Properties

Label 43.4.a.b.1.2
Level 43
Weight 4
Character 43.1
Self dual yes
Analytic conductor 2.537
Analytic rank 0
Dimension 6
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 43.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(2.53708213025\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\mathbb{Q}[x]/(x^{6} - \cdots)\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(4.15653\) of \(x^{6} - 32 x^{4} - 16 x^{3} + 251 x^{2} + 276 x + 60\)
Character \(\chi\) \(=\) 43.1

$q$-expansion

\(f(q)\) \(=\) \(q-3.15653 q^{2} +7.20925 q^{3} +1.96369 q^{4} +1.36370 q^{5} -22.7562 q^{6} +13.0131 q^{7} +19.0538 q^{8} +24.9733 q^{9} +O(q^{10})\) \(q-3.15653 q^{2} +7.20925 q^{3} +1.96369 q^{4} +1.36370 q^{5} -22.7562 q^{6} +13.0131 q^{7} +19.0538 q^{8} +24.9733 q^{9} -4.30455 q^{10} +64.7677 q^{11} +14.1567 q^{12} -19.2944 q^{13} -41.0763 q^{14} +9.83123 q^{15} -75.8534 q^{16} -54.1213 q^{17} -78.8289 q^{18} -69.0659 q^{19} +2.67787 q^{20} +93.8149 q^{21} -204.441 q^{22} +29.6031 q^{23} +137.364 q^{24} -123.140 q^{25} +60.9032 q^{26} -14.6112 q^{27} +25.5537 q^{28} +13.1279 q^{29} -31.0326 q^{30} +185.439 q^{31} +87.0032 q^{32} +466.927 q^{33} +170.836 q^{34} +17.7460 q^{35} +49.0397 q^{36} -369.949 q^{37} +218.009 q^{38} -139.098 q^{39} +25.9836 q^{40} -294.860 q^{41} -296.129 q^{42} -43.0000 q^{43} +127.183 q^{44} +34.0560 q^{45} -93.4431 q^{46} +367.319 q^{47} -546.846 q^{48} -173.659 q^{49} +388.696 q^{50} -390.174 q^{51} -37.8881 q^{52} +708.046 q^{53} +46.1207 q^{54} +88.3236 q^{55} +247.950 q^{56} -497.914 q^{57} -41.4385 q^{58} +116.159 q^{59} +19.3054 q^{60} +218.910 q^{61} -585.344 q^{62} +324.980 q^{63} +332.199 q^{64} -26.3116 q^{65} -1473.87 q^{66} -133.114 q^{67} -106.277 q^{68} +213.416 q^{69} -56.0156 q^{70} -926.738 q^{71} +475.836 q^{72} +455.867 q^{73} +1167.75 q^{74} -887.749 q^{75} -135.624 q^{76} +842.831 q^{77} +439.067 q^{78} -620.178 q^{79} -103.441 q^{80} -779.614 q^{81} +930.734 q^{82} -1317.85 q^{83} +184.223 q^{84} -73.8050 q^{85} +135.731 q^{86} +94.6419 q^{87} +1234.07 q^{88} +509.295 q^{89} -107.499 q^{90} -251.080 q^{91} +58.1312 q^{92} +1336.88 q^{93} -1159.45 q^{94} -94.1850 q^{95} +627.228 q^{96} +965.870 q^{97} +548.159 q^{98} +1617.46 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 6q^{2} + 7q^{3} + 22q^{4} + 43q^{5} - 3q^{6} + 8q^{7} + 54q^{8} + 81q^{9} + O(q^{10}) \) \( 6q + 6q^{2} + 7q^{3} + 22q^{4} + 43q^{5} - 3q^{6} + 8q^{7} + 54q^{8} + 81q^{9} + 57q^{10} - 28q^{11} - 157q^{12} + 56q^{13} - 184q^{14} - 124q^{15} - 54q^{16} + 19q^{17} - 81q^{18} - 75q^{19} + 135q^{20} - 18q^{21} - 504q^{22} + 131q^{23} - 567q^{24} + 105q^{25} + 44q^{26} + 238q^{27} - 404q^{28} + 515q^{29} - 396q^{30} + 237q^{31} + 558q^{32} + 540q^{33} - 107q^{34} + 198q^{35} + 73q^{36} + 269q^{37} + 527q^{38} + 290q^{39} + 613q^{40} + 471q^{41} + 362q^{42} - 258q^{43} - 428q^{44} + 334q^{45} - 67q^{46} + 415q^{47} - 989q^{48} + 350q^{49} + 1335q^{50} - 1241q^{51} - 8q^{52} + 450q^{53} + 402q^{54} - 1732q^{55} - 780q^{56} - 1000q^{57} - 1055q^{58} + 356q^{59} - 2732q^{60} - 1328q^{61} + 1603q^{62} - 2290q^{63} + 466q^{64} - 62q^{65} + 156q^{66} - 632q^{67} + 571q^{68} - 1130q^{69} - 1902q^{70} - 144q^{71} + 567q^{72} + 864q^{73} + 1207q^{74} - 2494q^{75} + 1005q^{76} + 2660q^{77} + 2222q^{78} - 1613q^{79} + 2399q^{80} - 102q^{81} + 1673q^{82} - 682q^{83} + 3758q^{84} + 84q^{85} - 258q^{86} + 449q^{87} - 608q^{88} + 3378q^{89} + 930q^{90} - 3900q^{91} + 3491q^{92} + 1879q^{93} + 3197q^{94} - 79q^{95} - 591q^{96} - 55q^{97} + 2398q^{98} - 1612q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.15653 −1.11600 −0.558001 0.829840i \(-0.688431\pi\)
−0.558001 + 0.829840i \(0.688431\pi\)
\(3\) 7.20925 1.38742 0.693710 0.720254i \(-0.255975\pi\)
0.693710 + 0.720254i \(0.255975\pi\)
\(4\) 1.96369 0.245461
\(5\) 1.36370 0.121973 0.0609864 0.998139i \(-0.480575\pi\)
0.0609864 + 0.998139i \(0.480575\pi\)
\(6\) −22.7562 −1.54836
\(7\) 13.0131 0.702643 0.351321 0.936255i \(-0.385732\pi\)
0.351321 + 0.936255i \(0.385732\pi\)
\(8\) 19.0538 0.842067
\(9\) 24.9733 0.924936
\(10\) −4.30455 −0.136122
\(11\) 64.7677 1.77529 0.887646 0.460527i \(-0.152339\pi\)
0.887646 + 0.460527i \(0.152339\pi\)
\(12\) 14.1567 0.340557
\(13\) −19.2944 −0.411638 −0.205819 0.978590i \(-0.565986\pi\)
−0.205819 + 0.978590i \(0.565986\pi\)
\(14\) −41.0763 −0.784151
\(15\) 9.83123 0.169227
\(16\) −75.8534 −1.18521
\(17\) −54.1213 −0.772138 −0.386069 0.922470i \(-0.626167\pi\)
−0.386069 + 0.922470i \(0.626167\pi\)
\(18\) −78.8289 −1.03223
\(19\) −69.0659 −0.833938 −0.416969 0.908921i \(-0.636908\pi\)
−0.416969 + 0.908921i \(0.636908\pi\)
\(20\) 2.67787 0.0299395
\(21\) 93.8149 0.974861
\(22\) −204.441 −1.98123
\(23\) 29.6031 0.268377 0.134189 0.990956i \(-0.457157\pi\)
0.134189 + 0.990956i \(0.457157\pi\)
\(24\) 137.364 1.16830
\(25\) −123.140 −0.985123
\(26\) 60.9032 0.459389
\(27\) −14.6112 −0.104145
\(28\) 25.5537 0.172471
\(29\) 13.1279 0.0840614 0.0420307 0.999116i \(-0.486617\pi\)
0.0420307 + 0.999116i \(0.486617\pi\)
\(30\) −31.0326 −0.188858
\(31\) 185.439 1.07438 0.537191 0.843461i \(-0.319486\pi\)
0.537191 + 0.843461i \(0.319486\pi\)
\(32\) 87.0032 0.480629
\(33\) 466.927 2.46308
\(34\) 170.836 0.861707
\(35\) 17.7460 0.0857032
\(36\) 49.0397 0.227035
