Properties

Label 8005.2.a.e.1.2
Level $8005$
Weight $2$
Character 8005.1
Self dual yes
Analytic conductor $63.920$
Analytic rank $1$
Dimension $126$
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] = [8005,2,Mod(1,8005)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8005, 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("8005.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8005 = 5 \cdot 1601 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8005.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: \(63.9202468180\)
Analytic rank: \(1\)
Dimension: \(126\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) \(=\) 8005.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.76854 q^{2} -3.01214 q^{3} +5.66482 q^{4} +1.00000 q^{5} +8.33923 q^{6} -2.50261 q^{7} -10.1462 q^{8} +6.07298 q^{9} +O(q^{10})\) \(q-2.76854 q^{2} -3.01214 q^{3} +5.66482 q^{4} +1.00000 q^{5} +8.33923 q^{6} -2.50261 q^{7} -10.1462 q^{8} +6.07298 q^{9} -2.76854 q^{10} -2.69707 q^{11} -17.0632 q^{12} +4.24001 q^{13} +6.92858 q^{14} -3.01214 q^{15} +16.7605 q^{16} +0.690069 q^{17} -16.8133 q^{18} +2.42673 q^{19} +5.66482 q^{20} +7.53822 q^{21} +7.46694 q^{22} -5.69511 q^{23} +30.5618 q^{24} +1.00000 q^{25} -11.7386 q^{26} -9.25626 q^{27} -14.1768 q^{28} +1.64674 q^{29} +8.33923 q^{30} -1.66321 q^{31} -26.1098 q^{32} +8.12394 q^{33} -1.91048 q^{34} -2.50261 q^{35} +34.4023 q^{36} +8.15047 q^{37} -6.71851 q^{38} -12.7715 q^{39} -10.1462 q^{40} +3.71560 q^{41} -20.8699 q^{42} -2.04638 q^{43} -15.2784 q^{44} +6.07298 q^{45} +15.7672 q^{46} -11.1338 q^{47} -50.4850 q^{48} -0.736930 q^{49} -2.76854 q^{50} -2.07858 q^{51} +24.0189 q^{52} +2.13498 q^{53} +25.6263 q^{54} -2.69707 q^{55} +25.3920 q^{56} -7.30966 q^{57} -4.55905 q^{58} +2.86001 q^{59} -17.0632 q^{60} -5.76997 q^{61} +4.60466 q^{62} -15.1983 q^{63} +38.7650 q^{64} +4.24001 q^{65} -22.4915 q^{66} -0.413507 q^{67} +3.90911 q^{68} +17.1545 q^{69} +6.92858 q^{70} -6.95110 q^{71} -61.6177 q^{72} +6.74409 q^{73} -22.5649 q^{74} -3.01214 q^{75} +13.7470 q^{76} +6.74971 q^{77} +35.3584 q^{78} +12.6083 q^{79} +16.7605 q^{80} +9.66219 q^{81} -10.2868 q^{82} +0.741885 q^{83} +42.7026 q^{84} +0.690069 q^{85} +5.66548 q^{86} -4.96020 q^{87} +27.3650 q^{88} +6.94176 q^{89} -16.8133 q^{90} -10.6111 q^{91} -32.2618 q^{92} +5.00982 q^{93} +30.8243 q^{94} +2.42673 q^{95} +78.6463 q^{96} +17.8179 q^{97} +2.04022 q^{98} -16.3792 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 126 q - 15 q^{2} - 46 q^{3} + 119 q^{4} + 126 q^{5} - 10 q^{6} - 60 q^{7} - 57 q^{8} + 112 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 126 q - 15 q^{2} - 46 q^{3} + 119 q^{4} + 126 q^{5} - 10 q^{6} - 60 q^{7} - 57 q^{8} + 112 q^{9} - 15 q^{10} - 35 q^{11} - 86 q^{12} - 36 q^{13} - 31 q^{14} - 46 q^{15} + 101 q^{16} - 62 q^{17} - 45 q^{18} - 29 q^{19} + 119 q^{20} - 16 q^{21} - 67 q^{22} - 107 q^{23} - 9 q^{24} + 126 q^{25} - 53 q^{26} - 181 q^{27} - 100 q^{28} - 39 q^{29} - 10 q^{30} - 29 q^{31} - 99 q^{32} - 72 q^{33} - 18 q^{34} - 60 q^{35} + 93 q^{36} - 72 q^{37} - 93 q^{38} - 8 q^{39} - 57 q^{40} - 28 q^{41} - 22 q^{42} - 103 q^{43} - 47 q^{44} + 112 q^{45} + q^{46} - 130 q^{47} - 134 q^{48} + 116 q^{49} - 15 q^{50} - 46 q^{51} - 117 q^{52} - 103 q^{53} + 11 q^{54} - 35 q^{55} - 84 q^{56} - 70 q^{57} - 77 q^{58} - 219 q^{59} - 86 q^{60} - 4 q^{61} - 77 q^{62} - 145 q^{63} + 51 q^{64} - 36 q^{65} + 16 q^{66} - 150 q^{67} - 130 q^{68} - 21 q^{69} - 31 q^{70} - 92 q^{71} - 115 q^{72} - 79 q^{73} - 57 q^{74} - 46 q^{75} - 38 q^{76} - 75 q^{77} - 23 q^{78} - 20 q^{79} + 101 q^{80} + 142 q^{81} - 63 q^{82} - 243 q^{83} - 2 q^{84} - 62 q^{85} - 14 q^{86} - 107 q^{87} - 121 q^{88} - 84 q^{89} - 45 q^{90} - 82 q^{91} - 228 q^{92} - 149 q^{93} - 29 q^{95} + 38 q^{96} - 85 q^{97} - 48 q^{98} - 33 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.76854 −1.95765 −0.978827 0.204690i \(-0.934382\pi\)
−0.978827 + 0.204690i \(0.934382\pi\)
\(3\) −3.01214 −1.73906 −0.869530 0.493881i \(-0.835578\pi\)
−0.869530 + 0.493881i \(0.835578\pi\)
\(4\) 5.66482 2.83241
\(5\) 1.00000 0.447214
\(6\) 8.33923 3.40448
\(7\) −2.50261 −0.945899 −0.472949 0.881090i \(-0.656811\pi\)
−0.472949 + 0.881090i \(0.656811\pi\)
\(8\) −10.1462 −3.58722
\(9\) 6.07298 2.02433
\(10\) −2.76854 −0.875489
\(11\) −2.69707 −0.813196 −0.406598 0.913607i \(-0.633285\pi\)
−0.406598 + 0.913607i \(0.633285\pi\)
\(12\) −17.0632 −4.92573
\(13\) 4.24001 1.17597 0.587983 0.808873i \(-0.299922\pi\)
0.587983 + 0.808873i \(0.299922\pi\)
\(14\) 6.92858 1.85174
\(15\) −3.01214 −0.777731
\(16\) 16.7605 4.19013
\(17\) 0.690069 0.167366 0.0836831 0.996492i \(-0.473332\pi\)
0.0836831 + 0.996492i \(0.473332\pi\)
\(18\) −16.8133 −3.96293
\(19\) 2.42673 0.556731 0.278366 0.960475i \(-0.410207\pi\)
0.278366 + 0.960475i \(0.410207\pi\)
\(20\) 5.66482 1.26669
\(21\) 7.53822 1.64497
\(22\) 7.46694 1.59196
\(23\) −5.69511 −1.18751 −0.593757 0.804645i \(-0.702356\pi\)
−0.593757 + 0.804645i \(0.702356\pi\)
\(24\) 30.5618 6.23839
\(25\) 1.00000 0.200000
\(26\) −11.7386 −2.30214
\(27\) −9.25626 −1.78137
\(28\) −14.1768 −2.67917
\(29\) 1.64674 0.305791 0.152896 0.988242i \(-0.451140\pi\)
0.152896 + 0.988242i \(0.451140\pi\)
\(30\) 8.33923 1.52253
\(31\) −1.66321 −0.298721 −0.149361 0.988783i \(-0.547722\pi\)
