Properties

Label 2667.2.a.j.1.1
Level $2667$
Weight $2$
Character 2667.1
Self dual yes
Analytic conductor $21.296$
Analytic rank $1$
Dimension $7$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2667 = 3 \cdot 7 \cdot 127 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2667.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(21.2961022191\)
Analytic rank: \(1\)
Dimension: \(7\)
Coefficient field: 7.7.118870813.1
Defining polynomial: \(x^{7} - 9 x^{5} - 3 x^{4} + 20 x^{3} + 7 x^{2} - 13 x - 4\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(1.13462\) of defining polynomial
Character \(\chi\) \(=\) 2667.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.48001 q^{2} +1.00000 q^{3} +4.15043 q^{4} -0.783950 q^{5} -2.48001 q^{6} +1.00000 q^{7} -5.33307 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.48001 q^{2} +1.00000 q^{3} +4.15043 q^{4} -0.783950 q^{5} -2.48001 q^{6} +1.00000 q^{7} -5.33307 q^{8} +1.00000 q^{9} +1.94420 q^{10} +4.88599 q^{11} +4.15043 q^{12} -6.65543 q^{13} -2.48001 q^{14} -0.783950 q^{15} +4.92520 q^{16} +1.25567 q^{17} -2.48001 q^{18} -2.07830 q^{19} -3.25373 q^{20} +1.00000 q^{21} -12.1173 q^{22} +6.86976 q^{23} -5.33307 q^{24} -4.38542 q^{25} +16.5055 q^{26} +1.00000 q^{27} +4.15043 q^{28} -9.79804 q^{29} +1.94420 q^{30} -3.45591 q^{31} -1.54837 q^{32} +4.88599 q^{33} -3.11406 q^{34} -0.783950 q^{35} +4.15043 q^{36} -2.67789 q^{37} +5.15419 q^{38} -6.65543 q^{39} +4.18086 q^{40} -4.19977 q^{41} -2.48001 q^{42} -4.11683 q^{43} +20.2789 q^{44} -0.783950 q^{45} -17.0370 q^{46} -6.51041 q^{47} +4.92520 q^{48} +1.00000 q^{49} +10.8759 q^{50} +1.25567 q^{51} -27.6229 q^{52} +3.48731 q^{53} -2.48001 q^{54} -3.83037 q^{55} -5.33307 q^{56} -2.07830 q^{57} +24.2992 q^{58} +12.2268 q^{59} -3.25373 q^{60} +6.13863 q^{61} +8.57067 q^{62} +1.00000 q^{63} -6.01043 q^{64} +5.21753 q^{65} -12.1173 q^{66} -15.0576 q^{67} +5.21155 q^{68} +6.86976 q^{69} +1.94420 q^{70} -7.18924 q^{71} -5.33307 q^{72} +2.24951 q^{73} +6.64118 q^{74} -4.38542 q^{75} -8.62583 q^{76} +4.88599 q^{77} +16.5055 q^{78} -7.38716 q^{79} -3.86111 q^{80} +1.00000 q^{81} +10.4154 q^{82} -3.82920 q^{83} +4.15043 q^{84} -0.984380 q^{85} +10.2098 q^{86} -9.79804 q^{87} -26.0573 q^{88} -16.4372 q^{89} +1.94420 q^{90} -6.65543 q^{91} +28.5124 q^{92} -3.45591 q^{93} +16.1458 q^{94} +1.62928 q^{95} -1.54837 q^{96} +16.8967 q^{97} -2.48001 q^{98} +4.88599 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q - 2q^{2} + 7q^{3} + 4q^{4} - 8q^{5} - 2q^{6} + 7q^{7} - 9q^{8} + 7q^{9} + O(q^{10}) \) \( 7q - 2q^{2} + 7q^{3} + 4q^{4} - 8q^{5} - 2q^{6} + 7q^{7} - 9q^{8} + 7q^{9} - 3q^{11} + 4q^{12} - 23q^{13} - 2q^{14} - 8q^{15} + 2q^{16} + 3q^{17} - 2q^{18} - 9q^{19} - 9q^{20} + 7q^{21} - 19q^{22} + 12q^{23} - 9q^{24} + 3q^{25} + 18q^{26} + 7q^{27} + 4q^{28} - 9q^{29} - 33q^{31} + 10q^{32} - 3q^{33} - 2q^{34} - 8q^{35} + 4q^{36} - 33q^{37} - 3q^{38} - 23q^{39} - 9q^{40} - 3q^{41} - 2q^{42} - 9q^{43} + 2q^{44} - 8q^{45} - 32q^{46} + 11q^{47} + 2q^{48} + 7q^{49} + 29q^{50} + 3q^{51} - 21q^{52} + q^{53} - 2q^{54} - 16q^{55} - 9q^{56} - 9q^{57} - 5q^{58} - 30q^{59} - 9q^{60} - 19q^{61} + 3q^{62} + 7q^{63} - 21q^{64} + 14q^{65} - 19q^{66} - 30q^{67} + 24q^{68} + 12q^{69} + 8q^{71} - 9q^{72} - 20q^{73} - 9q^{74} + 3q^{75} - 42q^{76} - 3q^{77} + 18q^{78} + 8q^{79} + 12q^{80} + 7q^{81} + 10q^{82} - 34q^{83} + 4q^{84} - 28q^{85} + 24q^{86} - 9q^{87} - q^{88} - 12q^{89} - 23q^{91} + 60q^{92} - 33q^{93} - 3q^{94} + 12q^{95} + 10q^{96} + 7q^{97} - 2q^{98} - 3q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.48001 −1.75363 −0.876814 0.480829i \(-0.840336\pi\)
−0.876814 + 0.480829i \(0.840336\pi\)
\(3\) 1.00000 0.577350
\(4\) 4.15043 2.07521
\(5\) −0.783950 −0.350593 −0.175297 0.984516i \(-0.556088\pi\)
−0.175297 + 0.984516i \(0.556088\pi\)
\(6\) −2.48001 −1.01246
\(7\) 1.00000 0.377964
\(8\) −5.33307 −1.88553
\(9\) 1.00000 0.333333
\(10\) 1.94420 0.614810
\(11\) 4.88599 1.47318 0.736590 0.676340i \(-0.236435\pi\)
0.736590 + 0.676340i \(0.236435\pi\)
\(12\) 4.15043 1.19813
\(13\) −6.65543 −1.84589 −0.922943 0.384937i \(-0.874223\pi\)
−0.922943 + 0.384937i \(0.874223\pi\)
\(14\) −2.48001 −0.662809
\(15\) −0.783950 −0.202415
\(16\) 4.92520 1.23130
\(17\) 1.25567 0.304544 0.152272 0.988339i \(-0.451341\pi\)
0.152272 + 0.988339i \(0.451341\pi\)
\(18\) −2.48001 −0.584543
\(19\) −2.07830 −0.476795 −0.238397 0.971168i \(-0.576622\pi\)
−0.238397 + 0.971168i \(0.576622\pi\)
\(20\) −3.25373 −0.727556
\(21\) 1.00000 0.218218
\(22\) −12.1173 −2.58341
\(23\) 6.86976 1.43244 0.716222 0.697872i \(-0.245870\pi\)
0.716222 + 0.697872i \(0.245870\pi\)
\(24\) −5.33307 −1.08861
\(25\) −4.38542 −0.877084
\(26\) 16.5055 3.23700
\(27\) 1.00000 0.192450
\(28\) 4.15043 0.784357
\(29\) −9.79804 −1.81945 −0.909726 0.415210i \(-0.863708\pi\)
−0.909726 + 0.415210i \(0.863708\pi\)
\(30\) 1.94420 0.354961
\(31\) −3.45591 −0.620699 −0.310349 0.950623i \(-0.600446\pi\)
−0.310349 + 0.950623i \(0.600446\pi\)
\(32\) −1.54837 −0.273715
\(33\) 4.88599 0.850541
\(34\) −3.11406 −0.534057
\(35\) −0.783950 −0.132512
\(36\) 4.15043 0.691738
\(37\) −2.67789 −0.440242 −0.220121 0.975473i \(-0.570645\pi\)
−0.220121 + 0.975473i \(0.570645\pi\)
\(38\) 5.15419 0.836121
\(39\) −6.65543 −1.06572
