Properties

Label 4034.2.a.d.1.7
Level 4034
Weight 2
Character 4034.1
Self dual yes
Analytic conductor 32.212
Analytic rank 0
Dimension 52
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4034 = 2 \cdot 2017 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4034.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.2116521754\)
Analytic rank: \(0\)
Dimension: \(52\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) = 4034.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -2.51773 q^{3} +1.00000 q^{4} +3.18361 q^{5} -2.51773 q^{6} +3.34442 q^{7} +1.00000 q^{8} +3.33897 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -2.51773 q^{3} +1.00000 q^{4} +3.18361 q^{5} -2.51773 q^{6} +3.34442 q^{7} +1.00000 q^{8} +3.33897 q^{9} +3.18361 q^{10} +4.39578 q^{11} -2.51773 q^{12} -1.65607 q^{13} +3.34442 q^{14} -8.01549 q^{15} +1.00000 q^{16} +0.437905 q^{17} +3.33897 q^{18} +6.06633 q^{19} +3.18361 q^{20} -8.42036 q^{21} +4.39578 q^{22} -0.910588 q^{23} -2.51773 q^{24} +5.13540 q^{25} -1.65607 q^{26} -0.853442 q^{27} +3.34442 q^{28} +2.74018 q^{29} -8.01549 q^{30} +7.69663 q^{31} +1.00000 q^{32} -11.0674 q^{33} +0.437905 q^{34} +10.6474 q^{35} +3.33897 q^{36} -2.14712 q^{37} +6.06633 q^{38} +4.16955 q^{39} +3.18361 q^{40} -1.40688 q^{41} -8.42036 q^{42} -7.88297 q^{43} +4.39578 q^{44} +10.6300 q^{45} -0.910588 q^{46} -6.37112 q^{47} -2.51773 q^{48} +4.18517 q^{49} +5.13540 q^{50} -1.10253 q^{51} -1.65607 q^{52} +8.11955 q^{53} -0.853442 q^{54} +13.9945 q^{55} +3.34442 q^{56} -15.2734 q^{57} +2.74018 q^{58} -6.11888 q^{59} -8.01549 q^{60} -0.584661 q^{61} +7.69663 q^{62} +11.1669 q^{63} +1.00000 q^{64} -5.27230 q^{65} -11.0674 q^{66} -14.0603 q^{67} +0.437905 q^{68} +2.29262 q^{69} +10.6474 q^{70} -4.06322 q^{71} +3.33897 q^{72} +5.02776 q^{73} -2.14712 q^{74} -12.9296 q^{75} +6.06633 q^{76} +14.7013 q^{77} +4.16955 q^{78} +2.79445 q^{79} +3.18361 q^{80} -7.86818 q^{81} -1.40688 q^{82} -12.6416 q^{83} -8.42036 q^{84} +1.39412 q^{85} -7.88297 q^{86} -6.89904 q^{87} +4.39578 q^{88} +4.54074 q^{89} +10.6300 q^{90} -5.53861 q^{91} -0.910588 q^{92} -19.3780 q^{93} -6.37112 q^{94} +19.3128 q^{95} -2.51773 q^{96} -10.5365 q^{97} +4.18517 q^{98} +14.6774 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52q + 52q^{2} + 16q^{3} + 52q^{4} + 24q^{5} + 16q^{6} + 12q^{7} + 52q^{8} + 70q^{9} + O(q^{10}) \) \( 52q + 52q^{2} + 16q^{3} + 52q^{4} + 24q^{5} + 16q^{6} + 12q^{7} + 52q^{8} + 70q^{9} + 24q^{10} + 19q^{11} + 16q^{12} + 27q^{13} + 12q^{14} + 5q^{15} + 52q^{16} + 43q^{17} + 70q^{18} + 35q^{19} + 24q^{20} + 29q^{21} + 19q^{22} + 2q^{23} + 16q^{24} + 88q^{25} + 27q^{26} + 49q^{27} + 12q^{28} + 31q^{29} + 5q^{30} + 59q^{31} + 52q^{32} + 45q^{33} + 43q^{34} + 18q^{35} + 70q^{36} + 60q^{37} + 35q^{38} + 6q^{39} + 24q^{40} + 56q^{41} + 29q^{42} + 34q^{43} + 19q^{44} + 61q^{45} + 2q^{46} - 4q^{47} + 16q^{48} + 102q^{49} + 88q^{50} + 23q^{51} + 27q^{52} + 30q^{53} + 49q^{54} + 24q^{55} + 12q^{56} + 32q^{57} + 31q^{58} + 27q^{59} + 5q^{60} + 107q^{61} + 59q^{62} - 4q^{63} + 52q^{64} + 46q^{65} + 45q^{66} + 22q^{67} + 43q^{68} + 36q^{69} + 18q^{70} + 8q^{71} + 70q^{72} + 66q^{73} + 60q^{74} + 53q^{75} + 35q^{76} + 26q^{77} + 6q^{78} + 50q^{79} + 24q^{80} + 108q^{81} + 56q^{82} + 52q^{83} + 29q^{84} + 19q^{85} + 34q^{86} - 32q^{87} + 19q^{88} + 62q^{89} + 61q^{90} + 69q^{91} + 2q^{92} + 21q^{93} - 4q^{94} - 44q^{95} + 16q^{96} + 82q^{97} + 102q^{98} + 16q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −2.51773 −1.45361 −0.726807 0.686842i \(-0.758996\pi\)
−0.726807 + 0.686842i \(0.758996\pi\)
\(4\) 1.00000 0.500000
\(5\) 3.18361 1.42376 0.711878 0.702303i \(-0.247845\pi\)
0.711878 + 0.702303i \(0.247845\pi\)
\(6\) −2.51773 −1.02786
\(7\) 3.34442 1.26407 0.632037 0.774938i \(-0.282219\pi\)
0.632037 + 0.774938i \(0.282219\pi\)
\(8\) 1.00000 0.353553
\(9\) 3.33897 1.11299
\(10\) 3.18361 1.00675
\(11\) 4.39578 1.32538 0.662689 0.748895i \(-0.269415\pi\)
0.662689 + 0.748895i \(0.269415\pi\)
\(12\) −2.51773 −0.726807
\(13\) −1.65607 −0.459312 −0.229656 0.973272i \(-0.573760\pi\)
−0.229656 + 0.973272i \(0.573760\pi\)
\(14\) 3.34442 0.893835
\(15\) −8.01549 −2.06959
\(16\) 1.00000 0.250000
\(17\) 0.437905 0.106207 0.0531037 0.998589i \(-0.483089\pi\)
0.0531037 + 0.998589i \(0.483089\pi\)
\(18\) 3.33897 0.787003
\(19\) 6.06633 1.39171 0.695856 0.718182i \(-0.255025\pi\)
0.695856 + 0.718182i \(0.255025\pi\)
\(20\) 3.18361 0.711878
\(21\) −8.42036 −1.83747
\(22\) 4.39578 0.937183
\(23\) −0.910588 −0.189871 −0.0949354 0.995483i \(-0.530264\pi\)
−0.0949354 + 0.995483i \(0.530264\pi\)
\(24\) −2.51773 −0.513930
\(25\) 5.13540 1.02708
\(26\) −1.65607 −0.324783
\(27\) −0.853442 −0.164245
\(28\) 3.34442 0.632037
\(29\) 2.74018 0.508839 0.254419 0.967094i \(-0.418116\pi\)
0.254419 + 0.967094i \(0.418116\pi\)
\(30\) −8.01549 −1.46342
\(31\) 7.69663 1.38236 0.691178 0.722685i \(-0.257092\pi\)
0.691178 + 0.722685i \(0.257092\pi\)
\(32\) 1.00000 0.176777
\(33\) −11.0674 −1.92659
\(34\) 0.437905 0.0751000
\(35\) 10.6474 1.79973
\(36\) 3.33897 0.556495
\(37\) −2.14712 −0.352984 −0.176492 0.984302i \(-0.556475\pi\)
−0.176492 + 0.984302i \(0.556475\pi\)
\(38\) 6.06633 0.984088
\(39\) 4.16955 0.667662
\(40\) 3.18361 0.503374
\(41\) −1.40688 −0.219718 −0.109859 0.993947i \(-0.535040\pi\)
