Properties

Label 1441.2.a.c.1.4
Level $1441$
Weight $2$
Character 1441.1
Self dual yes
Analytic conductor $11.506$
Analytic rank $1$
Dimension $23$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1441 = 11 \cdot 131 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1441.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(11.5064429313\)
Analytic rank: \(1\)
Dimension: \(23\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) \(=\) 1441.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.24881 q^{2} -1.99348 q^{3} +3.05713 q^{4} -0.623302 q^{5} +4.48295 q^{6} +4.70119 q^{7} -2.37729 q^{8} +0.973955 q^{9} +O(q^{10})\) \(q-2.24881 q^{2} -1.99348 q^{3} +3.05713 q^{4} -0.623302 q^{5} +4.48295 q^{6} +4.70119 q^{7} -2.37729 q^{8} +0.973955 q^{9} +1.40169 q^{10} +1.00000 q^{11} -6.09433 q^{12} +0.567789 q^{13} -10.5721 q^{14} +1.24254 q^{15} -0.768201 q^{16} -3.70843 q^{17} -2.19024 q^{18} -5.06100 q^{19} -1.90552 q^{20} -9.37172 q^{21} -2.24881 q^{22} -4.25322 q^{23} +4.73908 q^{24} -4.61149 q^{25} -1.27685 q^{26} +4.03888 q^{27} +14.3722 q^{28} +7.30433 q^{29} -2.79423 q^{30} +6.55184 q^{31} +6.48212 q^{32} -1.99348 q^{33} +8.33954 q^{34} -2.93026 q^{35} +2.97751 q^{36} -8.62363 q^{37} +11.3812 q^{38} -1.13188 q^{39} +1.48177 q^{40} -5.03087 q^{41} +21.0752 q^{42} +11.4375 q^{43} +3.05713 q^{44} -0.607068 q^{45} +9.56468 q^{46} -8.89138 q^{47} +1.53139 q^{48} +15.1012 q^{49} +10.3704 q^{50} +7.39267 q^{51} +1.73581 q^{52} -5.67901 q^{53} -9.08266 q^{54} -0.623302 q^{55} -11.1761 q^{56} +10.0890 q^{57} -16.4260 q^{58} -8.80006 q^{59} +3.79861 q^{60} -2.26077 q^{61} -14.7338 q^{62} +4.57874 q^{63} -13.0406 q^{64} -0.353904 q^{65} +4.48295 q^{66} +9.21849 q^{67} -11.3372 q^{68} +8.47871 q^{69} +6.58959 q^{70} -7.14734 q^{71} -2.31537 q^{72} +7.84898 q^{73} +19.3929 q^{74} +9.19291 q^{75} -15.4722 q^{76} +4.70119 q^{77} +2.54537 q^{78} +0.313442 q^{79} +0.478821 q^{80} -10.9733 q^{81} +11.3135 q^{82} +1.14071 q^{83} -28.6506 q^{84} +2.31147 q^{85} -25.7208 q^{86} -14.5610 q^{87} -2.37729 q^{88} -10.5520 q^{89} +1.36518 q^{90} +2.66928 q^{91} -13.0027 q^{92} -13.0609 q^{93} +19.9950 q^{94} +3.15453 q^{95} -12.9220 q^{96} +14.1568 q^{97} -33.9596 q^{98} +0.973955 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 23 q - 7 q^{2} - 3 q^{3} + 15 q^{4} - 9 q^{5} - 11 q^{6} - 12 q^{7} - 21 q^{8} + 12 q^{9} + O(q^{10}) \) \( 23 q - 7 q^{2} - 3 q^{3} + 15 q^{4} - 9 q^{5} - 11 q^{6} - 12 q^{7} - 21 q^{8} + 12 q^{9} - 2 q^{10} + 23 q^{11} + 8 q^{12} - 24 q^{13} - 13 q^{14} - 27 q^{15} + 7 q^{16} - 7 q^{17} - 14 q^{18} - 18 q^{19} - 4 q^{20} - 29 q^{21} - 7 q^{22} - 26 q^{23} - 4 q^{24} + 18 q^{25} + 8 q^{26} - 3 q^{27} - 11 q^{28} - 45 q^{29} + 19 q^{30} - 23 q^{31} - 34 q^{32} - 3 q^{33} - 2 q^{34} - 18 q^{35} - 6 q^{36} - 2 q^{37} - 8 q^{38} - 40 q^{39} - 24 q^{40} - 23 q^{41} + 59 q^{42} - 14 q^{43} + 15 q^{44} - 18 q^{45} - 12 q^{46} - 55 q^{47} + 10 q^{48} + 11 q^{49} - 41 q^{50} - 21 q^{51} - 37 q^{52} - 10 q^{53} - 68 q^{54} - 9 q^{55} + 2 q^{56} - 18 q^{57} + 27 q^{58} - 75 q^{59} - 63 q^{60} - 55 q^{61} + 14 q^{62} - 16 q^{63} + 19 q^{64} - 25 q^{65} - 11 q^{66} + 17 q^{67} + 41 q^{68} - 22 q^{69} + 27 q^{70} - 105 q^{71} - 11 q^{72} - 3 q^{73} - 39 q^{74} + 25 q^{75} - 30 q^{76} - 12 q^{77} + 25 q^{78} - 48 q^{79} - 37 q^{80} + 3 q^{81} + 36 q^{82} + 4 q^{83} - 111 q^{84} - 30 q^{85} + 22 q^{86} + 5 q^{87} - 21 q^{88} - 39 q^{89} + 100 q^{90} - 22 q^{91} - 30 q^{92} - 5 q^{93} + 11 q^{94} - 88 q^{95} + 13 q^{96} + 24 q^{97} - 91 q^{98} + 12 q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.24881 −1.59015 −0.795073 0.606513i \(-0.792568\pi\)
−0.795073 + 0.606513i \(0.792568\pi\)
\(3\) −1.99348 −1.15094 −0.575468 0.817825i \(-0.695180\pi\)
−0.575468 + 0.817825i \(0.695180\pi\)
\(4\) 3.05713 1.52857
\(5\) −0.623302 −0.278749 −0.139375 0.990240i \(-0.544509\pi\)
−0.139375 + 0.990240i \(0.544509\pi\)
\(6\) 4.48295 1.83016
\(7\) 4.70119 1.77688 0.888441 0.458991i \(-0.151789\pi\)
0.888441 + 0.458991i \(0.151789\pi\)
\(8\) −2.37729 −0.840499
\(9\) 0.973955 0.324652
\(10\) 1.40169 0.443252
\(11\) 1.00000 0.301511
\(12\) −6.09433 −1.75928
\(13\) 0.567789 0.157476 0.0787382 0.996895i \(-0.474911\pi\)
0.0787382 + 0.996895i \(0.474911\pi\)
\(14\) −10.5721 −2.82550
\(15\) 1.24254 0.320822
\(16\) −0.768201 −0.192050
\(17\) −3.70843 −0.899426 −0.449713 0.893173i \(-0.648474\pi\)
−0.449713 + 0.893173i \(0.648474\pi\)
\(18\) −2.19024 −0.516244
\(19\) −5.06100 −1.16107 −0.580537 0.814234i \(-0.697157\pi\)
−0.580537 + 0.814234i \(0.697157\pi\)
\(20\) −1.90552 −0.426087
\(21\) −9.37172 −2.04508
\(22\) −2.24881 −0.479447
\(23\) −4.25322 −0.886858 −0.443429 0.896309i \(-0.646238\pi\)
−0.443429 + 0.896309i \(0.646238\pi\)
\(24\) 4.73908 0.967360
\(25\) −4.61149 −0.922299
\(26\) −1.27685 −0.250411
\(27\) 4.03888 0.777282
\(28\) 14.3722 2.71608
\(29\) 7.30433 1.35638 0.678190 0.734887i \(-0.262765\pi\)
0.678190 + 0.734887i \(0.262765\pi\)
\(30\) −2.79423 −0.510154
\(31\) 6.55184 1.17675 0.588373 0.808590i \(-0.299769\pi\)
0.588373 + 0.808590i \(0.299769\pi\)
\(32\) 6.48212 1.14589
\(33\) −1.99348 −0.347020
\(34\) 8.33954 1.43022
\(35\) −2.93026 −0.495304
\(36\) 2.97751 0.496252
\(37\) −8.62363 −1.41772 −0.708858 0.705351i \(-0.750789\pi\)
