Properties

Label 4027.2.a.c.1.2
Level 4027
Weight 2
Character 4027.1
Self dual yes
Analytic conductor 32.156
Analytic rank 0
Dimension 174
CM no
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 4027 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4027.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.1557568940\)
Analytic rank: \(0\)
Dimension: \(174\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) = 4027.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.72607 q^{2} -2.28516 q^{3} +5.43147 q^{4} +2.07141 q^{5} +6.22952 q^{6} -3.86589 q^{7} -9.35442 q^{8} +2.22198 q^{9} +O(q^{10})\) \(q-2.72607 q^{2} -2.28516 q^{3} +5.43147 q^{4} +2.07141 q^{5} +6.22952 q^{6} -3.86589 q^{7} -9.35442 q^{8} +2.22198 q^{9} -5.64680 q^{10} -6.14227 q^{11} -12.4118 q^{12} +3.18989 q^{13} +10.5387 q^{14} -4.73350 q^{15} +14.6379 q^{16} +6.05605 q^{17} -6.05727 q^{18} +0.757799 q^{19} +11.2508 q^{20} +8.83419 q^{21} +16.7443 q^{22} +7.32285 q^{23} +21.3764 q^{24} -0.709281 q^{25} -8.69587 q^{26} +1.77791 q^{27} -20.9974 q^{28} -9.79643 q^{29} +12.9039 q^{30} -5.39248 q^{31} -21.1951 q^{32} +14.0361 q^{33} -16.5092 q^{34} -8.00782 q^{35} +12.0686 q^{36} +3.62339 q^{37} -2.06581 q^{38} -7.28943 q^{39} -19.3768 q^{40} +9.52390 q^{41} -24.0826 q^{42} -12.9396 q^{43} -33.3615 q^{44} +4.60262 q^{45} -19.9626 q^{46} +4.38641 q^{47} -33.4500 q^{48} +7.94507 q^{49} +1.93355 q^{50} -13.8391 q^{51} +17.3258 q^{52} +4.51083 q^{53} -4.84670 q^{54} -12.7231 q^{55} +36.1631 q^{56} -1.73169 q^{57} +26.7058 q^{58} -3.57226 q^{59} -25.7099 q^{60} +6.45296 q^{61} +14.7003 q^{62} -8.58991 q^{63} +28.5036 q^{64} +6.60756 q^{65} -38.2634 q^{66} -11.1385 q^{67} +32.8933 q^{68} -16.7339 q^{69} +21.8299 q^{70} -11.9182 q^{71} -20.7853 q^{72} -1.29003 q^{73} -9.87762 q^{74} +1.62082 q^{75} +4.11596 q^{76} +23.7453 q^{77} +19.8715 q^{78} +0.820910 q^{79} +30.3210 q^{80} -10.7287 q^{81} -25.9628 q^{82} +2.94992 q^{83} +47.9826 q^{84} +12.5445 q^{85} +35.2742 q^{86} +22.3865 q^{87} +57.4574 q^{88} -17.1833 q^{89} -12.5471 q^{90} -12.3318 q^{91} +39.7738 q^{92} +12.3227 q^{93} -11.9577 q^{94} +1.56971 q^{95} +48.4343 q^{96} -17.2215 q^{97} -21.6588 q^{98} -13.6480 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 174q + 21q^{2} + 17q^{3} + 187q^{4} + 72q^{5} + 21q^{6} + 24q^{7} + 54q^{8} + 197q^{9} + O(q^{10}) \) \( 174q + 21q^{2} + 17q^{3} + 187q^{4} + 72q^{5} + 21q^{6} + 24q^{7} + 54q^{8} + 197q^{9} + 20q^{10} + 35q^{11} + 23q^{12} + 91q^{13} + 18q^{14} + 16q^{15} + 201q^{16} + 148q^{17} + 39q^{18} + 36q^{19} + 128q^{20} + 57q^{21} + 17q^{22} + 96q^{23} + 24q^{24} + 226q^{25} + 44q^{26} + 62q^{27} + 32q^{28} + 122q^{29} + 25q^{30} + 23q^{31} + 104q^{32} + 91q^{33} + 6q^{34} + 80q^{35} + 222q^{36} + 71q^{37} + 125q^{38} + 16q^{39} + 53q^{40} + 97q^{41} + 14q^{42} + 38q^{43} + 70q^{44} + 185q^{45} - 23q^{46} + 110q^{47} + 36q^{48} + 210q^{49} + 51q^{50} + 33q^{51} + 118q^{52} + 214q^{53} + 8q^{54} + 37q^{55} + 41q^{56} + 76q^{57} + 2q^{58} + 66q^{59} - 12q^{60} + 114q^{61} + 175q^{62} + 62q^{63} + 190q^{64} + 128q^{65} + 12q^{66} - 6q^{67} + 348q^{68} + 115q^{69} - 38q^{70} + 54q^{71} + 101q^{72} + 107q^{73} + 71q^{74} - q^{75} + 31q^{76} + 368q^{77} - 14q^{78} - 14q^{79} + 205q^{80} + 222q^{81} + 26q^{82} + 246q^{83} + 41q^{84} + 87q^{85} + 33q^{86} + 100q^{87} - 6q^{88} + 147q^{89} + 50q^{90} - 23q^{91} + 189q^{92} + 117q^{93} + 23q^{94} + 42q^{95} + 38q^{96} + 52q^{97} + 148q^{98} + 38q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.72607 −1.92762 −0.963812 0.266583i \(-0.914105\pi\)
−0.963812 + 0.266583i \(0.914105\pi\)
\(3\) −2.28516 −1.31934 −0.659670 0.751555i \(-0.729304\pi\)
−0.659670 + 0.751555i \(0.729304\pi\)
\(4\) 5.43147 2.71573
\(5\) 2.07141 0.926361 0.463180 0.886264i \(-0.346708\pi\)
0.463180 + 0.886264i \(0.346708\pi\)
\(6\) 6.22952 2.54319
\(7\) −3.86589 −1.46117 −0.730584 0.682823i \(-0.760752\pi\)
−0.730584 + 0.682823i \(0.760752\pi\)
\(8\) −9.35442 −3.30729
\(9\) 2.22198 0.740659
\(10\) −5.64680 −1.78567
\(11\) −6.14227 −1.85196 −0.925982 0.377567i \(-0.876761\pi\)
−0.925982 + 0.377567i \(0.876761\pi\)
\(12\) −12.4118 −3.58298
\(13\) 3.18989 0.884717 0.442358 0.896838i \(-0.354142\pi\)
0.442358 + 0.896838i \(0.354142\pi\)
\(14\) 10.5387 2.81658
\(15\) −4.73350 −1.22219
\(16\) 14.6379 3.65947
\(17\) 6.05605 1.46881 0.734404 0.678712i \(-0.237462\pi\)
0.734404 + 0.678712i \(0.237462\pi\)
\(18\) −6.05727 −1.42771
\(19\) 0.757799 0.173851 0.0869255 0.996215i \(-0.472296\pi\)
0.0869255 + 0.996215i \(0.472296\pi\)
\(20\) 11.2508 2.51575
\(21\) 8.83419 1.92778
\(22\) 16.7443 3.56989
\(23\) 7.32285 1.52692 0.763460 0.645855i \(-0.223499\pi\)
0.763460 + 0.645855i \(0.223499\pi\)
\(24\) 21.3764 4.36344
\(25\) −0.709281 −0.141856
\(26\) −8.69587 −1.70540
\(27\) 1.77791 0.342158
\(28\) −20.9974 −3.96814
\(29\) −9.79643 −1.81915 −0.909576 0.415538i \(-0.863593\pi\)
−0.909576 + 0.415538i \(0.863593\pi\)
\(30\) 12.9039 2.35591
\(31\) −5.39248 −0.968517 −0.484259 0.874925i \(-0.660911\pi\)
−0.484259 + 0.874925i \(0.660911\pi\)
\(32\) −21.1951 −3.74680
\(33\) 14.0361 2.44337
\(34\) −16.5092 −2.83131
\(35\) −8.00782 −1.35357
\(36\) 12.0686 2.01143
\(37\) 3.62339 0.595682 0.297841 0.954616i \(-0.403734\pi\)
