Properties

Label 2667.2.a.j.1.5
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 1.5
Root \(-2.06168\) of defining polynomial
Character \(\chi\) \(=\) 2667.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.692358 q^{2} +1.00000 q^{3} -1.52064 q^{4} -2.78145 q^{5} +0.692358 q^{6} +1.00000 q^{7} -2.43754 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+0.692358 q^{2} +1.00000 q^{3} -1.52064 q^{4} -2.78145 q^{5} +0.692358 q^{6} +1.00000 q^{7} -2.43754 q^{8} +1.00000 q^{9} -1.92576 q^{10} -0.348849 q^{11} -1.52064 q^{12} +2.17757 q^{13} +0.692358 q^{14} -2.78145 q^{15} +1.35363 q^{16} +7.42626 q^{17} +0.692358 q^{18} -0.255629 q^{19} +4.22958 q^{20} +1.00000 q^{21} -0.241529 q^{22} -4.98233 q^{23} -2.43754 q^{24} +2.73644 q^{25} +1.50766 q^{26} +1.00000 q^{27} -1.52064 q^{28} -6.88124 q^{29} -1.92576 q^{30} -10.1038 q^{31} +5.81228 q^{32} -0.348849 q^{33} +5.14163 q^{34} -2.78145 q^{35} -1.52064 q^{36} -1.64279 q^{37} -0.176987 q^{38} +2.17757 q^{39} +6.77989 q^{40} +3.56990 q^{41} +0.692358 q^{42} -9.34628 q^{43} +0.530475 q^{44} -2.78145 q^{45} -3.44956 q^{46} +9.73885 q^{47} +1.35363 q^{48} +1.00000 q^{49} +1.89460 q^{50} +7.42626 q^{51} -3.31130 q^{52} -7.44666 q^{53} +0.692358 q^{54} +0.970306 q^{55} -2.43754 q^{56} -0.255629 q^{57} -4.76428 q^{58} -2.01055 q^{59} +4.22958 q^{60} -7.69549 q^{61} -6.99543 q^{62} +1.00000 q^{63} +1.31692 q^{64} -6.05678 q^{65} -0.241529 q^{66} -6.52951 q^{67} -11.2927 q^{68} -4.98233 q^{69} -1.92576 q^{70} +13.7550 q^{71} -2.43754 q^{72} -9.37124 q^{73} -1.13740 q^{74} +2.73644 q^{75} +0.388720 q^{76} -0.348849 q^{77} +1.50766 q^{78} -5.92206 q^{79} -3.76505 q^{80} +1.00000 q^{81} +2.47165 q^{82} +1.68660 q^{83} -1.52064 q^{84} -20.6557 q^{85} -6.47097 q^{86} -6.88124 q^{87} +0.850335 q^{88} -17.6750 q^{89} -1.92576 q^{90} +2.17757 q^{91} +7.57634 q^{92} -10.1038 q^{93} +6.74277 q^{94} +0.711019 q^{95} +5.81228 q^{96} -0.216772 q^{97} +0.692358 q^{98} -0.348849 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q - 2q^{2} + 7q^{3} + 4q^{4} - 8q^{5} - 2q^{6} + 7q^{7} - 9q^{8} + 7q^{9} + O(q^{10}) \) \( 7q - 2q^{2} + 7q^{3} + 4q^{4} - 8q^{5} - 2q^{6} + 7q^{7} - 9q^{8} + 7q^{9} - 3q^{11} + 4q^{12} - 23q^{13} - 2q^{14} - 8q^{15} + 2q^{16} + 3q^{17} - 2q^{18} - 9q^{19} - 9q^{20} + 7q^{21} - 19q^{22} + 12q^{23} - 9q^{24} + 3q^{25} + 18q^{26} + 7q^{27} + 4q^{28} - 9q^{29} - 33q^{31} + 10q^{32} - 3q^{33} - 2q^{34} - 8q^{35} + 4q^{36} - 33q^{37} - 3q^{38} - 23q^{39} - 9q^{40} - 3q^{41} - 2q^{42} - 9q^{43} + 2q^{44} - 8q^{45} - 32q^{46} + 11q^{47} + 2q^{48} + 7q^{49} + 29q^{50} + 3q^{51} - 21q^{52} + q^{53} - 2q^{54} - 16q^{55} - 9q^{56} - 9q^{57} - 5q^{58} - 30q^{59} - 9q^{60} - 19q^{61} + 3q^{62} + 7q^{63} - 21q^{64} + 14q^{65} - 19q^{66} - 30q^{67} + 24q^{68} + 12q^{69} + 8q^{71} - 9q^{72} - 20q^{73} - 9q^{74} + 3q^{75} - 42q^{76} - 3q^{77} + 18q^{78} + 8q^{79} + 12q^{80} + 7q^{81} + 10q^{82} - 34q^{83} + 4q^{84} - 28q^{85} + 24q^{86} - 9q^{87} - q^{88} - 12q^{89} - 23q^{91} + 60q^{92} - 33q^{93} - 3q^{94} + 12q^{95} + 10q^{96} + 7q^{97} - 2q^{98} - 3q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.692358 0.489571 0.244785 0.969577i \(-0.421282\pi\)
0.244785 + 0.969577i \(0.421282\pi\)
\(3\) 1.00000 0.577350
\(4\) −1.52064 −0.760320
\(5\) −2.78145 −1.24390 −0.621950 0.783057i \(-0.713659\pi\)
−0.621950 + 0.783057i \(0.713659\pi\)
\(6\) 0.692358 0.282654
\(7\) 1.00000 0.377964
\(8\) −2.43754 −0.861801
\(9\) 1.00000 0.333333
\(10\) −1.92576 −0.608977
\(11\) −0.348849 −0.105182 −0.0525910 0.998616i \(-0.516748\pi\)
−0.0525910 + 0.998616i \(0.516748\pi\)
\(12\) −1.52064 −0.438971
\(13\) 2.17757 0.603948 0.301974 0.953316i \(-0.402354\pi\)
0.301974 + 0.953316i \(0.402354\pi\)
\(14\) 0.692358 0.185040
\(15\) −2.78145 −0.718166
\(16\) 1.35363 0.338408
\(17\) 7.42626 1.80113 0.900567 0.434718i \(-0.143152\pi\)
0.900567 + 0.434718i \(0.143152\pi\)
\(18\) 0.692358 0.163190
\(19\) −0.255629 −0.0586454 −0.0293227 0.999570i \(-0.509335\pi\)
−0.0293227 + 0.999570i \(0.509335\pi\)
\(20\) 4.22958 0.945763
\(21\) 1.00000 0.218218
\(22\) −0.241529 −0.0514941
\(23\) −4.98233 −1.03889 −0.519444 0.854504i \(-0.673861\pi\)
−0.519444 + 0.854504i \(0.673861\pi\)
\(24\) −2.43754 −0.497561
\(25\) 2.73644 0.547288
\(26\) 1.50766 0.295676
\(27\) 1.00000 0.192450
\(28\) −1.52064 −0.287374
\(29\) −6.88124 −1.27781 −0.638907 0.769284i \(-0.720613\pi\)
−0.638907 + 0.769284i \(0.720613\pi\)
\(30\) −1.92576 −0.351593
\(31\) −10.1038 −1.81469 −0.907346 0.420385i \(-0.861895\pi\)
−0.907346 + 0.420385i \(0.861895\pi\)
\(32\) 5.81228 1.02748
\(33\) −0.348849 −0.0607269
\(34\) 5.14163 0.881782
\(35\) −2.78145 −0.470150
\(36\) −1.52064 −0.253440
\(37\) −1.64279 −0.270072 −0.135036 0.990841i \(-0.543115\pi\)
−0.135036 + 0.990841i \(0.543115\pi\)
\(38\) −0.176987 −0.0287111
\(39\) 2.17757 0.348690
\(40\) 6.77989 1.07200
\(41\) 3.56990 0.557525 0.278762 0.960360i \(-0.410076\pi\)
0.278762 + 0.960360i \(0.410076\pi\)
\(42\) 0.692358 0.106833
\(43\) −9.34628 −1.42529 −0.712647 0.701523i \(-0.752504\pi\)
−0.712647 + 0.701523i \(0.752504\pi\)
\(44\) 0.530475 0.0799721
\(45\) −2.78145 −0.414633
\(46\) −3.44956 −0.508610
\(47\) 9.73885 1.42056 0.710279 0.703920i \(-0.248569\pi\)