\(37\) −369.949 −1.64376 −0.821881 0.569659i \(-0.807075\pi\)
−0.821881 + 0.569659i \(0.807075\pi\)
\(38\) 218.009 0.930676
\(39\) −139.098 −0.571115
\(40\) 25.9836 0.102709
\(41\) −294.860 −1.12315 −0.561577 0.827424i \(-0.689805\pi\)
−0.561577 + 0.827424i \(0.689805\pi\)
\(42\) −296.129 −1.08795
\(43\) −43.0000 −0.152499
\(44\) 127.183 0.435764
\(45\) 34.0560 0.112817
\(46\) −93.4431 −0.299509
\(47\) 367.319 1.13998 0.569989 0.821652i \(-0.306947\pi\)
0.569989 + 0.821652i \(0.306947\pi\)
\(48\) −546.846 −1.64438
\(49\) −173.659 −0.506293
\(50\) 388.696 1.09940
\(51\) −390.174 −1.07128
\(52\) −37.8881 −0.101041
\(53\) 708.046 1.83505 0.917524 0.397680i \(-0.130185\pi\)
0.917524 + 0.397680i \(0.130185\pi\)
\(54\) 46.1207 0.116226
\(55\) 88.3236 0.216537
\(56\) 247.950 0.591672
\(57\) −497.914 −1.15702
\(58\) −41.4385 −0.0938127
\(59\) 116.159 0.256316 0.128158 0.991754i \(-0.459094\pi\)
0.128158 + 0.991754i \(0.459094\pi\)
\(60\) 19.3054 0.0415387
\(61\) 218.910 0.459484 0.229742 0.973252i \(-0.426212\pi\)
0.229742 + 0.973252i \(0.426212\pi\)
\(62\) −585.344 −1.19901
\(63\) 324.980 0.649899
\(64\) 332.199 0.648827
\(65\) −26.3116 −0.0502086
\(66\) −1473.87 −2.74880
\(67\) −133.114 −0.242723 −0.121361 0.992608i \(-0.538726\pi\)
−0.121361 + 0.992608i \(0.538726\pi\)
\(68\) −106.277 −0.189529
\(69\) 213.416 0.372352
\(70\) −56.0156 −0.0956450
\(71\) −926.738 −1.54906 −0.774532 0.632535i \(-0.782015\pi\)
−0.774532 + 0.632535i \(0.782015\pi\)
\(72\) 475.836 0.778858
\(73\) 455.867 0.730893 0.365446 0.930832i \(-0.380916\pi\)
0.365446 + 0.930832i \(0.380916\pi\)
\(74\) 1167.75 1.83444
\(75\) −887.749 −1.36678
\(76\) −135.624 −0.204699
\(77\) 842.831 1.24740
\(78\) 439.067 0.637365
\(79\) −620.178 −0.883234 −0.441617 0.897204i \(-0.645595\pi\)
−0.441617 + 0.897204i \(0.645595\pi\)
\(80\) −103.441 −0.144563
\(81\) −779.614 −1.06943
\(82\) 930.734 1.25344
\(83\) −1317.85 −1.74281 −0.871405 0.490564i \(-0.836791\pi\)
−0.871405 + 0.490564i \(0.836791\pi\)
\(84\) 184.223 0.239290
\(85\) −73.8050 −0.0941797
\(86\) 135.731 0.170189
\(87\) 94.6419 0.116629
\(88\) 1234.07 1.49492
\(89\) 509.295 0.606575 0.303287 0.952899i \(-0.401916\pi\)
0.303287 + 0.952899i \(0.401916\pi\)
\(90\) −107.499 −0.125904
\(91\) −251.080 −0.289234
\(92\) 58.1312 0.0658760
\(93\) 1336.88 1.49062
\(94\) −1159.45 −1.27222
\(95\) −94.1850 −0.101718
\(96\) 627.228 0.666835
\(97\) 965.870 1.01102 0.505511 0.862820i \(-0.331304\pi\)
0.505511 + 0.862820i \(0.331304\pi\)
\(98\) 548.159 0.565024
\(99\) 1617.46 1.64203
\(100\) −241.809 −0.241809
\(101\) −1501.80 −1.47955 −0.739776 0.672853i \(-0.765068\pi\)
−0.739776 + 0.672853i \(0.765068\pi\)
\(102\) 1231.60 1.19555
\(103\) 1312.60 1.25567 0.627837 0.778345i \(-0.283940\pi\)
0.627837 + 0.778345i \(0.283940\pi\)
\(104\) −367.631 −0.346627
\(105\) 127.935 0.118906
\(106\) −2234.97 −2.04792
\(107\) −611.656 −0.552627 −0.276313 0.961068i \(-0.589113\pi\)
−0.276313 + 0.961068i \(0.589113\pi\)
\(108\) −28.6918 −0.0255636
\(109\) −946.664 −0.831871 −0.415935 0.909394i \(-0.636546\pi\)
−0.415935 + 0.909394i \(0.636546\pi\)
\(110\) −278.796 −0.241656
\(111\) −2667.05 −2.28059
\(112\) −987.090 −0.832779
\(113\) 2109.50 1.75615 0.878076 0.478521i \(-0.158827\pi\)
0.878076 + 0.478521i \(0.158827\pi\)
\(114\) 1571.68 1.29124
\(115\) 40.3696 0.0327347
\(116\) 25.7790 0.0206338
\(117\) −481.843 −0.380739
\(118\) −366.660 −0.286049
\(119\) −704.287 −0.542537
\(120\) 187.322 0.142501
\(121\) 2863.86 2.15166
\(122\) −690.996 −0.512785
\(123\) −2125.72 −1.55829
\(124\) 364.144 0.263718
\(125\) −338.388 −0.242131
\(126\) −1025.81 −0.725289
\(127\) 788.583 0.550988 0.275494 0.961303i \(-0.411159\pi\)
0.275494 + 0.961303i \(0.411159\pi\)
\(128\) −1744.62 −1.20472
\(129\) −309.998 −0.211580
\(130\) 83.0535 0.0560329
\(131\) 1873.57 1.24957 0.624787 0.780795i \(-0.285186\pi\)
0.624787 + 0.780795i \(0.285186\pi\)
\(132\) 916.897 0.604588
\(133\) −898.764 −0.585960
\(134\) 420.177 0.270879
\(135\) −19.9252 −0.0127029
\(136\) −1031.22 −0.650192
\(137\) −1860.27 −1.16010 −0.580050 0.814581i \(-0.696967\pi\)
−0.580050 + 0.814581i \(0.696967\pi\)
\(138\) −673.654 −0.415545
\(139\) −2822.52 −1.72232 −0.861161 0.508333i \(-0.830262\pi\)
−0.861161 + 0.508333i \(0.830262\pi\)
\(140\) 34.8475 0.0210368
\(141\) 2648.09 1.58163
\(142\) 2925.28 1.72876
\(143\) −1249.65 −0.730777
\(144\) −1894.31 −1.09624
\(145\) 17.9024 0.0102532
\(146\) −1438.96 −0.815678
\(147\) −1251.95 −0.702442
\(148\) −726.463 −0.403479
\(149\) 1615.30 0.888126 0.444063 0.895996i \(-0.353537\pi\)
0.444063 + 0.895996i \(0.353537\pi\)
\(150\) 2802.21 1.52533
\(151\) 1399.96 0.754483 0.377241 0.926115i \(-0.376873\pi\)
0.377241 + 0.926115i \(0.376873\pi\)
\(152\) −1315.97 −0.702232
\(153\) −1351.59 −0.714178
\(154\) −2660.42 −1.39210
\(155\) 252.882 0.131045
\(156\) −273.144 −0.140186
\(157\) 2933.25 1.49108 0.745539 0.666462i \(-0.232192\pi\)
0.745539 + 0.666462i \(0.232192\pi\)
\(158\) 1957.61 0.985691
\(159\) 5104.48 2.54598
\(160\) 118.646 0.0586237
\(161\) 385.229 0.188573
\(162\) 2460.88 1.19349
\(163\) −166.212 −0.0798695 −0.0399347 0.999202i \(-0.512715\pi\)
−0.0399347 + 0.999202i \(0.512715\pi\)
\(164\) −579.012 −0.275690
\(165\) 636.746 0.300428
\(166\) 4159.85 1.94498
\(167\) 2143.42 0.993191 0.496595 0.867982i \(-0.334583\pi\)
0.496595 + 0.867982i \(0.334583\pi\)
