Properties

Label 4033.2.a.f.1.18
Level 4033
Weight 2
Character 4033.1
Self dual yes
Analytic conductor 32.204
Analytic rank 0
Dimension 85
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4033 = 37 \cdot 109 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4033.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.2036671352\)
Analytic rank: \(0\)
Dimension: \(85\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) = 4033.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.82466 q^{2} +0.0328358 q^{3} +1.32938 q^{4} -0.181740 q^{5} -0.0599140 q^{6} +4.41961 q^{7} +1.22366 q^{8} -2.99892 q^{9} +O(q^{10})\) \(q-1.82466 q^{2} +0.0328358 q^{3} +1.32938 q^{4} -0.181740 q^{5} -0.0599140 q^{6} +4.41961 q^{7} +1.22366 q^{8} -2.99892 q^{9} +0.331613 q^{10} -0.871253 q^{11} +0.0436510 q^{12} +3.03490 q^{13} -8.06427 q^{14} -0.00596756 q^{15} -4.89151 q^{16} +6.34816 q^{17} +5.47201 q^{18} -0.715988 q^{19} -0.241600 q^{20} +0.145121 q^{21} +1.58974 q^{22} +2.85067 q^{23} +0.0401798 q^{24} -4.96697 q^{25} -5.53765 q^{26} -0.196979 q^{27} +5.87532 q^{28} +5.73056 q^{29} +0.0108888 q^{30} +7.22926 q^{31} +6.47801 q^{32} -0.0286082 q^{33} -11.5832 q^{34} -0.803218 q^{35} -3.98669 q^{36} +1.00000 q^{37} +1.30643 q^{38} +0.0996531 q^{39} -0.222388 q^{40} -9.57735 q^{41} -0.264796 q^{42} -7.97679 q^{43} -1.15822 q^{44} +0.545023 q^{45} -5.20149 q^{46} +7.45694 q^{47} -0.160616 q^{48} +12.5329 q^{49} +9.06302 q^{50} +0.208447 q^{51} +4.03452 q^{52} +2.08916 q^{53} +0.359419 q^{54} +0.158341 q^{55} +5.40810 q^{56} -0.0235100 q^{57} -10.4563 q^{58} +9.13233 q^{59} -0.00793313 q^{60} +5.31105 q^{61} -13.1909 q^{62} -13.2541 q^{63} -2.03713 q^{64} -0.551561 q^{65} +0.0522003 q^{66} -7.64729 q^{67} +8.43909 q^{68} +0.0936038 q^{69} +1.46560 q^{70} +0.273822 q^{71} -3.66966 q^{72} +3.37228 q^{73} -1.82466 q^{74} -0.163094 q^{75} -0.951817 q^{76} -3.85059 q^{77} -0.181833 q^{78} +2.85327 q^{79} +0.888982 q^{80} +8.99030 q^{81} +17.4754 q^{82} -1.37879 q^{83} +0.192920 q^{84} -1.15371 q^{85} +14.5549 q^{86} +0.188167 q^{87} -1.06612 q^{88} -1.61133 q^{89} -0.994481 q^{90} +13.4131 q^{91} +3.78961 q^{92} +0.237378 q^{93} -13.6064 q^{94} +0.130123 q^{95} +0.212710 q^{96} +6.51903 q^{97} -22.8683 q^{98} +2.61282 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 85q + 11q^{2} + 21q^{3} + 93q^{4} + 12q^{5} + 4q^{6} + 17q^{7} + 30q^{8} + 98q^{9} + O(q^{10}) \) \( 85q + 11q^{2} + 21q^{3} + 93q^{4} + 12q^{5} + 4q^{6} + 17q^{7} + 30q^{8} + 98q^{9} + 9q^{10} + 37q^{11} + 44q^{12} + 14q^{13} + 26q^{14} + 27q^{15} + 85q^{16} + 34q^{17} + 3q^{18} + 15q^{19} + 15q^{20} + 17q^{21} + q^{22} + 72q^{23} + 15q^{24} + 85q^{25} + 33q^{26} + 69q^{27} + 7q^{28} + 19q^{29} - 9q^{30} + 23q^{31} + 51q^{32} + 32q^{33} + 49q^{34} + 40q^{35} + 121q^{36} + 85q^{37} + 84q^{38} + 39q^{39} + 22q^{40} + 55q^{41} - 28q^{42} + 78q^{44} + 28q^{45} + 17q^{46} + 184q^{47} + 97q^{48} + 88q^{49} + 26q^{50} + 27q^{51} + 73q^{52} + 64q^{53} + 31q^{54} + 39q^{55} + 68q^{56} - 33q^{57} + 28q^{58} + 60q^{59} - 22q^{60} + 7q^{61} + 70q^{62} + 28q^{63} + 102q^{64} + 17q^{65} - 15q^{66} + 82q^{67} + 92q^{68} + 22q^{69} - 41q^{70} + 113q^{71} - 19q^{73} + 11q^{74} + 45q^{75} + 34q^{76} + 64q^{77} + 29q^{78} + 23q^{79} + 54q^{80} + 149q^{81} + 4q^{82} + 100q^{83} - 49q^{84} - 5q^{85} - 24q^{86} + 65q^{87} + 14q^{88} + 84q^{89} - 21q^{90} + 32q^{91} + 95q^{92} + 19q^{93} - 47q^{94} + 102q^{95} + 29q^{96} + 7q^{97} + 26q^{98} + 107q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.82466 −1.29023 −0.645114 0.764086i \(-0.723190\pi\)
−0.645114 + 0.764086i \(0.723190\pi\)
\(3\) 0.0328358 0.0189577 0.00947887 0.999955i \(-0.496983\pi\)
0.00947887 + 0.999955i \(0.496983\pi\)
\(4\) 1.32938 0.664688
\(5\) −0.181740 −0.0812765 −0.0406382 0.999174i \(-0.512939\pi\)
−0.0406382 + 0.999174i \(0.512939\pi\)
\(6\) −0.0599140 −0.0244598
\(7\) 4.41961 1.67045 0.835227 0.549905i \(-0.185336\pi\)
0.835227 + 0.549905i \(0.185336\pi\)
\(8\) 1.22366 0.432629
\(9\) −2.99892 −0.999641
\(10\) 0.331613 0.104865
\(11\) −0.871253 −0.262693 −0.131346 0.991337i \(-0.541930\pi\)
−0.131346 + 0.991337i \(0.541930\pi\)
\(12\) 0.0436510 0.0126010
\(13\) 3.03490 0.841729 0.420865 0.907123i \(-0.361727\pi\)
0.420865 + 0.907123i \(0.361727\pi\)
\(14\) −8.06427 −2.15527
\(15\) −0.00596756 −0.00154082
\(16\) −4.89151 −1.22288
\(17\) 6.34816 1.53966 0.769828 0.638252i \(-0.220342\pi\)
0.769828 + 0.638252i \(0.220342\pi\)
\(18\) 5.47201 1.28976
\(19\) −0.715988 −0.164259 −0.0821294 0.996622i \(-0.526172\pi\)
−0.0821294 + 0.996622i \(0.526172\pi\)
\(20\) −0.241600 −0.0540235
\(21\) 0.145121 0.0316680
\(22\) 1.58974 0.338933
\(23\) 2.85067 0.594405 0.297203 0.954814i \(-0.403946\pi\)
0.297203 + 0.954814i \(0.403946\pi\)
\(24\) 0.0401798 0.00820167
\(25\) −4.96697 −0.993394
\(26\) −5.53765 −1.08602
\(27\) −0.196979 −0.0379086
\(28\) 5.87532 1.11033
\(29\) 5.73056 1.06414 0.532069 0.846701i \(-0.321415\pi\)
0.532069 + 0.846701i \(0.321415\pi\)
\(30\) 0.0108888 0.00198801
\(31\) 7.22926 1.29841 0.649206 0.760612i \(-0.275101\pi\)
0.649206 + 0.760612i \(0.275101\pi\)
\(32\) 6.47801 1.14516
\(33\) −0.0286082 −0.00498006
\(34\) −11.5832 −1.98651
\(35\) −0.803218 −0.135769
\(36\) −3.98669 −0.664449
\(37\) 1.00000 0.164399
\(38\) 1.30643 0.211931
\(39\) 0.0996531 0.0159573
\(40\) −0.222388 −0.0351626
\(41\) −9.57735 −1.49573 −0.747866 0.663850i \(-0.768921\pi\)