0.710279 + 0.703920i \(0.248569\pi\)
\(48\) 1.35363 0.195380
\(49\) 1.00000 0.142857
\(50\) 1.89460 0.267936
\(51\) 7.42626 1.03988
\(52\) −3.31130 −0.459194
\(53\) −7.44666 −1.02288 −0.511439 0.859320i \(-0.670887\pi\)
−0.511439 + 0.859320i \(0.670887\pi\)
\(54\) 0.692358 0.0942179
\(55\) 0.970306 0.130836
\(56\) −2.43754 −0.325730
\(57\) −0.255629 −0.0338589
\(58\) −4.76428 −0.625581
\(59\) −2.01055 −0.261752 −0.130876 0.991399i \(-0.541779\pi\)
−0.130876 + 0.991399i \(0.541779\pi\)
\(60\) 4.22958 0.546036
\(61\) −7.69549 −0.985306 −0.492653 0.870226i \(-0.663973\pi\)
−0.492653 + 0.870226i \(0.663973\pi\)
\(62\) −6.99543 −0.888420
\(63\) 1.00000 0.125988
\(64\) 1.31692 0.164615
\(65\) −6.05678 −0.751252
\(66\) −0.241529 −0.0297301
\(67\) −6.52951 −0.797706 −0.398853 0.917015i \(-0.630592\pi\)
−0.398853 + 0.917015i \(0.630592\pi\)
\(68\) −11.2927 −1.36944
\(69\) −4.98233 −0.599803
\(70\) −1.92576 −0.230172
\(71\) 13.7550 1.63242 0.816208 0.577758i \(-0.196072\pi\)
0.816208 + 0.577758i \(0.196072\pi\)
\(72\) −2.43754 −0.287267
\(73\) −9.37124 −1.09682 −0.548411 0.836209i \(-0.684767\pi\)
−0.548411 + 0.836209i \(0.684767\pi\)
\(74\) −1.13740 −0.132220
\(75\) 2.73644 0.315977
\(76\) 0.388720 0.0445893
\(77\) −0.348849 −0.0397551
\(78\) 1.50766 0.170708
\(79\) −5.92206 −0.666283 −0.333142 0.942877i \(-0.608109\pi\)
−0.333142 + 0.942877i \(0.608109\pi\)
\(80\) −3.76505 −0.420945
\(81\) 1.00000 0.111111
\(82\) 2.47165 0.272948
\(83\) 1.68660 0.185128 0.0925642 0.995707i \(-0.470494\pi\)
0.0925642 + 0.995707i \(0.470494\pi\)
\(84\) −1.52064 −0.165916
\(85\) −20.6557 −2.24043
\(86\) −6.47097 −0.697783
\(87\) −6.88124 −0.737747
\(88\) 0.850335 0.0906461
\(89\) −17.6750 −1.87355 −0.936775 0.349932i \(-0.886205\pi\)
−0.936775 + 0.349932i \(0.886205\pi\)
\(90\) −1.92576 −0.202992
\(91\) 2.17757 0.228271
\(92\) 7.57634 0.789888
\(93\) −10.1038 −1.04771
\(94\) 6.74277 0.695464
\(95\) 0.711019 0.0729490
\(96\) 5.81228 0.593214
\(97\) −0.216772 −0.0220099 −0.0110049 0.999939i \(-0.503503\pi\)
−0.0110049 + 0.999939i \(0.503503\pi\)
\(98\) 0.692358 0.0699387
\(99\) −0.348849 −0.0350607
\(100\) −4.16114 −0.416114
\(101\) −15.6270 −1.55494 −0.777472 0.628918i \(-0.783498\pi\)
−0.777472 + 0.628918i \(0.783498\pi\)
\(102\) 5.14163 0.509097
\(103\) −2.82388 −0.278245 −0.139122 0.990275i \(-0.544428\pi\)
−0.139122 + 0.990275i \(0.544428\pi\)
\(104\) −5.30791 −0.520484
\(105\) −2.78145 −0.271441
\(106\) −5.15575 −0.500771
\(107\) −13.6505 −1.31964 −0.659820 0.751424i \(-0.729367\pi\)
−0.659820 + 0.751424i \(0.729367\pi\)
\(108\) −1.52064 −0.146324
\(109\) −12.4581 −1.19327 −0.596633 0.802514i \(-0.703495\pi\)
−0.596633 + 0.802514i \(0.703495\pi\)
\(110\) 0.671799 0.0640535
\(111\) −1.64279 −0.155926
\(112\) 1.35363 0.127906
\(113\) 17.1295 1.61140 0.805702 0.592322i \(-0.201788\pi\)
0.805702 + 0.592322i \(0.201788\pi\)
\(114\) −0.176987 −0.0165763
\(115\) 13.8581 1.29227
\(116\) 10.4639 0.971549
\(117\) 2.17757 0.201316
\(118\) −1.39202 −0.128146
\(119\) 7.42626 0.680764
\(120\) 6.77989 0.618917
\(121\) −10.8783 −0.988937
\(122\) −5.32803 −0.482377
\(123\) 3.56990 0.321887
\(124\) 15.3642 1.37975
\(125\) 6.29597 0.563128
\(126\) 0.692358 0.0616801
\(127\) −1.00000 −0.0887357
\(128\) −10.7128 −0.946885
\(129\) −9.34628 −0.822894
\(130\) −4.19346 −0.367791
\(131\) 8.33905 0.728587 0.364293 0.931284i \(-0.381311\pi\)
0.364293 + 0.931284i \(0.381311\pi\)
\(132\) 0.530475 0.0461719
\(133\) −0.255629 −0.0221659
\(134\) −4.52075 −0.390534
\(135\) −2.78145 −0.239389
\(136\) −18.1018 −1.55222
\(137\) 20.9573 1.79050 0.895251 0.445563i \(-0.146996\pi\)
0.895251 + 0.445563i \(0.146996\pi\)
\(138\) −3.44956 −0.293646
\(139\) −10.1867 −0.864026 −0.432013 0.901867i \(-0.642197\pi\)
−0.432013 + 0.901867i \(0.642197\pi\)
\(140\) 4.22958 0.357465
\(141\) 9.73885 0.820159
\(142\) 9.52337 0.799183
\(143\) −0.759643 −0.0635245
\(144\) 1.35363 0.112803
\(145\) 19.1398 1.58947
\(146\) −6.48825 −0.536972
\(147\) 1.00000 0.0824786
\(148\) 2.49809 0.205342
\(149\) −4.86877 −0.398865 −0.199433 0.979912i \(-0.563910\pi\)
−0.199433 + 0.979912i \(0.563910\pi\)
\(150\) 1.89460 0.154693
\(151\) −1.93573 −0.157528 −0.0787638 0.996893i \(-0.525097\pi\)
−0.0787638 + 0.996893i \(0.525097\pi\)
\(152\) 0.623107 0.0505407
\(153\) 7.42626 0.600378
\(154\) −0.241529 −0.0194629
\(155\) 28.1031 2.25730
\(156\) −3.31130 −0.265116
\(157\) 4.29270 0.342595 0.171297 0.985219i \(-0.445204\pi\)
0.171297 + 0.985219i \(0.445204\pi\)
\(158\) −4.10018 −0.326193
\(159\) −7.44666 −0.590559
\(160\) −16.1665 −1.27808
\(161\) −4.98233 −0.392663
\(162\) 0.692358 0.0543968
\(163\) 4.96855 0.389167 0.194583 0.980886i \(-0.437664\pi\)
0.194583 + 0.980886i \(0.437664\pi\)
\(164\) −5.42854 −0.423897
\(165\) 0.970306 0.0755382
\(166\) 1.16773 0.0906335
\(167\) −14.3188 −1.10802 −0.554012 0.832508i \(-0.686904\pi\)
−0.554012 + 0.832508i \(0.686904\pi\)
\(168\) −2.43754 −0.188061
\(169\) −8.25820 −0.635246
\(170\) −14.3012 −1.09685
\(171\) −0.255629 −0.0195485
\(172\) 14.2123 1.08368
\(173\) −22.2870 −1.69445 −0.847225 0.531235i \(-0.821728\pi\)
−0.847225 + 0.531235i \(0.821728\pi\)
\(174\) −4.76428 −0.361179
\(175\) 2.73644 0.206855
\(176\) −0.472213 −0.0355944
\(177\) −2.01055 −0.151122