0.297841 + 0.954616i \(0.403734\pi\)
\(38\) −2.06581 −0.335119
\(39\) −7.28943 −1.16724
\(40\) −19.3768 −3.06374
\(41\) 9.52390 1.48738 0.743691 0.668523i \(-0.233073\pi\)
0.743691 + 0.668523i \(0.233073\pi\)
\(42\) −24.0826 −3.71603
\(43\) −12.9396 −1.97327 −0.986634 0.162954i \(-0.947898\pi\)
−0.986634 + 0.162954i \(0.947898\pi\)
\(44\) −33.3615 −5.02944
\(45\) 4.60262 0.686118
\(46\) −19.9626 −2.94333
\(47\) 4.38641 0.639823 0.319912 0.947447i \(-0.396347\pi\)
0.319912 + 0.947447i \(0.396347\pi\)
\(48\) −33.4500 −4.82809
\(49\) 7.94507 1.13501
\(50\) 1.93355 0.273445
\(51\) −13.8391 −1.93786
\(52\) 17.3258 2.40265
\(53\) 4.51083 0.619611 0.309805 0.950800i \(-0.399736\pi\)
0.309805 + 0.950800i \(0.399736\pi\)
\(54\) −4.84670 −0.659553
\(55\) −12.7231 −1.71559
\(56\) 36.1631 4.83250
\(57\) −1.73169 −0.229369
\(58\) 26.7058 3.50664
\(59\) −3.57226 −0.465069 −0.232535 0.972588i \(-0.574702\pi\)
−0.232535 + 0.972588i \(0.574702\pi\)
\(60\) −25.7099 −3.31913
\(61\) 6.45296 0.826217 0.413109 0.910682i \(-0.364443\pi\)
0.413109 + 0.910682i \(0.364443\pi\)
\(62\) 14.7003 1.86694
\(63\) −8.58991 −1.08223
\(64\) 28.5036 3.56295
\(65\) 6.60756 0.819567
\(66\) −38.2634 −4.70990
\(67\) −11.1385 −1.36079 −0.680395 0.732846i \(-0.738192\pi\)
−0.680395 + 0.732846i \(0.738192\pi\)
\(68\) 32.8933 3.98889
\(69\) −16.7339 −2.01453
\(70\) 21.8299 2.60917
\(71\) −11.9182 −1.41443 −0.707217 0.706996i \(-0.750050\pi\)
−0.707217 + 0.706996i \(0.750050\pi\)
\(72\) −20.7853 −2.44957
\(73\) −1.29003 −0.150986 −0.0754931 0.997146i \(-0.524053\pi\)
−0.0754931 + 0.997146i \(0.524053\pi\)
\(74\) −9.87762 −1.14825
\(75\) 1.62082 0.187157
\(76\) 4.11596 0.472133
\(77\) 23.7453 2.70603
\(78\) 19.8715 2.25000
\(79\) 0.820910 0.0923596 0.0461798 0.998933i \(-0.485295\pi\)
0.0461798 + 0.998933i \(0.485295\pi\)
\(80\) 30.3210 3.38999
\(81\) −10.7287 −1.19208
\(82\) −25.9628 −2.86711
\(83\) 2.94992 0.323796 0.161898 0.986807i \(-0.448238\pi\)
0.161898 + 0.986807i \(0.448238\pi\)
\(84\) 47.9826 5.23533
\(85\) 12.5445 1.36065
\(86\) 35.2742 3.80372
\(87\) 22.3865 2.40008
\(88\) 57.4574 6.12498
\(89\) −17.1833 −1.82142 −0.910712 0.413041i \(-0.864467\pi\)
−0.910712 + 0.413041i \(0.864467\pi\)
\(90\) −12.5471 −1.32258
\(91\) −12.3318 −1.29272
\(92\) 39.7738 4.14671
\(93\) 12.3227 1.27780
\(94\) −11.9577 −1.23334
\(95\) 1.56971 0.161049
\(96\) 48.4343 4.94330
\(97\) −17.2215 −1.74857 −0.874287 0.485409i \(-0.838671\pi\)
−0.874287 + 0.485409i \(0.838671\pi\)
\(98\) −21.6588 −2.18787
\(99\) −13.6480 −1.37167
\(100\) −3.85243 −0.385243
\(101\) 10.5025 1.04504 0.522520 0.852627i \(-0.324992\pi\)
0.522520 + 0.852627i \(0.324992\pi\)
\(102\) 37.7263 3.73546
\(103\) 3.98854 0.393002 0.196501 0.980504i \(-0.437042\pi\)
0.196501 + 0.980504i \(0.437042\pi\)
\(104\) −29.8396 −2.92601
\(105\) 18.2992 1.78582
\(106\) −12.2969 −1.19438
\(107\) 17.1240 1.65544 0.827719 0.561143i \(-0.189638\pi\)
0.827719 + 0.561143i \(0.189638\pi\)
\(108\) 9.65665 0.929211
\(109\) −8.22514 −0.787826 −0.393913 0.919148i \(-0.628879\pi\)
−0.393913 + 0.919148i \(0.628879\pi\)
\(110\) 34.6842 3.30701
\(111\) −8.28004 −0.785907
\(112\) −56.5884 −5.34710
\(113\) −2.46347 −0.231744 −0.115872 0.993264i \(-0.536966\pi\)
−0.115872 + 0.993264i \(0.536966\pi\)
\(114\) 4.72072 0.442136
\(115\) 15.1686 1.41448
\(116\) −53.2090 −4.94033
\(117\) 7.08787 0.655274
\(118\) 9.73825 0.896478
\(119\) −23.4120 −2.14618
\(120\) 44.2792 4.04212
\(121\) 26.7275 2.42977
\(122\) −17.5912 −1.59264
\(123\) −21.7637 −1.96236
\(124\) −29.2891 −2.63023
\(125\) −11.8262 −1.05777
\(126\) 23.4167 2.08613
\(127\) 6.82351 0.605489 0.302744 0.953072i \(-0.402097\pi\)
0.302744 + 0.953072i \(0.402097\pi\)
\(128\) −35.3126 −3.12122
\(129\) 29.5691 2.60341
\(130\) −18.0127 −1.57982
\(131\) 1.49699 0.130792 0.0653961 0.997859i \(-0.479169\pi\)
0.0653961 + 0.997859i \(0.479169\pi\)
\(132\) 76.2366 6.63555
\(133\) −2.92956 −0.254025
\(134\) 30.3645 2.62309
\(135\) 3.68277 0.316962
\(136\) −56.6509 −4.85777
\(137\) 4.34202 0.370964 0.185482 0.982648i \(-0.440615\pi\)
0.185482 + 0.982648i \(0.440615\pi\)
\(138\) 45.6179 3.88325
\(139\) −1.39765 −0.118547 −0.0592735 0.998242i \(-0.518878\pi\)
−0.0592735 + 0.998242i \(0.518878\pi\)
\(140\) −43.4942 −3.67593
\(141\) −10.0237 −0.844145
\(142\) 32.4900 2.72650
\(143\) −19.5932 −1.63846
\(144\) 32.5251 2.71042
\(145\) −20.2924 −1.68519
\(146\) 3.51670 0.291045
\(147\) −18.1558 −1.49746
\(148\) 19.6803 1.61771
\(149\) −1.19151 −0.0976121 −0.0488060 0.998808i \(-0.515542\pi\)
−0.0488060 + 0.998808i \(0.515542\pi\)
\(150\) −4.41848 −0.360767
\(151\) −0.814696 −0.0662990 −0.0331495 0.999450i \(-0.510554\pi\)
−0.0331495 + 0.999450i \(0.510554\pi\)
\(152\) −7.08877 −0.574975
\(153\) 13.4564 1.08789
\(154\) −64.7314 −5.21621
\(155\) −11.1700 −0.897196
\(156\) −39.5923 −3.16992
\(157\) −13.8336 −1.10404 −0.552020 0.833831i \(-0.686143\pi\)
−0.552020 + 0.833831i \(0.686143\pi\)
\(158\) −2.23786 −0.178035
\(159\) −10.3080 −0.817477
\(160\) −43.9036 −3.47089
\(161\) −28.3093 −2.23109
\(162\) 29.2473 2.29789
\(163\) 0.666862 0.0522327 0.0261163 0.999659i \(-0.491686\pi\)
0.0261163 + 0.999659i \(0.491686\pi\)
\(164\) 51.7287 4.03933
\(165\) 29.0745 2.26344
