Properties

Label 8281.2.a.bh.1.2
Level $8281$
Weight $2$
Character 8281.1
Self dual yes
Analytic conductor $66.124$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 8281 = 7^{2} \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8281.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(66.1241179138\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.404.1
Defining polynomial: \(x^{3} - x^{2} - 5 x - 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 637)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-0.210756\) of defining polynomial
Character \(\chi\) \(=\) 8281.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.21076 q^{2} +1.74483 q^{3} -0.534070 q^{4} +2.21076 q^{5} +2.11256 q^{6} -3.06814 q^{8} +0.0444180 q^{9} +O(q^{10})\) \(q+1.21076 q^{2} +1.74483 q^{3} -0.534070 q^{4} +2.21076 q^{5} +2.11256 q^{6} -3.06814 q^{8} +0.0444180 q^{9} +2.67669 q^{10} +0.789244 q^{11} -0.931860 q^{12} +3.85738 q^{15} -2.64663 q^{16} +1.74483 q^{17} +0.0537794 q^{18} +4.32331 q^{19} -1.18070 q^{20} +0.955582 q^{22} -1.11256 q^{23} -5.35337 q^{24} -0.112558 q^{25} -5.15698 q^{27} -8.48965 q^{29} +4.67035 q^{30} +5.70041 q^{31} +2.93186 q^{32} +1.37709 q^{33} +2.11256 q^{34} -0.0237224 q^{36} -2.27890 q^{37} +5.23448 q^{38} -6.78291 q^{40} +12.1363 q^{41} +8.06814 q^{43} -0.421512 q^{44} +0.0981974 q^{45} -1.34704 q^{46} +8.74483 q^{47} -4.61791 q^{48} -0.136281 q^{50} +3.04442 q^{51} +7.95558 q^{53} -6.24384 q^{54} +1.74483 q^{55} +7.54343 q^{57} -10.2789 q^{58} +10.9556 q^{59} -2.06011 q^{60} +13.0681 q^{61} +6.90180 q^{62} +8.84302 q^{64} +1.66732 q^{66} -6.55779 q^{67} -0.931860 q^{68} -1.94122 q^{69} -5.85738 q^{71} -0.136281 q^{72} +8.00936 q^{73} -2.75919 q^{74} -0.196395 q^{75} -2.30895 q^{76} -6.91116 q^{79} -5.85105 q^{80} -9.13128 q^{81} +14.6941 q^{82} +3.14262 q^{83} +3.85738 q^{85} +9.76855 q^{86} -14.8130 q^{87} -2.42151 q^{88} +3.39145 q^{89} +0.118893 q^{90} +0.594184 q^{92} +9.94622 q^{93} +10.5878 q^{94} +9.55779 q^{95} +5.11559 q^{96} -0.0981974 q^{97} +0.0350567 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + 2 q^{2} - 4 q^{3} + 6 q^{4} + 5 q^{5} + 2 q^{6} + 6 q^{8} + 11 q^{9} + O(q^{10}) \) \( 3 q + 2 q^{2} - 4 q^{3} + 6 q^{4} + 5 q^{5} + 2 q^{6} + 6 q^{8} + 11 q^{9} + 14 q^{10} + 4 q^{11} - 18 q^{12} - 2 q^{15} + 4 q^{16} - 4 q^{17} - 8 q^{18} + 7 q^{19} + 16 q^{20} - 8 q^{22} + q^{23} - 28 q^{24} + 4 q^{25} - 22 q^{27} - 7 q^{29} - 24 q^{30} - 3 q^{31} + 24 q^{32} - 10 q^{33} + 2 q^{34} + 26 q^{36} + 10 q^{37} - 12 q^{38} + 22 q^{40} + 6 q^{41} + 9 q^{43} + 2 q^{44} + 3 q^{45} + 28 q^{46} + 17 q^{47} - 16 q^{48} + 30 q^{50} + 20 q^{51} + 13 q^{53} + 28 q^{54} - 4 q^{55} - 4 q^{57} - 14 q^{58} + 22 q^{59} - 42 q^{60} + 24 q^{61} + 18 q^{62} + 20 q^{64} + 30 q^{66} + 14 q^{67} - 18 q^{68} - 2 q^{69} - 4 q^{71} + 30 q^{72} + 5 q^{73} + 8 q^{74} - 6 q^{75} - 8 q^{76} + q^{79} + 40 q^{80} + 15 q^{81} - 20 q^{82} + 23 q^{83} - 2 q^{85} - 6 q^{86} - 20 q^{87} - 4 q^{88} - 11 q^{89} + 40 q^{90} + 30 q^{92} + 38 q^{93} + 16 q^{94} - 5 q^{95} - 52 q^{96} - 3 q^{97} + 30 q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.21076 0.856134 0.428067 0.903747i \(-0.359195\pi\)
0.428067 + 0.903747i \(0.359195\pi\)
\(3\) 1.74483 1.00738 0.503688 0.863886i \(-0.331976\pi\)
0.503688 + 0.863886i \(0.331976\pi\)
\(4\) −0.534070 −0.267035
\(5\) 2.21076 0.988680 0.494340 0.869269i \(-0.335410\pi\)
0.494340 + 0.869269i \(0.335410\pi\)
\(6\) 2.11256 0.862448
\(7\) 0 0
\(8\) −3.06814 −1.08475
\(9\) 0.0444180 0.0148060
\(10\) 2.67669 0.846442
\(11\) 0.789244 0.237966 0.118983 0.992896i \(-0.462037\pi\)
0.118983 + 0.992896i \(0.462037\pi\)
\(12\) −0.931860 −0.269005
\(13\) 0 0
\(14\) 0 0
\(15\) 3.85738 0.995972
\(16\) −2.64663 −0.661657
\(17\) 1.74483 0.423182 0.211591 0.977358i \(-0.432135\pi\)
0.211591 + 0.977358i \(0.432135\pi\)
\(18\) 0.0537794 0.0126759
\(19\) 4.32331 0.991836 0.495918 0.868369i \(-0.334832\pi\)
0.495918 + 0.868369i \(0.334832\pi\)
\(20\) −1.18070 −0.264012
\(21\) 0 0
\(22\) 0.955582 0.203731
\(23\) −1.11256 −0.231984 −0.115992 0.993250i \(-0.537005\pi\)
−0.115992 + 0.993250i \(0.537005\pi\)
\(24\) −5.35337 −1.09275
\(25\) −0.112558 −0.0225117
\(26\) 0 0
\(27\) −5.15698 −0.992461
\(28\) 0 0
\(29\) −8.48965 −1.57649 −0.788244 0.615362i \(-0.789010\pi\)
−0.788244 + 0.615362i \(0.789010\pi\)
\(30\) 4.67035 0.852686
\(31\) 5.70041 1.02382 0.511912 0.859038i \(-0.328937\pi\)
0.511912 + 0.859038i \(0.328937\pi\)
\(32\) 2.93186 0.518284
\(33\) 1.37709 0.239721
\(34\) 2.11256 0.362301
\(35\) 0 0
\(36\) −0.0237224 −0.00395373
\(37\) −2.27890 −0.374648 −0.187324 0.982298i \(-0.559981\pi\)
−0.187324 + 0.982298i \(0.559981\pi\)
\(38\) 5.23448 0.849144
\(39\) 0 0
\(40\) −6.78291 −1.07247
\(41\) 12.1363 1.89537 0.947684 0.319209i \(-0.103417\pi\)
0.947684 + 0.319209i \(0.103417\pi\)
\(42\) 0 0
\(43\) 8.06814 1.23038 0.615190 0.788379i \(-0.289079\pi\)
0.615190 + 0.788379i \(0.289079\pi\)