−0.708858 + 0.705351i \(0.750789\pi\)
\(38\) 11.3812 1.84628
\(39\) −1.13188 −0.181245
\(40\) 1.48177 0.234288
\(41\) −5.03087 −0.785690 −0.392845 0.919605i \(-0.628509\pi\)
−0.392845 + 0.919605i \(0.628509\pi\)
\(42\) 21.0752 3.25197
\(43\) 11.4375 1.74421 0.872103 0.489322i \(-0.162756\pi\)
0.872103 + 0.489322i \(0.162756\pi\)
\(44\) 3.05713 0.460880
\(45\) −0.607068 −0.0904963
\(46\) 9.56468 1.41023
\(47\) −8.89138 −1.29694 −0.648471 0.761240i \(-0.724591\pi\)
−0.648471 + 0.761240i \(0.724591\pi\)
\(48\) 1.53139 0.221037
\(49\) 15.1012 2.15731
\(50\) 10.3704 1.46659
\(51\) 7.39267 1.03518
\(52\) 1.73581 0.240713
\(53\) −5.67901 −0.780073 −0.390036 0.920799i \(-0.627538\pi\)
−0.390036 + 0.920799i \(0.627538\pi\)
\(54\) −9.08266 −1.23599
\(55\) −0.623302 −0.0840460
\(56\) −11.1761 −1.49347
\(57\) 10.0890 1.33632
\(58\) −16.4260 −2.15684
\(59\) −8.80006 −1.14567 −0.572835 0.819671i \(-0.694156\pi\)
−0.572835 + 0.819671i \(0.694156\pi\)
\(60\) 3.79861 0.490398
\(61\) −2.26077 −0.289462 −0.144731 0.989471i \(-0.546232\pi\)
−0.144731 + 0.989471i \(0.546232\pi\)
\(62\) −14.7338 −1.87120
\(63\) 4.57874 0.576868
\(64\) −13.0406 −1.63008
\(65\) −0.353904 −0.0438964
\(66\) 4.48295 0.551813
\(67\) 9.21849 1.12622 0.563109 0.826383i \(-0.309605\pi\)
0.563109 + 0.826383i \(0.309605\pi\)
\(68\) −11.3372 −1.37483
\(69\) 8.47871 1.02072
\(70\) 6.58959 0.787607
\(71\) −7.14734 −0.848233 −0.424117 0.905608i \(-0.639415\pi\)
−0.424117 + 0.905608i \(0.639415\pi\)
\(72\) −2.31537 −0.272869
\(73\) 7.84898 0.918654 0.459327 0.888267i \(-0.348091\pi\)
0.459327 + 0.888267i \(0.348091\pi\)
\(74\) 19.3929 2.25438
\(75\) 9.19291 1.06151
\(76\) −15.4722 −1.77478
\(77\) 4.70119 0.535750
\(78\) 2.54537 0.288206
\(79\) 0.313442 0.0352650 0.0176325 0.999845i \(-0.494387\pi\)
0.0176325 + 0.999845i \(0.494387\pi\)
\(80\) 0.478821 0.0535338
\(81\) −10.9733 −1.21925
\(82\) 11.3135 1.24936
\(83\) 1.14071 0.125209 0.0626047 0.998038i \(-0.480059\pi\)
0.0626047 + 0.998038i \(0.480059\pi\)
\(84\) −28.6506 −3.12604
\(85\) 2.31147 0.250714
\(86\) −25.7208 −2.77354
\(87\) −14.5610 −1.56110
\(88\) −2.37729 −0.253420
\(89\) −10.5520 −1.11851 −0.559254 0.828996i \(-0.688912\pi\)
−0.559254 + 0.828996i \(0.688912\pi\)
\(90\) 1.36518 0.143902
\(91\) 2.66928 0.279817
\(92\) −13.0027 −1.35562
\(93\) −13.0609 −1.35436
\(94\) 19.9950 2.06233
\(95\) 3.15453 0.323648
\(96\) −12.9220 −1.31884
\(97\) 14.1568 1.43741 0.718703 0.695317i \(-0.244736\pi\)
0.718703 + 0.695317i \(0.244736\pi\)
\(98\) −33.9596 −3.43044
\(99\) 0.973955 0.0978861
\(100\) −14.0980 −1.40980
\(101\) −5.77522 −0.574656 −0.287328 0.957832i \(-0.592767\pi\)
−0.287328 + 0.957832i \(0.592767\pi\)
\(102\) −16.6247 −1.64609
\(103\) 4.21666 0.415480 0.207740 0.978184i \(-0.433389\pi\)
0.207740 + 0.978184i \(0.433389\pi\)
\(104\) −1.34980 −0.132359
\(105\) 5.84141 0.570063
\(106\) 12.7710 1.24043
\(107\) 8.54654 0.826225 0.413112 0.910680i \(-0.364442\pi\)
0.413112 + 0.910680i \(0.364442\pi\)
\(108\) 12.3474 1.18813
\(109\) −9.24390 −0.885405 −0.442703 0.896668i \(-0.645980\pi\)
−0.442703 + 0.896668i \(0.645980\pi\)
\(110\) 1.40169 0.133646
\(111\) 17.1910 1.63170
\(112\) −3.61146 −0.341251
\(113\) −11.7083 −1.10143 −0.550713 0.834694i \(-0.685644\pi\)
−0.550713 + 0.834694i \(0.685644\pi\)
\(114\) −22.6882 −2.12495
\(115\) 2.65104 0.247211
\(116\) 22.3303 2.07332
\(117\) 0.553001 0.0511249
\(118\) 19.7896 1.82178
\(119\) −17.4340 −1.59817
\(120\) −2.95388 −0.269651
\(121\) 1.00000 0.0909091
\(122\) 5.08404 0.460287
\(123\) 10.0289 0.904278
\(124\) 20.0298 1.79873
\(125\) 5.99086 0.535839
\(126\) −10.2967 −0.917304
\(127\) −19.9557 −1.77078 −0.885389 0.464851i \(-0.846108\pi\)
−0.885389 + 0.464851i \(0.846108\pi\)
\(128\) 16.3616 1.44618
\(129\) −22.8005 −2.00747
\(130\) 0.795862 0.0698017
\(131\) 1.00000 0.0873704
\(132\) −6.09433 −0.530443
\(133\) −23.7927 −2.06309
\(134\) −20.7306 −1.79085
\(135\) −2.51744 −0.216667
\(136\) 8.81601 0.755966
\(137\) 8.91759 0.761881 0.380940 0.924600i \(-0.375600\pi\)
0.380940 + 0.924600i \(0.375600\pi\)
\(138\) −19.0670 −1.62309
\(139\) −13.4529 −1.14106 −0.570529 0.821278i \(-0.693262\pi\)
−0.570529 + 0.821278i \(0.693262\pi\)
\(140\) −8.95820 −0.757106
\(141\) 17.7248 1.49270
\(142\) 16.0730 1.34882
\(143\) 0.567789 0.0474809
\(144\) −0.748193 −0.0623494
\(145\) −4.55280 −0.378090
\(146\) −17.6508 −1.46079
\(147\) −30.1039 −2.48292
\(148\) −26.3636 −2.16707
\(149\) −8.53780 −0.699444 −0.349722 0.936854i \(-0.613724\pi\)
−0.349722 + 0.936854i \(0.613724\pi\)
\(150\) −20.6731 −1.68795
\(151\) −18.0441 −1.46840 −0.734202 0.678931i \(-0.762444\pi\)
−0.734202 + 0.678931i \(0.762444\pi\)
\(152\) 12.0315 0.975881
\(153\) −3.61184 −0.292000
\(154\) −10.5721 −0.851921
\(155\) −4.08378 −0.328017
\(156\) −3.46029 −0.277045
\(157\) 22.4299 1.79010 0.895050 0.445965i \(-0.147139\pi\)
0.895050 + 0.445965i \(0.147139\pi\)
\(158\) −0.704872 −0.0560766
\(159\) 11.3210 0.897813
\(160\) −4.04032 −0.319415
\(161\) −19.9952 −1.57584
\(162\) 24.6768 1.93879
\(163\) −15.2356 −1.19334 −0.596672 0.802485i \(-0.703511\pi\)
−0.596672 + 0.802485i \(0.703511\pi\)
\(164\) −15.3800 −1.20098
\(165\) 1.24254 0.0967315
\(166\) −2.56524 −0.199101
