Properties

Label 4034.2.a.d.1.20
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 1.20
Character \(\chi\) = 4034.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -0.550547 q^{3} +1.00000 q^{4} +0.337407 q^{5} -0.550547 q^{6} +1.25225 q^{7} +1.00000 q^{8} -2.69690 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -0.550547 q^{3} +1.00000 q^{4} +0.337407 q^{5} -0.550547 q^{6} +1.25225 q^{7} +1.00000 q^{8} -2.69690 q^{9} +0.337407 q^{10} +4.84850 q^{11} -0.550547 q^{12} +5.51433 q^{13} +1.25225 q^{14} -0.185759 q^{15} +1.00000 q^{16} +1.55974 q^{17} -2.69690 q^{18} +2.11267 q^{19} +0.337407 q^{20} -0.689425 q^{21} +4.84850 q^{22} -3.60861 q^{23} -0.550547 q^{24} -4.88616 q^{25} +5.51433 q^{26} +3.13641 q^{27} +1.25225 q^{28} -7.56691 q^{29} -0.185759 q^{30} +9.14450 q^{31} +1.00000 q^{32} -2.66933 q^{33} +1.55974 q^{34} +0.422520 q^{35} -2.69690 q^{36} +8.35997 q^{37} +2.11267 q^{38} -3.03590 q^{39} +0.337407 q^{40} -8.23774 q^{41} -0.689425 q^{42} +4.67088 q^{43} +4.84850 q^{44} -0.909953 q^{45} -3.60861 q^{46} +2.43442 q^{47} -0.550547 q^{48} -5.43186 q^{49} -4.88616 q^{50} -0.858711 q^{51} +5.51433 q^{52} +10.2173 q^{53} +3.13641 q^{54} +1.63592 q^{55} +1.25225 q^{56} -1.16313 q^{57} -7.56691 q^{58} -13.2802 q^{59} -0.185759 q^{60} -6.78275 q^{61} +9.14450 q^{62} -3.37720 q^{63} +1.00000 q^{64} +1.86057 q^{65} -2.66933 q^{66} -1.78663 q^{67} +1.55974 q^{68} +1.98671 q^{69} +0.422520 q^{70} +1.41159 q^{71} -2.69690 q^{72} +5.62943 q^{73} +8.35997 q^{74} +2.69006 q^{75} +2.11267 q^{76} +6.07155 q^{77} -3.03590 q^{78} +11.6421 q^{79} +0.337407 q^{80} +6.36395 q^{81} -8.23774 q^{82} +2.29357 q^{83} -0.689425 q^{84} +0.526268 q^{85} +4.67088 q^{86} +4.16594 q^{87} +4.84850 q^{88} -7.46599 q^{89} -0.909953 q^{90} +6.90534 q^{91} -3.60861 q^{92} -5.03448 q^{93} +2.43442 q^{94} +0.712831 q^{95} -0.550547 q^{96} -0.461813 q^{97} -5.43186 q^{98} -13.0759 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52q + 52q^{2} + 16q^{3} + 52q^{4} + 24q^{5} + 16q^{6} + 12q^{7} + 52q^{8} + 70q^{9} + O(q^{10}) \) \( 52q + 52q^{2} + 16q^{3} + 52q^{4} + 24q^{5} + 16q^{6} + 12q^{7} + 52q^{8} + 70q^{9} + 24q^{10} + 19q^{11} + 16q^{12} + 27q^{13} + 12q^{14} + 5q^{15} + 52q^{16} + 43q^{17} + 70q^{18} + 35q^{19} + 24q^{20} + 29q^{21} + 19q^{22} + 2q^{23} + 16q^{24} + 88q^{25} + 27q^{26} + 49q^{27} + 12q^{28} + 31q^{29} + 5q^{30} + 59q^{31} + 52q^{32} + 45q^{33} + 43q^{34} + 18q^{35} + 70q^{36} + 60q^{37} + 35q^{38} + 6q^{39} + 24q^{40} + 56q^{41} + 29q^{42} + 34q^{43} + 19q^{44} + 61q^{45} + 2q^{46} - 4q^{47} + 16q^{48} + 102q^{49} + 88q^{50} + 23q^{51} + 27q^{52} + 30q^{53} + 49q^{54} + 24q^{55} + 12q^{56} + 32q^{57} + 31q^{58} + 27q^{59} + 5q^{60} + 107q^{61} + 59q^{62} - 4q^{63} + 52q^{64} + 46q^{65} + 45q^{66} + 22q^{67} + 43q^{68} + 36q^{69} + 18q^{70} + 8q^{71} + 70q^{72} + 66q^{73} + 60q^{74} + 53q^{75} + 35q^{76} + 26q^{77} + 6q^{78} + 50q^{79} + 24q^{80} + 108q^{81} + 56q^{82} + 52q^{83} + 29q^{84} + 19q^{85} + 34q^{86} - 32q^{87} + 19q^{88} + 62q^{89} + 61q^{90} + 69q^{91} + 2q^{92} + 21q^{93} - 4q^{94} - 44q^{95} + 16q^{96} + 82q^{97} + 102q^{98} + 16q^{99} + O(q^{100}) \)

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
\(3\) −0.550547 −0.317858 −0.158929 0.987290i \(-0.550804\pi\)
−0.158929 + 0.987290i \(0.550804\pi\)
\(4\) 1.00000 0.500000
\(5\) 0.337407 0.150893 0.0754465 0.997150i \(-0.475962\pi\)
0.0754465 + 0.997150i \(0.475962\pi\)
\(6\) −0.550547 −0.224760
\(7\) 1.25225 0.473308 0.236654 0.971594i \(-0.423949\pi\)
0.236654 + 0.971594i \(0.423949\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.69690 −0.898966
\(10\) 0.337407 0.106698
\(11\) 4.84850 1.46188 0.730939 0.682443i \(-0.239082\pi\)
0.730939 + 0.682443i \(0.239082\pi\)
\(12\) −0.550547 −0.158929
\(13\) 5.51433 1.52940 0.764700 0.644386i \(-0.222887\pi\)
0.764700 + 0.644386i \(0.222887\pi\)
\(14\) 1.25225 0.334679
\(15\) −0.185759 −0.0479626
\(16\) 1.00000 0.250000
\(17\) 1.55974 0.378293 0.189146 0.981949i \(-0.439428\pi\)
0.189146 + 0.981949i \(0.439428\pi\)
\(18\) −2.69690 −0.635665
\(19\) 2.11267 0.484680 0.242340 0.970191i \(-0.422085\pi\)
0.242340 + 0.970191i \(0.422085\pi\)
\(20\) 0.337407 0.0754465
\(21\) −0.689425 −0.150445
\(22\) 4.84850 1.03370
\(23\) −3.60861 −0.752446 −0.376223 0.926529i \(-0.622777\pi\)
−0.376223 + 0.926529i \(0.622777\pi\)
\(24\) −0.550547 −0.112380
\(25\) −4.88616 −0.977231
\(26\) 5.51433 1.08145
\(27\) 3.13641 0.603602
\(28\) 1.25225 0.236654
\(29\) −7.56691 −1.40514 −0.702570 0.711614i \(-0.747964\pi\)
−0.702570 + 0.711614i \(0.747964\pi\)
\(30\) −0.185759 −0.0339147
\(31\) 9.14450 1.64240 0.821200 0.570641i \(-0.193305\pi\)
0.821200 + 0.570641i \(0.193305\pi\)
\(32\) 1.00000 0.176777
\(33\) −2.66933 −0.464670
\(34\) 1.55974 0.267494
\(35\) 0.422520 0.0714188
\(36\) −2.69690 −0.449483
\(37\) 8.35997 1.37437 0.687185 0.726482i \(-0.258846\pi\)
0.687185 + 0.726482i \(0.258846\pi\)
\(38\) 2.11267 0.342721
\(39\) −3.03590 −0.486133
\(40\) 0.337407 0.0533488
\(41\) −8.23774 −1.28652 −0.643259 0.765648i \(-0.722418\pi\)
−0.643259 + 0.765648i \(0.722418\pi\)
\(42\) −0.689425 −0.106381
\(43\) 4.67088 0.712302 0.356151 0.934428i \(-0.384089\pi\)
0.356151 + 0.934428i \(0.384089\pi\)
\(44\) 4.84850 0.730939
\(45\) −0.909953 −0.135648