\(178\) −12.2374 −0.917235
\(179\) 26.5031 1.98093 0.990467 0.137748i \(-0.0439863\pi\)
0.990467 + 0.137748i \(0.0439863\pi\)
\(180\) 4.22958 0.315254
\(181\) −6.62020 −0.492076 −0.246038 0.969260i \(-0.579129\pi\)
−0.246038 + 0.969260i \(0.579129\pi\)
\(182\) 1.50766 0.111755
\(183\) −7.69549 −0.568867
\(184\) 12.1447 0.895316
\(185\) 4.56932 0.335943
\(186\) −6.99543 −0.512930
\(187\) −2.59065 −0.189447
\(188\) −14.8093 −1.08008
\(189\) 1.00000 0.0727393
\(190\) 0.492279 0.0357137
\(191\) 9.50979 0.688104 0.344052 0.938951i \(-0.388200\pi\)
0.344052 + 0.938951i \(0.388200\pi\)
\(192\) 1.31692 0.0950403
\(193\) 18.2187 1.31141 0.655706 0.755016i \(-0.272371\pi\)
0.655706 + 0.755016i \(0.272371\pi\)
\(194\) −0.150084 −0.0107754
\(195\) −6.05678 −0.433735
\(196\) −1.52064 −0.108617
\(197\) −6.73369 −0.479756 −0.239878 0.970803i \(-0.577107\pi\)
−0.239878 + 0.970803i \(0.577107\pi\)
\(198\) −0.241529 −0.0171647
\(199\) 19.1877 1.36018 0.680088 0.733130i \(-0.261941\pi\)
0.680088 + 0.733130i \(0.261941\pi\)
\(200\) −6.67019 −0.471654
\(201\) −6.52951 −0.460556
\(202\) −10.8195 −0.761255
\(203\) −6.88124 −0.482969
\(204\) −11.2927 −0.790646
\(205\) −9.92948 −0.693505
\(206\) −1.95513 −0.136221
\(207\) −4.98233 −0.346296
\(208\) 2.94762 0.204381
\(209\) 0.0891761 0.00616844
\(210\) −1.92576 −0.132890
\(211\) 3.89333 0.268028 0.134014 0.990979i \(-0.457213\pi\)
0.134014 + 0.990979i \(0.457213\pi\)
\(212\) 11.3237 0.777715
\(213\) 13.7550 0.942476
\(214\) −9.45100 −0.646057
\(215\) 25.9962 1.77292
\(216\) −2.43754 −0.165854
\(217\) −10.1038 −0.685889
\(218\) −8.62544 −0.584189
\(219\) −9.37124 −0.633250
\(220\) −1.47549 −0.0994773
\(221\) 16.1712 1.08779
\(222\) −1.13740 −0.0763370
\(223\) 17.8977 1.19852 0.599258 0.800556i \(-0.295462\pi\)
0.599258 + 0.800556i \(0.295462\pi\)
\(224\) 5.81228 0.388349
\(225\) 2.73644 0.182429
\(226\) 11.8597 0.788896
\(227\) 8.76418 0.581699 0.290850 0.956769i \(-0.406062\pi\)
0.290850 + 0.956769i \(0.406062\pi\)
\(228\) 0.388720 0.0257436
\(229\) −20.1983 −1.33474 −0.667371 0.744726i \(-0.732580\pi\)
−0.667371 + 0.744726i \(0.732580\pi\)
\(230\) 9.59476 0.632660
\(231\) −0.348849 −0.0229526
\(232\) 16.7733 1.10122
\(233\) −29.4789 −1.93122 −0.965612 0.259986i \(-0.916282\pi\)
−0.965612 + 0.259986i \(0.916282\pi\)
\(234\) 1.50766 0.0985585
\(235\) −27.0881 −1.76703
\(236\) 3.05733 0.199015
\(237\) −5.92206 −0.384679
\(238\) 5.14163 0.333282
\(239\) −22.7548 −1.47188 −0.735941 0.677045i \(-0.763260\pi\)
−0.735941 + 0.677045i \(0.763260\pi\)
\(240\) −3.76505 −0.243033
\(241\) 12.6179 0.812789 0.406395 0.913698i \(-0.366786\pi\)
0.406395 + 0.913698i \(0.366786\pi\)
\(242\) −7.53168 −0.484155
\(243\) 1.00000 0.0641500
\(244\) 11.7021 0.749148
\(245\) −2.78145 −0.177700
\(246\) 2.47165 0.157586
\(247\) −0.556650 −0.0354188
\(248\) 24.6284 1.56390
\(249\) 1.68660 0.106884
\(250\) 4.35906 0.275691
\(251\) −17.4819 −1.10345 −0.551725 0.834026i \(-0.686030\pi\)
−0.551725 + 0.834026i \(0.686030\pi\)
\(252\) −1.52064 −0.0957914
\(253\) 1.73808 0.109272
\(254\) −0.692358 −0.0434424
\(255\) −20.6557 −1.29351
\(256\) −10.0509 −0.628182
\(257\) 8.26061 0.515283 0.257641 0.966241i \(-0.417055\pi\)
0.257641 + 0.966241i \(0.417055\pi\)
\(258\) −6.47097 −0.402865
\(259\) −1.64279 −0.102078
\(260\) 9.21019 0.571192
\(261\) −6.88124 −0.425938
\(262\) 5.77361 0.356695
\(263\) 25.8026 1.59106 0.795530 0.605915i \(-0.207193\pi\)
0.795530 + 0.605915i \(0.207193\pi\)
\(264\) 0.850335 0.0523345
\(265\) 20.7125 1.27236
\(266\) −0.176987 −0.0108518
\(267\) −17.6750 −1.08169
\(268\) 9.92903 0.606512
\(269\) −6.10591 −0.372284 −0.186142 0.982523i \(-0.559598\pi\)
−0.186142 + 0.982523i \(0.559598\pi\)
\(270\) −1.92576 −0.117198
\(271\) −16.8740 −1.02503 −0.512513 0.858680i \(-0.671285\pi\)
−0.512513 + 0.858680i \(0.671285\pi\)
\(272\) 10.0524 0.609517
\(273\) 2.17757 0.131792
\(274\) 14.5099 0.876577
\(275\) −0.954606 −0.0575649
\(276\) 7.57634 0.456042
\(277\) 29.0357 1.74459 0.872293 0.488983i \(-0.162632\pi\)
0.872293 + 0.488983i \(0.162632\pi\)
\(278\) −7.05285 −0.423002
\(279\) −10.1038 −0.604897
\(280\) 6.77989 0.405176
\(281\) 3.71119 0.221391 0.110695 0.993854i \(-0.464692\pi\)
0.110695 + 0.993854i \(0.464692\pi\)
\(282\) 6.74277 0.401526
\(283\) −10.0392 −0.596770 −0.298385 0.954446i \(-0.596448\pi\)
−0.298385 + 0.954446i \(0.596448\pi\)
\(284\) −20.9164 −1.24116
\(285\) 0.711019 0.0421171
\(286\) −0.525945 −0.0310998
\(287\) 3.56990 0.210725
\(288\) 5.81228 0.342492
\(289\) 38.1494 2.24408
\(290\) 13.2516 0.778160
\(291\) −0.216772 −0.0127074
\(292\) 14.2503 0.833935
\(293\) 30.6862 1.79271 0.896355 0.443338i \(-0.146206\pi\)
0.896355 + 0.443338i \(0.146206\pi\)
\(294\) 0.692358 0.0403791
\(295\) 5.59224 0.325593
\(296\) 4.00436 0.232749
\(297\) −0.348849 −0.0202423
\(298\) −3.37093 −0.195273
\(299\) −10.8494 −0.627435
\(300\) −4.16114 −0.240244
\(301\) −9.34628 −0.538711
\(302\) −1.34022 −0.0771209
\(303\) −15.6270 −0.897747
\(304\) −0.346027 −0.0198460
\(305\) 21.4046 1.22562
\(306\) 5.14163 0.293927
\(307\) −7.58942 −0.433151 −0.216575 0.976266i \(-0.569489\pi\)
−0.216575 + 0.976266i \(0.569489\pi\)
\(308\) 0.530475 0.0302266
\(309\) −2.82388 −0.160645
\(310\) 19.4574 1.10511
