Properties

Label 6017.2.a.e.1.16
Level $6017$
Weight $2$
Character 6017.1
Self dual yes
Analytic conductor $48.046$
Analytic rank $0$
Dimension $119$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [6017,2,Mod(1,6017)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6017, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("6017.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6017 = 11 \cdot 547 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6017.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(48.0459868962\)
Analytic rank: \(0\)
Dimension: \(119\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) \(=\) 6017.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.22427 q^{2} +3.08840 q^{3} +2.94737 q^{4} -2.11023 q^{5} -6.86944 q^{6} +3.85755 q^{7} -2.10721 q^{8} +6.53822 q^{9} +O(q^{10})\) \(q-2.22427 q^{2} +3.08840 q^{3} +2.94737 q^{4} -2.11023 q^{5} -6.86944 q^{6} +3.85755 q^{7} -2.10721 q^{8} +6.53822 q^{9} +4.69372 q^{10} +1.00000 q^{11} +9.10267 q^{12} -0.535662 q^{13} -8.58022 q^{14} -6.51724 q^{15} -1.20774 q^{16} -3.98479 q^{17} -14.5428 q^{18} -1.04439 q^{19} -6.21963 q^{20} +11.9137 q^{21} -2.22427 q^{22} +6.16604 q^{23} -6.50791 q^{24} -0.546930 q^{25} +1.19146 q^{26} +10.9275 q^{27} +11.3696 q^{28} +0.156851 q^{29} +14.4961 q^{30} -2.30672 q^{31} +6.90076 q^{32} +3.08840 q^{33} +8.86325 q^{34} -8.14031 q^{35} +19.2706 q^{36} +3.47103 q^{37} +2.32301 q^{38} -1.65434 q^{39} +4.44670 q^{40} +4.04037 q^{41} -26.4992 q^{42} +8.50197 q^{43} +2.94737 q^{44} -13.7972 q^{45} -13.7149 q^{46} -6.52719 q^{47} -3.72999 q^{48} +7.88068 q^{49} +1.21652 q^{50} -12.3066 q^{51} -1.57879 q^{52} -12.8417 q^{53} -24.3056 q^{54} -2.11023 q^{55} -8.12867 q^{56} -3.22550 q^{57} -0.348879 q^{58} -0.140032 q^{59} -19.2087 q^{60} +3.16264 q^{61} +5.13076 q^{62} +25.2215 q^{63} -12.9337 q^{64} +1.13037 q^{65} -6.86944 q^{66} +9.51054 q^{67} -11.7447 q^{68} +19.0432 q^{69} +18.1062 q^{70} +5.43590 q^{71} -13.7774 q^{72} +2.85653 q^{73} -7.72051 q^{74} -1.68914 q^{75} -3.07821 q^{76} +3.85755 q^{77} +3.67969 q^{78} +10.8974 q^{79} +2.54861 q^{80} +14.1337 q^{81} -8.98688 q^{82} +4.34014 q^{83} +35.1140 q^{84} +8.40883 q^{85} -18.9107 q^{86} +0.484420 q^{87} -2.10721 q^{88} -0.346987 q^{89} +30.6886 q^{90} -2.06634 q^{91} +18.1736 q^{92} -7.12407 q^{93} +14.5182 q^{94} +2.20391 q^{95} +21.3123 q^{96} +10.3716 q^{97} -17.5287 q^{98} +6.53822 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 119 q + 15 q^{2} + 15 q^{3} + 133 q^{4} + 6 q^{5} + 16 q^{6} + 72 q^{7} + 39 q^{8} + 128 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 119 q + 15 q^{2} + 15 q^{3} + 133 q^{4} + 6 q^{5} + 16 q^{6} + 72 q^{7} + 39 q^{8} + 128 q^{9} + 22 q^{10} + 119 q^{11} + 40 q^{12} + 67 q^{13} + 3 q^{14} + 22 q^{15} + 145 q^{16} + 57 q^{17} + 53 q^{18} + 68 q^{19} + 25 q^{20} + 21 q^{21} + 15 q^{22} + 21 q^{23} + 34 q^{24} + 137 q^{25} + 10 q^{26} + 54 q^{27} + 149 q^{28} + 46 q^{29} + 10 q^{30} + 87 q^{31} + 58 q^{32} + 15 q^{33} + 16 q^{34} + 40 q^{35} + 137 q^{36} + 39 q^{37} + 27 q^{38} + 72 q^{39} + 46 q^{40} + 50 q^{41} - 4 q^{42} + 122 q^{43} + 133 q^{44} + 12 q^{45} + 22 q^{46} + 92 q^{47} + 9 q^{48} + 161 q^{49} + 2 q^{50} - 12 q^{51} + 177 q^{52} + 12 q^{53} + 19 q^{54} + 6 q^{55} - 16 q^{56} + 43 q^{57} + 56 q^{58} + 39 q^{59} + 27 q^{60} + 114 q^{61} + 66 q^{62} + 196 q^{63} + 161 q^{64} + 7 q^{65} + 16 q^{66} + 59 q^{67} + 139 q^{68} - 24 q^{69} + 9 q^{70} + 11 q^{71} + 92 q^{72} + 123 q^{73} + q^{74} + 19 q^{75} + 92 q^{76} + 72 q^{77} - 101 q^{78} + 78 q^{79} - 34 q^{80} + 139 q^{81} + 73 q^{82} + 108 q^{83} - 31 q^{84} + 30 q^{85} - 18 q^{86} + 164 q^{87} + 39 q^{88} + 15 q^{89} - 41 q^{90} + 60 q^{91} - 26 q^{92} - 2 q^{93} + 45 q^{94} + 75 q^{95} + 42 q^{96} + 73 q^{97} + 32 q^{98} + 128 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.22427 −1.57280 −0.786398 0.617720i \(-0.788056\pi\)
−0.786398 + 0.617720i \(0.788056\pi\)
\(3\) 3.08840 1.78309 0.891545 0.452933i \(-0.149622\pi\)
0.891545 + 0.452933i \(0.149622\pi\)
\(4\) 2.94737 1.47369
\(5\) −2.11023 −0.943723 −0.471862 0.881673i \(-0.656418\pi\)
−0.471862 + 0.881673i \(0.656418\pi\)
\(6\) −6.86944 −2.80444
\(7\) 3.85755 1.45802 0.729008 0.684505i \(-0.239982\pi\)
0.729008 + 0.684505i \(0.239982\pi\)
\(8\) −2.10721 −0.745012
\(9\) 6.53822 2.17941
\(10\) 4.69372 1.48428
\(11\) 1.00000 0.301511
\(12\) 9.10267 2.62771
\(13\) −0.535662 −0.148566 −0.0742829 0.997237i \(-0.523667\pi\)
−0.0742829 + 0.997237i \(0.523667\pi\)
\(14\) −8.58022 −2.29316
\(15\) −6.51724 −1.68274
\(16\) −1.20774 −0.301935
\(17\) −3.98479 −0.966455 −0.483227 0.875495i \(-0.660536\pi\)
−0.483227 + 0.875495i \(0.660536\pi\)
\(18\) −14.5428 −3.42776
\(19\) −1.04439 −0.239600 −0.119800 0.992798i \(-0.538225\pi\)
−0.119800 + 0.992798i \(0.538225\pi\)
\(20\) −6.21963 −1.39075
\(21\) 11.9137 2.59977
\(22\) −2.22427 −0.474216
\(23\) 6.16604 1.28571 0.642854 0.765989i \(-0.277750\pi\)
0.642854 + 0.765989i \(0.277750\pi\)
\(24\) −6.50791 −1.32842
\(25\) −0.546930 −0.109386
\(26\) 1.19146 0.233664
\(27\) 10.9275 2.10299
\(28\) 11.3696 2.14866
\(29\) 0.156851 0.0291266 0.0145633 0.999894i \(-0.495364\pi\)
0.0145633 + 0.999894i \(0.495364\pi\)
\(30\) 14.4961 2.64661
\(31\) −2.30672 −0.414299 −0.207149 0.978309i \(-0.566419\pi\)