\(167\) 18.7538 1.45121 0.725605 0.688111i \(-0.241560\pi\)
0.725605 + 0.688111i \(0.241560\pi\)
\(168\) 22.2793 1.71888
\(169\) −12.6776 −0.975201
\(170\) −5.19805 −0.398672
\(171\) −4.92919 −0.376944
\(172\) 34.9660 2.66614
\(173\) 1.03548 0.0787263 0.0393632 0.999225i \(-0.487467\pi\)
0.0393632 + 0.999225i \(0.487467\pi\)
\(174\) 32.7449 2.48239
\(175\) −21.6795 −1.63882
\(176\) −0.768201 −0.0579053
\(177\) 17.5427 1.31859
\(178\) 23.7294 1.77859
\(179\) −23.8377 −1.78172 −0.890858 0.454282i \(-0.849896\pi\)
−0.890858 + 0.454282i \(0.849896\pi\)
\(180\) −1.85589 −0.138330
\(181\) 14.2616 1.06005 0.530027 0.847981i \(-0.322182\pi\)
0.530027 + 0.847981i \(0.322182\pi\)
\(182\) −6.00270 −0.444950
\(183\) 4.50680 0.333152
\(184\) 10.1111 0.745403
\(185\) 5.37513 0.395187
\(186\) 29.3716 2.15363
\(187\) −3.70843 −0.271187
\(188\) −27.1821 −1.98246
\(189\) 18.9875 1.38114
\(190\) −7.09394 −0.514648
\(191\) 2.12024 0.153415 0.0767076 0.997054i \(-0.475559\pi\)
0.0767076 + 0.997054i \(0.475559\pi\)
\(192\) 25.9962 1.87611
\(193\) −10.6975 −0.770024 −0.385012 0.922912i \(-0.625803\pi\)
−0.385012 + 0.922912i \(0.625803\pi\)
\(194\) −31.8359 −2.28569
\(195\) 0.705500 0.0505219
\(196\) 46.1663 3.29759
\(197\) −8.20758 −0.584766 −0.292383 0.956301i \(-0.594448\pi\)
−0.292383 + 0.956301i \(0.594448\pi\)
\(198\) −2.19024 −0.155653
\(199\) 6.06957 0.430261 0.215130 0.976585i \(-0.430982\pi\)
0.215130 + 0.976585i \(0.430982\pi\)
\(200\) 10.9629 0.775191
\(201\) −18.3769 −1.29620
\(202\) 12.9874 0.913787
\(203\) 34.3390 2.41013
\(204\) 22.6004 1.58234
\(205\) 3.13575 0.219010
\(206\) −9.48245 −0.660674
\(207\) −4.14245 −0.287920
\(208\) −0.436176 −0.0302434
\(209\) −5.06100 −0.350077
\(210\) −13.1362 −0.906484
\(211\) −20.1636 −1.38812 −0.694059 0.719918i \(-0.744179\pi\)
−0.694059 + 0.719918i \(0.744179\pi\)
\(212\) −17.3615 −1.19239
\(213\) 14.2481 0.976262
\(214\) −19.2195 −1.31382
\(215\) −7.12903 −0.486196
\(216\) −9.60158 −0.653305
\(217\) 30.8014 2.09094
\(218\) 20.7878 1.40792
\(219\) −15.6468 −1.05731
\(220\) −1.90552 −0.128470
\(221\) −2.10560 −0.141638
\(222\) −38.6593 −2.59464
\(223\) −19.9453 −1.33563 −0.667817 0.744326i \(-0.732771\pi\)
−0.667817 + 0.744326i \(0.732771\pi\)
\(224\) 30.4736 2.03611
\(225\) −4.49139 −0.299426
\(226\) 26.3298 1.75143
\(227\) 13.3187 0.883994 0.441997 0.897017i \(-0.354270\pi\)
0.441997 + 0.897017i \(0.354270\pi\)
\(228\) 30.8434 2.04265
\(229\) 24.2564 1.60291 0.801455 0.598055i \(-0.204059\pi\)
0.801455 + 0.598055i \(0.204059\pi\)
\(230\) −5.96168 −0.393102
\(231\) −9.37172 −0.616614
\(232\) −17.3645 −1.14004
\(233\) 3.97762 0.260583 0.130291 0.991476i \(-0.458409\pi\)
0.130291 + 0.991476i \(0.458409\pi\)
\(234\) −1.24359 −0.0812962
\(235\) 5.54202 0.361521
\(236\) −26.9029 −1.75123
\(237\) −0.624841 −0.0405878
\(238\) 39.2057 2.54133
\(239\) 2.10661 0.136265 0.0681326 0.997676i \(-0.478296\pi\)
0.0681326 + 0.997676i \(0.478296\pi\)
\(240\) −0.954519 −0.0616140
\(241\) −22.3905 −1.44230 −0.721151 0.692778i \(-0.756387\pi\)
−0.721151 + 0.692778i \(0.756387\pi\)
\(242\) −2.24881 −0.144559
\(243\) 9.75835 0.625999
\(244\) −6.91148 −0.442462
\(245\) −9.41259 −0.601349
\(246\) −22.5531 −1.43794
\(247\) −2.87358 −0.182842
\(248\) −15.5756 −0.989053
\(249\) −2.27399 −0.144108
\(250\) −13.4723 −0.852063
\(251\) 3.18957 0.201324 0.100662 0.994921i \(-0.467904\pi\)
0.100662 + 0.994921i \(0.467904\pi\)
\(252\) 13.9978 0.881781
\(253\) −4.25322 −0.267398
\(254\) 44.8764 2.81580
\(255\) −4.60787 −0.288556
\(256\) −10.7129 −0.669555
\(257\) 4.54763 0.283674 0.141837 0.989890i \(-0.454699\pi\)
0.141837 + 0.989890i \(0.454699\pi\)
\(258\) 51.2738 3.19217
\(259\) −40.5413 −2.51912
\(260\) −1.08193 −0.0670986
\(261\) 7.11408 0.440351
\(262\) −2.24881 −0.138932
\(263\) −18.5241 −1.14224 −0.571121 0.820866i \(-0.693491\pi\)
−0.571121 + 0.820866i \(0.693491\pi\)
\(264\) 4.73908 0.291670
\(265\) 3.53974 0.217445
\(266\) 53.5053 3.28062
\(267\) 21.0352 1.28733
\(268\) 28.1822 1.72150
\(269\) −18.4427 −1.12447 −0.562234 0.826978i \(-0.690058\pi\)
−0.562234 + 0.826978i \(0.690058\pi\)
\(270\) 5.66124 0.344532
\(271\) −18.8429 −1.14463 −0.572313 0.820035i \(-0.693954\pi\)
−0.572313 + 0.820035i \(0.693954\pi\)
\(272\) 2.84882 0.172735
\(273\) −5.32116 −0.322051
\(274\) −20.0539 −1.21150
\(275\) −4.61149 −0.278084
\(276\) 25.9205 1.56023
\(277\) −12.9812 −0.779965 −0.389983 0.920822i \(-0.627519\pi\)
−0.389983 + 0.920822i \(0.627519\pi\)
\(278\) 30.2529 1.81445
\(279\) 6.38119 0.382032
\(280\) 6.96608 0.416303
\(281\) −4.01959 −0.239788 −0.119894 0.992787i \(-0.538256\pi\)
−0.119894 + 0.992787i \(0.538256\pi\)
\(282\) −39.8596 −2.37360
\(283\) −26.1663 −1.55543 −0.777713 0.628619i \(-0.783620\pi\)
−0.777713 + 0.628619i \(0.783620\pi\)
\(284\) −21.8504 −1.29658
\(285\) −6.28849 −0.372498
\(286\) −1.27685 −0.0755016
\(287\) −23.6511 −1.39608
\(288\) 6.31329 0.372014
\(289\) −3.24756 −0.191033
\(290\) 10.2384 0.601218
\(291\) −28.2213 −1.65436
\(292\) 23.9954 1.40422
\(293\) −14.5841 −0.852013 −0.426007 0.904720i \(-0.640080\pi\)
−0.426007 + 0.904720i \(0.640080\pi\)
\(294\) 67.6978 3.94821
\(295\) 5.48509 0.319354
\(296\) 20.5009 1.19159
\(297\) 4.03888 0.234359
\(298\) 19.1999 1.11222
\(299\) −2.41493 −0.139659
