Properties

Label 177.4.a.b.1.5
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: \(x^{7} - 41 x^{5} - 7 x^{4} + 484 x^{3} + 63 x^{2} - 1736 x - 44\)
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 1.5
Root \(-2.74916\) of defining polynomial
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.74916 q^{2} -3.00000 q^{3} -0.442134 q^{4} +13.7745 q^{5} -8.24747 q^{6} -35.6462 q^{7} -23.2088 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q+2.74916 q^{2} -3.00000 q^{3} -0.442134 q^{4} +13.7745 q^{5} -8.24747 q^{6} -35.6462 q^{7} -23.2088 q^{8} +9.00000 q^{9} +37.8683 q^{10} -30.8537 q^{11} +1.32640 q^{12} +14.6435 q^{13} -97.9970 q^{14} -41.3236 q^{15} -60.2674 q^{16} -77.8827 q^{17} +24.7424 q^{18} +98.6377 q^{19} -6.09019 q^{20} +106.939 q^{21} -84.8216 q^{22} -117.065 q^{23} +69.6263 q^{24} +64.7375 q^{25} +40.2572 q^{26} -27.0000 q^{27} +15.7604 q^{28} -54.2015 q^{29} -113.605 q^{30} -231.433 q^{31} +19.9854 q^{32} +92.5610 q^{33} -214.112 q^{34} -491.009 q^{35} -3.97921 q^{36} -258.311 q^{37} +271.171 q^{38} -43.9304 q^{39} -319.690 q^{40} +326.921 q^{41} +293.991 q^{42} +250.920 q^{43} +13.6415 q^{44} +123.971 q^{45} -321.830 q^{46} +509.390 q^{47} +180.802 q^{48} +927.650 q^{49} +177.974 q^{50} +233.648 q^{51} -6.47437 q^{52} -313.730 q^{53} -74.2272 q^{54} -424.994 q^{55} +827.304 q^{56} -295.913 q^{57} -149.008 q^{58} +59.0000 q^{59} +18.2706 q^{60} +528.854 q^{61} -636.245 q^{62} -320.816 q^{63} +537.082 q^{64} +201.707 q^{65} +254.465 q^{66} -373.284 q^{67} +34.4346 q^{68} +351.195 q^{69} -1349.86 q^{70} -521.969 q^{71} -208.879 q^{72} +809.404 q^{73} -710.137 q^{74} -194.212 q^{75} -43.6111 q^{76} +1099.82 q^{77} -120.771 q^{78} -926.088 q^{79} -830.155 q^{80} +81.0000 q^{81} +898.756 q^{82} -1311.77 q^{83} -47.2812 q^{84} -1072.80 q^{85} +689.818 q^{86} +162.604 q^{87} +716.075 q^{88} +510.201 q^{89} +340.815 q^{90} -521.983 q^{91} +51.7585 q^{92} +694.298 q^{93} +1400.39 q^{94} +1358.69 q^{95} -59.9561 q^{96} -856.449 q^{97} +2550.26 q^{98} -277.683 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q - 21q^{3} + 26q^{4} - 2q^{5} - 59q^{7} - 21q^{8} + 63q^{9} + O(q^{10}) \) \( 7q - 21q^{3} + 26q^{4} - 2q^{5} - 59q^{7} - 21q^{8} + 63q^{9} - 71q^{10} - 5q^{11} - 78q^{12} - 67q^{13} - 65q^{14} + 6q^{15} - 94q^{16} - 23q^{17} - 176q^{19} - 207q^{20} + 177q^{21} - 704q^{22} - 218q^{23} + 63q^{24} - 183q^{25} + 58q^{26} - 189q^{27} - 938q^{28} + 168q^{29} + 213q^{30} - 604q^{31} - 448q^{32} + 15q^{33} - 610q^{34} - 336q^{35} + 234q^{36} - 505q^{37} - 453q^{38} + 201q^{39} - 1080q^{40} - 265q^{41} + 195q^{42} - 493q^{43} + 504q^{44} - 18q^{45} + 381q^{46} - 244q^{47} + 282q^{48} + 770q^{49} + 1639q^{50} + 69q^{51} + 160q^{52} + 686q^{53} - 116q^{55} + 2190q^{56} + 528q^{57} + 1584q^{58} + 413q^{59} + 621q^{60} - 838q^{61} + 286q^{62} - 531q^{63} + 205q^{64} + 490q^{65} + 2112q^{66} - 1504q^{67} + 3047q^{68} + 654q^{69} + 1530q^{70} - 1267q^{71} - 189q^{72} - 666q^{73} + 528q^{74} + 549q^{75} - 64q^{76} + 1109q^{77} - 174q^{78} - 2741q^{79} + 1213q^{80} + 567q^{81} + 953q^{82} - 2025q^{83} + 2814q^{84} - 1274q^{85} + 4394q^{86} - 504q^{87} - 1639q^{88} + 616q^{89} - 639q^{90} - 2415q^{91} + 218q^{92} + 1812q^{93} + 900q^{94} + 2554q^{95} + 1344q^{96} - 1298q^{97} - 172q^{98} - 45q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.74916 0.971974 0.485987 0.873966i \(-0.338460\pi\)
0.485987 + 0.873966i \(0.338460\pi\)
\(3\) −3.00000 −0.577350
\(4\) −0.442134 −0.0552668
\(5\) 13.7745 1.23203 0.616015 0.787734i \(-0.288746\pi\)
0.616015 + 0.787734i \(0.288746\pi\)
\(6\) −8.24747 −0.561169
\(7\) −35.6462 −1.92471 −0.962357 0.271790i \(-0.912384\pi\)
−0.962357 + 0.271790i \(0.912384\pi\)
\(8\) −23.2088 −1.02569
\(9\) 9.00000 0.333333
\(10\) 37.8683 1.19750
\(11\) −30.8537 −0.845703 −0.422851 0.906199i \(-0.638971\pi\)
−0.422851 + 0.906199i \(0.638971\pi\)
\(12\) 1.32640 0.0319083
\(13\) 14.6435 0.312413 0.156206 0.987724i \(-0.450074\pi\)
0.156206 + 0.987724i \(0.450074\pi\)
\(14\) −97.9970 −1.87077
\(15\) −41.3236 −0.711313
\(16\) −60.2674 −0.941679
\(17\) −77.8827 −1.11114 −0.555568 0.831471i \(-0.687499\pi\)
−0.555568 + 0.831471i \(0.687499\pi\)
\(18\) 24.7424 0.323991
\(19\) 98.6377 1.19100 0.595501 0.803355i \(-0.296954\pi\)
0.595501 + 0.803355i \(0.296954\pi\)
\(20\) −6.09019 −0.0680904
\(21\) 106.939 1.11123
\(22\) −84.8216 −0.822001
\(23\) −117.065 −1.06129 −0.530647 0.847593i \(-0.678051\pi\)
−0.530647 + 0.847593i \(0.678051\pi\)
\(24\) 69.6263 0.592183
\(25\) 64.7375 0.517900
\(26\) 40.2572 0.303657
\(27\) −27.0000 −0.192450
\(28\) 15.7604 0.106373
\(29\) −54.2015 −0.347068 −0.173534 0.984828i \(-0.555519\pi\)
−0.173534 + 0.984828i \(0.555519\pi\)
\(30\) −113.605 −0.691378
\(31\) −231.433 −1.34086 −0.670428 0.741975i \(-0.733890\pi\)
−0.670428 + 0.741975i \(0.733890\pi\)
\(32\) 19.9854 0.110405
\(33\) 92.5610 0.488267
\(34\) −214.112 −1.08000
\(35\) −491.009 −2.37131
\(36\) −3.97921 −0.0184223
\(37\) −258.311 −1.14773 −0.573866 0.818950i \(-0.694557\pi\)
−0.573866 + 0.818950i \(0.694557\pi\)
\(38\) 271.171 1.15762
\(39\) −43.9304 −0.180371
\(40\) −319.690 −1.26368
\(41\) 326.921 1.24528 0.622639 0.782509i \(-0.286060\pi\)
0.622639 + 0.782509i \(0.286060\pi\)