\(46\) −3.60861 −0.532060
\(47\) 2.43442 0.355096 0.177548 0.984112i \(-0.443184\pi\)
0.177548 + 0.984112i \(0.443184\pi\)
\(48\) −0.550547 −0.0794646
\(49\) −5.43186 −0.775980
\(50\) −4.88616 −0.691007
\(51\) −0.858711 −0.120244
\(52\) 5.51433 0.764700
\(53\) 10.2173 1.40346 0.701728 0.712445i \(-0.252412\pi\)
0.701728 + 0.712445i \(0.252412\pi\)
\(54\) 3.13641 0.426811
\(55\) 1.63592 0.220587
\(56\) 1.25225 0.167340
\(57\) −1.16313 −0.154060
\(58\) −7.56691 −0.993584
\(59\) −13.2802 −1.72893 −0.864467 0.502689i \(-0.832344\pi\)
−0.864467 + 0.502689i \(0.832344\pi\)
\(60\) −0.185759 −0.0239813
\(61\) −6.78275 −0.868442 −0.434221 0.900806i \(-0.642976\pi\)
−0.434221 + 0.900806i \(0.642976\pi\)
\(62\) 9.14450 1.16135
\(63\) −3.37720 −0.425487
\(64\) 1.00000 0.125000
\(65\) 1.86057 0.230776
\(66\) −2.66933 −0.328571
\(67\) −1.78663 −0.218272 −0.109136 0.994027i \(-0.534808\pi\)
−0.109136 + 0.994027i \(0.534808\pi\)
\(68\) 1.55974 0.189146
\(69\) 1.98671 0.239171
\(70\) 0.422520 0.0505007
\(71\) 1.41159 0.167525 0.0837624 0.996486i \(-0.473306\pi\)
0.0837624 + 0.996486i \(0.473306\pi\)
\(72\) −2.69690 −0.317832
\(73\) 5.62943 0.658875 0.329437 0.944177i \(-0.393141\pi\)
0.329437 + 0.944177i \(0.393141\pi\)
\(74\) 8.35997 0.971827
\(75\) 2.69006 0.310621
\(76\) 2.11267 0.242340
\(77\) 6.07155 0.691918
\(78\) −3.03590 −0.343748
\(79\) 11.6421 1.30984 0.654921 0.755698i \(-0.272702\pi\)
0.654921 + 0.755698i \(0.272702\pi\)
\(80\) 0.337407 0.0377233
\(81\) 6.36395 0.707106
\(82\) −8.23774 −0.909706
\(83\) 2.29357 0.251752 0.125876 0.992046i \(-0.459826\pi\)
0.125876 + 0.992046i \(0.459826\pi\)
\(84\) −0.689425 −0.0752224
\(85\) 0.526268 0.0570818
\(86\) 4.67088 0.503674
\(87\) 4.16594 0.446636
\(88\) 4.84850 0.516852
\(89\) −7.46599 −0.791393 −0.395696 0.918381i \(-0.629497\pi\)
−0.395696 + 0.918381i \(0.629497\pi\)
\(90\) −0.909953 −0.0959174
\(91\) 6.90534 0.723877
\(92\) −3.60861 −0.376223
\(93\) −5.03448 −0.522051
\(94\) 2.43442 0.251091
\(95\) 0.712831 0.0731349
\(96\) −0.550547 −0.0561900
\(97\) −0.461813 −0.0468900 −0.0234450 0.999725i \(-0.507463\pi\)
−0.0234450 + 0.999725i \(0.507463\pi\)
\(98\) −5.43186 −0.548701
\(99\) −13.0759 −1.31418
\(100\) −4.88616 −0.488616
\(101\) −6.77064 −0.673704 −0.336852 0.941558i \(-0.609362\pi\)
−0.336852 + 0.941558i \(0.609362\pi\)
\(102\) −0.858711 −0.0850251
\(103\) 4.82410 0.475332 0.237666 0.971347i \(-0.423618\pi\)
0.237666 + 0.971347i \(0.423618\pi\)
\(104\) 5.51433 0.540725
\(105\) −0.232617 −0.0227011
\(106\) 10.2173 0.992393
\(107\) −5.68837 −0.549916 −0.274958 0.961456i \(-0.588664\pi\)
−0.274958 + 0.961456i \(0.588664\pi\)
\(108\) 3.13641 0.301801
\(109\) 6.59457 0.631646 0.315823 0.948818i \(-0.397719\pi\)
0.315823 + 0.948818i \(0.397719\pi\)
\(110\) 1.63592 0.155979
\(111\) −4.60256 −0.436855
\(112\) 1.25225 0.118327
\(113\) 13.6251 1.28175 0.640873 0.767647i \(-0.278573\pi\)
0.640873 + 0.767647i \(0.278573\pi\)
\(114\) −1.16313 −0.108937
\(115\) −1.21757 −0.113539
\(116\) −7.56691 −0.702570
\(117\) −14.8716 −1.37488
\(118\) −13.2802 −1.22254
\(119\) 1.95319 0.179049
\(120\) −0.185759 −0.0169574
\(121\) 12.5079 1.13709
\(122\) −6.78275 −0.614081
\(123\) 4.53526 0.408931
\(124\) 9.14450 0.821200
\(125\) −3.33566 −0.298351
\(126\) −3.37720 −0.300865
\(127\) 4.41015 0.391338 0.195669 0.980670i \(-0.437312\pi\)
0.195669 + 0.980670i \(0.437312\pi\)
\(128\) 1.00000 0.0883883
\(129\) −2.57154 −0.226411
\(130\) 1.86057 0.163183
\(131\) 19.6122 1.71352 0.856762 0.515712i \(-0.172473\pi\)
0.856762 + 0.515712i \(0.172473\pi\)
\(132\) −2.66933 −0.232335
\(133\) 2.64560 0.229403
\(134\) −1.78663 −0.154342
\(135\) 1.05825 0.0910794
\(136\) 1.55974 0.133747
\(137\) 6.30047 0.538285 0.269143 0.963100i \(-0.413260\pi\)
0.269143 + 0.963100i \(0.413260\pi\)
\(138\) 1.98671 0.169120
\(139\) 2.21497 0.187871 0.0939355 0.995578i \(-0.470055\pi\)
0.0939355 + 0.995578i \(0.470055\pi\)
\(140\) 0.422520 0.0357094
\(141\) −1.34026 −0.112870
\(142\) 1.41159 0.118458
\(143\) 26.7362 2.23580
\(144\) −2.69690 −0.224741
\(145\) −2.55313 −0.212026
\(146\) 5.62943 0.465895
\(147\) 2.99049 0.246652
\(148\) 8.35997 0.687185
\(149\) −17.5872 −1.44080 −0.720398 0.693561i \(-0.756041\pi\)
−0.720398 + 0.693561i \(0.756041\pi\)
\(150\) 2.69006 0.219642
\(151\) 23.5027 1.91262 0.956310 0.292354i \(-0.0944386\pi\)
0.956310 + 0.292354i \(0.0944386\pi\)
\(152\) 2.11267 0.171360
\(153\) −4.20646 −0.340072
\(154\) 6.07155 0.489260
\(155\) 3.08542 0.247827
\(156\) −3.03590 −0.243066
\(157\) 19.0240 1.51828 0.759140 0.650928i \(-0.225620\pi\)
0.759140 + 0.650928i \(0.225620\pi\)
\(158\) 11.6421 0.926198
\(159\) −5.62511 −0.446100
\(160\) 0.337407 0.0266744
\(161\) −4.51889 −0.356138
\(162\) 6.36395 0.499999
\(163\) −20.1306 −1.57675 −0.788376 0.615194i \(-0.789078\pi\)
−0.788376 + 0.615194i \(0.789078\pi\)
\(164\) −8.23774 −0.643259
\(165\) −0.900650 −0.0701155
\(166\) 2.29357 0.178016
\(167\) 2.67577 0.207058 0.103529 0.994626i \(-0.466987\pi\)
0.103529 + 0.994626i \(0.466987\pi\)
\(168\) −0.689425 −0.0531903
\(169\) 17.4078 1.33907
\(170\) 0.526268 0.0403629
\(171\) −5.69766 −0.435711
\(172\) 4.67088 0.356151
\(173\) −0.473939 −0.0360329 −0.0180165 0.999838i \(-0.505735\pi\)
−0.0180165 + 0.999838i \(0.505735\pi\)