\(168\) 1787.53 0.820899
\(169\) −1824.73 −0.830554
\(170\) 232.968 0.105105
\(171\) −1724.80 −0.771339
\(172\) −84.4385 −0.0374324
\(173\) −119.018 −0.0523050 −0.0261525 0.999658i \(-0.508326\pi\)
−0.0261525 + 0.999658i \(0.508326\pi\)
\(174\) −298.740 −0.130158
\(175\) −1602.44 −0.692189
\(176\) −4912.85 −2.10409
\(177\) 837.420 0.355618
\(178\) −1607.61 −0.676939
\(179\) 2572.05 1.07399 0.536995 0.843585i \(-0.319559\pi\)
0.536995 + 0.843585i \(0.319559\pi\)
\(180\) 66.8752 0.0276921
\(181\) 1429.30 0.586956 0.293478 0.955966i \(-0.405187\pi\)
0.293478 + 0.955966i \(0.405187\pi\)
\(182\) 792.541 0.322786
\(183\) 1578.18 0.637498
\(184\) 564.052 0.225992
\(185\) −504.498 −0.200494
\(186\) −4219.89 −1.66353
\(187\) −3505.31 −1.37077
\(188\) 721.299 0.279820
\(189\) −190.137 −0.0731769
\(190\) 297.298 0.113517
\(191\) 411.149 0.155758 0.0778788 0.996963i \(-0.475185\pi\)
0.0778788 + 0.996963i \(0.475185\pi\)
\(192\) 2394.91 0.900195
\(193\) −3108.57 −1.15938 −0.579689 0.814838i \(-0.696826\pi\)
−0.579689 + 0.814838i \(0.696826\pi\)
\(194\) −3048.80 −1.12830
\(195\) −189.687 −0.0696604
\(196\) −341.011 −0.124275
\(197\) 1960.75 0.709125 0.354563 0.935032i \(-0.384630\pi\)
0.354563 + 0.935032i \(0.384630\pi\)
\(198\) −5105.57 −1.83251
\(199\) 456.187 0.162504 0.0812519 0.996694i \(-0.474108\pi\)
0.0812519 + 0.996694i \(0.474108\pi\)
\(200\) −2346.29 −0.829540
\(201\) −959.650 −0.336759
\(202\) 4740.48 1.65118
\(203\) 170.834 0.0590651
\(204\) −766.179 −0.262957
\(205\) −402.099 −0.136994
\(206\) −4143.27 −1.40133
\(207\) 739.286 0.248232
\(208\) 1463.54 0.487877
\(209\) −4473.24 −1.48048
\(210\) −403.831 −0.132700
\(211\) −1742.50 −0.568524 −0.284262 0.958747i \(-0.591749\pi\)
−0.284262 + 0.958747i \(0.591749\pi\)
\(212\) 1390.38 0.450432
\(213\) −6681.08 −2.14920
\(214\) 1930.71 0.616732
\(215\) −58.6390 −0.0186007
\(216\) −278.399 −0.0876974
\(217\) 2413.14 0.754906
\(218\) 2988.17 0.928370
\(219\) 3286.46 1.01406
\(220\) 173.440 0.0531514
\(221\) 1044.24 0.317841
\(222\) 8418.63 2.54514
\(223\) 3149.26 0.945697 0.472848 0.881144i \(-0.343226\pi\)
0.472848 + 0.881144i \(0.343226\pi\)
\(224\) 1132.18 0.337711
\(225\) −3075.22 −0.911175
\(226\) −6658.71 −1.95987
\(227\) 2108.03 0.616365 0.308182 0.951327i \(-0.400279\pi\)
0.308182 + 0.951327i \(0.400279\pi\)
\(228\) −977.746 −0.284003
\(229\) 1529.66 0.441409 0.220704 0.975341i \(-0.429164\pi\)
0.220704 + 0.975341i \(0.429164\pi\)
\(230\) −127.428 −0.0365320
\(231\) 6076.18 1.73066
\(232\) 250.136 0.0707854
\(233\) 2999.86 0.843466 0.421733 0.906720i \(-0.361422\pi\)
0.421733 + 0.906720i \(0.361422\pi\)
\(234\) 1520.95 0.424905
\(235\) 500.912 0.139046
\(236\) 228.100 0.0629154
\(237\) −4471.02 −1.22542
\(238\) 2223.10 0.605472
\(239\) 3421.34 0.925976 0.462988 0.886364i \(-0.346777\pi\)
0.462988 + 0.886364i \(0.346777\pi\)
\(240\) −745.732 −0.200570
\(241\) −4496.86 −1.20194 −0.600971 0.799271i \(-0.705219\pi\)
−0.600971 + 0.799271i \(0.705219\pi\)
\(242\) −9039.86 −2.40126
\(243\) −5225.93 −1.37960
\(244\) 429.870 0.112785
\(245\) −236.818 −0.0617540
\(246\) 6709.89 1.73905
\(247\) 1332.58 0.343280
\(248\) 3533.32 0.904701
\(249\) −9500.74 −2.41801
\(250\) 1068.13 0.270219
\(251\) 1478.05 0.371688 0.185844 0.982579i \(-0.440498\pi\)
0.185844 + 0.982579i \(0.440498\pi\)
\(252\) 638.159 0.159525
\(253\) 1917.33 0.476448
\(254\) −2489.19 −0.614904
\(255\) −532.079 −0.130667
\(256\) 2849.36 0.695645
\(257\) 677.467 0.164433 0.0822164 0.996614i \(-0.473800\pi\)
0.0822164 + 0.996614i \(0.473800\pi\)
\(258\) 978.517 0.236123
\(259\) −4814.19 −1.15498
\(260\) −51.6678 −0.0123242
\(261\) 327.845 0.0777514
\(262\) −5913.97 −1.39453
\(263\) −7753.56 −1.81789 −0.908944 0.416917i \(-0.863110\pi\)
−0.908944 + 0.416917i \(0.863110\pi\)
\(264\) 8896.73 2.07408
\(265\) 965.560 0.223826
\(266\) 2836.97 0.653933
\(267\) 3671.63 0.841574
\(268\) −261.393 −0.0595789
\(269\) −300.965 −0.0682161 −0.0341081 0.999418i \(-0.510859\pi\)
−0.0341081 + 0.999418i \(0.510859\pi\)
\(270\) 62.8946 0.0141765
\(271\) −2176.33 −0.487833 −0.243917 0.969796i \(-0.578432\pi\)
−0.243917 + 0.969796i \(0.578432\pi\)
\(272\) 4105.28 0.915145
\(273\) −1810.10 −0.401290
\(274\) 5872.00 1.29467
\(275\) −7975.52 −1.74888
\(276\) 419.082 0.0913978
\(277\) 2947.64 0.639373 0.319687 0.947523i \(-0.396422\pi\)
0.319687 + 0.947523i \(0.396422\pi\)
\(278\) 8909.36 1.92211
\(279\) 4631.02 0.993734
\(280\) 338.128 0.0721679
\(281\) 459.209 0.0974879 0.0487440 0.998811i \(-0.484478\pi\)
0.0487440 + 0.998811i \(0.484478\pi\)
\(282\) −8358.79 −1.76510
\(283\) 6190.86 1.30038 0.650192 0.759770i \(-0.274688\pi\)
0.650192 + 0.759770i \(0.274688\pi\)
\(284\) −1819.82 −0.380234
\(285\) −679.003 −0.141125
\(286\) 3944.56 0.815549
\(287\) −3837.05 −0.789176
\(288\) 2172.75 0.444551
\(289\) −1983.89 −0.403803
\(290\) −56.5095 −0.0114426
\(291\) 6963.20 1.40271
\(292\) 895.179 0.179405
\(293\) 5693.95 1.13530 0.567652 0.823269i \(-0.307852\pi\)
0.567652 + 0.823269i \(0.307852\pi\)
\(294\) 3951.81 0.783927
\(295\) 158.406 0.0312635
\(296\) −7048.93 −1.38416
\(297\) −946.333 −0.184888
\(298\) −5098.75 −0.991150
\(299\) −571.173 −0.110474
\(300\) −1743.26 −0.335491
\(301\) −559.564 −0.107152
\(302\) −4419.01 −0.842005
\(303\) −10826.9 −2.05276
\(304\) 5238.89 0.988391