\(42\) 293.991 1.08009
\(43\) 250.920 0.889882 0.444941 0.895560i \(-0.353225\pi\)
0.444941 + 0.895560i \(0.353225\pi\)
\(44\) 13.6415 0.0467393
\(45\) 123.971 0.410677
\(46\) −321.830 −1.03155
\(47\) 509.390 1.58090 0.790449 0.612528i \(-0.209847\pi\)
0.790449 + 0.612528i \(0.209847\pi\)
\(48\) 180.802 0.543678
\(49\) 927.650 2.70452
\(50\) 177.974 0.503385
\(51\) 233.648 0.641515
\(52\) −6.47437 −0.0172660
\(53\) −313.730 −0.813097 −0.406549 0.913629i \(-0.633268\pi\)
−0.406549 + 0.913629i \(0.633268\pi\)
\(54\) −74.2272 −0.187056
\(55\) −424.994 −1.04193
\(56\) 827.304 1.97416
\(57\) −295.913 −0.687625
\(58\) −149.008 −0.337341
\(59\) 59.0000 0.130189
\(60\) 18.2706 0.0393120
\(61\) 528.854 1.11005 0.555023 0.831835i \(-0.312709\pi\)
0.555023 + 0.831835i \(0.312709\pi\)
\(62\) −636.245 −1.30328
\(63\) −320.816 −0.641571
\(64\) 537.082 1.04899
\(65\) 201.707 0.384902
\(66\) 254.465 0.474582
\(67\) −373.284 −0.680656 −0.340328 0.940307i \(-0.610538\pi\)
−0.340328 + 0.940307i \(0.610538\pi\)
\(68\) 34.4346 0.0614090
\(69\) 351.195 0.612738
\(70\) −1349.86 −2.30485
\(71\) −521.969 −0.872483 −0.436241 0.899830i \(-0.643691\pi\)
−0.436241 + 0.899830i \(0.643691\pi\)
\(72\) −208.879 −0.341897
\(73\) 809.404 1.29772 0.648860 0.760908i \(-0.275246\pi\)
0.648860 + 0.760908i \(0.275246\pi\)
\(74\) −710.137 −1.11556
\(75\) −194.212 −0.299010
\(76\) −43.6111 −0.0658229
\(77\) 1099.82 1.62773
\(78\) −120.771 −0.175316
\(79\) −926.088 −1.31890 −0.659449 0.751749i \(-0.729211\pi\)
−0.659449 + 0.751749i \(0.729211\pi\)
\(80\) −830.155 −1.16018
\(81\) 81.0000 0.111111
\(82\) 898.756 1.21038
\(83\) −1311.77 −1.73476 −0.867380 0.497646i \(-0.834198\pi\)
−0.867380 + 0.497646i \(0.834198\pi\)
\(84\) −47.2812 −0.0614143
\(85\) −1072.80 −1.36895
\(86\) 689.818 0.864942
\(87\) 162.604 0.200380
\(88\) 716.075 0.867430
\(89\) 510.201 0.607654 0.303827 0.952727i \(-0.401735\pi\)
0.303827 + 0.952727i \(0.401735\pi\)
\(90\) 340.815 0.399167
\(91\) −521.983 −0.601305
\(92\) 51.7585 0.0586543
\(93\) 694.298 0.774144
\(94\) 1400.39 1.53659
\(95\) 1358.69 1.46735
\(96\) −59.9561 −0.0637421
\(97\) −856.449 −0.896486 −0.448243 0.893912i \(-0.647950\pi\)
−0.448243 + 0.893912i \(0.647950\pi\)
\(98\) 2550.26 2.62872
\(99\) −277.683 −0.281901
\(100\) −28.6227 −0.0286227
\(101\) 811.456 0.799435 0.399717 0.916638i \(-0.369108\pi\)
0.399717 + 0.916638i \(0.369108\pi\)
\(102\) 642.335 0.623536
\(103\) −419.340 −0.401153 −0.200577 0.979678i \(-0.564282\pi\)
−0.200577 + 0.979678i \(0.564282\pi\)
\(104\) −339.856 −0.320439
\(105\) 1473.03 1.36907
\(106\) −862.494 −0.790309
\(107\) −1165.05 −1.05261 −0.526305 0.850296i \(-0.676423\pi\)
−0.526305 + 0.850296i \(0.676423\pi\)
\(108\) 11.9376 0.0106361
\(109\) −2016.17 −1.77169 −0.885844 0.463984i \(-0.846419\pi\)
−0.885844 + 0.463984i \(0.846419\pi\)
\(110\) −1168.38 −1.01273
\(111\) 774.933 0.662643
\(112\) 2148.30 1.81246
\(113\) −731.760 −0.609188 −0.304594 0.952482i \(-0.598521\pi\)
−0.304594 + 0.952482i \(0.598521\pi\)
\(114\) −813.512 −0.668354
\(115\) −1612.51 −1.30755
\(116\) 23.9643 0.0191813
\(117\) 131.791 0.104138
\(118\) 162.200 0.126540
\(119\) 2776.22 2.13862
\(120\) 959.069 0.729588
\(121\) −379.051 −0.284787
\(122\) 1453.90 1.07894
\(123\) −980.762 −0.718962
\(124\) 102.324 0.0741048
\(125\) −830.087 −0.593962
\(126\) −881.973 −0.623590
\(127\) −1187.43 −0.829666 −0.414833 0.909898i \(-0.636160\pi\)
−0.414833 + 0.909898i \(0.636160\pi\)
\(128\) 1316.64 0.909185
\(129\) −752.760 −0.513774
\(130\) 554.523 0.374115
\(131\) −250.996 −0.167402 −0.0837008 0.996491i \(-0.526674\pi\)
−0.0837008 + 0.996491i \(0.526674\pi\)
\(132\) −40.9244 −0.0269849
\(133\) −3516.06 −2.29234
\(134\) −1026.22 −0.661580
\(135\) −371.912 −0.237104
\(136\) 1807.56 1.13968
\(137\) 2474.51 1.54315 0.771576 0.636137i \(-0.219469\pi\)
0.771576 + 0.636137i \(0.219469\pi\)
\(138\) 965.490 0.595565
\(139\) 2067.65 1.26169 0.630847 0.775907i \(-0.282708\pi\)
0.630847 + 0.775907i \(0.282708\pi\)
\(140\) 217.092 0.131054
\(141\) −1528.17 −0.912731
\(142\) −1434.97 −0.848031
\(143\) −451.804 −0.264208
\(144\) −542.407 −0.313893
\(145\) −746.600 −0.427598
\(146\) 2225.18 1.26135
\(147\) −2782.95 −1.56146
\(148\) 114.208 0.0634314
\(149\) 70.2921 0.0386480 0.0193240 0.999813i \(-0.493849\pi\)
0.0193240 + 0.999813i \(0.493849\pi\)
\(150\) −533.921 −0.290630
\(151\) 2156.31 1.16211 0.581054 0.813865i \(-0.302641\pi\)
0.581054 + 0.813865i \(0.302641\pi\)
\(152\) −2289.26 −1.22160
\(153\) −700.944 −0.370379
\(154\) 3023.57 1.58212
\(155\) −3187.88 −1.65198
\(156\) 19.4231 0.00996855
\(157\) 105.729 0.0537459 0.0268729 0.999639i \(-0.491445\pi\)
0.0268729 + 0.999639i \(0.491445\pi\)
\(158\) −2545.96 −1.28194
\(159\) 941.191 0.469442
\(160\) 275.289 0.136022
\(161\) 4172.92 2.04268
\(162\) 222.682 0.107997
\(163\) −1006.11 −0.483463 −0.241731 0.970343i \(-0.577715\pi\)
−0.241731 + 0.970343i \(0.577715\pi\)
\(164\) −144.543 −0.0688226
\(165\) 1274.98 0.601560
\(166\) −3606.25 −1.68614
\(167\) −668.739 −0.309872 −0.154936 0.987925i \(-0.549517\pi\)
−0.154936 + 0.987925i \(0.549517\pi\)
\(168\) −2481.91 −1.13978
\(169\) −1982.57 −0.902398
\(170\) −2949.29 −1.33059
\(171\) 887.739 0.397001
\(172\) −110.940 −0.0491809