−0.109859 + 0.993947i \(0.535040\pi\)
\(42\) −8.42036 −1.29929
\(43\) −7.88297 −1.20214 −0.601071 0.799196i \(-0.705259\pi\)
−0.601071 + 0.799196i \(0.705259\pi\)
\(44\) 4.39578 0.662689
\(45\) 10.6300 1.58463
\(46\) −0.910588 −0.134259
\(47\) −6.37112 −0.929323 −0.464662 0.885488i \(-0.653824\pi\)
−0.464662 + 0.885488i \(0.653824\pi\)
\(48\) −2.51773 −0.363403
\(49\) 4.18517 0.597882
\(50\) 5.13540 0.726255
\(51\) −1.10253 −0.154385
\(52\) −1.65607 −0.229656
\(53\) 8.11955 1.11531 0.557653 0.830074i \(-0.311702\pi\)
0.557653 + 0.830074i \(0.311702\pi\)
\(54\) −0.853442 −0.116139
\(55\) 13.9945 1.88701
\(56\) 3.34442 0.446917
\(57\) −15.2734 −2.02301
\(58\) 2.74018 0.359803
\(59\) −6.11888 −0.796611 −0.398305 0.917253i \(-0.630402\pi\)
−0.398305 + 0.917253i \(0.630402\pi\)
\(60\) −8.01549 −1.03479
\(61\) −0.584661 −0.0748581 −0.0374291 0.999299i \(-0.511917\pi\)
−0.0374291 + 0.999299i \(0.511917\pi\)
\(62\) 7.69663 0.977473
\(63\) 11.1669 1.40690
\(64\) 1.00000 0.125000
\(65\) −5.27230 −0.653948
\(66\) −11.0674 −1.36230
\(67\) −14.0603 −1.71774 −0.858869 0.512195i \(-0.828832\pi\)
−0.858869 + 0.512195i \(0.828832\pi\)
\(68\) 0.437905 0.0531037
\(69\) 2.29262 0.275999
\(70\) 10.6474 1.27260
\(71\) −4.06322 −0.482216 −0.241108 0.970498i \(-0.577511\pi\)
−0.241108 + 0.970498i \(0.577511\pi\)
\(72\) 3.33897 0.393502
\(73\) 5.02776 0.588455 0.294228 0.955735i \(-0.404938\pi\)
0.294228 + 0.955735i \(0.404938\pi\)
\(74\) −2.14712 −0.249597
\(75\) −12.9296 −1.49298
\(76\) 6.06633 0.695856
\(77\) 14.7013 1.67537
\(78\) 4.16955 0.472108
\(79\) 2.79445 0.314400 0.157200 0.987567i \(-0.449753\pi\)
0.157200 + 0.987567i \(0.449753\pi\)
\(80\) 3.18361 0.355939
\(81\) −7.86818 −0.874242
\(82\) −1.40688 −0.155364
\(83\) −12.6416 −1.38759 −0.693796 0.720172i \(-0.744063\pi\)
−0.693796 + 0.720172i \(0.744063\pi\)
\(84\) −8.42036 −0.918737
\(85\) 1.39412 0.151213
\(86\) −7.88297 −0.850043
\(87\) −6.89904 −0.739655
\(88\) 4.39578 0.468592
\(89\) 4.54074 0.481318 0.240659 0.970610i \(-0.422636\pi\)
0.240659 + 0.970610i \(0.422636\pi\)
\(90\) 10.6300 1.12050
\(91\) −5.53861 −0.580604
\(92\) −0.910588 −0.0949354
\(93\) −19.3780 −2.00941
\(94\) −6.37112 −0.657131
\(95\) 19.3128 1.98146
\(96\) −2.51773 −0.256965
\(97\) −10.5365 −1.06982 −0.534911 0.844908i \(-0.679655\pi\)
−0.534911 + 0.844908i \(0.679655\pi\)
\(98\) 4.18517 0.422766
\(99\) 14.6774 1.47513
\(100\) 5.13540 0.513540
\(101\) 5.07975 0.505454 0.252727 0.967538i \(-0.418672\pi\)
0.252727 + 0.967538i \(0.418672\pi\)
\(102\) −1.10253 −0.109166
\(103\) −2.18522 −0.215316 −0.107658 0.994188i \(-0.534335\pi\)
−0.107658 + 0.994188i \(0.534335\pi\)
\(104\) −1.65607 −0.162391
\(105\) −26.8072 −2.61611
\(106\) 8.11955 0.788640
\(107\) −3.85364 −0.372545 −0.186273 0.982498i \(-0.559641\pi\)
−0.186273 + 0.982498i \(0.559641\pi\)
\(108\) −0.853442 −0.0821225
\(109\) 18.5633 1.77804 0.889021 0.457866i \(-0.151386\pi\)
0.889021 + 0.457866i \(0.151386\pi\)
\(110\) 13.9945 1.33432
\(111\) 5.40587 0.513102
\(112\) 3.34442 0.316018
\(113\) −15.9965 −1.50483 −0.752414 0.658691i \(-0.771110\pi\)
−0.752414 + 0.658691i \(0.771110\pi\)
\(114\) −15.2734 −1.43048
\(115\) −2.89896 −0.270330
\(116\) 2.74018 0.254419
\(117\) −5.52958 −0.511210
\(118\) −6.11888 −0.563289
\(119\) 1.46454 0.134254
\(120\) −8.01549 −0.731710
\(121\) 8.32287 0.756625
\(122\) −0.584661 −0.0529327
\(123\) 3.54215 0.319385
\(124\) 7.69663 0.691178
\(125\) 0.431051 0.0385544
\(126\) 11.1669 0.994830
\(127\) −11.7614 −1.04366 −0.521829 0.853050i \(-0.674750\pi\)
−0.521829 + 0.853050i \(0.674750\pi\)
\(128\) 1.00000 0.0883883
\(129\) 19.8472 1.74745
\(130\) −5.27230 −0.462411
\(131\) −22.5045 −1.96623 −0.983113 0.183001i \(-0.941419\pi\)
−0.983113 + 0.183001i \(0.941419\pi\)
\(132\) −11.0674 −0.963293
\(133\) 20.2884 1.75923
\(134\) −14.0603 −1.21462
\(135\) −2.71703 −0.233845
\(136\) 0.437905 0.0375500
\(137\) −0.172412 −0.0147301 −0.00736506 0.999973i \(-0.502344\pi\)
−0.00736506 + 0.999973i \(0.502344\pi\)
\(138\) 2.29262 0.195161
\(139\) −16.8581 −1.42989 −0.714945 0.699181i \(-0.753548\pi\)
−0.714945 + 0.699181i \(0.753548\pi\)
\(140\) 10.6474 0.899866
\(141\) 16.0408 1.35088
\(142\) −4.06322 −0.340978
\(143\) −7.27973 −0.608762
\(144\) 3.33897 0.278248
\(145\) 8.72368 0.724462
\(146\) 5.02776 0.416101
\(147\) −10.5371 −0.869089
\(148\) −2.14712 −0.176492
\(149\) 14.8882 1.21969 0.609843 0.792522i \(-0.291232\pi\)
0.609843 + 0.792522i \(0.291232\pi\)
\(150\) −12.9296 −1.05569
\(151\) 22.1203 1.80012 0.900061 0.435764i \(-0.143522\pi\)
0.900061 + 0.435764i \(0.143522\pi\)
\(152\) 6.06633 0.492044
\(153\) 1.46215 0.118208
\(154\) 14.7013 1.18467
\(155\) 24.5031 1.96814
\(156\) 4.16955 0.333831
\(157\) −5.70304 −0.455152 −0.227576 0.973760i \(-0.573080\pi\)
−0.227576 + 0.973760i \(0.573080\pi\)
\(158\) 2.79445 0.222315
\(159\) −20.4428 −1.62122
\(160\) 3.18361 0.251687
\(161\) −3.04539 −0.240011
\(162\) −7.86818 −0.618183
\(163\) −14.6908 −1.15067 −0.575336 0.817917i \(-0.695129\pi\)
−0.575336 + 0.817917i \(0.695129\pi\)
\(164\) −1.40688 −0.109859
\(165\) −35.2343 −2.74299
\(166\) −12.6416 −0.981175
\(167\) 17.6785 1.36800 0.684000 0.729482i \(-0.260239\pi\)
0.684000 + 0.729482i \(0.260239\pi\)
\(168\) −8.42036 −0.649645