\(174\) 4.16594 0.315819
\(175\) −6.11871 −0.462531
\(176\) 4.84850 0.365469
\(177\) 7.31137 0.549557
\(178\) −7.46599 −0.559599
\(179\) −13.3624 −0.998753 −0.499377 0.866385i \(-0.666438\pi\)
−0.499377 + 0.866385i \(0.666438\pi\)
\(180\) −0.909953 −0.0678239
\(181\) 13.0898 0.972956 0.486478 0.873693i \(-0.338281\pi\)
0.486478 + 0.873693i \(0.338281\pi\)
\(182\) 6.90534 0.511858
\(183\) 3.73422 0.276042
\(184\) −3.60861 −0.266030
\(185\) 2.82071 0.207383
\(186\) −5.03448 −0.369146
\(187\) 7.56241 0.553018
\(188\) 2.43442 0.177548
\(189\) 3.92758 0.285690
\(190\) 0.712831 0.0517142
\(191\) 13.8214 1.00008 0.500041 0.866002i \(-0.333318\pi\)
0.500041 + 0.866002i \(0.333318\pi\)
\(192\) −0.550547 −0.0397323
\(193\) 1.23168 0.0886582 0.0443291 0.999017i \(-0.485885\pi\)
0.0443291 + 0.999017i \(0.485885\pi\)
\(194\) −0.461813 −0.0331563
\(195\) −1.02433 −0.0733541
\(196\) −5.43186 −0.387990
\(197\) 8.14270 0.580144 0.290072 0.957005i \(-0.406321\pi\)
0.290072 + 0.957005i \(0.406321\pi\)
\(198\) −13.0759 −0.929264
\(199\) −21.2310 −1.50502 −0.752511 0.658579i \(-0.771158\pi\)
−0.752511 + 0.658579i \(0.771158\pi\)
\(200\) −4.88616 −0.345503
\(201\) 0.983626 0.0693796
\(202\) −6.77064 −0.476381
\(203\) −9.47570 −0.665064
\(204\) −0.858711 −0.0601218
\(205\) −2.77947 −0.194127
\(206\) 4.82410 0.336111
\(207\) 9.73204 0.676424
\(208\) 5.51433 0.382350
\(209\) 10.2433 0.708543
\(210\) −0.232617 −0.0160521
\(211\) −26.7233 −1.83971 −0.919856 0.392257i \(-0.871694\pi\)
−0.919856 + 0.392257i \(0.871694\pi\)
\(212\) 10.2173 0.701728
\(213\) −0.777147 −0.0532492
\(214\) −5.68837 −0.388849
\(215\) 1.57599 0.107481
\(216\) 3.13641 0.213406
\(217\) 11.4512 0.777360
\(218\) 6.59457 0.446641
\(219\) −3.09927 −0.209429
\(220\) 1.63592 0.110294
\(221\) 8.60093 0.578561
\(222\) −4.60256 −0.308903
\(223\) 12.8063 0.857574 0.428787 0.903406i \(-0.358941\pi\)
0.428787 + 0.903406i \(0.358941\pi\)
\(224\) 1.25225 0.0836698
\(225\) 13.1775 0.878498
\(226\) 13.6251 0.906331
\(227\) −19.0380 −1.26359 −0.631797 0.775134i \(-0.717682\pi\)
−0.631797 + 0.775134i \(0.717682\pi\)
\(228\) −1.16313 −0.0770299
\(229\) −0.294814 −0.0194819 −0.00974094 0.999953i \(-0.503101\pi\)
−0.00974094 + 0.999953i \(0.503101\pi\)
\(230\) −1.21757 −0.0802841
\(231\) −3.34268 −0.219932
\(232\) −7.56691 −0.496792
\(233\) 27.3480 1.79163 0.895814 0.444429i \(-0.146593\pi\)
0.895814 + 0.444429i \(0.146593\pi\)
\(234\) −14.8716 −0.972186
\(235\) 0.821389 0.0535815
\(236\) −13.2802 −0.864467
\(237\) −6.40954 −0.416344
\(238\) 1.95319 0.126607
\(239\) −10.0612 −0.650805 −0.325403 0.945576i \(-0.605500\pi\)
−0.325403 + 0.945576i \(0.605500\pi\)
\(240\) −0.185759 −0.0119907
\(241\) −17.7231 −1.14165 −0.570823 0.821073i \(-0.693376\pi\)
−0.570823 + 0.821073i \(0.693376\pi\)
\(242\) 12.5079 0.804041
\(243\) −12.9129 −0.828362
\(244\) −6.78275 −0.434221
\(245\) −1.83275 −0.117090
\(246\) 4.53526 0.289158
\(247\) 11.6500 0.741270
\(248\) 9.14450 0.580676
\(249\) −1.26272 −0.0800216
\(250\) −3.33566 −0.210966
\(251\) 0.608615 0.0384154 0.0192077 0.999816i \(-0.493886\pi\)
0.0192077 + 0.999816i \(0.493886\pi\)
\(252\) −3.37720 −0.212744
\(253\) −17.4963 −1.09998
\(254\) 4.41015 0.276718
\(255\) −0.289735 −0.0181439
\(256\) 1.00000 0.0625000
\(257\) 16.5189 1.03042 0.515212 0.857063i \(-0.327713\pi\)
0.515212 + 0.857063i \(0.327713\pi\)
\(258\) −2.57154 −0.160097
\(259\) 10.4688 0.650500
\(260\) 1.86057 0.115388
\(261\) 20.4072 1.26317
\(262\) 19.6122 1.21164
\(263\) 16.3838 1.01027 0.505134 0.863041i \(-0.331443\pi\)
0.505134 + 0.863041i \(0.331443\pi\)
\(264\) −2.66933 −0.164286
\(265\) 3.44739 0.211772
\(266\) 2.64560 0.162212
\(267\) 4.11038 0.251551
\(268\) −1.78663 −0.109136
\(269\) −20.4975 −1.24975 −0.624876 0.780724i \(-0.714851\pi\)
−0.624876 + 0.780724i \(0.714851\pi\)
\(270\) 1.05825 0.0644029
\(271\) −25.7751 −1.56572 −0.782862 0.622195i \(-0.786241\pi\)
−0.782862 + 0.622195i \(0.786241\pi\)
\(272\) 1.55974 0.0945732
\(273\) −3.80172 −0.230090
\(274\) 6.30047 0.380625
\(275\) −23.6905 −1.42859
\(276\) 1.98671 0.119586
\(277\) −9.45517 −0.568106 −0.284053 0.958809i \(-0.591679\pi\)
−0.284053 + 0.958809i \(0.591679\pi\)
\(278\) 2.21497 0.132845
\(279\) −24.6618 −1.47646
\(280\) 0.422520 0.0252504
\(281\) −8.35664 −0.498515 −0.249258 0.968437i \(-0.580187\pi\)
−0.249258 + 0.968437i \(0.580187\pi\)
\(282\) −1.34026 −0.0798113
\(283\) 12.5174 0.744079 0.372040 0.928217i \(-0.378659\pi\)
0.372040 + 0.928217i \(0.378659\pi\)
\(284\) 1.41159 0.0837624
\(285\) −0.392447 −0.0232466
\(286\) 26.7362 1.58095
\(287\) −10.3157 −0.608919
\(288\) −2.69690 −0.158916
\(289\) −14.5672 −0.856894
\(290\) −2.55313 −0.149925
\(291\) 0.254250 0.0149044
\(292\) 5.62943 0.329437
\(293\) −8.75817 −0.511658 −0.255829 0.966722i \(-0.582348\pi\)
−0.255829 + 0.966722i \(0.582348\pi\)
\(294\) 2.99049 0.174409
\(295\) −4.48083 −0.260884
\(296\) 8.35997 0.485913
\(297\) 15.2069 0.882393
\(298\) −17.5872 −1.01880
\(299\) −19.8990 −1.15079
\(300\) 2.69006 0.155311
\(301\) 5.84912 0.337138
\(302\) 23.5027 1.35243
\(303\) 3.72756 0.214143
\(304\) 2.11267 0.121170
\(305\) −2.28855 −0.131042
\(306\) −4.20646 −0.240468
\(307\) −20.3274 −1.16015 −0.580074 0.814564i \(-0.696976\pi\)
−0.580074 + 0.814564i \(0.696976\pi\)