−0.149361 + 0.988783i \(0.547722\pi\)
\(32\) −26.1098 −4.61560
\(33\) 8.12394 1.41420
\(34\) −1.91048 −0.327645
\(35\) −2.50261 −0.423019
\(36\) 34.4023 5.73372
\(37\) 8.15047 1.33993 0.669965 0.742393i \(-0.266309\pi\)
0.669965 + 0.742393i \(0.266309\pi\)
\(38\) −6.71851 −1.08989
\(39\) −12.7715 −2.04508
\(40\) −10.1462 −1.60425
\(41\) 3.71560 0.580280 0.290140 0.956984i \(-0.406298\pi\)
0.290140 + 0.956984i \(0.406298\pi\)
\(42\) −20.8699 −3.22029
\(43\) −2.04638 −0.312070 −0.156035 0.987752i \(-0.549871\pi\)
−0.156035 + 0.987752i \(0.549871\pi\)
\(44\) −15.2784 −2.30330
\(45\) 6.07298 0.905307
\(46\) 15.7672 2.32474
\(47\) −11.1338 −1.62403 −0.812015 0.583637i \(-0.801629\pi\)
−0.812015 + 0.583637i \(0.801629\pi\)
\(48\) −50.4850 −7.28689
\(49\) −0.736930 −0.105276
\(50\) −2.76854 −0.391531
\(51\) −2.07858 −0.291060
\(52\) 24.0189 3.33082
\(53\) 2.13498 0.293263 0.146631 0.989191i \(-0.453157\pi\)
0.146631 + 0.989191i \(0.453157\pi\)
\(54\) 25.6263 3.48730
\(55\) −2.69707 −0.363672
\(56\) 25.3920 3.39315
\(57\) −7.30966 −0.968189
\(58\) −4.55905 −0.598633
\(59\) 2.86001 0.372342 0.186171 0.982517i \(-0.440392\pi\)
0.186171 + 0.982517i \(0.440392\pi\)
\(60\) −17.0632 −2.20285
\(61\) −5.76997 −0.738769 −0.369384 0.929277i \(-0.620431\pi\)
−0.369384 + 0.929277i \(0.620431\pi\)
\(62\) 4.60466 0.584793
\(63\) −15.1983 −1.91481
\(64\) 38.7650 4.84562
\(65\) 4.24001 0.525908
\(66\) −22.4915 −2.76851
\(67\) −0.413507 −0.0505179 −0.0252589 0.999681i \(-0.508041\pi\)
−0.0252589 + 0.999681i \(0.508041\pi\)
\(68\) 3.90911 0.474049
\(69\) 17.1545 2.06516
\(70\) 6.92858 0.828124
\(71\) −6.95110 −0.824943 −0.412472 0.910970i \(-0.635334\pi\)
−0.412472 + 0.910970i \(0.635334\pi\)
\(72\) −61.6177 −7.26171
\(73\) 6.74409 0.789337 0.394668 0.918824i \(-0.370860\pi\)
0.394668 + 0.918824i \(0.370860\pi\)
\(74\) −22.5649 −2.62312
\(75\) −3.01214 −0.347812
\(76\) 13.7470 1.57689
\(77\) 6.74971 0.769201
\(78\) 35.3584 4.00355
\(79\) 12.6083 1.41854 0.709270 0.704937i \(-0.249025\pi\)
0.709270 + 0.704937i \(0.249025\pi\)
\(80\) 16.7605 1.87388
\(81\) 9.66219 1.07358
\(82\) −10.2868 −1.13599
\(83\) 0.741885 0.0814324 0.0407162 0.999171i \(-0.487036\pi\)
0.0407162 + 0.999171i \(0.487036\pi\)
\(84\) 42.7026 4.65924
\(85\) 0.690069 0.0748484
\(86\) 5.66548 0.610925
\(87\) −4.96020 −0.531789
\(88\) 27.3650 2.91711
\(89\) 6.94176 0.735825 0.367912 0.929860i \(-0.380073\pi\)
0.367912 + 0.929860i \(0.380073\pi\)
\(90\) −16.8133 −1.77228
\(91\) −10.6111 −1.11235
\(92\) −32.2618 −3.36352
\(93\) 5.00982 0.519494
\(94\) 30.8243 3.17929
\(95\) 2.42673 0.248978
\(96\) 78.6463 8.02681
\(97\) 17.8179 1.80914 0.904568 0.426329i \(-0.140193\pi\)
0.904568 + 0.426329i \(0.140193\pi\)
\(98\) 2.04022 0.206093
\(99\) −16.3792 −1.64618
\(100\) 5.66482 0.566482
\(101\) −5.89006 −0.586083 −0.293041 0.956100i \(-0.594667\pi\)
−0.293041 + 0.956100i \(0.594667\pi\)
\(102\) 5.75464 0.569794
\(103\) −6.20848 −0.611740 −0.305870 0.952073i \(-0.598947\pi\)
−0.305870 + 0.952073i \(0.598947\pi\)
\(104\) −43.0200 −4.21845
\(105\) 7.53822 0.735655
\(106\) −5.91079 −0.574107
\(107\) 10.4002 1.00542 0.502712 0.864454i \(-0.332336\pi\)
0.502712 + 0.864454i \(0.332336\pi\)
\(108\) −52.4350 −5.04556
\(109\) −17.1238 −1.64017 −0.820083 0.572244i \(-0.806073\pi\)
−0.820083 + 0.572244i \(0.806073\pi\)
\(110\) 7.46694 0.711944
\(111\) −24.5504 −2.33022
\(112\) −41.9451 −3.96344
\(113\) −14.1289 −1.32914 −0.664568 0.747228i \(-0.731384\pi\)
−0.664568 + 0.747228i \(0.731384\pi\)
\(114\) 20.2371 1.89538
\(115\) −5.69511 −0.531072
\(116\) 9.32845 0.866125
\(117\) 25.7495 2.38054
\(118\) −7.91806 −0.728917
\(119\) −1.72697 −0.158311
\(120\) 30.5618 2.78989
\(121\) −3.72584 −0.338712
\(122\) 15.9744 1.44625
\(123\) −11.1919 −1.00914
\(124\) −9.42178 −0.846101
\(125\) 1.00000 0.0894427
\(126\) 42.0772 3.74853
\(127\) −12.4650 −1.10609 −0.553046 0.833151i \(-0.686535\pi\)
−0.553046 + 0.833151i \(0.686535\pi\)
\(128\) −55.1028 −4.87045
\(129\) 6.16398 0.542708
\(130\) −11.7386 −1.02955
\(131\) 13.1798 1.15153 0.575763 0.817617i \(-0.304705\pi\)
0.575763 + 0.817617i \(0.304705\pi\)
\(132\) 46.0206 4.00558
\(133\) −6.07318 −0.526611
\(134\) 1.14481 0.0988965
\(135\) −9.25626 −0.796652
\(136\) −7.00157 −0.600380
\(137\) −10.1907 −0.870654 −0.435327 0.900272i \(-0.643367\pi\)
−0.435327 + 0.900272i \(0.643367\pi\)
\(138\) −47.4929 −4.04286
\(139\) −4.48278 −0.380225 −0.190112 0.981762i \(-0.560885\pi\)
−0.190112 + 0.981762i \(0.560885\pi\)
\(140\) −14.1768 −1.19816
\(141\) 33.5365 2.82428
\(142\) 19.2444 1.61495
\(143\) −11.4356 −0.956291
\(144\) 101.786 8.48220
\(145\) 1.64674 0.136754
\(146\) −18.6713 −1.54525
\(147\) 2.21974 0.183081
\(148\) 46.1709 3.79523
\(149\) −18.6283 −1.52609 −0.763045 0.646345i \(-0.776297\pi\)
−0.763045 + 0.646345i \(0.776297\pi\)
\(150\) 8.33923 0.680895
\(151\) −11.5208 −0.937548 −0.468774 0.883318i \(-0.655304\pi\)
−0.468774 + 0.883318i \(0.655304\pi\)
\(152\) −24.6221 −1.99712
\(153\) 4.19078 0.338804
\(154\) −18.6868 −1.50583
\(155\) −1.66321 −0.133592
\(156\) −72.3482 −5.79249
\(157\) 19.0766 1.52247 0.761237 0.648473i \(-0.224592\pi\)
0.761237 + 0.648473i \(0.224592\pi\)
\(158\) −34.9065 −2.77701
\(159\) −6.43087 −0.510001
\(160\) −26.1098 −2.06416
