Properties

Label 8015.2.a.o.1.7
Level $8015$
Weight $2$
Character 8015.1
Self dual yes
Analytic conductor $64.000$
Analytic rank $0$
Dimension $73$
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] = [8015,2,Mod(1,8015)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8015, 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("8015.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8015 = 5 \cdot 7 \cdot 229 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8015.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: \(64.0000972201\)
Analytic rank: \(0\)
Dimension: \(73\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) \(=\) 8015.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.45327 q^{2} +3.30020 q^{3} +4.01854 q^{4} +1.00000 q^{5} -8.09629 q^{6} +1.00000 q^{7} -4.95203 q^{8} +7.89132 q^{9} +O(q^{10})\) \(q-2.45327 q^{2} +3.30020 q^{3} +4.01854 q^{4} +1.00000 q^{5} -8.09629 q^{6} +1.00000 q^{7} -4.95203 q^{8} +7.89132 q^{9} -2.45327 q^{10} +4.61648 q^{11} +13.2620 q^{12} +4.15190 q^{13} -2.45327 q^{14} +3.30020 q^{15} +4.11160 q^{16} -4.49719 q^{17} -19.3595 q^{18} +1.21864 q^{19} +4.01854 q^{20} +3.30020 q^{21} -11.3255 q^{22} +5.38266 q^{23} -16.3427 q^{24} +1.00000 q^{25} -10.1857 q^{26} +16.1423 q^{27} +4.01854 q^{28} -7.49271 q^{29} -8.09629 q^{30} +1.81401 q^{31} -0.182804 q^{32} +15.2353 q^{33} +11.0328 q^{34} +1.00000 q^{35} +31.7116 q^{36} +2.04212 q^{37} -2.98966 q^{38} +13.7021 q^{39} -4.95203 q^{40} -12.0969 q^{41} -8.09629 q^{42} -3.37469 q^{43} +18.5515 q^{44} +7.89132 q^{45} -13.2051 q^{46} -1.81914 q^{47} +13.5691 q^{48} +1.00000 q^{49} -2.45327 q^{50} -14.8416 q^{51} +16.6846 q^{52} +1.43972 q^{53} -39.6015 q^{54} +4.61648 q^{55} -4.95203 q^{56} +4.02176 q^{57} +18.3817 q^{58} -13.3062 q^{59} +13.2620 q^{60} +11.6444 q^{61} -4.45025 q^{62} +7.89132 q^{63} -7.77473 q^{64} +4.15190 q^{65} -37.3763 q^{66} -13.1845 q^{67} -18.0722 q^{68} +17.7638 q^{69} -2.45327 q^{70} +16.7367 q^{71} -39.0781 q^{72} +7.06439 q^{73} -5.00988 q^{74} +3.30020 q^{75} +4.89716 q^{76} +4.61648 q^{77} -33.6150 q^{78} +6.79534 q^{79} +4.11160 q^{80} +29.5989 q^{81} +29.6770 q^{82} +10.3347 q^{83} +13.2620 q^{84} -4.49719 q^{85} +8.27903 q^{86} -24.7274 q^{87} -22.8610 q^{88} +13.0073 q^{89} -19.3595 q^{90} +4.15190 q^{91} +21.6304 q^{92} +5.98658 q^{93} +4.46284 q^{94} +1.21864 q^{95} -0.603289 q^{96} -9.66911 q^{97} -2.45327 q^{98} +36.4301 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 73 q + 7 q^{2} + 14 q^{3} + 95 q^{4} + 73 q^{5} - q^{6} + 73 q^{7} + 18 q^{8} + 111 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 