Properties

Label 177.4.a.c.1.2
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 1.2
Root \(-4.21744\) of defining polynomial
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-4.21744 q^{2} -3.00000 q^{3} +9.78684 q^{4} +17.5635 q^{5} +12.6523 q^{6} +14.8996 q^{7} -7.53588 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q-4.21744 q^{2} -3.00000 q^{3} +9.78684 q^{4} +17.5635 q^{5} +12.6523 q^{6} +14.8996 q^{7} -7.53588 q^{8} +9.00000 q^{9} -74.0731 q^{10} -18.9001 q^{11} -29.3605 q^{12} +31.7591 q^{13} -62.8381 q^{14} -52.6905 q^{15} -46.5125 q^{16} -84.1910 q^{17} -37.9570 q^{18} +126.537 q^{19} +171.891 q^{20} -44.6987 q^{21} +79.7102 q^{22} -21.1777 q^{23} +22.6076 q^{24} +183.477 q^{25} -133.942 q^{26} -27.0000 q^{27} +145.820 q^{28} -12.6033 q^{29} +222.219 q^{30} +215.817 q^{31} +256.451 q^{32} +56.7003 q^{33} +355.071 q^{34} +261.689 q^{35} +88.0815 q^{36} -3.62282 q^{37} -533.661 q^{38} -95.2774 q^{39} -132.357 q^{40} -381.728 q^{41} +188.514 q^{42} +168.813 q^{43} -184.972 q^{44} +158.072 q^{45} +89.3156 q^{46} +613.793 q^{47} +139.538 q^{48} -121.003 q^{49} -773.804 q^{50} +252.573 q^{51} +310.821 q^{52} +270.545 q^{53} +113.871 q^{54} -331.952 q^{55} -112.281 q^{56} -379.610 q^{57} +53.1537 q^{58} -59.0000 q^{59} -515.674 q^{60} +311.206 q^{61} -910.195 q^{62} +134.096 q^{63} -709.468 q^{64} +557.802 q^{65} -239.130 q^{66} +375.157 q^{67} -823.963 q^{68} +63.5330 q^{69} -1103.66 q^{70} -987.919 q^{71} -67.8229 q^{72} -359.475 q^{73} +15.2790 q^{74} -550.431 q^{75} +1238.39 q^{76} -281.604 q^{77} +401.827 q^{78} +933.998 q^{79} -816.923 q^{80} +81.0000 q^{81} +1609.92 q^{82} +1262.64 q^{83} -437.459 q^{84} -1478.69 q^{85} -711.960 q^{86} +37.8099 q^{87} +142.429 q^{88} +273.294 q^{89} -666.658 q^{90} +473.197 q^{91} -207.262 q^{92} -647.450 q^{93} -2588.64 q^{94} +2222.43 q^{95} -769.353 q^{96} -897.200 q^{97} +510.323 q^{98} -170.101 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 2q^{2} - 24q^{3} + 38q^{4} - 12q^{5} - 6q^{6} + 53q^{7} + 3q^{8} + 72q^{9} + O(q^{10}) \) \( 8q + 2q^{2} - 24q^{3} + 38q^{4} - 12q^{5} - 6q^{6} + 53q^{7} + 3q^{8} + 72q^{9} + 29q^{10} - 27q^{11} - 114q^{12} + 89q^{13} - 37q^{14} + 36q^{15} + 362q^{16} + 79q^{17} + 18q^{18} + 288q^{19} + 457q^{20} - 159q^{21} + 596q^{22} + 202q^{23} - 9q^{24} + 264q^{25} + 270q^{26} - 216q^{27} + 702q^{28} - 114q^{29} - 87q^{30} + 538q^{31} + 316q^{32} + 81q^{33} + 498q^{34} - 196q^{35} + 342q^{36} + 395q^{37} + 397q^{38} - 267q^{39} + 918q^{40} - 39q^{41} + 111q^{42} + 527q^{43} + 64q^{44} - 108q^{45} - 539q^{46} + 860q^{47} - 1086q^{48} + 347q^{49} - 591q^{50} - 237q^{51} - 644q^{52} - 812q^{53} - 54q^{54} + 536q^{55} - 2218q^{56} - 864q^{57} - 1154q^{58} - 472q^{59} - 1371q^{60} - 460q^{61} - 2014q^{62} + 477q^{63} - 451q^{64} - 986q^{65} - 1788q^{66} + 1934q^{67} - 69q^{68} - 606q^{69} - 1028q^{70} - 1687q^{71} + 27q^{72} + 1980q^{73} - 2400q^{74} - 792q^{75} - 940q^{76} - 821q^{77} - 810q^{78} + 3319q^{79} - 2119q^{80} + 648q^{81} + 429q^{82} + 2057q^{83} - 2106q^{84} + 566q^{85} - 6690q^{86} + 342q^{87} + 1189q^{88} + 1668q^{89} + 261q^{90} + 2427q^{91} - 980q^{92} - 1614q^{93} + 332q^{94} + 2146q^{95} - 948q^{96} + 1956q^{97} - 2026q^{98} - 243q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.21744 −1.49109 −0.745546 0.666454i \(-0.767811\pi\)
−0.745546 + 0.666454i \(0.767811\pi\)
\(3\) −3.00000 −0.577350
\(4\) 9.78684 1.22335
\(5\) 17.5635 1.57093 0.785464 0.618907i \(-0.212424\pi\)
0.785464 + 0.618907i \(0.212424\pi\)
\(6\) 12.6523 0.860882
\(7\) 14.8996 0.804501 0.402251 0.915530i \(-0.368228\pi\)
0.402251 + 0.915530i \(0.368228\pi\)
\(8\) −7.53588 −0.333042
\(9\) 9.00000 0.333333
\(10\) −74.0731 −2.34240
\(11\) −18.9001 −0.518054 −0.259027 0.965870i \(-0.583402\pi\)
−0.259027 + 0.965870i \(0.583402\pi\)
\(12\) −29.3605 −0.706304
\(13\) 31.7591 0.677569 0.338784 0.940864i \(-0.389984\pi\)
0.338784 + 0.940864i \(0.389984\pi\)
\(14\) −62.8381 −1.19958
\(15\) −52.6905 −0.906976
\(16\) −46.5125 −0.726758
\(17\) −84.1910 −1.20114 −0.600568 0.799574i \(-0.705059\pi\)
−0.600568 + 0.799574i \(0.705059\pi\)
\(18\) −37.9570 −0.497031
\(19\) 126.537 1.52787 0.763934 0.645294i \(-0.223265\pi\)
0.763934 + 0.645294i \(0.223265\pi\)
\(20\) 171.891 1.92180
\(21\) −44.6987 −0.464479
\(22\) 79.7102 0.772467
\(23\) −21.1777 −0.191993 −0.0959967 0.995382i \(-0.530604\pi\)
−0.0959967 + 0.995382i \(0.530604\pi\)
\(24\) 22.6076 0.192282
\(25\) 183.477 1.46782
\(26\) −133.942 −1.01032
\(27\) −27.0000 −0.192450
\(28\) 145.820 0.984190
\(29\) −12.6033 −0.0807025 −0.0403512 0.999186i \(-0.512848\pi\)
−0.0403512 + 0.999186i \(0.512848\pi\)
\(30\) 222.219 1.35238
\(31\) 215.817 1.25038 0.625191 0.780472i \(-0.285021\pi\)
0.625191 + 0.780472i \(0.285021\pi\)
\(32\) 256.451 1.41671
\(33\) 56.7003 0.299099
\(34\) 355.071 1.79100
\(35\) 261.689 1.26381
\(36\) 88.0815 0.407785
\(37\) −3.62282 −0.0160970 −0.00804848 0.999968i \(-0.502562\pi\)
−0.00804848 + 0.999968i \(0.502562\pi\)
\(38\) −533.661 −2.27819
\(39\) −95.2774 −0.391195
\(40\) −132.357 −0.523185
\(41\) −381.728 −1.45405 −0.727023 0.686613i \(-0.759097\pi\)
−0.727023 + 0.686613i \(0.759097\pi\)
\(42\) 188.514 0.692581
\(43\) 168.813 0.598692 0.299346 0.954145i \(-0.403231\pi\)
