i \(0.231556\pi\)
\(138\) 166.318 0.102594
\(139\) −1720.23 −1.04970 −0.524850 0.851195i \(-0.675879\pi\)
−0.524850 + 0.851195i \(0.675879\pi\)
\(140\) −670.182 −0.404576
\(141\) 414.679 0.247676
\(142\) −924.244 −0.546203
\(143\) 3068.24 1.79426
\(144\) 41.9193 0.0242589
\(145\) 498.110 0.285281
\(146\) 180.328 0.102220
\(147\) −60.0069 −0.0336686
\(148\) −2068.50 −1.14885
\(149\) −3053.69 −1.67898 −0.839490 0.543375i \(-0.817146\pi\)
−0.839490 + 0.543375i \(0.817146\pi\)
\(150\) −397.807 −0.216539
\(151\) 1862.79 1.00392 0.501960 0.864891i \(-0.332612\pi\)
0.501960 + 0.864891i \(0.332612\pi\)
\(152\) 3252.23 1.73547
\(153\) 432.176 0.228362
\(154\) −2085.46 −1.09124
\(155\) −963.954 −0.499527
\(156\) −731.730 −0.375547
\(157\) 2654.55 1.34940 0.674701 0.738091i \(-0.264272\pi\)
0.674701 + 0.738091i \(0.264272\pi\)
\(158\) −1654.90 −0.833271
\(159\) 1318.41 0.657591
\(160\) 1247.66 0.616478
\(161\) −631.349 −0.309051
\(162\) −135.516 −0.0657229
\(163\) −1355.54 −0.651375 −0.325688 0.945477i \(-0.605596\pi\)
−0.325688 + 0.945477i \(0.605596\pi\)
\(164\) 523.348 0.249186
\(165\) −1327.45 −0.626314
\(166\) 1222.29 0.571496
\(167\) 1406.91 0.651915 0.325958 0.945384i \(-0.394313\pi\)
0.325958 + 0.945384i \(0.394313\pi\)
\(168\) 1262.37 0.579725
\(169\) 2.33930 0.00106477
\(170\) 543.346 0.245134
\(171\) 1325.30 0.592680
\(172\) −2018.10 −0.894643
\(173\) 3037.13 1.33473 0.667366 0.744730i \(-0.267422\pi\)
0.667366 + 0.744730i \(0.267422\pi\)
\(174\) −369.655 −0.161054
\(175\) 1510.09 0.652296
\(176\) −304.729 −0.130510
\(177\) 177.000 0.0751646
\(178\) 2301.90 0.969296
\(179\) −1561.28 −0.651932 −0.325966 0.945382i \(-0.605689\pi\)
−0.325966 + 0.945382i \(0.605689\pi\)
\(180\) 316.578 0.131091
\(181\) −1573.85 −0.646316 −0.323158 0.946345i \(-0.604745\pi\)
−0.323158 + 0.946345i \(0.604745\pi\)
\(182\) −1494.88 −0.608833
\(183\) 1808.65 0.730597
\(184\) 731.854 0.293223
\(185\) −2689.83 −1.06898
\(186\) 715.365 0.282006
\(187\) −3141.67 −1.22856
\(188\) 718.910 0.278893
\(189\) 514.421 0.197982
\(190\) 1666.21 0.636209
\(191\) 820.690 0.310906 0.155453 0.987843i \(-0.450316\pi\)
0.155453 + 0.987843i \(0.450316\pi\)
\(192\) −814.126 −0.306013
\(193\) 4227.89 1.57684 0.788419 0.615138i \(-0.210900\pi\)
0.788419 + 0.615138i \(0.210900\pi\)
\(194\) 448.761 0.166078
\(195\) −951.528 −0.349438
\(196\) −104.031 −0.0379123
\(197\) −319.247 −0.115459 −0.0577295 0.998332i \(-0.518386\pi\)
−0.0577295 + 0.998332i \(0.518386\pi\)
\(198\) 985.121 0.353583
\(199\) −265.391 −0.0945381 −0.0472691 0.998882i \(-0.515052\pi\)
−0.0472691 + 0.998882i \(0.515052\pi\)
\(200\) −1750.48 −0.618888
\(201\) 464.183 0.162890
\(202\) −332.426 −0.115789
\(203\) 1403.22 0.485156
\(204\) 749.243 0.257145
\(205\) 680.551 0.231862
\(206\) −1853.25 −0.626805
\(207\) 298.234 0.100139
\(208\) −218.433 −0.0728153
\(209\) −9634.17 −3.18856
\(210\) 646.747 0.212523
\(211\) −3536.65 −1.15390 −0.576950 0.816779i \(-0.695757\pi\)
−0.576950 + 0.816779i \(0.695757\pi\)
\(212\) 2285.67 0.740475
\(213\) −1657.31 −0.533131
\(214\) 940.933 0.300565
\(215\) −2624.30 −0.832445
\(216\) −596.312 −0.187842
\(217\) −2715.54 −0.849508
\(218\) −1789.12 −0.555845
\(219\) 323.356 0.0997733
\(220\) −2301.34 −0.705255
\(221\) −2251.98 −0.685450
\(222\) 1996.17 0.603486
\(223\) 4045.80 1.21492 0.607460 0.794350i \(-0.292189\pi\)
0.607460 + 0.794350i \(0.292189\pi\)
\(224\) 3514.78 1.04840
\(225\) −713.329 −0.211357
\(226\) −2680.00 −0.788811
\(227\) 4609.18 1.34767 0.673837 0.738880i \(-0.264645\pi\)
0.673837 + 0.738880i \(0.264645\pi\)
\(228\) 2297.61 0.667382
\(229\) −1842.43 −0.531663 −0.265832 0.964019i \(-0.585647\pi\)
−0.265832 + 0.964019i \(0.585647\pi\)
\(230\) 374.950 0.107493
\(231\) −3739.54 −1.06513
\(232\) −1626.60 −0.460308
\(233\) −1938.03 −0.544913 −0.272456 0.962168i \(-0.587836\pi\)
−0.272456 + 0.962168i \(0.587836\pi\)
\(234\) 706.144 0.197274
\(235\) 934.857 0.259503
\(236\) 306.857 0.0846384
\(237\) −2967.49 −0.813329
\(238\) 1530.65 0.416880
\(239\) 4453.09 1.20522 0.602608 0.798038i \(-0.294128\pi\)
0.602608 + 0.798038i \(0.294128\pi\)
\(240\) 94.5033 0.0254173