\(308\) 6.07155 0.345959
\(309\) −2.65589 −0.151088
\(310\) 3.08542 0.175240
\(311\) 19.6769 1.11578 0.557888 0.829916i \(-0.311612\pi\)
0.557888 + 0.829916i \(0.311612\pi\)
\(312\) −3.03590 −0.171874
\(313\) −12.1901 −0.689026 −0.344513 0.938782i \(-0.611956\pi\)
−0.344513 + 0.938782i \(0.611956\pi\)
\(314\) 19.0240 1.07359
\(315\) −1.13949 −0.0642031
\(316\) 11.6421 0.654921
\(317\) −15.6048 −0.876454 −0.438227 0.898864i \(-0.644393\pi\)
−0.438227 + 0.898864i \(0.644393\pi\)
\(318\) −5.62511 −0.315440
\(319\) −36.6882 −2.05414
\(320\) 0.337407 0.0188616
\(321\) 3.13172 0.174795
\(322\) −4.51889 −0.251828
\(323\) 3.29522 0.183351
\(324\) 6.36395 0.353553
\(325\) −26.9439 −1.49458
\(326\) −20.1306 −1.11493
\(327\) −3.63062 −0.200774
\(328\) −8.23774 −0.454853
\(329\) 3.04851 0.168070
\(330\) −0.900650 −0.0495792
\(331\) 2.60334 0.143092 0.0715462 0.997437i \(-0.477207\pi\)
0.0715462 + 0.997437i \(0.477207\pi\)
\(332\) 2.29357 0.125876
\(333\) −22.5460 −1.23551
\(334\) 2.67577 0.146412
\(335\) −0.602823 −0.0329358
\(336\) −0.689425 −0.0376112
\(337\) −12.2376 −0.666624 −0.333312 0.942817i \(-0.608166\pi\)
−0.333312 + 0.942817i \(0.608166\pi\)
\(338\) 17.4078 0.946862
\(339\) −7.50128 −0.407414
\(340\) 0.526268 0.0285409
\(341\) 44.3371 2.40099
\(342\) −5.69766 −0.308094
\(343\) −15.5678 −0.840585
\(344\) 4.67088 0.251837
\(345\) 0.670329 0.0360893
\(346\) −0.473939 −0.0254791
\(347\) −4.04370 −0.217077 −0.108539 0.994092i \(-0.534617\pi\)
−0.108539 + 0.994092i \(0.534617\pi\)
\(348\) 4.16594 0.223318
\(349\) 15.3758 0.823048 0.411524 0.911399i \(-0.364997\pi\)
0.411524 + 0.911399i \(0.364997\pi\)
\(350\) −6.11871 −0.327059
\(351\) 17.2952 0.923150
\(352\) 4.84850 0.258426
\(353\) −14.9998 −0.798358 −0.399179 0.916873i \(-0.630705\pi\)
−0.399179 + 0.916873i \(0.630705\pi\)
\(354\) 7.31137 0.388595
\(355\) 0.476281 0.0252783
\(356\) −7.46599 −0.395696
\(357\) −1.07532 −0.0569122
\(358\) −13.3624 −0.706225
\(359\) 4.12956 0.217950 0.108975 0.994045i \(-0.465243\pi\)
0.108975 + 0.994045i \(0.465243\pi\)
\(360\) −0.909953 −0.0479587
\(361\) −14.5366 −0.765085
\(362\) 13.0898 0.687984
\(363\) −6.88621 −0.361432
\(364\) 6.90534 0.361938
\(365\) 1.89941 0.0994196
\(366\) 3.73422 0.195191
\(367\) 14.5734 0.760726 0.380363 0.924837i \(-0.375799\pi\)
0.380363 + 0.924837i \(0.375799\pi\)
\(368\) −3.60861 −0.188112
\(369\) 22.2163 1.15654
\(370\) 2.82071 0.146642
\(371\) 12.7947 0.664266
\(372\) −5.03448 −0.261025
\(373\) −6.71870 −0.347881 −0.173941 0.984756i \(-0.555650\pi\)
−0.173941 + 0.984756i \(0.555650\pi\)
\(374\) 7.56241 0.391043
\(375\) 1.83644 0.0948332
\(376\) 2.43442 0.125545
\(377\) −41.7265 −2.14902
\(378\) 3.92758 0.202013
\(379\) 25.4733 1.30847 0.654237 0.756290i \(-0.272990\pi\)
0.654237 + 0.756290i \(0.272990\pi\)
\(380\) 0.712831 0.0365675
\(381\) −2.42800 −0.124390
\(382\) 13.8214 0.707165
\(383\) 5.23057 0.267270 0.133635 0.991031i \(-0.457335\pi\)
0.133635 + 0.991031i \(0.457335\pi\)
\(384\) −0.550547 −0.0280950
\(385\) 2.04859 0.104406
\(386\) 1.23168 0.0626908
\(387\) −12.5969 −0.640335
\(388\) −0.461813 −0.0234450
\(389\) 38.7922 1.96684 0.983421 0.181339i \(-0.0580431\pi\)
0.983421 + 0.181339i \(0.0580431\pi\)
\(390\) −1.02433 −0.0518692
\(391\) −5.62849 −0.284645
\(392\) −5.43186 −0.274350
\(393\) −10.7974 −0.544658
\(394\) 8.14270 0.410223
\(395\) 3.92814 0.197646
\(396\) −13.0759 −0.657089
\(397\) 17.6872 0.887694 0.443847 0.896102i \(-0.353613\pi\)
0.443847 + 0.896102i \(0.353613\pi\)
\(398\) −21.2310 −1.06421
\(399\) −1.45653 −0.0729177
\(400\) −4.88616 −0.244308
\(401\) −11.6282 −0.580683 −0.290341 0.956923i \(-0.593769\pi\)
−0.290341 + 0.956923i \(0.593769\pi\)
\(402\) 0.983626 0.0490588
\(403\) 50.4258 2.51189
\(404\) −6.77064 −0.336852
\(405\) 2.14724 0.106697
\(406\) −9.47570 −0.470271
\(407\) 40.5333 2.00916
\(408\) −0.858711 −0.0425125
\(409\) 34.0010 1.68124 0.840620 0.541626i \(-0.182191\pi\)
0.840620 + 0.541626i \(0.182191\pi\)
\(410\) −2.77947 −0.137268
\(411\) −3.46870 −0.171099
\(412\) 4.82410 0.237666
\(413\) −16.6302 −0.818318
\(414\) 9.73204 0.478304
\(415\) 0.773868 0.0379877
\(416\) 5.51433 0.270362
\(417\) −1.21944 −0.0597164
\(418\) 10.2433 0.501016
\(419\) −11.2359 −0.548910 −0.274455 0.961600i \(-0.588497\pi\)
−0.274455 + 0.961600i \(0.588497\pi\)
\(420\) −0.232617 −0.0113505
\(421\) 17.3951 0.847786 0.423893 0.905712i \(-0.360663\pi\)
0.423893 + 0.905712i \(0.360663\pi\)
\(422\) −26.7233 −1.30087
\(423\) −6.56537 −0.319219
\(424\) 10.2173 0.496196
\(425\) −7.62114 −0.369680
\(426\) −0.777147 −0.0376529
\(427\) −8.49373 −0.411040
\(428\) −5.68837 −0.274958
\(429\) −14.7196 −0.710667
\(430\) 1.57599 0.0760009
\(431\) −31.9272 −1.53788 −0.768940 0.639320i \(-0.779216\pi\)
−0.768940 + 0.639320i \(0.779216\pi\)
\(432\) 3.13641 0.150901
\(433\) −9.32710 −0.448232 −0.224116 0.974562i \(-0.571949\pi\)
−0.224116 + 0.974562i \(0.571949\pi\)
\(434\) 11.4512 0.549677
\(435\) 1.40562 0.0673943
\(436\) 6.59457 0.315823
\(437\) −7.62380 −0.364696
\(438\) −3.09927 −0.148089
\(439\) −16.0384 −0.765470 −0.382735 0.923858i \(-0.625018\pi\)
−0.382735 + 0.923858i \(0.625018\pi\)
\(440\) 1.63592 0.0779894
\(441\) 14.6492 0.697580
\(442\) 8.60093 0.409105
\(443\) 17.1746 0.815992 0.407996 0.912984i \(-0.366228\pi\)