\(311\) −31.5432 −1.78865 −0.894324 0.447419i \(-0.852343\pi\)
−0.894324 + 0.447419i \(0.852343\pi\)
\(312\) −5.30791 −0.300501
\(313\) 25.5982 1.44689 0.723447 0.690379i \(-0.242556\pi\)
0.723447 + 0.690379i \(0.242556\pi\)
\(314\) 2.97208 0.167724
\(315\) −2.78145 −0.156717
\(316\) 9.00532 0.506589
\(317\) 20.7732 1.16674 0.583370 0.812206i \(-0.301734\pi\)
0.583370 + 0.812206i \(0.301734\pi\)
\(318\) −5.15575 −0.289120
\(319\) 2.40052 0.134403
\(320\) −3.66293 −0.204764
\(321\) −13.6505 −0.761894
\(322\) −3.44956 −0.192236
\(323\) −1.89837 −0.105628
\(324\) −1.52064 −0.0844800
\(325\) 5.95878 0.330534
\(326\) 3.44001 0.190525
\(327\) −12.4581 −0.688933
\(328\) −8.70178 −0.480476
\(329\) 9.73885 0.536920
\(330\) 0.671799 0.0369813
\(331\) −3.11825 −0.171394 −0.0856971 0.996321i \(-0.527312\pi\)
−0.0856971 + 0.996321i \(0.527312\pi\)
\(332\) −2.56471 −0.140757
\(333\) −1.64279 −0.0900241
\(334\) −9.91376 −0.542457
\(335\) 18.1615 0.992267
\(336\) 1.35363 0.0738466
\(337\) 0.0769121 0.00418967 0.00209483 0.999998i \(-0.499333\pi\)
0.00209483 + 0.999998i \(0.499333\pi\)
\(338\) −5.71763 −0.310998
\(339\) 17.1295 0.930344
\(340\) 31.4100 1.70344
\(341\) 3.52470 0.190873
\(342\) −0.176987 −0.00957035
\(343\) 1.00000 0.0539949
\(344\) 22.7820 1.22832
\(345\) 13.8581 0.746095
\(346\) −15.4306 −0.829553
\(347\) −7.04794 −0.378353 −0.189177 0.981943i \(-0.560582\pi\)
−0.189177 + 0.981943i \(0.560582\pi\)
\(348\) 10.4639 0.560924
\(349\) 15.4067 0.824703 0.412351 0.911025i \(-0.364708\pi\)
0.412351 + 0.911025i \(0.364708\pi\)
\(350\) 1.89460 0.101270
\(351\) 2.17757 0.116230
\(352\) −2.02761 −0.108072
\(353\) 15.3530 0.817157 0.408578 0.912723i \(-0.366025\pi\)
0.408578 + 0.912723i \(0.366025\pi\)
\(354\) −1.39202 −0.0739851
\(355\) −38.2587 −2.03056
\(356\) 26.8774 1.42450
\(357\) 7.42626 0.393039
\(358\) 18.3496 0.969808
\(359\) −2.58094 −0.136217 −0.0681084 0.997678i \(-0.521696\pi\)
−0.0681084 + 0.997678i \(0.521696\pi\)
\(360\) 6.77989 0.357332
\(361\) −18.9347 −0.996561
\(362\) −4.58355 −0.240906
\(363\) −10.8783 −0.570963
\(364\) −3.31130 −0.173559
\(365\) 26.0656 1.36434
\(366\) −5.32803 −0.278501
\(367\) 22.1135 1.15431 0.577157 0.816634i \(-0.304162\pi\)
0.577157 + 0.816634i \(0.304162\pi\)
\(368\) −6.74424 −0.351568
\(369\) 3.56990 0.185842
\(370\) 3.16360 0.164468
\(371\) −7.44666 −0.386612
\(372\) 15.3642 0.796597
\(373\) −16.3558 −0.846873 −0.423436 0.905926i \(-0.639176\pi\)
−0.423436 + 0.905926i \(0.639176\pi\)
\(374\) −1.79365 −0.0927477
\(375\) 6.29597 0.325122
\(376\) −23.7389 −1.22424
\(377\) −14.9844 −0.771734
\(378\) 0.692358 0.0356110
\(379\) 22.3125 1.14612 0.573059 0.819514i \(-0.305757\pi\)
0.573059 + 0.819514i \(0.305757\pi\)
\(380\) −1.08120 −0.0554646
\(381\) −1.00000 −0.0512316
\(382\) 6.58418 0.336876
\(383\) −18.0582 −0.922729 −0.461365 0.887211i \(-0.652640\pi\)
−0.461365 + 0.887211i \(0.652640\pi\)
\(384\) −10.7128 −0.546685
\(385\) 0.970306 0.0494514
\(386\) 12.6139 0.642029
\(387\) −9.34628 −0.475098
\(388\) 0.329632 0.0167346
\(389\) −1.96882 −0.0998232 −0.0499116 0.998754i \(-0.515894\pi\)
−0.0499116 + 0.998754i \(0.515894\pi\)
\(390\) −4.19346 −0.212344
\(391\) −37.0001 −1.87118
\(392\) −2.43754 −0.123114
\(393\) 8.33905 0.420650
\(394\) −4.66212 −0.234874
\(395\) 16.4719 0.828790
\(396\) 0.530475 0.0266574
\(397\) −13.1572 −0.660341 −0.330171 0.943921i \(-0.607106\pi\)
−0.330171 + 0.943921i \(0.607106\pi\)
\(398\) 13.2847 0.665903
\(399\) −0.255629 −0.0127975
\(400\) 3.70413 0.185206
\(401\) −27.6771 −1.38213 −0.691063 0.722794i \(-0.742857\pi\)
−0.691063 + 0.722794i \(0.742857\pi\)
\(402\) −4.52075 −0.225475
\(403\) −22.0017 −1.09598
\(404\) 23.7630 1.18226
\(405\) −2.78145 −0.138211
\(406\) −4.76428 −0.236447
\(407\) 0.573085 0.0284068
\(408\) −18.1018 −0.896174
\(409\) −23.5157 −1.16278 −0.581388 0.813626i \(-0.697490\pi\)
−0.581388 + 0.813626i \(0.697490\pi\)
\(410\) −6.87475 −0.339520
\(411\) 20.9573 1.03375
\(412\) 4.29410 0.211555
\(413\) −2.01055 −0.0989328
\(414\) −3.44956 −0.169537
\(415\) −4.69119 −0.230281
\(416\) 12.6566 0.620542
\(417\) −10.1867 −0.498846
\(418\) 0.0617418 0.00301989
\(419\) 3.78832 0.185072 0.0925359 0.995709i \(-0.470503\pi\)
0.0925359 + 0.995709i \(0.470503\pi\)
\(420\) 4.22958 0.206382
\(421\) −40.3970 −1.96883 −0.984415 0.175859i \(-0.943730\pi\)
−0.984415 + 0.175859i \(0.943730\pi\)
\(422\) 2.69558 0.131219
\(423\) 9.73885 0.473519
\(424\) 18.1516 0.881518
\(425\) 20.3215 0.985739
\(426\) 9.52337 0.461409
\(427\) −7.69549 −0.372411
\(428\) 20.7574 1.00335
\(429\) −0.759643 −0.0366759
\(430\) 17.9986 0.867972
\(431\) 26.3339 1.26846 0.634230 0.773144i \(-0.281317\pi\)
0.634230 + 0.773144i \(0.281317\pi\)
\(432\) 1.35363 0.0651266
\(433\) −6.47692 −0.311261 −0.155631 0.987815i \(-0.549741\pi\)
−0.155631 + 0.987815i \(0.549741\pi\)
\(434\) −6.99543 −0.335791
\(435\) 19.1398 0.917684
\(436\) 18.9443 0.907265
\(437\) 1.27363 0.0609260
\(438\) −6.48825 −0.310021
\(439\) 11.9232 0.569062 0.284531 0.958667i \(-0.408162\pi\)
0.284531 + 0.958667i \(0.408162\pi\)
\(440\) −2.36516 −0.112755
\(441\) 1.00000 0.0476190
\(442\) 11.1962 0.532551
\(443\) 31.9287 1.51698 0.758490 0.651685i \(-0.225938\pi\)
0.758490 + 0.651685i \(0.225938\pi\)
\(444\) 2.49809 0.118554