−0.207149 + 0.978309i \(0.566419\pi\)
\(32\) 6.90076 1.21989
\(33\) 3.08840 0.537622
\(34\) 8.86325 1.52004
\(35\) −8.14031 −1.37596
\(36\) 19.2706 3.21176
\(37\) 3.47103 0.570634 0.285317 0.958433i \(-0.407901\pi\)
0.285317 + 0.958433i \(0.407901\pi\)
\(38\) 2.32301 0.376842
\(39\) −1.65434 −0.264906
\(40\) 4.44670 0.703085
\(41\) 4.04037 0.631000 0.315500 0.948925i \(-0.397828\pi\)
0.315500 + 0.948925i \(0.397828\pi\)
\(42\) −26.4992 −4.08891
\(43\) 8.50197 1.29654 0.648269 0.761411i \(-0.275493\pi\)
0.648269 + 0.761411i \(0.275493\pi\)
\(44\) 2.94737 0.444333
\(45\) −13.7972 −2.05676
\(46\) −13.7149 −2.02216
\(47\) −6.52719 −0.952088 −0.476044 0.879421i \(-0.657930\pi\)
−0.476044 + 0.879421i \(0.657930\pi\)
\(48\) −3.72999 −0.538377
\(49\) 7.88068 1.12581
\(50\) 1.21652 0.172042
\(51\) −12.3066 −1.72328
\(52\) −1.57879 −0.218939
\(53\) −12.8417 −1.76395 −0.881973 0.471300i \(-0.843785\pi\)
−0.881973 + 0.471300i \(0.843785\pi\)
\(54\) −24.3056 −3.30757
\(55\) −2.11023 −0.284543
\(56\) −8.12867 −1.08624
\(57\) −3.22550 −0.427228
\(58\) −0.348879 −0.0458101
\(59\) −0.140032 −0.0182306 −0.00911528 0.999958i \(-0.502902\pi\)
−0.00911528 + 0.999958i \(0.502902\pi\)
\(60\) −19.2087 −2.47984
\(61\) 3.16264 0.404934 0.202467 0.979289i \(-0.435104\pi\)
0.202467 + 0.979289i \(0.435104\pi\)
\(62\) 5.13076 0.651607
\(63\) 25.2215 3.17761
\(64\) −12.9337 −1.61671
\(65\) 1.13037 0.140205
\(66\) −6.86944 −0.845569
\(67\) 9.51054 1.16190 0.580949 0.813940i \(-0.302682\pi\)
0.580949 + 0.813940i \(0.302682\pi\)
\(68\) −11.7447 −1.42425
\(69\) 19.0432 2.29253
\(70\) 18.1062 2.16411
\(71\) 5.43590 0.645123 0.322561 0.946549i \(-0.395456\pi\)
0.322561 + 0.946549i \(0.395456\pi\)
\(72\) −13.7774 −1.62368
\(73\) 2.85653 0.334332 0.167166 0.985929i \(-0.446538\pi\)
0.167166 + 0.985929i \(0.446538\pi\)
\(74\) −7.72051 −0.897491
\(75\) −1.68914 −0.195045
\(76\) −3.07821 −0.353095
\(77\) 3.85755 0.439608
\(78\) 3.67969 0.416643
\(79\) 10.8974 1.22606 0.613028 0.790061i \(-0.289951\pi\)
0.613028 + 0.790061i \(0.289951\pi\)
\(80\) 2.54861 0.284943
\(81\) 14.1337 1.57041
\(82\) −8.98688 −0.992435
\(83\) 4.34014 0.476392 0.238196 0.971217i \(-0.423444\pi\)
0.238196 + 0.971217i \(0.423444\pi\)
\(84\) 35.1140 3.83125
\(85\) 8.40883 0.912066
\(86\) −18.9107 −2.03919
\(87\) 0.484420 0.0519353
\(88\) −2.10721 −0.224629
\(89\) −0.346987 −0.0367806 −0.0183903 0.999831i \(-0.505854\pi\)
−0.0183903 + 0.999831i \(0.505854\pi\)
\(90\) 30.6886 3.23486
\(91\) −2.06634 −0.216611
\(92\) 18.1736 1.89473
\(93\) −7.12407 −0.738732
\(94\) 14.5182 1.49744
\(95\) 2.20391 0.226116
\(96\) 21.3123 2.17518
\(97\) 10.3716 1.05307 0.526537 0.850152i \(-0.323490\pi\)
0.526537 + 0.850152i \(0.323490\pi\)
\(98\) −17.5287 −1.77067
\(99\) 6.53822 0.657116
\(100\) −1.61201 −0.161201
\(101\) 9.06625 0.902126 0.451063 0.892492i \(-0.351045\pi\)
0.451063 + 0.892492i \(0.351045\pi\)
\(102\) 27.3733 2.71036
\(103\) 12.2871 1.21068 0.605341 0.795966i \(-0.293037\pi\)
0.605341 + 0.795966i \(0.293037\pi\)
\(104\) 1.12875 0.110683
\(105\) −25.1406 −2.45347
\(106\) 28.5634 2.77433
\(107\) −5.76006 −0.556846 −0.278423 0.960459i \(-0.589812\pi\)
−0.278423 + 0.960459i \(0.589812\pi\)
\(108\) 32.2073 3.09915
\(109\) −5.23952 −0.501855 −0.250927 0.968006i \(-0.580736\pi\)
−0.250927 + 0.968006i \(0.580736\pi\)
\(110\) 4.69372 0.447529
\(111\) 10.7199 1.01749
\(112\) −4.65892 −0.440226
\(113\) 1.67660 0.157721 0.0788607 0.996886i \(-0.474872\pi\)
0.0788607 + 0.996886i \(0.474872\pi\)
\(114\) 7.17439 0.671943
\(115\) −13.0118 −1.21335
\(116\) 0.462299 0.0429234
\(117\) −3.50228 −0.323785
\(118\) 0.311468 0.0286729
\(119\) −15.3715 −1.40911
\(120\) 13.7332 1.25366
\(121\) 1.00000 0.0909091
\(122\) −7.03456 −0.636879
\(123\) 12.4783 1.12513
\(124\) −6.79876 −0.610546
\(125\) 11.7053 1.04695
\(126\) −56.0994 −4.99774
\(127\) 12.8375 1.13914 0.569571 0.821942i \(-0.307110\pi\)
0.569571 + 0.821942i \(0.307110\pi\)
\(128\) 14.9664 1.32286
\(129\) 26.2575 2.31184
\(130\) −2.51424 −0.220514
\(131\) 3.92349 0.342797 0.171399 0.985202i \(-0.445171\pi\)
0.171399 + 0.985202i \(0.445171\pi\)
\(132\) 9.10267 0.792286
\(133\) −4.02880 −0.349341
\(134\) −21.1540 −1.82743
\(135\) −23.0594 −1.98464
\(136\) 8.39680 0.720020
\(137\) −14.5401 −1.24224 −0.621122 0.783714i \(-0.713323\pi\)
−0.621122 + 0.783714i \(0.713323\pi\)
\(138\) −42.3572 −3.60569
\(139\) 8.17531 0.693420 0.346710 0.937972i \(-0.387299\pi\)
0.346710 + 0.937972i \(0.387299\pi\)
\(140\) −23.9925 −2.02774
\(141\) −20.1586 −1.69766
\(142\) −12.0909 −1.01465
\(143\) −0.535662 −0.0447943
\(144\) −7.89648 −0.658040
\(145\) −0.330992 −0.0274874
\(146\) −6.35369 −0.525835
\(147\) 24.3387 2.00742
\(148\) 10.2304 0.840935
\(149\) 18.8259 1.54227 0.771137 0.636669i \(-0.219688\pi\)
0.771137 + 0.636669i \(0.219688\pi\)
\(150\) 3.75710 0.306766
\(151\) 3.93068 0.319874 0.159937 0.987127i \(-0.448871\pi\)
0.159937 + 0.987127i \(0.448871\pi\)
\(152\) 2.20076 0.178505
\(153\) −26.0535 −2.10630
\(154\) −8.58022 −0.691414
\(155\) 4.86770 0.390983
\(156\) −4.87595 −0.390388
\(157\) 17.0071 1.35732 0.678658 0.734454i \(-0.262562\pi\)
0.678658 + 0.734454i \(0.262562\pi\)
\(158\) −24.2388 −1.92834
\(159\) −39.6604 −3.14527
\(160\) −14.5622 −1.15124
\(161\) 23.7858 1.87458
