Properties

Label 8029.2.a.h.1.8
Level $8029$
Weight $2$
Character 8029.1
Self dual yes
Analytic conductor $64.112$
Analytic rank $0$
Dimension $71$
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] = [8029,2,Mod(1,8029)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8029, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("8029.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8029 = 7 \cdot 31 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8029.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: \(64.1118877829\)
Analytic rank: \(0\)
Dimension: \(71\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) \(=\) 8029.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.30726 q^{2} +1.92904 q^{3} +3.32347 q^{4} +4.29364 q^{5} -4.45079 q^{6} -1.00000 q^{7} -3.05358 q^{8} +0.721177 q^{9} +O(q^{10})\) \(q-2.30726 q^{2} +1.92904 q^{3} +3.32347 q^{4} +4.29364 q^{5} -4.45079 q^{6} -1.00000 q^{7} -3.05358 q^{8} +0.721177 q^{9} -9.90655 q^{10} +1.39887 q^{11} +6.41108 q^{12} +2.11313 q^{13} +2.30726 q^{14} +8.28257 q^{15} +0.398494 q^{16} -3.41873 q^{17} -1.66395 q^{18} +4.04767 q^{19} +14.2698 q^{20} -1.92904 q^{21} -3.22756 q^{22} -1.11969 q^{23} -5.89047 q^{24} +13.4353 q^{25} -4.87556 q^{26} -4.39593 q^{27} -3.32347 q^{28} +5.91808 q^{29} -19.1101 q^{30} -1.00000 q^{31} +5.18774 q^{32} +2.69847 q^{33} +7.88791 q^{34} -4.29364 q^{35} +2.39681 q^{36} +1.00000 q^{37} -9.33904 q^{38} +4.07631 q^{39} -13.1110 q^{40} +8.70509 q^{41} +4.45079 q^{42} +0.320874 q^{43} +4.64909 q^{44} +3.09647 q^{45} +2.58343 q^{46} +13.0091 q^{47} +0.768709 q^{48} +1.00000 q^{49} -30.9988 q^{50} -6.59485 q^{51} +7.02293 q^{52} -9.51840 q^{53} +10.1426 q^{54} +6.00623 q^{55} +3.05358 q^{56} +7.80810 q^{57} -13.6546 q^{58} -5.46939 q^{59} +27.5269 q^{60} +10.5744 q^{61} +2.30726 q^{62} -0.721177 q^{63} -12.7665 q^{64} +9.07303 q^{65} -6.22607 q^{66} -3.91995 q^{67} -11.3620 q^{68} -2.15993 q^{69} +9.90655 q^{70} +12.1447 q^{71} -2.20218 q^{72} -4.81354 q^{73} -2.30726 q^{74} +25.9172 q^{75} +13.4523 q^{76} -1.39887 q^{77} -9.40512 q^{78} +5.34478 q^{79} +1.71099 q^{80} -10.6434 q^{81} -20.0849 q^{82} -14.7032 q^{83} -6.41108 q^{84} -14.6788 q^{85} -0.740341 q^{86} +11.4162 q^{87} -4.27156 q^{88} +10.2420 q^{89} -7.14438 q^{90} -2.11313 q^{91} -3.72127 q^{92} -1.92904 q^{93} -30.0154 q^{94} +17.3792 q^{95} +10.0073 q^{96} -4.84009 q^{97} -2.30726 q^{98} +1.00883 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 71 q + 6 q^{2} + 8 q^{3} + 78 q^{4} + 5 q^{6} - 71 q^{7} + 18 q^{8} + 87 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 71 q + 6 q^{2} + 8 q^{3} + 78 q^{4} + 5 q^{6} - 71 q^{7} + 18 q^{8} + 87 q^{9} + 4 q^{10} + 57 q^{11} + 21 q^{12} - 20 q^{13} - 6 q^{14} + 22 q^{15} + 88 q^{16} - 19 q^{17} + q^{18} + 23 q^{19} + 25 q^{20} - 8 q^{21} + 18 q^{22} + 34 q^{23} + 15 q^{24} + 81 q^{25} - 13 q^{26} + 20 q^{27} - 78 q^{28} + 16 q^{29} + 6 q^{30} - 71 q^{31} + 47 q^{32} - 16 q^{33} + 32 q^{34} + 125 q^{36} + 71 q^{37} + 13 q^{38} + 30 q^{39} + 31 q^{40} + 17 q^{41} - 5 q^{42} + 38 q^{43} + 80 q^{44} - q^{45} + 26 q^{46} + 32 q^{47} + 61 q^{48} + 71 q^{49} + 47 q^{50} + 73 q^{51} - 23 q^{52} + 31 q^{53} + 47 q^{54} + 11 q^{55} - 18 q^{56} + 17 q^{57} - 2 q^{58} + 97 q^{59} + 103 q^{60} - q^{61} - 6 q^{62} - 87 q^{63} + 100 q^{64} + 46 q^{65} + 43 q^{66} + 75 q^{67} - 43 q^{68} + 10 q^{69} - 4 q^{70} + 131 q^{71} - 11 q^{72} - 15 q^{73} + 6 q^{74} + 76 q^{75} + 41 q^{76} - 57 q^{77} + 89 q^{78} + 8 q^{79} + 10 q^{80} + 171 q^{81} + 14 q^{82} + 18 q^{83} - 21 q^{84} + 47 q^{85} + 90 q^{86} - 59 q^{87} + 13 q^{88} + 18 q^{89} + 69 q^{90} + 20 q^{91} + 110 q^{92} - 8 q^{93} + 39 q^{94} + 72 q^{95} + 100 q^{96} + 23 q^{97} + 6 q^{98} + 168 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.30726 −1.63148 −0.815741 0.578417i \(-0.803670\pi\)
−0.815741 + 0.578417i \(0.803670\pi\)
\(3\) 1.92904 1.11373 0.556865 0.830603i \(-0.312004\pi\)
0.556865 + 0.830603i \(0.312004\pi\)
\(4\) 3.32347 1.66173
\(5\) 4.29364 1.92017 0.960086 0.279704i \(-0.0902365\pi\)
0.960086 + 0.279704i \(0.0902365\pi\)
\(6\) −4.45079 −1.81703
\(7\) −1.00000 −0.377964
\(8\) −3.05358 −1.07961
\(9\) 0.721177 0.240392
\(10\) −9.90655 −3.13273
\(11\) 1.39887 0.421775 0.210887 0.977510i \(-0.432365\pi\)
0.210887 + 0.977510i \(0.432365\pi\)
\(12\) 6.41108 1.85072
\(13\) 2.11313 0.586078 0.293039 0.956101i \(-0.405333\pi\)
0.293039 + 0.956101i \(0.405333\pi\)
\(14\) 2.30726 0.616642
\(15\) 8.28257 2.13855
\(16\) 0.398494 0.0996235
\(17\) −3.41873 −0.829163 −0.414582 0.910012i \(-0.636072\pi\)
−0.414582 + 0.910012i \(0.636072\pi\)
\(18\) −1.66395 −0.392196
\(19\) 4.04767 0.928599 0.464300 0.885678i \(-0.346306\pi\)
0.464300 + 0.885678i \(0.346306\pi\)
\(20\) 14.2698 3.19081
\(21\) −1.92904 −0.420950
\(22\) −3.22756 −0.688118
\(23\) −1.11969 −0.233472 −0.116736 0.993163i \(-0.537243\pi\)
−0.116736 + 0.993163i \(0.537243\pi\)
\(24\) −5.89047 −1.20239
\(25\) 13.4353 2.68706
\(26\) −4.87556 −0.956175
\(27\) −4.39593 −0.845997
\(28\) −3.32347 −0.628076
\(29\) 5.91808 1.09896 0.549480 0.835507i \(-0.314826\pi\)
0.549480 + 0.835507i \(0.314826\pi\)
\(30\) −19.1101 −3.48901
\(31\) −1.00000 −0.179605
\(32\) 5.18774 0.917071
\(33\) 2.69847 0.469743
\(34\) 7.88791 1.35276