\(44\) −0.421512 −0.0635453
\(45\) 0.0981974 0.0146384
\(46\) −1.34704 −0.198610
\(47\) 8.74483 1.27556 0.637782 0.770217i \(-0.279852\pi\)
0.637782 + 0.770217i \(0.279852\pi\)
\(48\) −4.61791 −0.666537
\(49\) 0 0
\(50\) −0.136281 −0.0192730
\(51\) 3.04442 0.426304
\(52\) 0 0
\(53\) 7.95558 1.09278 0.546392 0.837530i \(-0.316001\pi\)
0.546392 + 0.837530i \(0.316001\pi\)
\(54\) −6.24384 −0.849679
\(55\) 1.74483 0.235272
\(56\) 0 0
\(57\) 7.54343 0.999152
\(58\) −10.2789 −1.34969
\(59\) 10.9556 1.42630 0.713148 0.701014i \(-0.247269\pi\)
0.713148 + 0.701014i \(0.247269\pi\)
\(60\) −2.06011 −0.265960
\(61\) 13.0681 1.67320 0.836602 0.547811i \(-0.184539\pi\)
0.836602 + 0.547811i \(0.184539\pi\)
\(62\) 6.90180 0.876530
\(63\) 0 0
\(64\) 8.84302 1.10538
\(65\) 0 0
\(66\) 1.66732 0.205233
\(67\) −6.55779 −0.801162 −0.400581 0.916261i \(-0.631192\pi\)
−0.400581 + 0.916261i \(0.631192\pi\)
\(68\) −0.931860 −0.113005
\(69\) −1.94122 −0.233696
\(70\) 0 0
\(71\) −5.85738 −0.695144 −0.347572 0.937653i \(-0.612994\pi\)
−0.347572 + 0.937653i \(0.612994\pi\)
\(72\) −0.136281 −0.0160608
\(73\) 8.00936 0.937425 0.468712 0.883351i \(-0.344718\pi\)
0.468712 + 0.883351i \(0.344718\pi\)
\(74\) −2.75919 −0.320749
\(75\) −0.196395 −0.0226777
\(76\) −2.30895 −0.264855
\(77\) 0 0
\(78\) 0 0
\(79\) −6.91116 −0.777567 −0.388783 0.921329i \(-0.627105\pi\)
−0.388783 + 0.921329i \(0.627105\pi\)
\(80\) −5.85105 −0.654167
\(81\) −9.13128 −1.01459
\(82\) 14.6941 1.62269
\(83\) 3.14262 0.344947 0.172473 0.985014i \(-0.444824\pi\)
0.172473 + 0.985014i \(0.444824\pi\)
\(84\) 0 0
\(85\) 3.85738 0.418392
\(86\) 9.76855 1.05337
\(87\) −14.8130 −1.58812
\(88\) −2.42151 −0.258134
\(89\) 3.39145 0.359493 0.179747 0.983713i \(-0.442472\pi\)
0.179747 + 0.983713i \(0.442472\pi\)
\(90\) 0.118893 0.0125324
\(91\) 0 0
\(92\) 0.594184 0.0619480
\(93\) 9.94622 1.03138
\(94\) 10.5878 1.09205
\(95\) 9.55779 0.980609
\(96\) 5.11559 0.522107
\(97\) −0.0981974 −0.00997044 −0.00498522 0.999988i \(-0.501587\pi\)
−0.00498522 + 0.999988i \(0.501587\pi\)
\(98\) 0 0
\(99\) 0.0350567 0.00352333
\(100\) 0.0601141 0.00601141
\(101\) −6.90180 −0.686755 −0.343378 0.939197i \(-0.611571\pi\)
−0.343378 + 0.939197i \(0.611571\pi\)
\(102\) 3.68605 0.364973
\(103\) 15.8223 1.55902 0.779510 0.626390i \(-0.215468\pi\)
0.779510 + 0.626390i \(0.215468\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 9.63227 0.935569
\(107\) −2.02372 −0.195641 −0.0978203 0.995204i \(-0.531187\pi\)
−0.0978203 + 0.995204i \(0.531187\pi\)
\(108\) 2.75419 0.265022
\(109\) 17.3470 1.66154 0.830772 0.556612i \(-0.187899\pi\)
0.830772 + 0.556612i \(0.187899\pi\)
\(110\) 2.11256 0.201425
\(111\) −3.97628 −0.377412
\(112\) 0 0
\(113\) 10.1807 0.957720 0.478860 0.877891i \(-0.341050\pi\)
0.478860 + 0.877891i \(0.341050\pi\)
\(114\) 9.13325 0.855408
\(115\) −2.45960 −0.229358
\(116\) 4.53407 0.420978
\(117\) 0 0
\(118\) 13.2645 1.22110
\(119\) 0 0
\(120\) −11.8350 −1.08038
\(121\) −10.3771 −0.943372
\(122\) 15.8223 1.43249
\(123\) 21.1757 1.90935
\(124\) −3.04442 −0.273397
\(125\) −11.3026 −1.01094
\(126\) 0 0
\(127\) 16.4452 1.45928 0.729639 0.683832i \(-0.239688\pi\)
0.729639 + 0.683832i \(0.239688\pi\)
\(128\) 4.84302 0.428067
\(129\) 14.0775 1.23945
\(130\) 0 0
\(131\) −12.3327 −1.07751 −0.538755 0.842462i \(-0.681105\pi\)
−0.538755 + 0.842462i \(0.681105\pi\)
\(132\) −0.735465 −0.0640140
\(133\) 0 0
\(134\) −7.93989 −0.685902
\(135\) −11.4008 −0.981226
\(136\) −5.35337 −0.459048
\(137\) 3.34704 0.285957 0.142978 0.989726i \(-0.454332\pi\)
0.142978 + 0.989726i \(0.454332\pi\)
\(138\) −2.35034 −0.200075
\(139\) 6.16634 0.523022 0.261511 0.965201i \(-0.415779\pi\)
0.261511 + 0.965201i \(0.415779\pi\)
\(140\) 0 0
\(141\) 15.2582 1.28497
\(142\) −7.09186 −0.595136
\(143\) 0 0
\(144\) −0.117558 −0.00979651
\(145\) −18.7685 −1.55864
\(146\) 9.69738 0.802561
\(147\) 0 0
\(148\) 1.21709 0.100044
\(149\) −18.8367 −1.54316 −0.771581 0.636131i \(-0.780534\pi\)
−0.771581 + 0.636131i \(0.780534\pi\)
\(150\) −0.237786 −0.0194152
\(151\) −20.1901 −1.64304 −0.821522 0.570177i \(-0.806875\pi\)
−0.821522 + 0.570177i \(0.806875\pi\)
\(152\) −13.2645 −1.07590
\(153\) 0.0775018 0.00626565
\(154\) 0 0
\(155\) 12.6022 1.01223
\(156\) 0 0
\(157\) −13.8811 −1.10783 −0.553916 0.832572i \(-0.686867\pi\)
−0.553916 + 0.832572i \(0.686867\pi\)
\(158\) −8.36773 −0.665701
\(159\) 13.8811 1.10084
\(160\) 6.48163 0.512418
\(161\) 0 0
\(162\) −11.0558 −0.868622
\(163\) −11.4897 −0.899939 −0.449970 0.893044i \(-0.648565\pi\)
−0.449970 + 0.893044i \(0.648565\pi\)
\(164\) −6.48163 −0.506130
\(165\) 3.04442 0.237008
\(166\) 3.80494 0.295321
\(167\) −12.9699 −1.00364 −0.501822 0.864971i \(-0.667337\pi\)
−0.501822 + 0.864971i \(0.667337\pi\)
\(168\) 0 0
\(169\) 0 0
\(170\) 4.67035 0.358200
\(171\) 0.192033 0.0146851
\(172\) −4.30895 −0.328555
\(173\) −2.48029 −0.188573 −0.0942865 0.995545i \(-0.530057\pi\)
−0.0942865 + 0.995545i \(0.530057\pi\)
\(174\) −17.9349 −1.35964