\(173\) −2879.96 −1.26566 −0.632831 0.774290i \(-0.718107\pi\)
−0.632831 + 0.774290i \(0.718107\pi\)
\(174\) 447.025 0.194764
\(175\) −2307.64 −0.996809
\(176\) 1859.47 0.796380
\(177\) −177.000 −0.0751646
\(178\) 1402.62 0.590624
\(179\) 1700.00 0.709856 0.354928 0.934894i \(-0.384505\pi\)
0.354928 + 0.934894i \(0.384505\pi\)
\(180\) −54.8117 −0.0226968
\(181\) −1750.62 −0.718910 −0.359455 0.933162i \(-0.617037\pi\)
−0.359455 + 0.933162i \(0.617037\pi\)
\(182\) −1435.01 −0.584452
\(183\) −1586.56 −0.640886
\(184\) 2716.93 1.08856
\(185\) −3558.11 −1.41404
\(186\) 1908.73 0.752447
\(187\) 2402.97 0.939691
\(188\) −225.219 −0.0873711
\(189\) 962.447 0.370411
\(190\) 3735.24 1.42623
\(191\) 1504.78 0.570062 0.285031 0.958518i \(-0.407996\pi\)
0.285031 + 0.958518i \(0.407996\pi\)
\(192\) −1611.25 −0.605634
\(193\) −803.437 −0.299651 −0.149826 0.988712i \(-0.547871\pi\)
−0.149826 + 0.988712i \(0.547871\pi\)
\(194\) −2354.51 −0.871361
\(195\) −605.120 −0.222223
\(196\) −410.146 −0.149470
\(197\) −1329.45 −0.480808 −0.240404 0.970673i \(-0.577280\pi\)
−0.240404 + 0.970673i \(0.577280\pi\)
\(198\) −763.394 −0.274000
\(199\) −2857.91 −1.01805 −0.509025 0.860752i \(-0.669994\pi\)
−0.509025 + 0.860752i \(0.669994\pi\)
\(200\) −1502.48 −0.531206
\(201\) 1119.85 0.392977
\(202\) 2230.82 0.777030
\(203\) 1932.08 0.668006
\(204\) −103.304 −0.0354545
\(205\) 4503.18 1.53422
\(206\) −1152.83 −0.389911
\(207\) −1053.59 −0.353764
\(208\) −882.524 −0.294192
\(209\) −3043.33 −1.00723
\(210\) 4049.58 1.33070
\(211\) −3121.15 −1.01834 −0.509168 0.860667i \(-0.670047\pi\)
−0.509168 + 0.860667i \(0.670047\pi\)
\(212\) 138.711 0.0449373
\(213\) 1565.91 0.503728
\(214\) −3202.89 −1.02311
\(215\) 3456.30 1.09636
\(216\) 626.636 0.197394
\(217\) 8249.69 2.58076
\(218\) −5542.76 −1.72203
\(219\) −2428.21 −0.749239
\(220\) 187.905 0.0575842
\(221\) −1140.47 −0.347133
\(222\) 2130.41 0.644071
\(223\) −2100.41 −0.630734 −0.315367 0.948970i \(-0.602128\pi\)
−0.315367 + 0.948970i \(0.602128\pi\)
\(224\) −712.402 −0.212497
\(225\) 582.637 0.172633
\(226\) −2011.72 −0.592114
\(227\) 2601.37 0.760613 0.380306 0.924861i \(-0.375819\pi\)
0.380306 + 0.924861i \(0.375819\pi\)
\(228\) 130.833 0.0380029
\(229\) −1502.73 −0.433637 −0.216819 0.976212i \(-0.569568\pi\)
−0.216819 + 0.976212i \(0.569568\pi\)
\(230\) −4433.06 −1.27090
\(231\) −3299.45 −0.939773
\(232\) 1257.95 0.355984
\(233\) −1672.77 −0.470329 −0.235164 0.971956i \(-0.575563\pi\)
−0.235164 + 0.971956i \(0.575563\pi\)
\(234\) 362.314 0.101219
\(235\) 7016.60 1.94771
\(236\) −26.0859 −0.00719512
\(237\) 2778.26 0.761467
\(238\) 7632.27 2.07868
\(239\) 3489.49 0.944420 0.472210 0.881486i \(-0.343456\pi\)
0.472210 + 0.881486i \(0.343456\pi\)
\(240\) 2490.47 0.669829
\(241\) −872.061 −0.233089 −0.116544 0.993185i \(-0.537182\pi\)
−0.116544 + 0.993185i \(0.537182\pi\)
\(242\) −1042.07 −0.276806
\(243\) −243.000 −0.0641500
\(244\) −233.825 −0.0613487
\(245\) 12777.9 3.33205
\(246\) −2696.27 −0.698812
\(247\) 1444.40 0.372084
\(248\) 5371.26 1.37531
\(249\) 3935.30 1.00156
\(250\) −2282.04 −0.577316
\(251\) −463.531 −0.116565 −0.0582825 0.998300i \(-0.518562\pi\)
−0.0582825 + 0.998300i \(0.518562\pi\)
\(252\) 141.844 0.0354576
\(253\) 3611.88 0.897538
\(254\) −3264.44 −0.806413
\(255\) 3218.39 0.790366
\(256\) −677.006 −0.165285
\(257\) 2168.52 0.526338 0.263169 0.964750i \(-0.415232\pi\)
0.263169 + 0.964750i \(0.415232\pi\)
\(258\) −2069.46 −0.499375
\(259\) 9207.80 2.20905
\(260\) −89.1814 −0.0212723
\(261\) −487.813 −0.115689
\(262\) −690.027 −0.162710
\(263\) 567.749 0.133114 0.0665569 0.997783i \(-0.478799\pi\)
0.0665569 + 0.997783i \(0.478799\pi\)
\(264\) −2148.23 −0.500811
\(265\) −4321.48 −1.00176
\(266\) −9666.20 −2.22809
\(267\) −1530.60 −0.350829
\(268\) 165.042 0.0376177
\(269\) −326.225 −0.0739415 −0.0369708 0.999316i \(-0.511771\pi\)
−0.0369708 + 0.999316i \(0.511771\pi\)
\(270\) −1022.44 −0.230459
\(271\) 1478.00 0.331300 0.165650 0.986185i \(-0.447028\pi\)
0.165650 + 0.986185i \(0.447028\pi\)
\(272\) 4693.79 1.04633
\(273\) 1565.95 0.347163
\(274\) 6802.82 1.49990
\(275\) −1997.39 −0.437989
\(276\) −155.275 −0.0338641
\(277\) 8647.79 1.87580 0.937898 0.346911i \(-0.112769\pi\)
0.937898 + 0.346911i \(0.112769\pi\)
\(278\) 5684.29 1.22633
\(279\) −2082.89 −0.446952
\(280\) 11395.7 2.43223
\(281\) −4653.34 −0.987882 −0.493941 0.869495i \(-0.664444\pi\)
−0.493941 + 0.869495i \(0.664444\pi\)
\(282\) −4201.18 −0.887151
\(283\) −2594.93 −0.545062 −0.272531 0.962147i \(-0.587861\pi\)
−0.272531 + 0.962147i \(0.587861\pi\)
\(284\) 230.780 0.0482193
\(285\) −4076.06 −0.847176
\(286\) −1242.08 −0.256803
\(287\) −11653.5 −2.39680
\(288\) 179.868 0.0368015
\(289\) 1152.71 0.234625
\(290\) −2052.52 −0.415614
\(291\) 2569.35 0.517587
\(292\) −357.865 −0.0717208
\(293\) −7299.73 −1.45548 −0.727739 0.685854i \(-0.759429\pi\)
−0.727739 + 0.685854i \(0.759429\pi\)
\(294\) −7650.77 −1.51769
\(295\) 812.697 0.160397
\(296\) 5995.07 1.17722
\(297\) 833.049 0.162756
\(298\) 193.244 0.0375648
\(299\) −1714.24 −0.331561
\(300\) 85.8680 0.0165253
\(301\) −8944.34 −1.71277
\(302\) 5928.04 1.12954
\(303\) −2434.37 −0.461554
\(304\) −5944.64 −1.12154
\(305\) 7284.72 1.36761
\(306\) −1927.01 −0.359999