\(161\) 14.2527 1.12327
\(162\) −26.7502 −2.10169
\(163\) 1.32430 0.103727 0.0518636 0.998654i \(-0.483484\pi\)
0.0518636 + 0.998654i \(0.483484\pi\)
\(164\) 21.0482 1.64359
\(165\) 8.12394 0.632448
\(166\) −2.05394 −0.159417
\(167\) −11.5501 −0.893771 −0.446885 0.894591i \(-0.647467\pi\)
−0.446885 + 0.894591i \(0.647467\pi\)
\(168\) −76.4842 −5.90089
\(169\) 4.97767 0.382898
\(170\) −1.91048 −0.146527
\(171\) 14.7375 1.12701
\(172\) −11.5924 −0.883909
\(173\) −9.89021 −0.751939 −0.375970 0.926632i \(-0.622690\pi\)
−0.375970 + 0.926632i \(0.622690\pi\)
\(174\) 13.7325 1.04106
\(175\) −2.50261 −0.189180
\(176\) −45.2042 −3.40740
\(177\) −8.61476 −0.647525
\(178\) −19.2185 −1.44049
\(179\) 4.20597 0.314369 0.157185 0.987569i \(-0.449758\pi\)
0.157185 + 0.987569i \(0.449758\pi\)
\(180\) 34.4023 2.56420
\(181\) −16.0787 −1.19512 −0.597560 0.801824i \(-0.703863\pi\)
−0.597560 + 0.801824i \(0.703863\pi\)
\(182\) 29.3773 2.17759
\(183\) 17.3799 1.28476
\(184\) 57.7837 4.25987
\(185\) 8.15047 0.599235
\(186\) −13.8699 −1.01699
\(187\) −1.86116 −0.136102
\(188\) −63.0708 −4.59991
\(189\) 23.1648 1.68499
\(190\) −6.71851 −0.487412
\(191\) 22.9853 1.66316 0.831579 0.555407i \(-0.187437\pi\)
0.831579 + 0.555407i \(0.187437\pi\)
\(192\) −116.766 −8.42683
\(193\) −2.07766 −0.149553 −0.0747765 0.997200i \(-0.523824\pi\)
−0.0747765 + 0.997200i \(0.523824\pi\)
\(194\) −49.3297 −3.54166
\(195\) −12.7715 −0.914586
\(196\) −4.17458 −0.298184
\(197\) 19.2123 1.36882 0.684408 0.729099i \(-0.260061\pi\)
0.684408 + 0.729099i \(0.260061\pi\)
\(198\) 45.3466 3.22264
\(199\) 2.98337 0.211485 0.105743 0.994394i \(-0.466278\pi\)
0.105743 + 0.994394i \(0.466278\pi\)
\(200\) −10.1462 −0.717444
\(201\) 1.24554 0.0878536
\(202\) 16.3069 1.14735
\(203\) −4.12114 −0.289247
\(204\) −11.7748 −0.824400
\(205\) 3.71560 0.259509
\(206\) 17.1884 1.19757
\(207\) −34.5863 −2.40392
\(208\) 71.0647 4.92745
\(209\) −6.54506 −0.452731
\(210\) −20.8699 −1.44016
\(211\) −10.4886 −0.722064 −0.361032 0.932554i \(-0.617575\pi\)
−0.361032 + 0.932554i \(0.617575\pi\)
\(212\) 12.0943 0.830640
\(213\) 20.9377 1.43463
\(214\) −28.7933 −1.96827
\(215\) −2.04638 −0.139562
\(216\) 93.9158 6.39016
\(217\) 4.16237 0.282560
\(218\) 47.4080 3.21088
\(219\) −20.3142 −1.37270
\(220\) −15.2784 −1.03007
\(221\) 2.92590 0.196817
\(222\) 67.9687 4.56176
\(223\) 12.1410 0.813024 0.406512 0.913645i \(-0.366745\pi\)
0.406512 + 0.913645i \(0.366745\pi\)
\(224\) 65.3427 4.36589
\(225\) 6.07298 0.404866
\(226\) 39.1165 2.60199
\(227\) 18.6424 1.23734 0.618669 0.785652i \(-0.287672\pi\)
0.618669 + 0.785652i \(0.287672\pi\)
\(228\) −41.4079 −2.74231
\(229\) 16.3824 1.08258 0.541288 0.840837i \(-0.317937\pi\)
0.541288 + 0.840837i \(0.317937\pi\)
\(230\) 15.7672 1.03966
\(231\) −20.3311 −1.33769
\(232\) −16.7081 −1.09694
\(233\) 7.54060 0.494001 0.247000 0.969015i \(-0.420555\pi\)
0.247000 + 0.969015i \(0.420555\pi\)
\(234\) −71.2885 −4.66028
\(235\) −11.1338 −0.726288
\(236\) 16.2015 1.05462
\(237\) −37.9778 −2.46693
\(238\) 4.78120 0.309919
\(239\) 7.05731 0.456500 0.228250 0.973603i \(-0.426700\pi\)
0.228250 + 0.973603i \(0.426700\pi\)
\(240\) −50.4850 −3.25879
\(241\) −15.9314 −1.02623 −0.513115 0.858320i \(-0.671508\pi\)
−0.513115 + 0.858320i \(0.671508\pi\)
\(242\) 10.3151 0.663082
\(243\) −1.33508 −0.0856454
\(244\) −32.6858 −2.09249
\(245\) −0.736930 −0.0470807
\(246\) 30.9853 1.97555
\(247\) 10.2894 0.654697
\(248\) 16.8753 1.07158
\(249\) −2.23466 −0.141616
\(250\) −2.76854 −0.175098
\(251\) −13.3903 −0.845189 −0.422595 0.906319i \(-0.638881\pi\)
−0.422595 + 0.906319i \(0.638881\pi\)
\(252\) −86.0957 −5.42352
\(253\) 15.3601 0.965681
\(254\) 34.5099 2.16534
\(255\) −2.07858 −0.130166
\(256\) 75.0245 4.68903
\(257\) −28.4061 −1.77193 −0.885963 0.463757i \(-0.846501\pi\)
−0.885963 + 0.463757i \(0.846501\pi\)
\(258\) −17.0652 −1.06243
\(259\) −20.3975 −1.26744
\(260\) 24.0189 1.48959
\(261\) 10.0006 0.619021
\(262\) −36.4888 −2.25429
\(263\) 12.4424 0.767229 0.383615 0.923493i \(-0.374679\pi\)
0.383615 + 0.923493i \(0.374679\pi\)
\(264\) −82.4271 −5.07304
\(265\) 2.13498 0.131151
\(266\) 16.8138 1.03092
\(267\) −20.9095 −1.27964
\(268\) −2.34244 −0.143087
\(269\) 18.6614 1.13781 0.568904 0.822404i \(-0.307368\pi\)
0.568904 + 0.822404i \(0.307368\pi\)
\(270\) 25.6263 1.55957
\(271\) 12.6900 0.770865 0.385432 0.922736i \(-0.374052\pi\)
0.385432 + 0.922736i \(0.374052\pi\)
\(272\) 11.5659 0.701286
\(273\) 31.9621 1.93443
\(274\) 28.2135 1.70444
\(275\) −2.69707 −0.162639
\(276\) 97.1770 5.84937
\(277\) 17.4769 1.05009 0.525044 0.851075i \(-0.324049\pi\)
0.525044 + 0.851075i \(0.324049\pi\)
\(278\) 12.4108 0.744349
\(279\) −10.1006 −0.604710
\(280\) 25.3920 1.51746
\(281\) 14.7127 0.877686 0.438843 0.898564i \(-0.355388\pi\)
0.438843 + 0.898564i \(0.355388\pi\)
\(282\) −92.8472 −5.52897
\(283\) −7.74277 −0.460260 −0.230130 0.973160i \(-0.573915\pi\)
−0.230130 + 0.973160i \(0.573915\pi\)
\(284\) −39.3767 −2.33658
\(285\) −7.30966 −0.432987
\(286\) 31.6599 1.87209
\(287\) −9.29872 −0.548886
\(288\) −158.564 −9.34349
\(289\) −16.5238 −0.971989
\(290\) −4.55905 −0.267717
\(291\) −53.6701 −3.14620
\(292\) 38.2041 2.23572
\(293\) −26.0317 −1.52079 −0.760394 0.649463i \(-0.774994\pi\)
−0.760394 + 0.649463i \(0.774994\pi\)