−0.747866 + 0.663850i \(0.768921\pi\)
\(42\) −0.264796 −0.0408590
\(43\) −7.97679 −1.21645 −0.608225 0.793765i \(-0.708118\pi\)
−0.608225 + 0.793765i \(0.708118\pi\)
\(44\) −1.15822 −0.174609
\(45\) 0.545023 0.0812472
\(46\) −5.20149 −0.766918
\(47\) 7.45694 1.08771 0.543853 0.839180i \(-0.316965\pi\)
0.543853 + 0.839180i \(0.316965\pi\)
\(48\) −0.160616 −0.0231830
\(49\) 12.5329 1.79042
\(50\) 9.06302 1.28170
\(51\) 0.208447 0.0291884
\(52\) 4.03452 0.559487
\(53\) 2.08916 0.286968 0.143484 0.989653i \(-0.454169\pi\)
0.143484 + 0.989653i \(0.454169\pi\)
\(54\) 0.359419 0.0489108
\(55\) 0.158341 0.0213507
\(56\) 5.40810 0.722687
\(57\) −0.0235100 −0.00311398
\(58\) −10.4563 −1.37298
\(59\) 9.13233 1.18893 0.594464 0.804122i \(-0.297364\pi\)
0.594464 + 0.804122i \(0.297364\pi\)
\(60\) −0.00793313 −0.00102416
\(61\) 5.31105 0.680011 0.340005 0.940423i \(-0.389571\pi\)
0.340005 + 0.940423i \(0.389571\pi\)
\(62\) −13.1909 −1.67525
\(63\) −13.2541 −1.66985
\(64\) −2.03713 −0.254642
\(65\) −0.551561 −0.0684128
\(66\) 0.0522003 0.00642541
\(67\) −7.64729 −0.934266 −0.467133 0.884187i \(-0.654713\pi\)
−0.467133 + 0.884187i \(0.654713\pi\)
\(68\) 8.43909 1.02339
\(69\) 0.0936038 0.0112686
\(70\) 1.46560 0.175172
\(71\) 0.273822 0.0324967 0.0162483 0.999868i \(-0.494828\pi\)
0.0162483 + 0.999868i \(0.494828\pi\)
\(72\) −3.66966 −0.432474
\(73\) 3.37228 0.394696 0.197348 0.980333i \(-0.436767\pi\)
0.197348 + 0.980333i \(0.436767\pi\)
\(74\) −1.82466 −0.212112
\(75\) −0.163094 −0.0188325
\(76\) −0.951817 −0.109181
\(77\) −3.85059 −0.438816
\(78\) −0.181833 −0.0205885
\(79\) 2.85327 0.321018 0.160509 0.987034i \(-0.448686\pi\)
0.160509 + 0.987034i \(0.448686\pi\)
\(80\) 0.888982 0.0993912
\(81\) 8.99030 0.998922
\(82\) 17.4754 1.92983
\(83\) −1.37879 −0.151342 −0.0756709 0.997133i \(-0.524110\pi\)
−0.0756709 + 0.997133i \(0.524110\pi\)
\(84\) 0.192920 0.0210493
\(85\) −1.15371 −0.125138
\(86\) 14.5549 1.56950
\(87\) 0.188167 0.0201736
\(88\) −1.06612 −0.113649
\(89\) −1.61133 −0.170801 −0.0854003 0.996347i \(-0.527217\pi\)
−0.0854003 + 0.996347i \(0.527217\pi\)
\(90\) −0.994481 −0.104827
\(91\) 13.4131 1.40607
\(92\) 3.78961 0.395094
\(93\) 0.237378 0.0246150
\(94\) −13.6064 −1.40339
\(95\) 0.130123 0.0133504
\(96\) 0.212710 0.0217097
\(97\) 6.51903 0.661907 0.330954 0.943647i \(-0.392630\pi\)
0.330954 + 0.943647i \(0.392630\pi\)
\(98\) −22.8683 −2.31005
\(99\) 2.61282 0.262598
\(100\) −6.60297 −0.660297
\(101\) 0.617612 0.0614547 0.0307274 0.999528i \(-0.490218\pi\)
0.0307274 + 0.999528i \(0.490218\pi\)
\(102\) −0.380344 −0.0376596
\(103\) −0.111359 −0.0109725 −0.00548626 0.999985i \(-0.501746\pi\)
−0.00548626 + 0.999985i \(0.501746\pi\)
\(104\) 3.71368 0.364157
\(105\) −0.0263743 −0.00257386
\(106\) −3.81200 −0.370254
\(107\) 4.25583 0.411427 0.205714 0.978612i \(-0.434048\pi\)
0.205714 + 0.978612i \(0.434048\pi\)
\(108\) −0.261859 −0.0251974
\(109\) −1.00000 −0.0957826
\(110\) −0.288919 −0.0275473
\(111\) 0.0328358 0.00311663
\(112\) −21.6186 −2.04276
\(113\) −6.52506 −0.613826 −0.306913 0.951738i \(-0.599296\pi\)
−0.306913 + 0.951738i \(0.599296\pi\)
\(114\) 0.0428977 0.00401774
\(115\) −0.518079 −0.0483111
\(116\) 7.61807 0.707320
\(117\) −9.10142 −0.841427
\(118\) −16.6634 −1.53399
\(119\) 28.0564 2.57192
\(120\) −0.00730226 −0.000666602 0
\(121\) −10.2409 −0.930993
\(122\) −9.69086 −0.877369
\(123\) −0.314480 −0.0283557
\(124\) 9.61040 0.863039
\(125\) 1.81139 0.162016
\(126\) 24.1841 2.15449
\(127\) −17.5962 −1.56141 −0.780705 0.624900i \(-0.785140\pi\)
−0.780705 + 0.624900i \(0.785140\pi\)
\(128\) −9.23895 −0.816616
\(129\) −0.261924 −0.0230611
\(130\) 1.00641 0.0882680
\(131\) 7.64997 0.668381 0.334190 0.942506i \(-0.391537\pi\)
0.334190 + 0.942506i \(0.391537\pi\)
\(132\) −0.0380311 −0.00331018
\(133\) −3.16438 −0.274387
\(134\) 13.9537 1.20542
\(135\) 0.0357989 0.00308108
\(136\) 7.76799 0.666100
\(137\) −3.37036 −0.287949 −0.143975 0.989581i \(-0.545988\pi\)
−0.143975 + 0.989581i \(0.545988\pi\)
\(138\) −0.170795 −0.0145390
\(139\) −1.28695 −0.109157 −0.0545787 0.998509i \(-0.517382\pi\)
−0.0545787 + 0.998509i \(0.517382\pi\)
\(140\) −1.06778 −0.0902437
\(141\) 0.244854 0.0206204
\(142\) −0.499631 −0.0419281
\(143\) −2.64416 −0.221116
\(144\) 14.6693 1.22244
\(145\) −1.04147 −0.0864894
\(146\) −6.15327 −0.509248
\(147\) 0.411528 0.0339422
\(148\) 1.32938 0.109274
\(149\) 2.06500 0.169171 0.0845857 0.996416i \(-0.473043\pi\)
0.0845857 + 0.996416i \(0.473043\pi\)
\(150\) 0.297591 0.0242982
\(151\) 1.79641 0.146189 0.0730947 0.997325i \(-0.476712\pi\)
0.0730947 + 0.997325i \(0.476712\pi\)
\(152\) −0.876126 −0.0710632
\(153\) −19.0376 −1.53910
\(154\) 7.02602 0.566173
\(155\) −1.31384 −0.105530
\(156\) 0.132476 0.0106066
\(157\) −7.98701 −0.637433 −0.318717 0.947850i \(-0.603252\pi\)
−0.318717 + 0.947850i \(0.603252\pi\)
\(158\) −5.20624 −0.414187
\(159\) 0.0685992 0.00544027
\(160\) −1.17731 −0.0930747
\(161\) 12.5988 0.992927
\(162\) −16.4042 −1.28884
\(163\) −18.1570 −1.42217 −0.711083 0.703108i \(-0.751795\pi\)
−0.711083 + 0.703108i \(0.751795\pi\)
\(164\) −12.7319 −0.994194
\(165\) 0.00519925 0.000404761 0
\(166\) 2.51582 0.195265
\(167\) −6.29299 −0.486966 −0.243483 0.969905i \(-0.578290\pi\)
−0.243483 + 0.969905i \(0.578290\pi\)
\(168\) 0.177579 0.0137005
\(169\) −3.78940 −0.291492
\(170\) 2.10513 0.161456