\(40\) 4.18086 0.661052
\(41\) −4.19977 −0.655893 −0.327947 0.944696i \(-0.606357\pi\)
−0.327947 + 0.944696i \(0.606357\pi\)
\(42\) −2.48001 −0.382673
\(43\) −4.11683 −0.627811 −0.313906 0.949454i \(-0.601638\pi\)
−0.313906 + 0.949454i \(0.601638\pi\)
\(44\) 20.2789 3.05716
\(45\) −0.783950 −0.116864
\(46\) −17.0370 −2.51198
\(47\) −6.51041 −0.949640 −0.474820 0.880083i \(-0.657487\pi\)
−0.474820 + 0.880083i \(0.657487\pi\)
\(48\) 4.92520 0.710891
\(49\) 1.00000 0.142857
\(50\) 10.8759 1.53808
\(51\) 1.25567 0.175828
\(52\) −27.6229 −3.83061
\(53\) 3.48731 0.479019 0.239510 0.970894i \(-0.423013\pi\)
0.239510 + 0.970894i \(0.423013\pi\)
\(54\) −2.48001 −0.337486
\(55\) −3.83037 −0.516487
\(56\) −5.33307 −0.712662
\(57\) −2.07830 −0.275277
\(58\) 24.2992 3.19064
\(59\) 12.2268 1.59180 0.795899 0.605430i \(-0.206999\pi\)
0.795899 + 0.605430i \(0.206999\pi\)
\(60\) −3.25373 −0.420054
\(61\) 6.13863 0.785971 0.392986 0.919545i \(-0.371442\pi\)
0.392986 + 0.919545i \(0.371442\pi\)
\(62\) 8.57067 1.08848
\(63\) 1.00000 0.125988
\(64\) −6.01043 −0.751304
\(65\) 5.21753 0.647155
\(66\) −12.1173 −1.49153
\(67\) −15.0576 −1.83958 −0.919790 0.392412i \(-0.871641\pi\)
−0.919790 + 0.392412i \(0.871641\pi\)
\(68\) 5.21155 0.631994
\(69\) 6.86976 0.827022
\(70\) 1.94420 0.232376
\(71\) −7.18924 −0.853206 −0.426603 0.904439i \(-0.640290\pi\)
−0.426603 + 0.904439i \(0.640290\pi\)
\(72\) −5.33307 −0.628509
\(73\) 2.24951 0.263285 0.131643 0.991297i \(-0.457975\pi\)
0.131643 + 0.991297i \(0.457975\pi\)
\(74\) 6.64118 0.772021
\(75\) −4.38542 −0.506385
\(76\) −8.62583 −0.989451
\(77\) 4.88599 0.556810
\(78\) 16.5055 1.86888
\(79\) −7.38716 −0.831120 −0.415560 0.909566i \(-0.636414\pi\)
−0.415560 + 0.909566i \(0.636414\pi\)
\(80\) −3.86111 −0.431685
\(81\) 1.00000 0.111111
\(82\) 10.4154 1.15019
\(83\) −3.82920 −0.420310 −0.210155 0.977668i \(-0.567397\pi\)
−0.210155 + 0.977668i \(0.567397\pi\)
\(84\) 4.15043 0.452849
\(85\) −0.984380 −0.106771
\(86\) 10.2098 1.10095
\(87\) −9.79804 −1.05046
\(88\) −26.0573 −2.77772
\(89\) −16.4372 −1.74234 −0.871171 0.490980i \(-0.836639\pi\)
−0.871171 + 0.490980i \(0.836639\pi\)
\(90\) 1.94420 0.204937
\(91\) −6.65543 −0.697679
\(92\) 28.5124 2.97263
\(93\) −3.45591 −0.358361
\(94\) 16.1458 1.66532
\(95\) 1.62928 0.167161
\(96\) −1.54837 −0.158030
\(97\) 16.8967 1.71560 0.857798 0.513987i \(-0.171832\pi\)
0.857798 + 0.513987i \(0.171832\pi\)
\(98\) −2.48001 −0.250518
\(99\) 4.88599 0.491060
\(100\) −18.2014 −1.82014
\(101\) 0.691702 0.0688269 0.0344134 0.999408i \(-0.489044\pi\)
0.0344134 + 0.999408i \(0.489044\pi\)
\(102\) −3.11406 −0.308338
\(103\) −16.5225 −1.62801 −0.814003 0.580861i \(-0.802716\pi\)
−0.814003 + 0.580861i \(0.802716\pi\)
\(104\) 35.4939 3.48047
\(105\) −0.783950 −0.0765057
\(106\) −8.64855 −0.840022
\(107\) −19.1211 −1.84851 −0.924255 0.381776i \(-0.875313\pi\)
−0.924255 + 0.381776i \(0.875313\pi\)
\(108\) 4.15043 0.399375
\(109\) 14.7383 1.41167 0.705837 0.708374i \(-0.250571\pi\)
0.705837 + 0.708374i \(0.250571\pi\)
\(110\) 9.49933 0.905726
\(111\) −2.67789 −0.254174
\(112\) 4.92520 0.465387
\(113\) 12.5353 1.17922 0.589612 0.807686i \(-0.299281\pi\)
0.589612 + 0.807686i \(0.299281\pi\)
\(114\) 5.15419 0.482735
\(115\) −5.38555 −0.502205
\(116\) −40.6661 −3.77575
\(117\) −6.65543 −0.615295
\(118\) −30.3226 −2.79142
\(119\) 1.25567 0.115107
\(120\) 4.18086 0.381659
\(121\) 12.8729 1.17026
\(122\) −15.2238 −1.37830
\(123\) −4.19977 −0.378680
\(124\) −14.3435 −1.28808
\(125\) 7.35770 0.658093
\(126\) −2.48001 −0.220936
\(127\) −1.00000 −0.0887357
\(128\) 18.0026 1.59122
\(129\) −4.11683 −0.362467
\(130\) −12.9395 −1.13487
\(131\) −0.687639 −0.0600793 −0.0300397 0.999549i \(-0.509563\pi\)
−0.0300397 + 0.999549i \(0.509563\pi\)
\(132\) 20.2789 1.76505
\(133\) −2.07830 −0.180211
\(134\) 37.3429 3.22594
\(135\) −0.783950 −0.0674717
\(136\) −6.69656 −0.574225
\(137\) −7.96226 −0.680262 −0.340131 0.940378i \(-0.610471\pi\)
−0.340131 + 0.940378i \(0.610471\pi\)
\(138\) −17.0370 −1.45029
\(139\) −0.410908 −0.0348528 −0.0174264 0.999848i \(-0.505547\pi\)
−0.0174264 + 0.999848i \(0.505547\pi\)
\(140\) −3.25373 −0.274990
\(141\) −6.51041 −0.548275
\(142\) 17.8294 1.49621
\(143\) −32.5184 −2.71932
\(144\) 4.92520 0.410433
\(145\) 7.68118 0.637887
\(146\) −5.57880 −0.461705
\(147\) 1.00000 0.0824786
\(148\) −11.1144 −0.913597
\(149\) 23.6085 1.93408 0.967041 0.254620i \(-0.0819502\pi\)
0.967041 + 0.254620i \(0.0819502\pi\)
\(150\) 10.8759 0.888011
\(151\) −6.43593 −0.523748 −0.261874 0.965102i \(-0.584341\pi\)
−0.261874 + 0.965102i \(0.584341\pi\)
\(152\) 11.0837 0.899009
\(153\) 1.25567 0.101515
\(154\) −12.1173 −0.976438
\(155\) 2.70926 0.217613
\(156\) −27.6229 −2.21160
\(157\) −14.4987 −1.15712 −0.578561 0.815639i \(-0.696385\pi\)
−0.578561 + 0.815639i \(0.696385\pi\)
\(158\) 18.3202 1.45748
\(159\) 3.48731 0.276562
\(160\) 1.21384 0.0959627
\(161\) 6.86976 0.541413
\(162\) −2.48001 −0.194848
\(163\) 8.06383 0.631608 0.315804 0.948824i \(-0.397726\pi\)
0.315804 + 0.948824i \(0.397726\pi\)
\(164\) −17.4308 −1.36112
\(165\) −3.83037 −0.298194
\(166\) 9.49645 0.737067
\(167\) 4.60533 0.356371 0.178186 0.983997i \(-0.442977\pi\)
0.178186 + 0.983997i \(0.442977\pi\)