\(169\) −10.2574 −0.789033
\(170\) 1.39412 0.106924
\(171\) 20.2553 1.54896
\(172\) −7.88297 −0.601071
\(173\) 20.7270 1.57585 0.787924 0.615773i \(-0.211156\pi\)
0.787924 + 0.615773i \(0.211156\pi\)
\(174\) −6.89904 −0.523015
\(175\) 17.1749 1.29830
\(176\) 4.39578 0.331344
\(177\) 15.4057 1.15796
\(178\) 4.54074 0.340343
\(179\) 13.8040 1.03176 0.515881 0.856661i \(-0.327465\pi\)
0.515881 + 0.856661i \(0.327465\pi\)
\(180\) 10.6300 0.792313
\(181\) −16.0579 −1.19357 −0.596785 0.802401i \(-0.703556\pi\)
−0.596785 + 0.802401i \(0.703556\pi\)
\(182\) −5.53861 −0.410549
\(183\) 1.47202 0.108815
\(184\) −0.910588 −0.0671295
\(185\) −6.83560 −0.502563
\(186\) −19.3780 −1.42087
\(187\) 1.92493 0.140765
\(188\) −6.37112 −0.464662
\(189\) −2.85427 −0.207618
\(190\) 19.3128 1.40110
\(191\) −20.7159 −1.49895 −0.749475 0.662032i \(-0.769694\pi\)
−0.749475 + 0.662032i \(0.769694\pi\)
\(192\) −2.51773 −0.181702
\(193\) 26.8620 1.93357 0.966786 0.255589i \(-0.0822693\pi\)
0.966786 + 0.255589i \(0.0822693\pi\)
\(194\) −10.5365 −0.756479
\(195\) 13.2742 0.950587
\(196\) 4.18517 0.298941
\(197\) −15.6396 −1.11427 −0.557136 0.830421i \(-0.688100\pi\)
−0.557136 + 0.830421i \(0.688100\pi\)
\(198\) 14.6774 1.04308
\(199\) −5.44692 −0.386122 −0.193061 0.981187i \(-0.561842\pi\)
−0.193061 + 0.981187i \(0.561842\pi\)
\(200\) 5.13540 0.363127
\(201\) 35.4000 2.49693
\(202\) 5.07975 0.357410
\(203\) 9.16433 0.643210
\(204\) −1.10253 −0.0771923
\(205\) −4.47896 −0.312824
\(206\) −2.18522 −0.152251
\(207\) −3.04043 −0.211324
\(208\) −1.65607 −0.114828
\(209\) 26.6662 1.84454
\(210\) −26.8072 −1.84987
\(211\) 12.1769 0.838289 0.419145 0.907919i \(-0.362330\pi\)
0.419145 + 0.907919i \(0.362330\pi\)
\(212\) 8.11955 0.557653
\(213\) 10.2301 0.700955
\(214\) −3.85364 −0.263429
\(215\) −25.0963 −1.71156
\(216\) −0.853442 −0.0580694
\(217\) 25.7408 1.74740
\(218\) 18.5633 1.25727
\(219\) −12.6586 −0.855386
\(220\) 13.9945 0.943506
\(221\) −0.725202 −0.0487823
\(222\) 5.40587 0.362818
\(223\) 4.34013 0.290637 0.145318 0.989385i \(-0.453579\pi\)
0.145318 + 0.989385i \(0.453579\pi\)
\(224\) 3.34442 0.223459
\(225\) 17.1469 1.14313
\(226\) −15.9965 −1.06407
\(227\) −0.764918 −0.0507694 −0.0253847 0.999678i \(-0.508081\pi\)
−0.0253847 + 0.999678i \(0.508081\pi\)
\(228\) −15.2734 −1.01150
\(229\) 25.2083 1.66581 0.832904 0.553417i \(-0.186676\pi\)
0.832904 + 0.553417i \(0.186676\pi\)
\(230\) −2.89896 −0.191152
\(231\) −37.0141 −2.43535
\(232\) 2.74018 0.179902
\(233\) 7.59456 0.497536 0.248768 0.968563i \(-0.419974\pi\)
0.248768 + 0.968563i \(0.419974\pi\)
\(234\) −5.52958 −0.361480
\(235\) −20.2832 −1.32313
\(236\) −6.11888 −0.398305
\(237\) −7.03568 −0.457017
\(238\) 1.46454 0.0949319
\(239\) −1.10323 −0.0713622 −0.0356811 0.999363i \(-0.511360\pi\)
−0.0356811 + 0.999363i \(0.511360\pi\)
\(240\) −8.01549 −0.517397
\(241\) 10.8256 0.697341 0.348671 0.937245i \(-0.386633\pi\)
0.348671 + 0.937245i \(0.386633\pi\)
\(242\) 8.32287 0.535015
\(243\) 22.3703 1.43505
\(244\) −0.584661 −0.0374291
\(245\) 13.3240 0.851238
\(246\) 3.54215 0.225839
\(247\) −10.0463 −0.639230
\(248\) 7.69663 0.488736
\(249\) 31.8281 2.01702
\(250\) 0.431051 0.0272621
\(251\) −3.32831 −0.210081 −0.105041 0.994468i \(-0.533497\pi\)
−0.105041 + 0.994468i \(0.533497\pi\)
\(252\) 11.1669 0.703451
\(253\) −4.00275 −0.251650
\(254\) −11.7614 −0.737977
\(255\) −3.51002 −0.219806
\(256\) 1.00000 0.0625000
\(257\) −4.53769 −0.283053 −0.141527 0.989934i \(-0.545201\pi\)
−0.141527 + 0.989934i \(0.545201\pi\)
\(258\) 19.8472 1.23563
\(259\) −7.18088 −0.446198
\(260\) −5.27230 −0.326974
\(261\) 9.14939 0.566333
\(262\) −22.5045 −1.39033
\(263\) 12.6658 0.781009 0.390505 0.920601i \(-0.372301\pi\)
0.390505 + 0.920601i \(0.372301\pi\)
\(264\) −11.0674 −0.681151
\(265\) 25.8495 1.58792
\(266\) 20.2884 1.24396
\(267\) −11.4324 −0.699650
\(268\) −14.0603 −0.858869
\(269\) 9.39941 0.573092 0.286546 0.958066i \(-0.407493\pi\)
0.286546 + 0.958066i \(0.407493\pi\)
\(270\) −2.71703 −0.165353
\(271\) 20.7315 1.25935 0.629674 0.776860i \(-0.283188\pi\)
0.629674 + 0.776860i \(0.283188\pi\)
\(272\) 0.437905 0.0265519
\(273\) 13.9447 0.843974
\(274\) −0.172412 −0.0104158
\(275\) 22.5741 1.36127
\(276\) 2.29262 0.137999
\(277\) 18.1194 1.08869 0.544344 0.838862i \(-0.316779\pi\)
0.544344 + 0.838862i \(0.316779\pi\)
\(278\) −16.8581 −1.01108
\(279\) 25.6988 1.53855
\(280\) 10.6474 0.636301
\(281\) 6.87701 0.410248 0.205124 0.978736i \(-0.434240\pi\)
0.205124 + 0.978736i \(0.434240\pi\)
\(282\) 16.0408 0.955214
\(283\) 0.126831 0.00753930 0.00376965 0.999993i \(-0.498800\pi\)
0.00376965 + 0.999993i \(0.498800\pi\)
\(284\) −4.06322 −0.241108
\(285\) −48.6246 −2.88027
\(286\) −7.27973 −0.430459
\(287\) −4.70520 −0.277739
\(288\) 3.33897 0.196751
\(289\) −16.8082 −0.988720
\(290\) 8.72368 0.512272
\(291\) 26.5282 1.55511
\(292\) 5.02776 0.294228
\(293\) 24.1920 1.41331 0.706656 0.707557i \(-0.250203\pi\)
0.706656 + 0.707557i \(0.250203\pi\)
\(294\) −10.5371 −0.614539
\(295\) −19.4802 −1.13418
\(296\) −2.14712 −0.124799
\(297\) −3.75154 −0.217687
\(298\) 14.8882 0.862449
\(299\) 1.50800 0.0872099
\(300\) −12.9296 −0.746488
\(301\) −26.3640 −1.51960
\(302\) 22.1203 1.27288
\(303\) −12.7895 −0.734735
\(304\) 6.06633 0.347928