73 q + 7 q^{2} + 14 q^{3} + 95 q^{4} + 73 q^{5} - q^{6} + 73 q^{7} + 18 q^{8} + 111 q^{9} + 7 q^{10} + 27 q^{11} + 21 q^{12} + 21 q^{13} + 7 q^{14} + 14 q^{15} + 135 q^{16} + 23 q^{17} + 41 q^{18} + 26 q^{19} + 95 q^{20} + 14 q^{21} + 48 q^{22} + 16 q^{23} - q^{24} + 73 q^{25} + 7 q^{26} + 44 q^{27} + 95 q^{28} + 66 q^{29} - q^{30} + 23 q^{31} + 3 q^{32} + 77 q^{33} + 29 q^{34} + 73 q^{35} + 142 q^{36} + 66 q^{37} - 12 q^{38} + 53 q^{39} + 18 q^{40} + 50 q^{41} - q^{42} + 43 q^{43} + 37 q^{44} + 111 q^{45} + 65 q^{46} + 28 q^{47} - 20 q^{48} + 73 q^{49} + 7 q^{50} + 71 q^{51} + 29 q^{52} - 7 q^{53} - 16 q^{54} + 27 q^{55} + 18 q^{56} + 33 q^{57} + 48 q^{58} + 16 q^{59} + 21 q^{60} + 42 q^{61} - 3 q^{62} + 111 q^{63} + 216 q^{64} + 21 q^{65} - 53 q^{66} + 48 q^{67} + 13 q^{68} + 73 q^{69} + 7 q^{70} + 68 q^{71} + 18 q^{72} + 65 q^{73} + 4 q^{74} + 14 q^{75} + 37 q^{76} + 27 q^{77} + 60 q^{78} + 116 q^{79} + 135 q^{80} + 177 q^{81} + 20 q^{82} + 40 q^{83} + 21 q^{84} + 23 q^{85} + 35 q^{86} - 14 q^{87} + 47 q^{88} + 59 q^{89} + 41 q^{90} + 21 q^{91} + 3 q^{92} + 37 q^{93} - 11 q^{94} + 26 q^{95} - 23 q^{96} + 70 q^{97} + 7 q^{98} + 49 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.45327 −1.73473 −0.867363 0.497677i \(-0.834187\pi\)
−0.867363 + 0.497677i \(0.834187\pi\)
\(3\) 3.30020 1.90537 0.952686 0.303958i \(-0.0983081\pi\)
0.952686 + 0.303958i \(0.0983081\pi\)
\(4\) 4.01854 2.00927
\(5\) 1.00000 0.447214
\(6\) −8.09629 −3.30530
\(7\) 1.00000 0.377964
\(8\) −4.95203 −1.75081
\(9\) 7.89132 2.63044
\(10\) −2.45327 −0.775793
\(11\) 4.61648 1.39192 0.695960 0.718080i \(-0.254979\pi\)
0.695960 + 0.718080i \(0.254979\pi\)
\(12\) 13.2620 3.82841
\(13\) 4.15190 1.15153 0.575766 0.817615i \(-0.304704\pi\)
0.575766 + 0.817615i \(0.304704\pi\)
\(14\) −2.45327 −0.655664
\(15\) 3.30020 0.852108
\(16\) 4.11160 1.02790
\(17\) −4.49719 −1.09073 −0.545365 0.838199i \(-0.683609\pi\)
−0.545365 + 0.838199i \(0.683609\pi\)
\(18\) −19.3595 −4.56309
\(19\) 1.21864 0.279575 0.139788 0.990181i \(-0.455358\pi\)
0.139788 + 0.990181i \(0.455358\pi\)
\(20\) 4.01854 0.898573
\(21\) 3.30020 0.720163
\(22\) −11.3255 −2.41460
\(23\) 5.38266 1.12236 0.561181 0.827693i \(-0.310347\pi\)
0.561181 + 0.827693i \(0.310347\pi\)
\(24\) −16.3427 −3.33594
\(25\) 1.00000 0.200000
\(26\) −10.1857 −1.99759
\(27\) 16.1423 3.10659
\(28\) 4.01854 0.759433
\(29\) −7.49271 −1.39136 −0.695681 0.718351i \(-0.744897\pi\)
−0.695681 + 0.718351i \(0.744897\pi\)
\(30\) −8.09629 −1.47817
\(31\) 1.81401 0.325805 0.162902 0.986642i \(-0.447914\pi\)