\(168\) −5.33307 −0.411456
\(169\) 31.2948 2.40729
\(170\) 2.44127 0.187237
\(171\) −2.07830 −0.158932
\(172\) −17.0866 −1.30284
\(173\) −11.5019 −0.874475 −0.437237 0.899346i \(-0.644043\pi\)
−0.437237 + 0.899346i \(0.644043\pi\)
\(174\) 24.2992 1.84212
\(175\) −4.38542 −0.331507
\(176\) 24.0644 1.81393
\(177\) 12.2268 0.919025
\(178\) 40.7644 3.05542
\(179\) 22.8385 1.70703 0.853515 0.521068i \(-0.174466\pi\)
0.853515 + 0.521068i \(0.174466\pi\)
\(180\) −3.25373 −0.242519
\(181\) 4.40434 0.327372 0.163686 0.986512i \(-0.447662\pi\)
0.163686 + 0.986512i \(0.447662\pi\)
\(182\) 16.5055 1.22347
\(183\) 6.13863 0.453781
\(184\) −36.6369 −2.70091
\(185\) 2.09933 0.154346
\(186\) 8.57067 0.628432
\(187\) 6.13517 0.448648
\(188\) −27.0210 −1.97071
\(189\) 1.00000 0.0727393
\(190\) −4.04063 −0.293138
\(191\) 20.5561 1.48739 0.743695 0.668520i \(-0.233072\pi\)
0.743695 + 0.668520i \(0.233072\pi\)
\(192\) −6.01043 −0.433766
\(193\) −18.0715 −1.30082 −0.650409 0.759584i \(-0.725402\pi\)
−0.650409 + 0.759584i \(0.725402\pi\)
\(194\) −41.9038 −3.00852
\(195\) 5.21753 0.373635
\(196\) 4.15043 0.296459
\(197\) −24.7109 −1.76058 −0.880291 0.474434i \(-0.842653\pi\)
−0.880291 + 0.474434i \(0.842653\pi\)
\(198\) −12.1173 −0.861137
\(199\) 16.6604 1.18102 0.590511 0.807030i \(-0.298926\pi\)
0.590511 + 0.807030i \(0.298926\pi\)
\(200\) 23.3878 1.65377
\(201\) −15.0576 −1.06208
\(202\) −1.71542 −0.120697
\(203\) −9.79804 −0.687688
\(204\) 5.21155 0.364882
\(205\) 3.29241 0.229952
\(206\) 40.9758 2.85492
\(207\) 6.86976 0.477481
\(208\) −32.7793 −2.27284
\(209\) −10.1545 −0.702404
\(210\) 1.94420 0.134163
\(211\) 14.5672 1.00284 0.501422 0.865203i \(-0.332810\pi\)
0.501422 + 0.865203i \(0.332810\pi\)
\(212\) 14.4738 0.994067
\(213\) −7.18924 −0.492599
\(214\) 47.4205 3.24160
\(215\) 3.22739 0.220106
\(216\) −5.33307 −0.362870
\(217\) −3.45591 −0.234602
\(218\) −36.5511 −2.47555
\(219\) 2.24951 0.152008
\(220\) −15.8977 −1.07182
\(221\) −8.35701 −0.562153
\(222\) 6.64118 0.445727
\(223\) −9.76267 −0.653757 −0.326878 0.945066i \(-0.605997\pi\)
−0.326878 + 0.945066i \(0.605997\pi\)
\(224\) −1.54837 −0.103455
\(225\) −4.38542 −0.292361
\(226\) −31.0877 −2.06792
\(227\) −26.0747 −1.73064 −0.865321 0.501219i \(-0.832885\pi\)
−0.865321 + 0.501219i \(0.832885\pi\)
\(228\) −8.62583 −0.571260
\(229\) 6.24716 0.412824 0.206412 0.978465i \(-0.433821\pi\)
0.206412 + 0.978465i \(0.433821\pi\)
\(230\) 13.3562 0.880681
\(231\) 4.88599 0.321474
\(232\) 52.2537 3.43062
\(233\) 6.77809 0.444047 0.222024 0.975041i \(-0.428734\pi\)
0.222024 + 0.975041i \(0.428734\pi\)
\(234\) 16.5055 1.07900
\(235\) 5.10383 0.332937
\(236\) 50.7466 3.30332
\(237\) −7.38716 −0.479847
\(238\) −3.11406 −0.201855
\(239\) −23.7065 −1.53345 −0.766724 0.641977i \(-0.778115\pi\)
−0.766724 + 0.641977i \(0.778115\pi\)
\(240\) −3.86111 −0.249233
\(241\) −9.28434 −0.598057 −0.299028 0.954244i \(-0.596663\pi\)
−0.299028 + 0.954244i \(0.596663\pi\)
\(242\) −31.9247 −2.05220
\(243\) 1.00000 0.0641500
\(244\) 25.4779 1.63106
\(245\) −0.783950 −0.0500847
\(246\) 10.4154 0.664064
\(247\) 13.8320 0.880108
\(248\) 18.4306 1.17034
\(249\) −3.82920 −0.242666
\(250\) −18.2471 −1.15405
\(251\) 0.539366 0.0340445 0.0170222 0.999855i \(-0.494581\pi\)
0.0170222 + 0.999855i \(0.494581\pi\)
\(252\) 4.15043 0.261452
\(253\) 33.5656 2.11025
\(254\) 2.48001 0.155609
\(255\) −0.984380 −0.0616442
\(256\) −32.6258 −2.03911
\(257\) −4.16847 −0.260022 −0.130011 0.991513i \(-0.541501\pi\)
−0.130011 + 0.991513i \(0.541501\pi\)
\(258\) 10.2098 0.635633
\(259\) −2.67789 −0.166396
\(260\) 21.6550 1.34298
\(261\) −9.79804 −0.606484
\(262\) 1.70535 0.105357
\(263\) −23.9281 −1.47547 −0.737734 0.675092i \(-0.764104\pi\)
−0.737734 + 0.675092i \(0.764104\pi\)
\(264\) −26.0573 −1.60372
\(265\) −2.73388 −0.167941
\(266\) 5.15419 0.316024
\(267\) −16.4372 −1.00594
\(268\) −62.4955 −3.81752
\(269\) −30.9708 −1.88832 −0.944160 0.329487i \(-0.893124\pi\)
−0.944160 + 0.329487i \(0.893124\pi\)
\(270\) 1.94420 0.118320
\(271\) −23.8214 −1.44705 −0.723523 0.690300i \(-0.757478\pi\)
−0.723523 + 0.690300i \(0.757478\pi\)
\(272\) 6.18440 0.374985
\(273\) −6.65543 −0.402805
\(274\) 19.7465 1.19293
\(275\) −21.4271 −1.29210
\(276\) 28.5124 1.71625
\(277\) −14.3357 −0.861351 −0.430675 0.902507i \(-0.641725\pi\)
−0.430675 + 0.902507i \(0.641725\pi\)
\(278\) 1.01905 0.0611188
\(279\) −3.45591 −0.206900
\(280\) 4.18086 0.249854
\(281\) 20.6212 1.23016 0.615079 0.788466i \(-0.289124\pi\)
0.615079 + 0.788466i \(0.289124\pi\)
\(282\) 16.1458 0.961471
\(283\) 3.77609 0.224465 0.112233 0.993682i \(-0.464200\pi\)
0.112233 + 0.993682i \(0.464200\pi\)
\(284\) −29.8384 −1.77058
\(285\) 1.62928 0.0965104
\(286\) 80.6457 4.76868
\(287\) −4.19977 −0.247904
\(288\) −1.54837 −0.0912384
\(289\) −15.4233 −0.907253
\(290\) −19.0494 −1.11862
\(291\) 16.8967 0.990499
\(292\) 9.33644 0.546374
\(293\) −24.2919 −1.41915 −0.709573 0.704632i \(-0.751112\pi\)
−0.709573 + 0.704632i \(0.751112\pi\)
\(294\) −2.48001 −0.144637
\(295\) −9.58522 −0.558073
\(296\) 14.2814 0.830088
\(297\) 4.88599 0.283514
\(298\) −58.5492 −3.39166
\(299\) −45.7212 −2.64413
\(300\) −18.2014 −1.05086
\(301\) −4.11683 −0.237290
\(302\) 15.9611 0.918460
\(303\) 0.691702 0.0397372