\(171\) 2.14719 0.164200
\(172\) −10.6042 −0.808559
\(173\) 3.77449 0.286969 0.143484 0.989653i \(-0.454169\pi\)
0.143484 + 0.989653i \(0.454169\pi\)
\(174\) −0.343341 −0.0260286
\(175\) −21.9521 −1.65942
\(176\) 4.26174 0.321241
\(177\) 0.299867 0.0225394
\(178\) 2.94013 0.220372
\(179\) 17.4395 1.30349 0.651746 0.758437i \(-0.274037\pi\)
0.651746 + 0.758437i \(0.274037\pi\)
\(180\) 0.724540 0.0540041
\(181\) −22.9867 −1.70859 −0.854295 0.519788i \(-0.826011\pi\)
−0.854295 + 0.519788i \(0.826011\pi\)
\(182\) −24.4742 −1.81415
\(183\) 0.174392 0.0128915
\(184\) 3.48825 0.257157
\(185\) −0.181740 −0.0133618
\(186\) −0.433134 −0.0317589
\(187\) −5.53085 −0.404456
\(188\) 9.91308 0.722985
\(189\) −0.870570 −0.0633247
\(190\) −0.237431 −0.0172250
\(191\) −3.41809 −0.247325 −0.123662 0.992324i \(-0.539464\pi\)
−0.123662 + 0.992324i \(0.539464\pi\)
\(192\) −0.0668909 −0.00482743
\(193\) 15.1226 1.08855 0.544274 0.838908i \(-0.316805\pi\)
0.544274 + 0.838908i \(0.316805\pi\)
\(194\) −11.8950 −0.854011
\(195\) −0.0181109 −0.00129695
\(196\) 16.6610 1.19007
\(197\) 6.73896 0.480131 0.240065 0.970757i \(-0.422831\pi\)
0.240065 + 0.970757i \(0.422831\pi\)
\(198\) −4.76750 −0.338812
\(199\) −20.3316 −1.44127 −0.720633 0.693316i \(-0.756149\pi\)
−0.720633 + 0.693316i \(0.756149\pi\)
\(200\) −6.07788 −0.429771
\(201\) −0.251105 −0.0177116
\(202\) −1.12693 −0.0792906
\(203\) 25.3268 1.77759
\(204\) 0.277104 0.0194011
\(205\) 1.74058 0.121568
\(206\) 0.203192 0.0141571
\(207\) −8.54893 −0.594192
\(208\) −14.8452 −1.02933
\(209\) 0.623807 0.0431496
\(210\) 0.0481240 0.00332087
\(211\) 15.0764 1.03790 0.518950 0.854804i \(-0.326323\pi\)
0.518950 + 0.854804i \(0.326323\pi\)
\(212\) 2.77728 0.190744
\(213\) 0.00899115 0.000616063 0
\(214\) −7.76544 −0.530835
\(215\) 1.44970 0.0988687
\(216\) −0.241035 −0.0164004
\(217\) 31.9505 2.16894
\(218\) 1.82466 0.123581
\(219\) 0.110732 0.00748254
\(220\) 0.210495 0.0141916
\(221\) 19.2660 1.29597
\(222\) −0.0599140 −0.00402116
\(223\) −2.03558 −0.136312 −0.0681562 0.997675i \(-0.521712\pi\)
−0.0681562 + 0.997675i \(0.521712\pi\)
\(224\) 28.6303 1.91294
\(225\) 14.8956 0.993037
\(226\) 11.9060 0.791976
\(227\) −0.447937 −0.0297306 −0.0148653 0.999890i \(-0.504732\pi\)
−0.0148653 + 0.999890i \(0.504732\pi\)
\(228\) −0.0312536 −0.00206982
\(229\) 13.2252 0.873948 0.436974 0.899474i \(-0.356050\pi\)
0.436974 + 0.899474i \(0.356050\pi\)
\(230\) 0.945317 0.0623324
\(231\) −0.126437 −0.00831896
\(232\) 7.01226 0.460377
\(233\) 22.6912 1.48655 0.743277 0.668984i \(-0.233271\pi\)
0.743277 + 0.668984i \(0.233271\pi\)
\(234\) 16.6070 1.08563
\(235\) −1.35522 −0.0884049
\(236\) 12.1403 0.790266
\(237\) 0.0936893 0.00608578
\(238\) −51.1933 −3.31837
\(239\) 15.5780 1.00766 0.503829 0.863803i \(-0.331924\pi\)
0.503829 + 0.863803i \(0.331924\pi\)
\(240\) 0.0291904 0.00188423
\(241\) −6.05548 −0.390067 −0.195034 0.980797i \(-0.562482\pi\)
−0.195034 + 0.980797i \(0.562482\pi\)
\(242\) 18.6862 1.20119
\(243\) 0.886141 0.0568459
\(244\) 7.06039 0.451995
\(245\) −2.27773 −0.145519
\(246\) 0.573818 0.0365853
\(247\) −2.17295 −0.138261
\(248\) 8.84615 0.561731
\(249\) −0.0452736 −0.00286910
\(250\) −3.30517 −0.209038
\(251\) 2.14353 0.135298 0.0676491 0.997709i \(-0.478450\pi\)
0.0676491 + 0.997709i \(0.478450\pi\)
\(252\) −17.6196 −1.10993
\(253\) −2.48365 −0.156146
\(254\) 32.1070 2.01458
\(255\) −0.0378830 −0.00237233
\(256\) 20.9322 1.30826
\(257\) 16.8749 1.05263 0.526314 0.850290i \(-0.323574\pi\)
0.526314 + 0.850290i \(0.323574\pi\)
\(258\) 0.477922 0.0297541
\(259\) 4.41961 0.274621
\(260\) −0.733232 −0.0454731
\(261\) −17.1855 −1.06376
\(262\) −13.9586 −0.862364
\(263\) 11.2933 0.696375 0.348188 0.937425i \(-0.386797\pi\)
0.348188 + 0.937425i \(0.386797\pi\)
\(264\) −0.0350068 −0.00215452
\(265\) −0.379683 −0.0233238
\(266\) 5.77392 0.354022
\(267\) −0.0529092 −0.00323799
\(268\) −10.1661 −0.620995
\(269\) −3.05900 −0.186510 −0.0932552 0.995642i \(-0.529727\pi\)
−0.0932552 + 0.995642i \(0.529727\pi\)
\(270\) −0.0653208 −0.00397530
\(271\) −3.69945 −0.224726 −0.112363 0.993667i \(-0.535842\pi\)
−0.112363 + 0.993667i \(0.535842\pi\)
\(272\) −31.0521 −1.88281
\(273\) 0.440428 0.0266559
\(274\) 6.14975 0.371520
\(275\) 4.32749 0.260957
\(276\) 0.124435 0.00749008
\(277\) 23.8011 1.43007 0.715036 0.699088i \(-0.246410\pi\)
0.715036 + 0.699088i \(0.246410\pi\)
\(278\) 2.34824 0.140838
\(279\) −21.6800 −1.29795
\(280\) −0.982865 −0.0587374
\(281\) 18.8155 1.12244 0.561220 0.827666i \(-0.310332\pi\)
0.561220 + 0.827666i \(0.310332\pi\)
\(282\) −0.446775 −0.0266051
\(283\) −2.92530 −0.173891 −0.0869456 0.996213i \(-0.527711\pi\)
−0.0869456 + 0.996213i \(0.527711\pi\)
\(284\) 0.364012 0.0216002
\(285\) 0.00427270 0.000253093 0
\(286\) 4.82469 0.285290
\(287\) −42.3281 −2.49855
\(288\) −19.4271 −1.14475
\(289\) 23.2991 1.37054
\(290\) 1.90033 0.111591
\(291\) 0.214057 0.0125483
\(292\) 4.48303 0.262350
\(293\) −1.33645 −0.0780764 −0.0390382 0.999238i \(-0.512429\pi\)
−0.0390382 + 0.999238i \(0.512429\pi\)
\(294\) −0.750897 −0.0437932
\(295\) −1.65971 −0.0966319
\(296\) 1.22366 0.0711238
\(297\) 0.171619 0.00995832
\(298\) −3.76792 −0.218270
\(299\) 8.65148 0.500328
\(300\) −0.216813 −0.0125177
\(301\) −35.2543 −2.03202
\(302\) −3.27783 −0.188618
\(303\) 0.0202798 0.00116504
\(304\) 3.50226 0.200869
\(305\) −0.965229 −0.0552689