\(241\) −1268.11 −0.338948 −0.169474 0.985535i \(-0.554207\pi\)
−0.169474 + 0.985535i \(0.554207\pi\)
\(242\) −4934.46 −1.31074
\(243\) −243.000 −0.0641500
\(244\) 3135.57 0.822683
\(245\) −135.280 −0.0352765
\(246\) −505.047 −0.130897
\(247\) −6905.86 −1.77899
\(248\) 3147.84 0.805999
\(249\) 2191.75 0.557819
\(250\) −2311.21 −0.584695
\(251\) 3848.45 0.967776 0.483888 0.875130i \(-0.339224\pi\)
0.483888 + 0.875130i \(0.339224\pi\)
\(252\) 891.828 0.222936
\(253\) −2167.99 −0.538737
\(254\) 421.037 0.104009
\(255\) 974.301 0.239267
\(256\) −3880.51 −0.947390
\(257\) 3723.47 0.903749 0.451874 0.892082i \(-0.350756\pi\)
0.451874 + 0.892082i \(0.350756\pi\)
\(258\) 1947.53 0.469954
\(259\) −7577.50 −1.81793
\(260\) −1649.62 −0.393481
\(261\) −662.847 −0.157200
\(262\) −4168.13 −0.982854
\(263\) −1776.07 −0.416414 −0.208207 0.978085i \(-0.566763\pi\)
−0.208207 + 0.978085i \(0.566763\pi\)
\(264\) 4334.85 1.01057
\(265\) 2972.24 0.688994
\(266\) 4693.87 1.08195
\(267\) 4127.66 0.946099
\(268\) 804.733 0.183421
\(269\) −6356.42 −1.44073 −0.720367 0.693593i \(-0.756027\pi\)
−0.720367 + 0.693593i \(0.756027\pi\)
\(270\) −305.508 −0.0688615
\(271\) 3734.20 0.837036 0.418518 0.908209i \(-0.362550\pi\)
0.418518 + 0.908209i \(0.362550\pi\)
\(272\) 223.661 0.0498581
\(273\) −2680.54 −0.594262
\(274\) −4007.37 −0.883556
\(275\) 5185.49 1.13708
\(276\) 517.035 0.112760
\(277\) 2987.88 0.648102 0.324051 0.946040i \(-0.394955\pi\)
0.324051 + 0.946040i \(0.394955\pi\)
\(278\) 2878.01 0.620904
\(279\) 1282.76 0.275257
\(280\) 2845.89 0.607410
\(281\) −8120.56 −1.72396 −0.861978 0.506945i \(-0.830775\pi\)
−0.861978 + 0.506945i \(0.830775\pi\)
\(282\) −693.772 −0.146502
\(283\) 5876.00 1.23425 0.617123 0.786866i \(-0.288298\pi\)
0.617123 + 0.786866i \(0.288298\pi\)
\(284\) −2873.20 −0.600328
\(285\) 2987.77 0.620983
\(286\) −5133.26 −1.06131
\(287\) 1917.17 0.394311
\(288\) −1660.30 −0.339701
\(289\) −2607.13 −0.530659
\(290\) −833.354 −0.168746
\(291\) 804.697 0.162104
\(292\) 560.587 0.112349
\(293\) −1680.29 −0.335029 −0.167515 0.985870i \(-0.553574\pi\)
−0.167515 + 0.985870i \(0.553574\pi\)
\(294\) 100.394 0.0199152
\(295\) 399.031 0.0787541
\(296\) 8783.77 1.72482
\(297\) 1766.47 0.345121
\(298\) 5108.92 0.993127
\(299\) −1554.03 −0.300576
\(300\) −1236.66 −0.237996
\(301\) −7392.88 −1.41568
\(302\) −3116.51 −0.593825
\(303\) −596.091 −0.113018
\(304\) 685.872 0.129400
\(305\) 4077.44 0.765487
\(306\) −723.044 −0.135077
\(307\) −10436.9 −1.94028 −0.970138 0.242552i \(-0.922015\pi\)
−0.970138 + 0.242552i \(0.922015\pi\)
\(308\) −6483.07 −1.19937
\(309\) −3323.15 −0.611804
\(310\) 1612.73 0.295473
\(311\) −46.2544 −0.00843359 −0.00421680 0.999991i \(-0.501342\pi\)
−0.00421680 + 0.999991i \(0.501342\pi\)
\(312\) 3107.26 0.563826
\(313\) −1814.13 −0.327607 −0.163803 0.986493i \(-0.552376\pi\)
−0.163803 + 0.986493i \(0.552376\pi\)
\(314\) −4441.15 −0.798180
\(315\) 1159.72 0.207437
\(316\) −5144.59 −0.915842
\(317\) −2234.67 −0.395935 −0.197968 0.980209i \(-0.563434\pi\)
−0.197968 + 0.980209i \(0.563434\pi\)
\(318\) −2205.75 −0.388969
\(319\) 4818.52 0.845722
\(320\) −1835.37 −0.320627
\(321\) 1687.23 0.293372
\(322\) 1056.27 0.182806
\(323\) 7071.14 1.21811
\(324\) −421.278 −0.0722356
\(325\) 3717.01 0.634407
\(326\) 2267.87 0.385293
\(327\) −3208.15 −0.542542
\(328\) −2222.37 −0.374116
\(329\) 2633.57 0.441318
\(330\) 2220.87 0.370469
\(331\) 8239.89 1.36829 0.684147 0.729344i \(-0.260175\pi\)
0.684147 + 0.729344i \(0.260175\pi\)
\(332\) 3799.74 0.628127
\(333\) 3579.43 0.589043
\(334\) −2353.80 −0.385612
\(335\) 1046.46 0.170669
\(336\) 266.224 0.0432254
\(337\) −12009.1 −1.94118 −0.970590 0.240738i \(-0.922610\pi\)
−0.970590 + 0.240738i \(0.922610\pi\)
\(338\) −3.91372 −0.000629818 0
\(339\) −4805.65 −0.769933
\(340\) 1689.10 0.269425
\(341\) −9324.91 −1.48086
\(342\) −2217.27 −0.350574
\(343\) 6153.95 0.968753
\(344\) 8569.76 1.34317
\(345\) 672.342 0.104921
\(346\) −5081.21 −0.789502
\(347\) 2372.02 0.366965 0.183483 0.983023i \(-0.441263\pi\)
0.183483 + 0.983023i \(0.441263\pi\)
\(348\) −1149.15 −0.177014