0.162902 + 0.986642i \(0.447914\pi\)
\(32\) −0.182804 −0.0323154
\(33\) 15.2353 2.65213
\(34\) 11.0328 1.89212
\(35\) 1.00000 0.169031
\(36\) 31.7116 5.28527
\(37\) 2.04212 0.335723 0.167861 0.985811i \(-0.446314\pi\)
0.167861 + 0.985811i \(0.446314\pi\)
\(38\) −2.98966 −0.484987
\(39\) 13.7021 2.19409
\(40\) −4.95203 −0.782985
\(41\) −12.0969 −1.88922 −0.944611 0.328193i \(-0.893560\pi\)
−0.944611 + 0.328193i \(0.893560\pi\)
\(42\) −8.09629 −1.24928
\(43\) −3.37469 −0.514635 −0.257318 0.966327i \(-0.582839\pi\)
−0.257318 + 0.966327i \(0.582839\pi\)
\(44\) 18.5515 2.79675
\(45\) 7.89132 1.17637
\(46\) −13.2051 −1.94699
\(47\) −1.81914 −0.265349 −0.132674 0.991160i \(-0.542356\pi\)
−0.132674 + 0.991160i \(0.542356\pi\)
\(48\) 13.5691 1.95853
\(49\) 1.00000 0.142857
\(50\) −2.45327 −0.346945
\(51\) −14.8416 −2.07825
\(52\) 16.6846 2.31374
\(53\) 1.43972 0.197761 0.0988805 0.995099i \(-0.468474\pi\)
0.0988805 + 0.995099i \(0.468474\pi\)
\(54\) −39.6015 −5.38908
\(55\) 4.61648 0.622486
\(56\) −4.95203 −0.661743
\(57\) 4.02176 0.532695
\(58\) 18.3817 2.41363
\(59\) −13.3062 −1.73233 −0.866163 0.499761i \(-0.833421\pi\)
−0.866163 + 0.499761i \(0.833421\pi\)
\(60\) 13.2620 1.71212
\(61\) 11.6444 1.49091 0.745455 0.666555i \(-0.232232\pi\)
0.745455 + 0.666555i \(0.232232\pi\)
\(62\) −4.45025 −0.565182
\(63\) 7.89132 0.994213
\(64\) −7.77473 −0.971841
\(65\) 4.15190 0.514980
\(66\) −37.3763 −4.60071
\(67\) −13.1845 −1.61075 −0.805374 0.592767i \(-0.798035\pi\)
−0.805374 + 0.592767i \(0.798035\pi\)
\(68\) −18.0722 −2.19157
\(69\) 17.7638 2.13851
\(70\) −2.45327 −0.293222
\(71\) 16.7367 1.98628 0.993142 0.116912i \(-0.0372995\pi\)
0.993142 + 0.116912i \(0.0372995\pi\)
\(72\) −39.0781 −4.60539
\(73\) 7.06439 0.826824 0.413412 0.910544i \(-0.364337\pi\)
0.413412 + 0.910544i \(0.364337\pi\)
\(74\) −5.00988 −0.582387
\(75\) 3.30020 0.381074
\(76\) 4.89716 0.561743
\(77\) 4.61648 0.526097
\(78\) −33.6150 −3.80615
\(79\) 6.79534 0.764536 0.382268 0.924052i \(-0.375143\pi\)
0.382268 + 0.924052i \(0.375143\pi\)
\(80\) 4.11160 0.459691
\(81\) 29.5989 3.28877
\(82\) 29.6770 3.27728
\(83\) 10.3347 1.13438 0.567191 0.823586i \(-0.308030\pi\)
0.567191 + 0.823586i \(0.308030\pi\)
\(84\) 13.2620 1.44700
\(85\) −4.49719 −0.487789
\(86\) 8.27903 0.892750
\(87\) −24.7274 −2.65106
\(88\) −22.8610 −2.43699
\(89\) 13.0073 1.37877 0.689384 0.724396i \(-0.257881\pi\)
0.689384 + 0.724396i \(0.257881\pi\)
\(90\) −19.3595 −2.04068
\(91\) 4.15190 0.435238
\(92\) 21.6304 2.25513
\(93\) 5.98658 0.620779
\(94\) 4.46284 0.460307
\(95\) 1.21864 0.125030
\(96\) −0.603289 −0.0615729