\(306\) 34.7372 1.98579
\(307\) −23.7506 −1.35552 −0.677760 0.735283i \(-0.737049\pi\)
−0.677760 + 0.735283i \(0.737049\pi\)
\(308\) −5.11889 −0.291676
\(309\) −0.00365655 −0.000208014 0
\(310\) 2.39731 0.136158
\(311\) 15.3607 0.871025 0.435513 0.900183i \(-0.356567\pi\)
0.435513 + 0.900183i \(0.356567\pi\)
\(312\) 0.121942 0.00690358
\(313\) 23.8489 1.34802 0.674010 0.738723i \(-0.264571\pi\)
0.674010 + 0.738723i \(0.264571\pi\)
\(314\) 14.5736 0.822434
\(315\) 2.40879 0.135720
\(316\) 3.79307 0.213377
\(317\) −16.1302 −0.905962 −0.452981 0.891520i \(-0.649639\pi\)
−0.452981 + 0.891520i \(0.649639\pi\)
\(318\) −0.125170 −0.00701918
\(319\) −4.99277 −0.279541
\(320\) 0.370228 0.0206964
\(321\) 0.139744 0.00779972
\(322\) −22.9885 −1.28110
\(323\) −4.54521 −0.252902
\(324\) 11.9515 0.663971
\(325\) −15.0742 −0.836169
\(326\) 33.1303 1.83492
\(327\) −0.0328358 −0.00181582
\(328\) −11.7194 −0.647097
\(329\) 32.9567 1.81696
\(330\) −0.00948686 −0.000522234 0
\(331\) 0.930539 0.0511471 0.0255735 0.999673i \(-0.491859\pi\)
0.0255735 + 0.999673i \(0.491859\pi\)
\(332\) −1.83293 −0.100595
\(333\) −2.99892 −0.164340
\(334\) 11.4826 0.628297
\(335\) 1.38982 0.0759338
\(336\) −0.709861 −0.0387261
\(337\) 3.85631 0.210067 0.105033 0.994469i \(-0.466505\pi\)
0.105033 + 0.994469i \(0.466505\pi\)
\(338\) 6.91435 0.376091
\(339\) −0.214255 −0.0116368
\(340\) −1.53372 −0.0831775
\(341\) −6.29851 −0.341084
\(342\) −3.91789 −0.211855
\(343\) 24.4533 1.32035
\(344\) −9.76088 −0.526271
\(345\) −0.0170115 −0.000915870 0
\(346\) −6.88715 −0.370255
\(347\) −2.66480 −0.143054 −0.0715271 0.997439i \(-0.522787\pi\)
−0.0715271 + 0.997439i \(0.522787\pi\)
\(348\) 0.250145 0.0134092
\(349\) 25.1905 1.34842 0.674209 0.738541i \(-0.264485\pi\)
0.674209 + 0.738541i \(0.264485\pi\)
\(350\) 40.0550 2.14103
\(351\) −0.597811 −0.0319088
\(352\) −5.64399 −0.300826
\(353\) −13.7952 −0.734245 −0.367122 0.930173i \(-0.619657\pi\)
−0.367122 + 0.930173i \(0.619657\pi\)
\(354\) −0.547155 −0.0290809
\(355\) −0.0497643 −0.00264122
\(356\) −2.14206 −0.113529
\(357\) 0.921252 0.0487578
\(358\) −31.8212 −1.68180
\(359\) 29.8318 1.57446 0.787230 0.616659i \(-0.211514\pi\)
0.787230 + 0.616659i \(0.211514\pi\)
\(360\) 0.666923 0.0351499
\(361\) −18.4874 −0.973019
\(362\) 41.9429 2.20447
\(363\) −0.336268 −0.0176495
\(364\) 17.8310 0.934597
\(365\) −0.612878 −0.0320795
\(366\) −0.318207 −0.0166329
\(367\) 25.6699 1.33996 0.669978 0.742381i \(-0.266303\pi\)
0.669978 + 0.742381i \(0.266303\pi\)
\(368\) −13.9441 −0.726885
\(369\) 28.7217 1.49519
\(370\) 0.331613 0.0172397
\(371\) 9.23327 0.479367
\(372\) 0.315565 0.0163613
\(373\) 7.27377 0.376622 0.188311 0.982109i \(-0.439699\pi\)
0.188311 + 0.982109i \(0.439699\pi\)
\(374\) 10.0919 0.521840
\(375\) 0.0594785 0.00307146
\(376\) 9.12476 0.470574
\(377\) 17.3917 0.895716
\(378\) 1.58849 0.0817032
\(379\) −8.50299 −0.436769 −0.218385 0.975863i \(-0.570079\pi\)
−0.218385 + 0.975863i \(0.570079\pi\)
\(380\) 0.172983 0.00887383
\(381\) −0.577785 −0.0296008
\(382\) 6.23685 0.319105
\(383\) 22.7778 1.16389 0.581945 0.813228i \(-0.302292\pi\)
0.581945 + 0.813228i \(0.302292\pi\)
\(384\) −0.303368 −0.0154812
\(385\) 0.699806 0.0356654
\(386\) −27.5935 −1.40447
\(387\) 23.9218 1.21601
\(388\) 8.66624 0.439962
\(389\) −29.2481 −1.48294 −0.741468 0.670989i \(-0.765870\pi\)
−0.741468 + 0.670989i \(0.765870\pi\)
\(390\) 0.0330462 0.00167336
\(391\) 18.0965 0.915179
\(392\) 15.3360 0.774586
\(393\) 0.251192 0.0126710
\(394\) −12.2963 −0.619478
\(395\) −0.518553 −0.0260912
\(396\) 3.47342 0.174546
\(397\) −10.3602 −0.519963 −0.259981 0.965614i \(-0.583716\pi\)
−0.259981 + 0.965614i \(0.583716\pi\)
\(398\) 37.0982 1.85956
\(399\) −0.103905 −0.00520175
\(400\) 24.2960 1.21480
\(401\) −1.62989 −0.0813927 −0.0406963 0.999172i \(-0.512958\pi\)
−0.0406963 + 0.999172i \(0.512958\pi\)
\(402\) 0.458180 0.0228519
\(403\) 21.9401 1.09291
\(404\) 0.821039 0.0408482
\(405\) −1.63389 −0.0811888
\(406\) −46.2128 −2.29350
\(407\) −0.871253 −0.0431864
\(408\) 0.255068 0.0126277
\(409\) 5.76426 0.285024 0.142512 0.989793i \(-0.454482\pi\)
0.142512 + 0.989793i \(0.454482\pi\)
\(410\) −3.17597 −0.156850
\(411\) −0.110668 −0.00545886
\(412\) −0.148038 −0.00729330
\(413\) 40.3613 1.98605
\(414\) 15.5989 0.766643
\(415\) 0.250581 0.0123005
\(416\) 19.6601 0.963916
\(417\) −0.0422579 −0.00206938
\(418\) −1.13823 −0.0556728
\(419\) −15.1274 −0.739024 −0.369512 0.929226i \(-0.620475\pi\)
−0.369512 + 0.929226i \(0.620475\pi\)
\(420\) −0.0350613 −0.00171082
\(421\) 30.2113 1.47241 0.736204 0.676760i \(-0.236616\pi\)
0.736204 + 0.676760i \(0.236616\pi\)
\(422\) −27.5092 −1.33913
\(423\) −22.3628 −1.08732
\(424\) 2.55642 0.124151
\(425\) −31.5311 −1.52948
\(426\) −0.0164058 −0.000794862 0
\(427\) 23.4728 1.13593
\(428\) 5.65760 0.273471
\(429\) −0.0868231 −0.00419186
\(430\) −2.64521 −0.127563
\(431\) −10.2120 −0.491897 −0.245949 0.969283i \(-0.579099\pi\)
−0.245949 + 0.969283i \(0.579099\pi\)
\(432\) 0.963526 0.0463576
\(433\) 19.9128 0.956950 0.478475 0.878101i \(-0.341190\pi\)
0.478475 + 0.878101i \(0.341190\pi\)
\(434\) −58.2987 −2.79843
\(435\) −0.0341975 −0.00163964
\(436\) −1.32938 −0.0636655
\(437\) −2.04104 −0.0976363
\(438\) −0.202047 −0.00965418
\(439\) 26.2599 1.25331 0.626657 0.779295i \(-0.284423\pi\)
0.626657 + 0.779295i \(0.284423\pi\)
\(440\) 0.193756 0.00923695