\(300\) 28.1040 1.62258
\(301\) 53.7700 3.09925
\(302\) 40.5776 2.33498
\(303\) 11.5128 0.661392
\(304\) 3.88787 0.222984
\(305\) 1.40914 0.0806874
\(306\) 8.12233 0.464323
\(307\) 5.57883 0.318401 0.159200 0.987246i \(-0.449108\pi\)
0.159200 + 0.987246i \(0.449108\pi\)
\(308\) 14.3722 0.818930
\(309\) −8.40582 −0.478190
\(310\) 9.18362 0.521595
\(311\) 28.5812 1.62069 0.810346 0.585952i \(-0.199279\pi\)
0.810346 + 0.585952i \(0.199279\pi\)
\(312\) 2.69080 0.152336
\(313\) −30.7240 −1.73662 −0.868311 0.496020i \(-0.834794\pi\)
−0.868311 + 0.496020i \(0.834794\pi\)
\(314\) −50.4405 −2.84652
\(315\) −2.85394 −0.160801
\(316\) 0.958235 0.0539050
\(317\) 27.9872 1.57192 0.785959 0.618278i \(-0.212170\pi\)
0.785959 + 0.618278i \(0.212170\pi\)
\(318\) −25.4587 −1.42765
\(319\) 7.30433 0.408964
\(320\) 8.12825 0.454383
\(321\) −17.0373 −0.950931
\(322\) 44.9654 2.50582
\(323\) 18.7684 1.04430
\(324\) −33.5468 −1.86371
\(325\) −2.61836 −0.145240
\(326\) 34.2619 1.89759
\(327\) 18.4275 1.01904
\(328\) 11.9598 0.660372
\(329\) −41.8001 −2.30451
\(330\) −2.79423 −0.153817
\(331\) 7.59800 0.417624 0.208812 0.977956i \(-0.433040\pi\)
0.208812 + 0.977956i \(0.433040\pi\)
\(332\) 3.48731 0.191391
\(333\) −8.39903 −0.460264
\(334\) −42.1736 −2.30764
\(335\) −5.74590 −0.313932
\(336\) 7.19936 0.392757
\(337\) −14.0722 −0.766564 −0.383282 0.923631i \(-0.625206\pi\)
−0.383282 + 0.923631i \(0.625206\pi\)
\(338\) 28.5095 1.55071
\(339\) 23.3403 1.26767
\(340\) 7.06648 0.383233
\(341\) 6.55184 0.354802
\(342\) 11.0848 0.599397
\(343\) 38.0852 2.05640
\(344\) −27.1903 −1.46600
\(345\) −5.28480 −0.284524
\(346\) −2.32860 −0.125186
\(347\) −4.35285 −0.233673 −0.116837 0.993151i \(-0.537275\pi\)
−0.116837 + 0.993151i \(0.537275\pi\)
\(348\) −44.5150 −2.38625
\(349\) 13.6755 0.732033 0.366016 0.930608i \(-0.380721\pi\)
0.366016 + 0.930608i \(0.380721\pi\)
\(350\) 48.7530 2.60596
\(351\) 2.29323 0.122404
\(352\) 6.48212 0.345498
\(353\) 1.41800 0.0754723 0.0377361 0.999288i \(-0.487985\pi\)
0.0377361 + 0.999288i \(0.487985\pi\)
\(354\) −39.4502 −2.09675
\(355\) 4.45495 0.236444
\(356\) −32.2588 −1.70971
\(357\) 34.7543 1.83939
\(358\) 53.6065 2.83319
\(359\) 22.0112 1.16171 0.580853 0.814008i \(-0.302719\pi\)
0.580853 + 0.814008i \(0.302719\pi\)
\(360\) 1.44318 0.0760621
\(361\) 6.61375 0.348092
\(362\) −32.0715 −1.68564
\(363\) −1.99348 −0.104630
\(364\) 8.16036 0.427719
\(365\) −4.89229 −0.256074
\(366\) −10.1349 −0.529761
\(367\) −7.01423 −0.366140 −0.183070 0.983100i \(-0.558604\pi\)
−0.183070 + 0.983100i \(0.558604\pi\)
\(368\) 3.26733 0.170321
\(369\) −4.89984 −0.255076
\(370\) −12.0876 −0.628406
\(371\) −26.6981 −1.38610
\(372\) −39.9291 −2.07023
\(373\) 27.8412 1.44156 0.720781 0.693163i \(-0.243783\pi\)
0.720781 + 0.693163i \(0.243783\pi\)
\(374\) 8.33954 0.431227
\(375\) −11.9427 −0.616716
\(376\) 21.1374 1.09008
\(377\) 4.14732 0.213598
\(378\) −42.6993 −2.19621
\(379\) −13.3435 −0.685409 −0.342704 0.939443i \(-0.611343\pi\)
−0.342704 + 0.939443i \(0.611343\pi\)
\(380\) 9.64383 0.494718
\(381\) 39.7812 2.03805
\(382\) −4.76801 −0.243953
\(383\) −33.9312 −1.73380 −0.866902 0.498478i \(-0.833892\pi\)
−0.866902 + 0.498478i \(0.833892\pi\)
\(384\) −32.6165 −1.66446
\(385\) −2.93026 −0.149340
\(386\) 24.0566 1.22445
\(387\) 11.1396 0.566259
\(388\) 43.2793 2.19717
\(389\) 24.1604 1.22498 0.612490 0.790478i \(-0.290168\pi\)
0.612490 + 0.790478i \(0.290168\pi\)
\(390\) −1.58653 −0.0803373
\(391\) 15.7728 0.797663
\(392\) −35.8999 −1.81322
\(393\) −1.99348 −0.100558
\(394\) 18.4573 0.929863
\(395\) −0.195369 −0.00983010
\(396\) 2.97751 0.149625
\(397\) 14.7628 0.740925 0.370463 0.928847i \(-0.379199\pi\)
0.370463 + 0.928847i \(0.379199\pi\)
\(398\) −13.6493 −0.684177
\(399\) 47.4303 2.37448
\(400\) 3.54255 0.177128
\(401\) −15.0957 −0.753843 −0.376921 0.926245i \(-0.623017\pi\)
−0.376921 + 0.926245i \(0.623017\pi\)
\(402\) 41.3260 2.06115
\(403\) 3.72006 0.185310
\(404\) −17.6556 −0.878400
\(405\) 6.83967 0.339866
\(406\) −77.2218 −3.83246
\(407\) −8.62363 −0.427458
\(408\) −17.5745 −0.870068
\(409\) −23.9327 −1.18340 −0.591698 0.806159i \(-0.701542\pi\)
−0.591698 + 0.806159i \(0.701542\pi\)
\(410\) −7.05170 −0.348259
\(411\) −17.7770 −0.876875
\(412\) 12.8909 0.635089
\(413\) −41.3707 −2.03572
\(414\) 9.31556 0.457835
\(415\) −0.711008 −0.0349020
\(416\) 3.68047 0.180450
\(417\) 26.8180 1.31328
\(418\) 11.3812 0.556674
\(419\) −5.34588 −0.261164 −0.130582 0.991438i \(-0.541685\pi\)
−0.130582 + 0.991438i \(0.541685\pi\)
\(420\) 17.8580 0.871380
\(421\) −30.1871 −1.47123 −0.735615 0.677400i \(-0.763107\pi\)
−0.735615 + 0.677400i \(0.763107\pi\)
\(422\) 45.3440 2.20731
\(423\) −8.65980 −0.421054
\(424\) 13.5007 0.655650
\(425\) 17.1014 0.829540
\(426\) −32.0412 −1.55240
\(427\) −10.6283 −0.514340
\(428\) 26.1279 1.26294
\(429\) −1.13188 −0.0546474
\(430\) 16.0318 0.773123
\(431\) −21.0948 −1.01610 −0.508049 0.861328i \(-0.669633\pi\)
−0.508049 + 0.861328i \(0.669633\pi\)
\(432\) −3.10267 −0.149277
\(433\) 1.00762 0.0484230 0.0242115 0.999707i \(-0.492292\pi\)
0.0242115 + 0.999707i \(0.492292\pi\)
\(434\) −69.2665 −3.32490
\(435\) 9.07591 0.435157
\(436\) −28.2599 −1.35340
\(437\) 21.5256 1.02971
\(438\) 35.1866 1.68128