\(305\) 298.527 0.0560446
\(306\) 4266.32 0.797024
\(307\) −5108.18 −0.949639 −0.474819 0.880083i \(-0.657487\pi\)
−0.474819 + 0.880083i \(0.657487\pi\)
\(308\) 1655.05 0.306187
\(309\) 9462.87 1.74215
\(310\) −798.231 −0.146247
\(311\) −1048.11 −0.191102 −0.0955511 0.995425i \(-0.530461\pi\)
−0.0955511 + 0.995425i \(0.530461\pi\)
\(312\) −2650.34 −0.480917
\(313\) 4279.92 0.772893 0.386446 0.922312i \(-0.373702\pi\)
0.386446 + 0.922312i \(0.373702\pi\)
\(314\) −9258.91 −1.66405
\(315\) 443.175 0.0792700
\(316\) −1217.83 −0.216799
\(317\) 5929.95 1.05066 0.525330 0.850899i \(-0.323942\pi\)
0.525330 + 0.850899i \(0.323942\pi\)
\(318\) −16112.4 −2.84132
\(319\) 850.261 0.149234
\(320\) 453.019 0.0791392
\(321\) −4409.58 −0.766725
\(322\) −1215.99 −0.210448
\(323\) 3737.94 0.643915
\(324\) −1530.92 −0.262503
\(325\) 2375.91 0.405514
\(326\) 524.653 0.0891345
\(327\) −6824.73 −1.15415
\(328\) −5618.20 −0.945772
\(329\) 4779.97 0.800997
\(330\) −2009.91 −0.335278
\(331\) 509.174 0.0845521 0.0422761 0.999106i \(-0.486539\pi\)
0.0422761 + 0.999106i \(0.486539\pi\)
\(332\) −2587.85 −0.427792
\(333\) −9238.83 −1.52037
\(334\) −6765.77 −1.10840
\(335\) −181.527 −0.0296056
\(336\) −7116.18 −1.15541
\(337\) −10856.3 −1.75484 −0.877419 0.479724i \(-0.840737\pi\)
−0.877419 + 0.479724i \(0.840737\pi\)
\(338\) 5759.81 0.926900
\(339\) 15207.9 2.43652
\(340\) −144.930 −0.0231174
\(341\) 12010.5 1.90734
\(342\) 5444.39 0.860816
\(343\) −6723.34 −1.05839
\(344\) −819.314 −0.128414
\(345\) 291.035 0.0454168
\(346\) 375.684 0.0583725
\(347\) 8973.74 1.38829 0.694143 0.719837i \(-0.255783\pi\)
0.694143 + 0.719837i \(0.255783\pi\)
\(348\) 185.847 0.0286277
\(349\) −5.70408 −0.000874877 0 −0.000437439 1.00000i \(-0.500139\pi\)
−0.000437439 1.00000i \(0.500139\pi\)
\(350\) 5058.15 0.772485
\(351\) 281.913 0.0428702
\(352\) 5635.00 0.853257
\(353\) −1504.40 −0.226830 −0.113415 0.993548i \(-0.536179\pi\)
−0.113415 + 0.993548i \(0.536179\pi\)
\(354\) −2643.34 −0.396870
\(355\) −1263.79 −0.188944
\(356\) 1000.10 0.148890
\(357\) −5077.38 −0.752727
\(358\) −8118.76 −1.19857
\(359\) −1296.86 −0.190657 −0.0953285 0.995446i \(-0.530390\pi\)
−0.0953285 + 0.995446i \(0.530390\pi\)
\(360\) 648.896 0.0949995
\(361\) −2088.90 −0.304548
\(362\) −4511.63 −0.655044
\(363\) 20646.3 2.98526
\(364\) −493.042 −0.0709957
\(365\) 621.664 0.0891490
\(366\) −4981.56 −0.711449
\(367\) 12908.3 1.83599 0.917995 0.396592i \(-0.129807\pi\)
0.917995 + 0.396592i \(0.129807\pi\)
\(368\) −2245.50 −0.318083
\(369\) −7363.61 −1.03885
\(370\) 1592.46 0.223752
\(371\) 9213.89 1.28938
\(372\) 2625.20 0.365888
\(373\) −1371.48 −0.190382 −0.0951908 0.995459i \(-0.530346\pi\)
−0.0951908 + 0.995459i \(0.530346\pi\)
\(374\) 11064.6 1.52978
\(375\) −2439.52 −0.335937
\(376\) 6998.83 0.959939
\(377\) −253.293 −0.0346029
\(378\) 600.174 0.0816656
\(379\) −458.768 −0.0621776 −0.0310888 0.999517i \(-0.509897\pi\)
−0.0310888 + 0.999517i \(0.509897\pi\)
\(380\) −184.950 −0.0249677
\(381\) 5685.09 0.764452
\(382\) −1297.80 −0.173826
\(383\) 9513.45 1.26923 0.634614 0.772829i \(-0.281159\pi\)
0.634614 + 0.772829i \(0.281159\pi\)
\(384\) −12577.4 −1.67145
\(385\) 1149.37 0.152148
\(386\) 9812.31 1.29387
\(387\) −1073.85 −0.141051
\(388\) 1896.66 0.248166
\(389\) 5643.25 0.735538 0.367769 0.929917i \(-0.380122\pi\)
0.367769 + 0.929917i \(0.380122\pi\)
\(390\) 598.754 0.0777412
\(391\) −1602.16 −0.207224
\(392\) −3308.86 −0.426333
\(393\) 13507.0 1.73369
\(394\) −6189.17 −0.791385
\(395\) −845.735 −0.107730
\(396\) 3176.19 0.403054
\(397\) −13816.5 −1.74668 −0.873340 0.487110i \(-0.838051\pi\)
−0.873340 + 0.487110i \(0.838051\pi\)
\(398\) −1439.97 −0.181355
\(399\) −6479.41 −0.812973
\(400\) 9340.62 1.16758
\(401\) 3544.45 0.441400 0.220700 0.975342i \(-0.429166\pi\)
0.220700 + 0.975342i \(0.429166\pi\)
\(402\) 3029.16 0.375823
\(403\) −3577.93 −0.442256
\(404\) −2949.06 −0.363172
\(405\) −1063.16 −0.130441
\(406\) −539.244 −0.0659168
\(407\) −23960.7 −2.91816
\(408\) −7434.30 −0.902090
\(409\) −2736.88 −0.330880 −0.165440 0.986220i \(-0.552904\pi\)
−0.165440 + 0.986220i \(0.552904\pi\)
\(410\) 1269.24 0.152886
\(411\) −13411.2 −1.60955
\(412\) 2577.54 0.308219
\(413\) 1511.59 0.180098
\(414\) −2333.58 −0.277027
\(415\) −1797.15 −0.212575
\(416\) −1678.67 −0.197845
\(417\) −20348.2 −2.38958
\(418\) 14119.9 1.65222
\(419\) 9280.65 1.08208 0.541038 0.840998i \(-0.318032\pi\)
0.541038 + 0.840998i \(0.318032\pi\)
\(420\) 251.224 0.0291869
\(421\) −7308.00 −0.846010 −0.423005 0.906127i \(-0.639025\pi\)
−0.423005 + 0.906127i \(0.639025\pi\)
\(422\) 5500.26 0.634475
\(423\) 9173.16 1.05441
\(424\) 13491.0 1.54523
\(425\) 6664.51 0.760650
\(426\) 21089.0 2.39852
\(427\) 2848.70 0.322853
\(428\) −1201.10 −0.135648
\(429\) −9009.05 −1.01390
\(430\) 185.096 0.0207584
\(431\) −953.510 −0.106564 −0.0532818 0.998580i \(-0.516968\pi\)
−0.0532818 + 0.998580i \(0.516968\pi\)
\(432\) 1108.31 0.123434
\(433\) 3447.00 0.382569 0.191284 0.981535i \(-0.438735\pi\)
0.191284 + 0.981535i \(0.438735\pi\)
\(434\) −7617.15 −0.842477
\(435\) 129.063 0.0142255
\(436\) −1858.95 −0.204192
\(437\) −2044.57 −0.223810
\(438\) −10373.8 −1.13169
\(439\) −9245.65 −1.00517 −0.502586 0.864527i \(-0.667618\pi\)
−0.502586 + 0.864527i \(0.667618\pi\)
\(440\) 1682.90 0.182339
\(441\) −4336.82 −0.468289