\(35\) −4.29364 −0.725757
\(36\) 2.39681 0.399468
\(37\) 1.00000 0.164399
\(38\) −9.33904 −1.51499
\(39\) 4.07631 0.652732
\(40\) −13.1110 −2.07303
\(41\) 8.70509 1.35951 0.679753 0.733441i \(-0.262087\pi\)
0.679753 + 0.733441i \(0.262087\pi\)
\(42\) 4.45079 0.686772
\(43\) 0.320874 0.0489328 0.0244664 0.999701i \(-0.492211\pi\)
0.0244664 + 0.999701i \(0.492211\pi\)
\(44\) 4.64909 0.700877
\(45\) 3.09647 0.461595
\(46\) 2.58343 0.380906
\(47\) 13.0091 1.89757 0.948785 0.315921i \(-0.102313\pi\)
0.948785 + 0.315921i \(0.102313\pi\)
\(48\) 0.768709 0.110954
\(49\) 1.00000 0.142857
\(50\) −30.9988 −4.38389
\(51\) −6.59485 −0.923463
\(52\) 7.02293 0.973905
\(53\) −9.51840 −1.30745 −0.653726 0.756731i \(-0.726795\pi\)
−0.653726 + 0.756731i \(0.726795\pi\)
\(54\) 10.1426 1.38023
\(55\) 6.00623 0.809880
\(56\) 3.05358 0.408052
\(57\) 7.80810 1.03421
\(58\) −13.6546 −1.79293
\(59\) −5.46939 −0.712055 −0.356027 0.934476i \(-0.615869\pi\)
−0.356027 + 0.934476i \(0.615869\pi\)
\(60\) 27.5269 3.55370
\(61\) 10.5744 1.35391 0.676957 0.736022i \(-0.263298\pi\)
0.676957 + 0.736022i \(0.263298\pi\)
\(62\) 2.30726 0.293023
\(63\) −0.721177 −0.0908598
\(64\) −12.7665 −1.59581
\(65\) 9.07303 1.12537
\(66\) −6.22607 −0.766377
\(67\) −3.91995 −0.478898 −0.239449 0.970909i \(-0.576967\pi\)
−0.239449 + 0.970909i \(0.576967\pi\)
\(68\) −11.3620 −1.37785
\(69\) −2.15993 −0.260025
\(70\) 9.90655 1.18406
\(71\) 12.1447 1.44131 0.720655 0.693294i \(-0.243841\pi\)
0.720655 + 0.693294i \(0.243841\pi\)
\(72\) −2.20218 −0.259529
\(73\) −4.81354 −0.563382 −0.281691 0.959505i \(-0.590895\pi\)
−0.281691 + 0.959505i \(0.590895\pi\)
\(74\) −2.30726 −0.268214
\(75\) 25.9172 2.99266
\(76\) 13.4523 1.54308
\(77\) −1.39887 −0.159416
\(78\) −9.40512 −1.06492
\(79\) 5.34478 0.601335 0.300667 0.953729i \(-0.402791\pi\)
0.300667 + 0.953729i \(0.402791\pi\)
\(80\) 1.71099 0.191294
\(81\) −10.6434 −1.18260
\(82\) −20.0849 −2.21801
\(83\) −14.7032 −1.61388 −0.806941 0.590632i \(-0.798879\pi\)
−0.806941 + 0.590632i \(0.798879\pi\)
\(84\) −6.41108 −0.699506
\(85\) −14.6788 −1.59214
\(86\) −0.740341 −0.0798330
\(87\) 11.4162 1.22394
\(88\) −4.27156 −0.455350
\(89\) 10.2420 1.08565 0.542824 0.839846i \(-0.317355\pi\)
0.542824 + 0.839846i \(0.317355\pi\)
\(90\) −7.14438 −0.753083
\(91\) −2.11313 −0.221517
\(92\) −3.72127 −0.387969
\(93\) −1.92904 −0.200032
\(94\) −30.0154 −3.09585
\(95\) 17.3792 1.78307
\(96\) 10.0073 1.02137
\(97\) −4.84009 −0.491437 −0.245718 0.969341i \(-0.579024\pi\)
−0.245718 + 0.969341i \(0.579024\pi\)
\(98\) −2.30726 −0.233069
\(99\) 1.00883 0.101391
\(100\) 44.6518 4.46518
\(101\) 4.56890 0.454623 0.227311 0.973822i \(-0.427007\pi\)
0.227311 + 0.973822i \(0.427007\pi\)
\(102\) 15.2160 1.50661
\(103\) 9.43035 0.929200 0.464600 0.885521i \(-0.346198\pi\)
0.464600 + 0.885521i \(0.346198\pi\)
\(104\) −6.45263 −0.632733
\(105\) −8.28257 −0.808297
\(106\) 21.9614 2.13308
\(107\) −10.5773 −1.02255 −0.511273 0.859418i \(-0.670826\pi\)
−0.511273 + 0.859418i \(0.670826\pi\)
\(108\) −14.6097 −1.40582
\(109\) −13.6464 −1.30709 −0.653545 0.756888i \(-0.726719\pi\)
−0.653545 + 0.756888i \(0.726719\pi\)
\(110\) −13.8580 −1.32130
\(111\) 1.92904 0.183096
\(112\) −0.398494 −0.0376541
\(113\) −13.9576 −1.31302 −0.656510 0.754317i \(-0.727968\pi\)
−0.656510 + 0.754317i \(0.727968\pi\)
\(114\) −18.0153 −1.68729
\(115\) −4.80756 −0.448307
\(116\) 19.6685 1.82618
\(117\) 1.52394 0.140889
\(118\) 12.6193 1.16170
\(119\) 3.41873 0.313394
\(120\) −25.2915 −2.30879
\(121\) −9.04317 −0.822106
\(122\) −24.3980 −2.20889
\(123\) 16.7924 1.51412
\(124\) −3.32347 −0.298456
\(125\) 36.2181 3.23945
\(126\) 1.66395 0.148236
\(127\) 6.70895 0.595323 0.297661 0.954671i \(-0.403793\pi\)
0.297661 + 0.954671i \(0.403793\pi\)
\(128\) 19.0801 1.68646
\(129\) 0.618977 0.0544979
\(130\) −20.9339 −1.83602
\(131\) −10.8841 −0.950945 −0.475473 0.879730i \(-0.657723\pi\)
−0.475473 + 0.879730i \(0.657723\pi\)
\(132\) 8.96826 0.780587
\(133\) −4.04767 −0.350978
\(134\) 9.04435 0.781313
\(135\) −18.8745 −1.62446
\(136\) 10.4394 0.895169
\(137\) −3.13779 −0.268079 −0.134040 0.990976i \(-0.542795\pi\)
−0.134040 + 0.990976i \(0.542795\pi\)
\(138\) 4.98353 0.424226
\(139\) −18.8869 −1.60197 −0.800984 0.598685i \(-0.795690\pi\)
−0.800984 + 0.598685i \(0.795690\pi\)
\(140\) −14.2698 −1.20601
\(141\) 25.0950 2.11338
\(142\) −28.0210 −2.35147
\(143\) 2.95600 0.247193
\(144\) 0.287385 0.0239487
\(145\) 25.4101 2.11019
\(146\) 11.1061 0.919148
\(147\) 1.92904 0.159104
\(148\) 3.32347 0.273187
\(149\) −8.28242 −0.678522 −0.339261 0.940692i \(-0.610177\pi\)
−0.339261 + 0.940692i \(0.610177\pi\)
\(150\) −59.7978 −4.88247
\(151\) 11.3167 0.920944 0.460472 0.887674i \(-0.347680\pi\)
0.460472 + 0.887674i \(0.347680\pi\)
\(152\) −12.3599 −1.00252
\(153\) −2.46551 −0.199324
\(154\) 3.22756 0.260084
\(155\) −4.29364 −0.344873
\(156\) 13.5475 1.08467
\(157\) 10.7850 0.860737 0.430369 0.902653i \(-0.358384\pi\)
0.430369 + 0.902653i \(0.358384\pi\)
\(158\) −12.3318 −0.981066
\(159\) −18.3613 −1.45615
\(160\) 22.2743 1.76094
\(161\) 1.11969 0.0882443
\(162\) 24.5572 1.92940
\(163\) 13.0588 1.02285 0.511423 0.859329i \(-0.329118\pi\)
0.511423 + 0.859329i \(0.329118\pi\)
\(164\) 28.9311 2.25914