\(305\) −1.86133 −0.106580
\(306\) 1.46215 0.0835856
\(307\) 3.47382 0.198261 0.0991307 0.995074i \(-0.468394\pi\)
0.0991307 + 0.995074i \(0.468394\pi\)
\(308\) 14.7013 0.837687
\(309\) 5.50179 0.312986
\(310\) 24.5031 1.39168
\(311\) 10.1173 0.573699 0.286850 0.957976i \(-0.407392\pi\)
0.286850 + 0.957976i \(0.407392\pi\)
\(312\) 4.16955 0.236054
\(313\) −3.16036 −0.178634 −0.0893170 0.996003i \(-0.528468\pi\)
−0.0893170 + 0.996003i \(0.528468\pi\)
\(314\) −5.70304 −0.321841
\(315\) 35.5512 2.00308
\(316\) 2.79445 0.157200
\(317\) 16.6310 0.934091 0.467045 0.884233i \(-0.345318\pi\)
0.467045 + 0.884233i \(0.345318\pi\)
\(318\) −20.4428 −1.14638
\(319\) 12.0452 0.674404
\(320\) 3.18361 0.177969
\(321\) 9.70243 0.541537
\(322\) −3.04539 −0.169713
\(323\) 2.65647 0.147810
\(324\) −7.86818 −0.437121
\(325\) −8.50459 −0.471750
\(326\) −14.6908 −0.813648
\(327\) −46.7374 −2.58459
\(328\) −1.40688 −0.0776819
\(329\) −21.3077 −1.17473
\(330\) −35.2343 −1.93958
\(331\) −12.5326 −0.688855 −0.344427 0.938813i \(-0.611927\pi\)
−0.344427 + 0.938813i \(0.611927\pi\)
\(332\) −12.6416 −0.693796
\(333\) −7.16917 −0.392868
\(334\) 17.6785 0.967323
\(335\) −44.7625 −2.44564
\(336\) −8.42036 −0.459368
\(337\) −2.50968 −0.136711 −0.0683556 0.997661i \(-0.521775\pi\)
−0.0683556 + 0.997661i \(0.521775\pi\)
\(338\) −10.2574 −0.557930
\(339\) 40.2750 2.18744
\(340\) 1.39412 0.0756067
\(341\) 33.8327 1.83214
\(342\) 20.2553 1.09528
\(343\) −9.41397 −0.508307
\(344\) −7.88297 −0.425021
\(345\) 7.29881 0.392955
\(346\) 20.7270 1.11429
\(347\) 6.29608 0.337991 0.168996 0.985617i \(-0.445948\pi\)
0.168996 + 0.985617i \(0.445948\pi\)
\(348\) −6.89904 −0.369827
\(349\) 25.6196 1.37138 0.685692 0.727891i \(-0.259500\pi\)
0.685692 + 0.727891i \(0.259500\pi\)
\(350\) 17.1749 0.918039
\(351\) 1.41336 0.0754397
\(352\) 4.39578 0.234296
\(353\) −2.73598 −0.145621 −0.0728107 0.997346i \(-0.523197\pi\)
−0.0728107 + 0.997346i \(0.523197\pi\)
\(354\) 15.4057 0.818804
\(355\) −12.9357 −0.686557
\(356\) 4.54074 0.240659
\(357\) −3.68732 −0.195153
\(358\) 13.8040 0.729565
\(359\) −27.0672 −1.42855 −0.714277 0.699863i \(-0.753244\pi\)
−0.714277 + 0.699863i \(0.753244\pi\)
\(360\) 10.6300 0.560250
\(361\) 17.8003 0.936860
\(362\) −16.0579 −0.843982
\(363\) −20.9548 −1.09984
\(364\) −5.53861 −0.290302
\(365\) 16.0065 0.837816
\(366\) 1.47202 0.0769437
\(367\) −18.0955 −0.944579 −0.472289 0.881443i \(-0.656572\pi\)
−0.472289 + 0.881443i \(0.656572\pi\)
\(368\) −0.910588 −0.0474677
\(369\) −4.69753 −0.244544
\(370\) −6.83560 −0.355366
\(371\) 27.1552 1.40983
\(372\) −19.3780 −1.00470
\(373\) −21.7061 −1.12390 −0.561949 0.827172i \(-0.689948\pi\)
−0.561949 + 0.827172i \(0.689948\pi\)
\(374\) 1.92493 0.0995358
\(375\) −1.08527 −0.0560432
\(376\) −6.37112 −0.328565
\(377\) −4.53794 −0.233716
\(378\) −2.85427 −0.146808
\(379\) −30.4578 −1.56451 −0.782256 0.622957i \(-0.785931\pi\)
−0.782256 + 0.622957i \(0.785931\pi\)
\(380\) 19.3128 0.990728
\(381\) 29.6121 1.51707
\(382\) −20.7159 −1.05992
\(383\) 20.8528 1.06553 0.532765 0.846263i \(-0.321153\pi\)
0.532765 + 0.846263i \(0.321153\pi\)
\(384\) −2.51773 −0.128482
\(385\) 46.8034 2.38532
\(386\) 26.8620 1.36724
\(387\) −26.3210 −1.33797
\(388\) −10.5365 −0.534911
\(389\) −27.8182 −1.41044 −0.705219 0.708989i \(-0.749152\pi\)
−0.705219 + 0.708989i \(0.749152\pi\)
\(390\) 13.2742 0.672167
\(391\) −0.398751 −0.0201657
\(392\) 4.18517 0.211383
\(393\) 56.6602 2.85813
\(394\) −15.6396 −0.787910
\(395\) 8.89646 0.447629
\(396\) 14.6774 0.737566
\(397\) −33.5752 −1.68509 −0.842546 0.538624i \(-0.818944\pi\)
−0.842546 + 0.538624i \(0.818944\pi\)
\(398\) −5.44692 −0.273029
\(399\) −51.0807 −2.55723
\(400\) 5.13540 0.256770
\(401\) −19.4435 −0.970962 −0.485481 0.874247i \(-0.661355\pi\)
−0.485481 + 0.874247i \(0.661355\pi\)
\(402\) 35.4000 1.76559
\(403\) −12.7462 −0.634932
\(404\) 5.07975 0.252727
\(405\) −25.0492 −1.24471
\(406\) 9.16433 0.454818
\(407\) −9.43826 −0.467837
\(408\) −1.10253 −0.0545832
\(409\) −17.6302 −0.871758 −0.435879 0.900005i \(-0.643562\pi\)
−0.435879 + 0.900005i \(0.643562\pi\)
\(410\) −4.47896 −0.221200
\(411\) 0.434086 0.0214119
\(412\) −2.18522 −0.107658
\(413\) −20.4641 −1.00697
\(414\) −3.04043 −0.149429
\(415\) −40.2458 −1.97559
\(416\) −1.65607 −0.0811956
\(417\) 42.4443 2.07851
\(418\) 26.6662 1.30429
\(419\) 11.1342 0.543941 0.271971 0.962306i \(-0.412325\pi\)
0.271971 + 0.962306i \(0.412325\pi\)
\(420\) −26.8072 −1.30806
\(421\) −7.21336 −0.351558 −0.175779 0.984430i \(-0.556244\pi\)
−0.175779 + 0.984430i \(0.556244\pi\)
\(422\) 12.1769 0.592760
\(423\) −21.2730 −1.03433
\(424\) 8.11955 0.394320
\(425\) 2.24881 0.109083
\(426\) 10.2301 0.495650
\(427\) −1.95535 −0.0946262
\(428\) −3.85364 −0.186273
\(429\) 18.3284 0.884904
\(430\) −25.0963 −1.21025
\(431\) −3.95857 −0.190678 −0.0953389 0.995445i \(-0.530393\pi\)
−0.0953389 + 0.995445i \(0.530393\pi\)
\(432\) −0.853442 −0.0410613
\(433\) −4.67256 −0.224549 −0.112274 0.993677i \(-0.535814\pi\)
−0.112274 + 0.993677i \(0.535814\pi\)
\(434\) 25.7408 1.23560
\(435\) −21.9639 −1.05309
\(436\) 18.5633 0.889021
\(437\) −5.52393 −0.264245
\(438\) −12.6586 −0.604849
\(439\) 2.05782 0.0982145 0.0491072 0.998794i \(-0.484362\pi\)
0.0491072 + 0.998794i \(0.484362\pi\)