0.407996 + 0.912984i \(0.366228\pi\)
\(444\) −4.60256 −0.218428
\(445\) −2.51908 −0.119416
\(446\) 12.8063 0.606397
\(447\) 9.68256 0.457969
\(448\) 1.25225 0.0591634
\(449\) −10.1810 −0.480473 −0.240236 0.970714i \(-0.577225\pi\)
−0.240236 + 0.970714i \(0.577225\pi\)
\(450\) 13.1775 0.621192
\(451\) −39.9407 −1.88073
\(452\) 13.6251 0.640873
\(453\) −12.9393 −0.607943
\(454\) −19.0380 −0.893496
\(455\) 2.32991 0.109228
\(456\) −1.16313 −0.0544684
\(457\) 5.69689 0.266489 0.133245 0.991083i \(-0.457460\pi\)
0.133245 + 0.991083i \(0.457460\pi\)
\(458\) −0.294814 −0.0137758
\(459\) 4.89199 0.228339
\(460\) −1.21757 −0.0567695
\(461\) −27.1797 −1.26589 −0.632943 0.774198i \(-0.718153\pi\)
−0.632943 + 0.774198i \(0.718153\pi\)
\(462\) −3.34268 −0.155515
\(463\) −32.8499 −1.52666 −0.763332 0.646006i \(-0.776438\pi\)
−0.763332 + 0.646006i \(0.776438\pi\)
\(464\) −7.56691 −0.351285
\(465\) −1.69867 −0.0787738
\(466\) 27.3480 1.26687
\(467\) 6.79244 0.314316 0.157158 0.987573i \(-0.449767\pi\)
0.157158 + 0.987573i \(0.449767\pi\)
\(468\) −14.8716 −0.687439
\(469\) −2.23732 −0.103310
\(470\) 0.821389 0.0378879
\(471\) −10.4736 −0.482598
\(472\) −13.2802 −0.611271
\(473\) 22.6467 1.04130
\(474\) −6.40954 −0.294400
\(475\) −10.3228 −0.473645
\(476\) 1.95319 0.0895245
\(477\) −27.5550 −1.26166
\(478\) −10.0612 −0.460189
\(479\) −20.5432 −0.938641 −0.469320 0.883028i \(-0.655501\pi\)
−0.469320 + 0.883028i \(0.655501\pi\)
\(480\) −0.185759 −0.00847868
\(481\) 46.0997 2.10196
\(482\) −17.7231 −0.807265
\(483\) 2.48786 0.113202
\(484\) 12.5079 0.568543
\(485\) −0.155819 −0.00707538
\(486\) −12.9129 −0.585740
\(487\) 22.7661 1.03163 0.515815 0.856700i \(-0.327489\pi\)
0.515815 + 0.856700i \(0.327489\pi\)
\(488\) −6.78275 −0.307041
\(489\) 11.0828 0.501184
\(490\) −1.83275 −0.0827951
\(491\) −5.22516 −0.235808 −0.117904 0.993025i \(-0.537618\pi\)
−0.117904 + 0.993025i \(0.537618\pi\)
\(492\) 4.53526 0.204465
\(493\) −11.8024 −0.531555
\(494\) 11.6500 0.524157
\(495\) −4.41191 −0.198300
\(496\) 9.14450 0.410600
\(497\) 1.76767 0.0792908
\(498\) −1.26272 −0.0565838
\(499\) 18.4894 0.827698 0.413849 0.910346i \(-0.364184\pi\)
0.413849 + 0.910346i \(0.364184\pi\)
\(500\) −3.33566 −0.149175
\(501\) −1.47314 −0.0658150
\(502\) 0.608615 0.0271638
\(503\) 1.09184 0.0486829 0.0243414 0.999704i \(-0.492251\pi\)
0.0243414 + 0.999704i \(0.492251\pi\)
\(504\) −3.37720 −0.150433
\(505\) −2.28446 −0.101657
\(506\) −17.4963 −0.777806
\(507\) −9.58384 −0.425633
\(508\) 4.41015 0.195669
\(509\) 25.9973 1.15231 0.576156 0.817340i \(-0.304552\pi\)
0.576156 + 0.817340i \(0.304552\pi\)
\(510\) −0.289735 −0.0128297
\(511\) 7.04948 0.311850
\(512\) 1.00000 0.0441942
\(513\) 6.62621 0.292554
\(514\) 16.5189 0.728620
\(515\) 1.62768 0.0717244
\(516\) −2.57154 −0.113206
\(517\) 11.8033 0.519107
\(518\) 10.4688 0.459973
\(519\) 0.260926 0.0114534
\(520\) 1.86057 0.0815916
\(521\) 34.7337 1.52171 0.760856 0.648921i \(-0.224780\pi\)
0.760856 + 0.648921i \(0.224780\pi\)
\(522\) 20.4072 0.893199
\(523\) −44.2351 −1.93427 −0.967133 0.254270i \(-0.918165\pi\)
−0.967133 + 0.254270i \(0.918165\pi\)
\(524\) 19.6122 0.856762
\(525\) 3.36864 0.147019
\(526\) 16.3838 0.714367
\(527\) 14.2631 0.621308
\(528\) −2.66933 −0.116168
\(529\) −9.97797 −0.433825
\(530\) 3.44739 0.149745
\(531\) 35.8153 1.55425
\(532\) 2.64560 0.114701
\(533\) −45.4256 −1.96760
\(534\) 4.11038 0.177873
\(535\) −1.91930 −0.0829784
\(536\) −1.78663 −0.0771709
\(537\) 7.35663 0.317462
\(538\) −20.4975 −0.883709
\(539\) −26.3364 −1.13439
\(540\) 1.05825 0.0455397
\(541\) −8.12889 −0.349488 −0.174744 0.984614i \(-0.555910\pi\)
−0.174744 + 0.984614i \(0.555910\pi\)
\(542\) −25.7751 −1.10713
\(543\) −7.20654 −0.309262
\(544\) 1.55974 0.0668734
\(545\) 2.22506 0.0953110
\(546\) −3.80172 −0.162698
\(547\) −15.0891 −0.645162 −0.322581 0.946542i \(-0.604550\pi\)
−0.322581 + 0.946542i \(0.604550\pi\)
\(548\) 6.30047 0.269143
\(549\) 18.2924 0.780700
\(550\) −23.6905 −1.01017
\(551\) −15.9864 −0.681044
\(552\) 1.98671 0.0845599
\(553\) 14.5789 0.619958
\(554\) −9.45517 −0.401712
\(555\) −1.55294 −0.0659185
\(556\) 2.21497 0.0939355
\(557\) −21.5853 −0.914599 −0.457299 0.889313i \(-0.651183\pi\)
−0.457299 + 0.889313i \(0.651183\pi\)
\(558\) −24.6618 −1.04402
\(559\) 25.7568 1.08939
\(560\) 0.422520 0.0178547
\(561\) −4.16346 −0.175781
\(562\) −8.35664 −0.352504
\(563\) 4.61429 0.194469 0.0972345 0.995261i \(-0.469000\pi\)
0.0972345 + 0.995261i \(0.469000\pi\)
\(564\) −1.34026 −0.0564351
\(565\) 4.59722 0.193407
\(566\) 12.5174 0.526143
\(567\) 7.96929 0.334679
\(568\) 1.41159 0.0592290
\(569\) −34.1658 −1.43231 −0.716153 0.697943i \(-0.754099\pi\)
−0.716153 + 0.697943i \(0.754099\pi\)
\(570\) −0.392447 −0.0164378
\(571\) −1.96679 −0.0823077 −0.0411539 0.999153i \(-0.513103\pi\)
−0.0411539 + 0.999153i \(0.513103\pi\)
\(572\) 26.7362 1.11790
\(573\) −7.60934 −0.317885
\(574\) −10.3157 −0.430571
\(575\) 17.6322 0.735314
\(576\) −2.69690 −0.112371
\(577\) −27.6219 −1.14991 −0.574957 0.818183i \(-0.694981\pi\)
−0.574957 + 0.818183i \(0.694981\pi\)
\(578\) −14.5672 −0.605916
\(579\) −0.678097 −0.0281808
\(580\) −2.55313 −0.106013
\(581\) 2.87214 0.119156
\(582\) 0.254250 0.0105390
\(583\) 49.5386 2.05168
