Properties

Label 177.4.a.c.1.7
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 1.7
Root \(4.61734\) of defining polynomial
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+4.61734 q^{2} -3.00000 q^{3} +13.3198 q^{4} -3.21787 q^{5} -13.8520 q^{6} +15.9864 q^{7} +24.5634 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q+4.61734 q^{2} -3.00000 q^{3} +13.3198 q^{4} -3.21787 q^{5} -13.8520 q^{6} +15.9864 q^{7} +24.5634 q^{8} +9.00000 q^{9} -14.8580 q^{10} +54.2052 q^{11} -39.9594 q^{12} +85.2841 q^{13} +73.8148 q^{14} +9.65362 q^{15} +6.85884 q^{16} -48.1138 q^{17} +41.5560 q^{18} +64.2348 q^{19} -42.8615 q^{20} -47.9593 q^{21} +250.284 q^{22} -191.406 q^{23} -73.6901 q^{24} -114.645 q^{25} +393.786 q^{26} -27.0000 q^{27} +212.936 q^{28} -15.0020 q^{29} +44.5740 q^{30} -209.724 q^{31} -164.837 q^{32} -162.616 q^{33} -222.158 q^{34} -51.4424 q^{35} +119.878 q^{36} +418.134 q^{37} +296.594 q^{38} -255.852 q^{39} -79.0418 q^{40} +226.787 q^{41} -221.445 q^{42} -207.102 q^{43} +722.003 q^{44} -28.9609 q^{45} -883.784 q^{46} +330.575 q^{47} -20.5765 q^{48} -87.4334 q^{49} -529.356 q^{50} +144.341 q^{51} +1135.97 q^{52} -449.141 q^{53} -124.668 q^{54} -174.426 q^{55} +392.681 q^{56} -192.704 q^{57} -69.2694 q^{58} -59.0000 q^{59} +128.584 q^{60} -393.282 q^{61} -968.368 q^{62} +143.878 q^{63} -815.980 q^{64} -274.434 q^{65} -750.851 q^{66} -67.7305 q^{67} -640.866 q^{68} +574.217 q^{69} -237.527 q^{70} -589.737 q^{71} +221.070 q^{72} -229.329 q^{73} +1930.67 q^{74} +343.936 q^{75} +855.595 q^{76} +866.549 q^{77} -1181.36 q^{78} +563.476 q^{79} -22.0709 q^{80} +81.0000 q^{81} +1047.15 q^{82} +1179.22 q^{83} -638.809 q^{84} +154.824 q^{85} -956.258 q^{86} +45.0061 q^{87} +1331.46 q^{88} -1335.45 q^{89} -133.722 q^{90} +1363.39 q^{91} -2549.49 q^{92} +629.173 q^{93} +1526.37 q^{94} -206.699 q^{95} +494.512 q^{96} +1361.53 q^{97} -403.710 q^{98} +487.847 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 2q^{2} - 24q^{3} + 38q^{4} - 12q^{5} - 6q^{6} + 53q^{7} + 3q^{8} + 72q^{9} + O(q^{10}) \) \( 8q + 2q^{2} - 24q^{3} + 38q^{4} - 12q^{5} - 6q^{6} + 53q^{7} + 3q^{8} + 72q^{9} + 29q^{10} - 27q^{11} - 114q^{12} + 89q^{13} - 37q^{14} + 36q^{15} + 362q^{16} + 79q^{17} + 18q^{18} + 288q^{19} + 457q^{20} - 159q^{21} + 596q^{22} + 202q^{23} - 9q^{24} + 264q^{25} + 270q^{26} - 216q^{27} + 702q^{28} - 114q^{29} - 87q^{30} + 538q^{31} + 316q^{32} + 81q^{33} + 498q^{34} - 196q^{35} + 342q^{36} + 395q^{37} + 397q^{38} - 267q^{39} + 918q^{40} - 39q^{41} + 111q^{42} + 527q^{43} + 64q^{44} - 108q^{45} - 539q^{46} + 860q^{47} - 1086q^{48} + 347q^{49} - 591q^{50} - 237q^{51} - 644q^{52} - 812q^{53} - 54q^{54} + 536q^{55} - 2218q^{56} - 864q^{57} - 1154q^{58} - 472q^{59} - 1371q^{60} - 460q^{61} - 2014q^{62} + 477q^{63} - 451q^{64} - 986q^{65} - 1788q^{66} + 1934q^{67} - 69q^{68} - 606q^{69} - 1028q^{70} - 1687q^{71} + 27q^{72} + 1980q^{73} - 2400q^{74} - 792q^{75} - 940q^{76} - 821q^{77} - 810q^{78} + 3319q^{79} - 2119q^{80} + 648q^{81} + 429q^{82} + 2057q^{83} - 2106q^{84} + 566q^{85} - 6690q^{86} + 342q^{87} + 1189q^{88} + 1668q^{89} + 261q^{90} + 2427q^{91} - 980q^{92} - 1614q^{93} + 332q^{94} + 2146q^{95} - 948q^{96} + 1956q^{97} - 2026q^{98} - 243q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.61734 1.63248 0.816238 0.577716i \(-0.196056\pi\)
0.816238 + 0.577716i \(0.196056\pi\)
\(3\) −3.00000 −0.577350
\(4\) 13.3198 1.66498
\(5\) −3.21787 −0.287815 −0.143908 0.989591i \(-0.545967\pi\)
−0.143908 + 0.989591i \(0.545967\pi\)
\(6\) −13.8520 −0.942510
\(7\) 15.9864 0.863187 0.431594 0.902068i \(-0.357951\pi\)
0.431594 + 0.902068i \(0.357951\pi\)
\(8\) 24.5634 1.08556
\(9\) 9.00000 0.333333
\(10\) −14.8580 −0.469852
\(11\) 54.2052 1.48577 0.742886 0.669418i \(-0.233456\pi\)
0.742886 + 0.669418i \(0.233456\pi\)
\(12\) −39.9594 −0.961274
\(13\) 85.2841 1.81951 0.909753 0.415151i \(-0.136271\pi\)
0.909753 + 0.415151i \(0.136271\pi\)
\(14\) 73.8148 1.40913
\(15\) 9.65362 0.166170
\(16\) 6.85884 0.107169
\(17\) −48.1138 −0.686430 −0.343215 0.939257i \(-0.611516\pi\)
−0.343215 + 0.939257i \(0.611516\pi\)
\(18\) 41.5560 0.544158
\(19\) 64.2348 0.775604 0.387802 0.921743i \(-0.373235\pi\)
0.387802 + 0.921743i \(0.373235\pi\)
\(20\) −42.8615 −0.479206
\(21\) −47.9593 −0.498361
\(22\) 250.284 2.42549
\(23\) −191.406 −1.73525 −0.867627 0.497216i \(-0.834355\pi\)
−0.867627 + 0.497216i \(0.834355\pi\)
\(24\) −73.6901 −0.626747
\(25\) −114.645 −0.917162
\(26\) 393.786 2.97030
\(27\) −27.0000 −0.192450
\(28\) 212.936 1.43719
\(29\) −15.0020 −0.0960622 −0.0480311 0.998846i \(-0.515295\pi\)
−0.0480311 + 0.998846i \(0.515295\pi\)
\(30\) 44.5740 0.271269
\(31\) −209.724 −1.21508 −0.607542 0.794287i \(-0.707844\pi\)
−0.607542 + 0.794287i \(0.707844\pi\)
\(32\) −164.837 −0.910606
\(33\) −162.616 −0.857811
\(34\) −222.158 −1.12058
\(35\) −51.4424 −0.248439
\(36\) 119.878 0.554992
\(37\) 418.134 1.85786 0.928931 0.370254i \(-0.120729\pi\)
0.928931 + 0.370254i \(0.120729\pi\)
\(38\) 296.594 1.26615
\(39\) −255.852 −1.05049
\(40\) −79.0418 −0.312440
\(41\) 226.787 0.863859 0.431929 0.901907i \(-0.357833\pi\)
0.431929 + 0.901907i \(0.357833\pi\)
\(42\) −221.445 −0.813563
\(43\) −207.102 −0.734481 −0.367241 0.930126i \(-0.619697\pi\)