\(165\) 11.5862 0.901987
\(166\) 33.9241 2.63302
\(167\) −18.1744 −1.40638 −0.703188 0.711004i \(-0.748241\pi\)
−0.703188 + 0.711004i \(0.748241\pi\)
\(168\) 5.89047 0.454460
\(169\) −8.53467 −0.656513
\(170\) 33.8678 2.59754
\(171\) 2.91909 0.223228
\(172\) 1.06641 0.0813133
\(173\) −14.1896 −1.07881 −0.539407 0.842045i \(-0.681352\pi\)
−0.539407 + 0.842045i \(0.681352\pi\)
\(174\) −26.3401 −1.99684
\(175\) −13.4353 −1.01561
\(176\) 0.557440 0.0420187
\(177\) −10.5507 −0.793036
\(178\) −23.6310 −1.77122
\(179\) 3.69433 0.276127 0.138063 0.990423i \(-0.455912\pi\)
0.138063 + 0.990423i \(0.455912\pi\)
\(180\) 10.2910 0.767047
\(181\) 18.8353 1.40002 0.700008 0.714135i \(-0.253180\pi\)
0.700008 + 0.714135i \(0.253180\pi\)
\(182\) 4.87556 0.361400
\(183\) 20.3984 1.50789
\(184\) 3.41908 0.252058
\(185\) 4.29364 0.315674
\(186\) 4.45079 0.326348
\(187\) −4.78235 −0.349720
\(188\) 43.2353 3.15326
\(189\) 4.39593 0.319757
\(190\) −40.0985 −2.90905
\(191\) 15.0160 1.08652 0.543259 0.839565i \(-0.317190\pi\)
0.543259 + 0.839565i \(0.317190\pi\)
\(192\) −24.6270 −1.77730
\(193\) −6.34766 −0.456915 −0.228457 0.973554i \(-0.573368\pi\)
−0.228457 + 0.973554i \(0.573368\pi\)
\(194\) 11.1674 0.801770
\(195\) 17.5022 1.25336
\(196\) 3.32347 0.237390
\(197\) −13.6553 −0.972903 −0.486451 0.873708i \(-0.661709\pi\)
−0.486451 + 0.873708i \(0.661709\pi\)
\(198\) −2.32764 −0.165418
\(199\) 21.3616 1.51429 0.757144 0.653249i \(-0.226594\pi\)
0.757144 + 0.653249i \(0.226594\pi\)
\(200\) −41.0259 −2.90097
\(201\) −7.56172 −0.533362
\(202\) −10.5417 −0.741708
\(203\) −5.91808 −0.415368
\(204\) −21.9177 −1.53455
\(205\) 37.3765 2.61049
\(206\) −21.7583 −1.51597
\(207\) −0.807498 −0.0561250
\(208\) 0.842071 0.0583871
\(209\) 5.66216 0.391660
\(210\) 19.1101 1.31872
\(211\) 22.9427 1.57944 0.789719 0.613468i \(-0.210226\pi\)
0.789719 + 0.613468i \(0.210226\pi\)
\(212\) −31.6341 −2.17264
\(213\) 23.4275 1.60523
\(214\) 24.4046 1.66827
\(215\) 1.37772 0.0939594
\(216\) 13.4233 0.913343
\(217\) 1.00000 0.0678844
\(218\) 31.4859 2.13249
\(219\) −9.28549 −0.627455
\(220\) 19.9615 1.34580
\(221\) −7.22423 −0.485954
\(222\) −4.45079 −0.298718
\(223\) 20.4344 1.36839 0.684195 0.729299i \(-0.260154\pi\)
0.684195 + 0.729299i \(0.260154\pi\)
\(224\) −5.18774 −0.346620
\(225\) 9.68924 0.645949
\(226\) 32.2039 2.14217
\(227\) 2.31200 0.153453 0.0767264 0.997052i \(-0.475553\pi\)
0.0767264 + 0.997052i \(0.475553\pi\)
\(228\) 25.9500 1.71858
\(229\) −9.09111 −0.600757 −0.300379 0.953820i \(-0.597113\pi\)
−0.300379 + 0.953820i \(0.597113\pi\)
\(230\) 11.0923 0.731405
\(231\) −2.69847 −0.177546
\(232\) −18.0714 −1.18644
\(233\) 13.5067 0.884853 0.442427 0.896805i \(-0.354118\pi\)
0.442427 + 0.896805i \(0.354118\pi\)
\(234\) −3.51614 −0.229857
\(235\) 55.8563 3.64366
\(236\) −18.1773 −1.18324
\(237\) 10.3103 0.669724
\(238\) −7.88791 −0.511297
\(239\) 29.1065 1.88274 0.941371 0.337374i \(-0.109539\pi\)
0.941371 + 0.337374i \(0.109539\pi\)
\(240\) 3.30056 0.213050
\(241\) −15.6686 −1.00930 −0.504651 0.863323i \(-0.668379\pi\)
−0.504651 + 0.863323i \(0.668379\pi\)
\(242\) 20.8650 1.34125
\(243\) −7.34377 −0.471103
\(244\) 35.1437 2.24985
\(245\) 4.29364 0.274310
\(246\) −38.7446 −2.47026
\(247\) 8.55327 0.544231
\(248\) 3.05358 0.193903
\(249\) −28.3629 −1.79743
\(250\) −83.5648 −5.28510
\(251\) 12.4767 0.787525 0.393762 0.919212i \(-0.371173\pi\)
0.393762 + 0.919212i \(0.371173\pi\)
\(252\) −2.39681 −0.150985
\(253\) −1.56630 −0.0984727
\(254\) −15.4793 −0.971259
\(255\) −28.3159 −1.77321
\(256\) −18.4900 −1.15562
\(257\) 16.1317 1.00627 0.503133 0.864209i \(-0.332181\pi\)
0.503133 + 0.864209i \(0.332181\pi\)
\(258\) −1.42814 −0.0889123
\(259\) −1.00000 −0.0621370
\(260\) 30.1539 1.87007
\(261\) 4.26798 0.264181
\(262\) 25.1124 1.55145
\(263\) 25.7837 1.58989 0.794947 0.606679i \(-0.207499\pi\)
0.794947 + 0.606679i \(0.207499\pi\)
\(264\) −8.24000 −0.507137
\(265\) −40.8685 −2.51053
\(266\) 9.33904 0.572613
\(267\) 19.7572 1.20912
\(268\) −13.0278 −0.795800
\(269\) 4.57534 0.278963 0.139482 0.990225i \(-0.455456\pi\)
0.139482 + 0.990225i \(0.455456\pi\)
\(270\) 43.5485 2.65028
\(271\) −16.2713 −0.988410 −0.494205 0.869345i \(-0.664541\pi\)
−0.494205 + 0.869345i \(0.664541\pi\)
\(272\) −1.36234 −0.0826041
\(273\) −4.07631 −0.246709
\(274\) 7.23971 0.437367
\(275\) 18.7942 1.13333
\(276\) −7.17845 −0.432092
\(277\) 11.7911 0.708457 0.354228 0.935159i \(-0.384744\pi\)
0.354228 + 0.935159i \(0.384744\pi\)
\(278\) 43.5771 2.61358
\(279\) −0.721177 −0.0431757
\(280\) 13.1110 0.783531
\(281\) −25.6654 −1.53107 −0.765536 0.643393i \(-0.777526\pi\)
−0.765536 + 0.643393i \(0.777526\pi\)
\(282\) −57.9008 −3.44794
\(283\) 29.1175 1.73086 0.865429 0.501032i \(-0.167046\pi\)
0.865429 + 0.501032i \(0.167046\pi\)
\(284\) 40.3625 2.39507
\(285\) 33.5251 1.98586
\(286\) −6.82026 −0.403291
\(287\) −8.70509 −0.513845
\(288\) 3.74128 0.220457
\(289\) −5.31230 −0.312488
\(290\) −58.6277 −3.44274
\(291\) −9.33670 −0.547327
\(292\) −15.9976 −0.936191
\(293\) −20.2013 −1.18017 −0.590087 0.807340i \(-0.700907\pi\)
−0.590087 + 0.807340i \(0.700907\pi\)
\(294\) −4.45079 −0.259576
\(295\) −23.4836 −1.36727
\(296\) −3.05358 −0.177486
\(297\) −6.14933 −0.356820
\(298\) 19.1097 1.10700