\(166\) −8.04170 −0.624157
\(167\) −8.40688 −0.650544 −0.325272 0.945620i \(-0.605456\pi\)
−0.325272 + 0.945620i \(0.605456\pi\)
\(168\) −82.6387 −6.37571
\(169\) −2.82459 −0.217276
\(170\) −34.1973 −2.62281
\(171\) 1.68381 0.128764
\(172\) −70.2809 −5.35887
\(173\) 7.04223 0.535411 0.267705 0.963501i \(-0.413735\pi\)
0.267705 + 0.963501i \(0.413735\pi\)
\(174\) −61.0271 −4.62645
\(175\) 2.74200 0.207276
\(176\) −89.9099 −6.77721
\(177\) 8.16321 0.613585
\(178\) 46.8429 3.51102
\(179\) 17.2678 1.29065 0.645327 0.763907i \(-0.276721\pi\)
0.645327 + 0.763907i \(0.276721\pi\)
\(180\) 24.9990 1.86331
\(181\) −14.2990 −1.06284 −0.531419 0.847109i \(-0.678341\pi\)
−0.531419 + 0.847109i \(0.678341\pi\)
\(182\) 33.6172 2.49188
\(183\) −14.7461 −1.09006
\(184\) −68.5010 −5.04996
\(185\) 7.50551 0.551816
\(186\) −33.5926 −2.46313
\(187\) −37.1979 −2.72018
\(188\) 23.8246 1.73759
\(189\) −6.87319 −0.499951
\(190\) −4.27914 −0.310441
\(191\) −10.1148 −0.731881 −0.365941 0.930638i \(-0.619253\pi\)
−0.365941 + 0.930638i \(0.619253\pi\)
\(192\) −65.1354 −4.70074
\(193\) −0.585380 −0.0421366 −0.0210683 0.999778i \(-0.506707\pi\)
−0.0210683 + 0.999778i \(0.506707\pi\)
\(194\) 46.9469 3.37059
\(195\) −15.0994 −1.08129
\(196\) 43.1534 3.08238
\(197\) 7.04891 0.502214 0.251107 0.967959i \(-0.419205\pi\)
0.251107 + 0.967959i \(0.419205\pi\)
\(198\) 37.2054 2.64407
\(199\) 1.25169 0.0887299 0.0443649 0.999015i \(-0.485874\pi\)
0.0443649 + 0.999015i \(0.485874\pi\)
\(200\) 6.63491 0.469159
\(201\) 25.4534 1.79535
\(202\) −28.6306 −2.01444
\(203\) 37.8719 2.65808
\(204\) −75.1665 −5.26271
\(205\) 19.7278 1.37785
\(206\) −10.8730 −0.757560
\(207\) 16.2712 1.13093
\(208\) 46.6933 3.23760
\(209\) −4.65460 −0.321966
\(210\) −49.8849 −3.44238
\(211\) 21.8109 1.50153 0.750763 0.660572i \(-0.229686\pi\)
0.750763 + 0.660572i \(0.229686\pi\)
\(212\) 24.5004 1.68270
\(213\) 27.2351 1.86612
\(214\) −46.6812 −3.19106
\(215\) −26.8031 −1.82796
\(216\) −16.6313 −1.13162
\(217\) 20.8467 1.41517
\(218\) 22.4223 1.51863
\(219\) 2.94792 0.199202
\(220\) −69.1053 −4.65908
\(221\) 19.3182 1.29948
\(222\) 22.5720 1.51493
\(223\) 2.05986 0.137938 0.0689691 0.997619i \(-0.478029\pi\)
0.0689691 + 0.997619i \(0.478029\pi\)
\(224\) 81.9378 5.47470
\(225\) −1.57601 −0.105067
\(226\) 6.71560 0.446715
\(227\) 18.5597 1.23185 0.615925 0.787805i \(-0.288783\pi\)
0.615925 + 0.787805i \(0.288783\pi\)
\(228\) −9.40564 −0.622904
\(229\) −9.21881 −0.609196 −0.304598 0.952481i \(-0.598522\pi\)
−0.304598 + 0.952481i \(0.598522\pi\)
\(230\) −41.3507 −2.72658
\(231\) −54.2620 −3.57017
\(232\) 91.6399 6.01646
\(233\) −10.1405 −0.664326 −0.332163 0.943222i \(-0.607778\pi\)
−0.332163 + 0.943222i \(0.607778\pi\)
\(234\) −19.3220 −1.26312
\(235\) 9.08602 0.592707
\(236\) −19.4026 −1.26300
\(237\) −1.87592 −0.121854
\(238\) 63.8228 4.13702
\(239\) 9.08903 0.587920 0.293960 0.955818i \(-0.405027\pi\)
0.293960 + 0.955818i \(0.405027\pi\)
\(240\) −69.2885 −4.47255
\(241\) −3.46533 −0.223222 −0.111611 0.993752i \(-0.535601\pi\)
−0.111611 + 0.993752i \(0.535601\pi\)
\(242\) −72.8610 −4.68369
\(243\) 19.1832 1.23060
\(244\) 35.0490 2.24379
\(245\) 16.4575 1.05143
\(246\) 59.3293 3.78270
\(247\) 2.41730 0.153809
\(248\) 50.4435 3.20317
\(249\) −6.74106 −0.427197
\(250\) 32.2392 2.03898
\(251\) 16.6526 1.05110 0.525552 0.850761i \(-0.323859\pi\)
0.525552 + 0.850761i \(0.323859\pi\)
\(252\) −46.6558 −2.93904
\(253\) −44.9789 −2.82780
\(254\) −18.6014 −1.16715
\(255\) −28.6663 −1.79516
\(256\) 39.2575 2.45359
\(257\) −3.01780 −0.188245 −0.0941226 0.995561i \(-0.530005\pi\)
−0.0941226 + 0.995561i \(0.530005\pi\)
\(258\) −80.6074 −5.01840
\(259\) −14.0076 −0.870391
\(260\) 35.8887 2.22572
\(261\) −21.7675 −1.34737
\(262\) −4.08089 −0.252118
\(263\) −2.67198 −0.164762 −0.0823808 0.996601i \(-0.526252\pi\)
−0.0823808 + 0.996601i \(0.526252\pi\)
\(264\) −131.300 −8.08093
\(265\) 9.34376 0.573983
\(266\) 7.98620 0.489665
\(267\) 39.2666 2.40308
\(268\) −60.4986 −3.69554
\(269\) 24.2020 1.47562 0.737811 0.675008i \(-0.235860\pi\)
0.737811 + 0.675008i \(0.235860\pi\)
\(270\) −10.0395 −0.610984
\(271\) −22.2819 −1.35353 −0.676764 0.736200i \(-0.736618\pi\)
−0.676764 + 0.736200i \(0.736618\pi\)
\(272\) 88.6479 5.37507
\(273\) 28.1801 1.70554
\(274\) −11.8367 −0.715079
\(275\) 4.35659 0.262712
\(276\) −90.8897 −5.47092
\(277\) 6.64264 0.399118 0.199559 0.979886i \(-0.436049\pi\)
0.199559 + 0.979886i \(0.436049\pi\)
\(278\) 3.81009 0.228514
\(279\) −11.9820 −0.717341
\(280\) 74.9085 4.47664
\(281\) −22.5868 −1.34742 −0.673709 0.738997i \(-0.735300\pi\)
−0.673709 + 0.738997i \(0.735300\pi\)
\(282\) 27.3252 1.62719
\(283\) 28.3625 1.68598 0.842988 0.537932i \(-0.180794\pi\)
0.842988 + 0.537932i \(0.180794\pi\)
\(284\) −64.7335 −3.84123
\(285\) −3.58704 −0.212478
\(286\) 53.4124 3.15834
\(287\) −36.8183 −2.17331
\(288\) −47.0951 −2.77510
\(289\) 19.6758 1.15740
\(290\) 55.3185 3.24841
\(291\) 39.3539 2.30697
\(292\) −7.00673 −0.410038
\(293\) −9.03494 −0.527827 −0.263913 0.964546i \(-0.585013\pi\)
−0.263913 + 0.964546i \(0.585013\pi\)
\(294\) 49.4940 2.88655
\(295\) −7.39961 −0.430822
\(296\) −33.8947 −1.97009
\(297\) −10.9204 −0.633665
\(298\) 3.24813 0.188159
\(299\) 23.3591 1.35089