−0.367241 + 0.930126i \(0.619697\pi\)
\(44\) 722.003 2.47377
\(45\) −28.9609 −0.0959385
\(46\) −883.784 −2.83276
\(47\) 330.575 1.02594 0.512971 0.858406i \(-0.328545\pi\)
0.512971 + 0.858406i \(0.328545\pi\)
\(48\) −20.5765 −0.0618742
\(49\) −87.4334 −0.254908
\(50\) −529.356 −1.49724
\(51\) 144.341 0.396310
\(52\) 1135.97 3.02943
\(53\) −449.141 −1.16404 −0.582021 0.813173i \(-0.697738\pi\)
−0.582021 + 0.813173i \(0.697738\pi\)
\(54\) −124.668 −0.314170
\(55\) −174.426 −0.427628
\(56\) 392.681 0.937039
\(57\) −192.704 −0.447795
\(58\) −69.2694 −0.156819
\(59\) −59.0000 −0.130189
\(60\) 128.584 0.276670
\(61\) −393.282 −0.825485 −0.412743 0.910848i \(-0.635429\pi\)
−0.412743 + 0.910848i \(0.635429\pi\)
\(62\) −968.368 −1.98360
\(63\) 143.878 0.287729
\(64\) −815.980 −1.59371
\(65\) −274.434 −0.523682
\(66\) −750.851 −1.40035
\(67\) −67.7305 −0.123501 −0.0617507 0.998092i \(-0.519668\pi\)
−0.0617507 + 0.998092i \(0.519668\pi\)
\(68\) −640.866 −1.14289
\(69\) 574.217 1.00185
\(70\) −237.527 −0.405570
\(71\) −589.737 −0.985759 −0.492879 0.870098i \(-0.664056\pi\)
−0.492879 + 0.870098i \(0.664056\pi\)
\(72\) 221.070 0.361852
\(73\) −229.329 −0.367684 −0.183842 0.982956i \(-0.558853\pi\)
−0.183842 + 0.982956i \(0.558853\pi\)
\(74\) 1930.67 3.03291
\(75\) 343.936 0.529524
\(76\) 855.595 1.29136
\(77\) 866.549 1.28250
\(78\) −1181.36 −1.71490
\(79\) 563.476 0.802482 0.401241 0.915973i \(-0.368579\pi\)
0.401241 + 0.915973i \(0.368579\pi\)
\(80\) −22.0709 −0.0308450
\(81\) 81.0000 0.111111
\(82\) 1047.15 1.41023
\(83\) 1179.22 1.55947 0.779733 0.626112i \(-0.215355\pi\)
0.779733 + 0.626112i \(0.215355\pi\)
\(84\) −638.809 −0.829760
\(85\) 154.824 0.197565
\(86\) −956.258 −1.19902
\(87\) 45.0061 0.0554616
\(88\) 1331.46 1.61289
\(89\) −1335.45 −1.59053 −0.795266 0.606261i \(-0.792669\pi\)
−0.795266 + 0.606261i \(0.792669\pi\)
\(90\) −133.722 −0.156617
\(91\) 1363.39 1.57057
\(92\) −2549.49 −2.88915
\(93\) 629.173 0.701529
\(94\) 1526.37 1.67482
\(95\) −206.699 −0.223231
\(96\) 494.512 0.525739
\(97\) 1361.53 1.42518 0.712592 0.701578i \(-0.247521\pi\)
0.712592 + 0.701578i \(0.247521\pi\)
\(98\) −403.710 −0.416131
\(99\) 487.847 0.495257
\(100\) −1527.05 −1.52705
\(101\) 257.488 0.253673 0.126837 0.991924i \(-0.459518\pi\)
0.126837 + 0.991924i \(0.459518\pi\)
\(102\) 666.473 0.646967
\(103\) −343.256 −0.328370 −0.164185 0.986430i \(-0.552499\pi\)
−0.164185 + 0.986430i \(0.552499\pi\)
\(104\) 2094.86 1.97518
\(105\) 154.327 0.143436
\(106\) −2073.84 −1.90027
\(107\) −1319.34 −1.19201 −0.596007 0.802979i \(-0.703247\pi\)
−0.596007 + 0.802979i \(0.703247\pi\)
\(108\) −359.635 −0.320425
\(109\) 282.298 0.248067 0.124033 0.992278i \(-0.460417\pi\)
0.124033 + 0.992278i \(0.460417\pi\)
\(110\) −805.382 −0.698092
\(111\) −1254.40 −1.07264
\(112\) 109.648 0.0925072
\(113\) −2326.67 −1.93695 −0.968473 0.249119i \(-0.919859\pi\)
−0.968473 + 0.249119i \(0.919859\pi\)
\(114\) −889.781 −0.731014
\(115\) 615.919 0.499433
\(116\) −199.824 −0.159941
\(117\) 767.557 0.606502
\(118\) −272.423 −0.212530
\(119\) −769.169 −0.592517
\(120\) 237.125 0.180387
\(121\) 1607.21 1.20752
\(122\) −1815.92 −1.34758
\(123\) −680.361 −0.498749
\(124\) −2793.49 −2.02309
\(125\) 771.149 0.551789
\(126\) 664.334 0.469711
\(127\) 660.219 0.461299 0.230650 0.973037i \(-0.425915\pi\)
0.230650 + 0.973037i \(0.425915\pi\)
\(128\) −2448.96 −1.69109
\(129\) 621.305 0.424053
\(130\) −1267.15 −0.854898
\(131\) 338.174 0.225545 0.112772 0.993621i \(-0.464027\pi\)
0.112772 + 0.993621i \(0.464027\pi\)
\(132\) −2166.01 −1.42823
\(133\) 1026.89 0.669491
\(134\) −312.734 −0.201613
\(135\) 86.8826 0.0553901
\(136\) −1181.84 −0.745159
\(137\) −1007.22 −0.628121 −0.314061 0.949403i \(-0.601689\pi\)
−0.314061 + 0.949403i \(0.601689\pi\)
\(138\) 2651.35 1.63549
\(139\) 2107.75 1.28617 0.643084 0.765796i \(-0.277655\pi\)
0.643084 + 0.765796i \(0.277655\pi\)
\(140\) −685.203 −0.413644
\(141\) −991.724 −0.592328
\(142\) −2723.01 −1.60923
\(143\) 4622.85 2.70337
\(144\) 61.7295 0.0357231
\(145\) 48.2746 0.0276482
\(146\) −1058.89 −0.600235
\(147\) 262.300 0.147171
\(148\) 5569.47 3.09329
\(149\) −2275.39 −1.25105 −0.625527 0.780203i \(-0.715116\pi\)
−0.625527 + 0.780203i \(0.715116\pi\)
\(150\) 1588.07 0.864435
\(151\) 396.997 0.213955 0.106977 0.994261i \(-0.465883\pi\)
0.106977 + 0.994261i \(0.465883\pi\)
\(152\) 1577.82 0.841962
\(153\) −433.024 −0.228810
\(154\) 4001.15 2.09365
\(155\) 674.867 0.349720
\(156\) −3407.91 −1.74904
\(157\) −2285.11 −1.16160 −0.580802 0.814045i \(-0.697261\pi\)
−0.580802 + 0.814045i \(0.697261\pi\)
\(158\) 2601.76 1.31003
\(159\) 1347.42 0.672060
\(160\) 530.426 0.262086
\(161\) −3059.90 −1.49785
\(162\) 374.004 0.181386
\(163\) 1433.49 0.688831 0.344415 0.938817i \(-0.388077\pi\)
0.344415 + 0.938817i \(0.388077\pi\)
\(164\) 3020.76 1.43830
\(165\) 523.277 0.246891
\(166\) 5444.84 2.54579
\(167\) 270.302 0.125249 0.0626246 0.998037i \(-0.480053\pi\)
0.0626246 + 0.998037i \(0.480053\pi\)
\(168\) −1178.04 −0.541000
\(169\) 5076.39 2.31060
\(170\) 714.875 0.322520
\(171\) 578.113 0.258535
\(172\) −2758.55 −1.22289
\(173\) 1503.33 0.660673 0.330337 0.943863i \(-0.392838\pi\)