\(175\) 0 0
\(176\) −2.08884 −0.157452
\(177\) 19.1156 1.43682
\(178\) 4.10622 0.307774
\(179\) −8.15698 −0.609681 −0.304841 0.952403i \(-0.598603\pi\)
−0.304841 + 0.952403i \(0.598603\pi\)
\(180\) −0.0524443 −0.00390897
\(181\) −3.60855 −0.268221 −0.134111 0.990966i \(-0.542818\pi\)
−0.134111 + 0.990966i \(0.542818\pi\)
\(182\) 0 0
\(183\) 22.8016 1.68555
\(184\) 3.41349 0.251645
\(185\) −5.03808 −0.370407
\(186\) 12.0424 0.882995
\(187\) 1.37709 0.100703
\(188\) −4.67035 −0.340620
\(189\) 0 0
\(190\) 11.5722 0.839532
\(191\) 0.337675 0.0244333 0.0122167 0.999925i \(-0.496111\pi\)
0.0122167 + 0.999925i \(0.496111\pi\)
\(192\) 15.4295 1.11353
\(193\) −8.42151 −0.606194 −0.303097 0.952960i \(-0.598021\pi\)
−0.303097 + 0.952960i \(0.598021\pi\)
\(194\) −0.118893 −0.00853603
\(195\) 0 0
\(196\) 0 0
\(197\) 8.51035 0.606337 0.303169 0.952937i \(-0.401955\pi\)
0.303169 + 0.952937i \(0.401955\pi\)
\(198\) 0.0424451 0.00301644
\(199\) 14.6166 1.03614 0.518071 0.855338i \(-0.326650\pi\)
0.518071 + 0.855338i \(0.326650\pi\)
\(200\) 0.345345 0.0244196
\(201\) −11.4422 −0.807071
\(202\) −8.35640 −0.587954
\(203\) 0 0
\(204\) −1.62593 −0.113838
\(205\) 26.8304 1.87391
\(206\) 19.1570 1.33473
\(207\) −0.0494177 −0.00343477
\(208\) 0 0
\(209\) 3.41215 0.236023
\(210\) 0 0
\(211\) −23.8667 −1.64305 −0.821527 0.570169i \(-0.806878\pi\)
−0.821527 + 0.570169i \(0.806878\pi\)
\(212\) −4.24884 −0.291811
\(213\) −10.2201 −0.700271
\(214\) −2.45023 −0.167495
\(215\) 17.8367 1.21645
\(216\) 15.8223 1.07657
\(217\) 0 0
\(218\) 21.0030 1.42250
\(219\) 13.9749 0.944339
\(220\) −0.931860 −0.0628260
\(221\) 0 0
\(222\) −4.81430 −0.323115
\(223\) 1.27890 0.0856412 0.0428206 0.999083i \(-0.486366\pi\)
0.0428206 + 0.999083i \(0.486366\pi\)
\(224\) 0 0
\(225\) −0.00499963 −0.000333308 0
\(226\) 12.3263 0.819936
\(227\) 9.57849 0.635747 0.317873 0.948133i \(-0.397031\pi\)
0.317873 + 0.948133i \(0.397031\pi\)
\(228\) −4.02872 −0.266809
\(229\) −13.5134 −0.892989 −0.446494 0.894786i \(-0.647328\pi\)
−0.446494 + 0.894786i \(0.647328\pi\)
\(230\) −2.97797 −0.196361
\(231\) 0 0
\(232\) 26.0474 1.71010
\(233\) 28.9586 1.89714 0.948571 0.316565i \(-0.102530\pi\)
0.948571 + 0.316565i \(0.102530\pi\)
\(234\) 0 0
\(235\) 19.3327 1.26112
\(236\) −5.85105 −0.380871
\(237\) −12.0588 −0.783302
\(238\) 0 0
\(239\) 24.1363 1.56125 0.780623 0.625002i \(-0.214902\pi\)
0.780623 + 0.625002i \(0.214902\pi\)
\(240\) −10.2091 −0.658992
\(241\) −9.92552 −0.639359 −0.319680 0.947526i \(-0.603575\pi\)
−0.319680 + 0.947526i \(0.603575\pi\)
\(242\) −12.5641 −0.807653
\(243\) −0.461568 −0.0296096
\(244\) −6.97930 −0.446804
\(245\) 0 0
\(246\) 25.6386 1.63466
\(247\) 0 0
\(248\) −17.4897 −1.11059
\(249\) 5.48332 0.347491
\(250\) −13.6847 −0.865497
\(251\) −18.4990 −1.16765 −0.583824 0.811880i \(-0.698444\pi\)
−0.583824 + 0.811880i \(0.698444\pi\)
\(252\) 0 0
\(253\) −0.878080 −0.0552044
\(254\) 19.9112 1.24934
\(255\) 6.73047 0.421478
\(256\) −11.8223 −0.738895
\(257\) −16.6767 −1.04026 −0.520132 0.854086i \(-0.674117\pi\)
−0.520132 + 0.854086i \(0.674117\pi\)
\(258\) 17.0444 1.06114
\(259\) 0 0
\(260\) 0 0
\(261\) −0.377094 −0.0233415
\(262\) −14.9319 −0.922493
\(263\) −13.4690 −0.830531 −0.415266 0.909700i \(-0.636311\pi\)
−0.415266 + 0.909700i \(0.636311\pi\)
\(264\) −4.22512 −0.260038
\(265\) 17.5878 1.08041
\(266\) 0 0
\(267\) 5.91750 0.362145
\(268\) 3.50232 0.213938
\(269\) 30.5578 1.86314 0.931571 0.363560i \(-0.118439\pi\)
0.931571 + 0.363560i \(0.118439\pi\)
\(270\) −13.8036 −0.840061
\(271\) 4.22512 0.256658 0.128329 0.991732i \(-0.459039\pi\)
0.128329 + 0.991732i \(0.459039\pi\)
\(272\) −4.61791 −0.280002
\(273\) 0 0
\(274\) 4.05244 0.244817
\(275\) −0.0888361 −0.00535702
\(276\) 1.03675 0.0624049
\(277\) −3.00000 −0.180253 −0.0901263 0.995930i \(-0.528727\pi\)
−0.0901263 + 0.995930i \(0.528727\pi\)
\(278\) 7.46593 0.447777
\(279\) 0.253201 0.0151587
\(280\) 0 0
\(281\) 6.27890 0.374568 0.187284 0.982306i \(-0.440032\pi\)
0.187284 + 0.982306i \(0.440032\pi\)
\(282\) 18.4740 1.10011
\(283\) −23.5371 −1.39914 −0.699568 0.714566i \(-0.746624\pi\)
−0.699568 + 0.714566i \(0.746624\pi\)
\(284\) 3.12825 0.185628
\(285\) 16.6767 0.987842
\(286\) 0 0
\(287\) 0 0
\(288\) 0.130227 0.00767373
\(289\) −13.9556 −0.820917
\(290\) −22.7241 −1.33441
\(291\) −0.171337 −0.0100440
\(292\) −4.27756 −0.250325
\(293\) 21.6166 1.26285 0.631427 0.775435i \(-0.282470\pi\)
0.631427 + 0.775435i \(0.282470\pi\)
\(294\) 0 0
\(295\) 24.2201 1.41015
\(296\) 6.99197 0.406400
\(297\) −4.07011 −0.236172
\(298\) −22.8066 −1.32115
\(299\) 0 0
\(300\) 0.104889 0.00605575
\(301\) 0 0
\(302\) −24.4452 −1.40667
\(303\) −12.0424 −0.691820
\(304\) −11.4422 −0.656256
\(305\) 28.8905 1.65426
\(306\) 0.0938357 0.00536423
\(307\) −20.3945 −1.16397 −0.581987 0.813198i \(-0.697725\pi\)
−0.581987 + 0.813198i \(0.697725\pi\)
\(308\) 0 0
\(309\) 27.6072 1.57052
\(310\) 15.2582 0.866608