\(439\) −26.6511 −1.27199 −0.635994 0.771694i \(-0.719410\pi\)
−0.635994 + 0.771694i \(0.719410\pi\)
\(440\) 1.48177 0.0706406
\(441\) 14.7079 0.700374
\(442\) 4.73510 0.225226
\(443\) 29.8841 1.41984 0.709918 0.704284i \(-0.248732\pi\)
0.709918 + 0.704284i \(0.248732\pi\)
\(444\) 52.5553 2.49416
\(445\) 6.57707 0.311783
\(446\) 44.8530 2.12385
\(447\) 17.0199 0.805014
\(448\) −61.3064 −2.89646
\(449\) 5.08863 0.240147 0.120074 0.992765i \(-0.461687\pi\)
0.120074 + 0.992765i \(0.461687\pi\)
\(450\) 10.1003 0.476131
\(451\) −5.03087 −0.236895
\(452\) −35.7939 −1.68360
\(453\) 35.9704 1.69004
\(454\) −29.9512 −1.40568
\(455\) −1.66377 −0.0779987
\(456\) −23.9845 −1.12318
\(457\) 35.0128 1.63783 0.818916 0.573914i \(-0.194576\pi\)
0.818916 + 0.573914i \(0.194576\pi\)
\(458\) −54.5481 −2.54886
\(459\) −14.9779 −0.699108
\(460\) 8.10459 0.377879
\(461\) 23.1974 1.08041 0.540206 0.841533i \(-0.318346\pi\)
0.540206 + 0.841533i \(0.318346\pi\)
\(462\) 21.0752 0.980506
\(463\) 18.3017 0.850553 0.425276 0.905064i \(-0.360177\pi\)
0.425276 + 0.905064i \(0.360177\pi\)
\(464\) −5.61119 −0.260493
\(465\) 8.14092 0.377526
\(466\) −8.94490 −0.414365
\(467\) −41.9555 −1.94147 −0.970735 0.240153i \(-0.922802\pi\)
−0.970735 + 0.240153i \(0.922802\pi\)
\(468\) 1.69060 0.0781479
\(469\) 43.3379 2.00116
\(470\) −12.4629 −0.574872
\(471\) −44.7135 −2.06029
\(472\) 20.9203 0.962934
\(473\) 11.4375 0.525898
\(474\) 1.40515 0.0645405
\(475\) 23.3388 1.07086
\(476\) −53.2981 −2.44292
\(477\) −5.53110 −0.253252
\(478\) −4.73736 −0.216682
\(479\) −15.0551 −0.687887 −0.343944 0.938990i \(-0.611763\pi\)
−0.343944 + 0.938990i \(0.611763\pi\)
\(480\) 8.05428 0.367626
\(481\) −4.89640 −0.223257
\(482\) 50.3520 2.29347
\(483\) 39.8600 1.81369
\(484\) 3.05713 0.138961
\(485\) −8.82397 −0.400676
\(486\) −21.9447 −0.995430
\(487\) 2.35553 0.106739 0.0533695 0.998575i \(-0.483004\pi\)
0.0533695 + 0.998575i \(0.483004\pi\)
\(488\) 5.37451 0.243293
\(489\) 30.3718 1.37346
\(490\) 21.1671 0.956232
\(491\) −3.51607 −0.158678 −0.0793391 0.996848i \(-0.525281\pi\)
−0.0793391 + 0.996848i \(0.525281\pi\)
\(492\) 30.6598 1.38225
\(493\) −27.0876 −1.21996
\(494\) 6.46213 0.290745
\(495\) −0.607068 −0.0272857
\(496\) −5.03313 −0.225994
\(497\) −33.6010 −1.50721
\(498\) 5.11375 0.229153
\(499\) −25.8137 −1.15558 −0.577790 0.816185i \(-0.696085\pi\)
−0.577790 + 0.816185i \(0.696085\pi\)
\(500\) 18.3149 0.819066
\(501\) −37.3852 −1.67025
\(502\) −7.17274 −0.320135
\(503\) −6.11446 −0.272630 −0.136315 0.990666i \(-0.543526\pi\)
−0.136315 + 0.990666i \(0.543526\pi\)
\(504\) −10.8850 −0.484857
\(505\) 3.59971 0.160185
\(506\) 9.56468 0.425202
\(507\) 25.2725 1.12239
\(508\) −61.0071 −2.70675
\(509\) −2.07321 −0.0918935 −0.0459468 0.998944i \(-0.514630\pi\)
−0.0459468 + 0.998944i \(0.514630\pi\)
\(510\) 10.3622 0.458846
\(511\) 36.8995 1.63234
\(512\) −8.63204 −0.381486
\(513\) −20.4408 −0.902482
\(514\) −10.2268 −0.451083
\(515\) −2.62825 −0.115815
\(516\) −69.7040 −3.06855
\(517\) −8.89138 −0.391042
\(518\) 91.1696 4.00576
\(519\) −2.06421 −0.0906089
\(520\) 0.841333 0.0368949
\(521\) 5.44226 0.238430 0.119215 0.992868i \(-0.461962\pi\)
0.119215 + 0.992868i \(0.461962\pi\)
\(522\) −15.9982 −0.700222
\(523\) 12.4386 0.543903 0.271951 0.962311i \(-0.412331\pi\)
0.271951 + 0.962311i \(0.412331\pi\)
\(524\) 3.05713 0.133552
\(525\) 43.2176 1.88617
\(526\) 41.6570 1.81633
\(527\) −24.2970 −1.05840
\(528\) 1.53139 0.0666453
\(529\) −4.91010 −0.213482
\(530\) −7.96020 −0.345769
\(531\) −8.57085 −0.371943
\(532\) −72.7376 −3.15357
\(533\) −2.85647 −0.123728
\(534\) −47.3040 −2.04704
\(535\) −5.32707 −0.230309
\(536\) −21.9150 −0.946585
\(537\) 47.5200 2.05064
\(538\) 41.4740 1.78807
\(539\) 15.1012 0.650454
\(540\) −7.69615 −0.331190
\(541\) −17.9427 −0.771418 −0.385709 0.922621i \(-0.626043\pi\)
−0.385709 + 0.922621i \(0.626043\pi\)
\(542\) 42.3741 1.82012
\(543\) −28.4301 −1.22005
\(544\) −24.0385 −1.03064
\(545\) 5.76174 0.246806
\(546\) 11.9663 0.512109
\(547\) −16.2721 −0.695747 −0.347873 0.937542i \(-0.613096\pi\)
−0.347873 + 0.937542i \(0.613096\pi\)
\(548\) 27.2623 1.16459
\(549\) −2.20189 −0.0939744
\(550\) 10.3704 0.442194
\(551\) −36.9672 −1.57486
\(552\) −20.1563 −0.857911
\(553\) 1.47355 0.0626618
\(554\) 29.1922 1.24026
\(555\) −10.7152 −0.454835
\(556\) −41.1272 −1.74418
\(557\) 13.5632 0.574691 0.287346 0.957827i \(-0.407227\pi\)
0.287346 + 0.957827i \(0.407227\pi\)
\(558\) −14.3501 −0.607487
\(559\) 6.49410 0.274671
\(560\) 2.25103 0.0951233
\(561\) 7.39267 0.312119
\(562\) 9.03927 0.381299
\(563\) 7.62228 0.321241 0.160620 0.987016i \(-0.448651\pi\)
0.160620 + 0.987016i \(0.448651\pi\)
\(564\) 54.1870 2.28168
\(565\) 7.29782 0.307022
\(566\) 58.8430 2.47336
\(567\) −51.5874 −2.16647
\(568\) 16.9913 0.712939
\(569\) −13.3015 −0.557629 −0.278814 0.960345i \(-0.589941\pi\)
−0.278814 + 0.960345i \(0.589941\pi\)
\(570\) 14.1416 0.592327
\(571\) −29.7172 −1.24363 −0.621814 0.783165i \(-0.713604\pi\)
−0.621814 + 0.783165i \(0.713604\pi\)
\(572\) 1.73581 0.0725777
\(573\) −4.22665 −0.176571
\(574\) 53.1867 2.21997
\(575\) 19.6137 0.817948
\(576\) −12.7010 −0.529207
\(577\) 32.5756 1.35614 0.678070 0.734998i \(-0.262817\pi\)
0.678070 + 0.734998i \(0.262817\pi\)