\(294\) −6.14543 −0.358409
\(295\) 2.86001 0.166516
\(296\) −82.6963 −4.80662
\(297\) 24.9647 1.44860
\(298\) 51.5732 2.98756
\(299\) −24.1473 −1.39648
\(300\) −17.0632 −0.985145
\(301\) 5.12129 0.295186
\(302\) 31.8958 1.83539
\(303\) 17.7417 1.01923
\(304\) 40.6733 2.33278
\(305\) −5.76997 −0.330387
\(306\) −11.6023 −0.663261
\(307\) 25.4141 1.45046 0.725230 0.688506i \(-0.241733\pi\)
0.725230 + 0.688506i \(0.241733\pi\)
\(308\) 38.2359 2.17869
\(309\) 18.7008 1.06385
\(310\) 4.60466 0.261527
\(311\) 0.941557 0.0533908 0.0266954 0.999644i \(-0.491502\pi\)
0.0266954 + 0.999644i \(0.491502\pi\)
\(312\) 129.582 7.33614
\(313\) 11.7140 0.662116 0.331058 0.943610i \(-0.392594\pi\)
0.331058 + 0.943610i \(0.392594\pi\)
\(314\) −52.8142 −2.98048
\(315\) −15.1983 −0.856329
\(316\) 71.4235 4.01789
\(317\) 3.87286 0.217521 0.108761 0.994068i \(-0.465312\pi\)
0.108761 + 0.994068i \(0.465312\pi\)
\(318\) 17.8041 0.998406
\(319\) −4.44135 −0.248668
\(320\) 38.7650 2.16703
\(321\) −31.3268 −1.74849
\(322\) −39.4591 −2.19897
\(323\) 1.67461 0.0931780
\(324\) 54.7345 3.04081
\(325\) 4.24001 0.235193
\(326\) −3.66638 −0.203062
\(327\) 51.5794 2.85235
\(328\) −37.6992 −2.08159
\(329\) 27.8635 1.53617
\(330\) −22.4915 −1.23811
\(331\) 25.7940 1.41777 0.708884 0.705325i \(-0.249199\pi\)
0.708884 + 0.705325i \(0.249199\pi\)
\(332\) 4.20264 0.230650
\(333\) 49.4977 2.71246
\(334\) 31.9768 1.74969
\(335\) −0.413507 −0.0225923
\(336\) 126.344 6.89266
\(337\) −9.77008 −0.532210 −0.266105 0.963944i \(-0.585737\pi\)
−0.266105 + 0.963944i \(0.585737\pi\)
\(338\) −13.7809 −0.749581
\(339\) 42.5582 2.31145
\(340\) 3.90911 0.212001
\(341\) 4.48579 0.242919
\(342\) −40.8014 −2.20629
\(343\) 19.3625 1.04548
\(344\) 20.7630 1.11946
\(345\) 17.1545 0.923566
\(346\) 27.3815 1.47204
\(347\) 3.58853 0.192642 0.0963212 0.995350i \(-0.469292\pi\)
0.0963212 + 0.995350i \(0.469292\pi\)
\(348\) −28.0986 −1.50624
\(349\) −18.8296 −1.00792 −0.503962 0.863726i \(-0.668125\pi\)
−0.503962 + 0.863726i \(0.668125\pi\)
\(350\) 6.92858 0.370348
\(351\) −39.2466 −2.09483
\(352\) 70.4198 3.75339
\(353\) −5.48246 −0.291802 −0.145901 0.989299i \(-0.546608\pi\)
−0.145901 + 0.989299i \(0.546608\pi\)
\(354\) 23.8503 1.26763
\(355\) −6.95110 −0.368926
\(356\) 39.3238 2.08416
\(357\) 5.20189 0.275313
\(358\) −11.6444 −0.615426
\(359\) 18.5829 0.980767 0.490383 0.871507i \(-0.336857\pi\)
0.490383 + 0.871507i \(0.336857\pi\)
\(360\) −61.6177 −3.24754
\(361\) −13.1110 −0.690050
\(362\) 44.5145 2.33963
\(363\) 11.2227 0.589041
\(364\) −60.1099 −3.15062
\(365\) 6.74409 0.353002
\(366\) −48.1171 −2.51512
\(367\) 33.2531 1.73580 0.867899 0.496740i \(-0.165470\pi\)
0.867899 + 0.496740i \(0.165470\pi\)
\(368\) −95.4531 −4.97584
\(369\) 22.5648 1.17468
\(370\) −22.5649 −1.17309
\(371\) −5.34304 −0.277397
\(372\) 28.3797 1.47142
\(373\) −15.6300 −0.809289 −0.404645 0.914474i \(-0.632605\pi\)
−0.404645 + 0.914474i \(0.632605\pi\)
\(374\) 5.15270 0.266440
\(375\) −3.01214 −0.155546
\(376\) 112.966 5.82575
\(377\) 6.98217 0.359600
\(378\) −64.1328 −3.29863
\(379\) 9.42724 0.484245 0.242122 0.970246i \(-0.422156\pi\)
0.242122 + 0.970246i \(0.422156\pi\)
\(380\) 13.7470 0.705207
\(381\) 37.5464 1.92356
\(382\) −63.6357 −3.25589
\(383\) −32.2772 −1.64929 −0.824643 0.565653i \(-0.808624\pi\)
−0.824643 + 0.565653i \(0.808624\pi\)
\(384\) 165.977 8.47000
\(385\) 6.74971 0.343997
\(386\) 5.75208 0.292773
\(387\) −12.4276 −0.631732
\(388\) 100.935 5.12421
\(389\) 37.5651 1.90463 0.952313 0.305124i \(-0.0986979\pi\)
0.952313 + 0.305124i \(0.0986979\pi\)
\(390\) 35.3584 1.79044
\(391\) −3.93002 −0.198750
\(392\) 7.47704 0.377647
\(393\) −39.6994 −2.00257
\(394\) −53.1899 −2.67967
\(395\) 12.6083 0.634390
\(396\) −92.7854 −4.66264
\(397\) 14.5819 0.731844 0.365922 0.930645i \(-0.380754\pi\)
0.365922 + 0.930645i \(0.380754\pi\)
\(398\) −8.25957 −0.414015
\(399\) 18.2933 0.915808
\(400\) 16.7605 0.838026
\(401\) 17.5640 0.877106 0.438553 0.898705i \(-0.355491\pi\)
0.438553 + 0.898705i \(0.355491\pi\)
\(402\) −3.44833 −0.171987
\(403\) −7.05202 −0.351286
\(404\) −33.3661 −1.66003
\(405\) 9.66219 0.480118
\(406\) 11.4095 0.566246
\(407\) −21.9824 −1.08963
\(408\) 21.0897 1.04410
\(409\) 23.8667 1.18013 0.590067 0.807354i \(-0.299101\pi\)
0.590067 + 0.807354i \(0.299101\pi\)
\(410\) −10.2868 −0.508029
\(411\) 30.6959 1.51412
\(412\) −35.1699 −1.73270
\(413\) −7.15751 −0.352198
\(414\) 95.7537 4.70604
\(415\) 0.741885 0.0364177
\(416\) −110.706 −5.42779
\(417\) 13.5028 0.661234
\(418\) 18.1203 0.886292
\(419\) 12.5347 0.612359 0.306180 0.951974i \(-0.400949\pi\)
0.306180 + 0.951974i \(0.400949\pi\)
\(420\) 42.7026 2.08367
\(421\) −12.1373 −0.591537 −0.295768 0.955260i \(-0.595576\pi\)
−0.295768 + 0.955260i \(0.595576\pi\)
\(422\) 29.0381 1.41355
\(423\) −67.6153 −3.28757
\(424\) −21.6620 −1.05200
\(425\) 0.690069 0.0334732
\(426\) −57.9668 −2.80850
\(427\) 14.4400 0.698800
\(428\) 58.9151 2.84777
\(429\) 34.4456 1.66305
\(430\) 5.66548 0.273214
\(431\) −11.9966 −0.577858 −0.288929 0.957351i \(-0.593299\pi\)
−0.288929 + 0.957351i \(0.593299\pi\)
\(432\) −155.140 −7.46416
\(433\) −10.9161 −0.524592 −0.262296 0.964987i \(-0.584480\pi\)
−0.262296 + 0.964987i \(0.584480\pi\)
\(434\) −11.5237 −0.553155