\(162\) −31.4372 −2.46994
\(163\) −1.17678 −0.0921723 −0.0460862 0.998937i \(-0.514675\pi\)
−0.0460862 + 0.998937i \(0.514675\pi\)
\(164\) 11.9085 0.929897
\(165\) −6.51724 −0.507366
\(166\) −9.65364 −0.749268
\(167\) −8.96042 −0.693378 −0.346689 0.937980i \(-0.612694\pi\)
−0.346689 + 0.937980i \(0.612694\pi\)
\(168\) −25.1046 −1.93686
\(169\) −12.7131 −0.977928
\(170\) −18.7035 −1.43449
\(171\) −6.82847 −0.522186
\(172\) 25.0585 1.91069
\(173\) −10.0532 −0.764332 −0.382166 0.924094i \(-0.624822\pi\)
−0.382166 + 0.924094i \(0.624822\pi\)
\(174\) −1.07748 −0.0816835
\(175\) −2.10981 −0.159487
\(176\) −1.20774 −0.0910369
\(177\) −0.432474 −0.0325067
\(178\) 0.771793 0.0578483
\(179\) −8.23468 −0.615489 −0.307745 0.951469i \(-0.599574\pi\)
−0.307745 + 0.951469i \(0.599574\pi\)
\(180\) −40.6654 −3.03102
\(181\) −4.95249 −0.368116 −0.184058 0.982915i \(-0.558923\pi\)
−0.184058 + 0.982915i \(0.558923\pi\)
\(182\) 4.59610 0.340685
\(183\) 9.76750 0.722034
\(184\) −12.9931 −0.957868
\(185\) −7.32467 −0.538521
\(186\) 15.8459 1.16187
\(187\) −3.98479 −0.291397
\(188\) −19.2381 −1.40308
\(189\) 42.1532 3.06619
\(190\) −4.90209 −0.355635
\(191\) 7.39271 0.534918 0.267459 0.963569i \(-0.413816\pi\)
0.267459 + 0.963569i \(0.413816\pi\)
\(192\) −39.9444 −2.88274
\(193\) 7.02152 0.505420 0.252710 0.967542i \(-0.418678\pi\)
0.252710 + 0.967542i \(0.418678\pi\)
\(194\) −23.0692 −1.65627
\(195\) 3.49103 0.249998
\(196\) 23.2273 1.65909
\(197\) −23.4547 −1.67108 −0.835539 0.549431i \(-0.814844\pi\)
−0.835539 + 0.549431i \(0.814844\pi\)
\(198\) −14.5428 −1.03351
\(199\) 2.83149 0.200719 0.100359 0.994951i \(-0.468001\pi\)
0.100359 + 0.994951i \(0.468001\pi\)
\(200\) 1.15250 0.0814939
\(201\) 29.3724 2.07177
\(202\) −20.1658 −1.41886
\(203\) 0.605061 0.0424670
\(204\) −36.2723 −2.53957
\(205\) −8.52612 −0.595490
\(206\) −27.3298 −1.90416
\(207\) 40.3150 2.80208
\(208\) 0.646940 0.0448572
\(209\) −1.04439 −0.0722422
\(210\) 55.9194 3.85880
\(211\) −19.3646 −1.33311 −0.666556 0.745455i \(-0.732232\pi\)
−0.666556 + 0.745455i \(0.732232\pi\)
\(212\) −37.8493 −2.59950
\(213\) 16.7883 1.15031
\(214\) 12.8119 0.875805
\(215\) −17.9411 −1.22357
\(216\) −23.0265 −1.56675
\(217\) −8.89828 −0.604054
\(218\) 11.6541 0.789315
\(219\) 8.82211 0.596143
\(220\) −6.21963 −0.419328
\(221\) 2.13450 0.143582
\(222\) −23.8440 −1.60031
\(223\) −2.46289 −0.164927 −0.0824637 0.996594i \(-0.526279\pi\)
−0.0824637 + 0.996594i \(0.526279\pi\)
\(224\) 26.6200 1.77863
\(225\) −3.57595 −0.238397
\(226\) −3.72921 −0.248064
\(227\) 12.3511 0.819771 0.409886 0.912137i \(-0.365569\pi\)
0.409886 + 0.912137i \(0.365569\pi\)
\(228\) −9.50676 −0.629601
\(229\) −1.85335 −0.122473 −0.0612365 0.998123i \(-0.519504\pi\)
−0.0612365 + 0.998123i \(0.519504\pi\)
\(230\) 28.9417 1.90836
\(231\) 11.9137 0.783861
\(232\) −0.330519 −0.0216996
\(233\) −0.198599 −0.0130106 −0.00650532 0.999979i \(-0.502071\pi\)
−0.00650532 + 0.999979i \(0.502071\pi\)
\(234\) 7.79000 0.509248
\(235\) 13.7739 0.898508
\(236\) −0.412725 −0.0268661
\(237\) 33.6556 2.18617
\(238\) 34.1904 2.21624
\(239\) 9.27402 0.599887 0.299943 0.953957i \(-0.403032\pi\)
0.299943 + 0.953957i \(0.403032\pi\)
\(240\) 7.87113 0.508079
\(241\) 6.90113 0.444541 0.222271 0.974985i \(-0.428653\pi\)
0.222271 + 0.974985i \(0.428653\pi\)
\(242\) −2.22427 −0.142981
\(243\) 10.8682 0.697194
\(244\) 9.32147 0.596746
\(245\) −16.6300 −1.06245
\(246\) −27.7551 −1.76960
\(247\) 0.559441 0.0355964
\(248\) 4.86074 0.308657
\(249\) 13.4041 0.849450
\(250\) −26.0357 −1.64664
\(251\) −13.0171 −0.821630 −0.410815 0.911719i \(-0.634756\pi\)
−0.410815 + 0.911719i \(0.634756\pi\)
\(252\) 74.3372 4.68280
\(253\) 6.16604 0.387656
\(254\) −28.5540 −1.79164
\(255\) 25.9698 1.62630
\(256\) −7.42204 −0.463877
\(257\) −1.15523 −0.0720612 −0.0360306 0.999351i \(-0.511471\pi\)
−0.0360306 + 0.999351i \(0.511471\pi\)
\(258\) −58.4037 −3.63606
\(259\) 13.3897 0.831994
\(260\) 3.33162 0.206618
\(261\) 1.02553 0.0634786
\(262\) −8.72691 −0.539150
\(263\) 12.9324 0.797448 0.398724 0.917071i \(-0.369453\pi\)
0.398724 + 0.917071i \(0.369453\pi\)
\(264\) −6.50791 −0.400534
\(265\) 27.0990 1.66468
\(266\) 8.96112 0.549442
\(267\) −1.07164 −0.0655830
\(268\) 28.0311 1.71227
\(269\) −21.6300 −1.31880 −0.659402 0.751790i \(-0.729191\pi\)
−0.659402 + 0.751790i \(0.729191\pi\)
\(270\) 51.2904 3.12144
\(271\) 27.9706 1.69909 0.849546 0.527515i \(-0.176876\pi\)
0.849546 + 0.527515i \(0.176876\pi\)
\(272\) 4.81260 0.291807
\(273\) −6.38169 −0.386237
\(274\) 32.3411 1.95380
\(275\) −0.546930 −0.0329811
\(276\) 56.1274 3.37847
\(277\) 9.81001 0.589427 0.294713 0.955586i \(-0.404776\pi\)
0.294713 + 0.955586i \(0.404776\pi\)
\(278\) −18.1841 −1.09061
\(279\) −15.0818 −0.902926
\(280\) 17.1534 1.02511
\(281\) 14.1688 0.845243 0.422621 0.906306i \(-0.361110\pi\)
0.422621 + 0.906306i \(0.361110\pi\)
\(282\) 44.8381 2.67007
\(283\) 30.0213 1.78458 0.892292 0.451459i \(-0.149096\pi\)
0.892292 + 0.451459i \(0.149096\pi\)
\(284\) 16.0216 0.950709
\(285\) 6.80655 0.403185
\(286\) 1.19146 0.0704522
\(287\) 15.5859 0.920009
\(288\) 45.1187 2.65865
\(289\) −1.12141 −0.0659655
\(290\) 0.736216 0.0432321
\(291\) 32.0316 1.87773
\(292\) 8.41926 0.492700
\(293\) −30.8962 −1.80498 −0.902488 0.430716i \(-0.858261\pi\)