\(442\) −3296.16 −0.354711
\(443\) −3885.76 −0.416745 −0.208372 0.978050i \(-0.566817\pi\)
−0.208372 + 0.978050i \(0.566817\pi\)
\(444\) −5237.25 −0.559795
\(445\) 694.524 0.0739856
\(446\) −9940.75 −1.05540
\(447\) 11645.1 1.23220
\(448\) 4322.95 0.455893
\(449\) −14413.1 −1.51491 −0.757455 0.652887i \(-0.773557\pi\)
−0.757455 + 0.652887i \(0.773557\pi\)
\(450\) 9707.02 1.01687
\(451\) −19097.4 −1.99393
\(452\) 4142.40 0.431066
\(453\) 10092.6 1.04679
\(454\) −6654.06 −0.687864
\(455\) −342.397 −0.0352787
\(456\) −9487.15 −0.974291
\(457\) −1765.21 −0.180685 −0.0903424 0.995911i \(-0.528796\pi\)
−0.0903424 + 0.995911i \(0.528796\pi\)
\(458\) −4828.41 −0.492613
\(459\) 790.776 0.0804145
\(460\) 79.2733 0.00803508
\(461\) 7626.64 0.770517 0.385258 0.922809i \(-0.374112\pi\)
0.385258 + 0.922809i \(0.374112\pi\)
\(462\) −19179.6 −1.93142
\(463\) −5954.18 −0.597655 −0.298827 0.954307i \(-0.596595\pi\)
−0.298827 + 0.954307i \(0.596595\pi\)
\(464\) −995.792 −0.0996304
\(465\) 1823.09 0.181815
\(466\) −9469.16 −0.941310
\(467\) 153.388 0.0151991 0.00759954 0.999971i \(-0.497581\pi\)
0.00759954 + 0.999971i \(0.497581\pi\)
\(468\) −946.189 −0.0934564
\(469\) −1732.22 −0.170547
\(470\) −1581.14 −0.155176
\(471\) 21146.6 2.06875
\(472\) 2213.27 0.215835
\(473\) −2785.01 −0.270729
\(474\) 14112.9 1.36757
\(475\) 8504.80 0.821531
\(476\) −1383.00 −0.133171
\(477\) 17682.2 1.69730
\(478\) −10799.6 −1.03339
\(479\) −11334.3 −1.08117 −0.540584 0.841290i \(-0.681797\pi\)
−0.540584 + 0.841290i \(0.681797\pi\)
\(480\) 855.348 0.0813357
\(481\) 7137.92 0.676635
\(482\) 14194.5 1.34137
\(483\) 2777.21 0.261630
\(484\) 5623.72 0.528148
\(485\) 1317.15 0.123317
\(486\) 16495.8 1.53964
\(487\) −2845.89 −0.264804 −0.132402 0.991196i \(-0.542269\pi\)
−0.132402 + 0.991196i \(0.542269\pi\)
\(488\) 4171.07 0.386917
\(489\) −1198.26 −0.110813
\(490\) 747.522 0.0689176
\(491\) −8345.94 −0.767102 −0.383551 0.923520i \(-0.625299\pi\)
−0.383551 + 0.923520i \(0.625299\pi\)
\(492\) −4174.24 −0.382499
\(493\) −710.496 −0.0649070
\(494\) −4206.34 −0.383101
\(495\) 2205.73 0.200283
\(496\) −14066.2 −1.27337
\(497\) −12059.8 −1.08844
\(498\) 29989.4 2.69851
\(499\) 17591.1 1.57813 0.789064 0.614311i \(-0.210566\pi\)
0.789064 + 0.614311i \(0.210566\pi\)
\(500\) −664.488 −0.0594336
\(501\) 15452.5 1.37797
\(502\) −4665.51 −0.414805
\(503\) −7975.83 −0.707008 −0.353504 0.935433i \(-0.615010\pi\)
−0.353504 + 0.935433i \(0.615010\pi\)
\(504\) 6192.11 0.547259
\(505\) −2048.00 −0.180465
\(506\) −6052.10 −0.531717
\(507\) −13154.9 −1.15233
\(508\) 1548.53 0.135246
\(509\) −9016.94 −0.785204 −0.392602 0.919708i \(-0.628425\pi\)
−0.392602 + 0.919708i \(0.628425\pi\)
\(510\) 1679.52 0.145825
\(511\) 5932.25 0.513556
\(512\) 4962.89 0.428380
\(513\) 1009.14 0.0868507
\(514\) −2138.45 −0.183507
\(515\) 1789.99 0.153158
\(516\) −608.738 −0.0519345
\(517\) 23790.4 2.02379
\(518\) 15196.1 1.28896
\(519\) −858.030 −0.0725691
\(520\) −501.337 −0.0422790
\(521\) −3086.13 −0.259512 −0.129756 0.991546i \(-0.541419\pi\)
−0.129756 + 0.991546i \(0.541419\pi\)
\(522\) −1034.85 −0.0867707
\(523\) 8338.32 0.697149 0.348575 0.937281i \(-0.386666\pi\)
0.348575 + 0.937281i \(0.386666\pi\)
\(524\) 3679.10 0.306722
\(525\) −11552.4 −0.960358
\(526\) 24474.3 2.02877
\(527\) −10036.2 −0.829570
\(528\) −35418.0 −2.91926
\(529\) −11290.7 −0.927974
\(530\) −3047.82 −0.249790
\(531\) 2900.87 0.237076
\(532\) −1764.89 −0.143830
\(533\) 5689.13 0.462333
\(534\) −11589.6 −0.939199
\(535\) −834.114 −0.0674054
\(536\) −2536.32 −0.204389
\(537\) 18542.6 1.49008
\(538\) 950.004 0.0761293
\(539\) −11247.5 −0.898818
\(540\) −39.1269 −0.00311806
\(541\) −14924.6 −1.18606 −0.593029 0.805181i \(-0.702068\pi\)
−0.593029 + 0.805181i \(0.702068\pi\)
\(542\) 6869.66 0.544423
\(543\) 10304.2 0.814355
\(544\) −4708.72 −0.371112
\(545\) −1290.96 −0.101466
\(546\) 5713.63 0.447840
\(547\) 10658.3 0.833120 0.416560 0.909108i \(-0.363236\pi\)
0.416560 + 0.909108i \(0.363236\pi\)
\(548\) −3652.99 −0.284759
\(549\) 5466.90 0.424994
\(550\) 25175.0 1.95175
\(551\) −906.687 −0.0701020
\(552\) 4066.39 0.313545
\(553\) −8070.45 −0.620598
\(554\) −9304.31 −0.713542
\(555\) −3637.05 −0.278170
\(556\) −5542.53 −0.422762
\(557\) 4303.28 0.327354 0.163677 0.986514i \(-0.447665\pi\)
0.163677 + 0.986514i \(0.447665\pi\)
\(558\) −14617.9 −1.10901
\(559\) 829.657 0.0627742
\(560\) −1346.09 −0.101576
\(561\) −25270.7 −1.90183
\(562\) −1449.51 −0.108797
\(563\) −13280.8 −0.994173 −0.497086 0.867701i \(-0.665597\pi\)
−0.497086 + 0.867701i \(0.665597\pi\)
\(564\) 5200.02 0.388228
\(565\) 2876.72 0.214203
\(566\) −19541.7 −1.45123
\(567\) −10145.2 −0.751427
\(568\) −17657.9 −1.30442
\(569\) 11641.6 0.857720 0.428860 0.903371i \(-0.358915\pi\)
0.428860 + 0.903371i \(0.358915\pi\)
\(570\) 2143.29 0.157496
\(571\) 21799.0 1.59765 0.798825 0.601563i \(-0.205455\pi\)
0.798825 + 0.601563i \(0.205455\pi\)
\(572\) −2453.92 −0.179377
\(573\) 2964.07 0.216101
\(574\) 12111.8 0.880723
\(575\) −3645.34 −0.264384
\(576\) 8296.10 0.600123
\(577\) 6854.44 0.494548 0.247274 0.968946i \(-0.420465\pi\)
0.247274 + 0.968946i \(0.420465\pi\)
\(578\) 6262.20 0.450645
\(579\) −22410.5 −1.60855
\(580\) 35.1547 0.00251676
\(581\) −17149.4 −1.22457
\(582\) −21979.5 −1.56543
\(583\) 45858.5 3.25775