0.330337 + 0.943863i \(0.392838\pi\)
\(174\) 207.808 0.0905396
\(175\) −1832.77 −0.791683
\(176\) 371.785 0.159229
\(177\) 177.000 0.0751646
\(178\) −6166.22 −2.59650
\(179\) 1741.30 0.727100 0.363550 0.931575i \(-0.381565\pi\)
0.363550 + 0.931575i \(0.381565\pi\)
\(180\) −385.753 −0.159735
\(181\) −3734.67 −1.53368 −0.766839 0.641839i \(-0.778172\pi\)
−0.766839 + 0.641839i \(0.778172\pi\)
\(182\) 6295.24 2.56392
\(183\) 1179.85 0.476594
\(184\) −4701.56 −1.88372
\(185\) −1345.50 −0.534721
\(186\) 2905.11 1.14523
\(187\) −2608.02 −1.01988
\(188\) 4403.19 1.70817
\(189\) −431.634 −0.166120
\(190\) −954.401 −0.364419
\(191\) 1504.04 0.569782 0.284891 0.958560i \(-0.408043\pi\)
0.284891 + 0.958560i \(0.408043\pi\)
\(192\) 2447.94 0.920130
\(193\) 2674.51 0.997488 0.498744 0.866749i \(-0.333795\pi\)
0.498744 + 0.866749i \(0.333795\pi\)
\(194\) 6286.67 2.32658
\(195\) 823.301 0.302348
\(196\) −1164.60 −0.424416
\(197\) −2496.55 −0.902902 −0.451451 0.892296i \(-0.649093\pi\)
−0.451451 + 0.892296i \(0.649093\pi\)
\(198\) 2252.55 0.808495
\(199\) 4410.90 1.57126 0.785629 0.618698i \(-0.212339\pi\)
0.785629 + 0.618698i \(0.212339\pi\)
\(200\) −2816.07 −0.995632
\(201\) 203.191 0.0713036
\(202\) 1188.91 0.414115
\(203\) −239.829 −0.0829197
\(204\) 1922.60 0.659847
\(205\) −729.773 −0.248632
\(206\) −1584.93 −0.536055
\(207\) −1722.65 −0.578418
\(208\) 584.950 0.194995
\(209\) 3481.86 1.15237
\(210\) 712.581 0.234156
\(211\) −4046.61 −1.32029 −0.660143 0.751140i \(-0.729504\pi\)
−0.660143 + 0.751140i \(0.729504\pi\)
\(212\) −5982.47 −1.93810
\(213\) 1769.21 0.569128
\(214\) −6091.84 −1.94593
\(215\) 666.427 0.211395
\(216\) −663.211 −0.208916
\(217\) −3352.75 −1.04885
\(218\) 1303.47 0.404963
\(219\) 687.987 0.212283
\(220\) −2323.32 −0.711991
\(221\) −4103.34 −1.24896
\(222\) −5792.00 −1.75105
\(223\) 3533.34 1.06103 0.530516 0.847675i \(-0.321998\pi\)
0.530516 + 0.847675i \(0.321998\pi\)
\(224\) −2635.16 −0.786023
\(225\) −1031.81 −0.305721
\(226\) −10743.0 −3.16202
\(227\) 96.7822 0.0282981 0.0141490 0.999900i \(-0.495496\pi\)
0.0141490 + 0.999900i \(0.495496\pi\)
\(228\) −2566.78 −0.745568
\(229\) 1031.34 0.297611 0.148806 0.988866i \(-0.452457\pi\)
0.148806 + 0.988866i \(0.452457\pi\)
\(230\) 2843.91 0.815312
\(231\) −2599.65 −0.740451
\(232\) −368.500 −0.104281
\(233\) 4689.07 1.31842 0.659208 0.751961i \(-0.270892\pi\)
0.659208 + 0.751961i \(0.270892\pi\)
\(234\) 3544.07 0.990099
\(235\) −1063.75 −0.295282
\(236\) −785.869 −0.216761
\(237\) −1690.43 −0.463313
\(238\) −3551.51 −0.967270
\(239\) 234.661 0.0635103 0.0317551 0.999496i \(-0.489890\pi\)
0.0317551 + 0.999496i \(0.489890\pi\)
\(240\) 66.2126 0.0178084
\(241\) −1334.65 −0.356731 −0.178365 0.983964i \(-0.557081\pi\)
−0.178365 + 0.983964i \(0.557081\pi\)
\(242\) 7421.01 1.97124
\(243\) −243.000 −0.0641500
\(244\) −5238.44 −1.37441
\(245\) 281.350 0.0733664
\(246\) −3141.46 −0.814195
\(247\) 5478.21 1.41121
\(248\) −5151.54 −1.31904
\(249\) −3537.65 −0.900358
\(250\) 3560.65 0.900782
\(251\) 1112.88 0.279859 0.139929 0.990161i \(-0.455312\pi\)
0.139929 + 0.990161i \(0.455312\pi\)
\(252\) 1916.43 0.479062
\(253\) −10375.2 −2.57819
\(254\) 3048.46 0.753060
\(255\) −464.472 −0.114064
\(256\) −4779.82 −1.16695
\(257\) −2171.13 −0.526971 −0.263486 0.964663i \(-0.584872\pi\)
−0.263486 + 0.964663i \(0.584872\pi\)
\(258\) 2868.77 0.692256
\(259\) 6684.48 1.60368
\(260\) −3655.40 −0.871918
\(261\) −135.018 −0.0320207
\(262\) 1561.46 0.368196
\(263\) −5098.53 −1.19540 −0.597698 0.801722i \(-0.703918\pi\)
−0.597698 + 0.801722i \(0.703918\pi\)
\(264\) −3994.39 −0.931203
\(265\) 1445.28 0.335030
\(266\) 4741.48 1.09293
\(267\) 4006.35 0.918294
\(268\) −902.157 −0.205627
\(269\) −2491.37 −0.564689 −0.282344 0.959313i \(-0.591112\pi\)
−0.282344 + 0.959313i \(0.591112\pi\)
\(270\) 401.166 0.0904230
\(271\) −2614.02 −0.585943 −0.292972 0.956121i \(-0.594644\pi\)
−0.292972 + 0.956121i \(0.594644\pi\)
\(272\) −330.005 −0.0735642
\(273\) −4090.17 −0.906771
\(274\) −4650.67 −1.02539
\(275\) −6214.37 −1.36269
\(276\) 7648.46 1.66805
\(277\) 4270.47 0.926309 0.463154 0.886278i \(-0.346718\pi\)
0.463154 + 0.886278i \(0.346718\pi\)
\(278\) 9732.21 2.09964
\(279\) −1887.52 −0.405028
\(280\) −1263.60 −0.269694
\(281\) −4081.99 −0.866587 −0.433294 0.901253i \(-0.642649\pi\)
−0.433294 + 0.901253i \(0.642649\pi\)
\(282\) −4579.12 −0.966960
\(283\) 1547.60 0.325071 0.162535 0.986703i \(-0.448033\pi\)
0.162535 + 0.986703i \(0.448033\pi\)
\(284\) −7855.18 −1.64127
\(285\) 620.098 0.128882
\(286\) 21345.2 4.41318
\(287\) 3625.52 0.745672
\(288\) −1483.54 −0.303535
\(289\) −2598.06 −0.528814
\(290\) 222.900 0.0451350
\(291\) −4084.60 −0.822831
\(292\) −3054.62 −0.612185
\(293\) 3046.36 0.607407 0.303703 0.952767i \(-0.401777\pi\)
0.303703 + 0.952767i \(0.401777\pi\)
\(294\) 1211.13 0.240253
\(295\) 189.855 0.0374704
\(296\) 10270.8 2.01681
\(297\) −1463.54 −0.285937
\(298\) −10506.2 −2.04231
\(299\) −16323.9 −3.15730
\(300\) 4581.16 0.881645
\(301\) −3310.82 −0.633995
\(302\) 1833.07 0.349276
\(303\) −772.463 −0.146458
\(304\) 440.576 0.0831209
\(305\) 1265.53 0.237587
\(306\) −1999.42 −0.373527
\(307\) 5413.13 1.00633 0.503166 0.864190i \(-0.332168\pi\)