\(304\) −10.2360 −0.587077
\(305\) −4.81238 −0.275556
\(306\) −3.11406 −0.178019
\(307\) −18.6482 −1.06431 −0.532153 0.846648i \(-0.678617\pi\)
−0.532153 + 0.846648i \(0.678617\pi\)
\(308\) 20.2789 1.15550
\(309\) −16.5225 −0.939929
\(310\) −6.71897 −0.381612
\(311\) 20.8747 1.18370 0.591848 0.806050i \(-0.298399\pi\)
0.591848 + 0.806050i \(0.298399\pi\)
\(312\) 35.4939 2.00945
\(313\) −7.93347 −0.448426 −0.224213 0.974540i \(-0.571981\pi\)
−0.224213 + 0.974540i \(0.571981\pi\)
\(314\) 35.9568 2.02916
\(315\) −0.783950 −0.0441706
\(316\) −30.6599 −1.72475
\(317\) 11.3644 0.638290 0.319145 0.947706i \(-0.396604\pi\)
0.319145 + 0.947706i \(0.396604\pi\)
\(318\) −8.64855 −0.484987
\(319\) −47.8731 −2.68038
\(320\) 4.71188 0.263402
\(321\) −19.1211 −1.06724
\(322\) −17.0370 −0.949437
\(323\) −2.60965 −0.145205
\(324\) 4.15043 0.230579
\(325\) 29.1869 1.61900
\(326\) −19.9983 −1.10761
\(327\) 14.7383 0.815031
\(328\) 22.3977 1.23670
\(329\) −6.51041 −0.358930
\(330\) 9.49933 0.522921
\(331\) −19.1983 −1.05523 −0.527616 0.849483i \(-0.676914\pi\)
−0.527616 + 0.849483i \(0.676914\pi\)
\(332\) −15.8928 −0.872233
\(333\) −2.67789 −0.146747
\(334\) −11.4213 −0.624943
\(335\) 11.8044 0.644944
\(336\) 4.92520 0.268691
\(337\) 8.90770 0.485234 0.242617 0.970122i \(-0.421994\pi\)
0.242617 + 0.970122i \(0.421994\pi\)
\(338\) −77.6113 −4.22150
\(339\) 12.5353 0.680826
\(340\) −4.08560 −0.221573
\(341\) −16.8855 −0.914401
\(342\) 5.15419 0.278707
\(343\) 1.00000 0.0539949
\(344\) 21.9554 1.18375
\(345\) −5.38555 −0.289948
\(346\) 28.5248 1.53350
\(347\) −1.17952 −0.0633201 −0.0316601 0.999499i \(-0.510079\pi\)
−0.0316601 + 0.999499i \(0.510079\pi\)
\(348\) −40.6661 −2.17993
\(349\) −29.5422 −1.58136 −0.790679 0.612231i \(-0.790272\pi\)
−0.790679 + 0.612231i \(0.790272\pi\)
\(350\) 10.8759 0.581340
\(351\) −6.65543 −0.355241
\(352\) −7.56530 −0.403232
\(353\) 10.1955 0.542653 0.271327 0.962487i \(-0.412538\pi\)
0.271327 + 0.962487i \(0.412538\pi\)
\(354\) −30.3226 −1.61163
\(355\) 5.63601 0.299128
\(356\) −68.2215 −3.61573
\(357\) 1.25567 0.0664569
\(358\) −56.6396 −2.99350
\(359\) 30.6151 1.61580 0.807900 0.589319i \(-0.200604\pi\)
0.807900 + 0.589319i \(0.200604\pi\)
\(360\) 4.18086 0.220351
\(361\) −14.6807 −0.772667
\(362\) −10.9228 −0.574089
\(363\) 12.8729 0.675649
\(364\) −27.6229 −1.44783
\(365\) −1.76350 −0.0923061
\(366\) −15.2238 −0.795763
\(367\) −10.8181 −0.564702 −0.282351 0.959311i \(-0.591114\pi\)
−0.282351 + 0.959311i \(0.591114\pi\)
\(368\) 33.8349 1.76377
\(369\) −4.19977 −0.218631
\(370\) −5.20635 −0.270665
\(371\) 3.48731 0.181052
\(372\) −14.3435 −0.743675
\(373\) 10.2006 0.528169 0.264085 0.964499i \(-0.414930\pi\)
0.264085 + 0.964499i \(0.414930\pi\)
\(374\) −15.2153 −0.786762
\(375\) 7.35770 0.379950
\(376\) 34.7205 1.79057
\(377\) 65.2102 3.35850
\(378\) −2.48001 −0.127558
\(379\) 6.58231 0.338110 0.169055 0.985607i \(-0.445928\pi\)
0.169055 + 0.985607i \(0.445928\pi\)
\(380\) 6.76222 0.346895
\(381\) −1.00000 −0.0512316
\(382\) −50.9793 −2.60833
\(383\) −20.2431 −1.03438 −0.517188 0.855872i \(-0.673021\pi\)
−0.517188 + 0.855872i \(0.673021\pi\)
\(384\) 18.0026 0.918693
\(385\) −3.83037 −0.195214
\(386\) 44.8175 2.28115
\(387\) −4.11683 −0.209270
\(388\) 70.1283 3.56023
\(389\) 8.10612 0.410997 0.205498 0.978657i \(-0.434118\pi\)
0.205498 + 0.978657i \(0.434118\pi\)
\(390\) −12.9395 −0.655217
\(391\) 8.62613 0.436242
\(392\) −5.33307 −0.269361
\(393\) −0.687639 −0.0346868
\(394\) 61.2833 3.08741
\(395\) 5.79116 0.291385
\(396\) 20.2789 1.01905
\(397\) −15.9348 −0.799745 −0.399872 0.916571i \(-0.630946\pi\)
−0.399872 + 0.916571i \(0.630946\pi\)
\(398\) −41.3178 −2.07107
\(399\) −2.07830 −0.104045
\(400\) −21.5991 −1.07995
\(401\) 35.9972 1.79761 0.898807 0.438344i \(-0.144435\pi\)
0.898807 + 0.438344i \(0.144435\pi\)
\(402\) 37.3429 1.86250
\(403\) 23.0006 1.14574
\(404\) 2.87086 0.142831
\(405\) −0.783950 −0.0389548
\(406\) 24.2992 1.20595
\(407\) −13.0841 −0.648556
\(408\) −6.69656 −0.331529
\(409\) −21.3091 −1.05367 −0.526833 0.849969i \(-0.676621\pi\)
−0.526833 + 0.849969i \(0.676621\pi\)
\(410\) −8.16519 −0.403250
\(411\) −7.96226 −0.392749
\(412\) −68.5752 −3.37846
\(413\) 12.2268 0.601643
\(414\) −17.0370 −0.837325
\(415\) 3.00190 0.147358
\(416\) 10.3051 0.505247
\(417\) −0.410908 −0.0201223
\(418\) 25.1833 1.23176
\(419\) −26.8399 −1.31122 −0.655608 0.755101i \(-0.727588\pi\)
−0.655608 + 0.755101i \(0.727588\pi\)
\(420\) −3.25373 −0.158766
\(421\) 1.71312 0.0834923 0.0417462 0.999128i \(-0.486708\pi\)
0.0417462 + 0.999128i \(0.486708\pi\)
\(422\) −36.1266 −1.75862
\(423\) −6.51041 −0.316547
\(424\) −18.5981 −0.903203
\(425\) −5.50663 −0.267111
\(426\) 17.8294 0.863835
\(427\) 6.13863 0.297069
\(428\) −79.3609 −3.83605
\(429\) −32.5184 −1.57000
\(430\) −8.00395 −0.385985
\(431\) 29.8518 1.43791 0.718954 0.695057i \(-0.244621\pi\)
0.718954 + 0.695057i \(0.244621\pi\)
\(432\) 4.92520 0.236964
\(433\) −6.53077 −0.313849 −0.156924 0.987611i \(-0.550158\pi\)
−0.156924 + 0.987611i \(0.550158\pi\)
\(434\) 8.57067 0.411405
\(435\) 7.68118 0.368284
\(436\) 61.1703 2.92953
\(437\) −14.2774 −0.682982
\(438\) −5.57880 −0.266566
\(439\) −14.9276 −0.712457 −0.356228 0.934399i \(-0.615938\pi\)