\(299\) −2.36606 −0.136833
\(300\) 86.1349 4.97300
\(301\) −0.320874 −0.0184949
\(302\) −26.1107 −1.50250
\(303\) 8.81357 0.506326
\(304\) 1.61297 0.0925103
\(305\) 45.4027 2.59975
\(306\) 5.68858 0.325194
\(307\) −16.9571 −0.967793 −0.483897 0.875125i \(-0.660779\pi\)
−0.483897 + 0.875125i \(0.660779\pi\)
\(308\) −4.64909 −0.264907
\(309\) 18.1915 1.03488
\(310\) 9.90655 0.562654
\(311\) 3.07891 0.174589 0.0872944 0.996183i \(-0.472178\pi\)
0.0872944 + 0.996183i \(0.472178\pi\)
\(312\) −12.4474 −0.704693
\(313\) −28.8113 −1.62851 −0.814256 0.580506i \(-0.802855\pi\)
−0.814256 + 0.580506i \(0.802855\pi\)
\(314\) −24.8839 −1.40428
\(315\) −3.09647 −0.174466
\(316\) 17.7632 0.999257
\(317\) 21.3359 1.19834 0.599172 0.800620i \(-0.295497\pi\)
0.599172 + 0.800620i \(0.295497\pi\)
\(318\) 42.3644 2.37568
\(319\) 8.27861 0.463513
\(320\) −54.8146 −3.06423
\(321\) −20.4040 −1.13884
\(322\) −2.58343 −0.143969
\(323\) −13.8379 −0.769960
\(324\) −35.3731 −1.96517
\(325\) 28.3906 1.57483
\(326\) −30.1302 −1.66876
\(327\) −26.3244 −1.45574
\(328\) −26.5817 −1.46773
\(329\) −13.0091 −0.717214
\(330\) −26.7325 −1.47158
\(331\) 25.8065 1.41845 0.709227 0.704980i \(-0.249044\pi\)
0.709227 + 0.704980i \(0.249044\pi\)
\(332\) −48.8655 −2.68184
\(333\) 0.721177 0.0395203
\(334\) 41.9331 2.29448
\(335\) −16.8308 −0.919566
\(336\) −0.768709 −0.0419365
\(337\) −22.7729 −1.24052 −0.620258 0.784398i \(-0.712972\pi\)
−0.620258 + 0.784398i \(0.712972\pi\)
\(338\) 19.6917 1.07109
\(339\) −26.9247 −1.46235
\(340\) −48.7844 −2.64571
\(341\) −1.39887 −0.0757530
\(342\) −6.73510 −0.364193
\(343\) −1.00000 −0.0539949
\(344\) −0.979816 −0.0528281
\(345\) −9.27395 −0.499293
\(346\) 32.7391 1.76007
\(347\) 5.08848 0.273164 0.136582 0.990629i \(-0.456388\pi\)
0.136582 + 0.990629i \(0.456388\pi\)
\(348\) 37.9413 2.03387
\(349\) 28.1154 1.50498 0.752491 0.658603i \(-0.228852\pi\)
0.752491 + 0.658603i \(0.228852\pi\)
\(350\) 30.9988 1.65696
\(351\) −9.28919 −0.495820
\(352\) 7.25696 0.386798
\(353\) 27.6746 1.47297 0.736484 0.676455i \(-0.236485\pi\)
0.736484 + 0.676455i \(0.236485\pi\)
\(354\) 24.3431 1.29382
\(355\) 52.1449 2.76756
\(356\) 34.0389 1.80406
\(357\) 6.59485 0.349036
\(358\) −8.52379 −0.450496
\(359\) −28.8774 −1.52409 −0.762045 0.647524i \(-0.775804\pi\)
−0.762045 + 0.647524i \(0.775804\pi\)
\(360\) −9.45534 −0.498340
\(361\) −2.61636 −0.137703
\(362\) −43.4580 −2.28410
\(363\) −17.4446 −0.915603
\(364\) −7.02293 −0.368101
\(365\) −20.6676 −1.08179
\(366\) −47.0645 −2.46010
\(367\) 3.08789 0.161187 0.0805933 0.996747i \(-0.474319\pi\)
0.0805933 + 0.996747i \(0.474319\pi\)
\(368\) −0.446191 −0.0232593
\(369\) 6.27791 0.326815
\(370\) −9.90655 −0.515017
\(371\) 9.51840 0.494170
\(372\) −6.41108 −0.332399
\(373\) 10.6862 0.553310 0.276655 0.960969i \(-0.410774\pi\)
0.276655 + 0.960969i \(0.410774\pi\)
\(374\) 11.0341 0.570562
\(375\) 69.8661 3.60787
\(376\) −39.7244 −2.04863
\(377\) 12.5057 0.644076
\(378\) −10.1426 −0.521677
\(379\) 14.3387 0.736528 0.368264 0.929721i \(-0.379952\pi\)
0.368264 + 0.929721i \(0.379952\pi\)
\(380\) 57.7593 2.96299
\(381\) 12.9418 0.663028
\(382\) −34.6458 −1.77263
\(383\) 7.00517 0.357947 0.178974 0.983854i \(-0.442722\pi\)
0.178974 + 0.983854i \(0.442722\pi\)
\(384\) 36.8063 1.87826
\(385\) −6.00623 −0.306106
\(386\) 14.6457 0.745448
\(387\) 0.231407 0.0117631
\(388\) −16.0859 −0.816636
\(389\) 24.4251 1.23840 0.619202 0.785232i \(-0.287456\pi\)
0.619202 + 0.785232i \(0.287456\pi\)
\(390\) −40.3822 −2.04483
\(391\) 3.82793 0.193587
\(392\) −3.05358 −0.154229
\(393\) −20.9957 −1.05910
\(394\) 31.5065 1.58727
\(395\) 22.9485 1.15467
\(396\) 3.35282 0.168485
\(397\) −17.4894 −0.877770 −0.438885 0.898543i \(-0.644627\pi\)
−0.438885 + 0.898543i \(0.644627\pi\)
\(398\) −49.2870 −2.47053
\(399\) −7.80810 −0.390894
\(400\) 5.35389 0.267694
\(401\) −10.3323 −0.515972 −0.257986 0.966149i \(-0.583059\pi\)
−0.257986 + 0.966149i \(0.583059\pi\)
\(402\) 17.4469 0.870171
\(403\) −2.11313 −0.105263
\(404\) 15.1846 0.755461
\(405\) −45.6990 −2.27080
\(406\) 13.6546 0.677665
\(407\) 1.39887 0.0693393
\(408\) 20.1379 0.996976
\(409\) −2.51580 −0.124399 −0.0621993 0.998064i \(-0.519811\pi\)
−0.0621993 + 0.998064i \(0.519811\pi\)
\(410\) −86.2374 −4.25896
\(411\) −6.05291 −0.298568
\(412\) 31.3414 1.54408
\(413\) 5.46939 0.269131
\(414\) 1.86311 0.0915669
\(415\) −63.1301 −3.09893
\(416\) 10.9624 0.537475
\(417\) −36.4336 −1.78416
\(418\) −13.0641 −0.638986
\(419\) 8.72331 0.426162 0.213081 0.977035i \(-0.431650\pi\)
0.213081 + 0.977035i \(0.431650\pi\)
\(420\) −27.5269 −1.34317
\(421\) −10.5817 −0.515721 −0.257861 0.966182i \(-0.583018\pi\)
−0.257861 + 0.966182i \(0.583018\pi\)
\(422\) −52.9348 −2.57683
\(423\) 9.38186 0.456161
\(424\) 29.0652 1.41153
\(425\) −45.9317 −2.22801
\(426\) −54.0535 −2.61890
\(427\) −10.5744 −0.511732
\(428\) −35.1533 −1.69920
\(429\) 5.70222 0.275306
\(430\) −3.17875 −0.153293
\(431\) −18.8627 −0.908583 −0.454291 0.890853i \(-0.650107\pi\)
−0.454291 + 0.890853i \(0.650107\pi\)
\(432\) −1.75175 −0.0842812
\(433\) 0.797791 0.0383394 0.0191697 0.999816i \(-0.493898\pi\)
0.0191697 + 0.999816i \(0.493898\pi\)
\(434\) −2.30726 −0.110752
\(435\) 49.0169 2.35018
\(436\) −45.3534 −2.17203
\(437\) −4.53215 −0.216802