\(300\) 8.80344 0.508267
\(301\) 50.0229 2.88327
\(302\) 2.22092 0.127800
\(303\) −24.0000 −1.37876
\(304\) 11.0926 0.636203
\(305\) 13.3667 0.765375
\(306\) −36.6832 −2.09704
\(307\) 15.2929 0.872809 0.436405 0.899750i \(-0.356252\pi\)
0.436405 + 0.899750i \(0.356252\pi\)
\(308\) 128.972 7.34885
\(309\) −9.11446 −0.518504
\(310\) 30.4502 1.72946
\(311\) −24.7082 −1.40108 −0.700538 0.713615i \(-0.747057\pi\)
−0.700538 + 0.713615i \(0.747057\pi\)
\(312\) 68.1884 3.86041
\(313\) −19.5869 −1.10712 −0.553558 0.832811i \(-0.686730\pi\)
−0.553558 + 0.832811i \(0.686730\pi\)
\(314\) 37.7113 2.12817
\(315\) −17.7932 −1.00253
\(316\) 4.45875 0.250824
\(317\) −9.19818 −0.516621 −0.258311 0.966062i \(-0.583166\pi\)
−0.258311 + 0.966062i \(0.583166\pi\)
\(318\) 28.1003 1.57579
\(319\) 60.1723 3.36900
\(320\) 59.0424 3.30057
\(321\) −39.1311 −2.18409
\(322\) 77.1732 4.30069
\(323\) 4.58927 0.255354
\(324\) −58.2728 −3.23738
\(325\) −2.26253 −0.125502
\(326\) −1.81791 −0.100685
\(327\) 18.7958 1.03941
\(328\) −89.0905 −4.91920
\(329\) −16.9573 −0.934889
\(330\) −79.2590 −4.36307
\(331\) 1.61729 0.0888941 0.0444471 0.999012i \(-0.485847\pi\)
0.0444471 + 0.999012i \(0.485847\pi\)
\(332\) 16.0224 0.879344
\(333\) 8.05109 0.441197
\(334\) 22.9178 1.25400
\(335\) −23.0724 −1.26058
\(336\) 129.314 7.05465
\(337\) −1.76799 −0.0963084 −0.0481542 0.998840i \(-0.515334\pi\)
−0.0481542 + 0.998840i \(0.515334\pi\)
\(338\) 7.70004 0.418827
\(339\) 5.62944 0.305749
\(340\) 68.1353 3.69515
\(341\) 33.1220 1.79366
\(342\) −4.59019 −0.248209
\(343\) −3.65354 −0.197272
\(344\) 121.042 6.52616
\(345\) −34.6627 −1.86618
\(346\) −19.1976 −1.03207
\(347\) −2.65348 −0.142446 −0.0712231 0.997460i \(-0.522690\pi\)
−0.0712231 + 0.997460i \(0.522690\pi\)
\(348\) 121.591 6.51798
\(349\) 18.2086 0.974682 0.487341 0.873212i \(-0.337967\pi\)
0.487341 + 0.873212i \(0.337967\pi\)
\(350\) −7.47488 −0.399549
\(351\) 5.67133 0.302713
\(352\) 130.186 6.93894
\(353\) 16.7903 0.893658 0.446829 0.894619i \(-0.352553\pi\)
0.446829 + 0.894619i \(0.352553\pi\)
\(354\) −22.2535 −1.18276
\(355\) −24.6875 −1.31028
\(356\) −93.3304 −4.94650
\(357\) 53.5003 2.83154
\(358\) −47.0732 −2.48789
\(359\) 24.5247 1.29437 0.647183 0.762335i \(-0.275947\pi\)
0.647183 + 0.762335i \(0.275947\pi\)
\(360\) −43.0548 −2.26919
\(361\) −18.4257 −0.969776
\(362\) 38.9802 2.04875
\(363\) −61.0767 −3.20570
\(364\) −66.9795 −3.51068
\(365\) −2.67217 −0.139868
\(366\) 40.1989 2.10123
\(367\) −2.94049 −0.153493 −0.0767463 0.997051i \(-0.524453\pi\)
−0.0767463 + 0.997051i \(0.524453\pi\)
\(368\) 107.191 5.58772
\(369\) 21.1619 1.10164
\(370\) −20.4606 −1.06369
\(371\) −17.4384 −0.905355
\(372\) 66.9303 3.47017
\(373\) 5.86834 0.303851 0.151926 0.988392i \(-0.451453\pi\)
0.151926 + 0.988392i \(0.451453\pi\)
\(374\) 101.404 5.24349
\(375\) 27.0249 1.39556
\(376\) −41.0323 −2.11608
\(377\) −31.2495 −1.60943
\(378\) 18.7368 0.963717
\(379\) 8.04106 0.413042 0.206521 0.978442i \(-0.433786\pi\)
0.206521 + 0.978442i \(0.433786\pi\)
\(380\) 8.52582 0.437365
\(381\) −15.5929 −0.798846
\(382\) 27.5737 1.41079
\(383\) 17.8121 0.910158 0.455079 0.890451i \(-0.349611\pi\)
0.455079 + 0.890451i \(0.349611\pi\)
\(384\) 80.6951 4.11795
\(385\) 49.1862 2.50676
\(386\) 1.59579 0.0812235
\(387\) −28.7515 −1.46152
\(388\) −93.5378 −4.74866
\(389\) −9.02834 −0.457755 −0.228878 0.973455i \(-0.573506\pi\)
−0.228878 + 0.973455i \(0.573506\pi\)
\(390\) 41.1619 2.08432
\(391\) 44.3476 2.24275
\(392\) −74.3215 −3.75381
\(393\) −3.42086 −0.172559
\(394\) −19.2158 −0.968079
\(395\) 1.70044 0.0855583
\(396\) −74.1286 −3.72510
\(397\) 10.4179 0.522860 0.261430 0.965222i \(-0.415806\pi\)
0.261430 + 0.965222i \(0.415806\pi\)
\(398\) −3.41219 −0.171038
\(399\) 6.69453 0.335146
\(400\) −10.3824 −0.519119
\(401\) 26.2170 1.30921 0.654607 0.755969i \(-0.272834\pi\)
0.654607 + 0.755969i \(0.272834\pi\)
\(402\) −69.3878 −3.46075
\(403\) −17.2014 −0.856863
\(404\) 57.0441 2.83805
\(405\) −22.2236 −1.10430
\(406\) −103.241 −5.12379
\(407\) −22.2558 −1.10318
\(408\) 129.457 6.40906
\(409\) −30.6635 −1.51621 −0.758106 0.652131i \(-0.773875\pi\)
−0.758106 + 0.652131i \(0.773875\pi\)
\(410\) −53.7795 −2.65598
\(411\) −9.92224 −0.489428
\(412\) 21.6636 1.06729
\(413\) 13.8100 0.679544
\(414\) −44.3565 −2.18000
\(415\) 6.11049 0.299952
\(416\) −67.6101 −3.31486
\(417\) 3.19386 0.156404
\(418\) 12.6888 0.620629
\(419\) 20.2022 0.986943 0.493472 0.869762i \(-0.335728\pi\)
0.493472 + 0.869762i \(0.335728\pi\)
\(420\) 99.3914 4.84980
\(421\) −40.9927 −1.99786 −0.998931 0.0462359i \(-0.985277\pi\)
−0.998931 + 0.0462359i \(0.985277\pi\)
\(422\) −59.4581 −2.89438
\(423\) 9.74650 0.473891
\(424\) −42.1962 −2.04923
\(425\) −4.29544 −0.208359
\(426\) −74.2449 −3.59718
\(427\) −24.9464 −1.20724
\(428\) 93.0083 4.49573
\(429\) 44.7736 2.16169
\(430\) 73.0672 3.52361
\(431\) 24.3088 1.17091 0.585457 0.810704i \(-0.300915\pi\)
0.585457 + 0.810704i \(0.300915\pi\)
\(432\) 26.0248 1.25212
\(433\) −12.3844 −0.595158 −0.297579 0.954697i \(-0.596179\pi\)
−0.297579 + 0.954697i \(0.596179\pi\)
\(434\) −56.8296 −2.72791
\(435\) 46.3714 2.22334
\(436\) −44.6746 −2.13952
\(437\) 5.54925 0.265457
\(438\) −8.03625 −0.383987