\(307\) 3677.41 0.683651 0.341826 0.939763i \(-0.388955\pi\)
0.341826 + 0.939763i \(0.388955\pi\)
\(308\) −486.266 −0.0899597
\(309\) 1258.02 0.231606
\(310\) −8763.97 −1.60568
\(311\) 3389.46 0.618002 0.309001 0.951062i \(-0.400005\pi\)
0.309001 + 0.951062i \(0.400005\pi\)
\(312\) 1019.57 0.185006
\(313\) −4847.47 −0.875384 −0.437692 0.899125i \(-0.644204\pi\)
−0.437692 + 0.899125i \(0.644204\pi\)
\(314\) 290.666 0.0522396
\(315\) −4419.08 −0.790435
\(316\) 409.455 0.0728913
\(317\) 10460.9 1.85344 0.926721 0.375750i \(-0.122615\pi\)
0.926721 + 0.375750i \(0.122615\pi\)
\(318\) 2587.48 0.456285
\(319\) 1672.31 0.293516
\(320\) 7398.05 1.29239
\(321\) 3495.14 0.607724
\(322\) 11472.0 1.98544
\(323\) −7682.17 −1.32337
\(324\) −35.8129 −0.00614076
\(325\) 947.980 0.161798
\(326\) −2765.95 −0.469913
\(327\) 6048.50 1.02288
\(328\) −7587.42 −1.27727
\(329\) −18157.8 −3.04277
\(330\) 3505.13 0.584700
\(331\) −2859.84 −0.474898 −0.237449 0.971400i \(-0.576311\pi\)
−0.237449 + 0.971400i \(0.576311\pi\)
\(332\) 579.977 0.0958747
\(333\) −2324.80 −0.382577
\(334\) −1838.47 −0.301187
\(335\) −5141.82 −0.838589
\(336\) −6444.91 −1.04643
\(337\) 4699.94 0.759710 0.379855 0.925046i \(-0.375974\pi\)
0.379855 + 0.925046i \(0.375974\pi\)
\(338\) −5450.39 −0.877108
\(339\) 2195.28 0.351715
\(340\) 474.320 0.0756577
\(341\) 7140.55 1.13397
\(342\) 2440.53 0.385874
\(343\) −20840.6 −3.28071
\(344\) −5823.54 −0.912745
\(345\) 4837.54 0.754912
\(346\) −7917.47 −1.23019
\(347\) 951.938 0.147270 0.0736350 0.997285i \(-0.476540\pi\)
0.0736350 + 0.997285i \(0.476540\pi\)
\(348\) −71.8930 −0.0110743
\(349\) −10647.9 −1.63315 −0.816575 0.577239i \(-0.804130\pi\)
−0.816575 + 0.577239i \(0.804130\pi\)
\(350\) −6344.08 −0.968872
\(351\) −395.373 −0.0601238
\(352\) −616.622 −0.0933695
\(353\) 11818.1 1.78191 0.890957 0.454088i \(-0.150035\pi\)
0.890957 + 0.454088i \(0.150035\pi\)
\(354\) −486.601 −0.0730580
\(355\) −7189.87 −1.07493
\(356\) −225.578 −0.0335831
\(357\) −8328.66 −1.23473
\(358\) 4673.58 0.689962
\(359\) 8794.89 1.29297 0.646485 0.762926i \(-0.276238\pi\)
0.646485 + 0.762926i \(0.276238\pi\)
\(360\) −2877.21 −0.421228
\(361\) 2870.40 0.418486
\(362\) −4812.74 −0.698762
\(363\) 1137.15 0.164422
\(364\) 230.787 0.0332322
\(365\) 11149.2 1.59883
\(366\) −4361.71 −0.622924
\(367\) 13284.1 1.88945 0.944723 0.327869i \(-0.106331\pi\)
0.944723 + 0.327869i \(0.106331\pi\)
\(368\) 7055.21 0.999397
\(369\) 2942.29 0.415093
\(370\) −9781.80 −1.37441
\(371\) 11183.3 1.56498
\(372\) −306.973 −0.0427844
\(373\) −11897.3 −1.65153 −0.825763 0.564018i \(-0.809255\pi\)
−0.825763 + 0.564018i \(0.809255\pi\)
\(374\) 6606.13 0.913355
\(375\) 2490.26 0.342924
\(376\) −11822.3 −1.62151
\(377\) −793.697 −0.108428
\(378\) 2645.92 0.360030
\(379\) 1743.93 0.236357 0.118179 0.992992i \(-0.462294\pi\)
0.118179 + 0.992992i \(0.462294\pi\)
\(380\) −600.722 −0.0810958
\(381\) 3562.30 0.479008
\(382\) 4136.87 0.554085
\(383\) 1572.59 0.209806 0.104903 0.994482i \(-0.466547\pi\)
0.104903 + 0.994482i \(0.466547\pi\)
\(384\) −3949.92 −0.524918
\(385\) 15149.4 2.00542
\(386\) −2208.77 −0.291253
\(387\) 2258.28 0.296627
\(388\) 378.665 0.0495459
\(389\) −3545.77 −0.462153 −0.231077 0.972936i \(-0.574225\pi\)
−0.231077 + 0.972936i \(0.574225\pi\)
\(390\) −1663.57 −0.215995
\(391\) 9117.34 1.17924
\(392\) −21529.6 −2.77400
\(393\) 752.988 0.0966494
\(394\) −3654.86 −0.467333
\(395\) −12756.4 −1.62492
\(396\) 122.773 0.0155798
\(397\) 7176.14 0.907205 0.453602 0.891204i \(-0.350139\pi\)
0.453602 + 0.891204i \(0.350139\pi\)
\(398\) −7856.85 −0.989518
\(399\) 10548.2 1.32348
\(400\) −3901.56 −0.487695
\(401\) 7431.68 0.925487 0.462744 0.886492i \(-0.346865\pi\)
0.462744 + 0.886492i \(0.346865\pi\)
\(402\) 3078.65 0.381963
\(403\) −3388.97 −0.418900
\(404\) −358.773 −0.0441822
\(405\) 1115.74 0.136892
\(406\) 5311.58 0.649284
\(407\) 7969.84 0.970639
\(408\) −5422.68 −0.657997
\(409\) −5038.83 −0.609179 −0.304589 0.952484i \(-0.598519\pi\)
−0.304589 + 0.952484i \(0.598519\pi\)
\(410\) 12379.9 1.49122
\(411\) −7423.54 −0.890939
\(412\) 185.405 0.0221705
\(413\) −2103.12 −0.250576
\(414\) −2896.47 −0.343850
\(415\) −18069.0 −2.13728
\(416\) 292.655 0.0344918
\(417\) −6202.94 −0.728439
\(418\) −8366.60 −0.979005
\(419\) −3543.16 −0.413114 −0.206557 0.978435i \(-0.566226\pi\)
−0.206557 + 0.978435i \(0.566226\pi\)
\(420\) −651.276 −0.0756643
\(421\) 13131.9 1.52022 0.760109 0.649796i \(-0.225145\pi\)
0.760109 + 0.649796i \(0.225145\pi\)
\(422\) −8580.54 −0.989797
\(423\) 4584.51 0.526966
\(424\) 7281.29 0.833987
\(425\) −5041.93 −0.575458
\(426\) 4304.92 0.489611
\(427\) −18851.6 −2.13652
\(428\) 515.107 0.0581744
\(429\) 1355.41 0.152541
\(430\) 9501.92 1.06564
\(431\) −9117.45 −1.01896 −0.509480 0.860482i \(-0.670162\pi\)
−0.509480 + 0.860482i \(0.670162\pi\)
\(432\) 1627.22 0.181226
\(433\) −2554.40 −0.283502 −0.141751 0.989902i \(-0.545273\pi\)
−0.141751 + 0.989902i \(0.545273\pi\)
\(434\) 22679.7 2.50843
\(435\) 2239.80 0.246874
\(436\) 891.417 0.0979155
\(437\) −11547.0 −1.26400
\(438\) −6675.54 −0.728241
\(439\) 1523.94 0.165681 0.0828404 0.996563i \(-0.473601\pi\)
0.0828404 + 0.996563i \(0.473601\pi\)
\(440\) 9863.59 1.06870
\(441\) 8348.85 0.901507
\(442\) −3135.34 −0.337404