\(441\) −37.5852 −1.78977
\(442\) −35.1539 −1.67210
\(443\) 12.7417 0.605376 0.302688 0.953090i \(-0.402116\pi\)
0.302688 + 0.953090i \(0.402116\pi\)
\(444\) 0.0436510 0.00207159
\(445\) 0.292843 0.0138821
\(446\) 3.71424 0.175874
\(447\) 0.0678058 0.00320711
\(448\) −9.00333 −0.425368
\(449\) 40.9109 1.93070 0.965352 0.260951i \(-0.0840363\pi\)
0.965352 + 0.260951i \(0.0840363\pi\)
\(450\) −27.1793 −1.28124
\(451\) 8.34430 0.392918
\(452\) −8.67426 −0.408003
\(453\) 0.0589863 0.00277142
\(454\) 0.817332 0.0383593
\(455\) −2.43768 −0.114280
\(456\) −0.0287682 −0.00134720
\(457\) 13.7426 0.642852 0.321426 0.946935i \(-0.395838\pi\)
0.321426 + 0.946935i \(0.395838\pi\)
\(458\) −24.1315 −1.12759
\(459\) −1.25045 −0.0583662
\(460\) −0.688722 −0.0321118
\(461\) −12.0366 −0.560602 −0.280301 0.959912i \(-0.590434\pi\)
−0.280301 + 0.959912i \(0.590434\pi\)
\(462\) 0.230705 0.0107333
\(463\) −19.8234 −0.921273 −0.460636 0.887589i \(-0.652379\pi\)
−0.460636 + 0.887589i \(0.652379\pi\)
\(464\) −28.0311 −1.30131
\(465\) −0.0431410 −0.00200062
\(466\) −41.4038 −1.91799
\(467\) −19.9198 −0.921777 −0.460889 0.887458i \(-0.652469\pi\)
−0.460889 + 0.887458i \(0.652469\pi\)
\(468\) −12.0992 −0.559286
\(469\) −33.7980 −1.56065
\(470\) 2.47282 0.114063
\(471\) −0.262260 −0.0120843
\(472\) 11.1749 0.514365
\(473\) 6.94980 0.319552
\(474\) −0.170951 −0.00785204
\(475\) 3.55629 0.163174
\(476\) 37.2974 1.70953
\(477\) −6.26523 −0.286865
\(478\) −28.4245 −1.30011
\(479\) −6.87941 −0.314328 −0.157164 0.987572i \(-0.550235\pi\)
−0.157164 + 0.987572i \(0.550235\pi\)
\(480\) −0.0386579 −0.00176449
\(481\) 3.03490 0.138379
\(482\) 11.0492 0.503276
\(483\) 0.413692 0.0188236
\(484\) −13.6140 −0.618819
\(485\) −1.18477 −0.0537975
\(486\) −1.61690 −0.0733442
\(487\) 5.09771 0.230999 0.115500 0.993308i \(-0.463153\pi\)
0.115500 + 0.993308i \(0.463153\pi\)
\(488\) 6.49892 0.294192
\(489\) −0.596199 −0.0269610
\(490\) 4.15607 0.187752
\(491\) 24.7372 1.11637 0.558186 0.829716i \(-0.311497\pi\)
0.558186 + 0.829716i \(0.311497\pi\)
\(492\) −0.418061 −0.0188477
\(493\) 36.3785 1.63841
\(494\) 3.96489 0.178389
\(495\) −0.474853 −0.0213431
\(496\) −35.3620 −1.58780
\(497\) 1.21019 0.0542842
\(498\) 0.0826088 0.00370179
\(499\) 11.1809 0.500526 0.250263 0.968178i \(-0.419483\pi\)
0.250263 + 0.968178i \(0.419483\pi\)
\(500\) 2.40802 0.107690
\(501\) −0.206635 −0.00923178
\(502\) −3.91120 −0.174565
\(503\) −13.1193 −0.584961 −0.292480 0.956272i \(-0.594481\pi\)
−0.292480 + 0.956272i \(0.594481\pi\)
\(504\) −16.2185 −0.722427
\(505\) −0.112245 −0.00499482
\(506\) 4.53182 0.201464
\(507\) −0.124428 −0.00552603
\(508\) −23.3920 −1.03785
\(509\) −23.6723 −1.04926 −0.524629 0.851331i \(-0.675796\pi\)
−0.524629 + 0.851331i \(0.675796\pi\)
\(510\) 0.0691235 0.00306084
\(511\) 14.9042 0.659322
\(512\) −19.7162 −0.871341
\(513\) 0.141035 0.00622683
\(514\) −30.7909 −1.35813
\(515\) 0.0202383 0.000891808 0
\(516\) −0.348195 −0.0153284
\(517\) −6.49688 −0.285733
\(518\) −8.06427 −0.354324
\(519\) 0.123938 0.00544028
\(520\) −0.674924 −0.0295974
\(521\) −21.7838 −0.954365 −0.477182 0.878804i \(-0.658342\pi\)
−0.477182 + 0.878804i \(0.658342\pi\)
\(522\) 31.3577 1.37249
\(523\) 22.5880 0.987706 0.493853 0.869545i \(-0.335588\pi\)
0.493853 + 0.869545i \(0.335588\pi\)
\(524\) 10.1697 0.444265
\(525\) −0.720812 −0.0314588
\(526\) −20.6064 −0.898483
\(527\) 45.8925 1.99911
\(528\) 0.139938 0.00609000
\(529\) −14.8737 −0.646682
\(530\) 0.692792 0.0300930
\(531\) −27.3872 −1.18850
\(532\) −4.20665 −0.182382
\(533\) −29.0663 −1.25900
\(534\) 0.0965413 0.00417775
\(535\) −0.773454 −0.0334393
\(536\) −9.35769 −0.404191
\(537\) 0.572640 0.0247113
\(538\) 5.58162 0.240641
\(539\) −10.9193 −0.470329
\(540\) 0.0475902 0.00204796
\(541\) 17.9795 0.773001 0.386500 0.922289i \(-0.373684\pi\)
0.386500 + 0.922289i \(0.373684\pi\)
\(542\) 6.75024 0.289948
\(543\) −0.754787 −0.0323910
\(544\) 41.1235 1.76315
\(545\) 0.181740 0.00778487
\(546\) −0.803630 −0.0343922
\(547\) −4.29091 −0.183466 −0.0917330 0.995784i \(-0.529241\pi\)
−0.0917330 + 0.995784i \(0.529241\pi\)
\(548\) −4.48047 −0.191396
\(549\) −15.9274 −0.679766
\(550\) −7.89618 −0.336694
\(551\) −4.10301 −0.174794
\(552\) 0.114539 0.00487511
\(553\) 12.6103 0.536246
\(554\) −43.4289 −1.84512
\(555\) −0.00596756 −0.000253309 0
\(556\) −1.71084 −0.0725556
\(557\) 11.9035 0.504366 0.252183 0.967680i \(-0.418852\pi\)
0.252183 + 0.967680i \(0.418852\pi\)
\(558\) 39.5585 1.67465
\(559\) −24.2087 −1.02392
\(560\) 3.92895 0.166028
\(561\) −0.181610 −0.00766757
\(562\) −34.3319 −1.44820
\(563\) 11.6528 0.491106 0.245553 0.969383i \(-0.421031\pi\)
0.245553 + 0.969383i \(0.421031\pi\)
\(564\) 0.325503 0.0137062
\(565\) 1.18586 0.0498896
\(566\) 5.33768 0.224359
\(567\) 39.7336 1.66865
\(568\) 0.335065 0.0140590
\(569\) 15.1999 0.637213 0.318607 0.947887i \(-0.396785\pi\)
0.318607 + 0.947887i \(0.396785\pi\)
\(570\) −0.00779621 −0.000326547 0
\(571\) −38.0952 −1.59424 −0.797118 0.603824i \(-0.793643\pi\)
−0.797118 + 0.603824i \(0.793643\pi\)
\(572\) −3.51509 −0.146973
\(573\) −0.112236 −0.00468871
\(574\) 77.2343 3.22370
\(575\) −14.1592 −0.590479
\(576\) 6.10921 0.254550
\(577\) 32.0904 1.33594 0.667971 0.744188i \(-0.267163\pi\)
0.667971 + 0.744188i \(0.267163\pi\)
\(578\) −42.5130 −1.76831
\(579\) 0.496562 0.0206364
\(580\) −1.38450 −0.0574884
\(581\) −6.09371 −0.252810