\(438\) 21.4241 1.02368
\(439\) −34.8042 −1.66111 −0.830556 0.556935i \(-0.811977\pi\)
−0.830556 + 0.556935i \(0.811977\pi\)
\(440\) −18.3405 −0.874351
\(441\) 0.721177 0.0343418
\(442\) 16.6682 0.792825
\(443\) 17.7165 0.841737 0.420869 0.907122i \(-0.361725\pi\)
0.420869 + 0.907122i \(0.361725\pi\)
\(444\) 6.41108 0.304257
\(445\) 43.9754 2.08463
\(446\) −47.1476 −2.23250
\(447\) −15.9771 −0.755690
\(448\) 12.7665 0.603159
\(449\) 4.61766 0.217921 0.108960 0.994046i \(-0.465248\pi\)
0.108960 + 0.994046i \(0.465248\pi\)
\(450\) −22.3556 −1.05385
\(451\) 12.1773 0.573406
\(452\) −46.3876 −2.18189
\(453\) 21.8304 1.02568
\(454\) −5.33440 −0.250356
\(455\) −9.07303 −0.425350
\(456\) −23.8427 −1.11654
\(457\) −13.4884 −0.630959 −0.315479 0.948932i \(-0.602165\pi\)
−0.315479 + 0.948932i \(0.602165\pi\)
\(458\) 20.9756 0.980124
\(459\) 15.0285 0.701470
\(460\) −15.9778 −0.744967
\(461\) −11.5875 −0.539683 −0.269841 0.962905i \(-0.586971\pi\)
−0.269841 + 0.962905i \(0.586971\pi\)
\(462\) 6.22607 0.289663
\(463\) −11.7981 −0.548305 −0.274152 0.961686i \(-0.588397\pi\)
−0.274152 + 0.961686i \(0.588397\pi\)
\(464\) 2.35832 0.109482
\(465\) −8.28257 −0.384095
\(466\) −31.1635 −1.44362
\(467\) −27.9457 −1.29317 −0.646586 0.762841i \(-0.723804\pi\)
−0.646586 + 0.762841i \(0.723804\pi\)
\(468\) 5.06477 0.234119
\(469\) 3.91995 0.181006
\(470\) −128.875 −5.94457
\(471\) 20.8047 0.958628
\(472\) 16.7013 0.768738
\(473\) 0.448860 0.0206386
\(474\) −23.7885 −1.09264
\(475\) 54.3817 2.49520
\(476\) 11.3620 0.520778
\(477\) −6.86445 −0.314301
\(478\) −67.1563 −3.07166
\(479\) 22.5853 1.03195 0.515975 0.856604i \(-0.327430\pi\)
0.515975 + 0.856604i \(0.327430\pi\)
\(480\) 42.9678 1.96120
\(481\) 2.11313 0.0963506
\(482\) 36.1516 1.64666
\(483\) 2.15993 0.0982802
\(484\) −30.0547 −1.36612
\(485\) −20.7816 −0.943643
\(486\) 16.9440 0.768596
\(487\) −11.6778 −0.529172 −0.264586 0.964362i \(-0.585235\pi\)
−0.264586 + 0.964362i \(0.585235\pi\)
\(488\) −32.2899 −1.46169
\(489\) 25.1910 1.13917
\(490\) −9.90655 −0.447532
\(491\) −27.8628 −1.25743 −0.628716 0.777635i \(-0.716419\pi\)
−0.628716 + 0.777635i \(0.716419\pi\)
\(492\) 55.8091 2.51607
\(493\) −20.2323 −0.911217
\(494\) −19.7346 −0.887904
\(495\) 4.33156 0.194689
\(496\) −0.398494 −0.0178929
\(497\) −12.1447 −0.544764
\(498\) 65.4408 2.93247
\(499\) −26.8948 −1.20397 −0.601987 0.798506i \(-0.705624\pi\)
−0.601987 + 0.798506i \(0.705624\pi\)
\(500\) 120.370 5.38310
\(501\) −35.0590 −1.56632
\(502\) −28.7871 −1.28483
\(503\) −31.0710 −1.38539 −0.692693 0.721232i \(-0.743576\pi\)
−0.692693 + 0.721232i \(0.743576\pi\)
\(504\) 2.20218 0.0980927
\(505\) 19.6172 0.872954
\(506\) 3.61388 0.160656
\(507\) −16.4637 −0.731177
\(508\) 22.2970 0.989268
\(509\) −0.832404 −0.0368957 −0.0184478 0.999830i \(-0.505872\pi\)
−0.0184478 + 0.999830i \(0.505872\pi\)
\(510\) 65.3322 2.89296
\(511\) 4.81354 0.212938
\(512\) 4.50095 0.198916
\(513\) −17.7933 −0.785592
\(514\) −37.2200 −1.64170
\(515\) 40.4905 1.78422
\(516\) 2.05715 0.0905609
\(517\) 18.1980 0.800347
\(518\) 2.30726 0.101375
\(519\) −27.3722 −1.20151
\(520\) −27.7053 −1.21496
\(521\) 8.99534 0.394093 0.197047 0.980394i \(-0.436865\pi\)
0.197047 + 0.980394i \(0.436865\pi\)
\(522\) −9.84736 −0.431007
\(523\) 40.2812 1.76137 0.880686 0.473701i \(-0.157082\pi\)
0.880686 + 0.473701i \(0.157082\pi\)
\(524\) −36.1728 −1.58022
\(525\) −25.9172 −1.13112
\(526\) −59.4899 −2.59388
\(527\) 3.41873 0.148922
\(528\) 1.07532 0.0467974
\(529\) −21.7463 −0.945491
\(530\) 94.2945 4.09589
\(531\) −3.94440 −0.171172
\(532\) −13.4523 −0.583231
\(533\) 18.3950 0.796777
\(534\) −45.5850 −1.97265
\(535\) −45.4151 −1.96347
\(536\) 11.9699 0.517021
\(537\) 7.12649 0.307531
\(538\) −10.5565 −0.455123
\(539\) 1.39887 0.0602535
\(540\) −62.7288 −2.69942
\(541\) −16.0304 −0.689200 −0.344600 0.938750i \(-0.611986\pi\)
−0.344600 + 0.938750i \(0.611986\pi\)
\(542\) 37.5421 1.61257
\(543\) 36.3339 1.55924
\(544\) −17.7355 −0.760402
\(545\) −58.5927 −2.50984
\(546\) 9.40512 0.402502
\(547\) −22.0665 −0.943496 −0.471748 0.881733i \(-0.656377\pi\)
−0.471748 + 0.881733i \(0.656377\pi\)
\(548\) −10.4283 −0.445476
\(549\) 7.62602 0.325471
\(550\) −43.3632 −1.84901
\(551\) 23.9544 1.02049
\(552\) 6.59553 0.280724
\(553\) −5.34478 −0.227283
\(554\) −27.2051 −1.15583
\(555\) 8.28257 0.351576
\(556\) −62.7701 −2.66204
\(557\) 20.0965 0.851516 0.425758 0.904837i \(-0.360007\pi\)
0.425758 + 0.904837i \(0.360007\pi\)
\(558\) 1.66395 0.0704404
\(559\) 0.678049 0.0286784
\(560\) −1.71099 −0.0723024
\(561\) −9.22532 −0.389493
\(562\) 59.2169 2.49792
\(563\) 10.6001 0.446743 0.223371 0.974733i \(-0.428294\pi\)
0.223371 + 0.974733i \(0.428294\pi\)
\(564\) 83.4024 3.51187
\(565\) −59.9288 −2.52123
\(566\) −67.1818 −2.82386
\(567\) 10.6434 0.446982
\(568\) −37.0848 −1.55605
\(569\) 19.5307 0.818770 0.409385 0.912362i \(-0.365743\pi\)
0.409385 + 0.912362i \(0.365743\pi\)
\(570\) −77.3513 −3.23989
\(571\) −6.55585 −0.274354 −0.137177 0.990547i \(-0.543803\pi\)
−0.137177 + 0.990547i \(0.543803\pi\)
\(572\) 9.82415 0.410768
\(573\) 28.9663 1.21009
\(574\) 20.0849 0.838329
\(575\) −15.0434 −0.627355
\(576\) −9.20688 −0.383620
\(577\) 13.1476 0.547341 0.273670 0.961824i \(-0.411762\pi\)