\(349\) 9595.08 1.47167 0.735835 0.677161i \(-0.236790\pi\)
0.735835 + 0.677161i \(0.236790\pi\)
\(350\) −2526.42 −0.385837
\(351\) 1266.22 0.192553
\(352\) 12069.4 1.82756
\(353\) −1102.51 −0.166234 −0.0831168 0.996540i \(-0.526487\pi\)
−0.0831168 + 0.996540i \(0.526487\pi\)
\(354\) −296.127 −0.0444603
\(355\) −3736.25 −0.558591
\(356\) 7155.93 1.06535
\(357\) 2744.69 0.406904
\(358\) 2612.08 0.385622
\(359\) −1670.88 −0.245643 −0.122821 0.992429i \(-0.539194\pi\)
−0.122821 + 0.992429i \(0.539194\pi\)
\(360\) −1344.33 −0.196813
\(361\) 14825.2 2.16142
\(362\) 2633.10 0.382300
\(363\) −8848.22 −1.27937
\(364\) −4647.13 −0.669164
\(365\) 728.976 0.104538
\(366\) −3025.93 −0.432153
\(367\) 6862.08 0.976015 0.488008 0.872839i \(-0.337724\pi\)
0.488008 + 0.872839i \(0.337724\pi\)
\(368\) 154.343 0.0218632
\(369\) −905.626 −0.127764
\(370\) 4500.18 0.632306
\(371\) 8373.08 1.17172
\(372\) 2223.86 0.309951
\(373\) −6460.37 −0.896796 −0.448398 0.893834i \(-0.648005\pi\)
−0.448398 + 0.893834i \(0.648005\pi\)
\(374\) 5256.11 0.726704
\(375\) −4144.35 −0.570702
\(376\) −3052.82 −0.418716
\(377\) 3453.96 0.471851
\(378\) −860.643 −0.117108
\(379\) −1758.86 −0.238382 −0.119191 0.992871i \(-0.538030\pi\)
−0.119191 + 0.992871i \(0.538030\pi\)
\(380\) 5179.76 0.699253
\(381\) 754.982 0.101519
\(382\) −1373.04 −0.183903
\(383\) 5111.74 0.681978 0.340989 0.940067i \(-0.389238\pi\)
0.340989 + 0.940067i \(0.389238\pi\)
\(384\) −3065.40 −0.407372
\(385\) −8430.46 −1.11599
\(386\) −7073.39 −0.932710
\(387\) 3492.22 0.458707
\(388\) 1395.07 0.182535
\(389\) −7458.10 −0.972084 −0.486042 0.873936i \(-0.661560\pi\)
−0.486042 + 0.873936i \(0.661560\pi\)
\(390\) 1591.94 0.206695
\(391\) 1591.23 0.205810
\(392\) 441.764 0.0569195
\(393\) −7474.08 −0.959332
\(394\) 534.111 0.0682947
\(395\) −6689.93 −0.852169
\(396\) 3062.45 0.388621
\(397\) 12359.2 1.56245 0.781223 0.624252i \(-0.214596\pi\)
0.781223 + 0.624252i \(0.214596\pi\)
\(398\) 444.008 0.0559199
\(399\) 8416.81 1.05606
\(400\) −369.163 −0.0461454
\(401\) −4262.28 −0.530793 −0.265396 0.964139i \(-0.585503\pi\)
−0.265396 + 0.964139i \(0.585503\pi\)
\(402\) −776.593 −0.0963506
\(403\) −6684.18 −0.826211
\(404\) −1033.41 −0.127263
\(405\) −547.822 −0.0672135
\(406\) −2347.63 −0.286973
\(407\) −26020.4 −3.16900
\(408\) −3181.63 −0.386064
\(409\) −3546.96 −0.428816 −0.214408 0.976744i \(-0.568782\pi\)
−0.214408 + 0.976744i \(0.568782\pi\)
\(410\) −1138.58 −0.137148
\(411\) −7185.82 −0.862410
\(412\) −5761.20 −0.688917
\(413\) 1124.10 0.133931
\(414\) −498.955 −0.0592326
\(415\) 4941.11 0.584457
\(416\) 8651.47 1.01965
\(417\) 5160.70 0.606045
\(418\) 16118.3 1.88605
\(419\) −7458.96 −0.869676 −0.434838 0.900509i \(-0.643194\pi\)
−0.434838 + 0.900509i \(0.643194\pi\)
\(420\) 2010.54 0.233582
\(421\) 8742.87 1.01212 0.506059 0.862499i \(-0.331102\pi\)
0.506059 + 0.862499i \(0.331102\pi\)
\(422\) 5916.93 0.682540
\(423\) −1244.04 −0.142996
\(424\) −9706.00 −1.11171
\(425\) −3805.97 −0.434392
\(426\) 2772.73 0.315350
\(427\) 11486.5 1.30181
\(428\) 2925.08 0.330348
\(429\) −9204.71 −1.03591
\(430\) 4390.53 0.492396
\(431\) −784.232 −0.0876452 −0.0438226 0.999039i \(-0.513954\pi\)
−0.0438226 + 0.999039i \(0.513954\pi\)
\(432\) −125.758 −0.0140059
\(433\) 13723.6 1.52313 0.761564 0.648090i \(-0.224432\pi\)
0.761564 + 0.648090i \(0.224432\pi\)
\(434\) 4543.19 0.502489
\(435\) −1494.33 −0.164707
\(436\) −5561.83 −0.610925
\(437\) 4879.62 0.534151
\(438\) −540.984 −0.0590165
\(439\) 17585.6 1.91188 0.955939 0.293564i \(-0.0948415\pi\)
0.955939 + 0.293564i \(0.0948415\pi\)
\(440\) 9772.52 1.05883
\(441\) 180.021 0.0194386
\(442\) 3767.63 0.405448
\(443\) 12123.5 1.30023 0.650117 0.759834i \(-0.274720\pi\)
0.650117 + 0.759834i \(0.274720\pi\)
\(444\) 6205.49 0.663287
\(445\) 9305.43 0.991280
\(446\) −6768.76 −0.718633
\(447\) 9161.07 0.969359
\(448\) −5170.41 −0.545266
\(449\) 12374.8 1.30068 0.650338 0.759645i \(-0.274627\pi\)
0.650338 + 0.759645i \(0.274627\pi\)
\(450\) 1193.42 0.125019
\(451\) 6583.38 0.687360
\(452\) −8331.34 −0.866976
\(453\) −5588.38 −0.579614
\(454\) −7711.31 −0.797158