−0.356228 + 0.934399i \(0.615938\pi\)
\(440\) 20.4276 0.973849
\(441\) 1.00000 0.0476190
\(442\) 20.7254 0.985808
\(443\) −4.63421 −0.220178 −0.110089 0.993922i \(-0.535114\pi\)
−0.110089 + 0.993922i \(0.535114\pi\)
\(444\) −11.1144 −0.527465
\(445\) 12.8860 0.610853
\(446\) 24.2115 1.14645
\(447\) 23.6085 1.11664
\(448\) −6.01043 −0.283966
\(449\) −6.63579 −0.313162 −0.156581 0.987665i \(-0.550047\pi\)
−0.156581 + 0.987665i \(0.550047\pi\)
\(450\) 10.8759 0.512694
\(451\) −20.5200 −0.966249
\(452\) 52.0270 2.44714
\(453\) −6.43593 −0.302386
\(454\) 64.6655 3.03490
\(455\) 5.21753 0.244601
\(456\) 11.0837 0.519043
\(457\) −17.6826 −0.827157 −0.413578 0.910468i \(-0.635721\pi\)
−0.413578 + 0.910468i \(0.635721\pi\)
\(458\) −15.4930 −0.723940
\(459\) 1.25567 0.0586095
\(460\) −22.3523 −1.04218
\(461\) −40.2668 −1.87541 −0.937706 0.347431i \(-0.887054\pi\)
−0.937706 + 0.347431i \(0.887054\pi\)
\(462\) −12.1173 −0.563746
\(463\) −3.88536 −0.180568 −0.0902841 0.995916i \(-0.528777\pi\)
−0.0902841 + 0.995916i \(0.528777\pi\)
\(464\) −48.2573 −2.24029
\(465\) 2.70926 0.125639
\(466\) −16.8097 −0.778694
\(467\) −1.32929 −0.0615123 −0.0307561 0.999527i \(-0.509792\pi\)
−0.0307561 + 0.999527i \(0.509792\pi\)
\(468\) −27.6229 −1.27687
\(469\) −15.0576 −0.695296
\(470\) −12.6575 −0.583849
\(471\) −14.4987 −0.668064
\(472\) −65.2066 −3.00138
\(473\) −20.1148 −0.924879
\(474\) 18.3202 0.841474
\(475\) 9.11422 0.418189
\(476\) 5.21155 0.238871
\(477\) 3.48731 0.159673
\(478\) 58.7923 2.68910
\(479\) −10.9654 −0.501022 −0.250511 0.968114i \(-0.580599\pi\)
−0.250511 + 0.968114i \(0.580599\pi\)
\(480\) 1.21384 0.0554041
\(481\) 17.8225 0.812637
\(482\) 23.0252 1.04877
\(483\) 6.86976 0.312585
\(484\) 53.4278 2.42854
\(485\) −13.2461 −0.601476
\(486\) −2.48001 −0.112495
\(487\) 7.42363 0.336397 0.168198 0.985753i \(-0.446205\pi\)
0.168198 + 0.985753i \(0.446205\pi\)
\(488\) −32.7378 −1.48197
\(489\) 8.06383 0.364659
\(490\) 1.94420 0.0878300
\(491\) 10.4742 0.472694 0.236347 0.971669i \(-0.424050\pi\)
0.236347 + 0.971669i \(0.424050\pi\)
\(492\) −17.4308 −0.785842
\(493\) −12.3031 −0.554103
\(494\) −34.3034 −1.54338
\(495\) −3.83037 −0.172162
\(496\) −17.0210 −0.764266
\(497\) −7.18924 −0.322482
\(498\) 9.49645 0.425546
\(499\) 26.6794 1.19433 0.597167 0.802117i \(-0.296293\pi\)
0.597167 + 0.802117i \(0.296293\pi\)
\(500\) 30.5376 1.36568
\(501\) 4.60533 0.205751
\(502\) −1.33763 −0.0597013
\(503\) 27.1665 1.21129 0.605646 0.795734i \(-0.292915\pi\)
0.605646 + 0.795734i \(0.292915\pi\)
\(504\) −5.33307 −0.237554
\(505\) −0.542259 −0.0241302
\(506\) −83.2428 −3.70059
\(507\) 31.2948 1.38985
\(508\) −4.15043 −0.184145
\(509\) −5.67100 −0.251363 −0.125681 0.992071i \(-0.540112\pi\)
−0.125681 + 0.992071i \(0.540112\pi\)
\(510\) 2.44127 0.108101
\(511\) 2.24951 0.0995126
\(512\) 44.9069 1.98462
\(513\) −2.07830 −0.0917592
\(514\) 10.3378 0.455982
\(515\) 12.9528 0.570767
\(516\) −17.0866 −0.752197
\(517\) −31.8098 −1.39899
\(518\) 6.64118 0.291797
\(519\) −11.5019 −0.504878
\(520\) −27.8255 −1.22023
\(521\) 32.7163 1.43333 0.716664 0.697419i \(-0.245668\pi\)
0.716664 + 0.697419i \(0.245668\pi\)
\(522\) 24.2992 1.06355
\(523\) 20.8450 0.911486 0.455743 0.890111i \(-0.349374\pi\)
0.455743 + 0.890111i \(0.349374\pi\)
\(524\) −2.85400 −0.124677
\(525\) −4.38542 −0.191396
\(526\) 59.3417 2.58742
\(527\) −4.33946 −0.189030
\(528\) 24.0644 1.04727
\(529\) 24.1936 1.05190
\(530\) 6.78003 0.294506
\(531\) 12.2268 0.530599
\(532\) −8.62583 −0.373977
\(533\) 27.9513 1.21070
\(534\) 40.7644 1.76405
\(535\) 14.9900 0.648075
\(536\) 80.3033 3.46857
\(537\) 22.8385 0.985554
\(538\) 76.8077 3.31141
\(539\) 4.88599 0.210454
\(540\) −3.25373 −0.140018
\(541\) −21.1270 −0.908319 −0.454159 0.890920i \(-0.650060\pi\)
−0.454159 + 0.890920i \(0.650060\pi\)
\(542\) 59.0772 2.53758
\(543\) 4.40434 0.189008
\(544\) −1.94423 −0.0833583
\(545\) −11.5541 −0.494923
\(546\) 16.5055 0.706371
\(547\) 10.1713 0.434895 0.217448 0.976072i \(-0.430227\pi\)
0.217448 + 0.976072i \(0.430227\pi\)
\(548\) −33.0468 −1.41169
\(549\) 6.13863 0.261990
\(550\) 53.1394 2.26587
\(551\) 20.3633 0.867504
\(552\) −36.6369 −1.55937
\(553\) −7.38716 −0.314134
\(554\) 35.5527 1.51049
\(555\) 2.09933 0.0891116
\(556\) −1.70544 −0.0723270
\(557\) −29.5187 −1.25075 −0.625373 0.780326i \(-0.715053\pi\)
−0.625373 + 0.780326i \(0.715053\pi\)
\(558\) 8.57067 0.362825
\(559\) 27.3993 1.15887
\(560\) −3.86111 −0.163162
\(561\) 6.13517 0.259027
\(562\) −51.1407 −2.15724
\(563\) 29.4720 1.24210 0.621049 0.783772i \(-0.286707\pi\)
0.621049 + 0.783772i \(0.286707\pi\)
\(564\) −27.0210 −1.13779
\(565\) −9.82707 −0.413428
\(566\) −9.36473 −0.393629
\(567\) 1.00000 0.0419961
\(568\) 38.3408 1.60874
\(569\) 18.1639 0.761471 0.380735 0.924684i \(-0.375671\pi\)
0.380735 + 0.924684i \(0.375671\pi\)
\(570\) −4.04063 −0.169243
\(571\) −5.20524 −0.217832 −0.108916 0.994051i \(-0.534738\pi\)
−0.108916 + 0.994051i \(0.534738\pi\)
\(572\) −134.965 −5.64317
\(573\) 20.5561 0.858744
\(574\) 10.4154 0.434732
\(575\) −30.1268 −1.25637
\(576\) −6.01043 −0.250435
\(577\) 22.5036 0.936835 0.468418 0.883507i \(-0.344824\pi\)
0.468418 + 0.883507i \(0.344824\pi\)
\(578\) 38.2499 1.59099
\(579\) −18.0715 −0.751028
\(580\) 31.8802 1.32375