−0.902488 + 0.430716i \(0.858261\pi\)
\(294\) −54.1358 −3.15727
\(295\) 0.295499 0.0172046
\(296\) −7.31419 −0.425129
\(297\) 10.9275 0.634075
\(298\) −41.8738 −2.42568
\(299\) −3.30291 −0.191012
\(300\) −4.97853 −0.287435
\(301\) 32.7968 1.89037
\(302\) −8.74289 −0.503097
\(303\) 28.0002 1.60857
\(304\) 1.26136 0.0723437
\(305\) −6.67389 −0.382146
\(306\) 57.9499 3.31278
\(307\) −17.7558 −1.01338 −0.506688 0.862130i \(-0.669130\pi\)
−0.506688 + 0.862130i \(0.669130\pi\)
\(308\) 11.3696 0.647845
\(309\) 37.9474 2.15875
\(310\) −10.8271 −0.614937
\(311\) −5.69279 −0.322809 −0.161404 0.986888i \(-0.551602\pi\)
−0.161404 + 0.986888i \(0.551602\pi\)
\(312\) 3.48604 0.197358
\(313\) 9.14950 0.517160 0.258580 0.965990i \(-0.416745\pi\)
0.258580 + 0.965990i \(0.416745\pi\)
\(314\) −37.8284 −2.13478
\(315\) −53.2232 −2.99879
\(316\) 32.1188 1.80682
\(317\) −5.59589 −0.314296 −0.157148 0.987575i \(-0.550230\pi\)
−0.157148 + 0.987575i \(0.550230\pi\)
\(318\) 88.2154 4.94687
\(319\) 0.156851 0.00878199
\(320\) 27.2930 1.52573
\(321\) −17.7894 −0.992906
\(322\) −52.9060 −2.94834
\(323\) 4.16169 0.231563
\(324\) 41.6573 2.31429
\(325\) 0.292970 0.0162510
\(326\) 2.61747 0.144968
\(327\) −16.1817 −0.894852
\(328\) −8.51392 −0.470103
\(329\) −25.1789 −1.38816
\(330\) 14.4961 0.797983
\(331\) 7.13143 0.391979 0.195989 0.980606i \(-0.437208\pi\)
0.195989 + 0.980606i \(0.437208\pi\)
\(332\) 12.7920 0.702053
\(333\) 22.6944 1.24364
\(334\) 19.9304 1.09054
\(335\) −20.0694 −1.09651
\(336\) −14.3886 −0.784963
\(337\) −29.1161 −1.58606 −0.793028 0.609186i \(-0.791496\pi\)
−0.793028 + 0.609186i \(0.791496\pi\)
\(338\) 28.2773 1.53808
\(339\) 5.17802 0.281231
\(340\) 24.7840 1.34410
\(341\) −2.30672 −0.124916
\(342\) 15.1884 0.821293
\(343\) 3.39726 0.183435
\(344\) −17.9154 −0.965936
\(345\) −40.1855 −2.16352
\(346\) 22.3611 1.20214
\(347\) −10.9029 −0.585296 −0.292648 0.956220i \(-0.594536\pi\)
−0.292648 + 0.956220i \(0.594536\pi\)
\(348\) 1.42777 0.0765363
\(349\) −4.53780 −0.242903 −0.121451 0.992597i \(-0.538755\pi\)
−0.121451 + 0.992597i \(0.538755\pi\)
\(350\) 4.69279 0.250840
\(351\) −5.85342 −0.312432
\(352\) 6.90076 0.367812
\(353\) −19.0740 −1.01521 −0.507603 0.861591i \(-0.669468\pi\)
−0.507603 + 0.861591i \(0.669468\pi\)
\(354\) 0.961938 0.0511264
\(355\) −11.4710 −0.608818
\(356\) −1.02270 −0.0542030
\(357\) −47.4735 −2.51256
\(358\) 18.3162 0.968039
\(359\) −1.05316 −0.0555839 −0.0277919 0.999614i \(-0.508848\pi\)
−0.0277919 + 0.999614i \(0.508848\pi\)
\(360\) 29.0735 1.53231
\(361\) −17.9092 −0.942592
\(362\) 11.0157 0.578971
\(363\) 3.08840 0.162099
\(364\) −6.09027 −0.319217
\(365\) −6.02793 −0.315516
\(366\) −21.7255 −1.13561
\(367\) −27.5353 −1.43733 −0.718666 0.695355i \(-0.755247\pi\)
−0.718666 + 0.695355i \(0.755247\pi\)
\(368\) −7.44698 −0.388200
\(369\) 26.4169 1.37521
\(370\) 16.2920 0.846983
\(371\) −49.5376 −2.57186
\(372\) −20.9973 −1.08866
\(373\) 15.6898 0.812385 0.406193 0.913788i \(-0.366856\pi\)
0.406193 + 0.913788i \(0.366856\pi\)
\(374\) 8.86325 0.458308
\(375\) 36.1507 1.86681
\(376\) 13.7542 0.709317
\(377\) −0.0840192 −0.00432721
\(378\) −93.7601 −4.82250
\(379\) 14.6468 0.752355 0.376177 0.926548i \(-0.377238\pi\)
0.376177 + 0.926548i \(0.377238\pi\)
\(380\) 6.49574 0.333224
\(381\) 39.6473 2.03119
\(382\) −16.4434 −0.841317
\(383\) 10.6062 0.541951 0.270976 0.962586i \(-0.412654\pi\)
0.270976 + 0.962586i \(0.412654\pi\)
\(384\) 46.2224 2.35878
\(385\) −8.14031 −0.414869
\(386\) −15.6178 −0.794923
\(387\) 55.5878 2.82569
\(388\) 30.5689 1.55190
\(389\) −12.3692 −0.627145 −0.313572 0.949564i \(-0.601526\pi\)
−0.313572 + 0.949564i \(0.601526\pi\)
\(390\) −7.76500 −0.393196
\(391\) −24.5704 −1.24258
\(392\) −16.6063 −0.838742
\(393\) 12.1173 0.611238
\(394\) 52.1695 2.62826
\(395\) −22.9961 −1.15706
\(396\) 19.2706 0.968383
\(397\) −12.5684 −0.630789 −0.315395 0.948961i \(-0.602137\pi\)
−0.315395 + 0.948961i \(0.602137\pi\)
\(398\) −6.29799 −0.315690
\(399\) −12.4425 −0.622906
\(400\) 0.660550 0.0330275
\(401\) −27.3621 −1.36640 −0.683199 0.730233i \(-0.739412\pi\)
−0.683199 + 0.730233i \(0.739412\pi\)
\(402\) −65.3320 −3.25847
\(403\) 1.23562 0.0615506
\(404\) 26.7216 1.32945
\(405\) −29.8254 −1.48203
\(406\) −1.34582 −0.0667919
\(407\) 3.47103 0.172053
\(408\) 25.9327 1.28386
\(409\) 8.81213 0.435732 0.217866 0.975979i \(-0.430090\pi\)
0.217866 + 0.975979i \(0.430090\pi\)
\(410\) 18.9644 0.936584
\(411\) −44.9057 −2.21503
\(412\) 36.2146 1.78417
\(413\) −0.540179 −0.0265805
\(414\) −89.6713 −4.40710
\(415\) −9.15869 −0.449583
\(416\) −3.69647 −0.181235
\(417\) 25.2486 1.23643
\(418\) 2.32301 0.113622
\(419\) 8.05450 0.393488 0.196744 0.980455i \(-0.436963\pi\)
0.196744 + 0.980455i \(0.436963\pi\)
\(420\) −74.0986 −3.61564
\(421\) −19.9741 −0.973479 −0.486740 0.873547i \(-0.661814\pi\)
−0.486740 + 0.873547i \(0.661814\pi\)
\(422\) 43.0720 2.09671
\(423\) −42.6762 −2.07499
\(424\) 27.0602 1.31416
\(425\) 2.17941 0.105717
\(426\) −37.3416 −1.80921
\(427\) 12.2000 0.590401
\(428\) −16.9770 −0.820616
\(429\) −1.65434 −0.0798722
\(430\) 39.9058 1.92443
\(431\) −10.3440 −0.498253 −0.249126 0.968471i \(-0.580143\pi\)
−0.249126 + 0.968471i \(0.580143\pi\)
\(432\) −13.1975 −0.634967
\(433\) 15.4161 0.740851 0.370426 0.928862i \(-0.379212\pi\)