\(445\) 49.1622 2.33051
\(446\) 12.3916 0.586759
\(447\) −4.86877 −0.230285
\(448\) 1.31692 0.0622185
\(449\) 31.3379 1.47893 0.739463 0.673197i \(-0.235079\pi\)
0.739463 + 0.673197i \(0.235079\pi\)
\(450\) 1.89460 0.0893121
\(451\) −1.24536 −0.0586416
\(452\) −26.0477 −1.22518
\(453\) −1.93573 −0.0909486
\(454\) 6.06795 0.284783
\(455\) −6.05678 −0.283946
\(456\) 0.623107 0.0291797
\(457\) −17.5797 −0.822344 −0.411172 0.911558i \(-0.634880\pi\)
−0.411172 + 0.911558i \(0.634880\pi\)
\(458\) −13.9844 −0.653450
\(459\) 7.42626 0.346628
\(460\) −21.0732 −0.982542
\(461\) −27.4541 −1.27867 −0.639333 0.768930i \(-0.720789\pi\)
−0.639333 + 0.768930i \(0.720789\pi\)
\(462\) −0.241529 −0.0112369
\(463\) −18.2297 −0.847207 −0.423604 0.905848i \(-0.639235\pi\)
−0.423604 + 0.905848i \(0.639235\pi\)
\(464\) −9.31466 −0.432422
\(465\) 28.1031 1.30325
\(466\) −20.4099 −0.945471
\(467\) −6.72456 −0.311176 −0.155588 0.987822i \(-0.549727\pi\)
−0.155588 + 0.987822i \(0.549727\pi\)
\(468\) −3.31130 −0.153065
\(469\) −6.52951 −0.301505
\(470\) −18.7546 −0.865087
\(471\) 4.29270 0.197797
\(472\) 4.90081 0.225578
\(473\) 3.26044 0.149915
\(474\) −4.10018 −0.188328
\(475\) −0.699514 −0.0320959
\(476\) −11.2927 −0.517599
\(477\) −7.44666 −0.340959
\(478\) −15.7544 −0.720591
\(479\) 19.3112 0.882350 0.441175 0.897421i \(-0.354562\pi\)
0.441175 + 0.897421i \(0.354562\pi\)
\(480\) −16.1665 −0.737899
\(481\) −3.57728 −0.163110
\(482\) 8.73609 0.397918
\(483\) −4.98233 −0.226704
\(484\) 16.5420 0.751909
\(485\) 0.602940 0.0273781
\(486\) 0.692358 0.0314060
\(487\) −38.4870 −1.74401 −0.872007 0.489494i \(-0.837182\pi\)
−0.872007 + 0.489494i \(0.837182\pi\)
\(488\) 18.7581 0.849138
\(489\) 4.96855 0.224686
\(490\) −1.92576 −0.0869968
\(491\) 19.8484 0.895746 0.447873 0.894097i \(-0.352182\pi\)
0.447873 + 0.894097i \(0.352182\pi\)
\(492\) −5.42854 −0.244737
\(493\) −51.1019 −2.30151
\(494\) −0.385401 −0.0173400
\(495\) 0.970306 0.0436120
\(496\) −13.6768 −0.614105
\(497\) 13.7550 0.616995
\(498\) 1.16773 0.0523273
\(499\) 12.8775 0.576476 0.288238 0.957559i \(-0.406931\pi\)
0.288238 + 0.957559i \(0.406931\pi\)
\(500\) −9.57391 −0.428158
\(501\) −14.3188 −0.639718
\(502\) −12.1037 −0.540217
\(503\) −35.1228 −1.56605 −0.783024 0.621992i \(-0.786324\pi\)
−0.783024 + 0.621992i \(0.786324\pi\)
\(504\) −2.43754 −0.108577
\(505\) 43.4656 1.93419
\(506\) 1.20338 0.0534966
\(507\) −8.25820 −0.366760
\(508\) 1.52064 0.0674675
\(509\) −1.90456 −0.0844184 −0.0422092 0.999109i \(-0.513440\pi\)
−0.0422092 + 0.999109i \(0.513440\pi\)
\(510\) −14.3012 −0.633266
\(511\) −9.37124 −0.414559
\(512\) 14.4667 0.639346
\(513\) −0.255629 −0.0112863
\(514\) 5.71930 0.252267
\(515\) 7.85446 0.346109
\(516\) 14.2123 0.625663
\(517\) −3.39739 −0.149417
\(518\) −1.13740 −0.0499743
\(519\) −22.2870 −0.978291
\(520\) 14.7637 0.647430
\(521\) −31.1698 −1.36558 −0.682788 0.730617i \(-0.739233\pi\)
−0.682788 + 0.730617i \(0.739233\pi\)
\(522\) −4.76428 −0.208527
\(523\) −16.1856 −0.707748 −0.353874 0.935293i \(-0.615136\pi\)
−0.353874 + 0.935293i \(0.615136\pi\)
\(524\) −12.6807 −0.553959
\(525\) 2.73644 0.119428
\(526\) 17.8647 0.778936
\(527\) −75.0333 −3.26850
\(528\) −0.472213 −0.0205504
\(529\) 1.82366 0.0792896
\(530\) 14.3405 0.622909
\(531\) −2.01055 −0.0872505
\(532\) 0.388720 0.0168532
\(533\) 7.77370 0.336716
\(534\) −12.2374 −0.529566
\(535\) 37.9680 1.64150
\(536\) 15.9160 0.687464
\(537\) 26.5031 1.14369
\(538\) −4.22748 −0.182259
\(539\) −0.348849 −0.0150260
\(540\) 4.22958 0.182012
\(541\) −18.5894 −0.799221 −0.399610 0.916685i \(-0.630855\pi\)
−0.399610 + 0.916685i \(0.630855\pi\)
\(542\) −11.6829 −0.501822
\(543\) −6.62020 −0.284100
\(544\) 43.1635 1.85062
\(545\) 34.6514 1.48430
\(546\) 1.50766 0.0645217
\(547\) 16.3670 0.699802 0.349901 0.936787i \(-0.386215\pi\)
0.349901 + 0.936787i \(0.386215\pi\)
\(548\) −31.8685 −1.36135
\(549\) −7.69549 −0.328435
\(550\) −0.660929 −0.0281821
\(551\) 1.75905 0.0749379
\(552\) 12.1447 0.516911
\(553\) −5.92206 −0.251831
\(554\) 20.1031 0.854099
\(555\) 4.56932 0.193957
\(556\) 15.4903 0.656937
\(557\) 37.7810 1.60083 0.800417 0.599444i \(-0.204612\pi\)
0.800417 + 0.599444i \(0.204612\pi\)
\(558\) −6.99543 −0.296140
\(559\) −20.3522 −0.860804
\(560\) −3.76505 −0.159102
\(561\) −2.59065 −0.109377
\(562\) 2.56947 0.108386
\(563\) 13.6001 0.573176 0.286588 0.958054i \(-0.407479\pi\)
0.286588 + 0.958054i \(0.407479\pi\)
\(564\) −14.8093 −0.623584
\(565\) −47.6446 −2.00443
\(566\) −6.95074 −0.292161
\(567\) 1.00000 0.0419961
\(568\) −33.5284 −1.40682
\(569\) 9.94802 0.417043 0.208521 0.978018i \(-0.433135\pi\)
0.208521 + 0.978018i \(0.433135\pi\)
\(570\) 0.492279 0.0206193
\(571\) 8.42532 0.352588 0.176294 0.984338i \(-0.443589\pi\)
0.176294 + 0.984338i \(0.443589\pi\)
\(572\) 1.15514 0.0482990
\(573\) 9.50979 0.397277
\(574\) 2.47165 0.103165
\(575\) −13.6339 −0.568571
\(576\) 1.31692 0.0548715
\(577\) −20.5668 −0.856206 −0.428103 0.903730i \(-0.640818\pi\)
−0.428103 + 0.903730i \(0.640818\pi\)
\(578\) 26.4130 1.09864
\(579\) 18.2187 0.757145
\(580\) −29.1048 −1.20851
\(581\) 1.68660 0.0699720
\(582\) −0.150084 −0.00622117
\(583\) 2.59776 0.107588
\(584\) 22.8428 0.945242
\(585\) −6.05678 −0.250417
\(586\) 21.2459 0.877658