\(97\) −9.66911 −0.981749 −0.490875 0.871230i \(-0.663323\pi\)
−0.490875 + 0.871230i \(0.663323\pi\)
\(98\) −2.45327 −0.247818
\(99\) 36.4301 3.66136
\(100\) 4.01854 0.401854
\(101\) −5.59560 −0.556783 −0.278392 0.960468i \(-0.589801\pi\)
−0.278392 + 0.960468i \(0.589801\pi\)
\(102\) 36.4106 3.60518
\(103\) 1.33116 0.131163 0.0655815 0.997847i \(-0.479110\pi\)
0.0655815 + 0.997847i \(0.479110\pi\)
\(104\) −20.5604 −2.01611
\(105\) 3.30020 0.322067
\(106\) −3.53203 −0.343061
\(107\) −0.787195 −0.0761010 −0.0380505 0.999276i \(-0.512115\pi\)
−0.0380505 + 0.999276i \(0.512115\pi\)
\(108\) 64.8686 6.24199
\(109\) 6.36750 0.609895 0.304948 0.952369i \(-0.401361\pi\)
0.304948 + 0.952369i \(0.401361\pi\)
\(110\) −11.3255 −1.07984
\(111\) 6.73941 0.639676
\(112\) 4.11160 0.388510
\(113\) 8.04862 0.757151 0.378575 0.925571i \(-0.376414\pi\)
0.378575 + 0.925571i \(0.376414\pi\)
\(114\) −9.86647 −0.924080
\(115\) 5.38266 0.501935
\(116\) −30.1098 −2.79562
\(117\) 32.7640 3.02903
\(118\) 32.6438 3.00511
\(119\) −4.49719 −0.412257
\(120\) −16.3427 −1.49188
\(121\) 10.3119 0.937443
\(122\) −28.5668 −2.58632
\(123\) −39.9223 −3.59967
\(124\) 7.28966 0.654630
\(125\) 1.00000 0.0894427
\(126\) −19.3595 −1.72469
\(127\) −10.7748 −0.956106 −0.478053 0.878331i \(-0.658657\pi\)
−0.478053 + 0.878331i \(0.658657\pi\)
\(128\) 19.4391 1.71819
\(129\) −11.1371 −0.980571
\(130\) −10.1857 −0.893349
\(131\) −13.3552 −1.16685 −0.583424 0.812168i \(-0.698287\pi\)
−0.583424 + 0.812168i \(0.698287\pi\)
\(132\) 61.2237 5.32884
\(133\) 1.21864 0.105670
\(134\) 32.3452 2.79420
\(135\) 16.1423 1.38931
\(136\) 22.2703 1.90966
\(137\) −18.4109 −1.57295 −0.786475 0.617622i \(-0.788096\pi\)
−0.786475 + 0.617622i \(0.788096\pi\)
\(138\) −43.5795 −3.70974
\(139\) 2.35275 0.199558 0.0997790 0.995010i \(-0.468186\pi\)
0.0997790 + 0.995010i \(0.468186\pi\)
\(140\) 4.01854 0.339629
\(141\) −6.00352 −0.505588
\(142\) −41.0598 −3.44566
\(143\) 19.1672 1.60284
\(144\) 32.4459 2.70383
\(145\) −7.49271 −0.622236
\(146\) −17.3309 −1.43431
\(147\) 3.30020 0.272196
\(148\) 8.20635 0.674558
\(149\) 13.8937 1.13821 0.569107 0.822263i \(-0.307289\pi\)
0.569107 + 0.822263i \(0.307289\pi\)
\(150\) −8.09629 −0.661059
\(151\) −7.29837 −0.593933 −0.296967 0.954888i \(-0.595975\pi\)
−0.296967 + 0.954888i \(0.595975\pi\)
\(152\) −6.03475 −0.489483
\(153\) −35.4888 −2.86910
\(154\) −11.3255 −0.912633
\(155\) 1.81401 0.145704
\(156\) 55.0625 4.40853
\(157\) 14.5514 1.16132 0.580662 0.814144i \(-0.302794\pi\)
0.580662 + 0.814144i \(0.302794\pi\)
\(158\) −16.6708 −1.32626
\(159\) 4.75137 0.376808