\(443\) 10110.8 1.08437 0.542186 0.840258i \(-0.317597\pi\)
0.542186 + 0.840258i \(0.317597\pi\)
\(444\) −342.624 −0.0366221
\(445\) 7027.78 0.748649
\(446\) −5774.35 −0.613057
\(447\) −210.876 −0.0223134
\(448\) −19144.9 −2.01900
\(449\) 17927.7 1.88432 0.942162 0.335158i \(-0.108790\pi\)
0.942162 + 0.335158i \(0.108790\pi\)
\(450\) 1601.76 0.167795
\(451\) −10086.7 −1.05314
\(452\) 323.536 0.0336678
\(453\) −6468.94 −0.670943
\(454\) 7151.58 0.739296
\(455\) −7190.07 −0.740826
\(456\) 6867.77 0.705292
\(457\) −8911.04 −0.912125 −0.456062 0.889948i \(-0.650741\pi\)
−0.456062 + 0.889948i \(0.650741\pi\)
\(458\) −4131.23 −0.421484
\(459\) 2102.83 0.213838
\(460\) 712.948 0.0722639
\(461\) 16724.3 1.68965 0.844825 0.535042i \(-0.179704\pi\)
0.844825 + 0.535042i \(0.179704\pi\)
\(462\) −9070.70 −0.913435
\(463\) −14050.4 −1.41031 −0.705157 0.709051i \(-0.749123\pi\)
−0.705157 + 0.709051i \(0.749123\pi\)
\(464\) 3266.58 0.326826
\(465\) 9563.63 0.953769
\(466\) −4598.70 −0.457147
\(467\) 10526.3 1.04304 0.521520 0.853239i \(-0.325365\pi\)
0.521520 + 0.853239i \(0.325365\pi\)
\(468\) −58.2694 −0.00575535
\(469\) 13306.2 1.31007
\(470\) 19289.7 1.89313
\(471\) −317.187 −0.0310302
\(472\) −1369.32 −0.133534
\(473\) −7741.80 −0.752576
\(474\) 7637.88 0.740126
\(475\) 6385.56 0.616820
\(476\) −1227.46 −0.118195
\(477\) −2823.57 −0.271032
\(478\) 9593.16 0.917952
\(479\) −6393.78 −0.609894 −0.304947 0.952369i \(-0.598639\pi\)
−0.304947 + 0.952369i \(0.598639\pi\)
\(480\) −825.867 −0.0785323
\(481\) −3782.56 −0.358566
\(482\) −2397.43 −0.226556
\(483\) −12518.8 −1.17934
\(484\) 167.592 0.0157393
\(485\) −11797.2 −1.10450
\(486\) −668.045 −0.0623522
\(487\) 14196.4 1.32095 0.660473 0.750850i \(-0.270356\pi\)
0.660473 + 0.750850i \(0.270356\pi\)
\(488\) −12274.1 −1.13857
\(489\) 3018.32 0.279127
\(490\) 35128.6 3.23867
\(491\) −5867.49 −0.539299 −0.269650 0.962958i \(-0.586908\pi\)
−0.269650 + 0.962958i \(0.586908\pi\)
\(492\) 433.629 0.0397347
\(493\) 4221.36 0.385640
\(494\) 3970.87 0.361656
\(495\) −3824.95 −0.347311
\(496\) 13947.9 1.26266
\(497\) 18606.2 1.67928
\(498\) 10818.8 0.973495
\(499\) −8345.43 −0.748683 −0.374341 0.927291i \(-0.622131\pi\)
−0.374341 + 0.927291i \(0.622131\pi\)
\(500\) 367.010 0.0328264
\(501\) 2006.22 0.178905
\(502\) −1274.32 −0.113298
\(503\) −1607.53 −0.142498 −0.0712488 0.997459i \(-0.522698\pi\)
−0.0712488 + 0.997459i \(0.522698\pi\)
\(504\) 7445.73 0.658054
\(505\) 11177.4 0.984929
\(506\) 9929.64 0.872384
\(507\) 5947.71 0.521000
\(508\) 525.004 0.0458530
\(509\) −9106.68 −0.793018 −0.396509 0.918031i \(-0.629779\pi\)
−0.396509 + 0.918031i \(0.629779\pi\)
\(510\) 8847.86 0.768216
\(511\) −28852.2 −2.49774
\(512\) −12394.3 −1.06984
\(513\) −2663.22 −0.229208
\(514\) 5961.61 0.511586
\(515\) −5776.21 −0.494233
\(516\) 332.821 0.0283946
\(517\) −15716.5 −1.33697
\(518\) 25313.7 2.14714
\(519\) 8639.89 0.730731
\(520\) −4681.36 −0.394791
\(521\) −7301.03 −0.613942 −0.306971 0.951719i \(-0.599316\pi\)
−0.306971 + 0.951719i \(0.599316\pi\)
\(522\) −1341.08 −0.112447
\(523\) 4874.89 0.407579 0.203790 0.979015i \(-0.434674\pi\)
0.203790 + 0.979015i \(0.434674\pi\)
\(524\) 110.974 0.00925175
\(525\) 6922.93 0.575508
\(526\) 1560.83 0.129383
\(527\) 18024.6 1.48987
\(528\) −5578.41 −0.459790
\(529\) 1537.22 0.126343
\(530\) −11880.4 −0.973685
\(531\) 531.000 0.0433963
\(532\) 1554.57 0.126690
\(533\) 4787.25 0.389041
\(534\) −4207.87 −0.340997
\(535\) −16047.9 −1.29685
\(536\) 8663.47 0.698143
\(537\) −5100.01 −0.409836
\(538\) −896.843 −0.0718692
\(539\) −28621.4 −2.28722
\(540\) 164.435 0.0131040
\(541\) −1382.28 −0.109850 −0.0549249 0.998490i \(-0.517492\pi\)
−0.0549249 + 0.998490i \(0.517492\pi\)
\(542\) 4063.26 0.322015
\(543\) 5251.87 0.415063
\(544\) −1556.51 −0.122675
\(545\) −27771.8 −2.18277
\(546\) 4305.04 0.337434
\(547\) −20117.5 −1.57251 −0.786255 0.617902i \(-0.787983\pi\)
−0.786255 + 0.617902i \(0.787983\pi\)
\(548\) −1094.07 −0.0852851
\(549\) 4759.69 0.370016
\(550\) −5491.14 −0.425714
\(551\) −5346.31 −0.413358
\(552\) −8150.80 −0.628480
\(553\) 33011.5 2.53850
\(554\) 23774.1 1.82322
\(555\) 10674.3 0.816396
\(556\) −914.178 −0.0697298
\(557\) −12926.3 −0.983311 −0.491655 0.870790i \(-0.663608\pi\)
−0.491655 + 0.870790i \(0.663608\pi\)
\(558\) −5726.20 −0.434426
\(559\) 3674.33 0.278010
\(560\) 29591.9 2.23301
\(561\) −7208.90 −0.542531
\(562\) −12792.8 −0.960195
\(563\) 1483.56 0.111056 0.0555279 0.998457i \(-0.482316\pi\)
0.0555279 + 0.998457i \(0.482316\pi\)
\(564\) 675.657 0.0504437
\(565\) −10079.6 −0.750538
\(566\) −7133.87 −0.529786
\(567\) −2887.34 −0.213857
\(568\) 12114.2 0.894899
\(569\) 535.139 0.0394274 0.0197137 0.999806i \(-0.493725\pi\)
0.0197137 + 0.999806i \(0.493725\pi\)
\(570\) −11205.7 −0.823433
\(571\) 11303.3 0.828420 0.414210 0.910181i \(-0.364058\pi\)
0.414210 + 0.910181i \(0.364058\pi\)
\(572\) 199.758 0.0146019
\(573\) −4514.33 −0.329125
\(574\) −32037.2 −2.32963
\(575\) −7578.50 −0.549644
\(576\) 4833.74 0.349663
\(577\) −22867.6 −1.64990 −0.824950 0.565206i \(-0.808797\pi\)
−0.824950 + 0.565206i \(0.808797\pi\)
\(578\) 3168.99 0.228049
\(579\) 2410.31 0.173004
\(580\) 330.097 0.0236320
\(581\) 46759.5 3.33892
\(582\) 7063.54 0.503081