\(439\) −24.4620 −1.16751 −0.583754 0.811930i \(-0.698417\pi\)
−0.583754 + 0.811930i \(0.698417\pi\)
\(440\) 119.018 5.67394
\(441\) 17.6538 0.840656
\(442\) −52.6627 −2.50491
\(443\) −23.6989 −1.12597 −0.562984 0.826468i \(-0.690347\pi\)
−0.562984 + 0.826468i \(0.690347\pi\)
\(444\) −44.9728 −2.13431
\(445\) −35.5935 −1.68730
\(446\) −5.61532 −0.265893
\(447\) 2.72279 0.128784
\(448\) −110.192 −5.20606
\(449\) 2.04498 0.0965085 0.0482543 0.998835i \(-0.484634\pi\)
0.0482543 + 0.998835i \(0.484634\pi\)
\(450\) 4.29631 0.202530
\(451\) −58.4983 −2.75458
\(452\) −13.3803 −0.629355
\(453\) 1.86172 0.0874710
\(454\) −50.5950 −2.37454
\(455\) −25.5441 −1.19752
\(456\) 16.1990 0.758588
\(457\) 30.4406 1.42395 0.711975 0.702205i \(-0.247801\pi\)
0.711975 + 0.702205i \(0.247801\pi\)
\(458\) 25.1311 1.17430
\(459\) 10.7671 0.502565
\(460\) 82.3877 3.84135
\(461\) −9.32831 −0.434463 −0.217231 0.976120i \(-0.569703\pi\)
−0.217231 + 0.976120i \(0.569703\pi\)
\(462\) 147.922 6.88195
\(463\) 30.4538 1.41531 0.707653 0.706560i \(-0.249754\pi\)
0.707653 + 0.706560i \(0.249754\pi\)
\(464\) −143.399 −6.65714
\(465\) 25.5253 1.18371
\(466\) 27.6437 1.28057
\(467\) 1.33346 0.0617054 0.0308527 0.999524i \(-0.490178\pi\)
0.0308527 + 0.999524i \(0.490178\pi\)
\(468\) 38.4975 1.77955
\(469\) 43.0603 1.98834
\(470\) −24.7692 −1.14252
\(471\) 31.6120 1.45660
\(472\) 33.4165 1.53812
\(473\) 79.4784 3.65442
\(474\) 5.11388 0.234888
\(475\) −0.537492 −0.0246618
\(476\) −127.162 −5.82844
\(477\) 10.0230 0.458920
\(478\) −24.7773 −1.13329
\(479\) 6.55120 0.299332 0.149666 0.988737i \(-0.452180\pi\)
0.149666 + 0.988737i \(0.452180\pi\)
\(480\) 100.327 4.57928
\(481\) 11.5582 0.527010
\(482\) 9.44675 0.430288
\(483\) 64.6914 2.94356
\(484\) 145.169 6.59861
\(485\) −35.6726 −1.61981
\(486\) −52.2949 −2.37214
\(487\) 6.62625 0.300264 0.150132 0.988666i \(-0.452030\pi\)
0.150132 + 0.988666i \(0.452030\pi\)
\(488\) −60.3637 −2.73254
\(489\) −1.52389 −0.0689127
\(490\) −44.8642 −2.02676
\(491\) −12.1796 −0.549656 −0.274828 0.961493i \(-0.588621\pi\)
−0.274828 + 0.961493i \(0.588621\pi\)
\(492\) −118.209 −5.32926
\(493\) −59.3277 −2.67199
\(494\) −6.58972 −0.296486
\(495\) −28.2705 −1.27067
\(496\) −78.9345 −3.54426
\(497\) 46.0745 2.06673
\(498\) 18.3766 0.823476
\(499\) −17.1691 −0.768595 −0.384297 0.923209i \(-0.625556\pi\)
−0.384297 + 0.923209i \(0.625556\pi\)
\(500\) −64.2338 −2.87262
\(501\) 19.2111 0.858289
\(502\) −45.3963 −2.02613
\(503\) 29.3780 1.30990 0.654950 0.755672i \(-0.272690\pi\)
0.654950 + 0.755672i \(0.272690\pi\)
\(504\) 80.3537 3.57924
\(505\) 21.7550 0.968084
\(506\) 122.616 5.45094
\(507\) 6.45466 0.286661
\(508\) 37.0617 1.64435
\(509\) 40.9727 1.81608 0.908041 0.418881i \(-0.137578\pi\)
0.908041 + 0.418881i \(0.137578\pi\)
\(510\) 78.1465 3.46039
\(511\) 4.98709 0.220616
\(512\) −36.3935 −1.60838
\(513\) 1.34730 0.0594846
\(514\) 8.22674 0.362866
\(515\) 8.26187 0.364062
\(516\) 160.603 7.07017
\(517\) −26.9425 −1.18493
\(518\) 38.1858 1.67779
\(519\) −16.0926 −0.706389
\(520\) −61.8099 −2.71054
\(521\) 24.0855 1.05520 0.527602 0.849491i \(-0.323091\pi\)
0.527602 + 0.849491i \(0.323091\pi\)
\(522\) 59.3396 2.59723
\(523\) 1.72203 0.0752990 0.0376495 0.999291i \(-0.488013\pi\)
0.0376495 + 0.999291i \(0.488013\pi\)
\(524\) 8.13083 0.355197
\(525\) −6.26592 −0.273467
\(526\) 7.28402 0.317598
\(527\) −32.6571 −1.42257
\(528\) 205.459 8.94145
\(529\) 30.6242 1.33149
\(530\) −25.4718 −1.10642
\(531\) −7.93749 −0.344458
\(532\) −15.9118 −0.689865
\(533\) 30.3802 1.31591
\(534\) −107.044 −4.63223
\(535\) 35.4707 1.53353
\(536\) 104.195 4.50052
\(537\) −39.4597 −1.70281
\(538\) −65.9764 −2.84444
\(539\) −48.8008 −2.10200
\(540\) 20.0028 0.860785
\(541\) 21.5318 0.925723 0.462862 0.886431i \(-0.346823\pi\)
0.462862 + 0.886431i \(0.346823\pi\)
\(542\) 60.7420 2.60909
\(543\) 32.6756 1.40225
\(544\) −128.359 −5.50333
\(545\) −17.0376 −0.729811
\(546\) −76.8210 −3.28763
\(547\) 33.6962 1.44075 0.720374 0.693586i \(-0.243970\pi\)
0.720374 + 0.693586i \(0.243970\pi\)
\(548\) 23.5836 1.00744
\(549\) 14.3383 0.611945
\(550\) −11.8764 −0.506411
\(551\) −7.42372 −0.316261
\(552\) 156.536 6.66262
\(553\) −3.17354 −0.134953
\(554\) −18.1083 −0.769349
\(555\) −17.1513 −0.728033
\(556\) −7.59129 −0.321942
\(557\) 43.7948 1.85565 0.927823 0.373020i \(-0.121678\pi\)
0.927823 + 0.373020i \(0.121678\pi\)
\(558\) 32.6637 1.38276
\(559\) −41.2759 −1.74578
\(560\) −117.218 −4.95335
\(561\) 85.0034 3.58885
\(562\) 61.5734 2.59732
\(563\) −34.3526 −1.44779 −0.723894 0.689911i \(-0.757650\pi\)
−0.723894 + 0.689911i \(0.757650\pi\)
\(564\) −54.4432 −2.29247
\(565\) −5.10285 −0.214679
\(566\) −77.3182 −3.24993
\(567\) 41.4761 1.74183
\(568\) 111.488 4.67794
\(569\) 37.5780 1.57535 0.787677 0.616089i \(-0.211284\pi\)
0.787677 + 0.616089i \(0.211284\pi\)
\(570\) 9.77853 0.409578
\(571\) 8.45535 0.353845 0.176923 0.984225i \(-0.443386\pi\)
0.176923 + 0.984225i \(0.443386\pi\)
\(572\) −106.420 −4.44963
\(573\) 23.1140 0.965601
\(574\) 100.369 4.18933
\(575\) −5.19396 −0.216603
\(576\) 63.3343 2.63893
\(577\) 4.84244 0.201593 0.100797 0.994907i \(-0.467861\pi\)
0.100797 + 0.994907i \(0.467861\pi\)
\(578\) −53.6376 −2.23103
\(579\) 1.33769 0.0555925