\(581\) −3.82920 −0.158862
\(582\) −41.9038 −1.73697
\(583\) 17.0390 0.705681
\(584\) −11.9968 −0.496432
\(585\) 5.21753 0.215718
\(586\) 60.2440 2.48866
\(587\) −11.1742 −0.461208 −0.230604 0.973048i \(-0.574070\pi\)
−0.230604 + 0.973048i \(0.574070\pi\)
\(588\) 4.15043 0.171161
\(589\) 7.18241 0.295946
\(590\) 23.7714 0.978653
\(591\) −24.7109 −1.01647
\(592\) −13.1891 −0.542070
\(593\) 10.7553 0.441669 0.220835 0.975311i \(-0.429122\pi\)
0.220835 + 0.975311i \(0.429122\pi\)
\(594\) −12.1173 −0.497178
\(595\) −0.984380 −0.0403556
\(596\) 97.9853 4.01364
\(597\) 16.6604 0.681863
\(598\) 113.389 4.63682
\(599\) 16.4493 0.672099 0.336049 0.941844i \(-0.390909\pi\)
0.336049 + 0.941844i \(0.390909\pi\)
\(600\) 23.3878 0.954802
\(601\) 24.6614 1.00596 0.502979 0.864298i \(-0.332237\pi\)
0.502979 + 0.864298i \(0.332237\pi\)
\(602\) 10.2098 0.416119
\(603\) −15.0576 −0.613193
\(604\) −26.7118 −1.08689
\(605\) −10.0917 −0.410285
\(606\) −1.71542 −0.0696843
\(607\) −6.40510 −0.259975 −0.129988 0.991516i \(-0.541494\pi\)
−0.129988 + 0.991516i \(0.541494\pi\)
\(608\) 3.21797 0.130506
\(609\) −9.79804 −0.397037
\(610\) 11.9347 0.483223
\(611\) 43.3296 1.75293
\(612\) 5.21155 0.210665
\(613\) 9.77647 0.394868 0.197434 0.980316i \(-0.436739\pi\)
0.197434 + 0.980316i \(0.436739\pi\)
\(614\) 46.2475 1.86640
\(615\) 3.29241 0.132763
\(616\) −26.0573 −1.04988
\(617\) 36.0074 1.44960 0.724802 0.688958i \(-0.241931\pi\)
0.724802 + 0.688958i \(0.241931\pi\)
\(618\) 40.9758 1.64829
\(619\) −18.4220 −0.740441 −0.370220 0.928944i \(-0.620718\pi\)
−0.370220 + 0.928944i \(0.620718\pi\)
\(620\) 11.2446 0.451593
\(621\) 6.86976 0.275674
\(622\) −51.7694 −2.07576
\(623\) −16.4372 −0.658543
\(624\) −32.7793 −1.31222
\(625\) 16.1590 0.646362
\(626\) 19.6750 0.786373
\(627\) −10.1545 −0.405533
\(628\) −60.1758 −2.40127
\(629\) −3.36254 −0.134073
\(630\) 1.94420 0.0774588
\(631\) −21.8713 −0.870682 −0.435341 0.900266i \(-0.643372\pi\)
−0.435341 + 0.900266i \(0.643372\pi\)
\(632\) 39.3962 1.56710
\(633\) 14.5672 0.578992
\(634\) −28.1838 −1.11932
\(635\) 0.783950 0.0311101
\(636\) 14.4738 0.573925
\(637\) −6.65543 −0.263698
\(638\) 118.726 4.70039
\(639\) −7.18924 −0.284402
\(640\) −14.1132 −0.557872
\(641\) −5.35545 −0.211527 −0.105764 0.994391i \(-0.533729\pi\)
−0.105764 + 0.994391i \(0.533729\pi\)
\(642\) 47.4205 1.87154
\(643\) 12.1586 0.479488 0.239744 0.970836i \(-0.422936\pi\)
0.239744 + 0.970836i \(0.422936\pi\)
\(644\) 28.5124 1.12355
\(645\) 3.22739 0.127078
\(646\) 6.47195 0.254635
\(647\) −3.92615 −0.154353 −0.0771764 0.997017i \(-0.524590\pi\)
−0.0771764 + 0.997017i \(0.524590\pi\)
\(648\) −5.33307 −0.209503
\(649\) 59.7401 2.34500
\(650\) −72.3837 −2.83912
\(651\) −3.45591 −0.135448
\(652\) 33.4683 1.31072
\(653\) 3.49414 0.136736 0.0683681 0.997660i \(-0.478221\pi\)
0.0683681 + 0.997660i \(0.478221\pi\)
\(654\) −36.5511 −1.42926
\(655\) 0.539075 0.0210634
\(656\) −20.6847 −0.807601
\(657\) 2.24951 0.0877618
\(658\) 16.1458 0.629431
\(659\) 26.1167 1.01736 0.508682 0.860955i \(-0.330133\pi\)
0.508682 + 0.860955i \(0.330133\pi\)
\(660\) −15.8977 −0.618816
\(661\) −34.1023 −1.32643 −0.663213 0.748431i \(-0.730808\pi\)
−0.663213 + 0.748431i \(0.730808\pi\)
\(662\) 47.6118 1.85049
\(663\) −8.35701 −0.324559
\(664\) 20.4214 0.792505
\(665\) 1.62928 0.0631809
\(666\) 6.64118 0.257340
\(667\) −67.3102 −2.60626
\(668\) 19.1141 0.739547
\(669\) −9.76267 −0.377447
\(670\) −29.2750 −1.13099
\(671\) 29.9933 1.15788
\(672\) −1.54837 −0.0597296
\(673\) −11.3642 −0.438058 −0.219029 0.975718i \(-0.570289\pi\)
−0.219029 + 0.975718i \(0.570289\pi\)
\(674\) −22.0912 −0.850920
\(675\) −4.38542 −0.168795
\(676\) 129.887 4.99565
\(677\) −8.47890 −0.325870 −0.162935 0.986637i \(-0.552096\pi\)
−0.162935 + 0.986637i \(0.552096\pi\)
\(678\) −31.0877 −1.19392
\(679\) 16.8967 0.648434
\(680\) 5.24977 0.201319
\(681\) −26.0747 −0.999186
\(682\) 41.8761 1.60352
\(683\) 13.5516 0.518537 0.259269 0.965805i \(-0.416518\pi\)
0.259269 + 0.965805i \(0.416518\pi\)
\(684\) −8.62583 −0.329817
\(685\) 6.24201 0.238495
\(686\) −2.48001 −0.0946871
\(687\) 6.24716 0.238344
\(688\) −20.2762 −0.773023
\(689\) −23.2096 −0.884214
\(690\) 13.3562 0.508462
\(691\) −43.4677 −1.65359 −0.826794 0.562505i \(-0.809838\pi\)
−0.826794 + 0.562505i \(0.809838\pi\)
\(692\) −47.7379 −1.81472
\(693\) 4.88599 0.185603
\(694\) 2.92522 0.111040
\(695\) 0.322131 0.0122191
\(696\) 52.2537 1.98067
\(697\) −5.27351 −0.199748
\(698\) 73.2649 2.77312
\(699\) 6.77809 0.256371
\(700\) −18.2014 −0.687947
\(701\) 28.8144 1.08831 0.544153 0.838986i \(-0.316851\pi\)
0.544153 + 0.838986i \(0.316851\pi\)
\(702\) 16.5055 0.622960
\(703\) 5.56545 0.209905
\(704\) −29.3669 −1.10681
\(705\) 5.10383 0.192221
\(706\) −25.2850 −0.951612
\(707\) 0.691702 0.0260141
\(708\) 50.7466 1.90717
\(709\) −20.9862 −0.788154 −0.394077 0.919077i \(-0.628936\pi\)
−0.394077 + 0.919077i \(0.628936\pi\)
\(710\) −13.9773 −0.524560
\(711\) −7.38716 −0.277040
\(712\) 87.6609 3.28523
\(713\) −23.7412 −0.889117
\(714\) −3.11406 −0.116541
\(715\) 25.4928 0.953375
\(716\) 94.7896 3.54245
\(717\) −23.7065 −0.885337
\(718\) −75.9255 −2.83351
\(719\) −4.40085 −0.164124 −0.0820620 0.996627i \(-0.526151\pi\)
−0.0820620 + 0.996627i \(0.526151\pi\)