\(584\) 8686.00 0.615461
\(585\) −657.088 −0.0464397
\(586\) −17973.1 −1.26700
\(587\) −16741.7 −1.17718 −0.588589 0.808433i \(-0.700316\pi\)
−0.588589 + 0.808433i \(0.700316\pi\)
\(588\) −2458.43 −0.172422
\(589\) −12807.5 −0.895967
\(590\) −500.012 −0.0348902
\(591\) 14135.5 0.983855
\(592\) 28061.9 1.94820
\(593\) 21885.0 1.51553 0.757764 0.652529i \(-0.226292\pi\)
0.757764 + 0.652529i \(0.226292\pi\)
\(594\) 2987.13 0.206336
\(595\) −960.434 −0.0661747
\(596\) 3171.95 0.218000
\(597\) 3288.77 0.225461
\(598\) 1802.92 0.123289
\(599\) −14440.9 −0.985039 −0.492519 0.870301i \(-0.663924\pi\)
−0.492519 + 0.870301i \(0.663924\pi\)
\(600\) −16915.0 −1.15092
\(601\) 2570.21 0.174444 0.0872221 0.996189i \(-0.472201\pi\)
0.0872221 + 0.996189i \(0.472201\pi\)
\(602\) 1766.28 0.119582
\(603\) −3324.28 −0.224503
\(604\) 2749.08 0.185196
\(605\) 3905.44 0.262444
\(606\) 34175.3 2.29089
\(607\) −11683.5 −0.781249 −0.390624 0.920550i \(-0.627741\pi\)
−0.390624 + 0.920550i \(0.627741\pi\)
\(608\) −6008.96 −0.400815
\(609\) 1231.59 0.0819482
\(610\) −942.309 −0.0625458
\(611\) −7087.18 −0.469258
\(612\) −2654.09 −0.175303
\(613\) 12739.0 0.839356 0.419678 0.907673i \(-0.362143\pi\)
0.419678 + 0.907673i \(0.362143\pi\)
\(614\) 16124.1 1.05980
\(615\) −2898.83 −0.190069
\(616\) 16059.1 1.05039
\(617\) 4380.70 0.285835 0.142918 0.989735i \(-0.454352\pi\)
0.142918 + 0.989735i \(0.454352\pi\)
\(618\) −29869.8 −1.94424
\(619\) −5157.68 −0.334902 −0.167451 0.985880i \(-0.553554\pi\)
−0.167451 + 0.985880i \(0.553554\pi\)
\(620\) 496.582 0.0321665
\(621\) −432.536 −0.0279502
\(622\) 3308.39 0.213270
\(623\) 6627.52 0.426205
\(624\) 10551.0 0.676891
\(625\) 14931.1 0.955589
\(626\) −13509.7 −0.862550
\(627\) −32248.7 −2.05405
\(628\) 5759.99 0.366001
\(629\) 20022.1 1.26921
\(630\) −1398.89 −0.0884655
\(631\) −27679.9 −1.74631 −0.873154 0.487444i \(-0.837929\pi\)
−0.873154 + 0.487444i \(0.837929\pi\)
\(632\) −11816.8 −0.743743
\(633\) −12562.1 −0.788783
\(634\) −18718.1 −1.17254
\(635\) 1075.39 0.0672055
\(636\) 10023.6 0.624939
\(637\) 3350.63 0.208409
\(638\) −2683.88 −0.166545
\(639\) −23143.7 −1.43278
\(640\) −2379.14 −0.146943
\(641\) −16453.5 −1.01384 −0.506921 0.861992i \(-0.669217\pi\)
−0.506921 + 0.861992i \(0.669217\pi\)
\(642\) 13919.0 0.855667
\(643\) −29203.6 −1.79110 −0.895551 0.444958i \(-0.853219\pi\)
−0.895551 + 0.444958i \(0.853219\pi\)
\(644\) 756.468 0.0462873
\(645\) −422.743 −0.0258070
\(646\) −11798.9 −0.718610
\(647\) −16835.6 −1.02299 −0.511495 0.859286i \(-0.670908\pi\)
−0.511495 + 0.859286i \(0.670908\pi\)
\(648\) −14854.6 −0.900532
\(649\) 7523.36 0.455035
\(650\) −7499.64 −0.452554
\(651\) 17396.9 1.04737
\(652\) −326.388 −0.0196048
\(653\) −13735.1 −0.823117 −0.411558 0.911383i \(-0.635015\pi\)
−0.411558 + 0.911383i \(0.635015\pi\)
\(654\) 21542.5 1.28804
\(655\) 2554.98 0.152414
\(656\) 22366.1 1.33117
\(657\) 11384.5 0.676029
\(658\) −15088.1 −0.893915
\(659\) −5708.76 −0.337453 −0.168727 0.985663i \(-0.553966\pi\)
−0.168727 + 0.985663i \(0.553966\pi\)
\(660\) 1250.37 0.0737433
\(661\) 18339.5 1.07916 0.539578 0.841936i \(-0.318584\pi\)
0.539578 + 0.841936i \(0.318584\pi\)
\(662\) −1607.22 −0.0943604
\(663\) 7528.15 0.440979
\(664\) −25110.1 −1.46756
\(665\) −1225.64 −0.0714712
\(666\) 29162.7 1.69674
\(667\) 388.625 0.0225602
\(668\) 4209.00 0.243789
\(669\) 22703.8 1.31208
\(670\) 572.995 0.0330399
\(671\) 14178.3 0.815719
\(672\) 8162.19 0.468547
\(673\) −482.234 −0.0276207 −0.0138104 0.999905i \(-0.504396\pi\)
−0.0138104 + 0.999905i \(0.504396\pi\)
\(674\) 34268.3 1.95840
\(675\) 1799.23 0.102596
\(676\) −3583.19 −0.203868
\(677\) 31086.0 1.76474 0.882372 0.470553i \(-0.155945\pi\)
0.882372 + 0.470553i \(0.155945\pi\)
\(678\) −48004.3 −2.71916
\(679\) 12569.0 0.710388
\(680\) −1406.27 −0.0793057
\(681\) 15197.3 0.855157
\(682\) −37911.4 −2.12860
\(683\) 31381.0 1.75807 0.879034 0.476758i \(-0.158188\pi\)
0.879034 + 0.476758i \(0.158188\pi\)
\(684\) −3386.97 −0.189333
\(685\) −2536.85 −0.141501
\(686\) 21222.4 1.18116
\(687\) 11027.7 0.612420
\(688\) 3261.70 0.180743
\(689\) −13661.3 −0.755375
\(690\) −918.660 −0.0506852
\(691\) 19856.9 1.09319 0.546593 0.837398i \(-0.315924\pi\)
0.546593 + 0.837398i \(0.315924\pi\)
\(692\) −233.714 −0.0128388
\(693\) 21048.2 1.15376
\(694\) −28325.9 −1.54933
\(695\) −3849.06 −0.210076
\(696\) 1803.29 0.0982091
\(697\) 15958.2 0.867230
\(698\) 18.0051 0.000976365 0
\(699\) 21626.8 1.17024
\(700\) −3146.69 −0.169905
\(701\) 2722.80 0.146703 0.0733514 0.997306i \(-0.476631\pi\)
0.0733514 + 0.997306i \(0.476631\pi\)
\(702\) −889.868 −0.0478432
\(703\) 25550.9 1.37079
\(704\) 21515.8 1.15186
\(705\) 3611.20 0.192916
\(706\) 4748.67 0.253143
\(707\) −19543.1 −1.03960
\(708\) 1644.43 0.0872901
\(709\) −1225.30 −0.0649043 −0.0324521 0.999473i \(-0.510332\pi\)
−0.0324521 + 0.999473i \(0.510332\pi\)
\(710\) 3989.19 0.210861
\(711\) −15487.9 −0.816935
\(712\) 9704.01 0.510777
\(713\) 5489.57 0.288339
\(714\) 16026.9 0.840045
\(715\) −1704.15 −0.0891349
\(716\) 5050.70 0.263622
\(717\) 24665.3 1.28472
\(718\) 4093.59 0.212774
\(719\) −28875.1 −1.49772 −0.748858 0.662730i \(-0.769398\pi\)
−0.748858 + 0.662730i \(0.769398\pi\)
\(720\) −2583.26 −0.133712
\(721\) 17081.0 0.882290
\(722\) 6593.67 0.339876
\(723\) −32419.0 −1.66760
\(724\) 2806.70 0.144075