0.299346 + 0.954145i \(0.403231\pi\)
\(44\) −184.972 −0.633764
\(45\) 158.072 0.523643
\(46\) 89.3156 0.286280
\(47\) 613.793 1.90491 0.952457 0.304674i \(-0.0985475\pi\)
0.952457 + 0.304674i \(0.0985475\pi\)
\(48\) 139.538 0.419594
\(49\) −121.003 −0.352778
\(50\) −773.804 −2.18865
\(51\) 252.573 0.693476
\(52\) 310.821 0.828907
\(53\) 270.545 0.701173 0.350587 0.936530i \(-0.385982\pi\)
0.350587 + 0.936530i \(0.385982\pi\)
\(54\) 113.871 0.286961
\(55\) −331.952 −0.813826
\(56\) −112.281 −0.267933
\(57\) −379.610 −0.882115
\(58\) 53.1537 0.120335
\(59\) −59.0000 −0.130189
\(60\) −515.674 −1.10955
\(61\) 311.206 0.653211 0.326605 0.945161i \(-0.394095\pi\)
0.326605 + 0.945161i \(0.394095\pi\)
\(62\) −910.195 −1.86443
\(63\) 134.096 0.268167
\(64\) −709.468 −1.38568
\(65\) 557.802 1.06441
\(66\) −239.130 −0.445984
\(67\) 375.157 0.684071 0.342035 0.939687i \(-0.388884\pi\)
0.342035 + 0.939687i \(0.388884\pi\)
\(68\) −823.963 −1.46942
\(69\) 63.5330 0.110847
\(70\) −1103.66 −1.88446
\(71\) −987.919 −1.65133 −0.825665 0.564160i \(-0.809200\pi\)
−0.825665 + 0.564160i \(0.809200\pi\)
\(72\) −67.8229 −0.111014
\(73\) −359.475 −0.576348 −0.288174 0.957578i \(-0.593048\pi\)
−0.288174 + 0.957578i \(0.593048\pi\)
\(74\) 15.2790 0.0240020
\(75\) −550.431 −0.847444
\(76\) 1238.39 1.86912
\(77\) −281.604 −0.416775
\(78\) 401.827 0.583307
\(79\) 933.998 1.33016 0.665082 0.746770i \(-0.268397\pi\)
0.665082 + 0.746770i \(0.268397\pi\)
\(80\) −816.923 −1.14169
\(81\) 81.0000 0.111111
\(82\) 1609.92 2.16811
\(83\) 1262.64 1.66979 0.834893 0.550412i \(-0.185529\pi\)
0.834893 + 0.550412i \(0.185529\pi\)
\(84\) −437.459 −0.568222
\(85\) −1478.69 −1.88690
\(86\) −711.960 −0.892705
\(87\) 37.8099 0.0465936
\(88\) 142.429 0.172534
\(89\) 273.294 0.325496 0.162748 0.986668i \(-0.447964\pi\)
0.162748 + 0.986668i \(0.447964\pi\)
\(90\) −666.658 −0.780799
\(91\) 473.197 0.545105
\(92\) −207.262 −0.234876
\(93\) −647.450 −0.721908
\(94\) −2588.64 −2.84040
\(95\) 2222.43 2.40017
\(96\) −769.353 −0.817935
\(97\) −897.200 −0.939143 −0.469571 0.882895i \(-0.655592\pi\)
−0.469571 + 0.882895i \(0.655592\pi\)
\(98\) 510.323 0.526024
\(99\) −170.101 −0.172685
\(100\) 1795.66 1.79566
\(101\) 296.784 0.292387 0.146194 0.989256i \(-0.453298\pi\)
0.146194 + 0.989256i \(0.453298\pi\)
\(102\) −1065.21 −1.03404
\(103\) −36.8226 −0.0352257 −0.0176128 0.999845i \(-0.505607\pi\)
−0.0176128 + 0.999845i \(0.505607\pi\)
\(104\) −239.333 −0.225659
\(105\) −785.066 −0.729663
\(106\) −1141.01 −1.04551
\(107\) −479.349 −0.433088 −0.216544 0.976273i \(-0.569479\pi\)
−0.216544 + 0.976273i \(0.569479\pi\)
\(108\) −264.245 −0.235435
\(109\) 946.780 0.831973 0.415987 0.909371i \(-0.363436\pi\)
0.415987 + 0.909371i \(0.363436\pi\)
\(110\) 1399.99 1.21349
\(111\) 10.8684 0.00929358
\(112\) −693.017 −0.584678
\(113\) 2131.61 1.77456 0.887279 0.461234i \(-0.152593\pi\)
0.887279 + 0.461234i \(0.152593\pi\)
\(114\) 1600.98 1.31531
\(115\) −371.954 −0.301608
\(116\) −123.346 −0.0987277
\(117\) 285.832 0.225856
\(118\) 248.829 0.194124
\(119\) −1254.41 −0.966315
\(120\) 397.070 0.302061
\(121\) −973.786 −0.731620
\(122\) −1312.49 −0.973997
\(123\) 1145.18 0.839493
\(124\) 2112.16 1.52966
\(125\) 1027.06 0.734904
\(126\) −565.543 −0.399862
\(127\) 2054.51 1.43550 0.717751 0.696300i \(-0.245172\pi\)
0.717751 + 0.696300i \(0.245172\pi\)
\(128\) 940.532 0.649469
\(129\) −506.440 −0.345655
\(130\) −2352.50 −1.58714
\(131\) −602.309 −0.401710 −0.200855 0.979621i \(-0.564372\pi\)
−0.200855 + 0.979621i \(0.564372\pi\)
\(132\) 554.917 0.365904
\(133\) 1885.34 1.22917
\(134\) −1582.20 −1.02001
\(135\) −474.215 −0.302325
\(136\) 634.453 0.400029
\(137\) 1919.26 1.19689 0.598444 0.801164i \(-0.295786\pi\)
0.598444 + 0.801164i \(0.295786\pi\)
\(138\) −267.947 −0.165284
\(139\) −448.518 −0.273689 −0.136845 0.990593i \(-0.543696\pi\)
−0.136845 + 0.990593i \(0.543696\pi\)
\(140\) 2561.10 1.54609
\(141\) −1841.38 −1.09980
\(142\) 4166.49 2.46228
\(143\) −600.251 −0.351017
\(144\) −418.613 −0.242253
\(145\) −221.358 −0.126778
\(146\) 1516.07 0.859388
\(147\) 363.009 0.203676
\(148\) −35.4559 −0.0196923
\(149\) −1613.45 −0.887105 −0.443553 0.896248i \(-0.646282\pi\)
−0.443553 + 0.896248i \(0.646282\pi\)
\(150\) 2321.41 1.26362
\(151\) −1522.22 −0.820374 −0.410187 0.912002i \(-0.634537\pi\)
−0.410187 + 0.912002i \(0.634537\pi\)
\(152\) −953.565 −0.508844
\(153\) −757.719 −0.400379
\(154\) 1187.65 0.621450
\(155\) 3790.50 1.96426
\(156\) −932.464 −0.478570
\(157\) −79.4233 −0.0403737 −0.0201868 0.999796i \(-0.506426\pi\)
−0.0201868 + 0.999796i \(0.506426\pi\)
\(158\) −3939.08 −1.98340
\(159\) −811.634 −0.404823
\(160\) 4504.18 2.22554
\(161\) −315.538 −0.154459
\(162\) −341.613 −0.165677
\(163\) 2254.35 1.08328 0.541639 0.840611i \(-0.317804\pi\)
0.541639 + 0.840611i \(0.317804\pi\)
\(164\) −3735.91 −1.77881
\(165\) 995.857 0.469863
\(166\) −5325.10 −2.48981
\(167\) −382.224 −0.177110 −0.0885550 0.996071i \(-0.528225\pi\)
−0.0885550 + 0.996071i \(0.528225\pi\)
\(168\) 336.844 0.154691
\(169\) −1188.36 −0.540901
\(170\) 6236.29 2.81354
\(171\) 1138.83 0.509289
\(172\) 1652.15 0.732413
\(173\) −929.824 −0.408631 −0.204316 0.978905i \(-0.565497\pi\)