\(578\) 7.30314 0.303771
\(579\) 21.3252 0.886247
\(580\) −13.9185 −0.577935
\(581\) 5.36270 0.222482
\(582\) 63.4642 2.63068
\(583\) −5.67901 −0.235201
\(584\) −18.6593 −0.772127
\(585\) −0.344687 −0.0142510
\(586\) 32.7969 1.35483
\(587\) 20.4401 0.843653 0.421827 0.906677i \(-0.361389\pi\)
0.421827 + 0.906677i \(0.361389\pi\)
\(588\) −92.0315 −3.79532
\(589\) −33.1589 −1.36629
\(590\) −12.3349 −0.507820
\(591\) 16.3616 0.673027
\(592\) 6.62468 0.272273
\(593\) −13.8358 −0.568168 −0.284084 0.958799i \(-0.591689\pi\)
−0.284084 + 0.958799i \(0.591689\pi\)
\(594\) −9.08266 −0.372666
\(595\) 10.8667 0.445490
\(596\) −26.1012 −1.06915
\(597\) −12.0996 −0.495202
\(598\) 5.43072 0.222079
\(599\) −45.6273 −1.86428 −0.932140 0.362099i \(-0.882060\pi\)
−0.932140 + 0.362099i \(0.882060\pi\)
\(600\) −21.8542 −0.892195
\(601\) 16.1863 0.660252 0.330126 0.943937i \(-0.392909\pi\)
0.330126 + 0.943937i \(0.392909\pi\)
\(602\) −120.918 −4.92826
\(603\) 8.97839 0.365628
\(604\) −55.1631 −2.24455
\(605\) −0.623302 −0.0253408
\(606\) −25.8900 −1.05171
\(607\) −6.56790 −0.266583 −0.133291 0.991077i \(-0.542555\pi\)
−0.133291 + 0.991077i \(0.542555\pi\)
\(608\) −32.8060 −1.33046
\(609\) −68.4541 −2.77390
\(610\) −3.16889 −0.128305
\(611\) −5.04843 −0.204238
\(612\) −11.0419 −0.446342
\(613\) 10.5717 0.426987 0.213493 0.976944i \(-0.431516\pi\)
0.213493 + 0.976944i \(0.431516\pi\)
\(614\) −12.5457 −0.506304
\(615\) −6.25105 −0.252067
\(616\) −11.1761 −0.450297
\(617\) −44.8682 −1.80632 −0.903162 0.429299i \(-0.858761\pi\)
−0.903162 + 0.429299i \(0.858761\pi\)
\(618\) 18.9031 0.760393
\(619\) 15.5417 0.624673 0.312336 0.949972i \(-0.398888\pi\)
0.312336 + 0.949972i \(0.398888\pi\)
\(620\) −12.4846 −0.501395
\(621\) −17.1782 −0.689339
\(622\) −64.2736 −2.57714
\(623\) −49.6069 −1.98746
\(624\) 0.869507 0.0348081
\(625\) 19.3234 0.772934
\(626\) 69.0923 2.76148
\(627\) 10.0890 0.402916
\(628\) 68.5712 2.73629
\(629\) 31.9801 1.27513
\(630\) 6.41796 0.255698
\(631\) −31.0573 −1.23637 −0.618186 0.786031i \(-0.712132\pi\)
−0.618186 + 0.786031i \(0.712132\pi\)
\(632\) −0.745144 −0.0296402
\(633\) 40.1956 1.59763
\(634\) −62.9378 −2.49958
\(635\) 12.4384 0.493603
\(636\) 34.6098 1.37237
\(637\) 8.57428 0.339725
\(638\) −16.4260 −0.650313
\(639\) −6.96119 −0.275380
\(640\) −10.1982 −0.403121
\(641\) 12.8682 0.508265 0.254132 0.967169i \(-0.418210\pi\)
0.254132 + 0.967169i \(0.418210\pi\)
\(642\) 38.3137 1.51212
\(643\) −7.60342 −0.299850 −0.149925 0.988697i \(-0.547903\pi\)
−0.149925 + 0.988697i \(0.547903\pi\)
\(644\) −61.1280 −2.40878
\(645\) 14.2116 0.559580
\(646\) −42.2064 −1.66059
\(647\) −28.3973 −1.11641 −0.558207 0.829702i \(-0.688511\pi\)
−0.558207 + 0.829702i \(0.688511\pi\)
\(648\) 26.0867 1.02478
\(649\) −8.80006 −0.345432
\(650\) 5.88818 0.230953
\(651\) −61.4020 −2.40653
\(652\) −46.5773 −1.82411
\(653\) 28.7238 1.12405 0.562024 0.827121i \(-0.310023\pi\)
0.562024 + 0.827121i \(0.310023\pi\)
\(654\) −41.4399 −1.62043
\(655\) −0.623302 −0.0243544
\(656\) 3.86472 0.150892
\(657\) 7.64455 0.298242
\(658\) 94.0003 3.66451
\(659\) 43.7748 1.70523 0.852613 0.522543i \(-0.175017\pi\)
0.852613 + 0.522543i \(0.175017\pi\)
\(660\) 3.79861 0.147861
\(661\) −6.83583 −0.265883 −0.132941 0.991124i \(-0.542442\pi\)
−0.132941 + 0.991124i \(0.542442\pi\)
\(662\) −17.0864 −0.664084
\(663\) 4.19748 0.163016
\(664\) −2.71180 −0.105238
\(665\) 14.8301 0.575085
\(666\) 18.8878 0.731887
\(667\) −31.0669 −1.20292
\(668\) 57.3328 2.21827
\(669\) 39.7604 1.53723
\(670\) 12.9214 0.499198
\(671\) −2.26077 −0.0872761
\(672\) −60.7485 −2.34343
\(673\) −41.0835 −1.58365 −0.791825 0.610747i \(-0.790869\pi\)
−0.791825 + 0.610747i \(0.790869\pi\)
\(674\) 31.6458 1.21895
\(675\) −18.6253 −0.716887
\(676\) −38.7572 −1.49066
\(677\) −16.0765 −0.617872 −0.308936 0.951083i \(-0.599973\pi\)
−0.308936 + 0.951083i \(0.599973\pi\)
\(678\) −52.4878 −2.01578
\(679\) 66.5538 2.55410
\(680\) −5.49504 −0.210725
\(681\) −26.5506 −1.01742
\(682\) −14.7338 −0.564187
\(683\) 10.0322 0.383873 0.191937 0.981407i \(-0.438523\pi\)
0.191937 + 0.981407i \(0.438523\pi\)
\(684\) −15.0692 −0.576185
\(685\) −5.55835 −0.212374
\(686\) −85.6462 −3.26999
\(687\) −48.3547 −1.84485
\(688\) −8.78632 −0.334975
\(689\) −3.22448 −0.122843
\(690\) 11.8845 0.452435
\(691\) −26.6200 −1.01267 −0.506336 0.862336i \(-0.669000\pi\)
−0.506336 + 0.862336i \(0.669000\pi\)
\(692\) 3.16561 0.120338
\(693\) 4.57874 0.173932
\(694\) 9.78871 0.371574
\(695\) 8.38520 0.318069
\(696\) 34.6158 1.31211
\(697\) 18.6566 0.706670
\(698\) −30.7536 −1.16404
\(699\) −7.92930 −0.299914
\(700\) −66.2771 −2.50504
\(701\) 19.0431 0.719249 0.359625 0.933097i \(-0.382905\pi\)
0.359625 + 0.933097i \(0.382905\pi\)
\(702\) −5.15703 −0.194640
\(703\) 43.6442 1.64607
\(704\) −13.0406 −0.491487
\(705\) −11.0479 −0.416088
\(706\) −3.18880 −0.120012
\(707\) −27.1504 −1.02110
\(708\) 53.6304 2.01556
\(709\) 40.1812 1.50904 0.754518 0.656280i \(-0.227871\pi\)
0.754518 + 0.656280i \(0.227871\pi\)
\(710\) −10.0183 −0.375981
\(711\) 0.305279 0.0114488
\(712\) 25.0851 0.940105
\(713\) −27.8664 −1.04361
\(714\) −78.1558 −2.92491
\(715\) −0.353904 −0.0132353
\(716\) −72.8751 −2.72347
\(717\) −4.19948 −0.156832
\(718\) −49.4989 −1.84728