\(580\) −110.217 −4.57653
\(581\) −11.4041 −0.473120
\(582\) −107.282 −4.44696
\(583\) −27.7068 −1.14750
\(584\) 12.0675 0.499355
\(585\) 14.6819 0.607020
\(586\) 24.6299 1.01745
\(587\) 24.0691 0.993438 0.496719 0.867911i \(-0.334538\pi\)
0.496719 + 0.867911i \(0.334538\pi\)
\(588\) −98.6126 −4.06671
\(589\) −4.08641 −0.168378
\(590\) 20.1719 0.830462
\(591\) −16.1079 −0.662591
\(592\) 53.0388 2.17988
\(593\) −19.1666 −0.787078 −0.393539 0.919308i \(-0.628749\pi\)
−0.393539 + 0.919308i \(0.628749\pi\)
\(594\) 29.7698 1.22147
\(595\) −48.4958 −1.98813
\(596\) −6.47163 −0.265088
\(597\) −2.86031 −0.117065
\(598\) −63.6786 −2.60401
\(599\) 28.2490 1.15422 0.577112 0.816665i \(-0.304180\pi\)
0.577112 + 0.816665i \(0.304180\pi\)
\(600\) −15.1619 −0.618980
\(601\) 25.5535 1.04235 0.521174 0.853450i \(-0.325494\pi\)
0.521174 + 0.853450i \(0.325494\pi\)
\(602\) −136.366 −5.55787
\(603\) −24.7496 −1.00788
\(604\) −4.42499 −0.180050
\(605\) 55.3635 2.25084
\(606\) 65.4257 2.65774
\(607\) 8.41061 0.341376 0.170688 0.985325i \(-0.445401\pi\)
0.170688 + 0.985325i \(0.445401\pi\)
\(608\) −16.0616 −0.651385
\(609\) −86.5435 −3.50692
\(610\) −36.4386 −1.47535
\(611\) 13.9922 0.566062
\(612\) 73.0881 2.95441
\(613\) 25.7072 1.03831 0.519153 0.854681i \(-0.326248\pi\)
0.519153 + 0.854681i \(0.326248\pi\)
\(614\) −41.6894 −1.68245
\(615\) −45.0814 −1.81786
\(616\) −222.124 −8.94962
\(617\) 2.90387 0.116905 0.0584526 0.998290i \(-0.481383\pi\)
0.0584526 + 0.998290i \(0.481383\pi\)
\(618\) 24.8467 0.999480
\(619\) −2.49905 −0.100445 −0.0502226 0.998738i \(-0.515993\pi\)
−0.0502226 + 0.998738i \(0.515993\pi\)
\(620\) −60.6695 −2.43655
\(621\) 13.0194 0.522449
\(622\) 67.3564 2.70075
\(623\) 66.4286 2.66141
\(624\) −106.702 −4.27149
\(625\) −20.9505 −0.838021
\(626\) 53.3952 2.13410
\(627\) 10.6365 0.424782
\(628\) −75.1366 −2.99828
\(629\) 21.9434 0.874942
\(630\) 48.5055 1.93251
\(631\) −3.67302 −0.146221 −0.0731103 0.997324i \(-0.523293\pi\)
−0.0731103 + 0.997324i \(0.523293\pi\)
\(632\) −7.67914 −0.305460
\(633\) −49.8416 −1.98102
\(634\) 25.0749 0.995851
\(635\) 14.1343 0.560901
\(636\) −55.9875 −2.22005
\(637\) 25.3439 1.00416
\(638\) −164.034 −6.49417
\(639\) −26.4821 −1.04761
\(640\) −73.1467 −2.89138
\(641\) −13.8263 −0.546105 −0.273053 0.961999i \(-0.588033\pi\)
−0.273053 + 0.961999i \(0.588033\pi\)
\(642\) 106.674 4.21010
\(643\) −25.4295 −1.00284 −0.501421 0.865203i \(-0.667189\pi\)
−0.501421 + 0.865203i \(0.667189\pi\)
\(644\) −153.761 −6.05903
\(645\) 61.2495 2.41170
\(646\) −12.5107 −0.492226
\(647\) 16.0789 0.632128 0.316064 0.948738i \(-0.397639\pi\)
0.316064 + 0.948738i \(0.397639\pi\)
\(648\) 100.361 3.94256
\(649\) 21.9418 0.861291
\(650\) 6.16781 0.241922
\(651\) −47.6381 −1.86709
\(652\) 3.62204 0.141850
\(653\) 24.9361 0.975824 0.487912 0.872893i \(-0.337759\pi\)
0.487912 + 0.872893i \(0.337759\pi\)
\(654\) −51.2387 −2.00359
\(655\) 3.10086 0.121161
\(656\) 139.410 5.44304
\(657\) −2.86641 −0.111829
\(658\) 46.2269 1.80211
\(659\) 43.7648 1.70483 0.852417 0.522862i \(-0.175136\pi\)
0.852417 + 0.522862i \(0.175136\pi\)
\(660\) 157.917 6.14691
\(661\) −6.71325 −0.261115 −0.130558 0.991441i \(-0.541677\pi\)
−0.130558 + 0.991441i \(0.541677\pi\)
\(662\) −4.40884 −0.171354
\(663\) −44.1452 −1.71446
\(664\) −27.5948 −1.07089
\(665\) −6.06831 −0.235319
\(666\) −21.9479 −0.850462
\(667\) −71.7378 −2.77770
\(668\) −45.6617 −1.76670
\(669\) −4.70711 −0.181988
\(670\) 62.8971 2.42993
\(671\) −39.6358 −1.53012
\(672\) −187.241 −7.22300
\(673\) −18.6325 −0.718232 −0.359116 0.933293i \(-0.616922\pi\)
−0.359116 + 0.933293i \(0.616922\pi\)
\(674\) 4.81966 0.185646
\(675\) −1.26104 −0.0485373
\(676\) −15.3417 −0.590064
\(677\) 2.65791 0.102152 0.0510760 0.998695i \(-0.483735\pi\)
0.0510760 + 0.998695i \(0.483735\pi\)
\(678\) −15.3463 −0.589370
\(679\) 66.5762 2.55496
\(680\) −117.347 −4.50005
\(681\) −42.4119 −1.62523
\(682\) −90.2931 −3.45750
\(683\) −13.4241 −0.513660 −0.256830 0.966457i \(-0.582678\pi\)
−0.256830 + 0.966457i \(0.582678\pi\)
\(684\) 9.14557 0.349690
\(685\) 8.99409 0.343647
\(686\) 9.95980 0.380267
\(687\) 21.0665 0.803737
\(688\) −189.408 −7.22112
\(689\) 14.3891 0.548180
\(690\) 94.4931 3.59729
\(691\) 47.1512 1.79371 0.896857 0.442320i \(-0.145844\pi\)
0.896857 + 0.442320i \(0.145844\pi\)
\(692\) 38.2496 1.45403
\(693\) 52.7616 2.00425
\(694\) 7.23358 0.274583
\(695\) −2.89510 −0.109817
\(696\) −209.412 −7.93776
\(697\) 57.6772 2.18468
\(698\) −49.6378 −1.87882
\(699\) 23.1727 0.876472
\(700\) 14.8931 0.562905
\(701\) −2.30639 −0.0871113 −0.0435556 0.999051i \(-0.513869\pi\)
−0.0435556 + 0.999051i \(0.513869\pi\)
\(702\) −15.4605 −0.583517
\(703\) 2.74580 0.103560
\(704\) −175.077 −6.59845
\(705\) −20.7631 −0.781982
\(706\) −45.7716 −1.72264
\(707\) −40.6015 −1.52698
\(708\) 44.3382 1.66633
\(709\) 13.5611 0.509297 0.254648 0.967034i \(-0.418040\pi\)
0.254648 + 0.967034i \(0.418040\pi\)
\(710\) 67.2999 2.52572
\(711\) 1.82404 0.0684070
\(712\) 160.740 6.02398
\(713\) −39.4883 −1.47885
\(714\) −145.846 −5.45814
\(715\) −40.5854 −1.51781
\(716\) 93.7893 3.50507
\(717\) −20.7699 −0.775667
\(718\) −66.8562 −2.49505
\(719\) 10.6361 0.396658 0.198329 0.980136i \(-0.436449\pi\)