\(160\) −0.182804 −0.0144519
\(161\) 5.38266 0.424213
\(162\) −72.6142 −5.70511
\(163\) −12.9803 −1.01670 −0.508349 0.861151i \(-0.669744\pi\)
−0.508349 + 0.861151i \(0.669744\pi\)
\(164\) −48.6120 −3.79596
\(165\) 15.2353 1.18607
\(166\) −25.3539 −1.96784
\(167\) −11.2337 −0.869290 −0.434645 0.900602i \(-0.643126\pi\)
−0.434645 + 0.900602i \(0.643126\pi\)
\(168\) −16.3427 −1.26087
\(169\) 4.23831 0.326024
\(170\) 11.0328 0.846180
\(171\) 9.61669 0.735406
\(172\) −13.5613 −1.03404
\(173\) −23.7228 −1.80361 −0.901805 0.432144i \(-0.857757\pi\)
−0.901805 + 0.432144i \(0.857757\pi\)
\(174\) 60.6631 4.59886
\(175\) 1.00000 0.0755929
\(176\) 18.9811 1.43075
\(177\) −43.9133 −3.30072
\(178\) −31.9104 −2.39178
\(179\) 10.2014 0.762489 0.381245 0.924474i \(-0.375496\pi\)
0.381245 + 0.924474i \(0.375496\pi\)
\(180\) 31.7116 2.36364
\(181\) 5.66186 0.420843 0.210421 0.977611i \(-0.432516\pi\)
0.210421 + 0.977611i \(0.432516\pi\)
\(182\) −10.1857 −0.755018
\(183\) 38.4288 2.84074
\(184\) −26.6551 −1.96504
\(185\) 2.04212 0.150140
\(186\) −14.6867 −1.07688
\(187\) −20.7612 −1.51821
\(188\) −7.31029 −0.533157
\(189\) 16.1423 1.17418
\(190\) −2.98966 −0.216893
\(191\) −13.5830 −0.982833 −0.491417 0.870925i \(-0.663521\pi\)
−0.491417 + 0.870925i \(0.663521\pi\)
\(192\) −25.6582 −1.85172
\(193\) 12.9796 0.934293 0.467147 0.884180i \(-0.345282\pi\)
0.467147 + 0.884180i \(0.345282\pi\)
\(194\) 23.7210 1.70307
\(195\) 13.7021 0.981229
\(196\) 4.01854 0.287039
\(197\) −14.0268 −0.999366 −0.499683 0.866208i \(-0.666550\pi\)
−0.499683 + 0.866208i \(0.666550\pi\)
\(198\) −89.3729 −6.35146
\(199\) 7.37991 0.523148 0.261574 0.965183i \(-0.415758\pi\)
0.261574 + 0.965183i \(0.415758\pi\)
\(200\) −4.95203 −0.350162
\(201\) −43.5116 −3.06907
\(202\) 13.7275 0.965866
\(203\) −7.49271 −0.525885
\(204\) −59.6418 −4.17576
\(205\) −12.0969 −0.844886
\(206\) −3.26569 −0.227532
\(207\) 42.4762 2.95230
\(208\) 17.0710 1.18366
\(209\) 5.62583 0.389147
\(210\) −8.09629 −0.558697
\(211\) −5.75375 −0.396104 −0.198052 0.980191i \(-0.563462\pi\)
−0.198052 + 0.980191i \(0.563462\pi\)
\(212\) 5.78558 0.397355
\(213\) 55.2346 3.78461
\(214\) 1.93120 0.132014
\(215\) −3.37469 −0.230152
\(216\) −79.9373 −5.43905
\(217\) 1.81401 0.123143
\(218\) −15.6212 −1.05800
\(219\) 23.3139 1.57541
\(220\) 18.5515 1.25074
\(221\) −18.6719 −1.25601
\(222\) −16.5336 −1.10966
\(223\) 19.3037 1.29267 0.646337 0.763052i \(-0.276300\pi\)
0.646337 + 0.763052i \(0.276300\pi\)
\(224\) −0.182804 −0.0122141
\(225\) 7.89132 0.526088
\(226\) −19.7455 −1.31345
\(227\) 19.0919 1.26717 0.633586 0.773672i \(-0.281582\pi\)