0.370426 + 0.928862i \(0.379212\pi\)
\(434\) 19.7922 0.950054
\(435\) −1.02224 −0.0490125
\(436\) −15.4428 −0.739576
\(437\) −6.43977 −0.308056
\(438\) −19.6227 −0.937611
\(439\) 7.06583 0.337234 0.168617 0.985682i \(-0.446070\pi\)
0.168617 + 0.985682i \(0.446070\pi\)
\(440\) 4.44670 0.211988
\(441\) 51.5256 2.45360
\(442\) −4.74770 −0.225825
\(443\) −19.7417 −0.937956 −0.468978 0.883210i \(-0.655378\pi\)
−0.468978 + 0.883210i \(0.655378\pi\)
\(444\) 31.5956 1.49946
\(445\) 0.732223 0.0347107
\(446\) 5.47813 0.259397
\(447\) 58.1418 2.75001
\(448\) −49.8923 −2.35719
\(449\) 6.28157 0.296446 0.148223 0.988954i \(-0.452645\pi\)
0.148223 + 0.988954i \(0.452645\pi\)
\(450\) 7.95388 0.374950
\(451\) 4.04037 0.190254
\(452\) 4.94157 0.232432
\(453\) 12.1395 0.570364
\(454\) −27.4722 −1.28933
\(455\) 4.36045 0.204421
\(456\) 6.79682 0.318290
\(457\) 24.0253 1.12385 0.561927 0.827187i \(-0.310060\pi\)
0.561927 + 0.827187i \(0.310060\pi\)
\(458\) 4.12235 0.192625
\(459\) −43.5437 −2.03244
\(460\) −38.3505 −1.78810
\(461\) 33.3526 1.55339 0.776693 0.629880i \(-0.216896\pi\)
0.776693 + 0.629880i \(0.216896\pi\)
\(462\) −26.4992 −1.23285
\(463\) −13.9887 −0.650111 −0.325055 0.945695i \(-0.605383\pi\)
−0.325055 + 0.945695i \(0.605383\pi\)
\(464\) −0.189436 −0.00879433
\(465\) 15.0334 0.697159
\(466\) 0.441737 0.0204631
\(467\) −36.3572 −1.68241 −0.841205 0.540717i \(-0.818153\pi\)
−0.841205 + 0.540717i \(0.818153\pi\)
\(468\) −10.3225 −0.477158
\(469\) 36.6874 1.69406
\(470\) −30.6368 −1.41317
\(471\) 52.5249 2.42022
\(472\) 0.295076 0.0135820
\(473\) 8.50197 0.390921
\(474\) −74.8591 −3.43839
\(475\) 0.571210 0.0262089
\(476\) −45.3056 −2.07658
\(477\) −83.9621 −3.84436
\(478\) −20.6279 −0.943499
\(479\) 41.0972 1.87778 0.938890 0.344217i \(-0.111856\pi\)
0.938890 + 0.344217i \(0.111856\pi\)
\(480\) −44.9739 −2.05277
\(481\) −1.85930 −0.0847767
\(482\) −15.3500 −0.699172
\(483\) 73.4601 3.34255
\(484\) 2.94737 0.133971
\(485\) −21.8864 −0.993811
\(486\) −24.1738 −1.09654
\(487\) −9.62834 −0.436302 −0.218151 0.975915i \(-0.570002\pi\)
−0.218151 + 0.975915i \(0.570002\pi\)
\(488\) −6.66435 −0.301681
\(489\) −3.63436 −0.164351
\(490\) 36.9897 1.67102
\(491\) −38.0027 −1.71504 −0.857519 0.514452i \(-0.827995\pi\)
−0.857519 + 0.514452i \(0.827995\pi\)
\(492\) 36.7782 1.65809
\(493\) −0.625020 −0.0281495
\(494\) −1.24435 −0.0559858
\(495\) −13.7972 −0.620136
\(496\) 2.78592 0.125091
\(497\) 20.9693 0.940600
\(498\) −29.8143 −1.33601
\(499\) 0.226266 0.0101290 0.00506452 0.999987i \(-0.498388\pi\)
0.00506452 + 0.999987i \(0.498388\pi\)
\(500\) 34.4999 1.54288
\(501\) −27.6734 −1.23636
\(502\) 28.9535 1.29226
\(503\) 30.0905 1.34167 0.670835 0.741607i \(-0.265936\pi\)
0.670835 + 0.741607i \(0.265936\pi\)
\(504\) −53.1471 −2.36736
\(505\) −19.1319 −0.851357
\(506\) −13.7149 −0.609703
\(507\) −39.2631 −1.74373
\(508\) 37.8368 1.67874
\(509\) 20.9211 0.927309 0.463655 0.886016i \(-0.346538\pi\)
0.463655 + 0.886016i \(0.346538\pi\)
\(510\) −57.7639 −2.55783
\(511\) 11.0192 0.487461
\(512\) −13.4243 −0.593274
\(513\) −11.4126 −0.503877
\(514\) 2.56954 0.113337
\(515\) −25.9286 −1.14255
\(516\) 77.3906 3.40693
\(517\) −6.52719 −0.287065
\(518\) −29.7822 −1.30856
\(519\) −31.0484 −1.36287
\(520\) −2.38193 −0.104454
\(521\) 5.93620 0.260070 0.130035 0.991509i \(-0.458491\pi\)
0.130035 + 0.991509i \(0.458491\pi\)
\(522\) −2.28105 −0.0998389
\(523\) −5.09836 −0.222936 −0.111468 0.993768i \(-0.535555\pi\)
−0.111468 + 0.993768i \(0.535555\pi\)
\(524\) 11.5640 0.505176
\(525\) −6.51594 −0.284379
\(526\) −28.7652 −1.25422
\(527\) 9.19180 0.400401
\(528\) −3.72999 −0.162327
\(529\) 15.0200 0.653045
\(530\) −60.2754 −2.61820
\(531\) −0.915558 −0.0397318
\(532\) −11.8744 −0.514819
\(533\) −2.16427 −0.0937451
\(534\) 2.38361 0.103149
\(535\) 12.1550 0.525509
\(536\) −20.0407 −0.865627
\(537\) −25.4320 −1.09747
\(538\) 48.1110 2.07421
\(539\) 7.88068 0.339445
\(540\) −67.9648 −2.92474
\(541\) 37.7160 1.62154 0.810768 0.585367i \(-0.199050\pi\)
0.810768 + 0.585367i \(0.199050\pi\)
\(542\) −62.2141 −2.67232
\(543\) −15.2953 −0.656384
\(544\) −27.4981 −1.17897
\(545\) 11.0566 0.473612
\(546\) 14.1946 0.607472
\(547\) −1.00000 −0.0427569
\(548\) −42.8551 −1.83068
\(549\) 20.6780 0.882517
\(550\) 1.21652 0.0518726
\(551\) −0.163814 −0.00697873
\(552\) −40.1281 −1.70796
\(553\) 42.0373 1.78761
\(554\) −21.8201 −0.927048
\(555\) −22.6215 −0.960231
\(556\) 24.0957 1.02188
\(557\) −1.18570 −0.0502398 −0.0251199 0.999684i \(-0.507997\pi\)
−0.0251199 + 0.999684i \(0.507997\pi\)
\(558\) 33.5461 1.42012
\(559\) −4.55418 −0.192621
\(560\) 9.83139 0.415452
\(561\) −12.3066 −0.519587
\(562\) −31.5153 −1.32939
\(563\) 37.7381 1.59047 0.795235 0.606301i \(-0.207347\pi\)
0.795235 + 0.606301i \(0.207347\pi\)
\(564\) −59.4148 −2.50182
\(565\) −3.53802 −0.148845
\(566\) −66.7755 −2.80678
\(567\) 54.5215 2.28969
\(568\) −11.4546 −0.480624
\(569\) 43.6469 1.82977 0.914886 0.403712i \(-0.132280\pi\)
0.914886 + 0.403712i \(0.132280\pi\)
\(570\) −15.1396 −0.634128
\(571\) −33.6250 −1.40716 −0.703581 0.710615i \(-0.748417\pi\)
−0.703581 + 0.710615i \(0.748417\pi\)
\(572\) −1.57879 −0.0660127
\(573\) 22.8317 0.953807
\(574\) −34.6673 −1.44699
\(575\) −3.37239 −0.140639
\(576\) −84.5632 −3.52347