\(435\) −4.96020 −0.237823
\(436\) −97.0034 −4.64562
\(437\) −13.8205 −0.661126
\(438\) 56.2406 2.68728
\(439\) 16.2590 0.776002 0.388001 0.921659i \(-0.373166\pi\)
0.388001 + 0.921659i \(0.373166\pi\)
\(440\) 27.3650 1.30457
\(441\) −4.47537 −0.213113
\(442\) −8.10046 −0.385300
\(443\) 34.1307 1.62160 0.810800 0.585324i \(-0.199033\pi\)
0.810800 + 0.585324i \(0.199033\pi\)
\(444\) −139.073 −6.60013
\(445\) 6.94176 0.329071
\(446\) −33.6130 −1.59162
\(447\) 56.1111 2.65396
\(448\) −97.0137 −4.58347
\(449\) 9.14809 0.431725 0.215863 0.976424i \(-0.430744\pi\)
0.215863 + 0.976424i \(0.430744\pi\)
\(450\) −16.8133 −0.792587
\(451\) −10.0212 −0.471881
\(452\) −80.0377 −3.76466
\(453\) 34.7022 1.63045
\(454\) −51.6122 −2.42228
\(455\) −10.6111 −0.497456
\(456\) 74.1653 3.47311
\(457\) −29.7851 −1.39329 −0.696644 0.717417i \(-0.745324\pi\)
−0.696644 + 0.717417i \(0.745324\pi\)
\(458\) −45.3552 −2.11931
\(459\) −6.38745 −0.298141
\(460\) −32.2618 −1.50421
\(461\) 6.17372 0.287539 0.143769 0.989611i \(-0.454078\pi\)
0.143769 + 0.989611i \(0.454078\pi\)
\(462\) 56.2874 2.61873
\(463\) 11.9037 0.553212 0.276606 0.960983i \(-0.410790\pi\)
0.276606 + 0.960983i \(0.410790\pi\)
\(464\) 27.6001 1.28130
\(465\) 5.00982 0.232325
\(466\) −20.8765 −0.967083
\(467\) −12.6322 −0.584549 −0.292275 0.956334i \(-0.594412\pi\)
−0.292275 + 0.956334i \(0.594412\pi\)
\(468\) 145.866 6.74267
\(469\) 1.03485 0.0477848
\(470\) 30.8243 1.42182
\(471\) −57.4612 −2.64767
\(472\) −29.0183 −1.33567
\(473\) 5.51922 0.253774
\(474\) 105.143 4.82939
\(475\) 2.42673 0.111346
\(476\) −9.78299 −0.448403
\(477\) 12.9657 0.593660
\(478\) −19.5385 −0.893668
\(479\) −10.8534 −0.495904 −0.247952 0.968772i \(-0.579758\pi\)
−0.247952 + 0.968772i \(0.579758\pi\)
\(480\) 78.6463 3.58970
\(481\) 34.5581 1.57571
\(482\) 44.1066 2.00900
\(483\) −42.9310 −1.95343
\(484\) −21.1062 −0.959372
\(485\) 17.8179 0.809071
\(486\) 3.69622 0.167664
\(487\) 17.1432 0.776834 0.388417 0.921484i \(-0.373022\pi\)
0.388417 + 0.921484i \(0.373022\pi\)
\(488\) 58.5432 2.65013
\(489\) −3.98897 −0.180388
\(490\) 2.04022 0.0921678
\(491\) −33.7075 −1.52120 −0.760600 0.649221i \(-0.775095\pi\)
−0.760600 + 0.649221i \(0.775095\pi\)
\(492\) −63.4002 −2.85830
\(493\) 1.13636 0.0511791
\(494\) −28.4866 −1.28167
\(495\) −16.3792 −0.736192
\(496\) −27.8763 −1.25168
\(497\) 17.3959 0.780313
\(498\) 6.18675 0.277235
\(499\) 0.547428 0.0245062 0.0122531 0.999925i \(-0.496100\pi\)
0.0122531 + 0.999925i \(0.496100\pi\)
\(500\) 5.66482 0.253338
\(501\) 34.7904 1.55432
\(502\) 37.0716 1.65459
\(503\) −10.7403 −0.478888 −0.239444 0.970910i \(-0.576965\pi\)
−0.239444 + 0.970910i \(0.576965\pi\)
\(504\) 154.205 6.86885
\(505\) −5.89006 −0.262104
\(506\) −42.5251 −1.89047
\(507\) −14.9934 −0.665882
\(508\) −70.6120 −3.13290
\(509\) −17.6672 −0.783084 −0.391542 0.920160i \(-0.628058\pi\)
−0.391542 + 0.920160i \(0.628058\pi\)
\(510\) 5.75464 0.254820
\(511\) −16.8779 −0.746632
\(512\) −97.5027 −4.30905
\(513\) −22.4625 −0.991743
\(514\) 78.6435 3.46882
\(515\) −6.20848 −0.273578
\(516\) 34.9178 1.53717
\(517\) 30.0285 1.32065
\(518\) 56.4712 2.48120
\(519\) 29.7907 1.30767
\(520\) −43.0200 −1.88655
\(521\) −34.6464 −1.51789 −0.758944 0.651156i \(-0.774284\pi\)
−0.758944 + 0.651156i \(0.774284\pi\)
\(522\) −27.6871 −1.21183
\(523\) 45.2173 1.97721 0.988607 0.150517i \(-0.0480938\pi\)
0.988607 + 0.150517i \(0.0480938\pi\)
\(524\) 74.6612 3.26159
\(525\) 7.53822 0.328995
\(526\) −34.4472 −1.50197
\(527\) −1.14773 −0.0499958
\(528\) 136.161 5.92567
\(529\) 9.43433 0.410188
\(530\) −5.91079 −0.256748
\(531\) 17.3688 0.753743
\(532\) −34.4034 −1.49158
\(533\) 15.7542 0.682390
\(534\) 57.8889 2.50510
\(535\) 10.4002 0.449639
\(536\) 4.19552 0.181219
\(537\) −12.6690 −0.546707
\(538\) −51.6649 −2.22743
\(539\) 1.98755 0.0856098
\(540\) −52.4350 −2.25644
\(541\) 10.4143 0.447747 0.223873 0.974618i \(-0.428130\pi\)
0.223873 + 0.974618i \(0.428130\pi\)
\(542\) −35.1329 −1.50909
\(543\) 48.4313 2.07839
\(544\) −18.0175 −0.772496
\(545\) −17.1238 −0.733505
\(546\) −88.4884 −3.78695
\(547\) −39.9530 −1.70827 −0.854133 0.520055i \(-0.825912\pi\)
−0.854133 + 0.520055i \(0.825912\pi\)
\(548\) −57.7287 −2.46605
\(549\) −35.0409 −1.49551
\(550\) 7.46694 0.318391
\(551\) 3.99619 0.170243
\(552\) −174.053 −7.40818
\(553\) −31.5536 −1.34180
\(554\) −48.3856 −2.05571
\(555\) −24.5504 −1.04210
\(556\) −25.3942 −1.07695
\(557\) 11.9982 0.508378 0.254189 0.967155i \(-0.418191\pi\)
0.254189 + 0.967155i \(0.418191\pi\)
\(558\) 27.9641 1.18381
\(559\) −8.67666 −0.366984
\(560\) −41.9451 −1.77250
\(561\) 5.60607 0.236689
\(562\) −40.7327 −1.71821
\(563\) 38.4643 1.62108 0.810538 0.585686i \(-0.199175\pi\)
0.810538 + 0.585686i \(0.199175\pi\)
\(564\) 189.978 7.99952
\(565\) −14.1289 −0.594408
\(566\) 21.4362 0.901029
\(567\) −24.1807 −1.01549
\(568\) 70.5272 2.95925
\(569\) −19.8237 −0.831054 −0.415527 0.909581i \(-0.636403\pi\)
−0.415527 + 0.909581i \(0.636403\pi\)
\(570\) 20.2371 0.847639
\(571\) 46.3466 1.93955 0.969773 0.244008i \(-0.0784622\pi\)
0.969773 + 0.244008i \(0.0784622\pi\)
\(572\) −64.7805 −2.70861
\(573\) −69.2349 −2.89233
\(574\) 25.7439 1.07453
\(575\) −5.69511 −0.237503
\(576\) 235.419 9.80913
\(577\) −13.8951 −0.578459 −0.289230 0.957260i \(-0.593399\pi\)