0.633586 + 0.773672i \(0.281582\pi\)
\(228\) 16.1616 1.07033
\(229\) 1.00000 0.0660819
\(230\) −13.2051 −0.870720
\(231\) 15.2353 1.00241
\(232\) 37.1041 2.43601
\(233\) −6.16648 −0.403980 −0.201990 0.979388i \(-0.564741\pi\)
−0.201990 + 0.979388i \(0.564741\pi\)
\(234\) −80.3790 −5.25454
\(235\) −1.81914 −0.118668
\(236\) −53.4717 −3.48071
\(237\) 22.4260 1.45672
\(238\) 11.0328 0.715153
\(239\) −22.2256 −1.43766 −0.718829 0.695187i \(-0.755321\pi\)
−0.718829 + 0.695187i \(0.755321\pi\)
\(240\) 13.5691 0.875882
\(241\) 4.00615 0.258059 0.129030 0.991641i \(-0.458814\pi\)
0.129030 + 0.991641i \(0.458814\pi\)
\(242\) −25.2978 −1.62621
\(243\) 49.2554 3.15974
\(244\) 46.7935 2.99564
\(245\) 1.00000 0.0638877
\(246\) 97.9401 6.24443
\(247\) 5.05968 0.321940
\(248\) −8.98301 −0.570422
\(249\) 34.1066 2.16142
\(250\) −2.45327 −0.155159
\(251\) 26.4902 1.67205 0.836024 0.548693i \(-0.184874\pi\)
0.836024 + 0.548693i \(0.184874\pi\)
\(252\) 31.7116 1.99764
\(253\) 24.8489 1.56224
\(254\) 26.4334 1.65858
\(255\) −14.8416 −0.929420
\(256\) −32.1400 −2.00875
\(257\) −11.3636 −0.708844 −0.354422 0.935086i \(-0.615322\pi\)
−0.354422 + 0.935086i \(0.615322\pi\)
\(258\) 27.3224 1.70102
\(259\) 2.04212 0.126891
\(260\) 16.6846 1.03474
\(261\) −59.1273 −3.65989
\(262\) 32.7639 2.02416
\(263\) 6.04432 0.372709 0.186355 0.982483i \(-0.440333\pi\)
0.186355 + 0.982483i \(0.440333\pi\)
\(264\) −75.4457 −4.64336
\(265\) 1.43972 0.0884414
\(266\) −2.98966 −0.183308
\(267\) 42.9266 2.62706
\(268\) −52.9826 −3.23643
\(269\) 3.06868 0.187101 0.0935503 0.995615i \(-0.470178\pi\)
0.0935503 + 0.995615i \(0.470178\pi\)
\(270\) −39.6015 −2.41007
\(271\) −10.2213 −0.620898 −0.310449 0.950590i \(-0.600479\pi\)
−0.310449 + 0.950590i \(0.600479\pi\)
\(272\) −18.4907 −1.12116
\(273\) 13.7021 0.829290
\(274\) 45.1670 2.72864
\(275\) 4.61648 0.278384
\(276\) 71.3847 4.29686
\(277\) −17.7750 −1.06800 −0.533998 0.845486i \(-0.679311\pi\)
−0.533998 + 0.845486i \(0.679311\pi\)
\(278\) −5.77194 −0.346178
\(279\) 14.3149 0.857010
\(280\) −4.95203 −0.295941
\(281\) 3.15666 0.188311 0.0941553 0.995558i \(-0.469985\pi\)
0.0941553 + 0.995558i \(0.469985\pi\)
\(282\) 14.7283 0.877055
\(283\) −9.90363 −0.588710 −0.294355 0.955696i \(-0.595105\pi\)
−0.294355 + 0.955696i \(0.595105\pi\)
\(284\) 67.2573 3.99098
\(285\) 4.02176 0.238228
\(286\) −47.0223 −2.78049
\(287\) −12.0969 −0.714059
\(288\) −1.44256 −0.0850038
\(289\) 3.22476 0.189692
\(290\) 18.3817 1.07941
\(291\) −31.9100 −1.87060
\(292\) 28.3886 1.66131
\(293\) −28.0058 −1.63612 −0.818058 0.575135i \(-0.804949\pi\)