\(725\) −1616.57 −0.0828108
\(726\) −65170.6 −3.33155
\(727\) −25072.0 −1.27905 −0.639525 0.768770i \(-0.720869\pi\)
−0.639525 + 0.768770i \(0.720869\pi\)
\(728\) −4784.03 −0.243555
\(729\) −16625.5 −0.844660
\(730\) −1962.30 −0.0994905
\(731\) 2327.22 0.117750
\(732\) 3099.04 0.156481
\(733\) 1017.07 0.0512503 0.0256251 0.999672i \(-0.491842\pi\)
0.0256251 + 0.999672i \(0.491842\pi\)
\(734\) −40745.5 −2.04897
\(735\) −1707.28 −0.0856787
\(736\) 2575.56 0.128990
\(737\) −8621.47 −0.430904
\(738\) 23243.5 1.15935
\(739\) −1001.77 −0.0498658 −0.0249329 0.999689i \(-0.507937\pi\)
−0.0249329 + 0.999689i \(0.507937\pi\)
\(740\) −990.675 −0.0492134
\(741\) 9606.92 0.476274
\(742\) −29083.9 −1.43895
\(743\) −2115.35 −0.104448 −0.0522238 0.998635i \(-0.516631\pi\)
−0.0522238 + 0.998635i \(0.516631\pi\)
\(744\) 25472.6 1.25520
\(745\) 2202.78 0.108327
\(746\) 4329.11 0.212466
\(747\) −32911.1 −1.61199
\(748\) −6883.33 −0.336470
\(749\) −7959.56 −0.388299
\(750\) 7700.43 0.374907
\(751\) 39172.1 1.90334 0.951671 0.307119i \(-0.0993649\pi\)
0.951671 + 0.307119i \(0.0993649\pi\)
\(752\) −27862.4 −1.35111
\(753\) 10655.6 0.515688
\(754\) 799.528 0.0386169
\(755\) 1909.12 0.0920263
\(756\) −373.370 −0.0179621
\(757\) 5944.10 0.285392 0.142696 0.989767i \(-0.454423\pi\)
0.142696 + 0.989767i \(0.454423\pi\)
\(758\) 1448.12 0.0693904
\(759\) 13822.5 0.661033
\(760\) −1794.58 −0.0856531
\(761\) −1954.89 −0.0931205 −0.0465603 0.998915i \(-0.514826\pi\)
−0.0465603 + 0.998915i \(0.514826\pi\)
\(762\) −17945.2 −0.853130
\(763\) −12319.1 −0.584508
\(764\) 807.367 0.0382324
\(765\) −1843.15 −0.0871102
\(766\) −30029.5 −1.41646
\(767\) −2241.21 −0.105509
\(768\) 20541.7 0.965152
\(769\) −39312.9 −1.84351 −0.921756 0.387770i \(-0.873245\pi\)
−0.921756 + 0.387770i \(0.873245\pi\)
\(770\) −3628.01 −0.169798
\(771\) 4884.03 0.228138
\(772\) −6104.26 −0.284582
\(773\) −5102.38 −0.237413 −0.118706 0.992929i \(-0.537875\pi\)
−0.118706 + 0.992929i \(0.537875\pi\)
\(774\) 3389.64 0.157414
\(775\) −22835.0 −1.05840
\(776\) 18403.5 0.851349
\(777\) −34706.7 −1.60244
\(778\) −17813.1 −0.820862
\(779\) 20364.8 0.936641
\(780\) −372.486 −0.0170989
\(781\) −60022.7 −2.75004
\(782\) 5057.26 0.231262
\(783\) −191.813 −0.00875460
\(784\) 13172.6 0.600064
\(785\) 4000.07 0.181871
\(786\) −42635.3 −1.93480
\(787\) 21898.3 0.991855 0.495928 0.868364i \(-0.334828\pi\)
0.495928 + 0.868364i \(0.334828\pi\)
\(788\) 3850.30 0.174062
\(789\) −55897.3 −2.52218
\(790\) 2669.59 0.120227
\(791\) 27451.2 1.23395
\(792\) 30818.8 1.38270
\(793\) −4223.73 −0.189141
\(794\) 43612.3 1.94930
\(795\) 6960.96 0.310541
\(796\) 895.809 0.0398883
\(797\) 18262.4 0.811652 0.405826 0.913950i \(-0.366984\pi\)
0.405826 + 0.913950i \(0.366984\pi\)
\(798\) 20452.5 0.907280
\(799\) −19879.8 −0.880220
\(800\) −10713.6 −0.473479
\(801\) 12718.8 0.561043
\(802\) −11188.2 −0.492604
\(803\) 29525.5 1.29755
\(804\) −1884.45 −0.0826610
\(805\) 525.335 0.0230008
\(806\) 11293.8 0.493559
\(807\) −2169.73 −0.0946444
\(808\) −28615.0 −1.24588
\(809\) 26097.8 1.13418 0.567089 0.823656i \(-0.308069\pi\)
0.567089 + 0.823656i \(0.308069\pi\)
\(810\) 3355.89 0.145573
\(811\) 1067.58 0.0462243 0.0231122 0.999733i \(-0.492643\pi\)
0.0231122 + 0.999733i \(0.492643\pi\)
\(812\) 335.465 0.0144982
\(813\) −15689.7 −0.676830
\(814\) 75632.8 3.25667
\(815\) −226.663 −0.00974190
\(816\) 29596.0 1.26969
\(817\) 2969.84 0.127174
\(818\) 8639.05 0.369263
\(819\) −6270.29 −0.267523
\(820\) −789.596 −0.0336267
\(821\) −20127.0 −0.855585 −0.427793 0.903877i \(-0.640709\pi\)
−0.427793 + 0.903877i \(0.640709\pi\)
\(822\) 42332.7 1.79626
\(823\) −3011.70 −0.127559 −0.0637797 0.997964i \(-0.520315\pi\)
−0.0637797 + 0.997964i \(0.520315\pi\)
\(824\) 25010.1 1.05736
\(825\) −57497.5 −2.42643
\(826\) −4771.39 −0.200990
\(827\) −13138.4 −0.552437 −0.276219 0.961095i \(-0.589081\pi\)
−0.276219 + 0.961095i \(0.589081\pi\)
\(828\) 1451.73 0.0609311
\(829\) 19550.4 0.819075 0.409538 0.912293i \(-0.365690\pi\)
0.409538 + 0.912293i \(0.365690\pi\)
\(830\) 5672.77 0.237235
\(831\) 21250.2 0.887079
\(832\) −6409.57 −0.267082
\(833\) 9398.63 0.390928
\(834\) 64229.8 2.66678
\(835\) 2922.98 0.121142
\(836\) −8784.05 −0.363400
\(837\) −2709.48 −0.111892
\(838\) −29294.7 −1.20760
\(839\) 3227.69 0.132816 0.0664078 0.997793i \(-0.478846\pi\)
0.0664078 + 0.997793i \(0.478846\pi\)
\(840\) 2437.65 0.100127
\(841\) −24216.7 −0.992934
\(842\) 23067.9 0.944149
\(843\) 3310.55 0.135257
\(844\) −3421.72 −0.139550
\(845\) −2488.38 −0.101305
\(846\) −28955.4 −1.17672
\(847\) 37267.8 1.51185
\(848\) −53707.7 −2.17492
\(849\) 44631.5 1.80418
\(850\) −21036.7 −0.848887
\(851\) −10951.6 −0.441148
\(852\) −13119.5 −0.527545
\(853\) 12419.8 0.498530 0.249265 0.968435i \(-0.419811\pi\)
0.249265 + 0.968435i \(0.419811\pi\)
\(854\) −8992.01 −0.360305
\(855\) −2352.11 −0.0940823
\(856\) −11654.4 −0.465349
\(857\) 18592.3 0.741075 0.370537 0.928818i \(-0.379174\pi\)
0.370537 + 0.928818i \(0.379174\pi\)
\(858\) 28437.3 1.13151
\(859\) 6443.09 0.255920 0.127960 0.991779i \(-0.459157\pi\)
0.127960 + 0.991779i \(0.459157\pi\)
\(860\) −115.148 −0.00456573
\(861\) −27662.2 −1.09492
\(862\) 3009.78 0.118925
\(863\) −22085.1 −0.871132 −0.435566 0.900157i \(-0.643452\pi\)
−0.435566 + 0.900157i \(0.643452\pi\)