\(440\) 13.9945 0.667160
\(441\) 13.9742 0.665437
\(442\) −0.725202 −0.0344943
\(443\) −6.66947 −0.316876 −0.158438 0.987369i \(-0.550646\pi\)
−0.158438 + 0.987369i \(0.550646\pi\)
\(444\) 5.40587 0.256551
\(445\) 14.4560 0.685279
\(446\) 4.34013 0.205511
\(447\) −37.4844 −1.77295
\(448\) 3.34442 0.158009
\(449\) −5.68669 −0.268371 −0.134186 0.990956i \(-0.542842\pi\)
−0.134186 + 0.990956i \(0.542842\pi\)
\(450\) 17.1469 0.808315
\(451\) −6.18433 −0.291209
\(452\) −15.9965 −0.752414
\(453\) −55.6929 −2.61668
\(454\) −0.764918 −0.0358994
\(455\) −17.6328 −0.826638
\(456\) −15.2734 −0.715242
\(457\) 1.91582 0.0896185 0.0448092 0.998996i \(-0.485732\pi\)
0.0448092 + 0.998996i \(0.485732\pi\)
\(458\) 25.2083 1.17790
\(459\) −0.373726 −0.0174440
\(460\) −2.89896 −0.135165
\(461\) −5.00120 −0.232929 −0.116465 0.993195i \(-0.537156\pi\)
−0.116465 + 0.993195i \(0.537156\pi\)
\(462\) −37.0141 −1.72205
\(463\) −7.48957 −0.348070 −0.174035 0.984739i \(-0.555681\pi\)
−0.174035 + 0.984739i \(0.555681\pi\)
\(464\) 2.74018 0.127210
\(465\) −61.6922 −2.86091
\(466\) 7.59456 0.351811
\(467\) −6.23078 −0.288326 −0.144163 0.989554i \(-0.546049\pi\)
−0.144163 + 0.989554i \(0.546049\pi\)
\(468\) −5.52958 −0.255605
\(469\) −47.0236 −2.17135
\(470\) −20.2832 −0.935593
\(471\) 14.3587 0.661615
\(472\) −6.11888 −0.281644
\(473\) −34.6518 −1.59329
\(474\) −7.03568 −0.323160
\(475\) 31.1530 1.42940
\(476\) 1.46454 0.0671270
\(477\) 27.1109 1.24132
\(478\) −1.10323 −0.0504607
\(479\) −5.99882 −0.274093 −0.137046 0.990565i \(-0.543761\pi\)
−0.137046 + 0.990565i \(0.543761\pi\)
\(480\) −8.01549 −0.365855
\(481\) 3.55578 0.162130
\(482\) 10.8256 0.493095
\(483\) 7.66749 0.348883
\(484\) 8.32287 0.378312
\(485\) −33.5442 −1.52317
\(486\) 22.3703 1.01474
\(487\) −27.6837 −1.25447 −0.627233 0.778831i \(-0.715813\pi\)
−0.627233 + 0.778831i \(0.715813\pi\)
\(488\) −0.584661 −0.0264663
\(489\) 36.9875 1.67263
\(490\) 13.3240 0.601916
\(491\) −31.2593 −1.41071 −0.705355 0.708854i \(-0.749213\pi\)
−0.705355 + 0.708854i \(0.749213\pi\)
\(492\) 3.54215 0.159692
\(493\) 1.19994 0.0540425
\(494\) −10.0463 −0.452004
\(495\) 46.7271 2.10023
\(496\) 7.69663 0.345589
\(497\) −13.5891 −0.609556
\(498\) 31.8281 1.42625
\(499\) 17.8189 0.797683 0.398842 0.917020i \(-0.369412\pi\)
0.398842 + 0.917020i \(0.369412\pi\)
\(500\) 0.431051 0.0192772
\(501\) −44.5096 −1.98854
\(502\) −3.32831 −0.148550
\(503\) 6.96487 0.310548 0.155274 0.987871i \(-0.450374\pi\)
0.155274 + 0.987871i \(0.450374\pi\)
\(504\) 11.1669 0.497415
\(505\) 16.1720 0.719643
\(506\) −4.00275 −0.177944
\(507\) 25.8254 1.14695
\(508\) −11.7614 −0.521829
\(509\) 28.1001 1.24551 0.622757 0.782415i \(-0.286012\pi\)
0.622757 + 0.782415i \(0.286012\pi\)
\(510\) −3.51002 −0.155426
\(511\) 16.8150 0.743851
\(512\) 1.00000 0.0441942
\(513\) −5.17726 −0.228582
\(514\) −4.53769 −0.200149
\(515\) −6.95688 −0.306557
\(516\) 19.8472 0.873725
\(517\) −28.0060 −1.23170
\(518\) −7.18088 −0.315510
\(519\) −52.1851 −2.29067
\(520\) −5.27230 −0.231205
\(521\) −27.1116 −1.18778 −0.593890 0.804546i \(-0.702409\pi\)
−0.593890 + 0.804546i \(0.702409\pi\)
\(522\) 9.14939 0.400458
\(523\) 33.7768 1.47695 0.738477 0.674278i \(-0.235545\pi\)
0.738477 + 0.674278i \(0.235545\pi\)
\(524\) −22.5045 −0.983113
\(525\) −43.2419 −1.88723
\(526\) 12.6658 0.552257
\(527\) 3.37039 0.146816
\(528\) −11.0674 −0.481646
\(529\) −22.1708 −0.963949
\(530\) 25.8495 1.12283
\(531\) −20.4308 −0.886621
\(532\) 20.2884 0.879613
\(533\) 2.32990 0.100919
\(534\) −11.4324 −0.494727
\(535\) −12.2685 −0.530413
\(536\) −14.0603 −0.607312
\(537\) −34.7548 −1.49978
\(538\) 9.39941 0.405238
\(539\) 18.3971 0.792419
\(540\) −2.71703 −0.116922
\(541\) 28.9579 1.24500 0.622498 0.782621i \(-0.286118\pi\)
0.622498 + 0.782621i \(0.286118\pi\)
\(542\) 20.7315 0.890493
\(543\) 40.4294 1.73499
\(544\) 0.437905 0.0187750
\(545\) 59.0984 2.53150
\(546\) 13.9447 0.596779
\(547\) −31.1440 −1.33162 −0.665810 0.746121i \(-0.731914\pi\)
−0.665810 + 0.746121i \(0.731914\pi\)
\(548\) −0.172412 −0.00736506
\(549\) −1.95217 −0.0833164
\(550\) 22.5741 0.962562
\(551\) 16.6228 0.708157
\(552\) 2.29262 0.0975803
\(553\) 9.34583 0.397425
\(554\) 18.1194 0.769818
\(555\) 17.2102 0.730532
\(556\) −16.8581 −0.714945
\(557\) −28.6070 −1.21212 −0.606060 0.795419i \(-0.707251\pi\)
−0.606060 + 0.795419i \(0.707251\pi\)
\(558\) 25.6988 1.08792
\(559\) 13.0548 0.552158
\(560\) 10.6474 0.449933
\(561\) −4.84646 −0.204618
\(562\) 6.87701 0.290089
\(563\) 35.0156 1.47573 0.737866 0.674947i \(-0.235833\pi\)
0.737866 + 0.674947i \(0.235833\pi\)
\(564\) 16.0408 0.675438
\(565\) −50.9268 −2.14251
\(566\) 0.126831 0.00533109
\(567\) −26.3145 −1.10511
\(568\) −4.06322 −0.170489
\(569\) −6.23052 −0.261197 −0.130599 0.991435i \(-0.541690\pi\)
−0.130599 + 0.991435i \(0.541690\pi\)
\(570\) −48.6246 −2.03666
\(571\) 2.58529 0.108191 0.0540955 0.998536i \(-0.482772\pi\)
0.0540955 + 0.998536i \(0.482772\pi\)
\(572\) −7.27973 −0.304381
\(573\) 52.1571 2.17889
\(574\) −4.70520 −0.196391
\(575\) −4.67623 −0.195012
\(576\) 3.33897 0.139124
\(577\) −6.50698 −0.270889 −0.135445 0.990785i \(-0.543246\pi\)
−0.135445 + 0.990785i \(0.543246\pi\)
\(578\) −16.8082 −0.699131
\(579\) −67.6314 −2.81066
\(580\) 8.72368 0.362231