0.503166 + 0.864190i \(0.332168\pi\)
\(308\) 11542.3 2.13533
\(309\) 1029.77 0.189584
\(310\) 3116.09 0.570909
\(311\) −945.000 −0.172302 −0.0861512 0.996282i \(-0.527457\pi\)
−0.0861512 + 0.996282i \(0.527457\pi\)
\(312\) −6284.59 −1.14037
\(313\) 4954.26 0.894669 0.447335 0.894367i \(-0.352373\pi\)
0.447335 + 0.894367i \(0.352373\pi\)
\(314\) −10551.1 −1.89629
\(315\) −462.982 −0.0828129
\(316\) 7505.40 1.33611
\(317\) −3881.82 −0.687775 −0.343887 0.939011i \(-0.611744\pi\)
−0.343887 + 0.939011i \(0.611744\pi\)
\(318\) 6221.51 1.09712
\(319\) −813.188 −0.142727
\(320\) 2625.72 0.458695
\(321\) 3958.02 0.688209
\(322\) −14128.6 −2.44520
\(323\) −3090.58 −0.532397
\(324\) 1078.90 0.184997
\(325\) −9777.43 −1.66878
\(326\) 6618.90 1.12450
\(327\) −846.895 −0.143221
\(328\) 5570.65 0.937768
\(329\) 5284.71 0.885580
\(330\) 2416.15 0.403044
\(331\) 5526.01 0.917634 0.458817 0.888531i \(-0.348273\pi\)
0.458817 + 0.888531i \(0.348273\pi\)
\(332\) 15706.9 2.59647
\(333\) 3763.21 0.619287
\(334\) 1248.08 0.204466
\(335\) 217.948 0.0355456
\(336\) −328.945 −0.0534090
\(337\) 3200.62 0.517356 0.258678 0.965964i \(-0.416713\pi\)
0.258678 + 0.965964i \(0.416713\pi\)
\(338\) 23439.4 3.77200
\(339\) 6980.01 1.11830
\(340\) 2062.23 0.328941
\(341\) −11368.2 −1.80534
\(342\) 2669.34 0.422051
\(343\) −6881.10 −1.08322
\(344\) −5087.11 −0.797321
\(345\) −1847.76 −0.288348
\(346\) 6941.40 1.07853
\(347\) −3533.99 −0.546728 −0.273364 0.961911i \(-0.588136\pi\)
−0.273364 + 0.961911i \(0.588136\pi\)
\(348\) 599.472 0.0923422
\(349\) −2116.90 −0.324684 −0.162342 0.986735i \(-0.551905\pi\)
−0.162342 + 0.986735i \(0.551905\pi\)
\(350\) −8462.52 −1.29240
\(351\) −2302.67 −0.350164
\(352\) −8935.04 −1.35295
\(353\) −1961.72 −0.295784 −0.147892 0.989004i \(-0.547249\pi\)
−0.147892 + 0.989004i \(0.547249\pi\)
\(354\) 817.269 0.122704
\(355\) 1897.70 0.283717
\(356\) −17787.9 −2.64820
\(357\) 2307.51 0.342090
\(358\) 8040.17 1.18697
\(359\) 4288.50 0.630469 0.315234 0.949014i \(-0.397917\pi\)
0.315234 + 0.949014i \(0.397917\pi\)
\(360\) −711.376 −0.104147
\(361\) −2732.89 −0.398439
\(362\) −17244.2 −2.50369
\(363\) −4821.62 −0.697161
\(364\) 18160.1 2.61497
\(365\) 737.952 0.105825
\(366\) 5447.75 0.778028
\(367\) −1246.33 −0.177269 −0.0886345 0.996064i \(-0.528250\pi\)
−0.0886345 + 0.996064i \(0.528250\pi\)
\(368\) −1312.82 −0.185966
\(369\) 2041.08 0.287953
\(370\) −6212.65 −0.872919
\(371\) −7180.17 −1.00479
\(372\) 8380.47 1.16803
\(373\) 11151.5 1.54799 0.773996 0.633190i \(-0.218255\pi\)
0.773996 + 0.633190i \(0.218255\pi\)
\(374\) −12042.1 −1.66493
\(375\) −2313.45 −0.318576
\(376\) 8120.02 1.11372
\(377\) −1279.43 −0.174786
\(378\) −1993.00 −0.271188
\(379\) 6741.73 0.913719 0.456860 0.889539i \(-0.348974\pi\)
0.456860 + 0.889539i \(0.348974\pi\)
\(380\) −2753.20 −0.371674
\(381\) −1980.66 −0.266331
\(382\) 6944.65 0.930155
\(383\) 5172.09 0.690030 0.345015 0.938597i \(-0.387874\pi\)
0.345015 + 0.938597i \(0.387874\pi\)
\(384\) 7346.87 0.976350
\(385\) −2788.45 −0.369123
\(386\) 12349.1 1.62837
\(387\) −1863.91 −0.244827
\(388\) 18135.4 2.37290
\(389\) 10739.9 1.39983 0.699914 0.714228i \(-0.253222\pi\)
0.699914 + 0.714228i \(0.253222\pi\)
\(390\) 3801.46 0.493575
\(391\) 9209.25 1.19113
\(392\) −2147.66 −0.276717
\(393\) −1014.52 −0.130218
\(394\) −11527.4 −1.47397
\(395\) −1813.20 −0.230967
\(396\) 6498.03 0.824591
\(397\) 3755.94 0.474825 0.237412 0.971409i \(-0.423701\pi\)
0.237412 + 0.971409i \(0.423701\pi\)
\(398\) 20366.6 2.56504
\(399\) −3080.66 −0.386531
\(400\) −786.333 −0.0982916
\(401\) 10542.2 1.31285 0.656424 0.754392i \(-0.272068\pi\)
0.656424 + 0.754392i \(0.272068\pi\)
\(402\) 938.203 0.116401
\(403\) −17886.2 −2.21085
\(404\) 3429.69 0.422360
\(405\) −260.648 −0.0319795
\(406\) −1107.37 −0.135364
\(407\) 22665.1 2.76036
\(408\) 3545.51 0.430218
\(409\) −14298.9 −1.72870 −0.864348 0.502894i \(-0.832269\pi\)
−0.864348 + 0.502894i \(0.832269\pi\)
\(410\) −3369.61 −0.405885
\(411\) 3021.66 0.362646
\(412\) −4572.11 −0.546727
\(413\) −943.201 −0.112377
\(414\) −7954.06 −0.944253
\(415\) −3794.57 −0.448839
\(416\) −14058.0 −1.65685
\(417\) −6323.26 −0.742569
\(418\) 16076.9 1.88122
\(419\) 2605.91 0.303835 0.151917 0.988393i \(-0.451455\pi\)
0.151917 + 0.988393i \(0.451455\pi\)
\(420\) 2055.61 0.238818
\(421\) −11765.6 −1.36204 −0.681022 0.732263i \(-0.738464\pi\)
−0.681022 + 0.732263i \(0.738464\pi\)
\(422\) −18684.6 −2.15534
\(423\) 2975.17 0.341981
\(424\) −11032.4 −1.26364
\(425\) 5516.02 0.629568
\(426\) 8169.04 0.929088
\(427\) −6287.18 −0.712548
\(428\) −17573.4 −1.98467
\(429\) −13868.5 −1.56079
\(430\) 3077.12 0.345097
\(431\) 11883.8 1.32813 0.664063 0.747677i \(-0.268831\pi\)
0.664063 + 0.747677i \(0.268831\pi\)
\(432\) −185.189 −0.0206247
\(433\) 3187.43 0.353760 0.176880 0.984232i \(-0.443400\pi\)
0.176880 + 0.984232i \(0.443400\pi\)
\(434\) −15480.8 −1.71221
\(435\) −144.824 −0.0159627
\(436\) 3760.16 0.413025
\(437\) −12294.9 −1.34587
\(438\) 3176.67 0.346546
\(439\) 16420.7 1.78524 0.892618 0.450814i \(-0.148866\pi\)
0.892618 + 0.450814i \(0.148866\pi\)
\(440\) −4284.48 −0.464215
\(441\) −786.901 −0.0849693
\(442\) −18946.5 −2.03890
\(443\) 632.306 0.0678143 0.0339072 0.999425i \(-0.489205\pi\)