\(582\) −0.390581 −0.0161901
\(583\) −1.82019 −0.0753845
\(584\) 4.12653 0.170757
\(585\) 1.65409 0.0683882
\(586\) 2.43857 0.100736
\(587\) 18.3023 0.755419 0.377709 0.925924i \(-0.376712\pi\)
0.377709 + 0.925924i \(0.376712\pi\)
\(588\) 0.547075 0.0225610
\(589\) −5.17606 −0.213276
\(590\) 3.02840 0.124677
\(591\) 0.221279 0.00910219
\(592\) −4.89151 −0.201040
\(593\) 28.0579 1.15220 0.576099 0.817380i \(-0.304574\pi\)
0.576099 + 0.817380i \(0.304574\pi\)
\(594\) −0.313145 −0.0128485
\(595\) −5.09896 −0.209037
\(596\) 2.74516 0.112446
\(597\) −0.667602 −0.0273231
\(598\) −15.7860 −0.645537
\(599\) 45.3344 1.85231 0.926156 0.377141i \(-0.123093\pi\)
0.926156 + 0.377141i \(0.123093\pi\)
\(600\) −0.199572 −0.00814749
\(601\) −34.8077 −1.41984 −0.709919 0.704284i \(-0.751268\pi\)
−0.709919 + 0.704284i \(0.751268\pi\)
\(602\) 64.3270 2.62177
\(603\) 22.9336 0.933930
\(604\) 2.38810 0.0971703
\(605\) 1.86118 0.0756678
\(606\) −0.0370036 −0.00150317
\(607\) −22.3726 −0.908075 −0.454038 0.890982i \(-0.650017\pi\)
−0.454038 + 0.890982i \(0.650017\pi\)
\(608\) −4.63818 −0.188103
\(609\) 0.831625 0.0336992
\(610\) 1.76121 0.0713094
\(611\) 22.6311 0.915554
\(612\) −25.3082 −1.02302
\(613\) −36.6986 −1.48224 −0.741121 0.671372i \(-0.765705\pi\)
−0.741121 + 0.671372i \(0.765705\pi\)
\(614\) 43.3368 1.74893
\(615\) 0.0571534 0.00230465
\(616\) −4.71182 −0.189845
\(617\) 12.0705 0.485938 0.242969 0.970034i \(-0.421879\pi\)
0.242969 + 0.970034i \(0.421879\pi\)
\(618\) 0.00667196 0.000268386 0
\(619\) 26.0427 1.04675 0.523373 0.852104i \(-0.324674\pi\)
0.523373 + 0.852104i \(0.324674\pi\)
\(620\) −1.74659 −0.0701448
\(621\) −0.561522 −0.0225331
\(622\) −28.0280 −1.12382
\(623\) −7.12145 −0.285315
\(624\) −0.487455 −0.0195138
\(625\) 24.5057 0.980226
\(626\) −43.5161 −1.73925
\(627\) 0.0204832 0.000818019 0
\(628\) −10.6177 −0.423694
\(629\) 6.34816 0.253118
\(630\) −4.39521 −0.175109
\(631\) −40.9046 −1.62839 −0.814193 0.580594i \(-0.802820\pi\)
−0.814193 + 0.580594i \(0.802820\pi\)
\(632\) 3.49143 0.138882
\(633\) 0.495044 0.0196762
\(634\) 29.4321 1.16890
\(635\) 3.19793 0.126906
\(636\) 0.0911940 0.00361608
\(637\) 38.0361 1.50705
\(638\) 9.11009 0.360672
\(639\) −0.821171 −0.0324850
\(640\) 1.67908 0.0663717
\(641\) 25.7238 1.01603 0.508014 0.861349i \(-0.330380\pi\)
0.508014 + 0.861349i \(0.330380\pi\)
\(642\) −0.254984 −0.0100634
\(643\) −12.5429 −0.494643 −0.247321 0.968934i \(-0.579550\pi\)
−0.247321 + 0.968934i \(0.579550\pi\)
\(644\) 16.7486 0.659986
\(645\) 0.0476020 0.00187433
\(646\) 8.29344 0.326301
\(647\) −15.0310 −0.590929 −0.295465 0.955354i \(-0.595474\pi\)
−0.295465 + 0.955354i \(0.595474\pi\)
\(648\) 11.0011 0.432163
\(649\) −7.95657 −0.312323
\(650\) 27.5053 1.07885
\(651\) 1.04912 0.0411182
\(652\) −24.1375 −0.945296
\(653\) 34.3731 1.34512 0.672561 0.740042i \(-0.265194\pi\)
0.672561 + 0.740042i \(0.265194\pi\)
\(654\) 0.0599140 0.00234282
\(655\) −1.39030 −0.0543236
\(656\) 46.8477 1.82910
\(657\) −10.1132 −0.394554
\(658\) −60.1348 −2.34430
\(659\) −0.887520 −0.0345729 −0.0172864 0.999851i \(-0.505503\pi\)
−0.0172864 + 0.999851i \(0.505503\pi\)
\(660\) 0.00691176 0.000269040 0
\(661\) −32.9833 −1.28290 −0.641451 0.767164i \(-0.721667\pi\)
−0.641451 + 0.767164i \(0.721667\pi\)
\(662\) −1.69792 −0.0659914
\(663\) 0.632614 0.0245687
\(664\) −1.68717 −0.0654749
\(665\) 0.575094 0.0223012
\(666\) 5.47201 0.212036
\(667\) 16.3359 0.632529
\(668\) −8.36575 −0.323681
\(669\) −0.0668398 −0.00258418
\(670\) −2.53594 −0.0979719
\(671\) −4.62727 −0.178634
\(672\) 0.940096 0.0362650
\(673\) −7.52865 −0.290208 −0.145104 0.989416i \(-0.546352\pi\)
−0.145104 + 0.989416i \(0.546352\pi\)
\(674\) −7.03644 −0.271034
\(675\) 0.978389 0.0376582
\(676\) −5.03753 −0.193751
\(677\) −0.136032 −0.00522813 −0.00261406 0.999997i \(-0.500832\pi\)
−0.00261406 + 0.999997i \(0.500832\pi\)
\(678\) 0.390943 0.0150141
\(679\) 28.8116 1.10569
\(680\) −1.41175 −0.0541382
\(681\) −0.0147084 −0.000563626 0
\(682\) 11.4926 0.440075
\(683\) −35.5764 −1.36129 −0.680646 0.732613i \(-0.738301\pi\)
−0.680646 + 0.732613i \(0.738301\pi\)
\(684\) 2.85442 0.109142
\(685\) 0.612528 0.0234035
\(686\) −44.6189 −1.70356
\(687\) 0.434261 0.0165681
\(688\) 39.0186 1.48757
\(689\) 6.34039 0.241550
\(690\) 0.0310402 0.00118168
\(691\) 38.3542 1.45906 0.729531 0.683948i \(-0.239738\pi\)
0.729531 + 0.683948i \(0.239738\pi\)
\(692\) 5.01771 0.190745
\(693\) 11.5476 0.438658
\(694\) 4.86235 0.184572
\(695\) 0.233889 0.00887193
\(696\) 0.230253 0.00872771
\(697\) −60.7986 −2.30291
\(698\) −45.9641 −1.73977
\(699\) 0.745084 0.0281817
\(700\) −29.1825 −1.10300
\(701\) 29.6922 1.12146 0.560729 0.827999i \(-0.310521\pi\)
0.560729 + 0.827999i \(0.310521\pi\)
\(702\) 1.09080 0.0411696
\(703\) −0.715988 −0.0270040
\(704\) 1.77486 0.0668925
\(705\) −0.0444997 −0.00167596
\(706\) 25.1715 0.947343
\(707\) 2.72960 0.102657
\(708\) 0.398636 0.0149817
\(709\) 17.8156 0.669081 0.334540 0.942381i \(-0.391419\pi\)
0.334540 + 0.942381i \(0.391419\pi\)
\(710\) 0.0908028 0.00340777
\(711\) −8.55674 −0.320903
\(712\) −1.97172 −0.0738934
\(713\) 20.6082 0.771783
\(714\) −1.68097 −0.0629087
\(715\) 0.480549 0.0179715
\(716\) 23.1837 0.866415
\(717\) 0.511516 0.0191029
\(718\) −54.4327 −2.03141
\(719\) 31.1727 1.16255 0.581273 0.813709i \(-0.302555\pi\)
0.581273 + 0.813709i \(0.302555\pi\)