\(587\) 23.2118 0.958053 0.479027 0.877800i \(-0.340990\pi\)
0.479027 + 0.877800i \(0.340990\pi\)
\(588\) −1.52064 −0.0627102
\(589\) 2.58282 0.106423
\(590\) 3.87183 0.159401
\(591\) −6.73369 −0.276987
\(592\) −2.22373 −0.0913945
\(593\) 29.0658 1.19359 0.596795 0.802393i \(-0.296440\pi\)
0.596795 + 0.802393i \(0.296440\pi\)
\(594\) −0.241529 −0.00991004
\(595\) −20.6557 −0.846803
\(596\) 7.40365 0.303265
\(597\) 19.1877 0.785298
\(598\) −7.51164 −0.307174
\(599\) −31.7965 −1.29917 −0.649584 0.760290i \(-0.725057\pi\)
−0.649584 + 0.760290i \(0.725057\pi\)
\(600\) −6.67019 −0.272309
\(601\) 21.6226 0.882004 0.441002 0.897506i \(-0.354623\pi\)
0.441002 + 0.897506i \(0.354623\pi\)
\(602\) −6.47097 −0.263737
\(603\) −6.52951 −0.265902
\(604\) 2.94355 0.119771
\(605\) 30.2574 1.23014
\(606\) −10.8195 −0.439511
\(607\) 19.7589 0.801988 0.400994 0.916081i \(-0.368665\pi\)
0.400994 + 0.916081i \(0.368665\pi\)
\(608\) −1.48579 −0.0602567
\(609\) −6.88124 −0.278842
\(610\) 14.8196 0.600029
\(611\) 21.2070 0.857944
\(612\) −11.2927 −0.456479
\(613\) −7.69528 −0.310809 −0.155405 0.987851i \(-0.549668\pi\)
−0.155405 + 0.987851i \(0.549668\pi\)
\(614\) −5.25459 −0.212058
\(615\) −9.92948 −0.400395
\(616\) 0.850335 0.0342610
\(617\) −46.4653 −1.87062 −0.935310 0.353828i \(-0.884880\pi\)
−0.935310 + 0.353828i \(0.884880\pi\)
\(618\) −1.95513 −0.0786470
\(619\) −9.42955 −0.379006 −0.189503 0.981880i \(-0.560688\pi\)
−0.189503 + 0.981880i \(0.560688\pi\)
\(620\) −42.7347 −1.71627
\(621\) −4.98233 −0.199934
\(622\) −21.8391 −0.875670
\(623\) −17.6750 −0.708135
\(624\) 2.94762 0.117999
\(625\) −31.1941 −1.24776
\(626\) 17.7231 0.708357
\(627\) 0.0891761 0.00356135
\(628\) −6.52765 −0.260482
\(629\) −12.1998 −0.486436
\(630\) −1.92576 −0.0767239
\(631\) −34.1327 −1.35880 −0.679401 0.733768i \(-0.737760\pi\)
−0.679401 + 0.733768i \(0.737760\pi\)
\(632\) 14.4353 0.574204
\(633\) 3.89333 0.154746
\(634\) 14.3825 0.571202
\(635\) 2.78145 0.110378
\(636\) 11.3237 0.449014
\(637\) 2.17757 0.0862783
\(638\) 1.66202 0.0657999
\(639\) 13.7550 0.544139
\(640\) 29.7970 1.17783
\(641\) 35.7111 1.41050 0.705252 0.708956i \(-0.250834\pi\)
0.705252 + 0.708956i \(0.250834\pi\)
\(642\) −9.45100 −0.373001
\(643\) 0.292989 0.0115544 0.00577718 0.999983i \(-0.498161\pi\)
0.00577718 + 0.999983i \(0.498161\pi\)
\(644\) 7.57634 0.298550
\(645\) 25.9962 1.02360
\(646\) −1.31435 −0.0517124
\(647\) 7.55746 0.297114 0.148557 0.988904i \(-0.452537\pi\)
0.148557 + 0.988904i \(0.452537\pi\)
\(648\) −2.43754 −0.0957557
\(649\) 0.701380 0.0275316
\(650\) 4.12561 0.161820
\(651\) −10.1038 −0.395998
\(652\) −7.55538 −0.295892
\(653\) −43.1190 −1.68738 −0.843688 0.536833i \(-0.819620\pi\)
−0.843688 + 0.536833i \(0.819620\pi\)
\(654\) −8.62544 −0.337281
\(655\) −23.1946 −0.906289
\(656\) 4.83232 0.188671
\(657\) −9.37124 −0.365607
\(658\) 6.74277 0.262861
\(659\) −22.2019 −0.864865 −0.432433 0.901666i \(-0.642345\pi\)
−0.432433 + 0.901666i \(0.642345\pi\)
\(660\) −1.47549 −0.0574332
\(661\) 42.4146 1.64974 0.824868 0.565326i \(-0.191249\pi\)
0.824868 + 0.565326i \(0.191249\pi\)
\(662\) −2.15894 −0.0839096
\(663\) 16.1712 0.628037
\(664\) −4.11116 −0.159544
\(665\) 0.711019 0.0275721
\(666\) −1.13740 −0.0440732
\(667\) 34.2847 1.32751
\(668\) 21.7738 0.842454
\(669\) 17.8977 0.691964
\(670\) 12.5742 0.485785
\(671\) 2.68457 0.103637
\(672\) 5.81228 0.224214
\(673\) −21.3504 −0.822998 −0.411499 0.911410i \(-0.634995\pi\)
−0.411499 + 0.911410i \(0.634995\pi\)
\(674\) 0.0532507 0.00205114
\(675\) 2.73644 0.105326
\(676\) 12.5578 0.482991
\(677\) 6.31191 0.242587 0.121293 0.992617i \(-0.461296\pi\)
0.121293 + 0.992617i \(0.461296\pi\)
\(678\) 11.8597 0.455469
\(679\) −0.216772 −0.00831895
\(680\) 50.3493 1.93081
\(681\) 8.76418 0.335844
\(682\) 2.44035 0.0934459
\(683\) 44.6920 1.71009 0.855047 0.518551i \(-0.173528\pi\)
0.855047 + 0.518551i \(0.173528\pi\)
\(684\) 0.388720 0.0148631
\(685\) −58.2915 −2.22721
\(686\) 0.692358 0.0264343
\(687\) −20.1983 −0.770613
\(688\) −12.6514 −0.482330
\(689\) −16.2156 −0.617766
\(690\) 9.59476 0.365266
\(691\) −16.3228 −0.620948 −0.310474 0.950582i \(-0.600488\pi\)
−0.310474 + 0.950582i \(0.600488\pi\)
\(692\) 33.8905 1.28832
\(693\) −0.348849 −0.0132517
\(694\) −4.87970 −0.185231
\(695\) 28.3338 1.07476
\(696\) 16.7733 0.635791
\(697\) 26.5110 1.00418
\(698\) 10.6670 0.403750
\(699\) −29.4789 −1.11499
\(700\) −4.16114 −0.157276
\(701\) 16.1072 0.608360 0.304180 0.952615i \(-0.401618\pi\)
0.304180 + 0.952615i \(0.401618\pi\)
\(702\) 1.50766 0.0569028
\(703\) 0.419944 0.0158385
\(704\) −0.459406 −0.0173145
\(705\) −27.0881 −1.02020
\(706\) 10.6298 0.400056
\(707\) −15.6270 −0.587713
\(708\) 3.05733 0.114901
\(709\) 18.7118 0.702738 0.351369 0.936237i \(-0.385716\pi\)
0.351369 + 0.936237i \(0.385716\pi\)
\(710\) −26.4887 −0.994104
\(711\) −5.92206 −0.222094
\(712\) 43.0837 1.61463
\(713\) 50.3404 1.88526
\(714\) 5.14163 0.192421
\(715\) 2.11291 0.0790182
\(716\) −40.3017 −1.50615
\(717\) −22.7548 −0.849792
\(718\) −1.78693 −0.0666878
\(719\) 2.91001 0.108525 0.0542625 0.998527i \(-0.482719\pi\)
0.0542625 + 0.998527i \(0.482719\pi\)
\(720\) −3.76505 −0.140315
\(721\) −2.82388 −0.105167
\(722\) −13.1096 −0.487887