\(311\) −12.9492 −0.734284 −0.367142 0.930165i \(-0.619664\pi\)
−0.367142 + 0.930165i \(0.619664\pi\)
\(312\) 0 0
\(313\) 33.2345 1.87852 0.939262 0.343201i \(-0.111511\pi\)
0.939262 + 0.343201i \(0.111511\pi\)
\(314\) −16.8066 −0.948453
\(315\) 0 0
\(316\) 3.69105 0.207638
\(317\) 4.87175 0.273624 0.136812 0.990597i \(-0.456314\pi\)
0.136812 + 0.990597i \(0.456314\pi\)
\(318\) 16.8066 0.942469
\(319\) −6.70041 −0.375151
\(320\) 19.5498 1.09287
\(321\) −3.53104 −0.197084
\(322\) 0 0
\(323\) 7.54343 0.419728
\(324\) 4.87675 0.270930
\(325\) 0 0
\(326\) −13.9112 −0.770468
\(327\) 30.2676 1.67380
\(328\) −37.2358 −2.05600
\(329\) 0 0
\(330\) 3.68605 0.202910
\(331\) −6.87175 −0.377705 −0.188853 0.982005i \(-0.560477\pi\)
−0.188853 + 0.982005i \(0.560477\pi\)
\(332\) −1.67838 −0.0921129
\(333\) −0.101224 −0.00554705
\(334\) −15.7034 −0.859254
\(335\) −14.4977 −0.792093
\(336\) 0 0
\(337\) 11.0712 0.603085 0.301542 0.953453i \(-0.402499\pi\)
0.301542 + 0.953453i \(0.402499\pi\)
\(338\) 0 0
\(339\) 17.7635 0.964784
\(340\) −2.06011 −0.111725
\(341\) 4.49901 0.243635
\(342\) 0.232505 0.0125724
\(343\) 0 0
\(344\) −24.7542 −1.33466
\(345\) −4.29157 −0.231050
\(346\) −3.00303 −0.161444
\(347\) 5.62593 0.302016 0.151008 0.988533i \(-0.451748\pi\)
0.151008 + 0.988533i \(0.451748\pi\)
\(348\) 7.91116 0.424083
\(349\) 18.4783 0.989122 0.494561 0.869143i \(-0.335329\pi\)
0.494561 + 0.869143i \(0.335329\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 2.31395 0.123334
\(353\) 4.67035 0.248578 0.124289 0.992246i \(-0.460335\pi\)
0.124289 + 0.992246i \(0.460335\pi\)
\(354\) 23.1443 1.23011
\(355\) −12.9492 −0.687275
\(356\) −1.81127 −0.0959974
\(357\) 0 0
\(358\) −9.87611 −0.521968
\(359\) 11.7211 0.618616 0.309308 0.950962i \(-0.399903\pi\)
0.309308 + 0.950962i \(0.399903\pi\)
\(360\) −0.301284 −0.0158790
\(361\) −0.308953 −0.0162607
\(362\) −4.36907 −0.229633
\(363\) −18.1062 −0.950330
\(364\) 0 0
\(365\) 17.7067 0.926813
\(366\) 27.6072 1.44305
\(367\) −19.9699 −1.04242 −0.521211 0.853428i \(-0.674520\pi\)
−0.521211 + 0.853428i \(0.674520\pi\)
\(368\) 2.94453 0.153494
\(369\) 0.539070 0.0280629
\(370\) −6.09989 −0.317118
\(371\) 0 0
\(372\) −5.31198 −0.275413
\(373\) −4.42651 −0.229196 −0.114598 0.993412i \(-0.536558\pi\)
−0.114598 + 0.993412i \(0.536558\pi\)
\(374\) 1.66732 0.0862153
\(375\) −19.7211 −1.01839
\(376\) −26.8304 −1.38367
\(377\) 0 0
\(378\) 0 0
\(379\) 32.5702 1.67302 0.836509 0.547953i \(-0.184593\pi\)
0.836509 + 0.547953i \(0.184593\pi\)
\(380\) −5.10453 −0.261857
\(381\) 28.6941 1.47004
\(382\) 0.408842 0.0209182
\(383\) 14.1964 0.725402 0.362701 0.931906i \(-0.381855\pi\)
0.362701 + 0.931906i \(0.381855\pi\)
\(384\) 8.45023 0.431224
\(385\) 0 0
\(386\) −10.1964 −0.518983
\(387\) 0.358371 0.0182170
\(388\) 0.0524443 0.00266246
\(389\) 17.3170 0.878006 0.439003 0.898486i \(-0.355332\pi\)
0.439003 + 0.898486i \(0.355332\pi\)
\(390\) 0 0
\(391\) −1.94122 −0.0981718
\(392\) 0 0
\(393\) −21.5184 −1.08546
\(394\) 10.3040 0.519106
\(395\) −15.2789 −0.768765
\(396\) −0.0187227 −0.000940852 0
\(397\) 15.7241 0.789171 0.394586 0.918859i \(-0.370888\pi\)
0.394586 + 0.918859i \(0.370888\pi\)
\(398\) 17.6971 0.887075
\(399\) 0 0
\(400\) 0.297900 0.0148950
\(401\) −3.57849 −0.178701 −0.0893506 0.996000i \(-0.528479\pi\)
−0.0893506 + 0.996000i \(0.528479\pi\)
\(402\) −13.8537 −0.690961
\(403\) 0 0
\(404\) 3.68605 0.183388
\(405\) −20.1870 −1.00310
\(406\) 0 0
\(407\) −1.79861 −0.0891536
\(408\) −9.34070 −0.462434
\(409\) −31.3501 −1.55016 −0.775080 0.631863i \(-0.782291\pi\)
−0.775080 + 0.631863i \(0.782291\pi\)
\(410\) 32.4850 1.60432
\(411\) 5.84000 0.288066
\(412\) −8.45023 −0.416313
\(413\) 0 0
\(414\) −0.0598327 −0.00294062
\(415\) 6.94756 0.341042
\(416\) 0 0
\(417\) 10.7592 0.526880
\(418\) 4.13128 0.202068
\(419\) 28.7716 1.40558 0.702792 0.711396i \(-0.251937\pi\)
0.702792 + 0.711396i \(0.251937\pi\)
\(420\) 0 0
\(421\) 0.190060 0.00926297 0.00463148 0.999989i \(-0.498526\pi\)
0.00463148 + 0.999989i \(0.498526\pi\)
\(422\) −28.8968 −1.40667
\(423\) 0.388428 0.0188860
\(424\) −24.4088 −1.18540
\(425\) −0.196395 −0.00952655
\(426\) −12.3741 −0.599526
\(427\) 0 0
\(428\) 1.08081 0.0522429
\(429\) 0 0
\(430\) 21.5959 1.04145
\(431\) −25.6734 −1.23664 −0.618322 0.785925i \(-0.712187\pi\)
−0.618322 + 0.785925i \(0.712187\pi\)
\(432\) 13.6486 0.656669
\(433\) −1.82233 −0.0875755 −0.0437877 0.999041i \(-0.513943\pi\)
−0.0437877 + 0.999041i \(0.513943\pi\)
\(434\) 0 0
\(435\) −32.7479 −1.57014
\(436\) −9.26454 −0.443691
\(437\) −4.80994 −0.230091
\(438\) 16.9202 0.808481
\(439\) −0.735465 −0.0351018 −0.0175509 0.999846i \(-0.505587\pi\)
−0.0175509 + 0.999846i \(0.505587\pi\)
\(440\) −5.35337 −0.255212
\(441\) 0 0
\(442\) 0 0
\(443\) −3.71174 −0.176350 −0.0881751 0.996105i \(-0.528104\pi\)
−0.0881751 + 0.996105i \(0.528104\pi\)
\(444\) 2.12361 0.100782
\(445\) 7.49768 0.355424
\(446\) 1.54843 0.0733203
\(447\) −32.8667 −1.55454
\(448\) 0 0