\(584\) 5.62943 0.232947
\(585\) −5.01778 −0.207460
\(586\) −8.75817 −0.361797
\(587\) −3.81882 −0.157620 −0.0788098 0.996890i \(-0.525112\pi\)
−0.0788098 + 0.996890i \(0.525112\pi\)
\(588\) 2.99049 0.123326
\(589\) 19.3193 0.796039
\(590\) −4.48083 −0.184473
\(591\) −4.48294 −0.184404
\(592\) 8.35997 0.343593
\(593\) −20.4216 −0.838613 −0.419306 0.907845i \(-0.637727\pi\)
−0.419306 + 0.907845i \(0.637727\pi\)
\(594\) 15.2069 0.623946
\(595\) 0.659021 0.0270172
\(596\) −17.5872 −0.720398
\(597\) 11.6886 0.478384
\(598\) −19.8990 −0.813732
\(599\) 5.99768 0.245059 0.122529 0.992465i \(-0.460899\pi\)
0.122529 + 0.992465i \(0.460899\pi\)
\(600\) 2.69006 0.109821
\(601\) 27.9369 1.13957 0.569785 0.821794i \(-0.307027\pi\)
0.569785 + 0.821794i \(0.307027\pi\)
\(602\) 5.84912 0.238393
\(603\) 4.81837 0.196219
\(604\) 23.5027 0.956310
\(605\) 4.22027 0.171578
\(606\) 3.72756 0.151422
\(607\) −34.4916 −1.39997 −0.699985 0.714158i \(-0.746810\pi\)
−0.699985 + 0.714158i \(0.746810\pi\)
\(608\) 2.11267 0.0856802
\(609\) 5.21682 0.211396
\(610\) −2.28855 −0.0926606
\(611\) 13.4242 0.543084
\(612\) −4.20646 −0.170036
\(613\) −2.53509 −0.102391 −0.0511957 0.998689i \(-0.516303\pi\)
−0.0511957 + 0.998689i \(0.516303\pi\)
\(614\) −20.3274 −0.820348
\(615\) 1.53023 0.0617048
\(616\) 6.07155 0.244630
\(617\) −7.17482 −0.288847 −0.144424 0.989516i \(-0.546133\pi\)
−0.144424 + 0.989516i \(0.546133\pi\)
\(618\) −2.65589 −0.106836
\(619\) 25.1926 1.01258 0.506289 0.862364i \(-0.331017\pi\)
0.506289 + 0.862364i \(0.331017\pi\)
\(620\) 3.08542 0.123913
\(621\) −11.3181 −0.454178
\(622\) 19.6769 0.788972
\(623\) −9.34931 −0.374572
\(624\) −3.03590 −0.121533
\(625\) 23.3053 0.932212
\(626\) −12.1901 −0.487215
\(627\) −5.63941 −0.225217
\(628\) 19.0240 0.759140
\(629\) 13.0394 0.519915
\(630\) −1.13949 −0.0453985
\(631\) −33.9314 −1.35079 −0.675395 0.737456i \(-0.736027\pi\)
−0.675395 + 0.737456i \(0.736027\pi\)
\(632\) 11.6421 0.463099
\(633\) 14.7125 0.584768
\(634\) −15.6048 −0.619747
\(635\) 1.48802 0.0590502
\(636\) −5.62511 −0.223050
\(637\) −29.9531 −1.18678
\(638\) −36.6882 −1.45250
\(639\) −3.80691 −0.150599
\(640\) 0.337407 0.0133372
\(641\) −40.7304 −1.60875 −0.804377 0.594120i \(-0.797501\pi\)
−0.804377 + 0.594120i \(0.797501\pi\)
\(642\) 3.13172 0.123599
\(643\) 16.9992 0.670383 0.335192 0.942150i \(-0.391199\pi\)
0.335192 + 0.942150i \(0.391199\pi\)
\(644\) −4.51889 −0.178069
\(645\) −0.867655 −0.0341639
\(646\) 3.29522 0.129649
\(647\) −13.1064 −0.515265 −0.257633 0.966243i \(-0.582942\pi\)
−0.257633 + 0.966243i \(0.582942\pi\)
\(648\) 6.36395 0.250000
\(649\) −64.3890 −2.52749
\(650\) −26.9439 −1.05683
\(651\) −6.30444 −0.247091
\(652\) −20.1306 −0.788376
\(653\) −39.3898 −1.54144 −0.770720 0.637174i \(-0.780103\pi\)
−0.770720 + 0.637174i \(0.780103\pi\)
\(654\) −3.63062 −0.141969
\(655\) 6.61729 0.258559
\(656\) −8.23774 −0.321630
\(657\) −15.1820 −0.592306
\(658\) 3.04851 0.118843
\(659\) −31.5228 −1.22795 −0.613976 0.789325i \(-0.710431\pi\)
−0.613976 + 0.789325i \(0.710431\pi\)
\(660\) −0.900650 −0.0350578
\(661\) 13.6555 0.531138 0.265569 0.964092i \(-0.414440\pi\)
0.265569 + 0.964092i \(0.414440\pi\)
\(662\) 2.60334 0.101182
\(663\) −4.73522 −0.183901
\(664\) 2.29357 0.0890079
\(665\) 0.892646 0.0346153
\(666\) −22.5460 −0.873639
\(667\) 27.3060 1.05729
\(668\) 2.67577 0.103529
\(669\) −7.05048 −0.272587
\(670\) −0.602823 −0.0232891
\(671\) −32.8862 −1.26956
\(672\) −0.689425 −0.0265951
\(673\) 34.0736 1.31344 0.656721 0.754134i \(-0.271943\pi\)
0.656721 + 0.754134i \(0.271943\pi\)
\(674\) −12.2376 −0.471374
\(675\) −15.3250 −0.589859
\(676\) 17.4078 0.669533
\(677\) 21.5980 0.830080 0.415040 0.909803i \(-0.363768\pi\)
0.415040 + 0.909803i \(0.363768\pi\)
\(678\) −7.50128 −0.288085
\(679\) −0.578308 −0.0221934
\(680\) 0.526268 0.0201815
\(681\) 10.4813 0.401644
\(682\) 44.3371 1.69775
\(683\) 16.8192 0.643568 0.321784 0.946813i \(-0.395718\pi\)
0.321784 + 0.946813i \(0.395718\pi\)
\(684\) −5.69766 −0.217856
\(685\) 2.12582 0.0812235
\(686\) −15.5678 −0.594383
\(687\) 0.162309 0.00619248
\(688\) 4.67088 0.178075
\(689\) 56.3416 2.14644
\(690\) 0.670329 0.0255190
\(691\) −16.0690 −0.611292 −0.305646 0.952145i \(-0.598872\pi\)
−0.305646 + 0.952145i \(0.598872\pi\)
\(692\) −0.473939 −0.0180165
\(693\) −16.3744 −0.622010
\(694\) −4.04370 −0.153497
\(695\) 0.747346 0.0283484
\(696\) 4.16594 0.157910
\(697\) −12.8487 −0.486681
\(698\) 15.3758 0.581983
\(699\) −15.0564 −0.569484
\(700\) −6.11871 −0.231265
\(701\) −23.8503 −0.900814 −0.450407 0.892823i \(-0.648721\pi\)
−0.450407 + 0.892823i \(0.648721\pi\)
\(702\) 17.2952 0.652765
\(703\) 17.6619 0.666131
\(704\) 4.84850 0.182735
\(705\) −0.452213 −0.0170313
\(706\) −14.9998 −0.564524
\(707\) −8.47857 −0.318869
\(708\) 7.31137 0.274778
\(709\) −12.9237 −0.485359 −0.242679 0.970107i \(-0.578026\pi\)
−0.242679 + 0.970107i \(0.578026\pi\)
\(710\) 0.476281 0.0178745
\(711\) −31.3976 −1.17750
\(712\) −7.46599 −0.279800
\(713\) −32.9989 −1.23582
\(714\) −1.07532 −0.0402430
\(715\) 9.02100 0.337366
\(716\) −13.3624 −0.499377
\(717\) 5.53917 0.206864
\(718\) 4.12956 0.154114
\(719\) −26.7455 −0.997438 −0.498719 0.866764i \(-0.666196\pi\)
−0.498719 + 0.866764i \(0.666196\pi\)
\(720\) −0.909953 −0.0339119