\(577\) 16.9423 0.705319 0.352659 0.935752i \(-0.385277\pi\)
0.352659 + 0.935752i \(0.385277\pi\)
\(578\) 2.49433 0.103750
\(579\) 21.6853 0.901209
\(580\) −0.975557 −0.0405078
\(581\) 16.7423 0.694588
\(582\) −71.2469 −2.95328
\(583\) −12.8417 −0.531850
\(584\) −6.01931 −0.249081
\(585\) 7.39061 0.305564
\(586\) 68.7215 2.83886
\(587\) 38.1451 1.57442 0.787208 0.616688i \(-0.211526\pi\)
0.787208 + 0.616688i \(0.211526\pi\)
\(588\) 71.7352 2.95831
\(589\) 2.40912 0.0992660
\(590\) −0.657269 −0.0270593
\(591\) −72.4375 −2.97968
\(592\) −4.19210 −0.172294
\(593\) 25.1129 1.03126 0.515631 0.856811i \(-0.327558\pi\)
0.515631 + 0.856811i \(0.327558\pi\)
\(594\) −24.3056 −0.997271
\(595\) 32.4375 1.32981
\(596\) 55.4868 2.27283
\(597\) 8.74477 0.357900
\(598\) 7.34656 0.300423
\(599\) 24.9337 1.01876 0.509381 0.860541i \(-0.329874\pi\)
0.509381 + 0.860541i \(0.329874\pi\)
\(600\) 3.55938 0.145311
\(601\) −8.46712 −0.345381 −0.172691 0.984976i \(-0.555246\pi\)
−0.172691 + 0.984976i \(0.555246\pi\)
\(602\) −72.9488 −2.97317
\(603\) 62.1820 2.53225
\(604\) 11.5852 0.471394
\(605\) −2.11023 −0.0857930
\(606\) −62.2800 −2.52995
\(607\) −5.03143 −0.204219 −0.102110 0.994773i \(-0.532559\pi\)
−0.102110 + 0.994773i \(0.532559\pi\)
\(608\) −7.20711 −0.292287
\(609\) 1.86867 0.0757224
\(610\) 14.8445 0.601038
\(611\) 3.49636 0.141448
\(612\) −76.7893 −3.10402
\(613\) 28.4623 1.14958 0.574791 0.818300i \(-0.305083\pi\)
0.574791 + 0.818300i \(0.305083\pi\)
\(614\) 39.4936 1.59383
\(615\) −26.3321 −1.06181
\(616\) −8.12867 −0.327513
\(617\) 35.5711 1.43204 0.716020 0.698080i \(-0.245962\pi\)
0.716020 + 0.698080i \(0.245962\pi\)
\(618\) −84.4053 −3.39528
\(619\) −10.9889 −0.441681 −0.220841 0.975310i \(-0.570880\pi\)
−0.220841 + 0.975310i \(0.570880\pi\)
\(620\) 14.3469 0.576187
\(621\) 67.3791 2.70383
\(622\) 12.6623 0.507712
\(623\) −1.33852 −0.0536267
\(624\) 1.99801 0.0799845
\(625\) −21.9662 −0.878649
\(626\) −20.3509 −0.813388
\(627\) −3.22550 −0.128814
\(628\) 50.1264 2.00026
\(629\) −13.8313 −0.551492
\(630\) 118.383 4.71648
\(631\) −37.6573 −1.49911 −0.749557 0.661940i \(-0.769733\pi\)
−0.749557 + 0.661940i \(0.769733\pi\)
\(632\) −22.9632 −0.913426
\(633\) −59.8055 −2.37706
\(634\) 12.4468 0.494324
\(635\) −27.0900 −1.07503
\(636\) −116.894 −4.63515
\(637\) −4.22138 −0.167257
\(638\) −0.348879 −0.0138123
\(639\) 35.5412 1.40599
\(640\) −31.5826 −1.24841
\(641\) −10.3003 −0.406839 −0.203419 0.979092i \(-0.565205\pi\)
−0.203419 + 0.979092i \(0.565205\pi\)
\(642\) 39.5684 1.56164
\(643\) −47.8274 −1.88613 −0.943063 0.332613i \(-0.892070\pi\)
−0.943063 + 0.332613i \(0.892070\pi\)
\(644\) 70.1056 2.76255
\(645\) −55.4093 −2.18174
\(646\) −9.25672 −0.364201
\(647\) −3.68463 −0.144858 −0.0724289 0.997374i \(-0.523075\pi\)
−0.0724289 + 0.997374i \(0.523075\pi\)
\(648\) −29.7827 −1.16998
\(649\) −0.140032 −0.00549672
\(650\) −0.651643 −0.0255596
\(651\) −27.4814 −1.07708
\(652\) −3.46840 −0.135833
\(653\) −11.5337 −0.451350 −0.225675 0.974203i \(-0.572459\pi\)
−0.225675 + 0.974203i \(0.572459\pi\)
\(654\) 35.9925 1.40742
\(655\) −8.27947 −0.323506
\(656\) −4.87972 −0.190521
\(657\) 18.6766 0.728645
\(658\) 56.0047 2.18329
\(659\) −16.3376 −0.636424 −0.318212 0.948020i \(-0.603082\pi\)
−0.318212 + 0.948020i \(0.603082\pi\)
\(660\) −19.2087 −0.747699
\(661\) −11.2252 −0.436608 −0.218304 0.975881i \(-0.570052\pi\)
−0.218304 + 0.975881i \(0.570052\pi\)
\(662\) −15.8622 −0.616502
\(663\) 6.59220 0.256020
\(664\) −9.14559 −0.354918
\(665\) 8.50168 0.329681
\(666\) −50.4784 −1.95600
\(667\) 0.967151 0.0374482
\(668\) −26.4097 −1.02182
\(669\) −7.60639 −0.294080
\(670\) 44.6398 1.72459
\(671\) 3.16264 0.122092
\(672\) 82.2133 3.17145
\(673\) −26.4883 −1.02105 −0.510525 0.859863i \(-0.670549\pi\)
−0.510525 + 0.859863i \(0.670549\pi\)
\(674\) 64.7620 2.49454
\(675\) −5.97656 −0.230038
\(676\) −37.4701 −1.44116
\(677\) −30.4686 −1.17101 −0.585503 0.810671i \(-0.699103\pi\)
−0.585503 + 0.810671i \(0.699103\pi\)
\(678\) −11.5173 −0.442320
\(679\) 40.0089 1.53540
\(680\) −17.7192 −0.679500
\(681\) 38.1451 1.46173
\(682\) 5.13076 0.196467
\(683\) 44.2609 1.69360 0.846798 0.531914i \(-0.178527\pi\)
0.846798 + 0.531914i \(0.178527\pi\)
\(684\) −20.1261 −0.769539
\(685\) 30.6830 1.17234
\(686\) −7.55642 −0.288506
\(687\) −5.72390 −0.218380
\(688\) −10.2682 −0.391470
\(689\) 6.87882 0.262062
\(690\) 89.3835 3.40277
\(691\) 44.0606 1.67615 0.838073 0.545558i \(-0.183682\pi\)
0.838073 + 0.545558i \(0.183682\pi\)
\(692\) −29.6306 −1.12639
\(693\) 25.2215 0.958086
\(694\) 24.2509 0.920551
\(695\) −17.2518 −0.654397
\(696\) −1.02077 −0.0386924
\(697\) −16.1001 −0.609833
\(698\) 10.0933 0.382036
\(699\) −0.613353 −0.0231991
\(700\) −6.21840 −0.235033
\(701\) 37.2516 1.40698 0.703488 0.710708i \(-0.251625\pi\)
0.703488 + 0.710708i \(0.251625\pi\)
\(702\) 13.0196 0.491392
\(703\) −3.62512 −0.136724
\(704\) −12.9337 −0.487456
\(705\) 42.5392 1.60212
\(706\) 42.4257 1.59671
\(707\) 34.9735 1.31531
\(708\) −1.27466 −0.0479047
\(709\) 8.08734 0.303726 0.151863 0.988402i \(-0.451473\pi\)
0.151863 + 0.988402i \(0.451473\pi\)
\(710\) 25.5146 0.957546
\(711\) 71.2498 2.67208
\(712\) 0.731175 0.0274020
\(713\) −14.2233 −0.532667
\(714\) 105.594 3.95175
\(715\) 1.13037 0.0422734
\(716\) −24.2707 −0.907038