\(583\) 9679.73 0.687639
\(584\) −18785.3 −1.33106
\(585\) 1815.36 0.128301
\(586\) −20068.1 −1.41469
\(587\) −17589.4 −1.23679 −0.618393 0.785869i \(-0.712216\pi\)
−0.618393 + 0.785869i \(0.712216\pi\)
\(588\) 1230.44 0.0862966
\(589\) −22828.0 −1.59696
\(590\) 2234.23 0.155901
\(591\) 3988.34 0.277595
\(592\) 15567.7 1.08079
\(593\) −16110.5 −1.11565 −0.557825 0.829959i \(-0.688364\pi\)
−0.557825 + 0.829959i \(0.688364\pi\)
\(594\) 2290.18 0.158194
\(595\) 38241.1 2.63485
\(596\) −31.0785 −0.00213595
\(597\) 8573.74 0.587772
\(598\) −4712.70 −0.322269
\(599\) 22231.7 1.51646 0.758231 0.651986i \(-0.226064\pi\)
0.758231 + 0.651986i \(0.226064\pi\)
\(600\) 4507.43 0.306692
\(601\) −16668.9 −1.13135 −0.565673 0.824629i \(-0.691384\pi\)
−0.565673 + 0.824629i \(0.691384\pi\)
\(602\) −24589.4 −1.66477
\(603\) −3359.56 −0.226885
\(604\) −953.380 −0.0642259
\(605\) −5221.25 −0.350866
\(606\) −6692.46 −0.448618
\(607\) 11293.3 0.755155 0.377577 0.925978i \(-0.376757\pi\)
0.377577 + 0.925978i \(0.376757\pi\)
\(608\) 1971.31 0.131492
\(609\) −5796.23 −0.385673
\(610\) 20026.8 1.32928
\(611\) 7459.23 0.493892
\(612\) 309.912 0.0204697
\(613\) −9187.06 −0.605321 −0.302661 0.953098i \(-0.597875\pi\)
−0.302661 + 0.953098i \(0.597875\pi\)
\(614\) 10109.8 0.664491
\(615\) −13509.5 −0.885783
\(616\) −25525.3 −1.66955
\(617\) −5405.24 −0.352685 −0.176342 0.984329i \(-0.556427\pi\)
−0.176342 + 0.984329i \(0.556427\pi\)
\(618\) 3458.50 0.225115
\(619\) 26890.8 1.74610 0.873049 0.487633i \(-0.162140\pi\)
0.873049 + 0.487633i \(0.162140\pi\)
\(620\) 1409.47 0.0912994
\(621\) 3160.76 0.204246
\(622\) 9318.16 0.600682
\(623\) −18186.7 −1.16956
\(624\) 2647.57 0.169852
\(625\) −19526.2 −1.24968
\(626\) −13326.5 −0.850850
\(627\) 9130.00 0.581527
\(628\) −46.7465 −0.00297036
\(629\) 20117.9 1.27529
\(630\) −12148.8 −0.768282
\(631\) 13088.1 0.825718 0.412859 0.910795i \(-0.364530\pi\)
0.412859 + 0.910795i \(0.364530\pi\)
\(632\) 21493.3 1.35278
\(633\) 9363.46 0.587937
\(634\) 28758.6 1.80150
\(635\) −16356.3 −1.02217
\(636\) −416.133 −0.0259446
\(637\) 13584.0 0.844926
\(638\) 4597.46 0.285290
\(639\) −4697.72 −0.290828
\(640\) 18136.1 1.12014
\(641\) 11372.4 0.700754 0.350377 0.936609i \(-0.386053\pi\)
0.350377 + 0.936609i \(0.386053\pi\)
\(642\) 9608.68 0.590692
\(643\) 28882.8 1.77142 0.885712 0.464236i \(-0.153671\pi\)
0.885712 + 0.464236i \(0.153671\pi\)
\(644\) −1844.99 −0.112893
\(645\) −10368.9 −0.632985
\(646\) −21119.5 −1.28628
\(647\) 3509.03 0.213222 0.106611 0.994301i \(-0.466000\pi\)
0.106611 + 0.994301i \(0.466000\pi\)
\(648\) −1879.91 −0.113966
\(649\) −1820.37 −0.110101
\(650\) 2606.15 0.157264
\(651\) −24749.1 −1.49000
\(652\) 444.835 0.0267194
\(653\) −12551.5 −0.752185 −0.376092 0.926582i \(-0.622732\pi\)
−0.376092 + 0.926582i \(0.622732\pi\)
\(654\) 16628.3 0.994217
\(655\) −3457.35 −0.206244
\(656\) −19702.7 −1.17265
\(657\) 7284.64 0.432573
\(658\) −49918.7 −2.95750
\(659\) −26042.1 −1.53938 −0.769692 0.638415i \(-0.779590\pi\)
−0.769692 + 0.638415i \(0.779590\pi\)
\(660\) −563.714 −0.0332463
\(661\) 8841.43 0.520260 0.260130 0.965574i \(-0.416235\pi\)
0.260130 + 0.965574i \(0.416235\pi\)
\(662\) −7862.16 −0.461588
\(663\) 3421.41 0.200417
\(664\) 30444.5 1.77933
\(665\) −48432.0 −2.82423
\(666\) −6391.24 −0.371855
\(667\) 6345.10 0.368341
\(668\) 295.673 0.0171256
\(669\) 6301.22 0.364154
\(670\) −14135.7 −0.815087
\(671\) −16317.1 −0.938770
\(672\) 2137.21 0.122685
\(673\) 5539.99 0.317312 0.158656 0.987334i \(-0.449284\pi\)
0.158656 + 0.987334i \(0.449284\pi\)
\(674\) 12920.9 0.738418
\(675\) −1747.91 −0.0996699
\(676\) 876.562 0.0498727
\(677\) 6105.80 0.346625 0.173312 0.984867i \(-0.444553\pi\)
0.173312 + 0.984867i \(0.444553\pi\)
\(678\) 6035.17 0.341857
\(679\) 30529.1 1.72548
\(680\) 24898.3 1.40413
\(681\) −7804.11 −0.439140
\(682\) 19630.5 1.10218
\(683\) 6169.93 0.345660 0.172830 0.984952i \(-0.444709\pi\)
0.172830 + 0.984952i \(0.444709\pi\)
\(684\) −392.500 −0.0219410
\(685\) 34085.2 1.90121
\(686\) −57294.0 −3.18877
\(687\) 4508.18 0.250361
\(688\) −15122.3 −0.837983
\(689\) −4594.09 −0.254022
\(690\) 13299.2 0.733755
\(691\) −24137.5 −1.32885 −0.664423 0.747357i \(-0.731323\pi\)
−0.664423 + 0.747357i \(0.731323\pi\)
\(692\) 1273.33 0.0699491
\(693\) 9898.34 0.542578
\(694\) 2617.03 0.143143
\(695\) 28480.8 1.55445
\(696\) −3773.85 −0.205528
\(697\) −25461.5 −1.38368
\(698\) −29272.8 −1.58738
\(699\) 5018.30 0.271544
\(700\) 1020.29 0.0550904
\(701\) 1381.52 0.0744354 0.0372177 0.999307i \(-0.488151\pi\)
0.0372177 + 0.999307i \(0.488151\pi\)
\(702\) −1086.94 −0.0584388
\(703\) −25479.2 −1.36695
\(704\) −16571.0 −0.887133
\(705\) −21049.8 −1.12451
\(706\) 32489.9 1.73197
\(707\) −28925.3 −1.53868
\(708\) 78.2578 0.00415411
\(709\) 11440.3 0.605995 0.302998 0.952991i \(-0.402013\pi\)
0.302998 + 0.952991i \(0.402013\pi\)
\(710\) −19766.1 −1.04480
\(711\) −8334.79 −0.439633
\(712\) −11841.1 −0.623266
\(713\) 27092.7 1.42304
\(714\) −22896.8 −1.20013
\(715\) −6223.39 −0.325513
\(716\) −751.630 −0.0392315
\(717\) −10468.5 −0.545261
\(718\) 24178.5 1.25673
\(719\) 23773.0 1.23308 0.616539 0.787324i \(-0.288534\pi\)
0.616539 + 0.787324i \(0.288534\pi\)
\(720\) −7471.40 −0.386726