−0.289230 + 0.957260i \(0.593399\pi\)
\(578\) 45.7468 1.90282
\(579\) 6.25819 0.260082
\(580\) 9.32845 0.387343
\(581\) −1.85665 −0.0770268
\(582\) 148.588 6.15916
\(583\) −5.75819 −0.238480
\(584\) −68.4269 −2.83153
\(585\) 25.7495 1.06461
\(586\) 72.0698 2.97717
\(587\) 30.7790 1.27038 0.635192 0.772354i \(-0.280921\pi\)
0.635192 + 0.772354i \(0.280921\pi\)
\(588\) 12.5744 0.518560
\(589\) −4.03617 −0.166307
\(590\) −7.91806 −0.325982
\(591\) −57.8700 −2.38045
\(592\) 136.606 5.61448
\(593\) 17.7468 0.728774 0.364387 0.931248i \(-0.381279\pi\)
0.364387 + 0.931248i \(0.381279\pi\)
\(594\) −69.1159 −2.83586
\(595\) −1.72697 −0.0707990
\(596\) −105.526 −4.32251
\(597\) −8.98632 −0.367785
\(598\) 66.8529 2.73382
\(599\) −1.43162 −0.0584944 −0.0292472 0.999572i \(-0.509311\pi\)
−0.0292472 + 0.999572i \(0.509311\pi\)
\(600\) 30.5618 1.24768
\(601\) −14.7309 −0.600887 −0.300443 0.953800i \(-0.597135\pi\)
−0.300443 + 0.953800i \(0.597135\pi\)
\(602\) −14.1785 −0.577873
\(603\) −2.51122 −0.102265
\(604\) −65.2631 −2.65552
\(605\) −3.72584 −0.151477
\(606\) −49.1186 −1.99531
\(607\) −15.2816 −0.620261 −0.310130 0.950694i \(-0.600373\pi\)
−0.310130 + 0.950694i \(0.600373\pi\)
\(608\) −63.3615 −2.56965
\(609\) 12.4134 0.503018
\(610\) 15.9744 0.646784
\(611\) −47.2073 −1.90980
\(612\) 23.7400 0.959632
\(613\) −26.6706 −1.07722 −0.538608 0.842557i \(-0.681049\pi\)
−0.538608 + 0.842557i \(0.681049\pi\)
\(614\) −70.3600 −2.83950
\(615\) −11.1919 −0.451302
\(616\) −68.4839 −2.75929
\(617\) −35.1352 −1.41449 −0.707246 0.706968i \(-0.750062\pi\)
−0.707246 + 0.706968i \(0.750062\pi\)
\(618\) −51.7740 −2.08265
\(619\) −17.7790 −0.714600 −0.357300 0.933990i \(-0.616303\pi\)
−0.357300 + 0.933990i \(0.616303\pi\)
\(620\) −9.42178 −0.378388
\(621\) 52.7154 2.11540
\(622\) −2.60674 −0.104521
\(623\) −17.3725 −0.696016
\(624\) −214.057 −8.56913
\(625\) 1.00000 0.0400000
\(626\) −32.4308 −1.29619
\(627\) 19.7146 0.787327
\(628\) 108.065 4.31227
\(629\) 5.62439 0.224259
\(630\) 42.0772 1.67640
\(631\) 8.10402 0.322616 0.161308 0.986904i \(-0.448429\pi\)
0.161308 + 0.986904i \(0.448429\pi\)
\(632\) −127.926 −5.08862
\(633\) 31.5931 1.25571
\(634\) −10.7222 −0.425831
\(635\) −12.4650 −0.494659
\(636\) −36.4297 −1.44453
\(637\) −3.12459 −0.123801
\(638\) 12.2961 0.486806
\(639\) −42.2139 −1.66996
\(640\) −55.1028 −2.17813
\(641\) −41.2787 −1.63041 −0.815205 0.579172i \(-0.803376\pi\)
−0.815205 + 0.579172i \(0.803376\pi\)
\(642\) 86.7295 3.42294
\(643\) −5.15876 −0.203441 −0.101721 0.994813i \(-0.532435\pi\)
−0.101721 + 0.994813i \(0.532435\pi\)
\(644\) 80.7387 3.18155
\(645\) 6.16398 0.242706
\(646\) −4.63623 −0.182410
\(647\) −44.9058 −1.76543 −0.882715 0.469909i \(-0.844287\pi\)
−0.882715 + 0.469909i \(0.844287\pi\)
\(648\) −98.0344 −3.85116
\(649\) −7.71364 −0.302787
\(650\) −11.7386 −0.460427
\(651\) −12.5376 −0.491389
\(652\) 7.50191 0.293798
\(653\) −4.51806 −0.176805 −0.0884026 0.996085i \(-0.528176\pi\)
−0.0884026 + 0.996085i \(0.528176\pi\)
\(654\) −142.800 −5.58391
\(655\) 13.1798 0.514978
\(656\) 62.2754 2.43145
\(657\) 40.9568 1.59788
\(658\) −77.1414 −3.00728
\(659\) −48.8745 −1.90388 −0.951939 0.306287i \(-0.900913\pi\)
−0.951939 + 0.306287i \(0.900913\pi\)
\(660\) 46.0206 1.79135
\(661\) 24.1138 0.937920 0.468960 0.883220i \(-0.344629\pi\)
0.468960 + 0.883220i \(0.344629\pi\)
\(662\) −71.4118 −2.77550
\(663\) −8.81321 −0.342277
\(664\) −7.52731 −0.292116
\(665\) −6.07318 −0.235508
\(666\) −137.036 −5.31005
\(667\) −9.37835 −0.363131
\(668\) −65.4290 −2.53152
\(669\) −36.5705 −1.41390
\(670\) 1.14481 0.0442279
\(671\) 15.5620 0.600764
\(672\) −196.821 −7.59255
\(673\) −18.8466 −0.726482 −0.363241 0.931695i \(-0.618330\pi\)
−0.363241 + 0.931695i \(0.618330\pi\)
\(674\) 27.0489 1.04188
\(675\) −9.25626 −0.356274
\(676\) 28.1976 1.08452
\(677\) 44.6115 1.71456 0.857280 0.514850i \(-0.172152\pi\)
0.857280 + 0.514850i \(0.172152\pi\)
\(678\) −117.824 −4.52501
\(679\) −44.5914 −1.71126
\(680\) −7.00157 −0.268498
\(681\) −56.1534 −2.15180
\(682\) −12.4191 −0.475551
\(683\) −42.6610 −1.63238 −0.816189 0.577785i \(-0.803917\pi\)
−0.816189 + 0.577785i \(0.803917\pi\)
\(684\) 83.4854 3.19214
\(685\) −10.1907 −0.389368
\(686\) −53.6060 −2.04669
\(687\) −49.3460 −1.88267
\(688\) −34.2984 −1.30761
\(689\) 9.05235 0.344867
\(690\) −47.4929 −1.80802
\(691\) −4.83168 −0.183806 −0.0919029 0.995768i \(-0.529295\pi\)
−0.0919029 + 0.995768i \(0.529295\pi\)
\(692\) −56.0263 −2.12980
\(693\) 40.9909 1.55712
\(694\) −9.93500 −0.377127
\(695\) −4.48278 −0.170042
\(696\) 50.3271 1.90764
\(697\) 2.56402 0.0971192
\(698\) 52.1305 1.97317
\(699\) −22.7133 −0.859097
\(700\) −14.1768 −0.535834
\(701\) −45.4664 −1.71724 −0.858621 0.512611i \(-0.828678\pi\)
−0.858621 + 0.512611i \(0.828678\pi\)
\(702\) 108.656 4.10095
\(703\) 19.7790 0.745981
\(704\) −104.552 −3.94044
\(705\) 33.5365 1.26306
\(706\) 15.1784 0.571247
\(707\) 14.7405 0.554375
\(708\) −48.8010 −1.83406
\(709\) 14.5335 0.545818 0.272909 0.962040i \(-0.412014\pi\)
0.272909 + 0.962040i \(0.412014\pi\)
\(710\) 19.2444 0.722229
\(711\) 76.5698 2.87159
\(712\) −70.4324 −2.63957
\(713\) 9.47217 0.354736
\(714\) −14.4016 −0.538968
\(715\) −11.4356 −0.427666
\(716\) 23.8261 0.890422
\(717\) −21.2576 −0.793880