\(455\) −6043.03 −0.622641
\(456\) −9756.70 −1.00197
\(457\) 4878.50 0.499358 0.249679 0.968329i \(-0.419675\pi\)
0.249679 + 0.968329i \(0.419675\pi\)
\(458\) 3082.44 0.314482
\(459\) −1296.53 −0.131845
\(460\) 1165.61 0.118145
\(461\) 3931.03 0.397150 0.198575 0.980086i \(-0.436369\pi\)
0.198575 + 0.980086i \(0.436369\pi\)
\(462\) 6256.38 0.630028
\(463\) −342.424 −0.0343710 −0.0171855 0.999852i \(-0.505471\pi\)
−0.0171855 + 0.999852i \(0.505471\pi\)
\(464\) −343.038 −0.0343214
\(465\) 2891.86 0.288402
\(466\) 3242.39 0.322319
\(467\) 7929.38 0.785713 0.392857 0.919600i \(-0.371487\pi\)
0.392857 + 0.919600i \(0.371487\pi\)
\(468\) 2195.19 0.216822
\(469\) 2947.97 0.290244
\(470\) −1564.05 −0.153498
\(471\) −7963.65 −0.779078
\(472\) −1303.05 −0.127072
\(473\) −25386.4 −2.46780
\(474\) 4964.70 0.481089
\(475\) −11671.3 −1.12740
\(476\) 4758.35 0.458190
\(477\) −3955.24 −0.379660
\(478\) −7450.16 −0.712892
\(479\) −15158.1 −1.44591 −0.722957 0.690893i \(-0.757217\pi\)
−0.722957 + 0.690893i \(0.757217\pi\)
\(480\) −3742.99 −0.355924
\(481\) −18651.7 −1.76807
\(482\) 2121.60 0.200490
\(483\) 1894.05 0.178431
\(484\) −15339.8 −1.44062
\(485\) 1814.12 0.169845
\(486\) 406.547 0.0379451
\(487\) −3551.47 −0.330457 −0.165228 0.986255i \(-0.552836\pi\)
−0.165228 + 0.986255i \(0.552836\pi\)
\(488\) −13315.1 −1.23513
\(489\) 4066.62 0.376072
\(490\) 226.328 0.0208663
\(491\) 1681.06 0.154511 0.0772556 0.997011i \(-0.475384\pi\)
0.0772556 + 0.997011i \(0.475384\pi\)
\(492\) −1570.04 −0.143868
\(493\) −3536.62 −0.323086
\(494\) 11553.7 1.05228
\(495\) 3982.35 0.361603
\(496\) 663.856 0.0600968
\(497\) −10525.4 −0.949953
\(498\) −3666.88 −0.329953
\(499\) −5475.45 −0.491212 −0.245606 0.969370i \(-0.578987\pi\)
−0.245606 + 0.969370i \(0.578987\pi\)
\(500\) −7184.86 −0.642634
\(501\) −4220.72 −0.376383
\(502\) −6438.58 −0.572446
\(503\) 11336.5 1.00491 0.502453 0.864604i \(-0.332431\pi\)
0.502453 + 0.864604i \(0.332431\pi\)
\(504\) −3787.10 −0.334704
\(505\) −1343.83 −0.118415
\(506\) 3627.12 0.318666
\(507\) −7.01790 −0.000614745 0
\(508\) 1308.88 0.114315
\(509\) −15867.2 −1.38173 −0.690866 0.722983i \(-0.742771\pi\)
−0.690866 + 0.722983i \(0.742771\pi\)
\(510\) −1630.04 −0.141528
\(511\) 2053.59 0.177780
\(512\) −1682.19 −0.145201
\(513\) −3975.90 −0.342184
\(514\) −6229.48 −0.534573
\(515\) −7491.75 −0.641021
\(516\) 6054.30 0.516523
\(517\) 9043.44 0.769303
\(518\) 12677.4 1.07531
\(519\) −9111.38 −0.770607
\(520\) 7005.03 0.590752
\(521\) 831.612 0.0699301 0.0349650 0.999389i \(-0.488868\pi\)
0.0349650 + 0.999389i \(0.488868\pi\)
\(522\) 1108.97 0.0929848
\(523\) −2839.22 −0.237381 −0.118690 0.992931i \(-0.537870\pi\)
−0.118690 + 0.992931i \(0.537870\pi\)
\(524\) −12957.5 −1.08025
\(525\) −4530.26 −0.376603
\(526\) 2971.42 0.246312
\(527\) 6844.16 0.565723
\(528\) 914.188 0.0753502
\(529\) −11068.9 −0.909750
\(530\) −4972.66 −0.407545
\(531\) −531.000 −0.0433963
\(532\) 14591.8 1.18917
\(533\) 4719.03 0.383497
\(534\) −6905.70 −0.559623
\(535\) 3803.72 0.307381
\(536\) −3417.26 −0.275379
\(537\) 4683.85 0.376393
\(538\) 10634.5 0.852204
\(539\) −1308.65 −0.104578
\(540\) −949.733 −0.0756852
\(541\) −2903.19 −0.230717 −0.115359 0.993324i \(-0.536802\pi\)
−0.115359 + 0.993324i \(0.536802\pi\)
\(542\) −6247.44 −0.495112
\(543\) 4721.55 0.373151
\(544\) −8858.53 −0.698173
\(545\) −7232.49 −0.568451
\(546\) 4484.63 0.351510
\(547\) −5807.96 −0.453986 −0.226993 0.973896i \(-0.572889\pi\)
−0.226993 + 0.973896i \(0.572889\pi\)
\(548\) −12457.7 −0.971109
\(549\) −5425.95 −0.421811
\(550\) −8675.49 −0.672589
\(551\) −10845.3 −0.838524
\(552\) −2195.56 −0.169292
\(553\) −18846.1 −1.44922
\(554\) −4998.82 −0.383356
\(555\) 8069.50 0.617173
\(556\) 8946.87 0.682431
\(557\) 20165.3 1.53399 0.766993 0.641656i \(-0.221752\pi\)
0.766993 + 0.641656i \(0.221752\pi\)
\(558\) −2146.10 −0.162816
\(559\) −18197.2 −1.37685
\(560\) 600.178 0.0452896
\(561\) 9425.01 0.709312
\(562\) 13586.0 1.01973
\(563\) −5801.26 −0.434270 −0.217135 0.976142i \(-0.569671\pi\)
−0.217135 + 0.976142i \(0.569671\pi\)
\(564\) −2156.73 −0.161019
\(565\) −10833.9 −0.806701