\(449\) 5.17570 0.244256 0.122128 0.992514i \(-0.461028\pi\)
0.122128 + 0.992514i \(0.461028\pi\)
\(450\) −0.00605333 −0.000285357 0
\(451\) 9.57849 0.451033
\(452\) −5.43721 −0.255745
\(453\) −35.2281 −1.65516
\(454\) 11.5972 0.544284
\(455\) 0 0
\(456\) −23.1443 −1.08383
\(457\) 34.1299 1.59653 0.798266 0.602305i \(-0.205751\pi\)
0.798266 + 0.602305i \(0.205751\pi\)
\(458\) −16.3614 −0.764518
\(459\) −8.99803 −0.419992
\(460\) 1.31360 0.0612467
\(461\) −11.4008 −0.530989 −0.265494 0.964112i \(-0.585535\pi\)
−0.265494 + 0.964112i \(0.585535\pi\)
\(462\) 0 0
\(463\) 30.0124 1.39479 0.697397 0.716685i \(-0.254341\pi\)
0.697397 + 0.716685i \(0.254341\pi\)
\(464\) 22.4690 1.04310
\(465\) 21.9887 1.01970
\(466\) 35.0618 1.62421
\(467\) −34.1663 −1.58103 −0.790515 0.612443i \(-0.790187\pi\)
−0.790515 + 0.612443i \(0.790187\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 23.4072 1.07969
\(471\) −24.2201 −1.11600
\(472\) −33.6133 −1.54718
\(473\) 6.36773 0.292789
\(474\) −14.6002 −0.670611
\(475\) −0.486625 −0.0223279
\(476\) 0 0
\(477\) 0.353371 0.0161798
\(478\) 29.2231 1.33664
\(479\) −12.8761 −0.588324 −0.294162 0.955756i \(-0.595041\pi\)
−0.294162 + 0.955756i \(0.595041\pi\)
\(480\) 11.3093 0.516197
\(481\) 0 0
\(482\) −12.0174 −0.547377
\(483\) 0 0
\(484\) 5.54210 0.251913
\(485\) −0.217091 −0.00985758
\(486\) −0.558846 −0.0253498
\(487\) 21.9399 0.994191 0.497096 0.867696i \(-0.334400\pi\)
0.497096 + 0.867696i \(0.334400\pi\)
\(488\) −40.0949 −1.81501
\(489\) −20.0474 −0.906577
\(490\) 0 0
\(491\) 4.11256 0.185597 0.0927986 0.995685i \(-0.470419\pi\)
0.0927986 + 0.995685i \(0.470419\pi\)
\(492\) −11.3093 −0.509863
\(493\) −14.8130 −0.667142
\(494\) 0 0
\(495\) 0.0775018 0.00348344
\(496\) −15.0869 −0.677420
\(497\) 0 0
\(498\) 6.63896 0.297499
\(499\) −19.0331 −0.852038 −0.426019 0.904714i \(-0.640084\pi\)
−0.426019 + 0.904714i \(0.640084\pi\)
\(500\) 6.03639 0.269956
\(501\) −22.6303 −1.01105
\(502\) −22.3978 −0.999662
\(503\) 35.8698 1.59935 0.799677 0.600430i \(-0.205004\pi\)
0.799677 + 0.600430i \(0.205004\pi\)
\(504\) 0 0
\(505\) −15.2582 −0.678981
\(506\) −1.06314 −0.0472624
\(507\) 0 0
\(508\) −8.78291 −0.389679
\(509\) 17.5465 0.777733 0.388867 0.921294i \(-0.372867\pi\)
0.388867 + 0.921294i \(0.372867\pi\)
\(510\) 8.14895 0.360842
\(511\) 0 0
\(512\) −24.0000 −1.06066
\(513\) −22.2952 −0.984358
\(514\) −20.1914 −0.890604
\(515\) 34.9793 1.54137
\(516\) −7.51837 −0.330978
\(517\) 6.90180 0.303541
\(518\) 0 0
\(519\) −4.32768 −0.189964
\(520\) 0 0
\(521\) 8.84302 0.387420 0.193710 0.981059i \(-0.437948\pi\)
0.193710 + 0.981059i \(0.437948\pi\)
\(522\) −0.456568 −0.0199835
\(523\) −21.9112 −0.958108 −0.479054 0.877785i \(-0.659020\pi\)
−0.479054 + 0.877785i \(0.659020\pi\)
\(524\) 6.58651 0.287733
\(525\) 0 0
\(526\) −16.3076 −0.711046
\(527\) 9.94622 0.433264
\(528\) −3.64466 −0.158613
\(529\) −21.7622 −0.946183
\(530\) 21.2946 0.924978
\(531\) 0.486625 0.0211177
\(532\) 0 0
\(533\) 0 0
\(534\) 7.16465 0.310045
\(535\) −4.47396 −0.193426
\(536\) 20.1202 0.869061
\(537\) −14.2325 −0.614178
\(538\) 36.9980 1.59510
\(539\) 0 0
\(540\) 6.08884 0.262022
\(541\) −22.8654 −0.983061 −0.491530 0.870860i \(-0.663562\pi\)
−0.491530 + 0.870860i \(0.663562\pi\)
\(542\) 5.11559 0.219733
\(543\) −6.29628 −0.270199
\(544\) 5.11559 0.219329
\(545\) 38.3501 1.64274
\(546\) 0 0
\(547\) −35.2676 −1.50793 −0.753966 0.656913i \(-0.771862\pi\)
−0.753966 + 0.656913i \(0.771862\pi\)
\(548\) −1.78755 −0.0763605
\(549\) 0.580461 0.0247735
\(550\) −0.107559 −0.00458632
\(551\) −36.7034 −1.56362
\(552\) 5.95594 0.253502
\(553\) 0 0
\(554\) −3.63227 −0.154320
\(555\) −8.79058 −0.373139
\(556\) −3.29326 −0.139665
\(557\) −39.8698 −1.68934 −0.844668 0.535290i \(-0.820202\pi\)
−0.844668 + 0.535290i \(0.820202\pi\)
\(558\) 0.306565 0.0129779
\(559\) 0 0
\(560\) 0 0
\(561\) 2.40279 0.101446
\(562\) 7.60221 0.320680
\(563\) −25.5972 −1.07879 −0.539397 0.842052i \(-0.681348\pi\)
−0.539397 + 0.842052i \(0.681348\pi\)
\(564\) −8.14895 −0.343133
\(565\) 22.5070 0.946878
\(566\) −28.4977 −1.19785
\(567\) 0 0
\(568\) 17.9713 0.754058
\(569\) −25.0949 −1.05203 −0.526016 0.850475i \(-0.676315\pi\)
−0.526016 + 0.850475i \(0.676315\pi\)
\(570\) 20.1914 0.845724
\(571\) −31.2488 −1.30772 −0.653862 0.756614i \(-0.726852\pi\)
−0.653862 + 0.756614i \(0.726852\pi\)
\(572\) 0 0
\(573\) 0.589185 0.0246135
\(574\) 0 0
\(575\) 0.125228 0.00522236
\(576\) 0.392790 0.0163662
\(577\) −12.8717 −0.535858 −0.267929 0.963439i \(-0.586339\pi\)
−0.267929 + 0.963439i \(0.586339\pi\)
\(578\) −16.8968 −0.702814
\(579\) −14.6941 −0.610665
\(580\) 10.0237 0.416212
\(581\) 0 0
\(582\) −0.207448 −0.00859899
\(583\) 6.27890 0.260045
\(584\) −24.5738 −1.01687
\(585\) 0 0
\(586\) 26.1724 1.08117
\(587\) 9.96692 0.411379 0.205689 0.978617i \(-0.434056\pi\)
0.205689 + 0.978617i \(0.434056\pi\)
\(588\) 0 0
\(589\) 24.6447 1.01547
\(590\) 29.3246 1.20728
\(591\) 14.8491 0.610809