−0.818058 + 0.575135i \(0.804949\pi\)
\(294\) −8.09629 −0.472185
\(295\) −13.3062 −0.774720
\(296\) −10.1127 −0.587786
\(297\) 74.5207 4.32413
\(298\) −34.0850 −1.97449
\(299\) 22.3483 1.29243
\(300\) 13.2620 0.765682
\(301\) −3.37469 −0.194514
\(302\) 17.9049 1.03031
\(303\) −18.4666 −1.06088
\(304\) 5.01057 0.287376
\(305\) 11.6444 0.666756
\(306\) 87.0637 4.97710
\(307\) −3.46077 −0.197517 −0.0987583 0.995111i \(-0.531487\pi\)
−0.0987583 + 0.995111i \(0.531487\pi\)
\(308\) 18.5515 1.05707
\(309\) 4.39309 0.249914
\(310\) −4.45025 −0.252757
\(311\) −1.47297 −0.0835245 −0.0417622 0.999128i \(-0.513297\pi\)
−0.0417622 + 0.999128i \(0.513297\pi\)
\(312\) −67.8533 −3.84144
\(313\) −7.83996 −0.443141 −0.221570 0.975144i \(-0.571118\pi\)
−0.221570 + 0.975144i \(0.571118\pi\)
\(314\) −35.6984 −2.01458
\(315\) 7.89132 0.444625
\(316\) 27.3074 1.53616
\(317\) −16.8953 −0.948935 −0.474468 0.880273i \(-0.657359\pi\)
−0.474468 + 0.880273i \(0.657359\pi\)
\(318\) −11.6564 −0.653658
\(319\) −34.5899 −1.93666
\(320\) −7.77473 −0.434621
\(321\) −2.59790 −0.145001
\(322\) −13.2051 −0.735892
\(323\) −5.48047 −0.304941
\(324\) 118.945 6.60803
\(325\) 4.15190 0.230306
\(326\) 31.8443 1.76369
\(327\) 21.0140 1.16208
\(328\) 59.9044 3.30766
\(329\) −1.81914 −0.100292
\(330\) −37.3763 −2.05750
\(331\) 14.4108 0.792087 0.396043 0.918232i \(-0.370383\pi\)
0.396043 + 0.918232i \(0.370383\pi\)
\(332\) 41.5305 2.27928
\(333\) 16.1150 0.883098
\(334\) 27.5593 1.50798
\(335\) −13.1845 −0.720348
\(336\) 13.5691 0.740255
\(337\) 28.7195 1.56445 0.782224 0.622997i \(-0.214085\pi\)
0.782224 + 0.622997i \(0.214085\pi\)
\(338\) −10.3977 −0.565562
\(339\) 26.5621 1.44265
\(340\) −18.0722 −0.980101
\(341\) 8.37431 0.453495
\(342\) −23.5923 −1.27573
\(343\) 1.00000 0.0539949
\(344\) 16.7116 0.901027
\(345\) 17.7638 0.956373
\(346\) 58.1984 3.12877
\(347\) −14.9099 −0.800407 −0.400204 0.916426i \(-0.631061\pi\)
−0.400204 + 0.916426i \(0.631061\pi\)
\(348\) −99.3682 −5.32670
\(349\) −33.0642 −1.76988 −0.884942 0.465702i \(-0.845802\pi\)
−0.884942 + 0.465702i \(0.845802\pi\)
\(350\) −2.45327 −0.131133
\(351\) 67.0214 3.57734
\(352\) −0.843909 −0.0449805
\(353\) 33.7031 1.79384 0.896918 0.442197i \(-0.145801\pi\)
0.896918 + 0.442197i \(0.145801\pi\)
\(354\) 107.731 5.72585
\(355\) 16.7367 0.888293
\(356\) 52.2703 2.77032
\(357\) −14.8416 −0.785503
\(358\) −25.0268 −1.32271
\(359\) 20.5452 1.08434 0.542168 0.840270i \(-0.317604\pi\)
0.542168 + 0.840270i \(0.317604\pi\)
\(360\) −39.0781 −2.05960
\(361\) −17.5149 −0.921838
\(362\) −13.8901 −0.730046