\(581\) −42.2787 −1.75402
\(582\) 26.5282 1.09963
\(583\) 35.6917 1.47820
\(584\) 5.02776 0.208050
\(585\) −17.6041 −0.727838
\(586\) 24.1920 0.999363
\(587\) 27.7013 1.14336 0.571678 0.820478i \(-0.306293\pi\)
0.571678 + 0.820478i \(0.306293\pi\)
\(588\) −10.5371 −0.434544
\(589\) 46.6903 1.92384
\(590\) −19.4802 −0.801986
\(591\) 39.3762 1.61972
\(592\) −2.14712 −0.0882460
\(593\) −15.5154 −0.637141 −0.318571 0.947899i \(-0.603203\pi\)
−0.318571 + 0.947899i \(0.603203\pi\)
\(594\) −3.75154 −0.153928
\(595\) 4.66253 0.191145
\(596\) 14.8882 0.609843
\(597\) 13.7139 0.561272
\(598\) 1.50800 0.0616667
\(599\) 29.8959 1.22151 0.610756 0.791819i \(-0.290866\pi\)
0.610756 + 0.791819i \(0.290866\pi\)
\(600\) −12.9296 −0.527847
\(601\) 2.95486 0.120531 0.0602657 0.998182i \(-0.480805\pi\)
0.0602657 + 0.998182i \(0.480805\pi\)
\(602\) −26.3640 −1.07452
\(603\) −46.9469 −1.91183
\(604\) 22.1203 0.900061
\(605\) 26.4968 1.07725
\(606\) −12.7895 −0.519536
\(607\) 22.9224 0.930391 0.465195 0.885208i \(-0.345984\pi\)
0.465195 + 0.885208i \(0.345984\pi\)
\(608\) 6.06633 0.246022
\(609\) −23.0733 −0.934978
\(610\) −1.86133 −0.0753632
\(611\) 10.5510 0.426849
\(612\) 1.46215 0.0591040
\(613\) 43.4209 1.75376 0.876878 0.480714i \(-0.159622\pi\)
0.876878 + 0.480714i \(0.159622\pi\)
\(614\) 3.47382 0.140192
\(615\) 11.2768 0.454725
\(616\) 14.7013 0.592334
\(617\) 13.8734 0.558523 0.279262 0.960215i \(-0.409910\pi\)
0.279262 + 0.960215i \(0.409910\pi\)
\(618\) 5.50179 0.221314
\(619\) −12.9730 −0.521431 −0.260715 0.965416i \(-0.583958\pi\)
−0.260715 + 0.965416i \(0.583958\pi\)
\(620\) 24.5031 0.984068
\(621\) 0.777135 0.0311853
\(622\) 10.1173 0.405667
\(623\) 15.1862 0.608421
\(624\) 4.16955 0.166915
\(625\) −24.3047 −0.972187
\(626\) −3.16036 −0.126313
\(627\) −67.1384 −2.68125
\(628\) −5.70304 −0.227576
\(629\) −0.940233 −0.0374895
\(630\) 35.5512 1.41639
\(631\) 16.1694 0.643693 0.321847 0.946792i \(-0.395696\pi\)
0.321847 + 0.946792i \(0.395696\pi\)
\(632\) 2.79445 0.111157
\(633\) −30.6581 −1.21855
\(634\) 16.6310 0.660502
\(635\) −37.4438 −1.48591
\(636\) −20.4428 −0.810611
\(637\) −6.93095 −0.274614
\(638\) 12.0452 0.476875
\(639\) −13.5670 −0.536702
\(640\) 3.18361 0.125843
\(641\) −25.8442 −1.02078 −0.510392 0.859942i \(-0.670500\pi\)
−0.510392 + 0.859942i \(0.670500\pi\)
\(642\) 9.70243 0.382924
\(643\) −27.2371 −1.07413 −0.537063 0.843542i \(-0.680466\pi\)
−0.537063 + 0.843542i \(0.680466\pi\)
\(644\) −3.04539 −0.120005
\(645\) 63.1858 2.48794
\(646\) 2.65647 0.104518
\(647\) 13.9982 0.550326 0.275163 0.961398i \(-0.411268\pi\)
0.275163 + 0.961398i \(0.411268\pi\)
\(648\) −7.86818 −0.309091
\(649\) −26.8973 −1.05581
\(650\) −8.50459 −0.333577
\(651\) −64.8084 −2.54004
\(652\) −14.6908 −0.575336
\(653\) 30.3854 1.18907 0.594536 0.804069i \(-0.297336\pi\)
0.594536 + 0.804069i \(0.297336\pi\)
\(654\) −46.7374 −1.82758
\(655\) −71.6456 −2.79942
\(656\) −1.40688 −0.0549294
\(657\) 16.7876 0.654945
\(658\) −21.3077 −0.830661
\(659\) −11.4773 −0.447091 −0.223545 0.974694i \(-0.571763\pi\)
−0.223545 + 0.974694i \(0.571763\pi\)
\(660\) −35.2343 −1.37149
\(661\) −4.80840 −0.187025 −0.0935125 0.995618i \(-0.529810\pi\)
−0.0935125 + 0.995618i \(0.529810\pi\)
\(662\) −12.5326 −0.487094
\(663\) 1.82586 0.0709107
\(664\) −12.6416 −0.490588
\(665\) 64.5904 2.50471
\(666\) −7.16917 −0.277800
\(667\) −2.49518 −0.0966137
\(668\) 17.6785 0.684000
\(669\) −10.9273 −0.422473
\(670\) −44.7625 −1.72933
\(671\) −2.57004 −0.0992153
\(672\) −8.42036 −0.324823
\(673\) 39.2551 1.51317 0.756586 0.653894i \(-0.226866\pi\)
0.756586 + 0.653894i \(0.226866\pi\)
\(674\) −2.50968 −0.0966694
\(675\) −4.38276 −0.168693
\(676\) −10.2574 −0.394516
\(677\) −15.4538 −0.593937 −0.296969 0.954887i \(-0.595976\pi\)
−0.296969 + 0.954887i \(0.595976\pi\)
\(678\) 40.2750 1.54675
\(679\) −35.2386 −1.35233
\(680\) 1.39412 0.0534620
\(681\) 1.92586 0.0737990
\(682\) 33.8327 1.29552
\(683\) −24.9334 −0.954049 −0.477025 0.878890i \(-0.658285\pi\)
−0.477025 + 0.878890i \(0.658285\pi\)
\(684\) 20.2553 0.774481
\(685\) −0.548892 −0.0209721
\(686\) −9.41397 −0.359427
\(687\) −63.4676 −2.42144
\(688\) −7.88297 −0.300535
\(689\) −13.4466 −0.512273
\(690\) 7.29881 0.277861
\(691\) −16.0017 −0.608734 −0.304367 0.952555i \(-0.598445\pi\)
−0.304367 + 0.952555i \(0.598445\pi\)
\(692\) 20.7270 0.787924
\(693\) 49.0874 1.86468
\(694\) 6.29608 0.238996
\(695\) −53.6698 −2.03581
\(696\) −6.89904 −0.261508
\(697\) −0.616079 −0.0233357
\(698\) 25.6196 0.969715
\(699\) −19.1211 −0.723225
\(700\) 17.1749 0.649152
\(701\) 22.4155 0.846620 0.423310 0.905985i \(-0.360868\pi\)
0.423310 + 0.905985i \(0.360868\pi\)
\(702\) 1.41336 0.0533439
\(703\) −13.0251 −0.491252
\(704\) 4.39578 0.165672
\(705\) 51.0676 1.92332
\(706\) −2.73598 −0.102970
\(707\) 16.9888 0.638931
\(708\) 15.4057 0.578982
\(709\) 41.3395 1.55254 0.776268 0.630403i \(-0.217110\pi\)
0.776268 + 0.630403i \(0.217110\pi\)
\(710\) −12.9357 −0.485469
\(711\) 9.33060 0.349925
\(712\) 4.54074 0.170172
\(713\) −7.00846 −0.262469
\(714\) −3.68732 −0.137994
\(715\) −23.1758 −0.866728
\(716\) 13.8040 0.515881
\(717\) 2.77765 0.103733
\(718\) −27.0672 −1.01014
\(719\) 9.75775 0.363903 0.181951 0.983308i \(-0.441759\pi\)
0.181951 + 0.983308i \(0.441759\pi\)