\(718\) −51.4475 −1.92000
\(719\) 39.5220 1.47392 0.736961 0.675935i \(-0.236260\pi\)
0.736961 + 0.675935i \(0.236260\pi\)
\(720\) 101.786 3.79335
\(721\) 15.5374 0.578644
\(722\) 36.2982 1.35088
\(723\) 47.9875 1.78467
\(724\) −91.0829 −3.38507
\(725\) 1.64674 0.0611582
\(726\) −31.0706 −1.15314
\(727\) 22.7282 0.842944 0.421472 0.906842i \(-0.361514\pi\)
0.421472 + 0.906842i \(0.361514\pi\)
\(728\) 107.662 3.99023
\(729\) −24.9651 −0.924634
\(730\) −18.6713 −0.691056
\(731\) −1.41214 −0.0522300
\(732\) 98.4542 3.63897
\(733\) 4.40089 0.162551 0.0812753 0.996692i \(-0.474101\pi\)
0.0812753 + 0.996692i \(0.474101\pi\)
\(734\) −92.0626 −3.39809
\(735\) 2.21974 0.0818762
\(736\) 148.698 5.48109
\(737\) 1.11525 0.0410809
\(738\) −62.4716 −2.29961
\(739\) −7.93698 −0.291966 −0.145983 0.989287i \(-0.546635\pi\)
−0.145983 + 0.989287i \(0.546635\pi\)
\(740\) 46.1709 1.69728
\(741\) −30.9930 −1.13856
\(742\) 14.7924 0.543047
\(743\) 16.7652 0.615057 0.307528 0.951539i \(-0.400498\pi\)
0.307528 + 0.951539i \(0.400498\pi\)
\(744\) −50.8306 −1.86354
\(745\) −18.6283 −0.682489
\(746\) 43.2722 1.58431
\(747\) 4.50545 0.164846
\(748\) −10.5431 −0.385495
\(749\) −26.0276 −0.951028
\(750\) 8.33923 0.304506
\(751\) −11.9219 −0.435035 −0.217517 0.976056i \(-0.569796\pi\)
−0.217517 + 0.976056i \(0.569796\pi\)
\(752\) −186.608 −6.80489
\(753\) 40.3335 1.46983
\(754\) −19.3304 −0.703972
\(755\) −11.5208 −0.419284
\(756\) 131.225 4.77259
\(757\) 29.2836 1.06433 0.532165 0.846641i \(-0.321379\pi\)
0.532165 + 0.846641i \(0.321379\pi\)
\(758\) −26.0997 −0.947984
\(759\) −46.2668 −1.67938
\(760\) −24.6221 −0.893138
\(761\) 31.0015 1.12380 0.561902 0.827204i \(-0.310070\pi\)
0.561902 + 0.827204i \(0.310070\pi\)
\(762\) −103.949 −3.76566
\(763\) 42.8543 1.55143
\(764\) 130.207 4.71074
\(765\) 4.19078 0.151518
\(766\) 89.3607 3.22873
\(767\) 12.1265 0.437862
\(768\) −225.984 −8.15450
\(769\) −44.3196 −1.59821 −0.799103 0.601194i \(-0.794692\pi\)
−0.799103 + 0.601194i \(0.794692\pi\)
\(770\) −18.6868 −0.673427
\(771\) 85.5632 3.08148
\(772\) −11.7696 −0.423595
\(773\) 11.6248 0.418113 0.209057 0.977904i \(-0.432961\pi\)
0.209057 + 0.977904i \(0.432961\pi\)
\(774\) 34.4064 1.23671
\(775\) −1.66321 −0.0597443
\(776\) −180.784 −6.48978
\(777\) 61.4400 2.20415
\(778\) −104.000 −3.72860
\(779\) 9.01678 0.323060
\(780\) −72.3482 −2.59048
\(781\) 18.7476 0.670840
\(782\) 10.8804 0.389083
\(783\) −15.2426 −0.544726
\(784\) −12.3513 −0.441119
\(785\) 19.0766 0.680871
\(786\) 109.909 3.92034
\(787\) −19.6425 −0.700180 −0.350090 0.936716i \(-0.613849\pi\)
−0.350090 + 0.936716i \(0.613849\pi\)
\(788\) 108.834 3.87705
\(789\) −37.4782 −1.33426
\(790\) −34.9065 −1.24192
\(791\) 35.3592 1.25723
\(792\) 166.187 5.90520
\(793\) −24.4647 −0.868767
\(794\) −40.3706 −1.43270
\(795\) −6.43087 −0.228080
\(796\) 16.9002 0.599013
\(797\) −24.5901 −0.871027 −0.435514 0.900182i \(-0.643433\pi\)
−0.435514 + 0.900182i \(0.643433\pi\)
\(798\) −50.6456 −1.79284
\(799\) −7.68307 −0.271808
\(800\) −26.1098 −0.923121
\(801\) 42.1572 1.48955
\(802\) −48.6268 −1.71707
\(803\) −18.1893 −0.641885
\(804\) 7.05575 0.248837
\(805\) 14.2527 0.502340
\(806\) 19.5238 0.687697
\(807\) −56.2109 −1.97872
\(808\) 59.7617 2.10241
\(809\) 25.5573 0.898548 0.449274 0.893394i \(-0.351683\pi\)
0.449274 + 0.893394i \(0.351683\pi\)
\(810\) −26.7502 −0.939905
\(811\) 32.0207 1.12440 0.562199 0.827002i \(-0.309955\pi\)
0.562199 + 0.827002i \(0.309955\pi\)
\(812\) −23.3455 −0.819267
\(813\) −38.2242 −1.34058
\(814\) 60.8591 2.13311
\(815\) 1.32430 0.0463882
\(816\) −34.8381 −1.21958
\(817\) −4.96602 −0.173739
\(818\) −66.0761 −2.31030
\(819\) −64.4410 −2.25175
\(820\) 21.0482 0.735036
\(821\) −10.3653 −0.361751 −0.180876 0.983506i \(-0.557893\pi\)
−0.180876 + 0.983506i \(0.557893\pi\)
\(822\) −84.9830 −2.96412
\(823\) −39.1992 −1.36640 −0.683200 0.730232i \(-0.739412\pi\)
−0.683200 + 0.730232i \(0.739412\pi\)
\(824\) 62.9925 2.19445
\(825\) 8.12394 0.282839
\(826\) 19.8158 0.689482
\(827\) 23.7597 0.826206 0.413103 0.910684i \(-0.364445\pi\)
0.413103 + 0.910684i \(0.364445\pi\)
\(828\) −195.925 −6.80888
\(829\) −7.07428 −0.245700 −0.122850 0.992425i \(-0.539203\pi\)
−0.122850 + 0.992425i \(0.539203\pi\)
\(830\) −2.05394 −0.0712932
\(831\) −52.6430 −1.82616
\(832\) 164.364 5.69829
\(833\) −0.508532 −0.0176196
\(834\) −37.3830 −1.29447
\(835\) −11.5501 −0.399706
\(836\) −37.0766 −1.28232
\(837\) 15.3951 0.532132
\(838\) −34.7028 −1.19879
\(839\) −25.1614 −0.868669 −0.434335 0.900752i \(-0.643016\pi\)
−0.434335 + 0.900752i \(0.643016\pi\)
\(840\) −76.4842 −2.63896
\(841\) −26.2883 −0.906492
\(842\) 33.6027 1.15802
\(843\) −44.3167 −1.52635
\(844\) −59.4159 −2.04518
\(845\) 4.97767 0.171237
\(846\) 187.196 6.43592
\(847\) 9.32433 0.320388
\(848\) 35.7835 1.22881
\(849\) 23.3223 0.800419
\(850\) −1.91048 −0.0655290
\(851\) −46.4179 −1.59118
\(852\) 118.608 4.06345
\(853\) 46.3115 1.58568 0.792838 0.609432i \(-0.208603\pi\)
0.792838 + 0.609432i \(0.208603\pi\)
\(854\) −39.9777 −1.36801
\(855\) 14.7375 0.504013
\(856\) −105.522 −3.60668
\(857\) −41.9166 −1.43184 −0.715922 0.698180i \(-0.753993\pi\)
−0.715922 + 0.698180i \(0.753993\pi\)
\(858\) −95.3639 −3.25567
\(859\) −46.7191 −1.59404 −0.797018 0.603956i \(-0.793590\pi\)