\(566\) −9830.74 −0.730065
\(567\) −1543.26 −0.114305
\(568\) 12200.9 0.901301
\(569\) −24062.5 −1.77285 −0.886425 0.462873i \(-0.846819\pi\)
−0.886425 + 0.462873i \(0.846819\pi\)
\(570\) −4998.64 −0.367315
\(571\) 9913.83 0.726586 0.363293 0.931675i \(-0.381652\pi\)
0.363293 + 0.931675i \(0.381652\pi\)
\(572\) −15957.8 −1.16648
\(573\) −2462.07 −0.179502
\(574\) −3207.49 −0.233237
\(575\) −2626.41 −0.190485
\(576\) 2442.38 0.176677
\(577\) 18980.4 1.36944 0.684718 0.728808i \(-0.259925\pi\)
0.684718 + 0.728808i \(0.259925\pi\)
\(578\) 4361.81 0.313888
\(579\) −12683.7 −0.910388
\(580\) −2590.65 −0.185467
\(581\) 13919.6 0.993942
\(582\) −1346.28 −0.0958853
\(583\) 28752.3 2.04254
\(584\) −2380.51 −0.168675
\(585\) 2854.58 0.201748
\(586\) 2811.18 0.198172
\(587\) 2678.77 0.188356 0.0941778 0.995555i \(-0.469978\pi\)
0.0941778 + 0.995555i \(0.469978\pi\)
\(588\) 312.094 0.0218887
\(589\) 20988.1 1.46825
\(590\) −667.591 −0.0465835
\(591\) 957.741 0.0666603
\(592\) 1852.43 0.128606
\(593\) 15769.4 1.09202 0.546012 0.837777i \(-0.316145\pi\)
0.546012 + 0.837777i \(0.316145\pi\)
\(594\) −2955.36 −0.204141
\(595\) 6187.66 0.426335
\(596\) 15882.1 1.09154
\(597\) 796.174 0.0545816
\(598\) 2599.95 0.177792
\(599\) −20847.2 −1.42202 −0.711012 0.703180i \(-0.751763\pi\)
−0.711012 + 0.703180i \(0.751763\pi\)
\(600\) 5251.44 0.357315
\(601\) −7083.71 −0.480783 −0.240392 0.970676i \(-0.577276\pi\)
−0.240392 + 0.970676i \(0.577276\pi\)
\(602\) 12368.5 0.837381
\(603\) −1392.55 −0.0940448
\(604\) −9688.31 −0.652669
\(605\) −19947.5 −1.34047
\(606\) 997.279 0.0668510
\(607\) 9394.28 0.628175 0.314087 0.949394i \(-0.398301\pi\)
0.314087 + 0.949394i \(0.398301\pi\)
\(608\) −27165.4 −1.81201
\(609\) −4209.66 −0.280105
\(610\) −6821.69 −0.452790
\(611\) 6482.42 0.429215
\(612\) −2247.73 −0.148463
\(613\) −8222.66 −0.541778 −0.270889 0.962611i \(-0.587318\pi\)
−0.270889 + 0.962611i \(0.587318\pi\)
\(614\) 17461.3 1.14769
\(615\) −2041.65 −0.133866
\(616\) 27530.1 1.80068
\(617\) 23878.4 1.55803 0.779017 0.627003i \(-0.215719\pi\)
0.779017 + 0.627003i \(0.215719\pi\)
\(618\) 5559.74 0.361886
\(619\) −5763.65 −0.374250 −0.187125 0.982336i \(-0.559917\pi\)
−0.187125 + 0.982336i \(0.559917\pi\)
\(620\) 5013.49 0.324752
\(621\) −894.702 −0.0578151
\(622\) 77.3851 0.00498852
\(623\) 26214.2 1.68580
\(624\) 655.298 0.0420399
\(625\) 564.287 0.0361143
\(626\) 3035.11 0.193782
\(627\) 28902.5 1.84092
\(628\) −13806.2 −0.877274
\(629\) 19098.0 1.21063
\(630\) −1940.24 −0.122700
\(631\) −1351.42 −0.0852601 −0.0426301 0.999091i \(-0.513574\pi\)
−0.0426301 + 0.999091i \(0.513574\pi\)
\(632\) 21846.3 1.37500
\(633\) 10610.0 0.666205
\(634\) 3738.67 0.234198
\(635\) 1702.04 0.106368
\(636\) −6857.02 −0.427513
\(637\) −938.051 −0.0583468
\(638\) −8061.54 −0.500250
\(639\) 4971.93 0.307803
\(640\) −6910.67 −0.426826
\(641\) −3444.20 −0.212227 −0.106114 0.994354i \(-0.533841\pi\)
−0.106114 + 0.994354i \(0.533841\pi\)
\(642\) −2822.80 −0.173531
\(643\) −4572.20 −0.280420 −0.140210 0.990122i \(-0.544778\pi\)
−0.140210 + 0.990122i \(0.544778\pi\)
\(644\) 3283.62 0.200920
\(645\) 7872.89 0.480612
\(646\) −11830.3 −0.720519
\(647\) −2938.89 −0.178578 −0.0892889 0.996006i \(-0.528459\pi\)
−0.0892889 + 0.996006i \(0.528459\pi\)
\(648\) 1788.94 0.108451
\(649\) 3860.06 0.233468
\(650\) −6218.67 −0.375256
\(651\) 8146.63 0.490463
\(652\) 7050.12 0.423472
\(653\) 15550.7 0.931924 0.465962 0.884805i \(-0.345708\pi\)
0.465962 + 0.884805i \(0.345708\pi\)
\(654\) 5367.35 0.320917
\(655\) −16849.6 −1.00515
\(656\) −468.682 −0.0278947
\(657\) −970.067 −0.0576041
\(658\) −4406.06 −0.261042
\(659\) −10697.7 −0.632356 −0.316178 0.948700i \(-0.602400\pi\)
−0.316178 + 0.948700i \(0.602400\pi\)
\(660\) 6904.01 0.407179
\(661\) −4979.38 −0.293004 −0.146502 0.989210i \(-0.546801\pi\)
−0.146502 + 0.989210i \(0.546801\pi\)
\(662\) −13785.6 −0.809355
\(663\) 6755.93 0.395745
\(664\) −16135.4 −0.943037
\(665\) 18974.9 1.10649
\(666\) −5988.50 −0.348423
\(667\) −2440.54 −0.141676
\(668\) −7317.27 −0.423823
\(669\) −12137.4 −0.701434
\(670\) −1750.76 −0.100952