−0.204316 + 0.978905i \(0.565497\pi\)
\(174\) −159.461 −0.0694753
\(175\) 2733.73 1.18086
\(176\) 879.092 0.376500
\(177\) 177.000 0.0751646
\(178\) −1152.60 −0.485344
\(179\) −509.106 −0.212583 −0.106291 0.994335i \(-0.533898\pi\)
−0.106291 + 0.994335i \(0.533898\pi\)
\(180\) 1547.02 0.640601
\(181\) 824.865 0.338739 0.169369 0.985553i \(-0.445827\pi\)
0.169369 + 0.985553i \(0.445827\pi\)
\(182\) −1995.68 −0.812801
\(183\) −933.618 −0.377131
\(184\) 159.592 0.0639419
\(185\) −63.6294 −0.0252872
\(186\) 2730.58 1.07643
\(187\) 1591.22 0.622254
\(188\) 6007.09 2.33038
\(189\) −402.288 −0.154826
\(190\) −9372.97 −3.57888
\(191\) −3681.09 −1.39453 −0.697263 0.716815i \(-0.745599\pi\)
−0.697263 + 0.716815i \(0.745599\pi\)
\(192\) 2128.40 0.800022
\(193\) −3051.17 −1.13797 −0.568985 0.822348i \(-0.692664\pi\)
−0.568985 + 0.822348i \(0.692664\pi\)
\(194\) 3783.89 1.40035
\(195\) −1673.40 −0.614538
\(196\) −1184.23 −0.431573
\(197\) −5332.57 −1.92858 −0.964290 0.264849i \(-0.914678\pi\)
−0.964290 + 0.264849i \(0.914678\pi\)
\(198\) 717.391 0.257489
\(199\) −5371.72 −1.91352 −0.956761 0.290874i \(-0.906054\pi\)
−0.956761 + 0.290874i \(0.906054\pi\)
\(200\) −1382.66 −0.488844
\(201\) −1125.47 −0.394949
\(202\) −1251.67 −0.435976
\(203\) −187.784 −0.0649252
\(204\) 2471.89 0.848367
\(205\) −6704.48 −2.28420
\(206\) 155.297 0.0525247
\(207\) −190.599 −0.0639978
\(208\) −1477.20 −0.492429
\(209\) −2391.56 −0.791519
\(210\) 3310.97 1.08799
\(211\) 1896.92 0.618907 0.309454 0.950915i \(-0.399854\pi\)
0.309454 + 0.950915i \(0.399854\pi\)
\(212\) 2647.78 0.857784
\(213\) 2963.76 0.953396
\(214\) 2021.63 0.645775
\(215\) 2964.95 0.940503
\(216\) 203.469 0.0640940
\(217\) 3215.57 1.00593
\(218\) −3992.99 −1.24055
\(219\) 1078.43 0.332755
\(220\) −3248.76 −0.995598
\(221\) −2673.83 −0.813852
\(222\) −45.8371 −0.0138576
\(223\) −2808.85 −0.843472 −0.421736 0.906719i \(-0.638579\pi\)
−0.421736 + 0.906719i \(0.638579\pi\)
\(224\) 3821.01 1.13974
\(225\) 1651.29 0.489272
\(226\) −8989.95 −2.64603
\(227\) 3302.83 0.965711 0.482856 0.875700i \(-0.339600\pi\)
0.482856 + 0.875700i \(0.339600\pi\)
\(228\) −3715.18 −1.07914
\(229\) −5780.19 −1.66797 −0.833987 0.551785i \(-0.813947\pi\)
−0.833987 + 0.551785i \(0.813947\pi\)
\(230\) 1568.70 0.449725
\(231\) 844.811 0.240625
\(232\) 94.9769 0.0268773
\(233\) 4892.84 1.37571 0.687856 0.725847i \(-0.258552\pi\)
0.687856 + 0.725847i \(0.258552\pi\)
\(234\) −1205.48 −0.336772
\(235\) 10780.4 2.99248
\(236\) −577.423 −0.159267
\(237\) −2801.99 −0.767970
\(238\) 5290.40 1.44086
\(239\) −6461.39 −1.74876 −0.874378 0.485246i \(-0.838730\pi\)
−0.874378 + 0.485246i \(0.838730\pi\)
\(240\) 2450.77 0.659152
\(241\) −60.7729 −0.0162437 −0.00812184 0.999967i \(-0.502585\pi\)
−0.00812184 + 0.999967i \(0.502585\pi\)
\(242\) 4106.89 1.09091
\(243\) −243.000 −0.0641500
\(244\) 3045.72 0.799108
\(245\) −2125.23 −0.554189
\(246\) −4829.75 −1.25176
\(247\) 4018.69 1.03524
\(248\) −1626.37 −0.416429
\(249\) −3787.91 −0.964052
\(250\) −4331.57 −1.09581
\(251\) −3782.13 −0.951100 −0.475550 0.879689i \(-0.657751\pi\)
−0.475550 + 0.879689i \(0.657751\pi\)
\(252\) 1312.38 0.328063
\(253\) 400.260 0.0994630
\(254\) −8664.80 −2.14046
\(255\) 4436.07 1.08940
\(256\) 1709.10 0.417261
\(257\) −72.7427 −0.0176559 −0.00882795 0.999961i \(-0.502810\pi\)
−0.00882795 + 0.999961i \(0.502810\pi\)
\(258\) 2135.88 0.515404
\(259\) −53.9784 −0.0129500
\(260\) 5459.11 1.30215
\(261\) −113.430 −0.0269008
\(262\) 2540.20 0.598986
\(263\) −4787.49 −1.12247 −0.561235 0.827657i \(-0.689673\pi\)
−0.561235 + 0.827657i \(0.689673\pi\)
\(264\) −427.287 −0.0996125
\(265\) 4751.72 1.10149
\(266\) −7951.32 −1.83281
\(267\) −819.883 −0.187925
\(268\) 3671.60 0.836861
\(269\) 3320.18 0.752546 0.376273 0.926509i \(-0.377205\pi\)
0.376273 + 0.926509i \(0.377205\pi\)
\(270\) 1999.97 0.450795
\(271\) 7147.95 1.60224 0.801120 0.598504i \(-0.204238\pi\)
0.801120 + 0.598504i \(0.204238\pi\)
\(272\) 3915.94 0.872936
\(273\) −1419.59 −0.314716
\(274\) −8094.39 −1.78467
\(275\) −3467.73 −0.760408
\(276\) 621.787 0.135606
\(277\) 4611.19 1.00021 0.500107 0.865963i \(-0.333294\pi\)
0.500107 + 0.865963i \(0.333294\pi\)
\(278\) 1891.60 0.408096
\(279\) 1942.35 0.416794
\(280\) −1972.05 −0.420903
\(281\) 8307.67 1.76368 0.881840 0.471548i \(-0.156305\pi\)
0.881840 + 0.471548i \(0.156305\pi\)
\(282\) 7765.91 1.63991
\(283\) −8181.70 −1.71856 −0.859279 0.511507i \(-0.829087\pi\)
−0.859279 + 0.511507i \(0.829087\pi\)
\(284\) −9668.60 −2.02016
\(285\) −6667.28 −1.38574
\(286\) 2531.52 0.523399
\(287\) −5687.58 −1.16978
\(288\) 2308.06 0.472235
\(289\) 2175.12 0.442728
\(290\) 933.565 0.189037
\(291\) 2691.60 0.542214
\(292\) −3518.13 −0.705078
\(293\) −264.862 −0.0528102 −0.0264051 0.999651i \(-0.508406\pi\)
−0.0264051 + 0.999651i \(0.508406\pi\)
\(294\) −1530.97 −0.303700
\(295\) −1036.25 −0.204517
\(296\) 27.3011 0.00536096
\(297\) 510.303 0.0996996
\(298\) 6804.62 1.32276
\(299\) −672.584 −0.130089
\(300\) −5386.98 −1.03672
\(301\) 2515.24 0.481649
\(302\) 6419.87 1.22325
\(303\) −890.351 −0.168810
\(304\) −5885.54 −1.11039
\(305\) 5465.87 1.02615
\(306\) 3195.64 0.597001
\(307\) 4379.69 0.814209 0.407104 0.913382i \(-0.366539\pi\)