\(717\) 28.6419 1.06965
\(718\) 2.34252 0.0874221
\(719\) −31.9518 −1.19160 −0.595800 0.803133i \(-0.703165\pi\)
−0.595800 + 0.803133i \(0.703165\pi\)
\(720\) 16.6634 0.621008
\(721\) 47.3980 1.76519
\(722\) 39.8350 1.48250
\(723\) 21.3135 0.792657
\(724\) −14.5968 −0.542487
\(725\) −0.0857867 −0.00318604
\(726\) −6.86944 −0.254949
\(727\) −34.4763 −1.27865 −0.639327 0.768935i \(-0.720787\pi\)
−0.639327 + 0.768935i \(0.720787\pi\)
\(728\) 4.35422 0.161378
\(729\) −8.83579 −0.327252
\(730\) 13.4077 0.496243
\(731\) −33.8786 −1.25305
\(732\) 28.7885 1.06405
\(733\) −15.8583 −0.585741 −0.292870 0.956152i \(-0.594610\pi\)
−0.292870 + 0.956152i \(0.594610\pi\)
\(734\) 61.2460 2.26063
\(735\) −51.3603 −1.89445
\(736\) 42.5504 1.56843
\(737\) 9.51054 0.350325
\(738\) −58.7582 −2.16292
\(739\) 34.3327 1.26295 0.631475 0.775397i \(-0.282450\pi\)
0.631475 + 0.775397i \(0.282450\pi\)
\(740\) −21.5885 −0.793610
\(741\) 1.72778 0.0634715
\(742\) 110.185 4.04501
\(743\) 7.58532 0.278278 0.139139 0.990273i \(-0.455566\pi\)
0.139139 + 0.990273i \(0.455566\pi\)
\(744\) 15.0119 0.550364
\(745\) −39.7269 −1.45548
\(746\) −34.8982 −1.27772
\(747\) 28.3768 1.03825
\(748\) −11.7447 −0.429428
\(749\) −22.2197 −0.811890
\(750\) −80.4088 −2.93611
\(751\) 0.351350 0.0128210 0.00641048 0.999979i \(-0.497959\pi\)
0.00641048 + 0.999979i \(0.497959\pi\)
\(752\) 7.88315 0.287469
\(753\) −40.2020 −1.46504
\(754\) 0.186881 0.00680582
\(755\) −8.29464 −0.301873
\(756\) 124.241 4.51861
\(757\) −9.63210 −0.350085 −0.175042 0.984561i \(-0.556006\pi\)
−0.175042 + 0.984561i \(0.556006\pi\)
\(758\) −32.5784 −1.18330
\(759\) 19.0432 0.691225
\(760\) −4.64410 −0.168459
\(761\) −24.3509 −0.882721 −0.441360 0.897330i \(-0.645504\pi\)
−0.441360 + 0.897330i \(0.645504\pi\)
\(762\) −88.1862 −3.19465
\(763\) −20.2117 −0.731712
\(764\) 21.7891 0.788301
\(765\) 54.9788 1.98776
\(766\) −23.5910 −0.852378
\(767\) 0.0750095 0.00270844
\(768\) −22.9222 −0.827135
\(769\) −12.6126 −0.454821 −0.227410 0.973799i \(-0.573026\pi\)
−0.227410 + 0.973799i \(0.573026\pi\)
\(770\) 18.1062 0.652504
\(771\) −3.56781 −0.128492
\(772\) 20.6950 0.744831
\(773\) 11.8237 0.425267 0.212634 0.977132i \(-0.431796\pi\)
0.212634 + 0.977132i \(0.431796\pi\)
\(774\) −123.642 −4.44423
\(775\) 1.26161 0.0453185
\(776\) −21.8551 −0.784553
\(777\) 41.3527 1.48352
\(778\) 27.5125 0.986371
\(779\) −4.21974 −0.151188
\(780\) 10.2894 0.368419
\(781\) 5.43590 0.194512
\(782\) 54.6512 1.95432
\(783\) 1.71399 0.0612529
\(784\) −9.51782 −0.339922
\(785\) −35.8890 −1.28093
\(786\) −26.9522 −0.961353
\(787\) −53.3172 −1.90055 −0.950276 0.311408i \(-0.899200\pi\)
−0.950276 + 0.311408i \(0.899200\pi\)
\(788\) −69.1297 −2.46264
\(789\) 39.9406 1.42192
\(790\) 51.1494 1.81982
\(791\) 6.46757 0.229960
\(792\) −13.7774 −0.489559
\(793\) −1.69410 −0.0601594
\(794\) 27.9555 0.992103
\(795\) 83.6925 2.96827
\(796\) 8.34545 0.295797
\(797\) 43.4209 1.53805 0.769024 0.639220i \(-0.220743\pi\)
0.769024 + 0.639220i \(0.220743\pi\)
\(798\) 27.6755 0.979704
\(799\) 26.0095 0.920150
\(800\) −3.77424 −0.133439
\(801\) −2.26868 −0.0801599
\(802\) 60.8606 2.14906
\(803\) 2.85653 0.100805
\(804\) 86.5713 3.05313
\(805\) −50.1935 −1.76909
\(806\) −2.74835 −0.0968066
\(807\) −66.8022 −2.35155
\(808\) −19.1045 −0.672094
\(809\) −16.8206 −0.591382 −0.295691 0.955284i \(-0.595550\pi\)
−0.295691 + 0.955284i \(0.595550\pi\)
\(810\) 66.3396 2.33094
\(811\) −21.1110 −0.741309 −0.370655 0.928771i \(-0.620867\pi\)
−0.370655 + 0.928771i \(0.620867\pi\)
\(812\) 1.78334 0.0625830
\(813\) 86.3844 3.02963
\(814\) −7.72051 −0.270604
\(815\) 2.48327 0.0869852
\(816\) 14.8632 0.520317
\(817\) −8.87939 −0.310651
\(818\) −19.6005 −0.685317
\(819\) −13.5102 −0.472085
\(820\) −25.1296 −0.877565
\(821\) 20.4382 0.713300 0.356650 0.934238i \(-0.383919\pi\)
0.356650 + 0.934238i \(0.383919\pi\)
\(822\) 99.8823 3.48379
\(823\) 16.8610 0.587739 0.293869 0.955846i \(-0.405057\pi\)
0.293869 + 0.955846i \(0.405057\pi\)
\(824\) −25.8915 −0.901972
\(825\) −1.68914 −0.0588083
\(826\) 1.20150 0.0418056
\(827\) −32.1965 −1.11958 −0.559791 0.828634i \(-0.689119\pi\)
−0.559791 + 0.828634i \(0.689119\pi\)
\(828\) 118.823 4.12939
\(829\) −19.4300 −0.674831 −0.337416 0.941356i \(-0.609553\pi\)
−0.337416 + 0.941356i \(0.609553\pi\)
\(830\) 20.3714 0.707102
\(831\) 30.2973 1.05100
\(832\) 6.92807 0.240188
\(833\) −31.4029 −1.08805
\(834\) −56.1597 −1.94465
\(835\) 18.9085 0.654357
\(836\) −3.07821 −0.106462
\(837\) −25.2066 −0.871266
\(838\) −17.9154 −0.618877
\(839\) 20.6987 0.714598 0.357299 0.933990i \(-0.383698\pi\)
0.357299 + 0.933990i \(0.383698\pi\)
\(840\) 52.9765 1.82786
\(841\) −28.9754 −0.999152
\(842\) 44.4278 1.53108
\(843\) 43.7591 1.50714
\(844\) −57.0746 −1.96459
\(845\) 26.8275 0.922894
\(846\) 94.9234 3.26353
\(847\) 3.85755 0.132547
\(848\) 15.5095 0.532597
\(849\) 92.7179 3.18207
\(850\) −4.84758 −0.166271
\(851\) 21.4025 0.733669
\(852\) 49.4812 1.69520
\(853\) −38.2560 −1.30986 −0.654931 0.755689i \(-0.727302\pi\)
−0.654931 + 0.755689i \(0.727302\pi\)
\(854\) −27.1362 −0.928580
\(855\) 14.4096 0.492800
\(856\) 12.1377 0.414857
\(857\) −45.2811 −1.54677 −0.773386 0.633935i \(-0.781438\pi\)
−0.773386 + 0.633935i \(0.781438\pi\)
\(858\) 3.67969 0.125623