\(671\) 39443.6 2.26930
\(672\) −10544.3 −0.605293
\(673\) 26662.2 1.52712 0.763559 0.645738i \(-0.223450\pi\)
0.763559 + 0.645738i \(0.223450\pi\)
\(674\) 20091.6 1.14822
\(675\) 2139.99 0.122027
\(676\) −12.1666 −0.000692228 0
\(677\) −27190.8 −1.54362 −0.771808 0.635856i \(-0.780647\pi\)
−0.771808 + 0.635856i \(0.780647\pi\)
\(678\) 8040.01 0.455420
\(679\) 5110.53 0.288842
\(680\) −7172.69 −0.404500
\(681\) −13827.5 −0.778080
\(682\) 15600.9 0.875937
\(683\) 4166.70 0.233433 0.116716 0.993165i \(-0.462763\pi\)
0.116716 + 0.993165i \(0.462763\pi\)
\(684\) −6892.84 −0.385313
\(685\) −16199.8 −0.903594
\(686\) −10295.8 −0.573023
\(687\) 5527.28 0.306956
\(688\) 1807.30 0.100149
\(689\) 20609.9 1.13959
\(690\) −1124.85 −0.0620613
\(691\) 25963.4 1.42937 0.714684 0.699447i \(-0.246570\pi\)
0.714684 + 0.699447i \(0.246570\pi\)
\(692\) −15796.0 −0.867736
\(693\) 11218.6 0.614950
\(694\) −3968.48 −0.217062
\(695\) 11634.3 0.634986
\(696\) 4879.80 0.265759
\(697\) −4831.97 −0.262588
\(698\) −16052.9 −0.870502
\(699\) 5814.09 0.314605
\(700\) −7853.90 −0.424071
\(701\) −31569.0 −1.70092 −0.850459 0.526041i \(-0.823676\pi\)
−0.850459 + 0.526041i \(0.823676\pi\)
\(702\) −2118.43 −0.113896
\(703\) 58565.6 3.14203
\(704\) −17754.7 −0.950504
\(705\) −2804.57 −0.149824
\(706\) 1844.53 0.0983283
\(707\) −3785.70 −0.201380
\(708\) −920.570 −0.0488660
\(709\) 10296.1 0.545383 0.272691 0.962102i \(-0.412086\pi\)
0.272691 + 0.962102i \(0.412086\pi\)
\(710\) 6250.87 0.330410
\(711\) 8902.46 0.469576
\(712\) −30387.3 −1.59946
\(713\) 4722.99 0.248075
\(714\) −4591.96 −0.240686
\(715\) −20751.2 −1.08538
\(716\) 8120.18 0.423834
\(717\) −13359.3 −0.695831
\(718\) 2795.44 0.145299
\(719\) 14401.2 0.746976 0.373488 0.927635i \(-0.378162\pi\)
0.373488 + 0.927635i \(0.378162\pi\)
\(720\) −283.510 −0.0146747
\(721\) −21104.9 −1.09014
\(722\) −24803.0 −1.27850
\(723\) 3804.34 0.195692
\(724\) 8185.53 0.420183
\(725\) 5837.38 0.299027
\(726\) 14803.4 0.756756
\(727\) −1687.62 −0.0860940 −0.0430470 0.999073i \(-0.513707\pi\)
−0.0430470 + 0.999073i \(0.513707\pi\)
\(728\) 19733.8 1.00465
\(729\) 729.000 0.0370370
\(730\) −1219.60 −0.0618349
\(731\) 18632.7 0.942759
\(732\) −9406.72 −0.474976
\(733\) −28217.6 −1.42189 −0.710943 0.703250i \(-0.751732\pi\)
−0.710943 + 0.703250i \(0.751732\pi\)
\(734\) −11480.5 −0.577319
\(735\) 405.841 0.0203669
\(736\) −6113.05 −0.306155
\(737\) 10123.0 0.505952
\(738\) 1515.14 0.0755734
\(739\) −21535.4 −1.07198 −0.535989 0.844225i \(-0.680061\pi\)
−0.535989 + 0.844225i \(0.680061\pi\)
\(740\) 13989.7 0.694963
\(741\) 20717.6 1.02710
\(742\) −14008.4 −0.693080
\(743\) 7391.04 0.364941 0.182470 0.983211i \(-0.441591\pi\)
0.182470 + 0.983211i \(0.441591\pi\)
\(744\) −9443.51 −0.465344
\(745\) 20652.8 1.01565
\(746\) 10808.4 0.530461
\(747\) −6575.26 −0.322057
\(748\) 16339.7 0.798715
\(749\) 10715.4 0.522741
\(750\) 6933.63 0.337574
\(751\) 4661.31 0.226489 0.113245 0.993567i \(-0.463876\pi\)
0.113245 + 0.993567i \(0.463876\pi\)
\(752\) −643.817 −0.0312202
\(753\) −11545.3 −0.558746
\(754\) −5778.58 −0.279103
\(755\) −12598.5 −0.607293
\(756\) −2675.48 −0.128712
\(757\) −20667.4 −0.992297 −0.496149 0.868238i \(-0.665253\pi\)
−0.496149 + 0.868238i \(0.665253\pi\)
\(758\) 2942.63 0.141004
\(759\) 6503.97 0.311040
\(760\) −21995.6 −1.04982
\(761\) 35282.4 1.68066 0.840332 0.542071i \(-0.182360\pi\)
0.840332 + 0.542071i \(0.182360\pi\)
\(762\) −1263.11 −0.0600494
\(763\) −20374.6 −0.966722
\(764\) −4268.38 −0.202126
\(765\) −2922.90 −0.138141
\(766\) −8552.11 −0.403395
\(767\) 2766.93 0.130258
\(768\) 11641.5 0.546976
\(769\) −3764.58 −0.176533 −0.0882667 0.996097i \(-0.528133\pi\)
−0.0882667 + 0.996097i \(0.528133\pi\)
\(770\) 14104.4 0.660115
\(771\) −11170.4 −0.521779
\(772\) −21989.1 −1.02513
\(773\) 13143.1 0.611547 0.305773 0.952104i \(-0.401085\pi\)
0.305773 + 0.952104i \(0.401085\pi\)
\(774\) −5842.60 −0.271328
\(775\) −11296.6 −0.523596
\(776\) −5924.08 −0.274049
\(777\) 22732.5 1.04958
\(778\) 12477.6 0.574994
\(779\) −14817.6 −0.681510
\(780\) 4948.86 0.227176
\(781\) −36143.0 −1.65595