\(719\) 7.00276 0.261159 0.130579 0.991438i \(-0.458316\pi\)
0.130579 + 0.991438i \(0.458316\pi\)
\(720\) 0.466350 0.0173798
\(721\) 19.8233 0.738259
\(722\) −14.8730 −0.553517
\(723\) 44.6351 1.66000
\(724\) 43.5995 1.62036
\(725\) −33.6839 −1.25099
\(726\) 4.48295 0.166378
\(727\) 13.3520 0.495199 0.247600 0.968862i \(-0.420358\pi\)
0.247600 + 0.968862i \(0.420358\pi\)
\(728\) −6.34566 −0.235186
\(729\) 13.4668 0.498769
\(730\) 11.0018 0.407195
\(731\) −42.4152 −1.56878
\(732\) 13.7779 0.509245
\(733\) −6.84311 −0.252756 −0.126378 0.991982i \(-0.540335\pi\)
−0.126378 + 0.991982i \(0.540335\pi\)
\(734\) 15.7737 0.582216
\(735\) 18.7638 0.692113
\(736\) −27.5699 −1.01624
\(737\) 9.21849 0.339567
\(738\) 11.0188 0.405608
\(739\) 47.3700 1.74253 0.871267 0.490810i \(-0.163299\pi\)
0.871267 + 0.490810i \(0.163299\pi\)
\(740\) 16.4325 0.604070
\(741\) 5.72842 0.210439
\(742\) 60.0389 2.20410
\(743\) 12.6995 0.465899 0.232950 0.972489i \(-0.425162\pi\)
0.232950 + 0.972489i \(0.425162\pi\)
\(744\) 31.0497 1.13834
\(745\) 5.32163 0.194969
\(746\) −62.6095 −2.29230
\(747\) 1.11100 0.0406494
\(748\) −11.3372 −0.414528
\(749\) 40.1789 1.46810
\(750\) 26.8567 0.980669
\(751\) 10.4605 0.381709 0.190855 0.981618i \(-0.438874\pi\)
0.190855 + 0.981618i \(0.438874\pi\)
\(752\) 6.83037 0.249078
\(753\) −6.35835 −0.231711
\(754\) −9.32652 −0.339652
\(755\) 11.2469 0.409317
\(756\) 58.0474 2.11116
\(757\) −52.4638 −1.90683 −0.953415 0.301663i \(-0.902458\pi\)
−0.953415 + 0.301663i \(0.902458\pi\)
\(758\) 30.0069 1.08990
\(759\) 8.47871 0.307758
\(760\) −7.49924 −0.272026
\(761\) 27.9592 1.01352 0.506761 0.862087i \(-0.330843\pi\)
0.506761 + 0.862087i \(0.330843\pi\)
\(762\) −89.4602 −3.24080
\(763\) −43.4573 −1.57326
\(764\) 6.48186 0.234505
\(765\) 2.25127 0.0813948
\(766\) 76.3048 2.75700
\(767\) −4.99658 −0.180416
\(768\) 21.3559 0.770615
\(769\) 10.6309 0.383360 0.191680 0.981457i \(-0.438606\pi\)
0.191680 + 0.981457i \(0.438606\pi\)
\(770\) 6.58959 0.237472
\(771\) −9.06561 −0.326490
\(772\) −32.7037 −1.17703
\(773\) 25.3221 0.910773 0.455386 0.890294i \(-0.349501\pi\)
0.455386 + 0.890294i \(0.349501\pi\)
\(774\) −25.0509 −0.900435
\(775\) −30.2138 −1.08531
\(776\) −33.6548 −1.20814
\(777\) 80.8182 2.89934
\(778\) −54.3320 −1.94790
\(779\) 25.4613 0.912244
\(780\) 2.15681 0.0772261
\(781\) −7.14734 −0.255752
\(782\) −35.4699 −1.26840
\(783\) 29.5013 1.05429
\(784\) −11.6007 −0.414312
\(785\) −13.9806 −0.498989
\(786\) 4.48295 0.159901
\(787\) −16.2855 −0.580516 −0.290258 0.956948i \(-0.593741\pi\)
−0.290258 + 0.956948i \(0.593741\pi\)
\(788\) −25.0917 −0.893853
\(789\) 36.9273 1.31465
\(790\) 0.439348 0.0156313
\(791\) −55.0430 −1.95711
\(792\) −2.31537 −0.0822732
\(793\) −1.28364 −0.0455835
\(794\) −33.1988 −1.17818
\(795\) −7.05640 −0.250265
\(796\) 18.5555 0.657682
\(797\) 9.65476 0.341989 0.170995 0.985272i \(-0.445302\pi\)
0.170995 + 0.985272i \(0.445302\pi\)
\(798\) −106.662 −3.77578
\(799\) 32.9730 1.16650
\(800\) −29.8922 −1.05685
\(801\) −10.2772 −0.363125
\(802\) 33.9473 1.19872
\(803\) 7.84898 0.276984
\(804\) −56.1805 −1.98133
\(805\) 12.4631 0.439265
\(806\) −8.36570 −0.294669
\(807\) 36.7650 1.29419
\(808\) 13.7294 0.482998
\(809\) 34.0686 1.19779 0.598894 0.800828i \(-0.295607\pi\)
0.598894 + 0.800828i \(0.295607\pi\)
\(810\) −15.3811 −0.540436
\(811\) −30.2437 −1.06200 −0.531001 0.847371i \(-0.678184\pi\)
−0.531001 + 0.847371i \(0.678184\pi\)
\(812\) 104.979 3.68404
\(813\) 37.5630 1.31739
\(814\) 19.3929 0.679720
\(815\) 9.49638 0.332644
\(816\) −5.67905 −0.198807
\(817\) −57.8853 −2.02515
\(818\) 53.8201 1.88177
\(819\) 2.59976 0.0908430
\(820\) 9.58642 0.334772
\(821\) 14.9898 0.523148 0.261574 0.965183i \(-0.415759\pi\)
0.261574 + 0.965183i \(0.415759\pi\)
\(822\) 39.9771 1.39436
\(823\) −23.1882 −0.808290 −0.404145 0.914695i \(-0.632431\pi\)
−0.404145 + 0.914695i \(0.632431\pi\)
\(824\) −10.0242 −0.349210
\(825\) 9.19291 0.320056
\(826\) 93.0348 3.23709
\(827\) 54.7801 1.90489 0.952445 0.304711i \(-0.0985599\pi\)
0.952445 + 0.304711i \(0.0985599\pi\)
\(828\) −12.6640 −0.440105
\(829\) 46.3484 1.60975 0.804873 0.593447i \(-0.202233\pi\)
0.804873 + 0.593447i \(0.202233\pi\)
\(830\) 1.59892 0.0554994
\(831\) 25.8778 0.897689
\(832\) −7.40432 −0.256699
\(833\) −56.0016 −1.94034
\(834\) −60.3085 −2.08831
\(835\) −11.6893 −0.404524
\(836\) −15.4722 −0.535116
\(837\) 26.4621 0.914663
\(838\) 12.0219 0.415288
\(839\) 15.2183 0.525395 0.262698 0.964878i \(-0.415388\pi\)
0.262698 + 0.964878i \(0.415388\pi\)
\(840\) −13.8867 −0.479138
\(841\) 24.3532 0.839766
\(842\) 67.8850 2.33947
\(843\) 8.01296 0.275981
\(844\) −61.6427 −2.12183
\(845\) 7.90198 0.271837
\(846\) 19.4742 0.669538
\(847\) 4.70119 0.161535
\(848\) 4.36262 0.149813
\(849\) 52.1620 1.79019
\(850\) −38.4577 −1.31909
\(851\) 36.6782 1.25731
\(852\) 43.5582 1.49228
\(853\) −5.05097 −0.172942 −0.0864710 0.996254i \(-0.527559\pi\)
−0.0864710 + 0.996254i \(0.527559\pi\)
\(854\) 23.9010 0.817877
\(855\) 3.07237 0.105073
\(856\) −20.3176 −0.694441
\(857\) −10.2065 −0.348646 −0.174323 0.984688i \(-0.555774\pi\)
−0.174323 + 0.984688i \(0.555774\pi\)
\(858\) 2.54537 0.0868975
\(859\) −33.0113 −1.12633 −0.563165 0.826344i \(-0.690417\pi\)