\(720\) −3.86111 −0.143895
\(721\) −16.5225 −0.615328
\(722\) 36.4081 1.35497
\(723\) −9.28434 −0.345288
\(724\) 18.2799 0.679368
\(725\) 42.9686 1.59581
\(726\) −31.9247 −1.18484
\(727\) 21.6396 0.802568 0.401284 0.915954i \(-0.368564\pi\)
0.401284 + 0.915954i \(0.368564\pi\)
\(728\) 35.4939 1.31549
\(729\) 1.00000 0.0370370
\(730\) 4.37350 0.161871
\(731\) −5.16937 −0.191196
\(732\) 25.4779 0.941692
\(733\) 30.9010 1.14136 0.570678 0.821174i \(-0.306680\pi\)
0.570678 + 0.821174i \(0.306680\pi\)
\(734\) 26.8291 0.990279
\(735\) −0.783950 −0.0289164
\(736\) −10.6369 −0.392082
\(737\) −73.5712 −2.71003
\(738\) 10.4154 0.383398
\(739\) −32.2746 −1.18724 −0.593620 0.804745i \(-0.702302\pi\)
−0.593620 + 0.804745i \(0.702302\pi\)
\(740\) 8.71312 0.320301
\(741\) 13.8320 0.508131
\(742\) −8.64855 −0.317498
\(743\) 28.5122 1.04601 0.523006 0.852329i \(-0.324810\pi\)
0.523006 + 0.852329i \(0.324810\pi\)
\(744\) 18.4306 0.675699
\(745\) −18.5079 −0.678076
\(746\) −25.2977 −0.926213
\(747\) −3.82920 −0.140103
\(748\) 25.4636 0.931040
\(749\) −19.1211 −0.698671
\(750\) −18.2471 −0.666291
\(751\) −24.0517 −0.877659 −0.438829 0.898570i \(-0.644607\pi\)
−0.438829 + 0.898570i \(0.644607\pi\)
\(752\) −32.0650 −1.16929
\(753\) 0.539366 0.0196556
\(754\) −161.722 −5.88956
\(755\) 5.04544 0.183623
\(756\) 4.15043 0.150950
\(757\) −33.1952 −1.20650 −0.603249 0.797553i \(-0.706128\pi\)
−0.603249 + 0.797553i \(0.706128\pi\)
\(758\) −16.3242 −0.592920
\(759\) 33.5656 1.21835
\(760\) −8.68908 −0.315186
\(761\) 27.5176 0.997511 0.498755 0.866743i \(-0.333791\pi\)
0.498755 + 0.866743i \(0.333791\pi\)
\(762\) 2.48001 0.0898411
\(763\) 14.7383 0.533563
\(764\) 85.3167 3.08665
\(765\) −0.984380 −0.0355903
\(766\) 50.2031 1.81391
\(767\) −81.3748 −2.93828
\(768\) −32.6258 −1.17728
\(769\) −14.6074 −0.526757 −0.263378 0.964693i \(-0.584837\pi\)
−0.263378 + 0.964693i \(0.584837\pi\)
\(770\) 9.49933 0.342332
\(771\) −4.16847 −0.150124
\(772\) −75.0046 −2.69948
\(773\) 4.97622 0.178982 0.0894912 0.995988i \(-0.471476\pi\)
0.0894912 + 0.995988i \(0.471476\pi\)
\(774\) 10.2098 0.366983
\(775\) 15.1556 0.544405
\(776\) −90.1111 −3.23480
\(777\) −2.67789 −0.0960687
\(778\) −20.1032 −0.720736
\(779\) 8.72837 0.312726
\(780\) 21.6550 0.775372
\(781\) −35.1265 −1.25693
\(782\) −21.3928 −0.765007
\(783\) −9.79804 −0.350154
\(784\) 4.92520 0.175900
\(785\) 11.3662 0.405679
\(786\) 1.70535 0.0608278
\(787\) 20.1321 0.717633 0.358816 0.933408i \(-0.383180\pi\)
0.358816 + 0.933408i \(0.383180\pi\)
\(788\) −102.561 −3.65358
\(789\) −23.9281 −0.851862
\(790\) −14.3621 −0.510981
\(791\) 12.5353 0.445705
\(792\) −26.0573 −0.925906
\(793\) −40.8553 −1.45081
\(794\) 39.5184 1.40246
\(795\) −2.73388 −0.0969607
\(796\) 69.1476 2.45087
\(797\) −35.3654 −1.25271 −0.626354 0.779539i \(-0.715454\pi\)
−0.626354 + 0.779539i \(0.715454\pi\)
\(798\) 5.15419 0.182457
\(799\) −8.17490 −0.289207
\(800\) 6.79025 0.240071
\(801\) −16.4372 −0.580781
\(802\) −89.2733 −3.15235
\(803\) 10.9911 0.387867
\(804\) −62.4955 −2.20405
\(805\) −5.38555 −0.189816
\(806\) −57.0415 −2.00920
\(807\) −30.9708 −1.09022
\(808\) −3.68890 −0.129775
\(809\) 9.88279 0.347460 0.173730 0.984793i \(-0.444418\pi\)
0.173730 + 0.984793i \(0.444418\pi\)
\(810\) 1.94420 0.0683122
\(811\) 29.3646 1.03113 0.515566 0.856850i \(-0.327582\pi\)
0.515566 + 0.856850i \(0.327582\pi\)
\(812\) −40.6661 −1.42710
\(813\) −23.8214 −0.835452
\(814\) 32.4487 1.13733
\(815\) −6.32164 −0.221437
\(816\) 6.18440 0.216497
\(817\) 8.55601 0.299337
\(818\) 52.8466 1.84774
\(819\) −6.65543 −0.232560
\(820\) 13.6649 0.477199
\(821\) −11.5855 −0.404338 −0.202169 0.979351i \(-0.564799\pi\)
−0.202169 + 0.979351i \(0.564799\pi\)
\(822\) 19.7465 0.688737
\(823\) 32.4979 1.13281 0.566404 0.824128i \(-0.308334\pi\)
0.566404 + 0.824128i \(0.308334\pi\)
\(824\) 88.1154 3.06965
\(825\) −21.4271 −0.745996
\(826\) −30.3226 −1.05506
\(827\) −34.8327 −1.21125 −0.605626 0.795749i \(-0.707077\pi\)
−0.605626 + 0.795749i \(0.707077\pi\)
\(828\) 28.5124 0.990876
\(829\) 25.0563 0.870241 0.435120 0.900372i \(-0.356706\pi\)
0.435120 + 0.900372i \(0.356706\pi\)
\(830\) −7.44474 −0.258411
\(831\) −14.3357 −0.497301
\(832\) 40.0020 1.38682
\(833\) 1.25567 0.0435063
\(834\) 1.01905 0.0352870
\(835\) −3.61035 −0.124941
\(836\) −42.1457 −1.45764
\(837\) −3.45591 −0.119454
\(838\) 66.5632 2.29939
\(839\) −16.0782 −0.555082 −0.277541 0.960714i \(-0.589519\pi\)
−0.277541 + 0.960714i \(0.589519\pi\)
\(840\) 4.18086 0.144253
\(841\) 67.0017 2.31040
\(842\) −4.24855 −0.146415
\(843\) 20.6212 0.710232
\(844\) 60.4599 2.08112
\(845\) −24.5336 −0.843980
\(846\) 16.1458 0.555106
\(847\) 12.8729 0.442316
\(848\) 17.1757 0.589816
\(849\) 3.77609 0.129595
\(850\) 13.6565 0.468413
\(851\) −18.3965 −0.630622
\(852\) −29.8384 −1.02225
\(853\) 9.71995 0.332805 0.166402 0.986058i \(-0.446785\pi\)
0.166402 + 0.986058i \(0.446785\pi\)
\(854\) −15.2238 −0.520949
\(855\) 1.62928 0.0557203
\(856\) 101.974 3.48541
\(857\) 41.2846 1.41025 0.705127 0.709081i \(-0.250890\pi\)
0.705127 + 0.709081i \(0.250890\pi\)
\(858\) 80.6457 2.75320
\(859\) −1.05236 −0.0359061 −0.0179531 0.999839i \(-0.505715\pi\)
−0.0179531 + 0.999839i \(0.505715\pi\)
\(860\) 13.3951 0.456768