\(782\) −2662.18 −0.121738
\(783\) 1988.54 0.0907595
\(784\) 93.1648 0.00424402
\(785\) −17953.3 −0.816283
\(786\) 12504.4 0.567451
\(787\) −34738.5 −1.57344 −0.786718 0.617312i \(-0.788222\pi\)
−0.786718 + 0.617312i \(0.788222\pi\)
\(788\) 1660.39 0.0750622
\(789\) 5328.20 0.240417
\(790\) 11192.5 0.504064
\(791\) −30520.1 −1.37190
\(792\) −13004.5 −0.583455
\(793\) 28273.5 1.26611
\(794\) −20677.4 −0.924196
\(795\) −8916.73 −0.397791
\(796\) 1380.29 0.0614612
\(797\) −4155.16 −0.184672 −0.0923359 0.995728i \(-0.529433\pi\)
−0.0923359 + 0.995728i \(0.529433\pi\)
\(798\) −14081.6 −0.624666
\(799\) −6637.56 −0.293892
\(800\) 14621.5 0.646183
\(801\) −12383.0 −0.546230
\(802\) 7130.93 0.313967
\(803\) 7051.83 0.309905
\(804\) −2414.20 −0.105898
\(805\) 4269.96 0.186952
\(806\) 11182.9 0.488709
\(807\) 19069.3 0.831809
\(808\) 4388.35 0.191066
\(809\) 25096.7 1.09067 0.545335 0.838218i \(-0.316402\pi\)
0.545335 + 0.838218i \(0.316402\pi\)
\(810\) 916.523 0.0397572
\(811\) −15819.9 −0.684969 −0.342485 0.939523i \(-0.611268\pi\)
−0.342485 + 0.939523i \(0.611268\pi\)
\(812\) −7298.09 −0.315410
\(813\) −11202.6 −0.483263
\(814\) 43533.0 1.87448
\(815\) 9167.84 0.394031
\(816\) −670.982 −0.0287856
\(817\) 57138.7 2.44679
\(818\) 5934.18 0.253647
\(819\) 8041.62 0.343097
\(820\) −3539.52 −0.150738
\(821\) 4697.39 0.199684 0.0998418 0.995003i \(-0.468166\pi\)
0.0998418 + 0.995003i \(0.468166\pi\)
\(822\) 12022.1 0.510121
\(823\) −26318.7 −1.11472 −0.557359 0.830272i \(-0.688185\pi\)
−0.557359 + 0.830272i \(0.688185\pi\)
\(824\) 24464.7 1.03430
\(825\) −15556.5 −0.656493
\(826\) −1880.66 −0.0792211
\(827\) 24232.9 1.01894 0.509469 0.860489i \(-0.329842\pi\)
0.509469 + 0.860489i \(0.329842\pi\)
\(828\) −1551.10 −0.0651021
\(829\) −6139.03 −0.257198 −0.128599 0.991697i \(-0.541048\pi\)
−0.128599 + 0.991697i \(0.541048\pi\)
\(830\) −8266.64 −0.345710
\(831\) −8963.63 −0.374182
\(832\) −12726.7 −0.530312
\(833\) 960.502 0.0399513
\(834\) −8634.02 −0.358479
\(835\) −9515.24 −0.394357
\(836\) 50107.0 2.07295
\(837\) −3848.27 −0.158920
\(838\) 12479.1 0.514419
\(839\) 19605.1 0.806727 0.403364 0.915040i \(-0.367841\pi\)
0.403364 + 0.915040i \(0.367841\pi\)
\(840\) −8537.68 −0.350688
\(841\) −18964.7 −0.777593
\(842\) −14627.1 −0.598674
\(843\) 24361.7 0.995327
\(844\) 18394.0 0.750174
\(845\) −15.8212 −0.000644102 0
\(846\) 2081.31 0.0845828
\(847\) −56194.0 −2.27963
\(848\) −2046.92 −0.0828911
\(849\) −17628.0 −0.712593
\(850\) 6367.51 0.256945
\(851\) 13179.1 0.530874
\(852\) 8619.60 0.346599
\(853\) −33730.2 −1.35393 −0.676963 0.736017i \(-0.736704\pi\)
−0.676963 + 0.736017i \(0.736704\pi\)
\(854\) −19217.3 −0.770027
\(855\) −8963.31 −0.358525
\(856\) −12421.2 −0.495968
\(857\) −28613.3 −1.14050 −0.570251 0.821470i \(-0.693154\pi\)
−0.570251 + 0.821470i \(0.693154\pi\)
\(858\) 15399.8 0.612750
\(859\) −3049.90 −0.121142 −0.0605712 0.998164i \(-0.519292\pi\)
−0.0605712 + 0.998164i \(0.519292\pi\)
\(860\) 13648.9 0.541189
\(861\) −5751.52 −0.227655
\(862\) 1312.04 0.0518427
\(863\) −26717.9 −1.05387 −0.526934 0.849906i \(-0.676659\pi\)
−0.526934 + 0.849906i \(0.676659\pi\)
\(864\) 4980.90 0.196127
\(865\) −20540.8 −0.807408
\(866\) −22960.0 −0.900940
\(867\) 7821.38 0.306376
\(868\) 14123.4 0.552282
\(869\) −64715.8 −2.52627
\(870\) 2500.06 0.0974253
\(871\) 7256.28 0.282284
\(872\) 23618.0 0.917211
\(873\) −2414.09 −0.0935906
\(874\) −8163.77 −0.315954
\(875\) −26320.2 −1.01690
\(876\) −1681.76 −0.0648646
\(877\) −10007.0 −0.385303 −0.192652 0.981267i \(-0.561709\pi\)
−0.192652 + 0.981267i \(0.561709\pi\)
\(878\) −29421.3 −1.13089
\(879\) 5040.87 0.193429
\(880\) 2060.95 0.0789486
\(881\) 19155.2 0.732527 0.366263 0.930511i \(-0.380637\pi\)
0.366263 + 0.930511i \(0.380637\pi\)
\(882\) −301.181 −0.0114981
\(883\) −37716.3 −1.43743 −0.718716 0.695303i \(-0.755270\pi\)
−0.718716 + 0.695303i \(0.755270\pi\)
\(884\) 11712.4 0.445625
\(885\) −1197.09 −0.0454687
\(886\) −20283.0 −0.769096
\(887\) 44807.5 1.69616 0.848078 0.529872i \(-0.177760\pi\)
0.848078 + 0.529872i \(0.177760\pi\)
\(888\) −26351.3 −0.995825
\(889\) 4794.80 0.180891