\(721\) 6.04099 0.224978
\(722\) −14.5366 −0.540997
\(723\) 9.75740 0.362882
\(724\) 13.0898 0.486478
\(725\) 36.9731 1.37315
\(726\) −6.88621 −0.255571
\(727\) −41.2347 −1.52931 −0.764656 0.644439i \(-0.777091\pi\)
−0.764656 + 0.644439i \(0.777091\pi\)
\(728\) 6.90534 0.255929
\(729\) −11.9827 −0.443804
\(730\) 1.89941 0.0703003
\(731\) 7.28536 0.269459
\(732\) 3.73422 0.138021
\(733\) 26.2755 0.970506 0.485253 0.874374i \(-0.338727\pi\)
0.485253 + 0.874374i \(0.338727\pi\)
\(734\) 14.5734 0.537914
\(735\) 1.00901 0.0372181
\(736\) −3.60861 −0.133015
\(737\) −8.66250 −0.319087
\(738\) 22.2163 0.817795
\(739\) −14.3012 −0.526078 −0.263039 0.964785i \(-0.584725\pi\)
−0.263039 + 0.964785i \(0.584725\pi\)
\(740\) 2.82071 0.103692
\(741\) −6.41386 −0.235619
\(742\) 12.7947 0.469707
\(743\) −36.9983 −1.35734 −0.678668 0.734445i \(-0.737443\pi\)
−0.678668 + 0.734445i \(0.737443\pi\)
\(744\) −5.03448 −0.184573
\(745\) −5.93403 −0.217406
\(746\) −6.71870 −0.245989
\(747\) −6.18553 −0.226317
\(748\) 7.56241 0.276509
\(749\) −7.12329 −0.260279
\(750\) 1.83644 0.0670572
\(751\) −18.4352 −0.672709 −0.336355 0.941735i \(-0.609194\pi\)
−0.336355 + 0.941735i \(0.609194\pi\)
\(752\) 2.43442 0.0887740
\(753\) −0.335071 −0.0122107
\(754\) −41.7265 −1.51959
\(755\) 7.92997 0.288601
\(756\) 3.92758 0.142845
\(757\) −44.0789 −1.60207 −0.801037 0.598614i \(-0.795718\pi\)
−0.801037 + 0.598614i \(0.795718\pi\)
\(758\) 25.4733 0.925230
\(759\) 9.63255 0.349639
\(760\) 0.712831 0.0258571
\(761\) −33.0802 −1.19916 −0.599578 0.800316i \(-0.704665\pi\)
−0.599578 + 0.800316i \(0.704665\pi\)
\(762\) −2.42800 −0.0879571
\(763\) 8.25808 0.298963
\(764\) 13.8214 0.500041
\(765\) −1.41929 −0.0513146
\(766\) 5.23057 0.188988
\(767\) −73.2314 −2.64423
\(768\) −0.550547 −0.0198662
\(769\) 23.4076 0.844100 0.422050 0.906572i \(-0.361311\pi\)
0.422050 + 0.906572i \(0.361311\pi\)
\(770\) 2.04859 0.0738259
\(771\) −9.09446 −0.327529
\(772\) 1.23168 0.0443291
\(773\) 31.9992 1.15093 0.575465 0.817826i \(-0.304821\pi\)
0.575465 + 0.817826i \(0.304821\pi\)
\(774\) −12.5969 −0.452785
\(775\) −44.6814 −1.60500
\(776\) −0.461813 −0.0165781
\(777\) −5.76357 −0.206767
\(778\) 38.7922 1.39077
\(779\) −17.4036 −0.623550
\(780\) −1.02433 −0.0366770
\(781\) 6.84409 0.244901
\(782\) −5.62849 −0.201274
\(783\) −23.7329 −0.848146
\(784\) −5.43186 −0.193995
\(785\) 6.41883 0.229098
\(786\) −10.7974 −0.385131
\(787\) −27.2060 −0.969791 −0.484895 0.874572i \(-0.661142\pi\)
−0.484895 + 0.874572i \(0.661142\pi\)
\(788\) 8.14270 0.290072
\(789\) −9.02004 −0.321122
\(790\) 3.92814 0.139757
\(791\) 17.0621 0.606660
\(792\) −13.0759 −0.464632
\(793\) −37.4023 −1.32820
\(794\) 17.6872 0.627695
\(795\) −1.89795 −0.0673134
\(796\) −21.2310 −0.752511
\(797\) 23.6122 0.836389 0.418194 0.908358i \(-0.362663\pi\)
0.418194 + 0.908358i \(0.362663\pi\)
\(798\) −1.45653 −0.0515606
\(799\) 3.79706 0.134330
\(800\) −4.88616 −0.172752
\(801\) 20.1350 0.711435
\(802\) −11.6282 −0.410605
\(803\) 27.2943 0.963194
\(804\) 0.983626 0.0346898
\(805\) −1.52471 −0.0537388
\(806\) 50.4258 1.77617
\(807\) 11.2848 0.397245
\(808\) −6.77064 −0.238190
\(809\) 30.3474 1.06696 0.533479 0.845814i \(-0.320884\pi\)
0.533479 + 0.845814i \(0.320884\pi\)
\(810\) 2.14724 0.0754464
\(811\) 36.4711 1.28068 0.640338 0.768094i \(-0.278794\pi\)
0.640338 + 0.768094i \(0.278794\pi\)
\(812\) −9.47570 −0.332532
\(813\) 14.1904 0.497679
\(814\) 40.5333 1.42069
\(815\) −6.79221 −0.237921
\(816\) −0.858711 −0.0300609
\(817\) 9.86803 0.345239
\(818\) 34.0010 1.18882
\(819\) −18.6230 −0.650741
\(820\) −2.77947 −0.0970634
\(821\) 56.5535 1.97373 0.986866 0.161541i \(-0.0516465\pi\)
0.986866 + 0.161541i \(0.0516465\pi\)
\(822\) −3.46870 −0.120985
\(823\) −14.2150 −0.495504 −0.247752 0.968824i \(-0.579692\pi\)
−0.247752 + 0.968824i \(0.579692\pi\)
\(824\) 4.82410 0.168055
\(825\) 13.0427 0.454090
\(826\) −16.6302 −0.578638
\(827\) −37.1401 −1.29149 −0.645744 0.763554i \(-0.723453\pi\)
−0.645744 + 0.763554i \(0.723453\pi\)
\(828\) 9.73204 0.338212
\(829\) −44.5883 −1.54862 −0.774309 0.632808i \(-0.781902\pi\)
−0.774309 + 0.632808i \(0.781902\pi\)
\(830\) 0.773868 0.0268614
\(831\) 5.20552 0.180577
\(832\) 5.51433 0.191175
\(833\) −8.47230 −0.293548
\(834\) −1.21944 −0.0422259
\(835\) 0.902825 0.0312436
\(836\) 10.2433 0.354272
\(837\) 28.6809 0.991357
\(838\) −11.2359 −0.388138
\(839\) −11.0768 −0.382414 −0.191207 0.981550i \(-0.561240\pi\)
−0.191207 + 0.981550i \(0.561240\pi\)
\(840\) −0.232617 −0.00802605
\(841\) 28.2582 0.974420
\(842\) 17.3951 0.599476
\(843\) 4.60072 0.158457
\(844\) −26.7233 −0.919856
\(845\) 5.87353 0.202056
\(846\) −6.56537 −0.225722
\(847\) 15.6631 0.538191
\(848\) 10.2173 0.350864
\(849\) −6.89139 −0.236512
\(850\) −7.62114 −0.261403
\(851\) −30.1678 −1.03414
\(852\) −0.777147 −0.0266246
\(853\) −31.5878 −1.08155 −0.540773 0.841168i \(-0.681868\pi\)
−0.540773 + 0.841168i \(0.681868\pi\)
\(854\) −8.49373 −0.290649
\(855\) −1.92243 −0.0657458
\(856\) −5.68837 −0.194425
\(857\) 51.4898 1.75886 0.879429 0.476030i \(-0.157925\pi\)
0.879429 + 0.476030i \(0.157925\pi\)
\(858\) −14.7196 −0.502517
\(859\) −0.804777 −0.0274587 −0.0137293 0.999906i \(-0.504370\pi\)
−0.0137293 + 0.999906i \(0.504370\pi\)