0.198329 + 0.980136i \(0.436449\pi\)
\(720\) 67.3726 2.51083
\(721\) −15.4192 −0.574242
\(722\) 50.2299 1.86936
\(723\) 7.91886 0.294506
\(724\) −77.6647 −2.88639
\(725\) 6.94842 0.258058
\(726\) 166.500 6.17938
\(727\) 0.990585 0.0367388 0.0183694 0.999831i \(-0.494153\pi\)
0.0183694 + 0.999831i \(0.494153\pi\)
\(728\) 115.356 4.27539
\(729\) −11.6506 −0.431504
\(730\) 7.28452 0.269612
\(731\) −78.3628 −2.89835
\(732\) −80.0928 −2.96032
\(733\) −12.8622 −0.475078 −0.237539 0.971378i \(-0.576341\pi\)
−0.237539 + 0.971378i \(0.576341\pi\)
\(734\) 8.01600 0.295876
\(735\) −37.6080 −1.38719
\(736\) −155.209 −5.72106
\(737\) 68.4160 2.52013
\(738\) −57.6888 −2.12356
\(739\) 26.4736 0.973847 0.486924 0.873445i \(-0.338119\pi\)
0.486924 + 0.873445i \(0.338119\pi\)
\(740\) 40.7659 1.49858
\(741\) −5.52392 −0.202926
\(742\) 47.5382 1.74518
\(743\) 2.41005 0.0884160 0.0442080 0.999022i \(-0.485924\pi\)
0.0442080 + 0.999022i \(0.485924\pi\)
\(744\) −115.272 −4.22607
\(745\) −2.46809 −0.0904240
\(746\) −15.9975 −0.585711
\(747\) 6.55466 0.239823
\(748\) −202.039 −7.38729
\(749\) −66.1993 −2.41887
\(750\) −73.6718 −2.69011
\(751\) −15.0691 −0.549878 −0.274939 0.961462i \(-0.588658\pi\)
−0.274939 + 0.961462i \(0.588658\pi\)
\(752\) 64.2077 2.34142
\(753\) −38.0540 −1.38677
\(754\) 85.1885 3.10238
\(755\) −1.68757 −0.0614168
\(756\) −37.3315 −1.35773
\(757\) 16.8635 0.612913 0.306457 0.951885i \(-0.400857\pi\)
0.306457 + 0.951885i \(0.400857\pi\)
\(758\) −21.9205 −0.796189
\(759\) 102.784 3.73083
\(760\) −14.6837 −0.532634
\(761\) 33.1020 1.19995 0.599973 0.800020i \(-0.295178\pi\)
0.599973 + 0.800020i \(0.295178\pi\)
\(762\) 42.5072 1.53987
\(763\) 31.7975 1.15115
\(764\) −54.9382 −1.98759
\(765\) 27.8737 1.00778
\(766\) −48.5572 −1.75444
\(767\) −11.3951 −0.411454
\(768\) −89.7098 −3.23712
\(769\) 21.4190 0.772388 0.386194 0.922418i \(-0.373789\pi\)
0.386194 + 0.922418i \(0.373789\pi\)
\(770\) −134.085 −4.83209
\(771\) 6.89617 0.248360
\(772\) −3.17947 −0.114432
\(773\) −23.6280 −0.849839 −0.424919 0.905231i \(-0.639698\pi\)
−0.424919 + 0.905231i \(0.639698\pi\)
\(774\) 78.3786 2.81726
\(775\) 3.82478 0.137390
\(776\) 161.097 5.78304
\(777\) 32.0097 1.14834
\(778\) 24.6119 0.882379
\(779\) 7.21720 0.258583
\(780\) −82.0117 −2.93649
\(781\) 73.2050 2.61948
\(782\) −120.895 −4.32319
\(783\) −17.4171 −0.622438
\(784\) 116.299 4.15354
\(785\) −28.6550 −1.02274
\(786\) 9.32550 0.332630
\(787\) −16.5227 −0.588971 −0.294485 0.955656i \(-0.595148\pi\)
−0.294485 + 0.955656i \(0.595148\pi\)
\(788\) 38.2859 1.36388
\(789\) 6.10593 0.217377
\(790\) −4.63551 −0.164924
\(791\) 9.52351 0.338617
\(792\) 127.669 4.53652
\(793\) 20.5842 0.730968
\(794\) −28.4000 −1.00788
\(795\) −21.3520 −0.757279
\(796\) 6.79850 0.240967
\(797\) 24.8378 0.879801 0.439901 0.898047i \(-0.355014\pi\)
0.439901 + 0.898047i \(0.355014\pi\)
\(798\) −18.2498 −0.646035
\(799\) 26.5643 0.939778
\(800\) 15.0333 0.531506
\(801\) −38.1809 −1.34906
\(802\) −71.4694 −2.52367
\(803\) 7.92369 0.279621
\(804\) 138.249 4.87568
\(805\) −58.6400 −2.06679
\(806\) 46.8923 1.65171
\(807\) −55.3055 −1.94685
\(808\) −98.2450 −3.45625
\(809\) 0.279752 0.00983556 0.00491778 0.999988i \(-0.498435\pi\)
0.00491778 + 0.999988i \(0.498435\pi\)
\(810\) 60.5831 2.12867
\(811\) 15.9210 0.559062 0.279531 0.960137i \(-0.409821\pi\)
0.279531 + 0.960137i \(0.409821\pi\)
\(812\) 205.700 7.21865
\(813\) 50.9178 1.78576
\(814\) 60.6710 2.12652
\(815\) 1.38134 0.0483863
\(816\) −202.575 −7.09154
\(817\) −9.80560 −0.343054
\(818\) 83.5909 2.92269
\(819\) −27.4009 −0.957465
\(820\) 107.151 3.74188
\(821\) 40.4564 1.41194 0.705969 0.708242i \(-0.250512\pi\)
0.705969 + 0.708242i \(0.250512\pi\)
\(822\) 27.0487 0.943433
\(823\) −24.7327 −0.862129 −0.431065 0.902321i \(-0.641862\pi\)
−0.431065 + 0.902321i \(0.641862\pi\)
\(824\) −37.3105 −1.29977
\(825\) −9.95553 −0.346607
\(826\) −37.6469 −1.30990
\(827\) −44.1088 −1.53381 −0.766907 0.641758i \(-0.778205\pi\)
−0.766907 + 0.641758i \(0.778205\pi\)
\(828\) 88.3766 3.07130
\(829\) −22.0942 −0.767363 −0.383681 0.923465i \(-0.625344\pi\)
−0.383681 + 0.923465i \(0.625344\pi\)
\(830\) −16.6576 −0.578194
\(831\) −15.1795 −0.526572
\(832\) 90.9233 3.15220
\(833\) 48.1158 1.66711
\(834\) −8.70669 −0.301488
\(835\) −17.4141 −0.602638
\(836\) −25.2813 −0.874373
\(837\) −9.58732 −0.331386
\(838\) −55.0727 −1.90245
\(839\) −1.24134 −0.0428559 −0.0214280 0.999770i \(-0.506821\pi\)
−0.0214280 + 0.999770i \(0.506821\pi\)
\(840\) −171.178 −5.90621
\(841\) 66.9700 2.30931
\(842\) 111.749 3.85112
\(843\) 51.6147 1.77770
\(844\) 118.465 4.07774
\(845\) −5.85087 −0.201276
\(846\) −26.5697 −0.913484
\(847\) −103.325 −3.55030
\(848\) 66.0291 2.26745
\(849\) −64.8130 −2.22438
\(850\) 11.7097 0.401639
\(851\) 26.5335 0.909558
\(852\) 147.927 5.06788
\(853\) 32.5193 1.11344 0.556719 0.830701i \(-0.312060\pi\)
0.556719 + 0.830701i \(0.312060\pi\)
\(854\) 68.0057 2.32711
\(855\) 3.48786 0.119282
\(856\) −160.185 −5.47501
\(857\) −0.592345 −0.0202341 −0.0101171 0.999949i \(-0.503220\pi\)
−0.0101171 + 0.999949i \(0.503220\pi\)
\(858\) −122.056 −4.16693
\(859\) −57.4210 −1.95918 −0.979589 0.201012i \(-0.935577\pi\)
−0.979589 + 0.201012i \(0.935577\pi\)