\(592\) 6.03139 0.247889
\(593\) −20.5909 −0.845566 −0.422783 0.906231i \(-0.638947\pi\)
−0.422783 + 0.906231i \(0.638947\pi\)
\(594\) −4.92791 −0.202195
\(595\) 0 0
\(596\) 10.0601 0.412078
\(597\) 25.5034 1.04378
\(598\) 0 0
\(599\) −12.5371 −0.512252 −0.256126 0.966643i \(-0.582446\pi\)
−0.256126 + 0.966643i \(0.582446\pi\)
\(600\) 0.602567 0.0245997
\(601\) −1.82233 −0.0743343 −0.0371672 0.999309i \(-0.511833\pi\)
−0.0371672 + 0.999309i \(0.511833\pi\)
\(602\) 0 0
\(603\) −0.291284 −0.0118620
\(604\) 10.7829 0.438750
\(605\) −22.9412 −0.932693
\(606\) −14.5805 −0.592291
\(607\) 30.9780 1.25736 0.628678 0.777665i \(-0.283596\pi\)
0.628678 + 0.777665i \(0.283596\pi\)
\(608\) 12.6754 0.514053
\(609\) 0 0
\(610\) 34.9793 1.41627
\(611\) 0 0
\(612\) −0.0413914 −0.00167315
\(613\) −12.4502 −0.502860 −0.251430 0.967875i \(-0.580901\pi\)
−0.251430 + 0.967875i \(0.580901\pi\)
\(614\) −24.6927 −0.996518
\(615\) 46.8143 1.88773
\(616\) 0 0
\(617\) −31.7809 −1.27945 −0.639726 0.768603i \(-0.720952\pi\)
−0.639726 + 0.768603i \(0.720952\pi\)
\(618\) 33.4256 1.34457
\(619\) −4.22512 −0.169822 −0.0849109 0.996389i \(-0.527061\pi\)
−0.0849109 + 0.996389i \(0.527061\pi\)
\(620\) −6.73047 −0.270302
\(621\) 5.73744 0.230235
\(622\) −15.6784 −0.628646
\(623\) 0 0
\(624\) 0 0
\(625\) −24.4245 −0.976982
\(626\) 40.2388 1.60827
\(627\) 5.95361 0.237764
\(628\) 7.41349 0.295830
\(629\) −3.97628 −0.158545
\(630\) 0 0
\(631\) −7.31198 −0.291085 −0.145543 0.989352i \(-0.546493\pi\)
−0.145543 + 0.989352i \(0.546493\pi\)
\(632\) 21.2044 0.843467
\(633\) −41.6433 −1.65517
\(634\) 5.89849 0.234259
\(635\) 36.3564 1.44276
\(636\) −7.41349 −0.293964
\(637\) 0 0
\(638\) −8.11256 −0.321179
\(639\) −0.260174 −0.0102923
\(640\) 10.7067 0.423221
\(641\) −23.0474 −0.910319 −0.455160 0.890410i \(-0.650418\pi\)
−0.455160 + 0.890410i \(0.650418\pi\)
\(642\) −4.27523 −0.168730
\(643\) 48.9379 1.92992 0.964961 0.262392i \(-0.0845113\pi\)
0.964961 + 0.262392i \(0.0845113\pi\)
\(644\) 0 0
\(645\) 31.1219 1.22542
\(646\) 9.13325 0.359343
\(647\) −33.4309 −1.31430 −0.657152 0.753758i \(-0.728239\pi\)
−0.657152 + 0.753758i \(0.728239\pi\)
\(648\) 28.0161 1.10057
\(649\) 8.64663 0.339410
\(650\) 0 0
\(651\) 0 0
\(652\) 6.13628 0.240315
\(653\) −10.4629 −0.409445 −0.204723 0.978820i \(-0.565629\pi\)
−0.204723 + 0.978820i \(0.565629\pi\)
\(654\) 36.6466 1.43300
\(655\) −27.2645 −1.06531
\(656\) −32.1202 −1.25408
\(657\) 0.355760 0.0138795
\(658\) 0 0
\(659\) −8.73849 −0.340403 −0.170202 0.985409i \(-0.554442\pi\)
−0.170202 + 0.985409i \(0.554442\pi\)
\(660\) −1.62593 −0.0632894
\(661\) 4.61354 0.179446 0.0897230 0.995967i \(-0.471402\pi\)
0.0897230 + 0.995967i \(0.471402\pi\)
\(662\) −8.32001 −0.323366
\(663\) 0 0
\(664\) −9.64199 −0.374182
\(665\) 0 0
\(666\) −0.122558 −0.00474901
\(667\) 9.44523 0.365721
\(668\) 6.92686 0.268008
\(669\) 2.23145 0.0862729
\(670\) −17.5531 −0.678137
\(671\) 10.3140 0.398166
\(672\) 0 0
\(673\) 9.83802 0.379228 0.189614 0.981859i \(-0.439276\pi\)
0.189614 + 0.981859i \(0.439276\pi\)
\(674\) 13.4045 0.516321
\(675\) 0.580461 0.0223420
\(676\) 0 0
\(677\) 4.69541 0.180459 0.0902296 0.995921i \(-0.471240\pi\)
0.0902296 + 0.995921i \(0.471240\pi\)
\(678\) 21.5073 0.825984
\(679\) 0 0
\(680\) −11.8350 −0.453851
\(681\) 16.7128 0.640436
\(682\) 5.44721 0.208584
\(683\) −11.0207 −0.421695 −0.210848 0.977519i \(-0.567622\pi\)
−0.210848 + 0.977519i \(0.567622\pi\)
\(684\) −0.102559 −0.00392145
\(685\) 7.39948 0.282720
\(686\) 0 0
\(687\) −23.5785 −0.899575
\(688\) −21.3534 −0.814090
\(689\) 0 0
\(690\) −5.19604 −0.197810
\(691\) 38.7635 1.47463 0.737317 0.675546i \(-0.236092\pi\)
0.737317 + 0.675546i \(0.236092\pi\)
\(692\) 1.32465 0.0503556
\(693\) 0 0
\(694\) 6.81163 0.258566
\(695\) 13.6323 0.517101
\(696\) 45.4483 1.72271
\(697\) 21.1757 0.802087
\(698\) 22.3727 0.846820
\(699\) 50.5277 1.91113
\(700\) 0 0
\(701\) −32.0681 −1.21120 −0.605598 0.795770i \(-0.707066\pi\)
−0.605598 + 0.795770i \(0.707066\pi\)
\(702\) 0 0
\(703\) −9.85238 −0.371590
\(704\) 6.97930 0.263042
\(705\) 33.7322 1.27043
\(706\) 5.65465 0.212816
\(707\) 0 0
\(708\) −10.2091 −0.383680
\(709\) −38.3451 −1.44008 −0.720040 0.693933i \(-0.755876\pi\)
−0.720040 + 0.693933i \(0.755876\pi\)
\(710\) −15.6784 −0.588399
\(711\) −0.306980 −0.0115127
\(712\) −10.4055 −0.389961
\(713\) −6.34204 −0.237511
\(714\) 0 0
\(715\) 0 0
\(716\) 4.35640 0.162806
\(717\) 42.1136 1.57276
\(718\) 14.1914 0.529618
\(719\) −8.72413 −0.325355 −0.162678 0.986679i \(-0.552013\pi\)
−0.162678 + 0.986679i \(0.552013\pi\)
\(720\) −0.259892 −0.00968561
\(721\) 0 0
\(722\) −0.374067 −0.0139213
\(723\) −17.3183 −0.644075
\(724\) 1.92722 0.0716244
\(725\) 0.955582 0.0354894
\(726\) −21.9222 −0.813610
\(727\) 26.6754 0.989334 0.494667 0.869083i \(-0.335290\pi\)
0.494667 + 0.869083i \(0.335290\pi\)
\(728\) 0 0
\(729\) 26.5885 0.984759
\(730\) 21.4385 0.793476
\(731\) 14.0775 0.520675
\(732\) −12.1777 −0.450100