\(723\) 12.6179 0.469264
\(724\) 10.0669 0.374135
\(725\) −18.8301 −0.699333
\(726\) −7.53168 −0.279527
\(727\) −31.1593 −1.15563 −0.577817 0.816166i \(-0.696095\pi\)
−0.577817 + 0.816166i \(0.696095\pi\)
\(728\) −5.30791 −0.196724
\(729\) 1.00000 0.0370370
\(730\) 18.0467 0.667939
\(731\) −69.4079 −2.56715
\(732\) 11.7021 0.432521
\(733\) −35.0113 −1.29317 −0.646586 0.762841i \(-0.723804\pi\)
−0.646586 + 0.762841i \(0.723804\pi\)
\(734\) 15.3104 0.565118
\(735\) −2.78145 −0.102595
\(736\) −28.9587 −1.06743
\(737\) 2.27782 0.0839044
\(738\) 2.47165 0.0909826
\(739\) −31.9289 −1.17452 −0.587262 0.809397i \(-0.699794\pi\)
−0.587262 + 0.809397i \(0.699794\pi\)
\(740\) −6.94830 −0.255424
\(741\) −0.556650 −0.0204490
\(742\) −5.15575 −0.189274
\(743\) −9.30835 −0.341490 −0.170745 0.985315i \(-0.554618\pi\)
−0.170745 + 0.985315i \(0.554618\pi\)
\(744\) 24.6284 0.902920
\(745\) 13.5422 0.496149
\(746\) −11.3241 −0.414604
\(747\) 1.68660 0.0617095
\(748\) 3.93944 0.144040
\(749\) −13.6505 −0.498777
\(750\) 4.35906 0.159170
\(751\) 51.6363 1.88424 0.942118 0.335282i \(-0.108832\pi\)
0.942118 + 0.335282i \(0.108832\pi\)
\(752\) 13.1828 0.480728
\(753\) −17.4819 −0.637077
\(754\) −10.3745 −0.377819
\(755\) 5.38413 0.195949
\(756\) −1.52064 −0.0553052
\(757\) 42.6294 1.54939 0.774695 0.632335i \(-0.217903\pi\)
0.774695 + 0.632335i \(0.217903\pi\)
\(758\) 15.4482 0.561106
\(759\) 1.73808 0.0630885
\(760\) −1.73314 −0.0628675
\(761\) −31.2012 −1.13104 −0.565520 0.824734i \(-0.691325\pi\)
−0.565520 + 0.824734i \(0.691325\pi\)
\(762\) −0.692358 −0.0250815
\(763\) −12.4581 −0.451012
\(764\) −14.4610 −0.523180
\(765\) −20.6557 −0.746810
\(766\) −12.5027 −0.451741
\(767\) −4.37811 −0.158084
\(768\) −10.0509 −0.362681
\(769\) −14.0501 −0.506660 −0.253330 0.967380i \(-0.581526\pi\)
−0.253330 + 0.967380i \(0.581526\pi\)
\(770\) 0.671799 0.0242099
\(771\) 8.26061 0.297499
\(772\) −27.7041 −0.997094
\(773\) 14.5672 0.523945 0.261973 0.965075i \(-0.415627\pi\)
0.261973 + 0.965075i \(0.415627\pi\)
\(774\) −6.47097 −0.232594
\(775\) −27.6484 −0.993159
\(776\) 0.528391 0.0189681
\(777\) −1.64279 −0.0589346
\(778\) −1.36313 −0.0488705
\(779\) −0.912570 −0.0326962
\(780\) 9.21019 0.329778
\(781\) −4.79842 −0.171701
\(782\) −25.6173 −0.916074
\(783\) −6.88124 −0.245916
\(784\) 1.35363 0.0483439
\(785\) −11.9399 −0.426153
\(786\) 5.77361 0.205938
\(787\) 33.4906 1.19381 0.596905 0.802312i \(-0.296397\pi\)
0.596905 + 0.802312i \(0.296397\pi\)
\(788\) 10.2395 0.364768
\(789\) 25.8026 0.918599
\(790\) 11.4044 0.405751
\(791\) 17.1295 0.609053
\(792\) 0.850335 0.0302154
\(793\) −16.7574 −0.595074
\(794\) −9.10949 −0.323284
\(795\) 20.7125 0.734596
\(796\) −29.1775 −1.03417
\(797\) 18.4316 0.652880 0.326440 0.945218i \(-0.394151\pi\)
0.326440 + 0.945218i \(0.394151\pi\)
\(798\) −0.176987 −0.00626527
\(799\) 72.3233 2.55861
\(800\) 15.9050 0.562325
\(801\) −17.6750 −0.624517
\(802\) −19.1624 −0.676649
\(803\) 3.26915 0.115366
\(804\) 9.92903 0.350170
\(805\) 13.8581 0.488434
\(806\) −15.2330 −0.536560
\(807\) −6.10591 −0.214938
\(808\) 38.0914 1.34005
\(809\) 9.24970 0.325202 0.162601 0.986692i \(-0.448012\pi\)
0.162601 + 0.986692i \(0.448012\pi\)
\(810\) −1.92576 −0.0676641
\(811\) −43.2167 −1.51755 −0.758773 0.651356i \(-0.774201\pi\)
−0.758773 + 0.651356i \(0.774201\pi\)
\(812\) 10.4639 0.367211
\(813\) −16.8740 −0.591799
\(814\) 0.396780 0.0139071
\(815\) −13.8198 −0.484085
\(816\) 10.0524 0.351905
\(817\) 2.38918 0.0835869
\(818\) −16.2813 −0.569261
\(819\) 2.17757 0.0760903
\(820\) 15.0992 0.527286
\(821\) 29.3683 1.02496 0.512481 0.858699i \(-0.328727\pi\)
0.512481 + 0.858699i \(0.328727\pi\)
\(822\) 14.5099 0.506092
\(823\) 16.4590 0.573726 0.286863 0.957972i \(-0.407388\pi\)
0.286863 + 0.957972i \(0.407388\pi\)
\(824\) 6.88332 0.239792
\(825\) −0.954606 −0.0332351
\(826\) −1.39202 −0.0484346
\(827\) 42.9794 1.49454 0.747270 0.664521i \(-0.231364\pi\)
0.747270 + 0.664521i \(0.231364\pi\)
\(828\) 7.57634 0.263296
\(829\) 8.69707 0.302062 0.151031 0.988529i \(-0.451741\pi\)
0.151031 + 0.988529i \(0.451741\pi\)
\(830\) −3.24798 −0.112739
\(831\) 29.0357 1.00724
\(832\) 2.86768 0.0994188
\(833\) 7.42626 0.257305
\(834\) −7.05285 −0.244220
\(835\) 39.8271 1.37827
\(836\) −0.135605 −0.00468999
\(837\) −10.1038 −0.349238
\(838\) 2.62287 0.0906057
\(839\) 14.0856 0.486289 0.243144 0.969990i \(-0.421821\pi\)
0.243144 + 0.969990i \(0.421821\pi\)
\(840\) 6.77989 0.233929
\(841\) 18.3515 0.632811
\(842\) −27.9692 −0.963882
\(843\) 3.71119 0.127820
\(844\) −5.92036 −0.203787
\(845\) 22.9697 0.790183
\(846\) 6.74277 0.231821
\(847\) −10.8783 −0.373783
\(848\) −10.0800 −0.346150
\(849\) −10.0392 −0.344545
\(850\) 14.0698 0.482589
\(851\) 8.18491 0.280575
\(852\) −20.9164 −0.716584
\(853\) 21.4439 0.734225 0.367113 0.930176i \(-0.380346\pi\)
0.367113 + 0.930176i \(0.380346\pi\)
\(854\) −5.32803 −0.182321
\(855\) 0.711019 0.0243163
\(856\) 33.2736 1.13727
\(857\) 27.2216 0.929873 0.464936 0.885344i \(-0.346077\pi\)
0.464936 + 0.885344i \(0.346077\pi\)
\(858\) −0.525945 −0.0179555
\(859\) −47.7733 −1.63000 −0.815001 0.579459i \(-0.803264\pi\)
−0.815001 + 0.579459i \(0.803264\pi\)
\(860\) −39.5308 −1.34799
\(861\) 3.56990 0.121662