−0.563165 + 0.826344i \(0.690417\pi\)
\(860\) −21.7944 −0.743183
\(861\) 47.1479 1.60680
\(862\) 47.4380 1.61575
\(863\) −31.2708 −1.06447 −0.532236 0.846596i \(-0.678648\pi\)
−0.532236 + 0.846596i \(0.678648\pi\)
\(864\) 26.1805 0.890678
\(865\) −0.645419 −0.0219449
\(866\) −2.26594 −0.0769997
\(867\) 6.47394 0.219867
\(868\) 94.1641 3.19614
\(869\) 0.313442 0.0106328
\(870\) −20.4100 −0.691963
\(871\) 5.23416 0.177353
\(872\) 21.9754 0.744182
\(873\) 13.7881 0.466656
\(874\) −48.4069 −1.63739
\(875\) 28.1642 0.952123
\(876\) −47.8343 −1.61617
\(877\) 25.8641 0.873368 0.436684 0.899615i \(-0.356153\pi\)
0.436684 + 0.899615i \(0.356153\pi\)
\(878\) 59.9332 2.02265
\(879\) 29.0731 0.980612
\(880\) 0.478821 0.0161411
\(881\) 41.7507 1.40662 0.703309 0.710885i \(-0.251705\pi\)
0.703309 + 0.710885i \(0.251705\pi\)
\(882\) −33.0751 −1.11370
\(883\) 31.3090 1.05363 0.526816 0.849979i \(-0.323386\pi\)
0.526816 + 0.849979i \(0.323386\pi\)
\(884\) −6.43712 −0.216504
\(885\) −10.9344 −0.367556
\(886\) −67.2036 −2.25775
\(887\) 25.7789 0.865570 0.432785 0.901497i \(-0.357531\pi\)
0.432785 + 0.901497i \(0.357531\pi\)
\(888\) −40.8680 −1.37144
\(889\) −93.8153 −3.14646
\(890\) −14.7906 −0.495781
\(891\) −10.9733 −0.367619
\(892\) −60.9753 −2.04160
\(893\) 44.9993 1.50584
\(894\) −38.2745 −1.28009
\(895\) 14.8581 0.496652
\(896\) 76.9191 2.56969
\(897\) 4.81412 0.160739
\(898\) −11.4434 −0.381870
\(899\) 47.8568 1.59611
\(900\) −13.7308 −0.457692
\(901\) 21.0602 0.701618
\(902\) 11.3135 0.376697
\(903\) −107.189 −3.56703
\(904\) 27.8341 0.925748
\(905\) −8.88926 −0.295489
\(906\) −80.8906 −2.68741
\(907\) 29.7359 0.987363 0.493682 0.869643i \(-0.335651\pi\)
0.493682 + 0.869643i \(0.335651\pi\)
\(908\) 40.7171 1.35124
\(909\) −5.62480 −0.186563
\(910\) 3.74150 0.124029
\(911\) −32.2639 −1.06895 −0.534475 0.845185i \(-0.679490\pi\)
−0.534475 + 0.845185i \(0.679490\pi\)
\(912\) −7.75038 −0.256641
\(913\) 1.14071 0.0377521
\(914\) −78.7371 −2.60439
\(915\) −2.80910 −0.0928659
\(916\) 74.1552 2.45016
\(917\) 4.70119 0.155247
\(918\) 33.6824 1.11168
\(919\) −35.3222 −1.16517 −0.582585 0.812770i \(-0.697959\pi\)
−0.582585 + 0.812770i \(0.697959\pi\)
\(920\) −6.30230 −0.207781
\(921\) −11.1213 −0.366458
\(922\) −52.1665 −1.71801
\(923\) −4.05818 −0.133577
\(924\) −28.6506 −0.942535
\(925\) 39.7678 1.30756
\(926\) −41.1570 −1.35250
\(927\) 4.10683 0.134886
\(928\) 47.3475 1.55426
\(929\) 18.2887 0.600034 0.300017 0.953934i \(-0.403008\pi\)
0.300017 + 0.953934i \(0.403008\pi\)
\(930\) −18.3074 −0.600322
\(931\) −76.4271 −2.50480
\(932\) 12.1601 0.398318
\(933\) −56.9760 −1.86531
\(934\) 94.3499 3.08722
\(935\) 2.31147 0.0755932
\(936\) −1.31464 −0.0429705
\(937\) 14.5152 0.474192 0.237096 0.971486i \(-0.423804\pi\)
0.237096 + 0.971486i \(0.423804\pi\)
\(938\) −97.4585 −3.18213
\(939\) 61.2476 1.99874
\(940\) 16.9427 0.552609
\(941\) 29.6336 0.966028 0.483014 0.875613i \(-0.339542\pi\)
0.483014 + 0.875613i \(0.339542\pi\)
\(942\) 100.552 3.27616
\(943\) 21.3974 0.696796
\(944\) 6.76021 0.220026
\(945\) −11.8350 −0.384991
\(946\) −25.7208 −0.836255
\(947\) −21.3784 −0.694704 −0.347352 0.937735i \(-0.612919\pi\)
−0.347352 + 0.937735i \(0.612919\pi\)
\(948\) −1.91022 −0.0620411
\(949\) 4.45656 0.144666
\(950\) −52.4844 −1.70282
\(951\) −55.7919 −1.80918
\(952\) 41.4457 1.34326
\(953\) −54.0400 −1.75053 −0.875263 0.483647i \(-0.839312\pi\)
−0.875263 + 0.483647i \(0.839312\pi\)
\(954\) 12.4384 0.402708
\(955\) −1.32155 −0.0427643
\(956\) 6.44018 0.208290
\(957\) −14.5610 −0.470691
\(958\) 33.8561 1.09384
\(959\) 41.9233 1.35377
\(960\) −16.2035 −0.522965
\(961\) 11.9266 0.384729
\(962\) 11.0111 0.355011
\(963\) 8.32394 0.268235
\(964\) −68.4509 −2.20465
\(965\) 6.66778 0.214643
\(966\) −89.6374 −2.88404
\(967\) −5.17546 −0.166431 −0.0832157 0.996532i \(-0.526519\pi\)
−0.0832157 + 0.996532i \(0.526519\pi\)
\(968\) −2.37729 −0.0764090
\(969\) −37.4143 −1.20192
\(970\) 19.8434 0.637133
\(971\) 6.40183 0.205444 0.102722 0.994710i \(-0.467245\pi\)
0.102722 + 0.994710i \(0.467245\pi\)
\(972\) 29.8326 0.956881
\(973\) −63.2445 −2.02752
\(974\) −5.29712 −0.169731
\(975\) 5.21964 0.167162
\(976\) 1.73673 0.0555913
\(977\) 8.68052 0.277715 0.138857 0.990312i \(-0.455657\pi\)
0.138857 + 0.990312i \(0.455657\pi\)
\(978\) −68.3004 −2.18401
\(979\) −10.5520 −0.337243
\(980\) −28.7756 −0.919201
\(981\) −9.00314 −0.287448
\(982\) 7.90697 0.252322
\(983\) 0.299404 0.00954950 0.00477475 0.999989i \(-0.498480\pi\)
0.00477475 + 0.999989i \(0.498480\pi\)
\(984\) −23.8417 −0.760045
\(985\) 5.11580 0.163003
\(986\) 60.9147 1.93992
\(987\) 83.3275 2.65234
\(988\) −8.78492 −0.279486
\(989\) −48.6463 −1.54686
\(990\) 1.36518 0.0433882
\(991\) 15.0939 0.479473 0.239736 0.970838i \(-0.422939\pi\)
0.239736 + 0.970838i \(0.422939\pi\)
\(992\) 42.4698 1.34842
\(993\) −15.1465 −0.480658
\(994\) 75.5622 2.39669
\(995\) −3.78318 −0.119935
\(996\) −6.95188 −0.220279
\(997\) 20.7624 0.657552 0.328776 0.944408i \(-0.393364\pi\)
0.328776 + 0.944408i \(0.393364\pi\)
\(998\) 58.0500 1.83754
\(999\) −34.8298 −1.10197
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 1441.2.a.c.1.4 23
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1441.2.a.c.1.4 23 1.1 even 1 trivial