\(859\) 12.6853 0.432817 0.216409 0.976303i \(-0.430566\pi\)
0.216409 + 0.976303i \(0.430566\pi\)
\(860\) −52.8791 −1.80316
\(861\) 48.1356 1.64046
\(862\) 23.0078 0.783650
\(863\) −45.4025 −1.54552 −0.772759 0.634700i \(-0.781124\pi\)
−0.772759 + 0.634700i \(0.781124\pi\)
\(864\) 75.4078 2.56543
\(865\) 21.2146 0.721318
\(866\) −34.2896 −1.16521
\(867\) −3.46338 −0.117622
\(868\) −26.2265 −0.890187
\(869\) 10.8974 0.369670
\(870\) 2.27373 0.0770867
\(871\) −5.09443 −0.172618
\(872\) 11.0408 0.373888
\(873\) 67.8117 2.29508
\(874\) 14.3238 0.484509
\(875\) 45.1538 1.52648
\(876\) 26.0020 0.878528
\(877\) −13.1321 −0.443440 −0.221720 0.975110i \(-0.571167\pi\)
−0.221720 + 0.975110i \(0.571167\pi\)
\(878\) −15.7163 −0.530400
\(879\) −95.4199 −3.21843
\(880\) 2.54861 0.0859136
\(881\) 19.4261 0.654480 0.327240 0.944941i \(-0.393881\pi\)
0.327240 + 0.944941i \(0.393881\pi\)
\(882\) −114.607 −3.85902
\(883\) 40.3950 1.35940 0.679699 0.733491i \(-0.262110\pi\)
0.679699 + 0.733491i \(0.262110\pi\)
\(884\) 6.29117 0.211595
\(885\) 0.912619 0.0306774
\(886\) 43.9108 1.47521
\(887\) 53.8087 1.80672 0.903360 0.428884i \(-0.141093\pi\)
0.903360 + 0.428884i \(0.141093\pi\)
\(888\) −22.5892 −0.758043
\(889\) 49.5212 1.66089
\(890\) −1.62866 −0.0545928
\(891\) 14.1337 0.473497
\(892\) −7.25906 −0.243051
\(893\) 6.81695 0.228120
\(894\) −129.323 −4.32521
\(895\) 17.3771 0.580852
\(896\) 57.7338 1.92875
\(897\) −10.2007 −0.340592
\(898\) −13.9719 −0.466249
\(899\) −0.361812 −0.0120671
\(900\) −10.5397 −0.351322
\(901\) 51.1716 1.70477
\(902\) −8.98688 −0.299230
\(903\) 101.290 3.37070
\(904\) −3.53295 −0.117504
\(905\) 10.4509 0.347400
\(906\) −27.0016 −0.897067
\(907\) −25.4470 −0.844954 −0.422477 0.906374i \(-0.638839\pi\)
−0.422477 + 0.906374i \(0.638839\pi\)
\(908\) 36.4033 1.20809
\(909\) 59.2772 1.96610
\(910\) −9.69882 −0.321513
\(911\) −42.8365 −1.41924 −0.709619 0.704586i \(-0.751133\pi\)
−0.709619 + 0.704586i \(0.751133\pi\)
\(912\) 3.89557 0.128995
\(913\) 4.34014 0.143638
\(914\) −53.4386 −1.76759
\(915\) −20.6117 −0.681401
\(916\) −5.46252 −0.180487
\(917\) 15.1351 0.499804
\(918\) 96.8528 3.19662
\(919\) 26.9072 0.887585 0.443793 0.896129i \(-0.353633\pi\)
0.443793 + 0.896129i \(0.353633\pi\)
\(920\) 27.4185 0.903962
\(921\) −54.8369 −1.80694
\(922\) −74.1852 −2.44316
\(923\) −2.91180 −0.0958432
\(924\) 35.1140 1.15517
\(925\) −1.89841 −0.0624194
\(926\) 31.1147 1.02249
\(927\) 80.3357 2.63857
\(928\) 1.08239 0.0355313
\(929\) 36.9048 1.21081 0.605404 0.795919i \(-0.293012\pi\)
0.605404 + 0.795919i \(0.293012\pi\)
\(930\) −33.4384 −1.09649
\(931\) −8.23052 −0.269745
\(932\) −0.585345 −0.0191736
\(933\) −17.5816 −0.575597
\(934\) 80.8681 2.64609
\(935\) 8.40883 0.274998
\(936\) 7.38003 0.241224
\(937\) −34.5561 −1.12890 −0.564450 0.825467i \(-0.690912\pi\)
−0.564450 + 0.825467i \(0.690912\pi\)
\(938\) −81.6025 −2.66442
\(939\) 28.2573 0.922143
\(940\) 40.5967 1.32412
\(941\) 37.1850 1.21220 0.606098 0.795390i \(-0.292734\pi\)
0.606098 + 0.795390i \(0.292734\pi\)
\(942\) −116.829 −3.80651
\(943\) 24.9131 0.811282
\(944\) 0.169122 0.00550445
\(945\) −88.9529 −2.89364
\(946\) −18.9107 −0.614839
\(947\) 41.0397 1.33361 0.666806 0.745232i \(-0.267661\pi\)
0.666806 + 0.745232i \(0.267661\pi\)
\(948\) 99.1956 3.22172
\(949\) −1.53013 −0.0496702
\(950\) −1.27052 −0.0412213
\(951\) −17.2823 −0.560419
\(952\) 32.3911 1.04980
\(953\) 16.6201 0.538376 0.269188 0.963088i \(-0.413245\pi\)
0.269188 + 0.963088i \(0.413245\pi\)
\(954\) 186.754 6.04639
\(955\) −15.6003 −0.504815
\(956\) 27.3340 0.884045
\(957\) 0.484420 0.0156591
\(958\) −91.4113 −2.95336
\(959\) −56.0891 −1.81121
\(960\) 84.2918 2.72051
\(961\) −25.6791 −0.828357
\(962\) 4.13558 0.133336
\(963\) −37.6606 −1.21359
\(964\) 20.3402 0.655114
\(965\) −14.8170 −0.476977
\(966\) −163.395 −5.25715
\(967\) −7.22636 −0.232384 −0.116192 0.993227i \(-0.537069\pi\)
−0.116192 + 0.993227i \(0.537069\pi\)
\(968\) −2.10721 −0.0677283
\(969\) 12.8530 0.412897
\(970\) 48.6813 1.56306
\(971\) −35.3856 −1.13558 −0.567789 0.823174i \(-0.692201\pi\)
−0.567789 + 0.823174i \(0.692201\pi\)
\(972\) 32.0326 1.02745
\(973\) 31.5366 1.01102
\(974\) 21.4160 0.686213
\(975\) 0.904808 0.0289770
\(976\) −3.81965 −0.122264
\(977\) 33.6246 1.07575 0.537873 0.843026i \(-0.319228\pi\)
0.537873 + 0.843026i \(0.319228\pi\)
\(978\) 8.08380 0.258491
\(979\) −0.346987 −0.0110898
\(980\) −49.0149 −1.56572
\(981\) −34.2571 −1.09375
\(982\) 84.5283 2.69740
\(983\) −12.1506 −0.387543 −0.193772 0.981047i \(-0.562072\pi\)
−0.193772 + 0.981047i \(0.562072\pi\)
\(984\) −26.2944 −0.838235
\(985\) 49.4948 1.57704
\(986\) 1.39021 0.0442734
\(987\) −77.7627 −2.47521
\(988\) 1.64888 0.0524579
\(989\) 52.4235 1.66697
\(990\) 30.6886 0.975347
\(991\) 18.2194 0.578760 0.289380 0.957214i \(-0.406551\pi\)
0.289380 + 0.957214i \(0.406551\pi\)
\(992\) −15.9181 −0.505401
\(993\) 22.0247 0.698933
\(994\) −46.6413 −1.47937
\(995\) −5.97509 −0.189423
\(996\) 39.5069 1.25182
\(997\) 19.1067 0.605114 0.302557 0.953131i \(-0.402160\pi\)
0.302557 + 0.953131i \(0.402160\pi\)
\(998\) −0.503276 −0.0159309
\(999\) 37.9295 1.20004
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 6017.2.a.e.1.16 119
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6017.2.a.e.1.16 119 1.1 even 1 trivial