0.407104 + 0.913382i \(0.366539\pi\)
\(308\) −2756.01 −0.509864
\(309\) 110.468 0.0203375
\(310\) −15986.2 −2.92889
\(311\) 10544.6 1.92261 0.961303 0.275494i \(-0.0888413\pi\)
0.961303 + 0.275494i \(0.0888413\pi\)
\(312\) 717.999 0.130284
\(313\) −6496.71 −1.17321 −0.586607 0.809872i \(-0.699537\pi\)
−0.586607 + 0.809872i \(0.699537\pi\)
\(314\) 334.963 0.0602009
\(315\) 2355.20 0.421271
\(316\) 9140.88 1.62726
\(317\) 2628.81 0.465769 0.232884 0.972504i \(-0.425184\pi\)
0.232884 + 0.972504i \(0.425184\pi\)
\(318\) 3423.02 0.603628
\(319\) 238.204 0.0418083
\(320\) −12460.7 −2.17680
\(321\) 1438.05 0.250044
\(322\) 1330.76 0.230312
\(323\) −10653.2 −1.83518
\(324\) 792.734 0.135928
\(325\) 5827.06 0.994546
\(326\) −9507.59 −1.61527
\(327\) −2840.34 −0.480340
\(328\) 2876.65 0.484258
\(329\) 9145.25 1.53250
\(330\) −4199.97 −0.700608
\(331\) −3679.05 −0.610933 −0.305466 0.952203i \(-0.598812\pi\)
−0.305466 + 0.952203i \(0.598812\pi\)
\(332\) 12357.2 2.04274
\(333\) −32.6053 −0.00536565
\(334\) 1612.01 0.264087
\(335\) 6589.08 1.07463
\(336\) 2079.05 0.337564
\(337\) 1323.74 0.213972 0.106986 0.994261i \(-0.465880\pi\)
0.106986 + 0.994261i \(0.465880\pi\)
\(338\) 5011.84 0.806532
\(339\) −6394.83 −1.02454
\(340\) −14471.7 −2.30835
\(341\) −4078.96 −0.647765
\(342\) −4802.95 −0.759397
\(343\) −6913.44 −1.08831
\(344\) −1272.16 −0.199390
\(345\) 1115.86 0.174133
\(346\) 3921.48 0.609307
\(347\) 5541.30 0.857270 0.428635 0.903478i \(-0.358995\pi\)
0.428635 + 0.903478i \(0.358995\pi\)
\(348\) 370.039 0.0570005
\(349\) −6590.45 −1.01083 −0.505414 0.862877i \(-0.668660\pi\)
−0.505414 + 0.862877i \(0.668660\pi\)
\(350\) −11529.3 −1.76077
\(351\) −857.496 −0.130398
\(352\) −4846.95 −0.733930
\(353\) −5633.11 −0.849349 −0.424674 0.905346i \(-0.639611\pi\)
−0.424674 + 0.905346i \(0.639611\pi\)
\(354\) −746.488 −0.112077
\(355\) −17351.3 −2.59412
\(356\) 2674.69 0.398197
\(357\) 3763.23 0.557902
\(358\) 2147.13 0.316981
\(359\) 2672.65 0.392916 0.196458 0.980512i \(-0.437056\pi\)
0.196458 + 0.980512i \(0.437056\pi\)
\(360\) −1191.21 −0.174395
\(361\) 9152.52 1.33438
\(362\) −3478.82 −0.505091
\(363\) 2921.36 0.422401
\(364\) 4631.10 0.666856
\(365\) −6313.65 −0.905402
\(366\) 3937.48 0.562337
\(367\) −2881.92 −0.409904 −0.204952 0.978772i \(-0.565704\pi\)
−0.204952 + 0.978772i \(0.565704\pi\)
\(368\) 985.027 0.139533
\(369\) −3435.55 −0.484682
\(370\) 268.353 0.0377055
\(371\) 4031.00 0.564095
\(372\) −6336.49 −0.883149
\(373\) 7349.59 1.02023 0.510117 0.860105i \(-0.329602\pi\)
0.510117 + 0.860105i \(0.329602\pi\)
\(374\) −6710.88 −0.927837
\(375\) −3081.18 −0.424297
\(376\) −4625.47 −0.634416
\(377\) −400.269 −0.0546815
\(378\) 1696.63 0.230860
\(379\) 6001.29 0.813366 0.406683 0.913569i \(-0.366685\pi\)
0.406683 + 0.913569i \(0.366685\pi\)
\(380\) 21750.5 2.93626
\(381\) −6163.54 −0.828787
\(382\) 15524.8 2.07937
\(383\) −7844.21 −1.04653 −0.523264 0.852171i \(-0.675286\pi\)
−0.523264 + 0.852171i \(0.675286\pi\)
\(384\) −2821.60 −0.374971
\(385\) −4945.95 −0.654724
\(386\) 12868.2 1.69682
\(387\) 1519.32 0.199564
\(388\) −8780.75 −1.14890
\(389\) −574.603 −0.0748934 −0.0374467 0.999299i \(-0.511922\pi\)
−0.0374467 + 0.999299i \(0.511922\pi\)
\(390\) 7057.49 0.916333
\(391\) 1782.97 0.230610
\(392\) 911.863 0.117490
\(393\) 1806.93 0.231927
\(394\) 22489.8 2.87569
\(395\) 16404.3 2.08959
\(396\) −1664.75 −0.211255
\(397\) −14329.0 −1.81147 −0.905735 0.423844i \(-0.860680\pi\)
−0.905735 + 0.423844i \(0.860680\pi\)
\(398\) 22654.9 2.85324
\(399\) −5656.02 −0.709663
\(400\) −8533.98 −1.06675
\(401\) 8440.51 1.05112 0.525560 0.850757i \(-0.323856\pi\)
0.525560 + 0.850757i \(0.323856\pi\)
\(402\) 4746.61 0.588904
\(403\) 6854.15 0.847219
\(404\) 2904.57 0.357693
\(405\) 1422.64 0.174548
\(406\) 791.967 0.0968095
\(407\) 68.4716 0.00833910
\(408\) −1903.36 −0.230957
\(409\) −3995.02 −0.482985 −0.241492 0.970403i \(-0.577637\pi\)
−0.241492 + 0.970403i \(0.577637\pi\)
\(410\) 28275.8 3.40595
\(411\) −5757.79 −0.691024
\(412\) −360.377 −0.0430935
\(413\) −879.075 −0.104737
\(414\) 803.840 0.0954266
\(415\) 22176.3 2.62312
\(416\) 8144.66 0.959915
\(417\) 1345.56 0.158015
\(418\) 10086.3 1.18023
\(419\) −1885.71 −0.219864 −0.109932 0.993939i \(-0.535063\pi\)
−0.109932 + 0.993939i \(0.535063\pi\)
\(420\) −7683.31 −0.892637
\(421\) −9268.38 −1.07295 −0.536477 0.843915i \(-0.680245\pi\)
−0.536477 + 0.843915i \(0.680245\pi\)
\(422\) −8000.16 −0.922848
\(423\) 5524.14 0.634971
\(424\) −2038.79 −0.233520
\(425\) −15447.1 −1.76305
\(426\) −12499.5 −1.42160
\(427\) 4636.84 0.525509
\(428\) −4691.31 −0.529821
\(429\) 1800.75 0.202660
\(430\) −12504.5 −1.40238
\(431\) −3346.11 −0.373959 −0.186980 0.982364i \(-0.559870\pi\)
−0.186980 + 0.982364i \(0.559870\pi\)
\(432\) 1255.84 0.139865
\(433\) −927.848 −0.102978 −0.0514891 0.998674i \(-0.516397\pi\)
−0.0514891 + 0.998674i \(0.516397\pi\)
\(434\) −13561.5 −1.49994
\(435\) 664.074 0.0731952
\(436\) 9265.98 1.01780
\(437\) −2679.75 −0.293341
\(438\) −4548.20 −0.496168
\(439\) 10124.5 1.10072 0.550361 0.834927i \(-0.314490\pi\)
0.550361 + 0.834927i \(0.314490\pi\)
\(440\) 2501.55 0.271038
\(441\) −1089.03 −0.117593
\(442\) 11276.7 1.21353
\(443\) −6492.44 −0.696310 −0.348155 0.937437i \(-0.613192\pi\)