0.0339072 + 0.999425i \(0.489205\pi\)
\(444\) −16708.4 −1.78591
\(445\) 4297.31 0.457780
\(446\) 16314.6 1.73211
\(447\) 6826.16 0.722296
\(448\) −13044.6 −1.37567
\(449\) 6771.85 0.711767 0.355884 0.934530i \(-0.384180\pi\)
0.355884 + 0.934530i \(0.384180\pi\)
\(450\) −4764.20 −0.499082
\(451\) 12293.0 1.28350
\(452\) −30990.8 −3.22497
\(453\) −1190.99 −0.123527
\(454\) 446.876 0.0461959
\(455\) −4387.22 −0.452035
\(456\) −4733.46 −0.486107
\(457\) −12278.5 −1.25681 −0.628406 0.777886i \(-0.716292\pi\)
−0.628406 + 0.777886i \(0.716292\pi\)
\(458\) 4762.06 0.485843
\(459\) 1299.07 0.132103
\(460\) 8203.93 0.831543
\(461\) −10989.3 −1.11024 −0.555120 0.831770i \(-0.687328\pi\)
−0.555120 + 0.831770i \(0.687328\pi\)
\(462\) −12003.4 −1.20877
\(463\) −12034.6 −1.20798 −0.603990 0.796992i \(-0.706423\pi\)
−0.603990 + 0.796992i \(0.706423\pi\)
\(464\) −102.896 −0.0102949
\(465\) −2024.60 −0.201911
\(466\) 21651.0 2.15228
\(467\) −9494.20 −0.940769 −0.470384 0.882462i \(-0.655885\pi\)
−0.470384 + 0.882462i \(0.655885\pi\)
\(468\) 10223.7 1.00981
\(469\) −1082.77 −0.106605
\(470\) −4911.68 −0.482040
\(471\) 6855.33 0.670652
\(472\) −1449.24 −0.141328
\(473\) −11226.0 −1.09127
\(474\) −7805.28 −0.756347
\(475\) −7364.21 −0.711354
\(476\) −10245.2 −0.986527
\(477\) −4042.27 −0.388014
\(478\) 1083.51 0.103679
\(479\) 1700.69 0.162227 0.0811135 0.996705i \(-0.474152\pi\)
0.0811135 + 0.996705i \(0.474152\pi\)
\(480\) −1591.28 −0.151316
\(481\) 35660.2 3.38039
\(482\) −6162.51 −0.582354
\(483\) 9179.69 0.864783
\(484\) 21407.7 2.01049
\(485\) −4381.25 −0.410190
\(486\) −1122.01 −0.104723
\(487\) 3687.27 0.343093 0.171546 0.985176i \(-0.445124\pi\)
0.171546 + 0.985176i \(0.445124\pi\)
\(488\) −9660.33 −0.896112
\(489\) −4300.46 −0.397697
\(490\) 1299.09 0.119769
\(491\) 14020.6 1.28867 0.644337 0.764742i \(-0.277134\pi\)
0.644337 + 0.764742i \(0.277134\pi\)
\(492\) −9062.28 −0.830405
\(493\) 721.804 0.0659400
\(494\) 25294.7 2.30377
\(495\) −1569.83 −0.142543
\(496\) −1438.47 −0.130220
\(497\) −9427.80 −0.850894
\(498\) −16334.5 −1.46981
\(499\) 831.548 0.0745996 0.0372998 0.999304i \(-0.488124\pi\)
0.0372998 + 0.999304i \(0.488124\pi\)
\(500\) 10271.6 0.918715
\(501\) −810.907 −0.0723127
\(502\) 5138.56 0.456862
\(503\) 14503.5 1.28565 0.642824 0.766014i \(-0.277763\pi\)
0.642824 + 0.766014i \(0.277763\pi\)
\(504\) 3534.13 0.312346
\(505\) −828.563 −0.0730110
\(506\) −47905.7 −4.20883
\(507\) −15229.2 −1.33402
\(508\) 8794.00 0.768052
\(509\) 3554.46 0.309526 0.154763 0.987952i \(-0.450539\pi\)
0.154763 + 0.987952i \(0.450539\pi\)
\(510\) −2144.63 −0.186207
\(511\) −3666.16 −0.317380
\(512\) −2478.40 −0.213927
\(513\) −1734.34 −0.149265
\(514\) −10024.9 −0.860267
\(515\) 1104.56 0.0945098
\(516\) 8275.66 0.706038
\(517\) 17918.9 1.52431
\(518\) 30864.5 2.61797
\(519\) −4510.00 −0.381440
\(520\) −6741.01 −0.568486
\(521\) 3095.33 0.260286 0.130143 0.991495i \(-0.458456\pi\)
0.130143 + 0.991495i \(0.458456\pi\)
\(522\) −623.425 −0.0522731
\(523\) −10451.2 −0.873802 −0.436901 0.899510i \(-0.643924\pi\)
−0.436901 + 0.899510i \(0.643924\pi\)
\(524\) 4504.41 0.375527
\(525\) 5498.31 0.457078
\(526\) −23541.6 −1.95145
\(527\) 10090.6 0.834070
\(528\) −1115.35 −0.0919310
\(529\) 24469.1 2.01110
\(530\) 6673.35 0.546928
\(531\) −531.000 −0.0433963
\(532\) 13677.9 1.11469
\(533\) 19341.3 1.57179
\(534\) 18498.7 1.49909
\(535\) 4245.47 0.343080
\(536\) −1663.69 −0.134068
\(537\) −5223.90 −0.419792
\(538\) −11503.5 −0.921841
\(539\) −4739.35 −0.378735
\(540\) 1157.26 0.0922232
\(541\) −8714.59 −0.692550 −0.346275 0.938133i \(-0.612554\pi\)
−0.346275 + 0.938133i \(0.612554\pi\)
\(542\) −12069.8 −0.956538
\(543\) 11204.0 0.885470
\(544\) 7930.95 0.625067
\(545\) −908.401 −0.0713975
\(546\) −18885.7 −1.48028
\(547\) −7782.31 −0.608314 −0.304157 0.952622i \(-0.598375\pi\)
−0.304157 + 0.952622i \(0.598375\pi\)
\(548\) −13416.0 −1.04581
\(549\) −3539.54 −0.275162
\(550\) −28693.9 −2.22456
\(551\) −963.651 −0.0745062
\(552\) 14104.7 1.08756
\(553\) 9007.99 0.692692
\(554\) 19718.2 1.51218
\(555\) 4036.51 0.308721
\(556\) 28074.9 2.14144
\(557\) −12895.7 −0.980982 −0.490491 0.871446i \(-0.663183\pi\)
−0.490491 + 0.871446i \(0.663183\pi\)
\(558\) −8715.32 −0.661199
\(559\) −17662.5 −1.33639
\(560\) −352.835 −0.0266250
\(561\) 7824.06 0.588827
\(562\) −18847.9 −1.41468
\(563\) 10805.3 0.808863 0.404431 0.914568i \(-0.367469\pi\)
0.404431 + 0.914568i \(0.367469\pi\)
\(564\) −13209.6 −0.986211
\(565\) 7486.94 0.557483
\(566\) 7145.78 0.530670
\(567\) 1294.90 0.0959097
\(568\) −14485.9 −1.07010
\(569\) −11897.7 −0.876589 −0.438294 0.898831i \(-0.644417\pi\)
−0.438294 + 0.898831i \(0.644417\pi\)
\(570\) 2863.20 0.210397
\(571\) 20402.8 1.49532 0.747662 0.664080i \(-0.231176\pi\)
0.747662 + 0.664080i \(0.231176\pi\)
\(572\) 61575.4 4.50105
\(573\) −4512.11 −0.328964
\(574\) 16740.3 1.21729
\(575\) 21943.7 1.59151
\(576\) −7343.82 −0.531237
\(577\) 21770.5 1.57074 0.785370 0.619027i \(-0.212473\pi\)
0.785370 + 0.619027i \(0.212473\pi\)
\(578\) −11996.1 −0.863276
\(579\) −8023.52 −0.575900
\(580\) 643.009 0.0460336
\(581\) 18851.5 1.34611
\(582\) −18860.0 −1.34325
\(583\) −24345.8 −1.72950
\(584\) −5633.09 −0.399142