\(860\) 1.57599 0.0537407
\(861\) 5.67930 0.193550
\(862\) −31.9272 −1.08745
\(863\) −21.7710 −0.741092 −0.370546 0.928814i \(-0.620829\pi\)
−0.370546 + 0.928814i \(0.620829\pi\)
\(864\) 3.13641 0.106703
\(865\) −0.159910 −0.00543712
\(866\) −9.32710 −0.316948
\(867\) 8.01993 0.272371
\(868\) 11.4512 0.388680
\(869\) 56.4468 1.91483
\(870\) 1.40562 0.0476549
\(871\) −9.85209 −0.333825
\(872\) 6.59457 0.223320
\(873\) 1.24546 0.0421525
\(874\) −7.62380 −0.257879
\(875\) −4.17709 −0.141212
\(876\) −3.09927 −0.104714
\(877\) −14.4418 −0.487666 −0.243833 0.969817i \(-0.578405\pi\)
−0.243833 + 0.969817i \(0.578405\pi\)
\(878\) −16.0384 −0.541269
\(879\) 4.82178 0.162635
\(880\) 1.63592 0.0551468
\(881\) −18.4984 −0.623229 −0.311614 0.950209i \(-0.600870\pi\)
−0.311614 + 0.950209i \(0.600870\pi\)
\(882\) 14.6492 0.493263
\(883\) −22.3161 −0.750997 −0.375499 0.926823i \(-0.622528\pi\)
−0.375499 + 0.926823i \(0.622528\pi\)
\(884\) 8.60093 0.289281
\(885\) 2.46691 0.0829243
\(886\) 17.1746 0.576994
\(887\) −42.6558 −1.43224 −0.716120 0.697977i \(-0.754084\pi\)
−0.716120 + 0.697977i \(0.754084\pi\)
\(888\) −4.60256 −0.154452
\(889\) 5.52263 0.185223
\(890\) −2.51908 −0.0844397
\(891\) 30.8556 1.03370
\(892\) 12.8063 0.428787
\(893\) 5.14312 0.172108
\(894\) 9.68256 0.323833
\(895\) −4.50857 −0.150705
\(896\) 1.25225 0.0418349
\(897\) 10.9554 0.365789
\(898\) −10.1810 −0.339746
\(899\) −69.1956 −2.30780
\(900\) 13.1775 0.439249
\(901\) 15.9364 0.530917
\(902\) −39.9407 −1.32988
\(903\) −3.22022 −0.107162
\(904\) 13.6251 0.453166
\(905\) 4.41659 0.146812
\(906\) −12.9393 −0.429880
\(907\) −14.8392 −0.492729 −0.246365 0.969177i \(-0.579236\pi\)
−0.246365 + 0.969177i \(0.579236\pi\)
\(908\) −19.0380 −0.631797
\(909\) 18.2597 0.605637
\(910\) 2.32991 0.0772359
\(911\) 8.86624 0.293752 0.146876 0.989155i \(-0.453078\pi\)
0.146876 + 0.989155i \(0.453078\pi\)
\(912\) −1.16313 −0.0385149
\(913\) 11.1204 0.368031
\(914\) 5.69689 0.188436
\(915\) 1.25995 0.0416528
\(916\) −0.294814 −0.00974094
\(917\) 24.5594 0.811024
\(918\) 4.89199 0.161460
\(919\) 10.7955 0.356111 0.178056 0.984020i \(-0.443019\pi\)
0.178056 + 0.984020i \(0.443019\pi\)
\(920\) −1.21757 −0.0401421
\(921\) 11.1912 0.368763
\(922\) −27.1797 −0.895117
\(923\) 7.78397 0.256213
\(924\) −3.34268 −0.109966
\(925\) −40.8481 −1.34308
\(926\) −32.8499 −1.07951
\(927\) −13.0101 −0.427308
\(928\) −7.56691 −0.248396
\(929\) −24.4091 −0.800836 −0.400418 0.916333i \(-0.631135\pi\)
−0.400418 + 0.916333i \(0.631135\pi\)
\(930\) −1.69867 −0.0557015
\(931\) −11.4757 −0.376102
\(932\) 27.3480 0.895814
\(933\) −10.8331 −0.354659
\(934\) 6.79244 0.222255
\(935\) 2.55161 0.0834466
\(936\) −14.8716 −0.486093
\(937\) −1.04534 −0.0341499 −0.0170749 0.999854i \(-0.505435\pi\)
−0.0170749 + 0.999854i \(0.505435\pi\)
\(938\) −2.23732 −0.0730511
\(939\) 6.71123 0.219013
\(940\) 0.821389 0.0267908
\(941\) 22.3454 0.728438 0.364219 0.931313i \(-0.381336\pi\)
0.364219 + 0.931313i \(0.381336\pi\)
\(942\) −10.4736 −0.341248
\(943\) 29.7267 0.968036
\(944\) −13.2802 −0.432234
\(945\) 1.32519 0.0431086
\(946\) 22.6467 0.736309
\(947\) −12.4898 −0.405865 −0.202932 0.979193i \(-0.565047\pi\)
−0.202932 + 0.979193i \(0.565047\pi\)
\(948\) −6.40954 −0.208172
\(949\) 31.0425 1.00768
\(950\) −10.3228 −0.334917
\(951\) 8.59119 0.278588
\(952\) 1.95319 0.0633034
\(953\) 5.23263 0.169501 0.0847507 0.996402i \(-0.472991\pi\)
0.0847507 + 0.996402i \(0.472991\pi\)
\(954\) −27.5550 −0.892127
\(955\) 4.66345 0.150906
\(956\) −10.0612 −0.325403
\(957\) 20.1986 0.652927
\(958\) −20.5432 −0.663719
\(959\) 7.88979 0.254774
\(960\) −0.185759 −0.00599533
\(961\) 52.6218 1.69748
\(962\) 46.0997 1.48631
\(963\) 15.3410 0.494355
\(964\) −17.7231 −0.570823
\(965\) 0.415577 0.0133779
\(966\) 2.48786 0.0800456
\(967\) 15.5371 0.499640 0.249820 0.968292i \(-0.419628\pi\)
0.249820 + 0.968292i \(0.419628\pi\)
\(968\) 12.5079 0.402021
\(969\) −1.81418 −0.0582797
\(970\) −0.155819 −0.00500305
\(971\) −14.9060 −0.478356 −0.239178 0.970976i \(-0.576878\pi\)
−0.239178 + 0.970976i \(0.576878\pi\)
\(972\) −12.9129 −0.414181
\(973\) 2.77370 0.0889208
\(974\) 22.7661 0.729473
\(975\) 14.8339 0.475064
\(976\) −6.78275 −0.217111
\(977\) −32.1486 −1.02852 −0.514262 0.857633i \(-0.671934\pi\)
−0.514262 + 0.857633i \(0.671934\pi\)
\(978\) 11.0828 0.354390
\(979\) −36.1988 −1.15692
\(980\) −1.83275 −0.0585450
\(981\) −17.7849 −0.567828
\(982\) −5.22516 −0.166742
\(983\) −48.0732 −1.53330 −0.766648 0.642068i \(-0.778077\pi\)
−0.766648 + 0.642068i \(0.778077\pi\)
\(984\) 4.53526 0.144579
\(985\) 2.74741 0.0875396
\(986\) −11.8024 −0.375866
\(987\) −1.67835 −0.0534224
\(988\) 11.6500 0.370635
\(989\) −16.8553 −0.535969
\(990\) −4.41191 −0.140220
\(991\) 41.4866 1.31787 0.658933 0.752202i \(-0.271008\pi\)
0.658933 + 0.752202i \(0.271008\pi\)
\(992\) 9.14450 0.290338
\(993\) −1.43326 −0.0454831
\(994\) 1.76767 0.0560671
\(995\) −7.16348 −0.227097
\(996\) −1.26272 −0.0400108
\(997\) 43.9090 1.39061 0.695306 0.718714i \(-0.255269\pi\)
0.695306 + 0.718714i \(0.255269\pi\)
\(998\) 18.4894 0.585271
\(999\) 26.2203 0.829574
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.1.20 52
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4034.2.a.d.1.20 52 1.1 even 1 trivial