\(861\) −4.19977 −0.143128
\(862\) −74.0325 −2.52156
\(863\) 34.4783 1.17365 0.586827 0.809712i \(-0.300377\pi\)
0.586827 + 0.809712i \(0.300377\pi\)
\(864\) −1.54837 −0.0526765
\(865\) 9.01693 0.306585
\(866\) 16.1963 0.550374
\(867\) −15.4233 −0.523803
\(868\) −14.3435 −0.486850
\(869\) −36.0935 −1.22439
\(870\) −19.0494 −0.645834
\(871\) 100.215 3.39565
\(872\) −78.6005 −2.66175
\(873\) 16.8967 0.571865
\(874\) 35.4081 1.19770
\(875\) 7.35770 0.248736
\(876\) 9.33644 0.315449
\(877\) 41.2483 1.39285 0.696427 0.717627i \(-0.254772\pi\)
0.696427 + 0.717627i \(0.254772\pi\)
\(878\) 37.0206 1.24939
\(879\) −24.2919 −0.819345
\(880\) −18.8653 −0.635950
\(881\) 16.3701 0.551523 0.275761 0.961226i \(-0.411070\pi\)
0.275761 + 0.961226i \(0.411070\pi\)
\(882\) −2.48001 −0.0835061
\(883\) 39.4843 1.32875 0.664376 0.747398i \(-0.268697\pi\)
0.664376 + 0.747398i \(0.268697\pi\)
\(884\) −34.6851 −1.16659
\(885\) −9.58522 −0.322204
\(886\) 11.4929 0.386110
\(887\) −14.0226 −0.470831 −0.235416 0.971895i \(-0.575645\pi\)
−0.235416 + 0.971895i \(0.575645\pi\)
\(888\) 14.2814 0.479252
\(889\) −1.00000 −0.0335389
\(890\) −31.9572 −1.07121
\(891\) 4.88599 0.163687
\(892\) −40.5193 −1.35669
\(893\) 13.5306 0.452783
\(894\) −58.5492 −1.95818
\(895\) −17.9042 −0.598473
\(896\) 18.0026 0.601426
\(897\) −45.7212 −1.52659
\(898\) 16.4568 0.549171
\(899\) 33.8611 1.12933
\(900\) −18.2014 −0.606713
\(901\) 4.37890 0.145882
\(902\) 50.8897 1.69444
\(903\) −4.11683 −0.137000
\(904\) −66.8518 −2.22346
\(905\) −3.45278 −0.114774
\(906\) 15.9611 0.530273
\(907\) −35.6241 −1.18288 −0.591440 0.806349i \(-0.701440\pi\)
−0.591440 + 0.806349i \(0.701440\pi\)
\(908\) −108.221 −3.59145
\(909\) 0.691702 0.0229423
\(910\) −12.9395 −0.428940
\(911\) 4.45318 0.147541 0.0737703 0.997275i \(-0.476497\pi\)
0.0737703 + 0.997275i \(0.476497\pi\)
\(912\) −10.2360 −0.338949
\(913\) −18.7094 −0.619192
\(914\) 43.8529 1.45053
\(915\) −4.81238 −0.159092
\(916\) 25.9284 0.856698
\(917\) −0.687639 −0.0227078
\(918\) −3.11406 −0.102779
\(919\) 38.4633 1.26879 0.634394 0.773010i \(-0.281250\pi\)
0.634394 + 0.773010i \(0.281250\pi\)
\(920\) 28.7215 0.946921
\(921\) −18.6482 −0.614478
\(922\) 99.8618 3.28877
\(923\) 47.8475 1.57492
\(924\) 20.2789 0.667128
\(925\) 11.7437 0.386130
\(926\) 9.63572 0.316649
\(927\) −16.5225 −0.542668
\(928\) 15.1710 0.498012
\(929\) 41.8359 1.37259 0.686295 0.727323i \(-0.259236\pi\)
0.686295 + 0.727323i \(0.259236\pi\)
\(930\) −6.71897 −0.220324
\(931\) −2.07830 −0.0681135
\(932\) 28.1320 0.921493
\(933\) 20.8747 0.683407
\(934\) 3.29665 0.107870
\(935\) −4.80966 −0.157293
\(936\) 35.4939 1.16016
\(937\) 27.1190 0.885938 0.442969 0.896537i \(-0.353925\pi\)
0.442969 + 0.896537i \(0.353925\pi\)
\(938\) 37.3429 1.21929
\(939\) −7.93347 −0.258899
\(940\) 21.1831 0.690916
\(941\) −28.1483 −0.917608 −0.458804 0.888538i \(-0.651722\pi\)
−0.458804 + 0.888538i \(0.651722\pi\)
\(942\) 35.9568 1.17154
\(943\) −28.8514 −0.939531
\(944\) 60.2195 1.95998
\(945\) −0.783950 −0.0255019
\(946\) 49.8848 1.62189
\(947\) 26.7498 0.869251 0.434625 0.900611i \(-0.356881\pi\)
0.434625 + 0.900611i \(0.356881\pi\)
\(948\) −30.6599 −0.995786
\(949\) −14.9715 −0.485995
\(950\) −22.6033 −0.733349
\(951\) 11.3644 0.368517
\(952\) −6.69656 −0.217037
\(953\) −59.4329 −1.92522 −0.962611 0.270888i \(-0.912683\pi\)
−0.962611 + 0.270888i \(0.912683\pi\)
\(954\) −8.64855 −0.280007
\(955\) −16.1150 −0.521468
\(956\) −98.3923 −3.18223
\(957\) −47.8731 −1.54752
\(958\) 27.1943 0.878607
\(959\) −7.96226 −0.257115
\(960\) 4.71188 0.152075
\(961\) −19.0567 −0.614733
\(962\) −44.1999 −1.42506
\(963\) −19.1211 −0.616170
\(964\) −38.5340 −1.24110
\(965\) 14.1672 0.456058
\(966\) −17.0370 −0.548158
\(967\) −4.26909 −0.137285 −0.0686424 0.997641i \(-0.521867\pi\)
−0.0686424 + 0.997641i \(0.521867\pi\)
\(968\) −68.6519 −2.20655
\(969\) −2.60965 −0.0838341
\(970\) 32.8505 1.05477
\(971\) 53.2969 1.71038 0.855190 0.518315i \(-0.173441\pi\)
0.855190 + 0.518315i \(0.173441\pi\)
\(972\) 4.15043 0.133125
\(973\) −0.410908 −0.0131731
\(974\) −18.4106 −0.589915
\(975\) 29.1869 0.934729
\(976\) 30.2340 0.967766
\(977\) 19.3371 0.618647 0.309324 0.950957i \(-0.399897\pi\)
0.309324 + 0.950957i \(0.399897\pi\)
\(978\) −19.9983 −0.639476
\(979\) −80.3120 −2.56678
\(980\) −3.25373 −0.103937
\(981\) 14.7383 0.470558
\(982\) −25.9761 −0.828930
\(983\) −38.4570 −1.22659 −0.613294 0.789855i \(-0.710156\pi\)
−0.613294 + 0.789855i \(0.710156\pi\)
\(984\) 22.3977 0.714011
\(985\) 19.3721 0.617248
\(986\) 30.5117 0.971690
\(987\) −6.51041 −0.207229
\(988\) 57.4087 1.82641
\(989\) −28.2817 −0.899305
\(990\) 9.49933 0.301909
\(991\) 25.2038 0.800626 0.400313 0.916379i \(-0.368901\pi\)
0.400313 + 0.916379i \(0.368901\pi\)
\(992\) 5.35101 0.169895
\(993\) −19.1983 −0.609238
\(994\) 17.8294 0.565513
\(995\) −13.0609 −0.414058
\(996\) −15.8928 −0.503584
\(997\) 42.0562 1.33193 0.665966 0.745982i \(-0.268019\pi\)
0.665966 + 0.745982i \(0.268019\pi\)
\(998\) −66.1651 −2.09442
\(999\) −2.67789 −0.0847247
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 2667.2.a.j.1.1 7
3.2 odd 2 8001.2.a.l.1.7 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2667.2.a.j.1.1 7 1.1 even 1 trivial
8001.2.a.l.1.7 7 3.2 odd 2