\(585\) −2469.90 −0.174561
\(586\) 14066.1 0.991576
\(587\) 21616.4 1.51994 0.759970 0.649959i \(-0.225214\pi\)
0.759970 + 0.649959i \(0.225214\pi\)
\(588\) 3493.79 0.245036
\(589\) −13471.6 −0.942424
\(590\) 876.623 0.0611695
\(591\) 7489.65 0.521291
\(592\) 2867.91 0.199106
\(593\) −18257.7 −1.26434 −0.632172 0.774828i \(-0.717836\pi\)
−0.632172 + 0.774828i \(0.717836\pi\)
\(594\) −6757.66 −0.466785
\(595\) 2475.09 0.170536
\(596\) −30307.7 −2.08297
\(597\) −13232.7 −0.907166
\(598\) −75372.8 −5.15422
\(599\) −2679.25 −0.182756 −0.0913781 0.995816i \(-0.529127\pi\)
−0.0913781 + 0.995816i \(0.529127\pi\)
\(600\) 8448.22 0.574828
\(601\) −19874.2 −1.34889 −0.674447 0.738324i \(-0.735618\pi\)
−0.674447 + 0.738324i \(0.735618\pi\)
\(602\) −15287.2 −1.03498
\(603\) −609.574 −0.0411671
\(604\) 5287.93 0.356230
\(605\) −5171.79 −0.347542
\(606\) −3566.72 −0.239089
\(607\) −20437.2 −1.36659 −0.683297 0.730141i \(-0.739454\pi\)
−0.683297 + 0.730141i \(0.739454\pi\)
\(608\) −10588.3 −0.706269
\(609\) 719.487 0.0478737
\(610\) 5843.39 0.387856
\(611\) 28192.8 1.86671
\(612\) −5767.80 −0.380963
\(613\) 19812.1 1.30539 0.652695 0.757621i \(-0.273638\pi\)
0.652695 + 0.757621i \(0.273638\pi\)
\(614\) 24994.3 1.64281
\(615\) 2189.32 0.143548
\(616\) 21285.4 1.39223
\(617\) 27960.5 1.82439 0.912194 0.409758i \(-0.134387\pi\)
0.912194 + 0.409758i \(0.134387\pi\)
\(618\) 4754.79 0.309492
\(619\) −28522.1 −1.85202 −0.926008 0.377503i \(-0.876783\pi\)
−0.926008 + 0.377503i \(0.876783\pi\)
\(620\) 8989.10 0.582276
\(621\) 5167.95 0.333950
\(622\) −4363.38 −0.281279
\(623\) −21349.1 −1.37293
\(624\) −1754.85 −0.112580
\(625\) 11849.2 0.758349
\(626\) 22875.5 1.46053
\(627\) −10445.6 −0.665321
\(628\) −30437.2 −1.93404
\(629\) −20118.0 −1.27529
\(630\) −2137.74 −0.135190
\(631\) −13610.9 −0.858706 −0.429353 0.903137i \(-0.641258\pi\)
−0.429353 + 0.903137i \(0.641258\pi\)
\(632\) 13840.9 0.871140
\(633\) 12139.8 0.762268
\(634\) −17923.7 −1.12278
\(635\) −2124.50 −0.132769
\(636\) 17947.4 1.11896
\(637\) −7456.68 −0.463806
\(638\) −3754.76 −0.232998
\(639\) −5307.63 −0.328586
\(640\) 7880.44 0.486721
\(641\) −19792.9 −1.21961 −0.609807 0.792550i \(-0.708753\pi\)
−0.609807 + 0.792550i \(0.708753\pi\)
\(642\) 18275.5 1.12348
\(643\) 14995.9 0.919719 0.459859 0.887992i \(-0.347900\pi\)
0.459859 + 0.887992i \(0.347900\pi\)
\(644\) −40757.2 −2.49388
\(645\) −1999.28 −0.122049
\(646\) −14270.2 −0.869126
\(647\) 29860.2 1.81441 0.907207 0.420684i \(-0.138210\pi\)
0.907207 + 0.420684i \(0.138210\pi\)
\(648\) 1989.63 0.120617
\(649\) −3198.11 −0.193431
\(650\) −45145.7 −2.72424
\(651\) 10058.2 0.605551
\(652\) 19093.8 1.14689
\(653\) 17572.2 1.05307 0.526533 0.850155i \(-0.323492\pi\)
0.526533 + 0.850155i \(0.323492\pi\)
\(654\) −3910.40 −0.233806
\(655\) −1088.20 −0.0649153
\(656\) 1555.50 0.0925791
\(657\) −2063.96 −0.122561
\(658\) 24401.3 1.44569
\(659\) 14231.1 0.841222 0.420611 0.907241i \(-0.361816\pi\)
0.420611 + 0.907241i \(0.361816\pi\)
\(660\) 6969.95 0.411068
\(661\) −28811.1 −1.69535 −0.847673 0.530520i \(-0.821997\pi\)
−0.847673 + 0.530520i \(0.821997\pi\)
\(662\) 25515.4 1.49802
\(663\) 12310.0 0.721089
\(664\) 28965.5 1.69289
\(665\) −3304.39 −0.192690
\(666\) 17376.0 1.01097
\(667\) 2871.47 0.166692
\(668\) 3600.38 0.208537
\(669\) −10600.0 −0.612587
\(670\) 1006.34 0.0580273
\(671\) −21317.9 −1.22648
\(672\) 7905.49 0.453811
\(673\) 16148.1 0.924909 0.462455 0.886643i \(-0.346969\pi\)
0.462455 + 0.886643i \(0.346969\pi\)
\(674\) 14778.4 0.844572
\(675\) 3095.42 0.176508
\(676\) 67616.5 3.84709
\(677\) 20624.3 1.17084 0.585418 0.810731i \(-0.300930\pi\)
0.585418 + 0.810731i \(0.300930\pi\)
\(678\) 32229.1 1.82559
\(679\) 21766.1 1.23020
\(680\) 3803.00 0.214468
\(681\) −290.346 −0.0163379
\(682\) −52490.6 −2.94717
\(683\) −26607.3 −1.49063 −0.745314 0.666714i \(-0.767700\pi\)
−0.745314 + 0.666714i \(0.767700\pi\)
\(684\) 7700.35 0.430454
\(685\) 3241.11 0.180783
\(686\) −31772.4 −1.76833
\(687\) −3094.03 −0.171826
\(688\) −1420.48 −0.0787138
\(689\) −38304.6 −2.11798
\(690\) −8531.72 −0.470720
\(691\) 31832.9 1.75251 0.876254 0.481850i \(-0.160035\pi\)
0.876254 + 0.481850i \(0.160035\pi\)
\(692\) 20024.1 1.10000
\(693\) 7798.94 0.427500
\(694\) −16317.6 −0.892520
\(695\) −6782.49 −0.370179
\(696\) 1105.50 0.0602067
\(697\) −10911.6 −0.592978
\(698\) −9774.42 −0.530039
\(699\) −14067.2 −0.761188
\(700\) −24412.2 −1.31813
\(701\) −26303.0 −1.41719 −0.708594 0.705616i \(-0.750670\pi\)
−0.708594 + 0.705616i \(0.750670\pi\)
\(702\) −10632.2 −0.571634
\(703\) 26858.8 1.44096
\(704\) −44230.4 −2.36789
\(705\) 3191.24 0.170481
\(706\) −9057.92 −0.482860
\(707\) 4116.31 0.218967
\(708\) 2357.61 0.125147
\(709\) 31256.4 1.65565 0.827826 0.560984i \(-0.189577\pi\)
0.827826 + 0.560984i \(0.189577\pi\)
\(710\) 8762.32 0.463160
\(711\) 5071.29 0.267494
\(712\) −32803.1 −1.72661
\(713\) 40142.4 2.10848
\(714\) 10654.5 0.558454
\(715\) −14875.7 −0.778072
\(716\) 23193.8 1.21060
\(717\) −703.983 −0.0366677
\(718\) 19801.4 1.02922
\(719\) 20206.1 1.04807 0.524034 0.851697i \(-0.324426\pi\)
0.524034 + 0.851697i \(0.324426\pi\)
\(720\) −198.638 −0.0102817
\(721\) −5487.45 −0.283444
\(722\) −12618.7 −0.650442