−0.797018 + 0.603956i \(0.793590\pi\)
\(860\) −11.5924 −0.395296
\(861\) 28.0090 0.954545
\(862\) 33.2132 1.13125
\(863\) 46.8241 1.59391 0.796956 0.604037i \(-0.206442\pi\)
0.796956 + 0.604037i \(0.206442\pi\)
\(864\) 241.679 8.22209
\(865\) −9.89021 −0.336277
\(866\) 30.2215 1.02697
\(867\) 49.7720 1.69035
\(868\) 23.5791 0.800326
\(869\) −34.0053 −1.15355
\(870\) 13.7325 0.465576
\(871\) −1.75327 −0.0594073
\(872\) 173.742 5.88364
\(873\) 108.208 3.66229
\(874\) 38.2627 1.29426
\(875\) −2.50261 −0.0846037
\(876\) −115.076 −3.88806
\(877\) −31.7358 −1.07164 −0.535821 0.844331i \(-0.679998\pi\)
−0.535821 + 0.844331i \(0.679998\pi\)
\(878\) −45.0138 −1.51914
\(879\) 78.4111 2.64474
\(880\) −45.2042 −1.52383
\(881\) 24.1310 0.812995 0.406498 0.913652i \(-0.366750\pi\)
0.406498 + 0.913652i \(0.366750\pi\)
\(882\) 12.3902 0.417201
\(883\) 49.9052 1.67944 0.839721 0.543018i \(-0.182718\pi\)
0.839721 + 0.543018i \(0.182718\pi\)
\(884\) 16.5747 0.557466
\(885\) −8.61476 −0.289582
\(886\) −94.4923 −3.17453
\(887\) 0.380344 0.0127707 0.00638535 0.999980i \(-0.497967\pi\)
0.00638535 + 0.999980i \(0.497967\pi\)
\(888\) 249.093 8.35901
\(889\) 31.1951 1.04625
\(890\) −19.2185 −0.644207
\(891\) −26.0596 −0.873028
\(892\) 68.7768 2.30282
\(893\) −27.0187 −0.904148
\(894\) −155.346 −5.19554
\(895\) 4.20597 0.140590
\(896\) 137.901 4.60695
\(897\) 72.7351 2.42856
\(898\) −25.3269 −0.845169
\(899\) −2.73887 −0.0913463
\(900\) 34.4023 1.14674
\(901\) 1.47329 0.0490823
\(902\) 27.7442 0.923780
\(903\) −15.4261 −0.513347
\(904\) 143.355 4.76791
\(905\) −16.0787 −0.534474
\(906\) −96.0745 −3.19186
\(907\) −39.9864 −1.32773 −0.663863 0.747854i \(-0.731084\pi\)
−0.663863 + 0.747854i \(0.731084\pi\)
\(908\) 105.606 3.50465
\(909\) −35.7702 −1.18642
\(910\) 29.3773 0.973847
\(911\) 17.5380 0.581061 0.290530 0.956866i \(-0.406168\pi\)
0.290530 + 0.956866i \(0.406168\pi\)
\(912\) −122.514 −4.05684
\(913\) −2.00091 −0.0662205
\(914\) 82.4613 2.72758
\(915\) 17.3799 0.574563
\(916\) 92.8031 3.06630
\(917\) −32.9840 −1.08923
\(918\) 17.6839 0.583656
\(919\) −25.3706 −0.836900 −0.418450 0.908240i \(-0.637427\pi\)
−0.418450 + 0.908240i \(0.637427\pi\)
\(920\) 57.7837 1.90507
\(921\) −76.5509 −2.52244
\(922\) −17.0922 −0.562901
\(923\) −29.4727 −0.970106
\(924\) −115.172 −3.78887
\(925\) 8.15047 0.267986
\(926\) −32.9559 −1.08300
\(927\) −37.7040 −1.23836
\(928\) −42.9959 −1.41141
\(929\) −2.64760 −0.0868649 −0.0434324 0.999056i \(-0.513829\pi\)
−0.0434324 + 0.999056i \(0.513829\pi\)
\(930\) −13.8699 −0.454812
\(931\) −1.78833 −0.0586103
\(932\) 42.7161 1.39921
\(933\) −2.83610 −0.0928498
\(934\) 34.9728 1.14434
\(935\) −1.86116 −0.0608664
\(936\) −261.259 −8.53953
\(937\) 37.2446 1.21673 0.608364 0.793658i \(-0.291826\pi\)
0.608364 + 0.793658i \(0.291826\pi\)
\(938\) −2.86501 −0.0935461
\(939\) −35.2843 −1.15146
\(940\) −63.0708 −2.05714
\(941\) −2.98457 −0.0972943 −0.0486472 0.998816i \(-0.515491\pi\)
−0.0486472 + 0.998816i \(0.515491\pi\)
\(942\) 159.084 5.18323
\(943\) −21.1608 −0.689090
\(944\) 47.9353 1.56016
\(945\) 23.1648 0.753552
\(946\) −15.2802 −0.496802
\(947\) −58.0874 −1.88759 −0.943793 0.330537i \(-0.892770\pi\)
−0.943793 + 0.330537i \(0.892770\pi\)
\(948\) −215.138 −6.98734
\(949\) 28.5950 0.928234
\(950\) −6.71851 −0.217977
\(951\) −11.6656 −0.378283
\(952\) 17.5222 0.567898
\(953\) 20.0137 0.648307 0.324153 0.946005i \(-0.394921\pi\)
0.324153 + 0.946005i \(0.394921\pi\)
\(954\) −35.8961 −1.16218
\(955\) 22.9853 0.743787
\(956\) 39.9784 1.29299
\(957\) 13.3780 0.432448
\(958\) 30.0481 0.970809
\(959\) 25.5035 0.823551
\(960\) −116.766 −3.76859
\(961\) −28.2337 −0.910766
\(962\) −95.6754 −3.08470
\(963\) 63.1601 2.03531
\(964\) −90.2483 −2.90670
\(965\) −2.07766 −0.0668822
\(966\) 118.856 3.82414
\(967\) 36.8362 1.18457 0.592286 0.805728i \(-0.298226\pi\)
0.592286 + 0.805728i \(0.298226\pi\)
\(968\) 37.8031 1.21504
\(969\) −5.04417 −0.162042
\(970\) −49.3297 −1.58388
\(971\) −51.7636 −1.66117 −0.830586 0.556891i \(-0.811994\pi\)
−0.830586 + 0.556891i \(0.811994\pi\)
\(972\) −7.56298 −0.242583
\(973\) 11.2187 0.359654
\(974\) −47.4617 −1.52077
\(975\) −12.7715 −0.409015
\(976\) −96.7076 −3.09554
\(977\) −42.8538 −1.37101 −0.685507 0.728066i \(-0.740419\pi\)
−0.685507 + 0.728066i \(0.740419\pi\)
\(978\) 11.0436 0.353136
\(979\) −18.7224 −0.598370
\(980\) −4.17458 −0.133352
\(981\) −103.993 −3.32023
\(982\) 93.3207 2.97798
\(983\) −28.9764 −0.924204 −0.462102 0.886827i \(-0.652905\pi\)
−0.462102 + 0.886827i \(0.652905\pi\)
\(984\) 113.555 3.62001
\(985\) 19.2123 0.612153
\(986\) −3.14606 −0.100191
\(987\) −83.9289 −2.67149
\(988\) 58.2874 1.85437
\(989\) 11.6544 0.370587
\(990\) 45.3466 1.44121
\(991\) 18.7791 0.596539 0.298270 0.954482i \(-0.403591\pi\)
0.298270 + 0.954482i \(0.403591\pi\)
\(992\) 43.4261 1.37878
\(993\) −77.6952 −2.46558
\(994\) −48.1613 −1.52758
\(995\) 2.98337 0.0945791
\(996\) −12.6589 −0.401114
\(997\) −53.8370 −1.70504 −0.852518 0.522699i \(-0.824925\pi\)
−0.852518 + 0.522699i \(0.824925\pi\)
\(998\) −1.51558 −0.0479747
\(999\) −75.4429 −2.38691
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 8005.2.a.e.1.2 126
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8005.2.a.e.1.2 126 1.1 even 1 trivial