\(733\) −26.7211 −0.986966 −0.493483 0.869755i \(-0.664277\pi\)
−0.493483 + 0.869755i \(0.664277\pi\)
\(734\) −24.1787 −0.892453
\(735\) 0 0
\(736\) −3.26187 −0.120234
\(737\) −5.17570 −0.190649
\(738\) 0.652682 0.0240256
\(739\) −36.0538 −1.32626 −0.663130 0.748504i \(-0.730772\pi\)
−0.663130 + 0.748504i \(0.730772\pi\)
\(740\) 2.69069 0.0989117
\(741\) 0 0
\(742\) 0 0
\(743\) 2.96058 0.108613 0.0543066 0.998524i \(-0.482705\pi\)
0.0543066 + 0.998524i \(0.482705\pi\)
\(744\) −30.5164 −1.11879
\(745\) −41.6433 −1.52569
\(746\) −5.35942 −0.196222
\(747\) 0.139589 0.00510729
\(748\) −0.735465 −0.0268913
\(749\) 0 0
\(750\) −23.8774 −0.871881
\(751\) 43.1550 1.57475 0.787374 0.616475i \(-0.211440\pi\)
0.787374 + 0.616475i \(0.211440\pi\)
\(752\) −23.1443 −0.843986
\(753\) −32.2776 −1.17626
\(754\) 0 0
\(755\) −44.6353 −1.62444
\(756\) 0 0
\(757\) 18.7335 0.680880 0.340440 0.940266i \(-0.389424\pi\)
0.340440 + 0.940266i \(0.389424\pi\)
\(758\) 39.4345 1.43233
\(759\) −1.53210 −0.0556116
\(760\) −29.3246 −1.06372
\(761\) 4.22948 0.153318 0.0766592 0.997057i \(-0.475575\pi\)
0.0766592 + 0.997057i \(0.475575\pi\)
\(762\) 34.7415 1.25855
\(763\) 0 0
\(764\) −0.180342 −0.00652456
\(765\) 0.171337 0.00619472
\(766\) 17.1884 0.621041
\(767\) 0 0
\(768\) −20.6279 −0.744345
\(769\) 21.1299 0.761965 0.380983 0.924582i \(-0.375586\pi\)
0.380983 + 0.924582i \(0.375586\pi\)
\(770\) 0 0
\(771\) −29.0979 −1.04794
\(772\) 4.49768 0.161875
\(773\) −33.0742 −1.18960 −0.594798 0.803875i \(-0.702768\pi\)
−0.594798 + 0.803875i \(0.702768\pi\)
\(774\) 0.433900 0.0155962
\(775\) −0.641629 −0.0230480
\(776\) 0.301284 0.0108154
\(777\) 0 0
\(778\) 20.9666 0.751690
\(779\) 52.4690 1.87990
\(780\) 0 0
\(781\) −4.62291 −0.165421
\(782\) −2.35034 −0.0840482
\(783\) 43.7809 1.56460
\(784\) 0 0
\(785\) −30.6877 −1.09529
\(786\) −26.0535 −0.929297
\(787\) −6.23948 −0.222413 −0.111207 0.993797i \(-0.535472\pi\)
−0.111207 + 0.993797i \(0.535472\pi\)
\(788\) −4.54512 −0.161913
\(789\) −23.5010 −0.836657
\(790\) −18.4990 −0.658165
\(791\) 0 0
\(792\) −0.107559 −0.00382194
\(793\) 0 0
\(794\) 19.0381 0.675636
\(795\) 30.6877 1.08838
\(796\) −7.80628 −0.276686
\(797\) −32.1837 −1.14001 −0.570003 0.821643i \(-0.693058\pi\)
−0.570003 + 0.821643i \(0.693058\pi\)
\(798\) 0 0
\(799\) 15.2582 0.539796
\(800\) −0.330006 −0.0116675
\(801\) 0.150642 0.00532267
\(802\) −4.33268 −0.152992
\(803\) 6.32134 0.223075
\(804\) 6.11094 0.215516
\(805\) 0 0
\(806\) 0 0
\(807\) 53.3180 1.87688
\(808\) 21.1757 0.744958
\(809\) 47.8016 1.68062 0.840308 0.542109i \(-0.182374\pi\)
0.840308 + 0.542109i \(0.182374\pi\)
\(810\) −24.4416 −0.858789
\(811\) 37.4957 1.31665 0.658326 0.752733i \(-0.271265\pi\)
0.658326 + 0.752733i \(0.271265\pi\)
\(812\) 0 0
\(813\) 7.37209 0.258551
\(814\) −2.17767 −0.0763274
\(815\) −25.4008 −0.889752
\(816\) −8.05744 −0.282067
\(817\) 34.8811 1.22034
\(818\) −37.9573 −1.32714
\(819\) 0 0
\(820\) −14.3293 −0.500401
\(821\) −39.6447 −1.38361 −0.691804 0.722085i \(-0.743184\pi\)
−0.691804 + 0.722085i \(0.743184\pi\)
\(822\) 7.07081 0.246623
\(823\) −17.4659 −0.608824 −0.304412 0.952540i \(-0.598460\pi\)
−0.304412 + 0.952540i \(0.598460\pi\)
\(824\) −48.5451 −1.69115
\(825\) −0.155004 −0.00539653
\(826\) 0 0
\(827\) 1.53104 0.0532396 0.0266198 0.999646i \(-0.491526\pi\)
0.0266198 + 0.999646i \(0.491526\pi\)
\(828\) 0.0263925 0.000917203 0
\(829\) 37.2218 1.29277 0.646383 0.763013i \(-0.276281\pi\)
0.646383 + 0.763013i \(0.276281\pi\)
\(830\) 8.41179 0.291978
\(831\) −5.23448 −0.181582
\(832\) 0 0
\(833\) 0 0
\(834\) 13.0267 0.451079
\(835\) −28.6734 −0.992283
\(836\) −1.82233 −0.0630265
\(837\) −29.3969 −1.01610
\(838\) 34.8354 1.20337
\(839\) −7.37209 −0.254513 −0.127256 0.991870i \(-0.540617\pi\)
−0.127256 + 0.991870i \(0.540617\pi\)
\(840\) 0 0
\(841\) 43.0742 1.48532
\(842\) 0.230116 0.00793034
\(843\) 10.9556 0.377330
\(844\) 12.7465 0.438753
\(845\) 0 0
\(846\) 0.470292 0.0161690
\(847\) 0 0
\(848\) −21.0555 −0.723048
\(849\) −41.0681 −1.40945
\(850\) −0.237786 −0.00815600
\(851\) 2.53541 0.0869126
\(852\) 5.45826 0.186997
\(853\) 4.57215 0.156548 0.0782738 0.996932i \(-0.475059\pi\)
0.0782738 + 0.996932i \(0.475059\pi\)
\(854\) 0 0
\(855\) 0.424538 0.0145189
\(856\) 6.20906 0.212221
\(857\) 52.0348 1.77747 0.888737 0.458417i \(-0.151584\pi\)
0.888737 + 0.458417i \(0.151584\pi\)
\(858\) 0 0
\(859\) −42.8905 −1.46340 −0.731702 0.681625i \(-0.761274\pi\)
−0.731702 + 0.681625i \(0.761274\pi\)
\(860\) −9.52604 −0.324835
\(861\) 0 0
\(862\) −31.0842 −1.05873
\(863\) 7.82233 0.266275 0.133138 0.991098i \(-0.457495\pi\)
0.133138 + 0.991098i \(0.457495\pi\)
\(864\) −15.1195 −0.514377
\(865\) −5.48332 −0.186438
\(866\) −2.20639 −0.0749763
\(867\) −24.3501 −0.826972
\(868\) 0 0
\(869\) −5.45460 −0.185034
\(870\) −39.6497 −1.34425
\(871\) 0 0
\(872\) −53.2231 −1.80236
\(873\) −0.00436174 −0.000147622 0
\(874\) −5.82366 −0.196988
\(875\) 0 0
\(876\) −7.46360 −0.252172