\(862\) 18.2325 0.621001
\(863\) 8.00836 0.272608 0.136304 0.990667i \(-0.456478\pi\)
0.136304 + 0.990667i \(0.456478\pi\)
\(864\) 5.81228 0.197738
\(865\) 61.9901 2.10773
\(866\) −4.48435 −0.152384
\(867\) 38.1494 1.29562
\(868\) 15.3642 0.521495
\(869\) 2.06591 0.0700811
\(870\) 13.2516 0.449271
\(871\) −14.2184 −0.481773
\(872\) 30.3671 1.02836
\(873\) −0.216772 −0.00733662
\(874\) 0.881808 0.0298276
\(875\) 6.29597 0.212843
\(876\) 14.2503 0.481473
\(877\) −29.0720 −0.981691 −0.490845 0.871247i \(-0.663312\pi\)
−0.490845 + 0.871247i \(0.663312\pi\)
\(878\) 8.25510 0.278596
\(879\) 30.6862 1.03502
\(880\) 1.31344 0.0442759
\(881\) −34.1165 −1.14941 −0.574707 0.818360i \(-0.694884\pi\)
−0.574707 + 0.818360i \(0.694884\pi\)
\(882\) 0.692358 0.0233129
\(883\) 50.0021 1.68271 0.841353 0.540486i \(-0.181760\pi\)
0.841353 + 0.540486i \(0.181760\pi\)
\(884\) −24.5906 −0.827070
\(885\) 5.59224 0.187981
\(886\) 22.1061 0.742669
\(887\) 7.91800 0.265861 0.132930 0.991125i \(-0.457561\pi\)
0.132930 + 0.991125i \(0.457561\pi\)
\(888\) 4.00436 0.134378
\(889\) −1.00000 −0.0335389
\(890\) 34.0378 1.14095
\(891\) −0.348849 −0.0116869
\(892\) −27.2159 −0.911257
\(893\) −2.48953 −0.0833091
\(894\) −3.37093 −0.112741
\(895\) −73.7169 −2.46409
\(896\) −10.7128 −0.357889
\(897\) −10.8494 −0.362250
\(898\) 21.6970 0.724039
\(899\) 69.5266 2.31884
\(900\) −4.16114 −0.138705
\(901\) −55.3009 −1.84234
\(902\) −0.862233 −0.0287092
\(903\) −9.34628 −0.311025
\(904\) −41.7538 −1.38871
\(905\) 18.4137 0.612093
\(906\) −1.34022 −0.0445258
\(907\) 11.4971 0.381756 0.190878 0.981614i \(-0.438867\pi\)
0.190878 + 0.981614i \(0.438867\pi\)
\(908\) −13.3272 −0.442278
\(909\) −15.6270 −0.518314
\(910\) −4.19346 −0.139012
\(911\) 15.6924 0.519913 0.259957 0.965620i \(-0.416292\pi\)
0.259957 + 0.965620i \(0.416292\pi\)
\(912\) −0.346027 −0.0114581
\(913\) −0.588370 −0.0194722
\(914\) −12.1714 −0.402596
\(915\) 21.4046 0.707614
\(916\) 30.7144 1.01483
\(917\) 8.33905 0.275380
\(918\) 5.14163 0.169699
\(919\) −17.3175 −0.571252 −0.285626 0.958341i \(-0.592202\pi\)
−0.285626 + 0.958341i \(0.592202\pi\)
\(920\) −33.7797 −1.11368
\(921\) −7.58942 −0.250080
\(922\) −19.0081 −0.625997
\(923\) 29.9524 0.985895
\(924\) 0.530475 0.0174513
\(925\) −4.49539 −0.147807
\(926\) −12.6215 −0.414768
\(927\) −2.82388 −0.0927483
\(928\) −39.9957 −1.31292
\(929\) 24.5131 0.804249 0.402125 0.915585i \(-0.368272\pi\)
0.402125 + 0.915585i \(0.368272\pi\)
\(930\) 19.4574 0.638033
\(931\) −0.255629 −0.00837791
\(932\) 44.8268 1.46835
\(933\) −31.5432 −1.03268
\(934\) −4.65580 −0.152342
\(935\) 7.20575 0.235653
\(936\) −5.30791 −0.173495
\(937\) 39.1077 1.27759 0.638796 0.769376i \(-0.279433\pi\)
0.638796 + 0.769376i \(0.279433\pi\)
\(938\) −4.52075 −0.147608
\(939\) 25.5982 0.835365
\(940\) 41.1913 1.34351
\(941\) −24.8154 −0.808958 −0.404479 0.914547i \(-0.632547\pi\)
−0.404479 + 0.914547i \(0.632547\pi\)
\(942\) 2.97208 0.0968357
\(943\) −17.7864 −0.579206
\(944\) −2.72154 −0.0885787
\(945\) −2.78145 −0.0904804
\(946\) 2.25739 0.0733942
\(947\) −7.86086 −0.255444 −0.127722 0.991810i \(-0.540766\pi\)
−0.127722 + 0.991810i \(0.540766\pi\)
\(948\) 9.00532 0.292479
\(949\) −20.4065 −0.662423
\(950\) −0.484314 −0.0157132
\(951\) 20.7732 0.673618
\(952\) −18.1018 −0.586684
\(953\) 19.4522 0.630119 0.315060 0.949072i \(-0.397976\pi\)
0.315060 + 0.949072i \(0.397976\pi\)
\(954\) −5.15575 −0.166924
\(955\) −26.4510 −0.855933
\(956\) 34.6018 1.11910
\(957\) 2.40052 0.0775977
\(958\) 13.3702 0.431973
\(959\) 20.9573 0.676746
\(960\) −3.66293 −0.118221
\(961\) 71.0863 2.29311
\(962\) −2.47676 −0.0798538
\(963\) −13.6505 −0.439880
\(964\) −19.1873 −0.617980
\(965\) −50.6744 −1.63127
\(966\) −3.44956 −0.110988
\(967\) −31.4602 −1.01169 −0.505846 0.862624i \(-0.668819\pi\)
−0.505846 + 0.862624i \(0.668819\pi\)
\(968\) 26.5163 0.852267
\(969\) −1.89837 −0.0609844
\(970\) 0.417450 0.0134035
\(971\) 9.05176 0.290485 0.145242 0.989396i \(-0.453604\pi\)
0.145242 + 0.989396i \(0.453604\pi\)
\(972\) −1.52064 −0.0487746
\(973\) −10.1867 −0.326571
\(974\) −26.6468 −0.853818
\(975\) 5.95878 0.190834
\(976\) −10.4168 −0.333435
\(977\) 7.31839 0.234136 0.117068 0.993124i \(-0.462650\pi\)
0.117068 + 0.993124i \(0.462650\pi\)
\(978\) 3.44001 0.110000
\(979\) 6.16593 0.197064
\(980\) 4.22958 0.135109
\(981\) −12.4581 −0.397756
\(982\) 13.7422 0.438531
\(983\) 7.36329 0.234852 0.117426 0.993082i \(-0.462536\pi\)
0.117426 + 0.993082i \(0.462536\pi\)
\(984\) −8.70178 −0.277403
\(985\) 18.7294 0.596768
\(986\) −35.3808 −1.12675
\(987\) 9.73885 0.309991
\(988\) 0.846464 0.0269296
\(989\) 46.5663 1.48072
\(990\) 0.671799 0.0213512
\(991\) 41.9301 1.33195 0.665976 0.745973i \(-0.268015\pi\)
0.665976 + 0.745973i \(0.268015\pi\)
\(992\) −58.7260 −1.86455
\(993\) −3.11825 −0.0989545
\(994\) 9.52337 0.302063
\(995\) −53.3694 −1.69192
\(996\) −2.56471 −0.0812660
\(997\) 42.0879 1.33294 0.666468 0.745533i \(-0.267805\pi\)
0.666468 + 0.745533i \(0.267805\pi\)
\(998\) 8.91583 0.282226
\(999\) −1.64279 −0.0519755
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.1.5 7
3.2 odd 2 8001.2.a.l.1.3 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2667.2.a.j.1.5 7 1.1 even 1 trivial
8001.2.a.l.1.3 7 3.2 odd 2