\(720\) 10.6300 0.396157
\(721\) −7.30829 −0.272175
\(722\) 17.8003 0.662460
\(723\) −27.2561 −1.01366
\(724\) −16.0579 −0.596785
\(725\) 14.0719 0.522618
\(726\) −20.9548 −0.777704
\(727\) 17.3195 0.642345 0.321173 0.947021i \(-0.395923\pi\)
0.321173 + 0.947021i \(0.395923\pi\)
\(728\) −5.53861 −0.205275
\(729\) −32.7179 −1.21177
\(730\) 16.0065 0.592425
\(731\) −3.45199 −0.127676
\(732\) 1.47202 0.0544074
\(733\) −6.81193 −0.251604 −0.125802 0.992055i \(-0.540150\pi\)
−0.125802 + 0.992055i \(0.540150\pi\)
\(734\) −18.0955 −0.667918
\(735\) −33.5462 −1.23737
\(736\) −0.910588 −0.0335647
\(737\) −61.8059 −2.27665
\(738\) −4.69753 −0.172919
\(739\) 31.1679 1.14653 0.573266 0.819370i \(-0.305676\pi\)
0.573266 + 0.819370i \(0.305676\pi\)
\(740\) −6.83560 −0.251282
\(741\) 25.2938 0.929192
\(742\) 27.1552 0.996899
\(743\) −18.6503 −0.684212 −0.342106 0.939661i \(-0.611140\pi\)
−0.342106 + 0.939661i \(0.611140\pi\)
\(744\) −19.3780 −0.710434
\(745\) 47.3982 1.73654
\(746\) −21.7061 −0.794715
\(747\) −42.2098 −1.54438
\(748\) 1.92493 0.0703825
\(749\) −12.8882 −0.470925
\(750\) −1.08527 −0.0396285
\(751\) −29.1265 −1.06284 −0.531420 0.847108i \(-0.678341\pi\)
−0.531420 + 0.847108i \(0.678341\pi\)
\(752\) −6.37112 −0.232331
\(753\) 8.37979 0.305377
\(754\) −4.53794 −0.165262
\(755\) 70.4224 2.56293
\(756\) −2.85427 −0.103809
\(757\) −18.4932 −0.672146 −0.336073 0.941836i \(-0.609099\pi\)
−0.336073 + 0.941836i \(0.609099\pi\)
\(758\) −30.4578 −1.10628
\(759\) 10.0778 0.365802
\(760\) 19.3128 0.700551
\(761\) −6.20305 −0.224861 −0.112430 0.993660i \(-0.535863\pi\)
−0.112430 + 0.993660i \(0.535863\pi\)
\(762\) 29.6121 1.07273
\(763\) 62.0836 2.24758
\(764\) −20.7159 −0.749475
\(765\) 4.65493 0.168299
\(766\) 20.8528 0.753444
\(767\) 10.1333 0.365893
\(768\) −2.51773 −0.0908508
\(769\) 44.5042 1.60486 0.802431 0.596745i \(-0.203540\pi\)
0.802431 + 0.596745i \(0.203540\pi\)
\(770\) 46.8034 1.68668
\(771\) 11.4247 0.411450
\(772\) 26.8620 0.966786
\(773\) −9.63658 −0.346604 −0.173302 0.984869i \(-0.555444\pi\)
−0.173302 + 0.984869i \(0.555444\pi\)
\(774\) −26.3210 −0.946090
\(775\) 39.5252 1.41979
\(776\) −10.5365 −0.378239
\(777\) 18.0795 0.648599
\(778\) −27.8182 −0.997331
\(779\) −8.53460 −0.305784
\(780\) 13.2742 0.475294
\(781\) −17.8610 −0.639118
\(782\) −0.398751 −0.0142593
\(783\) −2.33859 −0.0835743
\(784\) 4.18517 0.149470
\(785\) −18.1563 −0.648026
\(786\) 56.6602 2.02100
\(787\) 6.40595 0.228347 0.114174 0.993461i \(-0.463578\pi\)
0.114174 + 0.993461i \(0.463578\pi\)
\(788\) −15.6396 −0.557136
\(789\) −31.8892 −1.13529
\(790\) 8.89646 0.316522
\(791\) −53.4992 −1.90221
\(792\) 14.6774 0.521538
\(793\) 0.968241 0.0343832
\(794\) −33.5752 −1.19154
\(795\) −65.0821 −2.30822
\(796\) −5.44692 −0.193061
\(797\) 16.3754 0.580048 0.290024 0.957019i \(-0.406337\pi\)
0.290024 + 0.957019i \(0.406337\pi\)
\(798\) −51.0807 −1.80824
\(799\) −2.78994 −0.0987010
\(800\) 5.13540 0.181564
\(801\) 15.1614 0.535702
\(802\) −19.4435 −0.686574
\(803\) 22.1009 0.779925
\(804\) 35.4000 1.24846
\(805\) −9.69536 −0.341717
\(806\) −12.7462 −0.448965
\(807\) −23.6652 −0.833055
\(808\) 5.07975 0.178705
\(809\) −43.0960 −1.51517 −0.757587 0.652735i \(-0.773622\pi\)
−0.757587 + 0.652735i \(0.773622\pi\)
\(810\) −25.0492 −0.880141
\(811\) −6.88519 −0.241772 −0.120886 0.992666i \(-0.538573\pi\)
−0.120886 + 0.992666i \(0.538573\pi\)
\(812\) 9.16433 0.321605
\(813\) −52.1963 −1.83060
\(814\) −9.43826 −0.330811
\(815\) −46.7698 −1.63827
\(816\) −1.10253 −0.0385961
\(817\) −47.8207 −1.67303
\(818\) −17.6302 −0.616426
\(819\) −18.4933 −0.646207
\(820\) −4.47896 −0.156412
\(821\) −14.5351 −0.507279 −0.253639 0.967299i \(-0.581628\pi\)
−0.253639 + 0.967299i \(0.581628\pi\)
\(822\) 0.434086 0.0151405
\(823\) −33.3012 −1.16081 −0.580404 0.814329i \(-0.697105\pi\)
−0.580404 + 0.814329i \(0.697105\pi\)
\(824\) −2.18522 −0.0761256
\(825\) −56.8354 −1.97876
\(826\) −20.4641 −0.712039
\(827\) −39.3524 −1.36842 −0.684209 0.729286i \(-0.739852\pi\)
−0.684209 + 0.729286i \(0.739852\pi\)
\(828\) −3.04043 −0.105662
\(829\) 51.4599 1.78728 0.893638 0.448788i \(-0.148144\pi\)
0.893638 + 0.448788i \(0.148144\pi\)
\(830\) −40.2458 −1.39695
\(831\) −45.6197 −1.58253
\(832\) −1.65607 −0.0574140
\(833\) 1.83271 0.0634995
\(834\) 42.4443 1.46973
\(835\) 56.2814 1.94770
\(836\) 26.6662 0.922271
\(837\) −6.56863 −0.227045
\(838\) 11.1342 0.384624
\(839\) −39.7819 −1.37343 −0.686713 0.726929i \(-0.740947\pi\)
−0.686713 + 0.726929i \(0.740947\pi\)
\(840\) −26.8072 −0.924936
\(841\) −21.4914 −0.741083
\(842\) −7.21336 −0.248589
\(843\) −17.3145 −0.596342
\(844\) 12.1769 0.419145
\(845\) −32.6557 −1.12339
\(846\) −21.2730 −0.731380
\(847\) 27.8352 0.956429
\(848\) 8.11955 0.278826
\(849\) −0.319325 −0.0109592
\(850\) 2.24881 0.0771337
\(851\) 1.95514 0.0670214
\(852\) 10.2301 0.350478
\(853\) 31.4934 1.07831 0.539157 0.842205i \(-0.318743\pi\)
0.539157 + 0.842205i \(0.318743\pi\)
\(854\) −1.95535 −0.0669108
\(855\) 64.4851 2.20534
\(856\) −3.85364 −0.131715
\(857\) −10.0814 −0.344373 −0.172187 0.985064i \(-0.555083\pi\)
−0.172187 + 0.985064i \(0.555083\pi\)
\(858\) 18.3284 0.625721
\(859\) −14.2783 −0.487171 −0.243585 0.969879i \(-0.578324\pi\)
−0.243585 + 0.969879i \(0.578324\pi\)