−0.348155 + 0.937437i \(0.613192\pi\)
\(444\) 106.368 0.0113693
\(445\) 4800.01 0.511331
\(446\) 11846.2 1.25769
\(447\) 4840.34 0.512170
\(448\) −10570.8 −1.11478
\(449\) −17708.0 −1.86123 −0.930614 0.366003i \(-0.880726\pi\)
−0.930614 + 0.366003i \(0.880726\pi\)
\(450\) −6964.23 −0.729549
\(451\) 7214.70 0.753275
\(452\) 20861.7 2.17091
\(453\) 4566.66 0.473643
\(454\) −13929.5 −1.43996
\(455\) 8311.00 0.856321
\(456\) 2860.70 0.293781
\(457\) 10785.3 1.10397 0.551984 0.833855i \(-0.313871\pi\)
0.551984 + 0.833855i \(0.313871\pi\)
\(458\) 24377.6 2.48710
\(459\) 2273.16 0.231159
\(460\) −3640.25 −0.368973
\(461\) −14512.5 −1.46619 −0.733097 0.680124i \(-0.761926\pi\)
−0.733097 + 0.680124i \(0.761926\pi\)
\(462\) −3562.94 −0.358794
\(463\) −9637.81 −0.967402 −0.483701 0.875233i \(-0.660708\pi\)
−0.483701 + 0.875233i \(0.660708\pi\)
\(464\) 586.211 0.0586512
\(465\) −11371.5 −1.13407
\(466\) −20635.3 −2.05131
\(467\) −7260.33 −0.719417 −0.359709 0.933065i \(-0.617124\pi\)
−0.359709 + 0.933065i \(0.617124\pi\)
\(468\) 2797.39 0.276302
\(469\) 5589.68 0.550336
\(470\) −45465.6 −4.46207
\(471\) 238.270 0.0233098
\(472\) 444.617 0.0433584
\(473\) −3190.59 −0.310155
\(474\) 11817.2 1.14511
\(475\) 23216.6 2.24263
\(476\) −12276.7 −1.18215
\(477\) 2434.90 0.233724
\(478\) 27250.6 2.60756
\(479\) 12069.4 1.15128 0.575641 0.817703i \(-0.304753\pi\)
0.575641 + 0.817703i \(0.304753\pi\)
\(480\) −13512.5 −1.28492
\(481\) −115.057 −0.0109068
\(482\) 256.306 0.0242208
\(483\) 946.614 0.0891769
\(484\) −9530.28 −0.895030
\(485\) −15758.0 −1.47533
\(486\) 1024.84 0.0956536
\(487\) −6015.96 −0.559773 −0.279886 0.960033i \(-0.590297\pi\)
−0.279886 + 0.960033i \(0.590297\pi\)
\(488\) −2345.21 −0.217547
\(489\) −6763.05 −0.625430
\(490\) 8963.06 0.826346
\(491\) 4022.81 0.369749 0.184875 0.982762i \(-0.440812\pi\)
0.184875 + 0.982762i \(0.440812\pi\)
\(492\) 11207.7 1.02700
\(493\) 1061.08 0.0969347
\(494\) −16948.6 −1.54363
\(495\) −2987.57 −0.271275
\(496\) −10038.2 −0.908725
\(497\) −14719.6 −1.32850
\(498\) 15975.3 1.43749
\(499\) −14112.8 −1.26608 −0.633042 0.774117i \(-0.718194\pi\)
−0.633042 + 0.774117i \(0.718194\pi\)
\(500\) 10051.7 0.899048
\(501\) 1146.67 0.102255
\(502\) 15950.9 1.41818
\(503\) 689.493 0.0611192 0.0305596 0.999533i \(-0.490271\pi\)
0.0305596 + 0.999533i \(0.490271\pi\)
\(504\) −1010.53 −0.0893109
\(505\) 5212.56 0.459319
\(506\) −1688.07 −0.148308
\(507\) 3565.08 0.312289
\(508\) 20107.2 1.75613
\(509\) −12620.3 −1.09899 −0.549495 0.835497i \(-0.685180\pi\)
−0.549495 + 0.835497i \(0.685180\pi\)
\(510\) −18708.9 −1.62440
\(511\) −5356.03 −0.463673
\(512\) −14732.3 −1.27164
\(513\) −3416.49 −0.294038
\(514\) 306.788 0.0263266
\(515\) −646.735 −0.0553370
\(516\) −4956.44 −0.422859
\(517\) −11600.8 −0.986849
\(518\) 227.651 0.0193097
\(519\) 2789.47 0.235923
\(520\) −4203.53 −0.354494
\(521\) 2186.17 0.183835 0.0919174 0.995767i \(-0.470700\pi\)
0.0919174 + 0.995767i \(0.470700\pi\)
\(522\) 478.383 0.0401116
\(523\) −18639.4 −1.55840 −0.779202 0.626773i \(-0.784375\pi\)
−0.779202 + 0.626773i \(0.784375\pi\)
\(524\) −5894.70 −0.491433
\(525\) −8201.18 −0.681769
\(526\) 20191.0 1.67370
\(527\) −18169.8 −1.50188
\(528\) −2637.28 −0.217373
\(529\) −11718.5 −0.963139
\(530\) −20040.1 −1.64243
\(531\) −531.000 −0.0433963
\(532\) 18451.5 1.50371
\(533\) −12123.3 −0.985216
\(534\) 3457.81 0.280214
\(535\) −8419.06 −0.680351
\(536\) −2827.14 −0.227824
\(537\) 1527.32 0.122735
\(538\) −14002.7 −1.12211
\(539\) 2286.97 0.182758
\(540\) −4641.06 −0.369851
\(541\) −6609.92 −0.525291 −0.262646 0.964892i \(-0.584595\pi\)
−0.262646 + 0.964892i \(0.584595\pi\)
\(542\) −30146.1 −2.38909
\(543\) −2474.59 −0.195571
\(544\) −21590.9 −1.70166
\(545\) 16628.8 1.30697
\(546\) 5987.05 0.469271
\(547\) 8883.37 0.694379 0.347190 0.937795i \(-0.387136\pi\)
0.347190 + 0.937795i \(0.387136\pi\)
\(548\) 18783.5 1.46422
\(549\) 2800.85 0.217737
\(550\) 14625.0 1.13384
\(551\) −1594.78 −0.123303
\(552\) −478.777 −0.0369168
\(553\) 13916.2 1.07012
\(554\) −19447.4 −1.49141
\(555\) 190.888 0.0145995
\(556\) −4389.58 −0.334819
\(557\) 13797.8 1.04961 0.524805 0.851222i \(-0.324138\pi\)
0.524805 + 0.851222i \(0.324138\pi\)
\(558\) −8191.75 −0.621478
\(559\) 5361.36 0.405655
\(560\) −12171.8 −0.918487
\(561\) −4773.66 −0.359258
\(562\) −35037.1 −2.62981
\(563\) −666.036 −0.0498581 −0.0249290 0.999689i \(-0.507936\pi\)
−0.0249290 + 0.999689i \(0.507936\pi\)
\(564\) −18021.3 −1.34545
\(565\) 37438.6 2.78770
\(566\) 34505.9 2.56253
\(567\) 1206.87 0.0893890
\(568\) 7444.84 0.549962
\(569\) −18945.7 −1.39586 −0.697932 0.716164i \(-0.745896\pi\)
−0.697932 + 0.716164i \(0.745896\pi\)
\(570\) 28118.9 2.06626
\(571\) 23781.4 1.74295 0.871473 0.490443i \(-0.163165\pi\)
0.871473 + 0.490443i \(0.163165\pi\)
\(572\) −5874.56 −0.429419
\(573\) 11043.3 0.805130
\(574\) 23987.0 1.74425
\(575\) −3885.61 −0.281811
\(576\) −6385.21 −0.461893
\(577\) 12773.4 0.921601 0.460800 0.887504i \(-0.347562\pi\)
0.460800 + 0.887504i \(0.347562\pi\)
\(578\) −9173.45 −0.660148
\(579\) 9153.52 0.657007
\(580\) −2166.39 −0.155094
\(581\) 18812.7 1.34335
\(582\) −11351.7 −0.808491
\(583\) −5113.33 −0.363246
\(584\) 2708.96 0.191948