0.273670 + 0.961824i \(0.411762\pi\)
\(578\) 12.2569 0.509819
\(579\) −12.2449 −0.508879
\(580\) 84.4495 3.50658
\(581\) 14.7032 0.609990
\(582\) 21.5422 0.892954
\(583\) −13.3150 −0.551450
\(584\) 14.6985 0.608230
\(585\) 6.54326 0.270530
\(586\) 46.6098 1.92543
\(587\) −11.3558 −0.468706 −0.234353 0.972152i \(-0.575297\pi\)
−0.234353 + 0.972152i \(0.575297\pi\)
\(588\) 6.41108 0.264389
\(589\) −4.04767 −0.166781
\(590\) 54.1828 2.23067
\(591\) −26.3416 −1.08355
\(592\) 0.398494 0.0163780
\(593\) 26.6770 1.09549 0.547746 0.836645i \(-0.315486\pi\)
0.547746 + 0.836645i \(0.315486\pi\)
\(594\) 14.1881 0.582146
\(595\) 14.6788 0.601771
\(596\) −27.5263 −1.12752
\(597\) 41.2074 1.68651
\(598\) 5.45913 0.223241
\(599\) 22.4145 0.915832 0.457916 0.888995i \(-0.348596\pi\)
0.457916 + 0.888995i \(0.348596\pi\)
\(600\) −79.1403 −3.23089
\(601\) −11.2532 −0.459028 −0.229514 0.973305i \(-0.573714\pi\)
−0.229514 + 0.973305i \(0.573714\pi\)
\(602\) 0.740341 0.0301740
\(603\) −2.82698 −0.115123
\(604\) 37.6108 1.53036
\(605\) −38.8281 −1.57859
\(606\) −20.3352 −0.826062
\(607\) 20.9119 0.848787 0.424393 0.905478i \(-0.360487\pi\)
0.424393 + 0.905478i \(0.360487\pi\)
\(608\) 20.9983 0.851592
\(609\) −11.4162 −0.462607
\(610\) −104.756 −4.24144
\(611\) 27.4899 1.11212
\(612\) −8.19403 −0.331224
\(613\) −43.6287 −1.76215 −0.881073 0.472980i \(-0.843178\pi\)
−0.881073 + 0.472980i \(0.843178\pi\)
\(614\) 39.1245 1.57894
\(615\) 72.1006 2.90738
\(616\) 4.27156 0.172106
\(617\) 43.6757 1.75832 0.879159 0.476529i \(-0.158105\pi\)
0.879159 + 0.476529i \(0.158105\pi\)
\(618\) −41.9725 −1.68838
\(619\) −19.3468 −0.777612 −0.388806 0.921320i \(-0.627112\pi\)
−0.388806 + 0.921320i \(0.627112\pi\)
\(620\) −14.2698 −0.573087
\(621\) 4.92210 0.197517
\(622\) −7.10385 −0.284839
\(623\) −10.2420 −0.410337
\(624\) 1.62438 0.0650274
\(625\) 88.3310 3.53324
\(626\) 66.4753 2.65689
\(627\) 10.9225 0.436203
\(628\) 35.8436 1.43032
\(629\) −3.41873 −0.136314
\(630\) 7.14438 0.284639
\(631\) 32.3599 1.28823 0.644113 0.764930i \(-0.277227\pi\)
0.644113 + 0.764930i \(0.277227\pi\)
\(632\) −16.3207 −0.649204
\(633\) 44.2572 1.75907
\(634\) −49.2276 −1.95508
\(635\) 28.8058 1.14312
\(636\) −61.0232 −2.41973
\(637\) 2.11313 0.0837254
\(638\) −19.1009 −0.756214
\(639\) 8.75847 0.346480
\(640\) 81.9232 3.23830
\(641\) 19.6092 0.774516 0.387258 0.921971i \(-0.373422\pi\)
0.387258 + 0.921971i \(0.373422\pi\)
\(642\) 47.0774 1.85800
\(643\) −41.0425 −1.61856 −0.809280 0.587423i \(-0.800142\pi\)
−0.809280 + 0.587423i \(0.800142\pi\)
\(644\) 3.72127 0.146638
\(645\) 2.65766 0.104645
\(646\) 31.9276 1.25618
\(647\) −18.9003 −0.743048 −0.371524 0.928423i \(-0.621165\pi\)
−0.371524 + 0.928423i \(0.621165\pi\)
\(648\) 32.5006 1.27675
\(649\) −7.65096 −0.300327
\(650\) −65.5046 −2.56930
\(651\) 1.92904 0.0756049
\(652\) 43.4006 1.69970
\(653\) 30.5677 1.19621 0.598104 0.801419i \(-0.295921\pi\)
0.598104 + 0.801419i \(0.295921\pi\)
\(654\) 60.7374 2.37502
\(655\) −46.7322 −1.82598
\(656\) 3.46893 0.135439
\(657\) −3.47141 −0.135433
\(658\) 30.0154 1.17012
\(659\) 4.80866 0.187319 0.0936594 0.995604i \(-0.470144\pi\)
0.0936594 + 0.995604i \(0.470144\pi\)
\(660\) 38.5064 1.49886
\(661\) 8.83833 0.343771 0.171886 0.985117i \(-0.445014\pi\)
0.171886 + 0.985117i \(0.445014\pi\)
\(662\) −59.5424 −2.31418
\(663\) −13.9358 −0.541221
\(664\) 44.8974 1.74236
\(665\) −17.3792 −0.673937
\(666\) −1.66395 −0.0644766
\(667\) −6.62644 −0.256577
\(668\) −60.4019 −2.33702
\(669\) 39.4187 1.52402
\(670\) 38.8332 1.50026
\(671\) 14.7922 0.571047
\(672\) −10.0073 −0.386041
\(673\) −37.0177 −1.42693 −0.713464 0.700691i \(-0.752875\pi\)
−0.713464 + 0.700691i \(0.752875\pi\)
\(674\) 52.5430 2.02388
\(675\) −59.0607 −2.27325
\(676\) −28.3647 −1.09095
\(677\) −23.6474 −0.908844 −0.454422 0.890786i \(-0.650154\pi\)
−0.454422 + 0.890786i \(0.650154\pi\)
\(678\) 62.1224 2.38580
\(679\) 4.84009 0.185746
\(680\) 44.8229 1.71888
\(681\) 4.45993 0.170905
\(682\) 3.22756 0.123590
\(683\) 20.2113 0.773363 0.386682 0.922213i \(-0.373621\pi\)
0.386682 + 0.922213i \(0.373621\pi\)
\(684\) 9.70149 0.370946
\(685\) −13.4725 −0.514759
\(686\) 2.30726 0.0880917
\(687\) −17.5371 −0.669081
\(688\) 0.127866 0.00487486
\(689\) −20.1136 −0.766269
\(690\) 21.3975 0.814587
\(691\) 7.57622 0.288213 0.144106 0.989562i \(-0.453969\pi\)
0.144106 + 0.989562i \(0.453969\pi\)
\(692\) −47.1586 −1.79270
\(693\) −1.00883 −0.0383223
\(694\) −11.7405 −0.445662
\(695\) −81.0936 −3.07606
\(696\) −34.8603 −1.32138
\(697\) −29.7603 −1.12725
\(698\) −64.8696 −2.45535
\(699\) 26.0549 0.985487
\(700\) −44.6518 −1.68768
\(701\) 8.33491 0.314805 0.157403 0.987535i \(-0.449688\pi\)
0.157403 + 0.987535i \(0.449688\pi\)
\(702\) 21.4326 0.808922
\(703\) 4.04767 0.152661
\(704\) −17.8586 −0.673072
\(705\) 107.749 4.05805
\(706\) −63.8525 −2.40312
\(707\) −4.56890 −0.171831
\(708\) −35.0647 −1.31781
\(709\) −17.8952 −0.672068 −0.336034 0.941850i \(-0.609086\pi\)
−0.336034 + 0.941850i \(0.609086\pi\)
\(710\) −120.312 −4.51523
\(711\) 3.85453 0.144556
\(712\) −31.2748 −1.17207
\(713\) 1.11969 0.0419329
\(714\) −15.2160 −0.569446
\(715\) 12.6920 0.474653
\(716\) 12.2780 0.458849
\(717\) 56.1474 2.09686
\(718\) 66.6277 2.48652