\(877\) 34.7191 1.17238 0.586191 0.810173i \(-0.300627\pi\)
0.586191 + 0.810173i \(0.300627\pi\)
\(878\) −0.890468 −0.0300518
\(879\) 37.7172 1.27217
\(880\) −4.61791 −0.155670
\(881\) −11.4422 −0.385498 −0.192749 0.981248i \(-0.561740\pi\)
−0.192749 + 0.981248i \(0.561740\pi\)
\(882\) 0 0
\(883\) −31.0217 −1.04396 −0.521982 0.852956i \(-0.674807\pi\)
−0.521982 + 0.852956i \(0.674807\pi\)
\(884\) 0 0
\(885\) 42.2599 1.42055
\(886\) −4.49401 −0.150979
\(887\) −12.8304 −0.430801 −0.215401 0.976526i \(-0.569106\pi\)
−0.215401 + 0.976526i \(0.569106\pi\)
\(888\) 12.1998 0.409398
\(889\) 0 0
\(890\) 9.07786 0.304291
\(891\) −7.20681 −0.241437
\(892\) −0.683020 −0.0228692
\(893\) 37.8066 1.26515
\(894\) −39.7936 −1.33090
\(895\) −18.0331 −0.602780
\(896\) 0 0
\(897\) 0 0
\(898\) 6.26651 0.209116
\(899\) −48.3945 −1.61405
\(900\) 0.00267015 8.90050e−5 0
\(901\) 13.8811 0.462447
\(902\) 11.5972 0.386145
\(903\) 0 0
\(904\) −31.2358 −1.03889
\(905\) −7.97761 −0.265185
\(906\) −42.6527 −1.41704
\(907\) 10.1620 0.337423 0.168711 0.985665i \(-0.446039\pi\)
0.168711 + 0.985665i \(0.446039\pi\)
\(908\) −5.11559 −0.169767
\(909\) −0.306565 −0.0101681
\(910\) 0 0
\(911\) 34.4008 1.13975 0.569875 0.821731i \(-0.306992\pi\)
0.569875 + 0.821731i \(0.306992\pi\)
\(912\) −19.9647 −0.661096
\(913\) 2.48029 0.0820856
\(914\) 41.3230 1.36684
\(915\) 50.4088 1.66646
\(916\) 7.21709 0.238459
\(917\) 0 0
\(918\) −10.8944 −0.359569
\(919\) 8.15500 0.269009 0.134504 0.990913i \(-0.457056\pi\)
0.134504 + 0.990913i \(0.457056\pi\)
\(920\) 7.54638 0.248797
\(921\) −35.5848 −1.17256
\(922\) −13.8036 −0.454598
\(923\) 0 0
\(924\) 0 0
\(925\) 0.256509 0.00843396
\(926\) 36.3377 1.19413
\(927\) 0.702797 0.0230829
\(928\) −24.8905 −0.817070
\(929\) 4.80994 0.157809 0.0789045 0.996882i \(-0.474858\pi\)
0.0789045 + 0.996882i \(0.474858\pi\)
\(930\) 26.6229 0.872999
\(931\) 0 0
\(932\) −15.4659 −0.506603
\(933\) −22.5942 −0.739700
\(934\) −41.3671 −1.35357
\(935\) 3.04442 0.0995631
\(936\) 0 0
\(937\) 47.1931 1.54173 0.770865 0.636998i \(-0.219824\pi\)
0.770865 + 0.636998i \(0.219824\pi\)
\(938\) 0 0
\(939\) 57.9884 1.89238
\(940\) −10.3250 −0.336765
\(941\) 27.5702 0.898762 0.449381 0.893340i \(-0.351645\pi\)
0.449381 + 0.893340i \(0.351645\pi\)
\(942\) −29.3246 −0.955449
\(943\) −13.5023 −0.439696
\(944\) −28.9954 −0.943718
\(945\) 0 0
\(946\) 7.70977 0.250666
\(947\) 27.8698 0.905646 0.452823 0.891600i \(-0.350417\pi\)
0.452823 + 0.891600i \(0.350417\pi\)
\(948\) 6.44023 0.209169
\(949\) 0 0
\(950\) −0.589185 −0.0191157
\(951\) 8.50035 0.275643
\(952\) 0 0
\(953\) −27.1076 −0.878100 −0.439050 0.898463i \(-0.644685\pi\)
−0.439050 + 0.898463i \(0.644685\pi\)
\(954\) 0.427846 0.0138520
\(955\) 0.746518 0.0241567
\(956\) −12.8905 −0.416908
\(957\) −11.6910 −0.377918
\(958\) −15.5898 −0.503684
\(959\) 0 0
\(960\) 34.1109 1.10093
\(961\) 1.49465 0.0482146
\(962\) 0 0
\(963\) −0.0898898 −0.00289666
\(964\) 5.30093 0.170731
\(965\) −18.6179 −0.599332
\(966\) 0 0
\(967\) 4.45657 0.143314 0.0716568 0.997429i \(-0.477171\pi\)
0.0716568 + 0.997429i \(0.477171\pi\)
\(968\) 31.8384 1.02332
\(969\) 13.1620 0.422824
\(970\) −0.262844 −0.00843940
\(971\) 18.9192 0.607146 0.303573 0.952808i \(-0.401820\pi\)
0.303573 + 0.952808i \(0.401820\pi\)
\(972\) 0.246510 0.00790680
\(973\) 0 0
\(974\) 26.5638 0.851161
\(975\) 0 0
\(976\) −34.5865 −1.10709
\(977\) −17.4359 −0.557823 −0.278911 0.960317i \(-0.589974\pi\)
−0.278911 + 0.960317i \(0.589974\pi\)
\(978\) −24.2726 −0.776151
\(979\) 2.67669 0.0855472
\(980\) 0 0
\(981\) 0.770521 0.0246009
\(982\) 4.97930 0.158896
\(983\) −15.3815 −0.490592 −0.245296 0.969448i \(-0.578885\pi\)
−0.245296 + 0.969448i \(0.578885\pi\)
\(984\) −64.9700 −2.07117
\(985\) 18.8143 0.599473
\(986\) −17.9349 −0.571163
\(987\) 0 0
\(988\) 0 0
\(989\) −8.97628 −0.285429
\(990\) 0.0938357 0.00298229
\(991\) 2.42651 0.0770807 0.0385403 0.999257i \(-0.487729\pi\)
0.0385403 + 0.999257i \(0.487729\pi\)
\(992\) 16.7128 0.530632
\(993\) −11.9900 −0.380491
\(994\) 0 0
\(995\) 32.3137 1.02441
\(996\) −2.92848 −0.0927923
\(997\) 15.0869 0.477806 0.238903 0.971043i \(-0.423212\pi\)
0.238903 + 0.971043i \(0.423212\pi\)
\(998\) −23.0444 −0.729458
\(999\) 11.7522 0.371824
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 8281.2.a.bh.1.2 3
7.6 odd 2 8281.2.a.bk.1.2 3
13.12 even 2 637.2.a.h.1.2 3
39.38 odd 2 5733.2.a.be.1.2 3
91.12 odd 6 637.2.e.k.508.2 6
91.25 even 6 637.2.e.l.79.2 6
91.38 odd 6 637.2.e.k.79.2 6
91.51 even 6 637.2.e.l.508.2 6
91.90 odd 2 637.2.a.i.1.2 yes 3
273.272 even 2 5733.2.a.bd.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
637.2.a.h.1.2 3 13.12 even 2
637.2.a.i.1.2 yes 3 91.90 odd 2
637.2.e.k.79.2 6 91.38 odd 6
637.2.e.k.508.2 6 91.12 odd 6
637.2.e.l.79.2 6 91.25 even 6
637.2.e.l.508.2 6 91.51 even 6
5733.2.a.bd.1.2 3 273.272 even 2
5733.2.a.be.1.2 3 39.38 odd 2
8281.2.a.bh.1.2 3 1.1 even 1 trivial
8281.2.a.bk.1.2 3 7.6 odd 2