\(585\) 5020.21 0.354804
\(586\) 1117.04 0.0787448
\(587\) 11287.3 0.793658 0.396829 0.917893i \(-0.370111\pi\)
0.396829 + 0.917893i \(0.370111\pi\)
\(588\) 3552.70 0.249169
\(589\) 27308.7 1.91042
\(590\) 4370.31 0.304954
\(591\) 15997.7 1.11347
\(592\) 168.506 0.0116986
\(593\) −23122.5 −1.60123 −0.800614 0.599181i \(-0.795493\pi\)
−0.800614 + 0.599181i \(0.795493\pi\)
\(594\) −2152.17 −0.148661
\(595\) −22031.8 −1.51801
\(596\) −15790.5 −1.08524
\(597\) 16115.2 1.10477
\(598\) 2836.58 0.193974
\(599\) −28372.3 −1.93533 −0.967665 0.252239i \(-0.918833\pi\)
−0.967665 + 0.252239i \(0.918833\pi\)
\(600\) 4147.98 0.282234
\(601\) −15958.6 −1.08314 −0.541569 0.840656i \(-0.682170\pi\)
−0.541569 + 0.840656i \(0.682170\pi\)
\(602\) −10607.9 −0.718182
\(603\) 3376.42 0.228024
\(604\) −14897.7 −1.00361
\(605\) −17103.1 −1.14932
\(606\) 3755.01 0.251711
\(607\) 12001.9 0.802540 0.401270 0.915960i \(-0.368569\pi\)
0.401270 + 0.915960i \(0.368569\pi\)
\(608\) 32450.5 2.16454
\(609\) 563.351 0.0374846
\(610\) −23052.0 −1.53008
\(611\) 19493.5 1.29071
\(612\) −7415.67 −0.489805
\(613\) −17040.5 −1.12277 −0.561384 0.827555i \(-0.689731\pi\)
−0.561384 + 0.827555i \(0.689731\pi\)
\(614\) −18471.1 −1.21406
\(615\) 20113.4 1.31878
\(616\) 2122.13 0.138804
\(617\) −23366.1 −1.52461 −0.762304 0.647219i \(-0.775932\pi\)
−0.762304 + 0.647219i \(0.775932\pi\)
\(618\) −465.892 −0.0303251
\(619\) 3475.30 0.225661 0.112831 0.993614i \(-0.464008\pi\)
0.112831 + 0.993614i \(0.464008\pi\)
\(620\) 37097.0 2.40298
\(621\) 571.797 0.0369491
\(622\) −44471.3 −2.86678
\(623\) 4071.97 0.261862
\(624\) 4431.59 0.284304
\(625\) −4895.84 −0.313334
\(626\) 27399.5 1.74937
\(627\) 7174.67 0.456984
\(628\) −777.303 −0.0493913
\(629\) 305.008 0.0193346
\(630\) −9932.92 −0.628154
\(631\) 16882.7 1.06512 0.532561 0.846392i \(-0.321230\pi\)
0.532561 + 0.846392i \(0.321230\pi\)
\(632\) −7038.49 −0.443000
\(633\) −5690.77 −0.357326
\(634\) −11086.9 −0.694504
\(635\) 36084.5 2.25507
\(636\) −7943.33 −0.495242
\(637\) −3842.94 −0.239031
\(638\) −1004.61 −0.0623400
\(639\) −8891.27 −0.550443
\(640\) 16519.0 1.02027
\(641\) 19928.1 1.22794 0.613971 0.789328i \(-0.289571\pi\)
0.613971 + 0.789328i \(0.289571\pi\)
\(642\) −6064.89 −0.372838
\(643\) −27843.0 −1.70765 −0.853827 0.520556i \(-0.825725\pi\)
−0.853827 + 0.520556i \(0.825725\pi\)
\(644\) −3088.12 −0.188958
\(645\) −8894.86 −0.543000
\(646\) 44929.5 2.73642
\(647\) 28838.3 1.75232 0.876160 0.482021i \(-0.160097\pi\)
0.876160 + 0.482021i \(0.160097\pi\)
\(648\) −610.406 −0.0370047
\(649\) 1115.11 0.0674449
\(650\) −24575.3 −1.48296
\(651\) −9646.72 −0.580776
\(652\) 22062.9 1.32523
\(653\) 17697.2 1.06056 0.530280 0.847823i \(-0.322087\pi\)
0.530280 + 0.847823i \(0.322087\pi\)
\(654\) 11979.0 0.716231
\(655\) −10578.7 −0.631057
\(656\) 17755.1 1.05674
\(657\) −3235.28 −0.192116
\(658\) −38569.6 −2.28511
\(659\) 21288.4 1.25839 0.629196 0.777247i \(-0.283384\pi\)
0.629196 + 0.777247i \(0.283384\pi\)
\(660\) 9746.29 0.574809
\(661\) −3564.16 −0.209727 −0.104864 0.994487i \(-0.533441\pi\)
−0.104864 + 0.994487i \(0.533441\pi\)
\(662\) 15516.2 0.910957
\(663\) 8021.49 0.469878
\(664\) −9515.07 −0.556109
\(665\) 33113.2 1.93094
\(666\) 137.511 0.00800068
\(667\) 266.908 0.0154943
\(668\) −3740.76 −0.216668
\(669\) 8426.54 0.486979
\(670\) −27789.1 −1.60237
\(671\) −5881.83 −0.338399
\(672\) −11463.0 −0.658030
\(673\) 803.878 0.0460434 0.0230217 0.999735i \(-0.492671\pi\)
0.0230217 + 0.999735i \(0.492671\pi\)
\(674\) −5582.80 −0.319053
\(675\) −4953.88 −0.282481
\(676\) −11630.3 −0.661713
\(677\) −14587.1 −0.828106 −0.414053 0.910253i \(-0.635887\pi\)
−0.414053 + 0.910253i \(0.635887\pi\)
\(678\) 26969.8 1.52768
\(679\) −13367.9 −0.755541
\(680\) 11143.2 0.628416
\(681\) −9908.48 −0.557554
\(682\) 17202.8 0.965878
\(683\) 19187.3 1.07494 0.537469 0.843284i \(-0.319381\pi\)
0.537469 + 0.843284i \(0.319381\pi\)
\(684\) 11145.5 0.623042
\(685\) 33709.0 1.88023
\(686\) 29157.1 1.62277
\(687\) 17340.6 0.963005
\(688\) −7851.93 −0.435105
\(689\) 8592.26 0.475093
\(690\) −4706.09 −0.259649
\(691\) 19785.3 1.08924 0.544622 0.838682i \(-0.316673\pi\)
0.544622 + 0.838682i \(0.316673\pi\)
\(692\) −9100.03 −0.499901
\(693\) −2534.43 −0.138925
\(694\) −23370.1 −1.27827
\(695\) −7877.56 −0.429946
\(696\) −284.931 −0.0155176
\(697\) 32138.0 1.74651
\(698\) 27794.9 1.50724
\(699\) −14678.5 −0.794267
\(700\) 26754.5 1.44461
\(701\) −14311.7 −0.771104 −0.385552 0.922686i \(-0.625989\pi\)
−0.385552 + 0.922686i \(0.625989\pi\)
\(702\) 3616.44 0.194436
\(703\) −458.419 −0.0245940
\(704\) 13409.0 0.717857
\(705\) −32341.1 −1.72771
\(706\) 23757.3 1.26646
\(707\) 4421.95 0.235226
\(708\) 1732.27 0.0919530
\(709\) −11747.7 −0.622277 −0.311139 0.950365i \(-0.600710\pi\)
−0.311139 + 0.950365i \(0.600710\pi\)
\(710\) 73178.3 3.86807
\(711\) 8405.98 0.443388
\(712\) −2059.51 −0.108404
\(713\) −4570.49 −0.240065
\(714\) −15871.2 −0.831884
\(715\) −10542.5 −0.551423
\(716\) −4982.53 −0.260064
\(717\) 19384.2 1.00964
\(718\) −11271.7 −0.585874
\(719\) 1263.52 0.0655374 0.0327687 0.999463i \(-0.489568\pi\)
0.0327687 + 0.999463i \(0.489568\pi\)
\(720\) −7352.31 −0.380562
\(721\) −548.642 −0.0283391
\(722\) −38600.3 −1.98969