\(719\) 17.4259 0.649876 0.324938 0.945735i \(-0.394657\pi\)
0.324938 + 0.945735i \(0.394657\pi\)
\(720\) 1.23392 0.0459857
\(721\) −9.43035 −0.351204
\(722\) 6.03664 0.224660
\(723\) −30.2253 −1.12409
\(724\) 62.5984 2.32645
\(725\) 79.5112 2.95297
\(726\) 40.2493 1.49379
\(727\) −38.7381 −1.43672 −0.718359 0.695673i \(-0.755106\pi\)
−0.718359 + 0.695673i \(0.755106\pi\)
\(728\) 6.45263 0.239151
\(729\) 17.7639 0.657923
\(730\) 47.6856 1.76492
\(731\) −1.09698 −0.0405733
\(732\) 67.7934 2.50572
\(733\) 17.4379 0.644085 0.322042 0.946725i \(-0.395631\pi\)
0.322042 + 0.946725i \(0.395631\pi\)
\(734\) −7.12458 −0.262973
\(735\) 8.28257 0.305507
\(736\) −5.80868 −0.214111
\(737\) −5.48349 −0.201987
\(738\) −14.4848 −0.533193
\(739\) −18.6831 −0.687269 −0.343635 0.939103i \(-0.611658\pi\)
−0.343635 + 0.939103i \(0.611658\pi\)
\(740\) 14.2698 0.524567
\(741\) 16.4996 0.606126
\(742\) −21.9614 −0.806230
\(743\) 33.5624 1.23128 0.615642 0.788026i \(-0.288897\pi\)
0.615642 + 0.788026i \(0.288897\pi\)
\(744\) 5.89047 0.215955
\(745\) −35.5617 −1.30288
\(746\) −24.6558 −0.902715
\(747\) −10.6036 −0.387965
\(748\) −15.8940 −0.581141
\(749\) 10.5773 0.386486
\(750\) −161.199 −5.88617
\(751\) 19.5412 0.713068 0.356534 0.934282i \(-0.383958\pi\)
0.356534 + 0.934282i \(0.383958\pi\)
\(752\) 5.18404 0.189043
\(753\) 24.0681 0.877089
\(754\) −28.8539 −1.05080
\(755\) 48.5900 1.76837
\(756\) 14.6097 0.531350
\(757\) −38.0217 −1.38192 −0.690961 0.722892i \(-0.742812\pi\)
−0.690961 + 0.722892i \(0.742812\pi\)
\(758\) −33.0831 −1.20163
\(759\) −3.02146 −0.109672
\(760\) −53.0689 −1.92501
\(761\) −11.9877 −0.434554 −0.217277 0.976110i \(-0.569717\pi\)
−0.217277 + 0.976110i \(0.569717\pi\)
\(762\) −29.8601 −1.08172
\(763\) 13.6464 0.494033
\(764\) 49.9051 1.80550
\(765\) −10.5860 −0.382737
\(766\) −16.1628 −0.583985
\(767\) −11.5576 −0.417319
\(768\) −35.6678 −1.28705
\(769\) 43.5976 1.57217 0.786084 0.618119i \(-0.212105\pi\)
0.786084 + 0.618119i \(0.212105\pi\)
\(770\) 13.8580 0.499406
\(771\) 31.1186 1.12071
\(772\) −21.0962 −0.759270
\(773\) −0.776548 −0.0279305 −0.0139652 0.999902i \(-0.504445\pi\)
−0.0139652 + 0.999902i \(0.504445\pi\)
\(774\) −0.533917 −0.0191912
\(775\) −13.4353 −0.482611
\(776\) 14.7796 0.530558
\(777\) −1.92904 −0.0692038
\(778\) −56.3552 −2.02043
\(779\) 35.2353 1.26244
\(780\) 58.1679 2.08275
\(781\) 16.9888 0.607908
\(782\) −8.83204 −0.315833
\(783\) −26.0155 −0.929717
\(784\) 0.398494 0.0142319
\(785\) 46.3069 1.65276
\(786\) 48.4427 1.72789
\(787\) 3.58891 0.127931 0.0639653 0.997952i \(-0.479625\pi\)
0.0639653 + 0.997952i \(0.479625\pi\)
\(788\) −45.3831 −1.61670
\(789\) 49.7377 1.77071
\(790\) −52.9483 −1.88382
\(791\) 13.9576 0.496275
\(792\) −3.08055 −0.109463
\(793\) 22.3451 0.793500
\(794\) 40.3528 1.43207
\(795\) −78.8368 −2.79605
\(796\) 70.9947 2.51634
\(797\) 35.3104 1.25076 0.625380 0.780321i \(-0.284944\pi\)
0.625380 + 0.780321i \(0.284944\pi\)
\(798\) 18.0153 0.637736
\(799\) −44.4745 −1.57340
\(800\) 69.6989 2.46423
\(801\) 7.38629 0.260982
\(802\) 23.8394 0.841799
\(803\) −6.73351 −0.237620
\(804\) −25.1311 −0.886306
\(805\) 4.80756 0.169444
\(806\) 4.87556 0.171734
\(807\) 8.82599 0.310689
\(808\) −13.9515 −0.490813
\(809\) −10.5463 −0.370787 −0.185394 0.982664i \(-0.559356\pi\)
−0.185394 + 0.982664i \(0.559356\pi\)
\(810\) 105.440 3.70477
\(811\) −10.1111 −0.355047 −0.177524 0.984117i \(-0.556809\pi\)
−0.177524 + 0.984117i \(0.556809\pi\)
\(812\) −19.6685 −0.690230
\(813\) −31.3879 −1.10082
\(814\) −3.22756 −0.113126
\(815\) 56.0699 1.96404
\(816\) −2.62801 −0.0919986
\(817\) 1.29879 0.0454390
\(818\) 5.80462 0.202954
\(819\) −1.52394 −0.0532509
\(820\) 124.220 4.33793
\(821\) 12.1586 0.424336 0.212168 0.977233i \(-0.431948\pi\)
0.212168 + 0.977233i \(0.431948\pi\)
\(822\) 13.9656 0.487108
\(823\) 2.18408 0.0761321 0.0380661 0.999275i \(-0.487880\pi\)
0.0380661 + 0.999275i \(0.487880\pi\)
\(824\) −28.7964 −1.00317
\(825\) 36.2547 1.26223
\(826\) −12.6193 −0.439083
\(827\) −3.49929 −0.121682 −0.0608411 0.998147i \(-0.519378\pi\)
−0.0608411 + 0.998147i \(0.519378\pi\)
\(828\) −2.68369 −0.0932647
\(829\) −18.6725 −0.648522 −0.324261 0.945968i \(-0.605116\pi\)
−0.324261 + 0.945968i \(0.605116\pi\)
\(830\) 145.658 5.05585
\(831\) 22.7454 0.789029
\(832\) −26.9773 −0.935268
\(833\) −3.41873 −0.118452
\(834\) 84.0618 2.91082
\(835\) −78.0342 −2.70048
\(836\) 18.8180 0.650834
\(837\) 4.39593 0.151946
\(838\) −20.1270 −0.695275
\(839\) 39.2784 1.35604 0.678020 0.735043i \(-0.262838\pi\)
0.678020 + 0.735043i \(0.262838\pi\)
\(840\) 25.2915 0.872641
\(841\) 6.02365 0.207712
\(842\) 24.4148 0.841390
\(843\) −49.5095 −1.70520
\(844\) 76.2492 2.62461
\(845\) −36.6447 −1.26062
\(846\) −21.6464 −0.744219
\(847\) 9.04317 0.310727
\(848\) −3.79302 −0.130253
\(849\) 56.1687 1.92771
\(850\) 105.976 3.63496
\(851\) −1.11969 −0.0383826
\(852\) 77.8606 2.66746
\(853\) −18.5575 −0.635398 −0.317699 0.948192i \(-0.602910\pi\)
−0.317699 + 0.948192i \(0.602910\pi\)
\(854\) 24.3980 0.834881
\(855\) 12.5335 0.428637
\(856\) 32.2987 1.10395
\(857\) 43.7033 1.49288 0.746438 0.665454i \(-0.231762\pi\)
0.746438 + 0.665454i \(0.231762\pi\)
\(858\) −13.1565 −0.449156
\(859\) −17.7615 −0.606014 −0.303007 0.952988i \(-0.597991\pi\)