\(723\) 4003.94 0.205959
\(724\) −49745.1 −2.55354
\(725\) 1719.91 0.0881047
\(726\) −22263.0 −1.13810
\(727\) −15044.8 −0.767510 −0.383755 0.923435i \(-0.625369\pi\)
−0.383755 + 0.923435i \(0.625369\pi\)
\(728\) 33489.5 1.70495
\(729\) 729.000 0.0370370
\(730\) 3407.37 0.172757
\(731\) 9964.44 0.504170
\(732\) 15715.3 0.793518
\(733\) 30276.0 1.52560 0.762802 0.646632i \(-0.223823\pi\)
0.762802 + 0.646632i \(0.223823\pi\)
\(734\) −5754.71 −0.289387
\(735\) −844.049 −0.0423581
\(736\) 31550.8 1.58013
\(737\) −3671.35 −0.183495
\(738\) 9424.38 0.470076
\(739\) −7587.02 −0.377663 −0.188832 0.982009i \(-0.560470\pi\)
−0.188832 + 0.982009i \(0.560470\pi\)
\(740\) −17921.9 −0.890298
\(741\) −16434.6 −0.814765
\(742\) −33153.3 −1.64029
\(743\) −12898.6 −0.636882 −0.318441 0.947943i \(-0.603159\pi\)
−0.318441 + 0.947943i \(0.603159\pi\)
\(744\) 15454.6 0.761550
\(745\) 7321.91 0.360072
\(746\) 51490.1 2.52706
\(747\) 10612.9 0.519822
\(748\) −34738.3 −1.69807
\(749\) −21091.6 −1.02893
\(750\) −10682.0 −0.520067
\(751\) −18857.3 −0.916260 −0.458130 0.888885i \(-0.651481\pi\)
−0.458130 + 0.888885i \(0.651481\pi\)
\(752\) 2267.36 0.109949
\(753\) −3338.65 −0.161576
\(754\) −5907.58 −0.285333
\(755\) −1277.49 −0.0615795
\(756\) −5749.28 −0.276587
\(757\) −25156.1 −1.20781 −0.603905 0.797056i \(-0.706390\pi\)
−0.603905 + 0.797056i \(0.706390\pi\)
\(758\) 31128.9 1.49162
\(759\) 31125.5 1.48852
\(760\) −5077.23 −0.242330
\(761\) 2380.10 0.113375 0.0566875 0.998392i \(-0.481946\pi\)
0.0566875 + 0.998392i \(0.481946\pi\)
\(762\) −9145.37 −0.434779
\(763\) 4512.95 0.214128
\(764\) 20033.5 0.948673
\(765\) 1393.42 0.0658550
\(766\) 23881.3 1.12646
\(767\) −5031.76 −0.236879
\(768\) 14339.5 0.673738
\(769\) −27770.6 −1.30226 −0.651128 0.758968i \(-0.725704\pi\)
−0.651128 + 0.758968i \(0.725704\pi\)
\(770\) −12875.2 −0.602584
\(771\) 6513.40 0.304247
\(772\) 35623.9 1.66079
\(773\) −15649.4 −0.728165 −0.364082 0.931367i \(-0.618617\pi\)
−0.364082 + 0.931367i \(0.618617\pi\)
\(774\) −8606.32 −0.399674
\(775\) 24043.9 1.11443
\(776\) 33443.9 1.54712
\(777\) −20053.4 −0.925886
\(778\) 49589.6 2.28518
\(779\) 14567.6 0.670012
\(780\) 10966.2 0.503402
\(781\) −31966.8 −1.46461
\(782\) 42522.2 1.94449
\(783\) 405.055 0.0184872
\(784\) −599.691 −0.0273183
\(785\) 7353.20 0.334327
\(786\) −4684.38 −0.212578
\(787\) 12216.7 0.553338 0.276669 0.960965i \(-0.410769\pi\)
0.276669 + 0.960965i \(0.410769\pi\)
\(788\) −33253.6 −1.50331
\(789\) 15295.6 0.690162
\(790\) −8372.14 −0.377047
\(791\) −37195.2 −1.67195
\(792\) 11983.2 0.537630
\(793\) −33540.7 −1.50197
\(794\) 17342.5 0.775140
\(795\) −4335.84 −0.193429
\(796\) 58752.3 2.61611
\(797\) 31212.6 1.38721 0.693605 0.720356i \(-0.256021\pi\)
0.693605 + 0.720356i \(0.256021\pi\)
\(798\) −14224.4 −0.631002
\(799\) −15905.2 −0.704237
\(800\) 18897.8 0.835173
\(801\) −12019.0 −0.530177
\(802\) 48676.9 2.14319
\(803\) −12430.8 −0.546295
\(804\) 2706.47 0.118719
\(805\) 9846.36 0.431104
\(806\) −82586.5 −3.60916
\(807\) 7474.10 0.326023
\(808\) 6324.76 0.275377
\(809\) −27090.0 −1.17730 −0.588650 0.808388i \(-0.700340\pi\)
−0.588650 + 0.808388i \(0.700340\pi\)
\(810\) −1203.50 −0.0522057
\(811\) 2136.04 0.0924863 0.0462431 0.998930i \(-0.485275\pi\)
0.0462431 + 0.998930i \(0.485275\pi\)
\(812\) −3194.48 −0.138059
\(813\) 7842.07 0.338295
\(814\) 104652. 4.50622
\(815\) −4612.78 −0.198256
\(816\) 990.014 0.0424723
\(817\) −13303.1 −0.569666
\(818\) −66023.0 −2.82205
\(819\) 12270.5 0.523524
\(820\) −9720.43 −0.413966
\(821\) −13041.2 −0.554373 −0.277187 0.960816i \(-0.589402\pi\)
−0.277187 + 0.960816i \(0.589402\pi\)
\(822\) 13952.0 0.592010
\(823\) −15741.7 −0.666734 −0.333367 0.942797i \(-0.608185\pi\)
−0.333367 + 0.942797i \(0.608185\pi\)
\(824\) −8431.53 −0.356464
\(825\) 18643.1 0.786752
\(826\) −4355.08 −0.183453
\(827\) 29188.2 1.22730 0.613648 0.789580i \(-0.289701\pi\)
0.613648 + 0.789580i \(0.289701\pi\)
\(828\) −22945.4 −0.963052
\(829\) −23688.9 −0.992461 −0.496230 0.868191i \(-0.665283\pi\)
−0.496230 + 0.868191i \(0.665283\pi\)
\(830\) −17520.8 −0.732718
\(831\) −12811.4 −0.534805
\(832\) −69590.2 −2.89977
\(833\) 4206.75 0.174976
\(834\) −29196.6 −1.21223
\(835\) −869.799 −0.0360487
\(836\) 46377.7 1.91867
\(837\) 5662.56 0.233843
\(838\) 12032.3 0.496003
\(839\) 46609.6 1.91793 0.958965 0.283525i \(-0.0915040\pi\)
0.958965 + 0.283525i \(0.0915040\pi\)
\(840\) 3790.79 0.155708
\(841\) −24163.9 −0.990772
\(842\) −54325.8 −2.22350
\(843\) 12246.0 0.500324
\(844\) −53900.1 −2.19825
\(845\) −16335.2 −0.665026
\(846\) 13737.4 0.558275
\(847\) 25693.5 1.04231
\(848\) −3080.59 −0.124750
\(849\) −4642.79 −0.187680
\(850\) 25469.3 1.02775
\(851\) −80033.2 −3.22386
\(852\) 23565.5 0.947585
\(853\) 15069.2 0.604877 0.302439 0.953169i \(-0.402199\pi\)
0.302439 + 0.953169i \(0.402199\pi\)
\(854\) −29030.1 −1.16322
\(855\) −1860.30 −0.0744102
\(856\) −32407.4 −1.29400
\(857\) −32618.8 −1.30016 −0.650081 0.759865i \(-0.725265\pi\)
−0.650081 + 0.759865i \(0.725265\pi\)
\(858\) −64035.7 −2.54795
\(859\) −6931.99 −0.275339 −0.137670 0.990478i \(-0.543961\pi\)
−0.137670 + 0.990478i \(0.543961\pi\)
\(860\) 8876.68 0.351968
\(861\) −10876.6 −0.430514