\(721\) 14947.9 0.772105
\(722\) 7891.17 0.406757
\(723\) 2616.18 0.134574
\(724\) 774.010 0.0397319
\(725\) −3508.87 −0.179746
\(726\) 3126.22 0.159814
\(727\) −38328.7 −1.95534 −0.977670 0.210146i \(-0.932606\pi\)
−0.977670 + 0.210146i \(0.932606\pi\)
\(728\) 12114.6 0.616753
\(729\) 729.000 0.0370370
\(730\) 30650.8 1.55402
\(731\) −19542.3 −0.988781
\(732\) 701.474 0.0354197
\(733\) −23440.6 −1.18117 −0.590586 0.806975i \(-0.701103\pi\)
−0.590586 + 0.806975i \(0.701103\pi\)
\(734\) 36520.2 1.83649
\(735\) −38333.8 −1.92376
\(736\) −2339.59 −0.117172
\(737\) 11517.2 0.575633
\(738\) 8088.81 0.403459
\(739\) −20289.0 −1.00994 −0.504968 0.863138i \(-0.668496\pi\)
−0.504968 + 0.863138i \(0.668496\pi\)
\(740\) 1573.16 0.0781495
\(741\) −4333.19 −0.214823
\(742\) 30744.6 1.52112
\(743\) −21978.5 −1.08521 −0.542607 0.839987i \(-0.682563\pi\)
−0.542607 + 0.839987i \(0.682563\pi\)
\(744\) −16113.8 −0.794033
\(745\) 968.240 0.0476155
\(746\) −32707.6 −1.60524
\(747\) −11805.9 −0.578254
\(748\) −1062.43 −0.0519337
\(749\) 41529.4 2.02597
\(750\) 6846.12 0.333313
\(751\) −11321.9 −0.550122 −0.275061 0.961427i \(-0.588698\pi\)
−0.275061 + 0.961427i \(0.588698\pi\)
\(752\) −30699.6 −1.48870
\(753\) 1390.59 0.0672988
\(754\) −2182.00 −0.105389
\(755\) 29702.2 1.43175
\(756\) −425.531 −0.0204714
\(757\) −29868.4 −1.43406 −0.717031 0.697042i \(-0.754499\pi\)
−0.717031 + 0.697042i \(0.754499\pi\)
\(758\) 4794.33 0.229733
\(759\) −10835.7 −0.518194
\(760\) −31533.4 −1.50505
\(761\) 25711.9 1.22478 0.612388 0.790557i \(-0.290209\pi\)
0.612388 + 0.790557i \(0.290209\pi\)
\(762\) 9793.31 0.465583
\(763\) 71868.7 3.40999
\(764\) −665.313 −0.0315055
\(765\) −9655.17 −0.456318
\(766\) 4323.31 0.203926
\(767\) 863.964 0.0406727
\(768\) 2031.02 0.0954271
\(769\) −16360.5 −0.767199 −0.383600 0.923500i \(-0.625316\pi\)
−0.383600 + 0.923500i \(0.625316\pi\)
\(770\) 41648.2 1.94922
\(771\) −6505.57 −0.303881
\(772\) 355.227 0.0165608
\(773\) −8952.62 −0.416563 −0.208282 0.978069i \(-0.566787\pi\)
−0.208282 + 0.978069i \(0.566787\pi\)
\(774\) 6208.37 0.288314
\(775\) −14982.4 −0.694429
\(776\) 19877.1 0.919519
\(777\) −27623.4 −1.27540
\(778\) −9747.88 −0.449201
\(779\) 32246.7 1.48313
\(780\) 267.544 0.0122816
\(781\) 16104.6 0.737861
\(782\) 25065.0 1.14619
\(783\) 1463.44 0.0667932
\(784\) −55907.1 −2.54679
\(785\) 1456.37 0.0662166
\(786\) 2070.08 0.0939407
\(787\) −1427.86 −0.0646731 −0.0323365 0.999477i \(-0.510295\pi\)
−0.0323365 + 0.999477i \(0.510295\pi\)
\(788\) 587.794 0.0265727
\(789\) −1703.25 −0.0768532
\(790\) −35069.4 −1.57938
\(791\) 26084.5 1.17251
\(792\) 6444.68 0.289143
\(793\) 7744.25 0.346793
\(794\) 19728.3 0.881779
\(795\) 12964.5 0.578367
\(796\) 1263.58 0.0562644
\(797\) 33475.6 1.48779 0.743894 0.668297i \(-0.232977\pi\)
0.743894 + 0.668297i \(0.232977\pi\)
\(798\) 28998.6 1.28639
\(799\) −39672.7 −1.75659
\(800\) 1293.80 0.0571785
\(801\) 4591.81 0.202551
\(802\) 20430.9 0.899549
\(803\) −24973.1 −1.09749
\(804\) −495.126 −0.0217186
\(805\) 57480.0 2.51665
\(806\) −9316.82 −0.407160
\(807\) 978.674 0.0426902
\(808\) −18832.9 −0.819974
\(809\) 18354.9 0.797679 0.398839 0.917021i \(-0.369413\pi\)
0.398839 + 0.917021i \(0.369413\pi\)
\(810\) 3067.33 0.133056
\(811\) 18590.6 0.804937 0.402469 0.915434i \(-0.368152\pi\)
0.402469 + 0.915434i \(0.368152\pi\)
\(812\) −854.237 −0.0369185
\(813\) −4434.01 −0.191276
\(814\) 21910.3 0.943436
\(815\) −13858.7 −0.595641
\(816\) −14081.4 −0.604101
\(817\) 24750.2 1.05985
\(818\) −13852.5 −0.592106
\(819\) −4697.85 −0.200435
\(820\) −1991.01 −0.0847915
\(821\) 11083.4 0.471151 0.235575 0.971856i \(-0.424303\pi\)
0.235575 + 0.971856i \(0.424303\pi\)
\(822\) −20408.5 −0.865970
\(823\) −11533.7 −0.488506 −0.244253 0.969712i \(-0.578543\pi\)
−0.244253 + 0.969712i \(0.578543\pi\)
\(824\) 9732.36 0.411460
\(825\) 5992.17 0.252873
\(826\) −5781.82 −0.243554
\(827\) −25859.7 −1.08734 −0.543670 0.839299i \(-0.682966\pi\)
−0.543670 + 0.839299i \(0.682966\pi\)
\(828\) 465.826 0.0195514
\(829\) −20734.3 −0.868674 −0.434337 0.900750i \(-0.643017\pi\)
−0.434337 + 0.900750i \(0.643017\pi\)
\(830\) −49674.4 −2.07738
\(831\) −25943.4 −1.08299
\(832\) 7864.74 0.327717
\(833\) −72247.9 −3.00509
\(834\) −17052.9 −0.708024
\(835\) −9211.56 −0.381772
\(836\) 1345.56 0.0556666
\(837\) 6248.68 0.258048
\(838\) −9740.71 −0.401536
\(839\) 8282.44 0.340812 0.170406 0.985374i \(-0.445492\pi\)
0.170406 + 0.985374i \(0.445492\pi\)
\(840\) −34187.1 −1.40425
\(841\) −21451.2 −0.879544
\(842\) 36101.8 1.47761
\(843\) 13960.0 0.570354
\(844\) 1379.97 0.0562802
\(845\) −27308.9 −1.11178
\(846\) 12603.5 0.512197
\(847\) 13511.7 0.548133
\(848\) 18907.7 0.765676
\(849\) 7784.79 0.314692
\(850\) −13861.1 −0.559330
\(851\) 30239.2 1.21808
\(852\) −692.341 −0.0278394
\(853\) 27976.9 1.12299 0.561495 0.827480i \(-0.310226\pi\)
0.561495 + 0.827480i \(0.310226\pi\)
\(854\) −51826.1 −2.07664
\(855\) 12228.2 0.489117
\(856\) 27039.3 1.07965
\(857\) −30334.1 −1.20910 −0.604548 0.796569i \(-0.706646\pi\)
−0.604548 + 0.796569i \(0.706646\pi\)
\(858\) 3726.24 0.148266
\(859\) 35079.4 1.39336 0.696679 0.717383i \(-0.254660\pi\)
0.696679 + 0.717383i \(0.254660\pi\)
\(860\) −1528.15 −0.0605924
\(861\) 34960.4 1.38380