\(860\) −145.580 −4.96424
\(861\) 84.1359 2.86734
\(862\) −66.2675 −2.25708
\(863\) −0.0219008 −0.000745512 0 −0.000372756 1.00000i \(-0.500119\pi\)
−0.000372756 1.00000i \(0.500119\pi\)
\(864\) −37.6829 −1.28200
\(865\) 14.5873 0.495983
\(866\) 33.7608 1.14724
\(867\) −44.9624 −1.52700
\(868\) 113.228 3.84321
\(869\) −5.04225 −0.171047
\(870\) −126.412 −4.28576
\(871\) −35.5307 −1.20391
\(872\) 76.9415 2.60557
\(873\) −38.2657 −1.29510
\(874\) −15.1276 −0.511700
\(875\) 45.7189 1.54558
\(876\) 16.0115 0.540980
\(877\) −14.0224 −0.473504 −0.236752 0.971570i \(-0.576083\pi\)
−0.236752 + 0.971570i \(0.576083\pi\)
\(878\) 66.6852 2.25052
\(879\) 20.6463 0.696383
\(880\) −186.240 −6.27814
\(881\) −17.6017 −0.593016 −0.296508 0.955030i \(-0.595822\pi\)
−0.296508 + 0.955030i \(0.595822\pi\)
\(882\) −48.1255 −1.62047
\(883\) 1.39119 0.0468174 0.0234087 0.999726i \(-0.492548\pi\)
0.0234087 + 0.999726i \(0.492548\pi\)
\(884\) 104.926 3.52904
\(885\) 16.9093 0.568401
\(886\) 64.6048 2.17044
\(887\) −29.5738 −0.992991 −0.496495 0.868039i \(-0.665380\pi\)
−0.496495 + 0.868039i \(0.665380\pi\)
\(888\) 77.4550 2.59922
\(889\) −26.3789 −0.884721
\(890\) 97.0306 3.25247
\(891\) 65.8989 2.20770
\(892\) 11.1880 0.374604
\(893\) 3.32401 0.111234
\(894\) −7.42252 −0.248246
\(895\) 35.7685 1.19561
\(896\) 136.514 4.56063
\(897\) −53.3794 −1.78229
\(898\) −5.57476 −0.186032
\(899\) 52.8270 1.76188
\(900\) −8.56002 −0.285334
\(901\) 27.3178 0.910089
\(902\) 159.471 5.30979
\(903\) −114.311 −3.80402
\(904\) 23.0444 0.766444
\(905\) −29.6191 −0.984572
\(906\) −5.07517 −0.168611
\(907\) 51.3212 1.70409 0.852046 0.523467i \(-0.175362\pi\)
0.852046 + 0.523467i \(0.175362\pi\)
\(908\) 100.806 3.34537
\(909\) 23.3364 0.774019
\(910\) 69.6349 2.30838
\(911\) −2.21296 −0.0733188 −0.0366594 0.999328i \(-0.511672\pi\)
−0.0366594 + 0.999328i \(0.511672\pi\)
\(912\) −25.3484 −0.839368
\(913\) −18.1192 −0.599659
\(914\) −82.9831 −2.74484
\(915\) −30.5451 −1.00979
\(916\) −50.0716 −1.65441
\(917\) −5.78717 −0.191109
\(918\) −29.3519 −0.968757
\(919\) −17.0559 −0.562622 −0.281311 0.959617i \(-0.590769\pi\)
−0.281311 + 0.959617i \(0.590769\pi\)
\(920\) −141.893 −4.67809
\(921\) −34.9467 −1.15153
\(922\) 25.4296 0.837481
\(923\) −38.0179 −1.25137
\(924\) −294.722 −9.69564
\(925\) −2.57000 −0.0845011
\(926\) −83.0192 −2.72818
\(927\) 8.86244 0.291081
\(928\) 207.636 6.81600
\(929\) −26.6813 −0.875384 −0.437692 0.899125i \(-0.644204\pi\)
−0.437692 + 0.899125i \(0.644204\pi\)
\(930\) −69.5838 −2.28174
\(931\) 6.02076 0.197323
\(932\) −55.0778 −1.80413
\(933\) 56.4624 1.84850
\(934\) −3.63512 −0.118945
\(935\) −77.0520 −2.51987
\(936\) −66.3029 −2.16718
\(937\) −9.89749 −0.323337 −0.161668 0.986845i \(-0.551688\pi\)
−0.161668 + 0.986845i \(0.551688\pi\)
\(938\) −117.386 −3.83277
\(939\) 44.7592 1.46066
\(940\) 49.3504 1.60963
\(941\) −24.7747 −0.807633 −0.403817 0.914840i \(-0.632317\pi\)
−0.403817 + 0.914840i \(0.632317\pi\)
\(942\) −86.1766 −2.80779
\(943\) 69.7421 2.27111
\(944\) −52.2904 −1.70191
\(945\) −14.2372 −0.463135
\(946\) −216.664 −7.04435
\(947\) −35.2983 −1.14704 −0.573521 0.819191i \(-0.694423\pi\)
−0.573521 + 0.819191i \(0.694423\pi\)
\(948\) −10.1890 −0.330922
\(949\) −4.11504 −0.133580
\(950\) 1.46524 0.0475387
\(951\) 21.0194 0.681599
\(952\) 219.006 7.09802
\(953\) 56.5330 1.83128 0.915642 0.401995i \(-0.131683\pi\)
0.915642 + 0.401995i \(0.131683\pi\)
\(954\) −27.3233 −0.884626
\(955\) −20.9519 −0.677986
\(956\) 49.3667 1.59663
\(957\) −137.504 −4.44486
\(958\) −17.8590 −0.577000
\(959\) −16.7858 −0.542041
\(960\) −134.922 −4.35458
\(961\) −1.92120 −0.0619743
\(962\) −31.5085 −1.01588
\(963\) 38.0491 1.22612
\(964\) −18.8218 −0.606211
\(965\) −1.21256 −0.0390337
\(966\) −176.353 −5.67408
\(967\) 20.8090 0.669173 0.334586 0.942365i \(-0.391403\pi\)
0.334586 + 0.942365i \(0.391403\pi\)
\(968\) −250.020 −8.03595
\(969\) −10.4872 −0.336899
\(970\) 97.2461 3.12239
\(971\) −4.13974 −0.132851 −0.0664253 0.997791i \(-0.521159\pi\)
−0.0664253 + 0.997791i \(0.521159\pi\)
\(972\) 104.193 3.34199
\(973\) 5.40315 0.173217
\(974\) −18.0636 −0.578796
\(975\) 5.17025 0.165581
\(976\) 94.4578 3.02352
\(977\) 20.3941 0.652466 0.326233 0.945289i \(-0.394221\pi\)
0.326233 + 0.945289i \(0.394221\pi\)
\(978\) 4.15423 0.132838
\(979\) 105.544 3.37321
\(980\) 89.3881 2.85540
\(981\) −18.2761 −0.583511
\(982\) 33.2024 1.05953
\(983\) −15.5371 −0.495558 −0.247779 0.968817i \(-0.579701\pi\)
−0.247779 + 0.968817i \(0.579701\pi\)
\(984\) 203.587 6.49010
\(985\) 14.6011 0.465231
\(986\) 161.732 5.15058
\(987\) 38.7503 1.23344
\(988\) 13.1295 0.417704
\(989\) −94.7546 −3.01302
\(990\) 77.0675 2.44936
\(991\) 4.87743 0.154937 0.0774683 0.996995i \(-0.475316\pi\)
0.0774683 + 0.996995i \(0.475316\pi\)
\(992\) 114.294 3.62884
\(993\) −3.69577 −0.117282
\(994\) −125.602 −3.98387
\(995\) 2.59275 0.0821958
\(996\) −36.6138 −1.16015
\(997\) −29.0403 −0.919715 −0.459858 0.887993i \(-0.652100\pi\)
−0.459858 + 0.887993i \(0.652100\pi\)
\(998\) 46.8042 1.48156
\(999\) 6.44205 0.203818
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 4027.2.a.c.1.2 174
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4027.2.a.c.1.2 174 1.1 even 1 trivial