\(864\) −1271.22 −0.0500553
\(865\) −162.304 −0.00637979
\(866\) −10880.6 −0.426948
\(867\) −14302.3 −0.560245
\(868\) 4738.65 0.185300
\(869\) −40167.5 −1.56800
\(870\) −407.391 −0.0158757
\(871\) 2568.34 0.0999139
\(872\) −18037.5 −0.700491
\(873\) 24120.9 0.935131
\(874\) 6453.73 0.249772
\(875\) −4403.49 −0.170131
\(876\) 6453.57 0.248911
\(877\) 39786.3 1.53191 0.765956 0.642893i \(-0.222266\pi\)
0.765956 + 0.642893i \(0.222266\pi\)
\(878\) 29184.2 1.12177
\(879\) 41049.1 1.57514
\(880\) −6699.64 −0.256642
\(881\) 38834.0 1.48508 0.742538 0.669804i \(-0.233622\pi\)
0.742538 + 0.669804i \(0.233622\pi\)
\(882\) 13689.3 0.522611
\(883\) −5483.65 −0.208992 −0.104496 0.994525i \(-0.533323\pi\)
−0.104496 + 0.994525i \(0.533323\pi\)
\(884\) 2050.55 0.0780175
\(885\) 1141.99 0.0433756
\(886\) 12265.5 0.465088
\(887\) 21289.7 0.805905 0.402953 0.915221i \(-0.367984\pi\)
0.402953 + 0.915221i \(0.367984\pi\)
\(888\) −50817.5 −1.92041
\(889\) 10261.9 0.387148
\(890\) −2192.29 −0.0825681
\(891\) −50493.8 −1.89855
\(892\) 6184.17 0.232131
\(893\) −25369.2 −0.950671
\(894\) −36758.2 −1.37514
\(895\) 3507.50 0.130997
\(896\) −22703.0 −0.846488
\(897\) −4117.73 −0.153274
\(898\) 45495.3 1.69064
\(899\) 2434.41 0.0903140
\(900\) −6038.76 −0.223658
\(901\) −38320.4 −1.41691
\(902\) 60281.5 2.22523
\(903\) −4034.04 −0.148665
\(904\) 40194.0 1.47880
\(905\) 1949.13 0.0715927
\(906\) −31857.7 −1.16821
\(907\) 16875.4 0.617794 0.308897 0.951095i \(-0.400040\pi\)
0.308897 + 0.951095i \(0.400040\pi\)
\(908\) 4139.51 0.151293
\(909\) −37504.9 −1.36849
\(910\) 1080.79 0.0393711
\(911\) 17586.7 0.639597 0.319799 0.947486i \(-0.396385\pi\)
0.319799 + 0.947486i \(0.396385\pi\)
\(912\) 37768.4 1.37131
\(913\) −85354.4 −3.09400
\(914\) 5571.94 0.201645
\(915\) 2152.15 0.0777574
\(916\) 3003.77 0.108349
\(917\) 24381.0 0.878005
\(918\) −2496.11 −0.0897428
\(919\) −43891.7 −1.57547 −0.787733 0.616017i \(-0.788745\pi\)
−0.787733 + 0.616017i \(0.788745\pi\)
\(920\) 769.196 0.0275648
\(921\) −36826.1 −1.31755
\(922\) −24073.7 −0.859898
\(923\) 17880.8 0.637653
\(924\) 11931.7 0.424810
\(925\) 45555.6 1.61931
\(926\) 18794.5 0.666984
\(927\) 32779.9 1.16142
\(928\) 1142.16 0.0404024
\(929\) −41161.8 −1.45369 −0.726844 0.686803i \(-0.759013\pi\)
−0.726844 + 0.686803i \(0.759013\pi\)
\(930\) −5754.65 −0.202906
\(931\) 11993.9 0.422217
\(932\) 5890.79 0.207038
\(933\) −7556.08 −0.265139
\(934\) −484.175 −0.0169622
\(935\) −4780.18 −0.167197
\(936\) −9180.95 −0.320608
\(937\) 41754.1 1.45576 0.727880 0.685705i \(-0.240506\pi\)
0.727880 + 0.685705i \(0.240506\pi\)
\(938\) 5467.82 0.190331
\(939\) 30855.0 1.07233
\(940\) 983.633 0.0341304
\(941\) −37587.5 −1.30214 −0.651071 0.759016i \(-0.725680\pi\)
−0.651071 + 0.759016i \(0.725680\pi\)
\(942\) −66749.8 −2.30873
\(943\) −8728.76 −0.301429
\(944\) −8811.06 −0.303788
\(945\) −259.289 −0.00892559
\(946\) 8790.98 0.302135
\(947\) −25689.0 −0.881500 −0.440750 0.897630i \(-0.645287\pi\)
−0.440750 + 0.897630i \(0.645287\pi\)
\(948\) −8779.67 −0.300792
\(949\) −8795.66 −0.300863
\(950\) −26845.7 −0.916830
\(951\) 42750.5 1.45771
\(952\) −13419.4 −0.456853
\(953\) −10527.3 −0.357831 −0.178916 0.983864i \(-0.557259\pi\)
−0.178916 + 0.983864i \(0.557259\pi\)
\(954\) −55814.5 −1.89419
\(955\) 560.682 0.0189982
\(956\) 6718.44 0.227291
\(957\) 6129.75 0.207050
\(958\) 35777.2 1.20659
\(959\) −24207.9 −0.815136
\(960\) 3265.93 0.109799
\(961\) 4596.60 0.154295
\(962\) −22531.1 −0.755126
\(963\) −15275.1 −0.511144
\(964\) −8830.41 −0.295029
\(965\) −4239.15 −0.141413
\(966\) −8766.35 −0.291980
\(967\) 4292.71 0.142755 0.0713776 0.997449i \(-0.477260\pi\)
0.0713776 + 0.997449i \(0.477260\pi\)
\(968\) 54567.5 1.81184
\(969\) 26947.7 0.893380
\(970\) −4157.63 −0.137622
\(971\) −41459.8 −1.37025 −0.685123 0.728427i \(-0.740252\pi\)
−0.685123 + 0.728427i \(0.740252\pi\)
\(972\) −10262.1 −0.338638
\(973\) −36729.8 −1.21018
\(974\) 8983.13 0.295522
\(975\) 17128.6 0.562618
\(976\) −16605.1 −0.544585
\(977\) 3577.72 0.117156 0.0585779 0.998283i \(-0.481343\pi\)
0.0585779 + 0.998283i \(0.481343\pi\)
\(978\) 3782.36 0.123667
\(979\) 32985.9 1.07685
\(980\) −465.035 −0.0151582
\(981\) −23641.3 −0.769427
\(982\) 26344.2 0.856088
\(983\) 50532.3 1.63960 0.819802 0.572647i \(-0.194083\pi\)
0.819802 + 0.572647i \(0.194083\pi\)
\(984\) −40503.0 −1.31218
\(985\) 2673.87 0.0864939
\(986\) 2242.70 0.0724363
\(987\) 34460.0 1.11132
\(988\) 2616.77 0.0842618
\(989\) −1272.93 −0.0409271
\(990\) −6962.45 −0.223516
\(991\) 46280.6 1.48350 0.741752 0.670674i \(-0.233995\pi\)
0.741752 + 0.670674i \(0.233995\pi\)
\(992\) 16133.8 0.516379
\(993\) 3670.76 0.117309
\(994\) 38067.0 1.21470
\(995\) 622.101 0.0198210
\(996\) −18656.5 −0.593527
\(997\) 53334.8 1.69421 0.847107 0.531423i \(-0.178342\pi\)
0.847107 + 0.531423i \(0.178342\pi\)
\(998\) −55526.9 −1.76119
\(999\) 5405.39 0.171190
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 43.4.a.b.1.2 6
3.2 odd 2 387.4.a.h.1.5 6
4.3 odd 2 688.4.a.i.1.2 6
5.4 even 2 1075.4.a.b.1.5 6
7.6 odd 2 2107.4.a.c.1.2 6
43.42 odd 2 1849.4.a.c.1.5 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.4.a.b.1.2 6 1.1 even 1 trivial
387.4.a.h.1.5 6 3.2 odd 2
688.4.a.i.1.2 6 4.3 odd 2
1075.4.a.b.1.5 6 5.4 even 2
1849.4.a.c.1.5 6 43.42 odd 2
2107.4.a.c.1.2 6 7.6 odd 2