\(720\) −2.66599 −0.0993555
\(721\) −0.492163 −0.0183291
\(722\) 33.7331 1.25542
\(723\) −0.198836 −0.00739479
\(724\) −30.5580 −1.13568
\(725\) −28.4635 −1.05711
\(726\) 0.613574 0.0227719
\(727\) −22.7175 −0.842546 −0.421273 0.906934i \(-0.638417\pi\)
−0.421273 + 0.906934i \(0.638417\pi\)
\(728\) 16.4130 0.608307
\(729\) −26.9418 −0.997844
\(730\) 1.11829 0.0413899
\(731\) −50.6380 −1.87291
\(732\) 0.231833 0.00856880
\(733\) 27.9900 1.03383 0.516917 0.856035i \(-0.327079\pi\)
0.516917 + 0.856035i \(0.327079\pi\)
\(734\) −46.8387 −1.72885
\(735\) −0.0747909 −0.00275870
\(736\) 18.4667 0.680690
\(737\) 6.66273 0.245425
\(738\) −52.4073 −1.92914
\(739\) −13.1227 −0.482726 −0.241363 0.970435i \(-0.577594\pi\)
−0.241363 + 0.970435i \(0.577594\pi\)
\(740\) −0.241600 −0.00888140
\(741\) −0.0713504 −0.00262112
\(742\) −16.8475 −0.618493
\(743\) −5.90025 −0.216459 −0.108230 0.994126i \(-0.534518\pi\)
−0.108230 + 0.994126i \(0.534518\pi\)
\(744\) 0.290470 0.0106492
\(745\) −0.375292 −0.0137497
\(746\) −13.2721 −0.485928
\(747\) 4.13488 0.151287
\(748\) −7.35258 −0.268837
\(749\) 18.8091 0.687270
\(750\) −0.108528 −0.00396288
\(751\) 12.1280 0.442556 0.221278 0.975211i \(-0.428977\pi\)
0.221278 + 0.975211i \(0.428977\pi\)
\(752\) −36.4757 −1.33013
\(753\) 0.0703843 0.00256495
\(754\) −31.7338 −1.15568
\(755\) −0.326478 −0.0118818
\(756\) −1.15731 −0.0420911
\(757\) 5.77583 0.209926 0.104963 0.994476i \(-0.466528\pi\)
0.104963 + 0.994476i \(0.466528\pi\)
\(758\) 15.5151 0.563532
\(759\) −0.0815526 −0.00296017
\(760\) 0.159227 0.00577576
\(761\) −42.9840 −1.55817 −0.779084 0.626919i \(-0.784316\pi\)
−0.779084 + 0.626919i \(0.784316\pi\)
\(762\) 1.05426 0.0381918
\(763\) −4.41961 −0.160000
\(764\) −4.54393 −0.164394
\(765\) 3.45989 0.125093
\(766\) −41.5616 −1.50168
\(767\) 27.7157 1.00076
\(768\) 0.687325 0.0248017
\(769\) 31.6929 1.14288 0.571438 0.820645i \(-0.306386\pi\)
0.571438 + 0.820645i \(0.306386\pi\)
\(770\) −1.27691 −0.0460165
\(771\) 0.554101 0.0199554
\(772\) 20.1036 0.723544
\(773\) −15.3141 −0.550809 −0.275405 0.961328i \(-0.588812\pi\)
−0.275405 + 0.961328i \(0.588812\pi\)
\(774\) −43.6491 −1.56893
\(775\) −35.9075 −1.28984
\(776\) 7.97708 0.286360
\(777\) 0.145121 0.00520619
\(778\) 53.3677 1.91332
\(779\) 6.85727 0.245687
\(780\) −0.0240762 −0.000862067 0
\(781\) −0.238568 −0.00853664
\(782\) −33.0199 −1.18079
\(783\) −1.12880 −0.0403400
\(784\) −61.3049 −2.18946
\(785\) 1.45156 0.0518083
\(786\) −0.458340 −0.0163485
\(787\) 45.2933 1.61453 0.807265 0.590189i \(-0.200947\pi\)
0.807265 + 0.590189i \(0.200947\pi\)
\(788\) 8.95860 0.319137
\(789\) 0.370824 0.0132017
\(790\) 0.946181 0.0336636
\(791\) −28.8382 −1.02537
\(792\) 3.19720 0.113608
\(793\) 16.1185 0.572385
\(794\) 18.9038 0.670871
\(795\) −0.0124672 −0.000442166 0
\(796\) −27.0283 −0.957992
\(797\) −55.5884 −1.96904 −0.984522 0.175262i \(-0.943923\pi\)
−0.984522 + 0.175262i \(0.943923\pi\)
\(798\) 0.189591 0.00671145
\(799\) 47.3379 1.67469
\(800\) −32.1761 −1.13760
\(801\) 4.83225 0.170739
\(802\) 2.97399 0.105015
\(803\) −2.93811 −0.103684
\(804\) −0.333812 −0.0117727
\(805\) −2.28971 −0.0807016
\(806\) −40.0331 −1.41011
\(807\) −0.100444 −0.00353581
\(808\) 0.755747 0.0265871
\(809\) 2.91410 0.102454 0.0512271 0.998687i \(-0.483687\pi\)
0.0512271 + 0.998687i \(0.483687\pi\)
\(810\) 2.98130 0.104752
\(811\) 56.1811 1.97279 0.986393 0.164403i \(-0.0525698\pi\)
0.986393 + 0.164403i \(0.0525698\pi\)
\(812\) 33.6689 1.18155
\(813\) −0.121474 −0.00426029
\(814\) 1.58974 0.0557203
\(815\) 3.29985 0.115589
\(816\) −1.01962 −0.0356938
\(817\) 5.71129 0.199813
\(818\) −10.5178 −0.367746
\(819\) −40.2247 −1.40556
\(820\) 2.31389 0.0808046
\(821\) 42.0865 1.46883 0.734415 0.678700i \(-0.237456\pi\)
0.734415 + 0.678700i \(0.237456\pi\)
\(822\) 0.201932 0.00704317
\(823\) −25.7167 −0.896427 −0.448214 0.893926i \(-0.647940\pi\)
−0.448214 + 0.893926i \(0.647940\pi\)
\(824\) −0.136265 −0.00474703
\(825\) 0.142096 0.00494716
\(826\) −73.6456 −2.56246
\(827\) −40.9718 −1.42473 −0.712364 0.701810i \(-0.752375\pi\)
−0.712364 + 0.701810i \(0.752375\pi\)
\(828\) −11.3647 −0.394952
\(829\) 0.208982 0.00725824 0.00362912 0.999993i \(-0.498845\pi\)
0.00362912 + 0.999993i \(0.498845\pi\)
\(830\) −0.457224 −0.0158705
\(831\) 0.781528 0.0271109
\(832\) −6.18250 −0.214339
\(833\) 79.5610 2.75662
\(834\) 0.0771061 0.00266997
\(835\) 1.14369 0.0395789
\(836\) 0.829273 0.0286810
\(837\) −1.42401 −0.0492211
\(838\) 27.6024 0.953509
\(839\) −19.5696 −0.675617 −0.337808 0.941215i \(-0.609686\pi\)
−0.337808 + 0.941215i \(0.609686\pi\)
\(840\) −0.0322731 −0.00111353
\(841\) 3.83932 0.132390
\(842\) −55.1252 −1.89974
\(843\) 0.617822 0.0212789
\(844\) 20.0422 0.689880
\(845\) 0.688684 0.0236914
\(846\) 40.8044 1.40288
\(847\) −45.2608 −1.55518
\(848\) −10.2192 −0.350927
\(849\) −0.0960546 −0.00329658
\(850\) 57.5335 1.97338
\(851\) 2.85067 0.0977196
\(852\) 0.0119526 0.000409490 0
\(853\) −8.33474 −0.285376 −0.142688 0.989768i \(-0.545575\pi\)
−0.142688 + 0.989768i \(0.545575\pi\)
\(854\) −42.8298 −1.46560
\(855\) −0.390230 −0.0133456
\(856\) 5.20769 0.177995
\(857\) 53.6212 1.83166 0.915832 0.401562i \(-0.131533\pi\)
0.915832 + 0.401562i \(0.131533\pi\)
\(858\) 0.158422 0.00540845
\(859\) −52.7087 −1.79840 −0.899199 0.437540i \(-0.855850\pi\)
−0.899199 + 0.437540i \(0.855850\pi\)
\(860\) 1.92720 0.0657168