\(890\) −15568.3 −0.586348
\(891\) −5299.41 −0.199256
\(892\) −21042.1 −0.789844
\(893\) −20354.6 −0.762756
\(894\) −15326.8 −0.573382
\(895\) 10559.3 0.394368
\(896\) −19468.0 −0.725870
\(897\) 4662.10 0.173538
\(898\) −20703.5 −0.769358
\(899\) −10497.2 −0.389434
\(900\) 3709.99 0.137407
\(901\) −21103.2 −0.780299
\(902\) −11014.2 −0.406578
\(903\) 22178.6 0.817341
\(904\) 35378.6 1.30163
\(905\) 10644.3 0.390971
\(906\) 9349.54 0.342845
\(907\) 548.725 0.0200883 0.0100442 0.999950i \(-0.496803\pi\)
0.0100442 + 0.999950i \(0.496803\pi\)
\(908\) −23972.2 −0.876151
\(909\) 1788.27 0.0652511
\(910\) 10110.2 0.368296
\(911\) 23571.3 0.857246 0.428623 0.903483i \(-0.358999\pi\)
0.428623 + 0.903483i \(0.358999\pi\)
\(912\) −2057.62 −0.0747089
\(913\) 47798.4 1.73264
\(914\) −8161.89 −0.295373
\(915\) −12232.3 −0.441954
\(916\) 9582.38 0.345645
\(917\) −47467.0 −1.70938
\(918\) 2169.13 0.0779870
\(919\) 24363.5 0.874513 0.437256 0.899337i \(-0.355950\pi\)
0.437256 + 0.899337i \(0.355950\pi\)
\(920\) −4949.70 −0.177377
\(921\) 31310.7 1.12022
\(922\) −6576.73 −0.234917
\(923\) −25907.7 −0.923902
\(924\) 19449.2 0.692459
\(925\) −31522.3 −1.12048
\(926\) 572.886 0.0203307
\(927\) 9969.46 0.353225
\(928\) 13586.7 0.480610
\(929\) 7503.02 0.264980 0.132490 0.991184i \(-0.457703\pi\)
0.132490 + 0.991184i \(0.457703\pi\)
\(930\) −4838.18 −0.170592
\(931\) 2945.45 0.103688
\(932\) 10079.6 0.354259
\(933\) 138.763 0.00486914
\(934\) −13266.1 −0.464754
\(935\) 21247.8 0.743185
\(936\) −9321.77 −0.325525
\(937\) 33994.7 1.18523 0.592613 0.805487i \(-0.298096\pi\)
0.592613 + 0.805487i \(0.298096\pi\)
\(938\) −4932.05 −0.171681
\(939\) 5442.40 0.189144
\(940\) −4862.15 −0.168708
\(941\) 35769.7 1.23917 0.619585 0.784929i \(-0.287301\pi\)
0.619585 + 0.784929i \(0.287301\pi\)
\(942\) 13323.5 0.460830
\(943\) −3334.43 −0.115147
\(944\) −274.804 −0.00947470
\(945\) −3479.15 −0.119764
\(946\) 42472.3 1.45972
\(947\) 15352.1 0.526798 0.263399 0.964687i \(-0.415156\pi\)
0.263399 + 0.964687i \(0.415156\pi\)
\(948\) 15433.8 0.528762
\(949\) 5054.81 0.172904
\(950\) 19526.4 0.666865
\(951\) 6704.01 0.228593
\(952\) −20206.1 −0.687903
\(953\) −38129.6 −1.29605 −0.648027 0.761617i \(-0.724406\pi\)
−0.648027 + 0.761617i \(0.724406\pi\)
\(954\) 6617.25 0.224572
\(955\) −5550.52 −0.188074
\(956\) −23160.3 −0.783535
\(957\) −14455.6 −0.488278
\(958\) 25360.0 0.855267
\(959\) −45636.3 −1.53668
\(960\) 5506.12 0.185114
\(961\) −9476.58 −0.318102
\(962\) 31204.8 1.04583
\(963\) −5061.70 −0.169378
\(964\) 6595.41 0.220357
\(965\) −28594.2 −0.953864
\(966\) −3168.80 −0.105543
\(967\) −32504.3 −1.08094 −0.540469 0.841364i \(-0.681753\pi\)
−0.540469 + 0.841364i \(0.681753\pi\)
\(968\) 65139.6 2.16288
\(969\) −21213.4 −0.703275
\(970\) −3035.08 −0.100464
\(971\) −20184.6 −0.667100 −0.333550 0.942732i \(-0.608247\pi\)
−0.333550 + 0.942732i \(0.608247\pi\)
\(972\) 1263.83 0.0417052
\(973\) 32775.0 1.07987
\(974\) 5941.72 0.195467
\(975\) −11151.0 −0.366275
\(976\) −2808.05 −0.0920938
\(977\) 34251.1 1.12159 0.560794 0.827956i \(-0.310496\pi\)
0.560794 + 0.827956i \(0.310496\pi\)
\(978\) −6803.60 −0.222449
\(979\) 90017.0 2.93867
\(980\) 703.587 0.0229340
\(981\) 9624.46 0.313237
\(982\) −2812.46 −0.0913944
\(983\) 26633.5 0.864169 0.432084 0.901833i \(-0.357778\pi\)
0.432084 + 0.901833i \(0.357778\pi\)
\(984\) 6667.11 0.215996
\(985\) 2159.14 0.0698436
\(986\) 5916.89 0.191108
\(987\) −7900.72 −0.254795
\(988\) 35917.1 1.15655
\(989\) 12858.0 0.413408
\(990\) −6662.60 −0.213890
\(991\) −28729.1 −0.920900 −0.460450 0.887686i \(-0.652312\pi\)
−0.460450 + 0.887686i \(0.652312\pi\)
\(992\) −26293.3 −0.841547
\(993\) −24719.7 −0.789985
\(994\) 17609.3 0.561903
\(995\) 1794.90 0.0571882
\(996\) −11399.2 −0.362649
\(997\) −8221.82 −0.261171 −0.130586 0.991437i \(-0.541686\pi\)
−0.130586 + 0.991437i \(0.541686\pi\)
\(998\) 9160.61 0.290555
\(999\) −10738.3 −0.340084
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.c.1.3 8
3.2 odd 2 531.4.a.f.1.6 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.4.a.c.1.3 8 1.1 even 1 trivial
531.4.a.f.1.6 8 3.2 odd 2