−0.303007 + 0.952988i \(0.597991\pi\)
\(860\) 4.57879 0.156135
\(861\) −16.7924 −0.572284
\(862\) 43.5211 1.48234
\(863\) 6.20644 0.211270 0.105635 0.994405i \(-0.466313\pi\)
0.105635 + 0.994405i \(0.466313\pi\)
\(864\) −22.8049 −0.775840
\(865\) −60.9249 −2.07151
\(866\) −1.84071 −0.0625500
\(867\) −10.2476 −0.348027
\(868\) 3.32347 0.112806
\(869\) 7.47664 0.253628
\(870\) −113.095 −3.83428
\(871\) −8.28337 −0.280671
\(872\) 41.6705 1.41114
\(873\) −3.49056 −0.118138
\(874\) 10.4569 0.353709
\(875\) −36.2181 −1.22440
\(876\) −30.8600 −1.04266
\(877\) 35.6868 1.20506 0.602528 0.798098i \(-0.294160\pi\)
0.602528 + 0.798098i \(0.294160\pi\)
\(878\) 80.3024 2.71008
\(879\) −38.9691 −1.31439
\(880\) 2.39345 0.0806831
\(881\) 39.6969 1.33742 0.668711 0.743522i \(-0.266846\pi\)
0.668711 + 0.743522i \(0.266846\pi\)
\(882\) −1.66395 −0.0560280
\(883\) −50.1279 −1.68694 −0.843470 0.537176i \(-0.819491\pi\)
−0.843470 + 0.537176i \(0.819491\pi\)
\(884\) −24.0095 −0.807526
\(885\) −45.3007 −1.52277
\(886\) −40.8767 −1.37328
\(887\) −25.2144 −0.846617 −0.423309 0.905986i \(-0.639131\pi\)
−0.423309 + 0.905986i \(0.639131\pi\)
\(888\) −5.89047 −0.197671
\(889\) −6.70895 −0.225011
\(890\) −101.463 −3.40104
\(891\) −14.8888 −0.498792
\(892\) 67.9131 2.27390
\(893\) 52.6565 1.76208
\(894\) 36.8633 1.23289
\(895\) 15.8621 0.530211
\(896\) −19.0801 −0.637423
\(897\) −4.56422 −0.152395
\(898\) −10.6542 −0.355534
\(899\) −5.91808 −0.197379
\(900\) 32.2018 1.07339
\(901\) 32.5408 1.08409
\(902\) −28.0962 −0.935501
\(903\) −0.618977 −0.0205983
\(904\) 42.6207 1.41754
\(905\) 80.8719 2.68827
\(906\) −50.3685 −1.67338
\(907\) −37.6951 −1.25165 −0.625823 0.779965i \(-0.715237\pi\)
−0.625823 + 0.779965i \(0.715237\pi\)
\(908\) 7.68386 0.254998
\(909\) 3.29499 0.109288
\(910\) 20.9339 0.693951
\(911\) −32.0233 −1.06098 −0.530490 0.847691i \(-0.677992\pi\)
−0.530490 + 0.847691i \(0.677992\pi\)
\(912\) 3.11148 0.103031
\(913\) −20.5678 −0.680695
\(914\) 31.1212 1.02940
\(915\) 87.5834 2.89542
\(916\) −30.2140 −0.998298
\(917\) 10.8841 0.359424
\(918\) −34.6747 −1.14444
\(919\) 30.2631 0.998288 0.499144 0.866519i \(-0.333648\pi\)
0.499144 + 0.866519i \(0.333648\pi\)
\(920\) 14.6803 0.483995
\(921\) −32.7109 −1.07786
\(922\) 26.7354 0.880482
\(923\) 25.6634 0.844720
\(924\) −8.96826 −0.295034
\(925\) 13.4353 0.441750
\(926\) 27.2214 0.894549
\(927\) 6.80095 0.223372
\(928\) 30.7014 1.00782
\(929\) −20.5867 −0.675428 −0.337714 0.941249i \(-0.609654\pi\)
−0.337714 + 0.941249i \(0.609654\pi\)
\(930\) 19.1101 0.626644
\(931\) 4.04767 0.132657
\(932\) 44.8891 1.47039
\(933\) 5.93932 0.194445
\(934\) 64.4780 2.10979
\(935\) −20.5337 −0.671523
\(936\) −4.65349 −0.152104
\(937\) 28.6268 0.935196 0.467598 0.883941i \(-0.345120\pi\)
0.467598 + 0.883941i \(0.345120\pi\)
\(938\) −9.04435 −0.295309
\(939\) −55.5780 −1.81372
\(940\) 185.637 6.05480
\(941\) −52.4613 −1.71019 −0.855094 0.518472i \(-0.826501\pi\)
−0.855094 + 0.518472i \(0.826501\pi\)
\(942\) −48.0018 −1.56398
\(943\) −9.74704 −0.317407
\(944\) −2.17952 −0.0709373
\(945\) 18.8745 0.613988
\(946\) −1.03564 −0.0336715
\(947\) 23.3437 0.758568 0.379284 0.925280i \(-0.376170\pi\)
0.379284 + 0.925280i \(0.376170\pi\)
\(948\) 34.2658 1.11290
\(949\) −10.1717 −0.330186
\(950\) −125.473 −4.07088
\(951\) 41.1577 1.33463
\(952\) −10.4394 −0.338342
\(953\) −7.61229 −0.246586 −0.123293 0.992370i \(-0.539346\pi\)
−0.123293 + 0.992370i \(0.539346\pi\)
\(954\) 15.8381 0.512777
\(955\) 64.4731 2.08630
\(956\) 96.7344 3.12861
\(957\) 15.9697 0.516228
\(958\) −52.1103 −1.68361
\(959\) 3.13779 0.101324
\(960\) −105.739 −3.41272
\(961\) 1.00000 0.0322581
\(962\) −4.87556 −0.157194
\(963\) −7.62811 −0.245812
\(964\) −52.0740 −1.67719
\(965\) −27.2545 −0.877355
\(966\) −4.98353 −0.160342
\(967\) −0.0585208 −0.00188190 −0.000940952 1.00000i \(-0.500300\pi\)
−0.000940952 1.00000i \(0.500300\pi\)
\(968\) 27.6141 0.887550
\(969\) −26.6938 −0.857527
\(970\) 47.9486 1.53954
\(971\) −27.4773 −0.881788 −0.440894 0.897559i \(-0.645338\pi\)
−0.440894 + 0.897559i \(0.645338\pi\)
\(972\) −24.4068 −0.782848
\(973\) 18.8869 0.605487
\(974\) 26.9438 0.863335
\(975\) 54.7665 1.75393
\(976\) 4.21384 0.134882
\(977\) −21.7156 −0.694745 −0.347372 0.937727i \(-0.612926\pi\)
−0.347372 + 0.937727i \(0.612926\pi\)
\(978\) −58.1222 −1.85854
\(979\) 14.3272 0.457899
\(980\) 14.2698 0.455831
\(981\) −9.84148 −0.314214
\(982\) 64.2869 2.05148
\(983\) −19.0261 −0.606840 −0.303420 0.952857i \(-0.598128\pi\)
−0.303420 + 0.952857i \(0.598128\pi\)
\(984\) −51.2771 −1.63465
\(985\) −58.6311 −1.86814
\(986\) 46.6812 1.48663
\(987\) −25.0950 −0.798783
\(988\) 28.4265 0.904367
\(989\) −0.359281 −0.0114245
\(990\) −9.99404 −0.317631
\(991\) −41.1695 −1.30779 −0.653896 0.756585i \(-0.726867\pi\)
−0.653896 + 0.756585i \(0.726867\pi\)
\(992\) −5.18774 −0.164711
\(993\) 49.7816 1.57977
\(994\) 28.0210 0.888772
\(995\) 91.7191 2.90769
\(996\) −94.2633 −2.98685
\(997\) −37.6059 −1.19099 −0.595496 0.803359i \(-0.703044\pi\)
−0.595496 + 0.803359i \(0.703044\pi\)
\(998\) 62.0533 1.96426
\(999\) −4.39593 −0.139081
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 8029.2.a.h.1.8 71
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8029.2.a.h.1.8 71 1.1 even 1 trivial