\(861\) −1.38988 −0.0473668
\(862\) 18.6335 0.634659
\(863\) 5.96238 0.202962 0.101481 0.994837i \(-0.467642\pi\)
0.101481 + 0.994837i \(0.467642\pi\)
\(864\) −1.27603 −0.0434115
\(865\) −0.685974 −0.0233238
\(866\) −36.3341 −1.23468
\(867\) 0.765045 0.0259823
\(868\) 42.4742 1.44167
\(869\) −2.48592 −0.0843291
\(870\) 0.0623987 0.00211551
\(871\) −23.2088 −0.786399
\(872\) −1.22366 −0.0414384
\(873\) −19.5501 −0.661670
\(874\) 3.72420 0.125973
\(875\) 8.00565 0.270640
\(876\) 0.147204 0.00497355
\(877\) −19.7094 −0.665539 −0.332770 0.943008i \(-0.607983\pi\)
−0.332770 + 0.943008i \(0.607983\pi\)
\(878\) −47.9153 −1.61706
\(879\) −0.0438834 −0.00148015
\(880\) −0.774528 −0.0261093
\(881\) 22.4766 0.757255 0.378627 0.925549i \(-0.376396\pi\)
0.378627 + 0.925549i \(0.376396\pi\)
\(882\) 68.5802 2.30922
\(883\) 4.31252 0.145128 0.0725640 0.997364i \(-0.476882\pi\)
0.0725640 + 0.997364i \(0.476882\pi\)
\(884\) 25.6118 0.861417
\(885\) −0.0544977 −0.00183192
\(886\) −23.2492 −0.781073
\(887\) −49.2187 −1.65260 −0.826301 0.563229i \(-0.809559\pi\)
−0.826301 + 0.563229i \(0.809559\pi\)
\(888\) 0.0401798 0.00134835
\(889\) −77.7683 −2.60826
\(890\) −0.534338 −0.0179110
\(891\) −7.83282 −0.262409
\(892\) −2.70605 −0.0906052
\(893\) −5.33908 −0.178665
\(894\) −0.123722 −0.00413790
\(895\) −3.16946 −0.105943
\(896\) −40.8325 −1.36412
\(897\) 0.284078 0.00948509
\(898\) −74.6484 −2.49105
\(899\) 41.4277 1.38169
\(900\) 19.8018 0.660060
\(901\) 13.2623 0.441832
\(902\) −15.2255 −0.506953
\(903\) −1.15760 −0.0385225
\(904\) −7.98446 −0.265559
\(905\) 4.17760 0.138868
\(906\) −0.107630 −0.00357576
\(907\) −39.9674 −1.32710 −0.663548 0.748133i \(-0.730950\pi\)
−0.663548 + 0.748133i \(0.730950\pi\)
\(908\) −0.595477 −0.0197616
\(909\) −1.85217 −0.0614326
\(910\) 4.44794 0.147448
\(911\) −11.2248 −0.371893 −0.185946 0.982560i \(-0.559535\pi\)
−0.185946 + 0.982560i \(0.559535\pi\)
\(912\) 0.114999 0.00380801
\(913\) 1.20127 0.0397564
\(914\) −25.0755 −0.829425
\(915\) −0.0316940 −0.00104777
\(916\) 17.5813 0.580903
\(917\) 33.8098 1.11650
\(918\) 2.28165 0.0753057
\(919\) −47.1611 −1.55570 −0.777850 0.628450i \(-0.783690\pi\)
−0.777850 + 0.628450i \(0.783690\pi\)
\(920\) −0.633953 −0.0209008
\(921\) −0.779870 −0.0256976
\(922\) 21.9627 0.723304
\(923\) 0.831022 0.0273534
\(924\) −0.168082 −0.00552951
\(925\) −4.96697 −0.163313
\(926\) 36.1710 1.18865
\(927\) 0.333957 0.0109686
\(928\) 37.1227 1.21861
\(929\) −12.9394 −0.424527 −0.212263 0.977212i \(-0.568084\pi\)
−0.212263 + 0.977212i \(0.568084\pi\)
\(930\) 0.0787176 0.00258125
\(931\) −8.97342 −0.294092
\(932\) 30.1652 0.988094
\(933\) 0.504380 0.0165127
\(934\) 36.3468 1.18930
\(935\) 1.00518 0.0328728
\(936\) −11.1370 −0.364026
\(937\) −45.8355 −1.49738 −0.748691 0.662919i \(-0.769317\pi\)
−0.748691 + 0.662919i \(0.769317\pi\)
\(938\) 61.6698 2.01359
\(939\) 0.783096 0.0255554
\(940\) −1.80160 −0.0587617
\(941\) −34.0441 −1.10980 −0.554902 0.831916i \(-0.687244\pi\)
−0.554902 + 0.831916i \(0.687244\pi\)
\(942\) 0.478534 0.0155915
\(943\) −27.3018 −0.889070
\(944\) −44.6709 −1.45391
\(945\) 0.158217 0.00514680
\(946\) −12.6810 −0.412295
\(947\) 9.29654 0.302097 0.151049 0.988526i \(-0.451735\pi\)
0.151049 + 0.988526i \(0.451735\pi\)
\(948\) 0.124548 0.00404514
\(949\) 10.2345 0.332227
\(950\) −6.48901 −0.210531
\(951\) −0.529647 −0.0171750
\(952\) 34.3315 1.11269
\(953\) −3.58126 −0.116008 −0.0580042 0.998316i \(-0.518474\pi\)
−0.0580042 + 0.998316i \(0.518474\pi\)
\(954\) 11.4319 0.370121
\(955\) 0.621203 0.0201017
\(956\) 20.7090 0.669778
\(957\) −0.163941 −0.00529947
\(958\) 12.5526 0.405555
\(959\) −14.8956 −0.481006
\(960\) 0.0121567 0.000392357 0
\(961\) 21.2622 0.685876
\(962\) −5.53765 −0.178541
\(963\) −12.7629 −0.411279
\(964\) −8.05000 −0.259273
\(965\) −2.74837 −0.0884733
\(966\) −0.754846 −0.0242868
\(967\) −10.8163 −0.347829 −0.173914 0.984761i \(-0.555642\pi\)
−0.173914 + 0.984761i \(0.555642\pi\)
\(968\) −12.5314 −0.402775
\(969\) −0.149245 −0.00479445
\(970\) 2.16179 0.0694110
\(971\) −10.1285 −0.325039 −0.162519 0.986705i \(-0.551962\pi\)
−0.162519 + 0.986705i \(0.551962\pi\)
\(972\) 1.17801 0.0377848
\(973\) −5.68780 −0.182342
\(974\) −9.30157 −0.298042
\(975\) −0.494974 −0.0158519
\(976\) −25.9791 −0.831570
\(977\) −8.29432 −0.265359 −0.132679 0.991159i \(-0.542358\pi\)
−0.132679 + 0.991159i \(0.542358\pi\)
\(978\) 1.08786 0.0347859
\(979\) 1.40388 0.0448681
\(980\) −3.02796 −0.0967245
\(981\) 2.99892 0.0957482
\(982\) −45.1369 −1.44038
\(983\) 28.1559 0.898035 0.449017 0.893523i \(-0.351774\pi\)
0.449017 + 0.893523i \(0.351774\pi\)
\(984\) −0.384816 −0.0122675
\(985\) −1.22474 −0.0390233
\(986\) −66.3783 −2.11392
\(987\) 1.08216 0.0344455
\(988\) −2.88867 −0.0919007
\(989\) −22.7392 −0.723064
\(990\) 0.866444 0.0275374
\(991\) −38.7204 −1.23000 −0.614998 0.788529i \(-0.710843\pi\)
−0.614998 + 0.788529i \(0.710843\pi\)
\(992\) 46.8312 1.48689
\(993\) 0.0305550 0.000969632 0
\(994\) −2.20817 −0.0700390
\(995\) 3.69505 0.117141
\(996\) −0.0601856 −0.00190705
\(997\) −15.2243 −0.482157 −0.241079 0.970506i \(-0.577501\pi\)
−0.241079 + 0.970506i \(0.577501\pi\)
\(998\) −20.4013 −0.645793
\(999\) −0.196979 −0.00623214
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 4033.2.a.f.1.18 85
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4033.2.a.f.1.18 85 1.1 even 1 trivial