\(862\) 54871.5 2.16813
\(863\) 6692.94 0.263998 0.131999 0.991250i \(-0.457860\pi\)
0.131999 + 0.991250i \(0.457860\pi\)
\(864\) 4450.61 0.175246
\(865\) −4837.54 −0.190152
\(866\) 14717.4 0.577505
\(867\) 7794.19 0.305311
\(868\) −44658.0 −1.74630
\(869\) 30543.4 1.19230
\(870\) −668.701 −0.0260587
\(871\) −5776.34 −0.224711
\(872\) 6934.20 0.269291
\(873\) 12253.8 0.475062
\(874\) −56769.7 −2.19710
\(875\) 12327.9 0.476297
\(876\) 9163.86 0.353445
\(877\) 7773.39 0.299303 0.149652 0.988739i \(-0.452185\pi\)
0.149652 + 0.988739i \(0.452185\pi\)
\(878\) 75820.0 2.91435
\(879\) −9139.07 −0.350686
\(880\) −1196.36 −0.0458286
\(881\) −8298.43 −0.317345 −0.158673 0.987331i \(-0.550721\pi\)
−0.158673 + 0.987331i \(0.550721\pi\)
\(882\) −3633.39 −0.138710
\(883\) −30480.9 −1.16168 −0.580841 0.814017i \(-0.697276\pi\)
−0.580841 + 0.814017i \(0.697276\pi\)
\(884\) −54655.7 −2.07949
\(885\) −569.564 −0.0216335
\(886\) 2919.57 0.110705
\(887\) 7695.04 0.291290 0.145645 0.989337i \(-0.453474\pi\)
0.145645 + 0.989337i \(0.453474\pi\)
\(888\) −30812.3 −1.16441
\(889\) 10554.6 0.398188
\(890\) 19842.1 0.747314
\(891\) 4390.62 0.165086
\(892\) 47063.4 1.76659
\(893\) 21234.4 0.795724
\(894\) 31518.7 1.17913
\(895\) −5603.29 −0.209271
\(896\) −39150.1 −1.45973
\(897\) 48971.6 1.82287
\(898\) 31267.9 1.16194
\(899\) 3146.29 0.116724
\(900\) −13743.5 −0.509018
\(901\) 21609.9 0.799034
\(902\) 56761.1 2.09528
\(903\) 9932.46 0.366037
\(904\) −57150.9 −2.10267
\(905\) 12017.7 0.441416
\(906\) −5499.21 −0.201655
\(907\) 20682.7 0.757176 0.378588 0.925565i \(-0.376410\pi\)
0.378588 + 0.925565i \(0.376410\pi\)
\(908\) 1289.12 0.0471156
\(909\) 2317.39 0.0845577
\(910\) −20257.3 −0.737937
\(911\) −27515.9 −1.00071 −0.500353 0.865822i \(-0.666796\pi\)
−0.500353 + 0.865822i \(0.666796\pi\)
\(912\) −1321.73 −0.0479899
\(913\) 63919.6 2.31701
\(914\) −56693.9 −2.05171
\(915\) −3796.60 −0.137171
\(916\) 13737.3 0.495516
\(917\) 5406.19 0.194687
\(918\) 5998.26 0.215656
\(919\) −4136.30 −0.148470 −0.0742350 0.997241i \(-0.523651\pi\)
−0.0742350 + 0.997241i \(0.523651\pi\)
\(920\) 15129.0 0.542163
\(921\) −16239.4 −0.581006
\(922\) −50741.1 −1.81244
\(923\) −50295.2 −1.79359
\(924\) −34626.8 −1.23283
\(925\) −47937.1 −1.70396
\(926\) −55567.7 −1.97200
\(927\) −3089.31 −0.109457
\(928\) 2472.89 0.0874748
\(929\) −41730.5 −1.47377 −0.736886 0.676017i \(-0.763705\pi\)
−0.736886 + 0.676017i \(0.763705\pi\)
\(930\) −9348.27 −0.329615
\(931\) −5616.27 −0.197708
\(932\) 62457.5 2.19513
\(933\) 2835.00 0.0994788
\(934\) −43837.9 −1.53578
\(935\) 8392.28 0.293537
\(936\) 18853.8 0.658392
\(937\) 21380.2 0.745422 0.372711 0.927947i \(-0.378428\pi\)
0.372711 + 0.927947i \(0.378428\pi\)
\(938\) −4999.51 −0.174030
\(939\) −14862.8 −0.516538
\(940\) −14168.9 −0.491637
\(941\) −21613.7 −0.748764 −0.374382 0.927275i \(-0.622145\pi\)
−0.374382 + 0.927275i \(0.622145\pi\)
\(942\) 31653.4 1.09482
\(943\) −43408.3 −1.49901
\(944\) −404.671 −0.0139523
\(945\) 1388.94 0.0478120
\(946\) −51834.2 −1.78147
\(947\) −6008.44 −0.206175 −0.103088 0.994672i \(-0.532872\pi\)
−0.103088 + 0.994672i \(0.532872\pi\)
\(948\) −22516.2 −0.771405
\(949\) −19558.1 −0.669003
\(950\) −34003.1 −1.16127
\(951\) 11645.5 0.397087
\(952\) −18893.4 −0.643212
\(953\) −5173.79 −0.175861 −0.0879305 0.996127i \(-0.528025\pi\)
−0.0879305 + 0.996127i \(0.528025\pi\)
\(954\) −18664.5 −0.633424
\(955\) −4839.80 −0.163992
\(956\) 3125.64 0.105743
\(957\) 2439.56 0.0824032
\(958\) 7852.68 0.264832
\(959\) −16101.9 −0.542186
\(960\) −7877.17 −0.264828
\(961\) 14193.3 0.476430
\(962\) 164655. 5.51840
\(963\) −11874.1 −0.397338
\(964\) −17777.2 −0.593948
\(965\) −8606.22 −0.287092
\(966\) 42385.7 1.41174
\(967\) 26508.3 0.881540 0.440770 0.897620i \(-0.354705\pi\)
0.440770 + 0.897620i \(0.354705\pi\)
\(968\) 39478.4 1.31083
\(969\) 9271.73 0.307380
\(970\) −20229.7 −0.669625
\(971\) −22770.6 −0.752569 −0.376285 0.926504i \(-0.622798\pi\)
−0.376285 + 0.926504i \(0.622798\pi\)
\(972\) −3236.71 −0.106808
\(973\) 33695.5 1.11020
\(974\) 17025.4 0.560091
\(975\) 29332.3 0.963471
\(976\) −2697.46 −0.0884667
\(977\) −10137.9 −0.331974 −0.165987 0.986128i \(-0.553081\pi\)
−0.165987 + 0.986128i \(0.553081\pi\)
\(978\) −19856.7 −0.649230
\(979\) −72388.3 −2.36317
\(980\) 3747.53 0.122153
\(981\) 2540.69 0.0826889
\(982\) 64737.6 2.10373
\(983\) −19066.2 −0.618635 −0.309317 0.950959i \(-0.600101\pi\)
−0.309317 + 0.950959i \(0.600101\pi\)
\(984\) −16712.0 −0.541420
\(985\) 8033.58 0.259869
\(986\) 3332.81 0.107645
\(987\) −15854.1 −0.511290
\(988\) 72968.7 2.34964
\(989\) 39640.4 1.27451
\(990\) −7248.44 −0.232697
\(991\) −17491.5 −0.560681 −0.280341 0.959901i \(-0.590447\pi\)
−0.280341 + 0.959901i \(0.590447\pi\)
\(992\) 34570.4 1.10646
\(993\) −16578.0 −0.529796
\(994\) −43531.3 −1.38906
\(995\) −14193.7 −0.452232
\(996\) −47120.8 −1.49908
\(997\) −7297.85 −0.231821 −0.115910 0.993260i \(-0.536979\pi\)
−0.115910 + 0.993260i \(0.536979\pi\)
\(998\) 3839.54 0.121782
\(999\) −11289.6 −0.357546
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.1.7 8
3.2 odd 2 531.4.a.f.1.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.4.a.c.1.7 8 1.1 even 1 trivial
531.4.a.f.1.2 8 3.2 odd 2