\(723\) 182.319 0.00937829
\(724\) 8072.82 0.414398
\(725\) −2312.41 −0.118456
\(726\) −12320.7 −0.629838
\(727\) −15608.6 −0.796275 −0.398138 0.917326i \(-0.630343\pi\)
−0.398138 + 0.917326i \(0.630343\pi\)
\(728\) −3565.96 −0.181543
\(729\) 729.000 0.0370370
\(730\) 26627.5 1.35004
\(731\) −14212.6 −0.719111
\(732\) −9137.17 −0.461365
\(733\) 5555.30 0.279931 0.139966 0.990156i \(-0.455301\pi\)
0.139966 + 0.990156i \(0.455301\pi\)
\(734\) 12154.3 0.611205
\(735\) 6375.70 0.319961
\(736\) −5431.03 −0.271998
\(737\) −7090.51 −0.354386
\(738\) 14489.2 0.722705
\(739\) −6833.98 −0.340179 −0.170089 0.985429i \(-0.554406\pi\)
−0.170089 + 0.985429i \(0.554406\pi\)
\(740\) −622.730 −0.0309352
\(741\) −12056.1 −0.597694
\(742\) −17000.5 −0.841117
\(743\) 35475.6 1.75165 0.875823 0.482633i \(-0.160319\pi\)
0.875823 + 0.482633i \(0.160319\pi\)
\(744\) 4879.11 0.240426
\(745\) −28337.8 −1.39358
\(746\) −30996.5 −1.52126
\(747\) 11363.7 0.556596
\(748\) 15573.0 0.761237
\(749\) −7142.10 −0.348420
\(750\) 12994.7 0.632666
\(751\) −33087.6 −1.60770 −0.803850 0.594832i \(-0.797218\pi\)
−0.803850 + 0.594832i \(0.797218\pi\)
\(752\) −28549.1 −1.38441
\(753\) 11346.4 0.549118
\(754\) 1688.11 0.0815351
\(755\) −26735.5 −1.28875
\(756\) −3937.13 −0.189407
\(757\) −11497.2 −0.552013 −0.276007 0.961156i \(-0.589011\pi\)
−0.276007 + 0.961156i \(0.589011\pi\)
\(758\) −25310.1 −1.21280
\(759\) −1200.78 −0.0574250
\(760\) −16747.9 −0.799358
\(761\) 7865.73 0.374681 0.187341 0.982295i \(-0.440013\pi\)
0.187341 + 0.982295i \(0.440013\pi\)
\(762\) 25994.4 1.23580
\(763\) 14106.6 0.669323
\(764\) −36026.3 −1.70600
\(765\) −13308.2 −0.628966
\(766\) 33082.5 1.56047
\(767\) −1873.79 −0.0882119
\(768\) −5127.30 −0.240906
\(769\) 8020.94 0.376128 0.188064 0.982157i \(-0.439779\pi\)
0.188064 + 0.982157i \(0.439779\pi\)
\(770\) 20859.3 0.976254
\(771\) 218.228 0.0101936
\(772\) −29861.3 −1.39214
\(773\) −17731.7 −0.825053 −0.412526 0.910946i \(-0.635354\pi\)
−0.412526 + 0.910946i \(0.635354\pi\)
\(774\) −6407.64 −0.297568
\(775\) 39597.4 1.83533
\(776\) 6761.19 0.312774
\(777\) 161.935 0.00747670
\(778\) 2423.36 0.111673
\(779\) −48302.5 −2.22159
\(780\) −16377.3 −0.751798
\(781\) 18671.8 0.855479
\(782\) −7519.57 −0.343861
\(783\) 340.289 0.0155312
\(784\) 5628.15 0.256384
\(785\) −1394.95 −0.0634242
\(786\) −7620.61 −0.345825
\(787\) −10866.2 −0.492170 −0.246085 0.969248i \(-0.579144\pi\)
−0.246085 + 0.969248i \(0.579144\pi\)
\(788\) −52189.0 −2.35934
\(789\) 14362.5 0.648058
\(790\) −69184.1 −3.11577
\(791\) 31760.1 1.42763
\(792\) 1281.86 0.0575113
\(793\) 9883.63 0.442595
\(794\) 60431.9 2.70107
\(795\) −14255.2 −0.635947
\(796\) −52572.1 −2.34092
\(797\) −36334.0 −1.61483 −0.807414 0.589985i \(-0.799134\pi\)
−0.807414 + 0.589985i \(0.799134\pi\)
\(798\) 23854.0 1.05817
\(799\) −51675.8 −2.28806
\(800\) 47052.8 2.07946
\(801\) 2459.65 0.108499
\(802\) −35597.4 −1.56731
\(803\) 6794.13 0.298580
\(804\) −11014.8 −0.483162
\(805\) −5541.96 −0.242644
\(806\) −28907.0 −1.26328
\(807\) −9960.53 −0.434483
\(808\) −2236.53 −0.0973772
\(809\) 29433.4 1.27914 0.639569 0.768734i \(-0.279113\pi\)
0.639569 + 0.768734i \(0.279113\pi\)
\(810\) −5999.92 −0.260266
\(811\) −6295.17 −0.272569 −0.136284 0.990670i \(-0.543516\pi\)
−0.136284 + 0.990670i \(0.543516\pi\)
\(812\) −1837.81 −0.0794266
\(813\) −21443.8 −0.925053
\(814\) −288.775 −0.0124344
\(815\) 39594.3 1.70175
\(816\) −11747.8 −0.503990
\(817\) 21361.1 0.914723
\(818\) 16848.8 0.720175
\(819\) 4258.77 0.181702
\(820\) −65615.6 −2.79439
\(821\) 39899.7 1.69611 0.848057 0.529905i \(-0.177772\pi\)
0.848057 + 0.529905i \(0.177772\pi\)
\(822\) 24283.2 1.03038
\(823\) −1122.81 −0.0475560 −0.0237780 0.999717i \(-0.507569\pi\)
−0.0237780 + 0.999717i \(0.507569\pi\)
\(824\) 277.491 0.0117316
\(825\) 10403.2 0.439022
\(826\) 3707.45 0.156173
\(827\) −11050.5 −0.464649 −0.232325 0.972638i \(-0.574633\pi\)
−0.232325 + 0.972638i \(0.574633\pi\)
\(828\) −1865.36 −0.0782920
\(829\) 28472.9 1.19289 0.596444 0.802654i \(-0.296580\pi\)
0.596444 + 0.802654i \(0.296580\pi\)
\(830\) −93527.4 −3.91131
\(831\) −13833.6 −0.577474
\(832\) −22532.1 −0.938893
\(833\) 10187.3 0.423734
\(834\) −5674.80 −0.235614
\(835\) −6713.19 −0.278227
\(836\) −23405.8 −0.968308
\(837\) −5827.05 −0.240636
\(838\) 7952.88 0.327837
\(839\) 6906.38 0.284189 0.142095 0.989853i \(-0.454616\pi\)
0.142095 + 0.989853i \(0.454616\pi\)
\(840\) 5916.16 0.243008
\(841\) −24230.2 −0.993487
\(842\) 39088.9 1.59987
\(843\) −24923.0 −1.01826
\(844\) 18564.9 0.757143
\(845\) −20871.7 −0.849716
\(846\) −23297.7 −0.946800
\(847\) −14509.0 −0.588589
\(848\) −12583.7 −0.509584
\(849\) 24545.1 0.992210
\(850\) 65147.3 2.62886
\(851\) 76.7228 0.00309051
\(852\) 29005.8 1.16634
\(853\) −22035.5 −0.884504 −0.442252 0.896891i \(-0.645820\pi\)
−0.442252 + 0.896891i \(0.645820\pi\)
\(854\) −19555.6 −0.783582
\(855\) 20001.9 0.800057
\(856\) 3612.32 0.144237
\(857\) 39983.9 1.59373 0.796864 0.604159i \(-0.206491\pi\)
0.796864 + 0.604159i \(0.206491\pi\)
\(858\) −7594.57 −0.302185
\(859\) −17967.4 −0.713668 −0.356834 0.934168i \(-0.616144\pi\)
−0.356834 + 0.934168i \(0.616144\pi\)
\(860\) 29017.5 1.15057
\(861\) 17062.7 0.675373