\(862\) −25065.3 −0.990403
\(863\) −8904.72 −0.351240 −0.175620 0.984458i \(-0.556193\pi\)
−0.175620 + 0.984458i \(0.556193\pi\)
\(864\) −539.605 −0.0212474
\(865\) −39670.1 −1.55934
\(866\) −7022.44 −0.275557
\(867\) −3458.14 −0.135461
\(868\) −3647.47 −0.142631
\(869\) 28573.2 1.11540
\(870\) 6157.56 0.239955
\(871\) −5466.17 −0.212645
\(872\) 46792.8 1.81720
\(873\) −7708.04 −0.298829
\(874\) −31744.6 −1.22858
\(875\) 29589.4 1.14321
\(876\) 1073.60 0.0414081
\(877\) 5487.15 0.211275 0.105637 0.994405i \(-0.466312\pi\)
0.105637 + 0.994405i \(0.466312\pi\)
\(878\) 4189.56 0.161037
\(879\) 21899.2 0.840321
\(880\) 25613.3 0.981165
\(881\) −12650.9 −0.483792 −0.241896 0.970302i \(-0.577769\pi\)
−0.241896 + 0.970302i \(0.577769\pi\)
\(882\) 22952.3 0.876241
\(883\) 31973.4 1.21856 0.609282 0.792954i \(-0.291458\pi\)
0.609282 + 0.792954i \(0.291458\pi\)
\(884\) 504.242 0.0191849
\(885\) −2438.09 −0.0926051
\(886\) 27796.1 1.05398
\(887\) −48252.3 −1.82655 −0.913277 0.407338i \(-0.866457\pi\)
−0.913277 + 0.407338i \(0.866457\pi\)
\(888\) −17985.2 −0.679667
\(889\) 42327.4 1.59687
\(890\) 19320.5 0.727667
\(891\) −2499.15 −0.0939670
\(892\) 928.662 0.0348586
\(893\) 50245.1 1.88285
\(894\) −579.732 −0.0216881
\(895\) 23416.8 0.874565
\(896\) −46933.2 −1.74992
\(897\) 5142.71 0.191427
\(898\) 49286.1 1.83151
\(899\) 12544.0 0.465368
\(900\) −257.604 −0.00954089
\(901\) 24434.1 0.903462
\(902\) −27729.9 −1.02362
\(903\) 26833.0 0.988867
\(904\) 16983.2 0.624839
\(905\) −24114.0 −0.885719
\(906\) −17784.1 −0.652139
\(907\) 33861.7 1.23964 0.619822 0.784742i \(-0.287205\pi\)
0.619822 + 0.784742i \(0.287205\pi\)
\(908\) −1150.16 −0.0420366
\(909\) 7303.11 0.266478
\(910\) −19766.6 −0.720063
\(911\) 45845.4 1.66732 0.833659 0.552280i \(-0.186242\pi\)
0.833659 + 0.552280i \(0.186242\pi\)
\(912\) 17833.9 0.647522
\(913\) 40472.8 1.46709
\(914\) −24497.9 −0.886561
\(915\) −21854.2 −0.789591
\(916\) 664.407 0.0239657
\(917\) 8947.05 0.322200
\(918\) 5781.02 0.207845
\(919\) −14126.6 −0.507066 −0.253533 0.967327i \(-0.581593\pi\)
−0.253533 + 0.967327i \(0.581593\pi\)
\(920\) 37424.5 1.34114
\(921\) −11032.2 −0.394706
\(922\) 45977.8 1.64230
\(923\) −7643.42 −0.272575
\(924\) 1458.80 0.0519383
\(925\) −16722.4 −0.594410
\(926\) −38626.6 −1.37079
\(927\) −3774.06 −0.133718
\(928\) −1083.24 −0.0383179
\(929\) 27790.5 0.981461 0.490730 0.871311i \(-0.336730\pi\)
0.490730 + 0.871311i \(0.336730\pi\)
\(930\) 26291.9 0.927038
\(931\) 91501.3 3.22109
\(932\) 739.588 0.0259936
\(933\) −10168.4 −0.356804
\(934\) 28938.5 1.01381
\(935\) 33099.7 1.15773
\(936\) −3058.71 −0.106813
\(937\) −6472.88 −0.225677 −0.112839 0.993613i \(-0.535994\pi\)
−0.112839 + 0.993613i \(0.535994\pi\)
\(938\) 36580.7 1.27335
\(939\) 14542.4 0.505403
\(940\) −3102.28 −0.107644
\(941\) −12312.7 −0.426550 −0.213275 0.976992i \(-0.568413\pi\)
−0.213275 + 0.976992i \(0.568413\pi\)
\(942\) −871.998 −0.0301605
\(943\) −38271.0 −1.32161
\(944\) −3555.78 −0.122596
\(945\) 13257.2 0.456358
\(946\) −21283.4 −0.731484
\(947\) 4368.65 0.149907 0.0749536 0.997187i \(-0.476119\pi\)
0.0749536 + 0.997187i \(0.476119\pi\)
\(948\) −1228.37 −0.0420838
\(949\) 11852.5 0.405424
\(950\) 17554.9 0.599533
\(951\) −31382.6 −1.07009
\(952\) −64432.6 −2.19356
\(953\) 2917.34 0.0991627 0.0495814 0.998770i \(-0.484211\pi\)
0.0495814 + 0.998770i \(0.484211\pi\)
\(954\) −7762.44 −0.263436
\(955\) 20727.6 0.702333
\(956\) −1542.82 −0.0521951
\(957\) −5016.94 −0.169462
\(958\) −17577.5 −0.592801
\(959\) −88206.9 −2.97012
\(960\) −22194.2 −0.746160
\(961\) 23770.1 0.797895
\(962\) −10398.9 −0.348516
\(963\) −10485.4 −0.350870
\(964\) 385.568 0.0128821
\(965\) −11067.0 −0.369179
\(966\) −34416.0 −1.14629
\(967\) 42945.5 1.42816 0.714082 0.700062i \(-0.246845\pi\)
0.714082 + 0.700062i \(0.246845\pi\)
\(968\) 8797.31 0.292104
\(969\) 23046.5 0.764046
\(970\) −32432.3 −1.07354
\(971\) 43742.9 1.44570 0.722851 0.691004i \(-0.242831\pi\)
0.722851 + 0.691004i \(0.242831\pi\)
\(972\) 107.439 0.00354537
\(973\) −73703.7 −2.42840
\(974\) 39028.1 1.28392
\(975\) −2843.94 −0.0934144
\(976\) −31872.7 −1.04531
\(977\) −29917.5 −0.979679 −0.489839 0.871813i \(-0.662945\pi\)
−0.489839 + 0.871813i \(0.662945\pi\)
\(978\) 8297.84 0.271304
\(979\) −15741.6 −0.513895
\(980\) −5649.57 −0.184152
\(981\) −18145.5 −0.590562
\(982\) −16130.6 −0.524185
\(983\) −48495.4 −1.57351 −0.786756 0.617264i \(-0.788241\pi\)
−0.786756 + 0.617264i \(0.788241\pi\)
\(984\) 22762.3 0.737433
\(985\) −18312.5 −0.592370
\(986\) 11605.2 0.374832
\(987\) 54473.4 1.75675
\(988\) −638.617 −0.0205639
\(989\) −29373.9 −0.944426
\(990\) −10515.4 −0.337577
\(991\) −14192.8 −0.454944 −0.227472 0.973785i \(-0.573046\pi\)
−0.227472 + 0.973785i \(0.573046\pi\)
\(992\) −4625.27 −0.148037
\(993\) 8579.53 0.274182
\(994\) 51151.4 1.63222
\(995\) −39366.4 −1.25427
\(996\) −1739.93 −0.0553533
\(997\) −49366.8 −1.56817 −0.784083 0.620656i \(-0.786866\pi\)
−0.784083 + 0.620656i \(0.786866\pi\)
\(998\) −22942.9 −0.727700
\(999\) 6974.39 0.220881
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.b.1.5 7
3.2 odd 2 531.4.a.c.1.3 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.4.a.b.1.5 7 1.1 even 1 trivial
531.4.a.c.1.3 7 3.2 odd 2