\(860\) −25.0963 −0.855778
\(861\) 11.8464 0.403726
\(862\) −3.95857 −0.134830
\(863\) −36.5707 −1.24488 −0.622441 0.782667i \(-0.713859\pi\)
−0.622441 + 0.782667i \(0.713859\pi\)
\(864\) −0.853442 −0.0290347
\(865\) 65.9869 2.24362
\(866\) −4.67256 −0.158780
\(867\) 42.3186 1.43722
\(868\) 25.7408 0.873699
\(869\) 12.2838 0.416699
\(870\) −21.9639 −0.744645
\(871\) 23.2849 0.788978
\(872\) 18.5633 0.628633
\(873\) −35.1812 −1.19070
\(874\) −5.52393 −0.186850
\(875\) 1.44162 0.0487356
\(876\) −12.6586 −0.427693
\(877\) −27.5853 −0.931489 −0.465745 0.884919i \(-0.654213\pi\)
−0.465745 + 0.884919i \(0.654213\pi\)
\(878\) 2.05782 0.0694481
\(879\) −60.9090 −2.05441
\(880\) 13.9945 0.471753
\(881\) 20.8586 0.702744 0.351372 0.936236i \(-0.385715\pi\)
0.351372 + 0.936236i \(0.385715\pi\)
\(882\) 13.9742 0.470535
\(883\) 26.4272 0.889346 0.444673 0.895693i \(-0.353320\pi\)
0.444673 + 0.895693i \(0.353320\pi\)
\(884\) −0.725202 −0.0243912
\(885\) 49.0458 1.64866
\(886\) −6.66947 −0.224065
\(887\) 23.1562 0.777509 0.388755 0.921341i \(-0.372905\pi\)
0.388755 + 0.921341i \(0.372905\pi\)
\(888\) 5.40587 0.181409
\(889\) −39.3352 −1.31926
\(890\) 14.4560 0.484565
\(891\) −34.5868 −1.15870
\(892\) 4.34013 0.145318
\(893\) −38.6493 −1.29335
\(894\) −37.4844 −1.25367
\(895\) 43.9467 1.46898
\(896\) 3.34442 0.111729
\(897\) −3.79674 −0.126769
\(898\) −5.68669 −0.189767
\(899\) 21.0902 0.703396
\(900\) 17.1469 0.571565
\(901\) 3.55559 0.118454
\(902\) −6.18433 −0.205916
\(903\) 66.3775 2.20890
\(904\) −15.9965 −0.532037
\(905\) −51.1220 −1.69935
\(906\) −55.6929 −1.85027
\(907\) 46.3026 1.53745 0.768726 0.639578i \(-0.220891\pi\)
0.768726 + 0.639578i \(0.220891\pi\)
\(908\) −0.764918 −0.0253847
\(909\) 16.9612 0.562566
\(910\) −17.6328 −0.584521
\(911\) −0.461564 −0.0152923 −0.00764615 0.999971i \(-0.502434\pi\)
−0.00764615 + 0.999971i \(0.502434\pi\)
\(912\) −15.2734 −0.505752
\(913\) −55.5695 −1.83908
\(914\) 1.91582 0.0633698
\(915\) 4.68634 0.154926
\(916\) 25.2083 0.832904
\(917\) −75.2645 −2.48545
\(918\) −0.373726 −0.0123348
\(919\) −8.18435 −0.269977 −0.134988 0.990847i \(-0.543100\pi\)
−0.134988 + 0.990847i \(0.543100\pi\)
\(920\) −2.89896 −0.0955760
\(921\) −8.74615 −0.288195
\(922\) −5.00120 −0.164706
\(923\) 6.72899 0.221487
\(924\) −37.0141 −1.21767
\(925\) −11.0263 −0.362543
\(926\) −7.48957 −0.246123
\(927\) −7.29637 −0.239644
\(928\) 2.74018 0.0899509
\(929\) 25.7043 0.843331 0.421665 0.906751i \(-0.361446\pi\)
0.421665 + 0.906751i \(0.361446\pi\)
\(930\) −61.6922 −2.02297
\(931\) 25.3886 0.832079
\(932\) 7.59456 0.248768
\(933\) −25.4726 −0.833937
\(934\) −6.23078 −0.203877
\(935\) 6.12824 0.200415
\(936\) −5.52958 −0.180740
\(937\) 4.17527 0.136400 0.0682000 0.997672i \(-0.478274\pi\)
0.0682000 + 0.997672i \(0.478274\pi\)
\(938\) −47.0236 −1.53537
\(939\) 7.95694 0.259665
\(940\) −20.2832 −0.661564
\(941\) −37.3633 −1.21801 −0.609004 0.793167i \(-0.708431\pi\)
−0.609004 + 0.793167i \(0.708431\pi\)
\(942\) 14.3587 0.467833
\(943\) 1.28109 0.0417180
\(944\) −6.11888 −0.199153
\(945\) −9.08690 −0.295597
\(946\) −34.6518 −1.12663
\(947\) −11.6440 −0.378380 −0.189190 0.981941i \(-0.560586\pi\)
−0.189190 + 0.981941i \(0.560586\pi\)
\(948\) −7.03568 −0.228508
\(949\) −8.32634 −0.270284
\(950\) 31.1530 1.01074
\(951\) −41.8724 −1.35781
\(952\) 1.46454 0.0474660
\(953\) −2.35260 −0.0762083 −0.0381042 0.999274i \(-0.512132\pi\)
−0.0381042 + 0.999274i \(0.512132\pi\)
\(954\) 27.1109 0.877749
\(955\) −65.9515 −2.13414
\(956\) −1.10323 −0.0356811
\(957\) −30.3267 −0.980322
\(958\) −5.99882 −0.193813
\(959\) −0.576618 −0.0186200
\(960\) −8.01549 −0.258699
\(961\) 28.2381 0.910906
\(962\) 3.55578 0.114643
\(963\) −12.8672 −0.414640
\(964\) 10.8256 0.348671
\(965\) 85.5183 2.75293
\(966\) 7.66749 0.246697
\(967\) −40.8516 −1.31370 −0.656849 0.754022i \(-0.728111\pi\)
−0.656849 + 0.754022i \(0.728111\pi\)
\(968\) 8.32287 0.267507
\(969\) −6.68829 −0.214859
\(970\) −33.5442 −1.07704
\(971\) 32.9014 1.05586 0.527928 0.849289i \(-0.322969\pi\)
0.527928 + 0.849289i \(0.322969\pi\)
\(972\) 22.3703 0.717527
\(973\) −56.3808 −1.80749
\(974\) −27.6837 −0.887042
\(975\) 21.4123 0.685742
\(976\) −0.584661 −0.0187145
\(977\) −46.5290 −1.48859 −0.744297 0.667848i \(-0.767215\pi\)
−0.744297 + 0.667848i \(0.767215\pi\)
\(978\) 36.9875 1.18273
\(979\) 19.9601 0.637928
\(980\) 13.3240 0.425619
\(981\) 61.9824 1.97895
\(982\) −31.2593 −0.997523
\(983\) −29.7410 −0.948592 −0.474296 0.880365i \(-0.657297\pi\)
−0.474296 + 0.880365i \(0.657297\pi\)
\(984\) 3.54215 0.112919
\(985\) −49.7903 −1.58645
\(986\) 1.19994 0.0382138
\(987\) 53.6471 1.70761
\(988\) −10.0463 −0.319615
\(989\) 7.17814 0.228252
\(990\) 46.7271 1.48509
\(991\) 35.3249 1.12213 0.561066 0.827771i \(-0.310391\pi\)
0.561066 + 0.827771i \(0.310391\pi\)
\(992\) 7.69663 0.244368
\(993\) 31.5538 1.00133
\(994\) −13.5891 −0.431021
\(995\) −17.3409 −0.549743
\(996\) 31.8281 1.00851
\(997\) −14.2769 −0.452153 −0.226077 0.974110i \(-0.572590\pi\)
−0.226077 + 0.974110i \(0.572590\pi\)
\(998\) 17.8189 0.564047
\(999\) 1.83244 0.0579759
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 4034.2.a.d.1.7 52
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4034.2.a.d.1.7 52 1.1 even 1 trivial