\(862\) 14112.0 0.557608
\(863\) 42533.4 1.67770 0.838850 0.544363i \(-0.183229\pi\)
0.838850 + 0.544363i \(0.183229\pi\)
\(864\) −6924.18 −0.272645
\(865\) −16331.0 −0.641930
\(866\) 3913.15 0.153550
\(867\) −6525.36 −0.255609
\(868\) 31470.3 1.23061
\(869\) −17652.7 −0.689097
\(870\) −2800.69 −0.109141
\(871\) 11914.7 0.463505
\(872\) −7134.82 −0.277082
\(873\) −8074.80 −0.313048
\(874\) 11301.7 0.437398
\(875\) 15302.8 0.591231
\(876\) 10554.4 0.407077
\(877\) 48368.0 1.86234 0.931169 0.364589i \(-0.118791\pi\)
0.931169 + 0.364589i \(0.118791\pi\)
\(878\) −42699.6 −1.64128
\(879\) 794.585 0.0304900
\(880\) 15439.9 0.591455
\(881\) 29172.9 1.11562 0.557810 0.829969i \(-0.311642\pi\)
0.557810 + 0.829969i \(0.311642\pi\)
\(882\) 4592.90 0.175341
\(883\) −17067.5 −0.650471 −0.325235 0.945633i \(-0.605444\pi\)
−0.325235 + 0.945633i \(0.605444\pi\)
\(884\) −26168.3 −0.995630
\(885\) 3108.74 0.118078
\(886\) 27381.5 1.03826
\(887\) 19672.0 0.744671 0.372335 0.928098i \(-0.378557\pi\)
0.372335 + 0.928098i \(0.378557\pi\)
\(888\) −81.9033 −0.00309515
\(889\) 30611.4 1.15486
\(890\) −20243.8 −0.762441
\(891\) −1530.91 −0.0575616
\(892\) −27489.7 −1.03187
\(893\) 77667.3 2.91046
\(894\) −20413.9 −0.763693
\(895\) −8941.68 −0.333953
\(896\) 14013.5 0.522499
\(897\) 2017.75 0.0751067
\(898\) 74682.4 2.77526
\(899\) −2720.00 −0.100909
\(900\) 16160.9 0.598553
\(901\) −22777.4 −0.842205
\(902\) −30427.6 −1.12320
\(903\) −7545.73 −0.278080
\(904\) −16063.6 −0.591002
\(905\) 14487.5 0.532134
\(906\) −19259.6 −0.706245
\(907\) −6730.37 −0.246393 −0.123196 0.992382i \(-0.539315\pi\)
−0.123196 + 0.992382i \(0.539315\pi\)
\(908\) 32324.2 1.18141
\(909\) 2671.05 0.0974623
\(910\) −35051.2 −1.27685
\(911\) 5094.05 0.185262 0.0926308 0.995701i \(-0.470472\pi\)
0.0926308 + 0.995701i \(0.470472\pi\)
\(912\) 17656.6 0.641085
\(913\) −23864.0 −0.865040
\(914\) −45486.2 −1.64612
\(915\) −16397.6 −0.592446
\(916\) −56569.8 −2.04052
\(917\) −8974.14 −0.323176
\(918\) −9586.91 −0.344679
\(919\) −18873.8 −0.677464 −0.338732 0.940883i \(-0.609998\pi\)
−0.338732 + 0.940883i \(0.609998\pi\)
\(920\) 2803.00 0.100448
\(921\) −13139.1 −0.470084
\(922\) 61205.7 2.18623
\(923\) −31375.4 −1.11889
\(924\) 8268.02 0.294370
\(925\) −664.703 −0.0236274
\(926\) 40646.9 1.44248
\(927\) −331.404 −0.0117419
\(928\) −3232.13 −0.114332
\(929\) 42077.8 1.48603 0.743017 0.669272i \(-0.233394\pi\)
0.743017 + 0.669272i \(0.233394\pi\)
\(930\) 47958.6 1.69100
\(931\) −15311.3 −0.538998
\(932\) 47885.4 1.68298
\(933\) −31633.9 −1.11002
\(934\) 30620.0 1.07272
\(935\) 27947.4 0.977516
\(936\) −2154.00 −0.0752196
\(937\) −16791.9 −0.585452 −0.292726 0.956196i \(-0.594562\pi\)
−0.292726 + 0.956196i \(0.594562\pi\)
\(938\) −23574.2 −0.820601
\(939\) 19490.1 0.677355
\(940\) 105506. 3.66087
\(941\) −21099.3 −0.730943 −0.365472 0.930822i \(-0.619092\pi\)
−0.365472 + 0.930822i \(0.619092\pi\)
\(942\) −1004.89 −0.0347570
\(943\) 8084.10 0.279167
\(944\) 2744.24 0.0946159
\(945\) −7065.60 −0.243221
\(946\) 13456.1 0.462470
\(947\) −13159.7 −0.451567 −0.225783 0.974178i \(-0.572494\pi\)
−0.225783 + 0.974178i \(0.572494\pi\)
\(948\) −27422.6 −0.939500
\(949\) −11416.6 −0.390516
\(950\) −97914.5 −3.34396
\(951\) −7886.43 −0.268912
\(952\) 9453.08 0.321824
\(953\) −14229.9 −0.483685 −0.241843 0.970315i \(-0.577752\pi\)
−0.241843 + 0.970315i \(0.577752\pi\)
\(954\) −10269.1 −0.348505
\(955\) −64652.9 −2.19070
\(956\) −63236.6 −2.13935
\(957\) −714.611 −0.0241380
\(958\) −50901.9 −1.71667
\(959\) 28596.2 0.962898
\(960\) 37382.2 1.25678
\(961\) 16785.8 0.563453
\(962\) 485.248 0.0162630
\(963\) −4314.15 −0.144363
\(964\) −594.774 −0.0198718
\(965\) −53589.3 −1.78767
\(966\) −3992.29 −0.132971
\(967\) −43103.2 −1.43341 −0.716704 0.697377i \(-0.754350\pi\)
−0.716704 + 0.697377i \(0.754350\pi\)
\(968\) 7338.33 0.243660
\(969\) 31959.7 1.05954
\(970\) 66458.4 2.19985
\(971\) −24953.4 −0.824710 −0.412355 0.911023i \(-0.635294\pi\)
−0.412355 + 0.911023i \(0.635294\pi\)
\(972\) −2378.20 −0.0784782
\(973\) −6682.73 −0.220183
\(974\) 25372.0 0.834673
\(975\) −17481.2 −0.574201
\(976\) −14475.0 −0.474726
\(977\) −7739.34 −0.253432 −0.126716 0.991939i \(-0.540444\pi\)
−0.126716 + 0.991939i \(0.540444\pi\)
\(978\) 28522.8 0.932574
\(979\) −5165.29 −0.168625
\(980\) −20799.3 −0.677969
\(981\) 8521.02 0.277324
\(982\) −16966.0 −0.551330
\(983\) 19799.0 0.642410 0.321205 0.947010i \(-0.395912\pi\)
0.321205 + 0.947010i \(0.395912\pi\)
\(984\) −8629.96 −0.279587
\(985\) −93658.7 −3.02966
\(986\) −4475.06 −0.144538
\(987\) −27435.8 −0.884792
\(988\) 39330.3 1.26646
\(989\) −3575.07 −0.114945
\(990\) 12599.9 0.404497
\(991\) 10262.8 0.328968 0.164484 0.986380i \(-0.447404\pi\)
0.164484 + 0.986380i \(0.447404\pi\)
\(992\) 55346.4 1.77142
\(993\) 11037.1 0.352722
\(994\) 62079.0 1.98091
\(995\) −94346.2 −3.00601
\(996\) −37071.6 −1.17938
\(997\) −18748.2 −0.595549 −0.297774 0.954636i \(-0.596244\pi\)
−0.297774 + 0.954636i \(0.596244\pi\)
\(998\) 59520.0 1.88785
\(999\) 97.8160 0.00309786
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.1.2 8
3.2 odd 2 531.4.a.f.1.7 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.4.a.c.1.2 8 1.1 even 1 trivial
531.4.a.f.1.7 8 3.2 odd 2