\(363\) 34.0312 1.78618
\(364\) 16.6846 0.874511
\(365\) 7.06439 0.369767
\(366\) −94.2763 −4.92790
\(367\) 34.1882 1.78461 0.892304 0.451435i \(-0.149088\pi\)
0.892304 + 0.451435i \(0.149088\pi\)
\(368\) 22.1313 1.15367
\(369\) −95.4606 −4.96948
\(370\) −5.00988 −0.260451
\(371\) 1.43972 0.0747466
\(372\) 24.0573 1.24731
\(373\) −16.4680 −0.852680 −0.426340 0.904563i \(-0.640197\pi\)
−0.426340 + 0.904563i \(0.640197\pi\)
\(374\) 50.9329 2.63368
\(375\) 3.30020 0.170422
\(376\) 9.00843 0.464575
\(377\) −31.1090 −1.60220
\(378\) −39.6015 −2.03688
\(379\) 12.8552 0.660330 0.330165 0.943923i \(-0.392896\pi\)
0.330165 + 0.943923i \(0.392896\pi\)
\(380\) 4.89716 0.251219
\(381\) −35.5589 −1.82174
\(382\) 33.3228 1.70495
\(383\) −20.6000 −1.05261 −0.526305 0.850296i \(-0.676423\pi\)
−0.526305 + 0.850296i \(0.676423\pi\)
\(384\) 64.1530 3.27380
\(385\) 4.61648 0.235278
\(386\) −31.8425 −1.62074
\(387\) −26.6307 −1.35372
\(388\) −38.8557 −1.97260
\(389\) −37.8831 −1.92075 −0.960375 0.278712i \(-0.910092\pi\)
−0.960375 + 0.278712i \(0.910092\pi\)
\(390\) −33.6150 −1.70216
\(391\) −24.2069 −1.22419
\(392\) −4.95203 −0.250115
\(393\) −44.0748 −2.22328
\(394\) 34.4115 1.73362
\(395\) 6.79534 0.341911
\(396\) 146.396 7.35667
\(397\) −7.91886 −0.397436 −0.198718 0.980057i \(-0.563678\pi\)
−0.198718 + 0.980057i \(0.563678\pi\)
\(398\) −18.1049 −0.907518
\(399\) 4.02176 0.201340
\(400\) 4.11160 0.205580
\(401\) 9.03341 0.451107 0.225554 0.974231i \(-0.427581\pi\)
0.225554 + 0.974231i \(0.427581\pi\)
\(402\) 106.746 5.32400
\(403\) 7.53158 0.375174
\(404\) −22.4862 −1.11873
\(405\) 29.5989 1.47078
\(406\) 18.3817 0.912266
\(407\) 9.42741 0.467299
\(408\) 73.4963 3.63861
\(409\) −7.27221 −0.359588 −0.179794 0.983704i \(-0.557543\pi\)
−0.179794 + 0.983704i \(0.557543\pi\)
\(410\) 29.6770 1.46564
\(411\) −60.7597 −2.99705
\(412\) 5.34932 0.263542
\(413\) −13.3062 −0.654758
\(414\) −104.206 −5.12143
\(415\) 10.3347 0.507311
\(416\) −0.758983 −0.0372122
\(417\) 7.76456 0.380232
\(418\) −13.8017 −0.675063
\(419\) 16.4955 0.805857 0.402929 0.915231i \(-0.367992\pi\)
0.402929 + 0.915231i \(0.367992\pi\)
\(420\) 13.2620 0.647119
\(421\) 25.2285 1.22956 0.614782 0.788697i \(-0.289244\pi\)
0.614782 + 0.788697i \(0.289244\pi\)
\(422\) 14.1155 0.687132
\(423\) −14.3554 −0.697983
\(424\) −7.12955 −0.346242
\(425\) −4.49719 −0.218146
\(426\) −135.505 −6.56526
\(427\) 11.6444 0.563511
\(428\) −3.16338 −0.152908
\(429\) 63.2555 3.05400
\(430\) 8.27903 0.399250
\(431\) 21.0442 1.01366 0.506832 0.862045i \(-0.330816\pi\)
0.506832 + 0.862045i \(0.330816\pi\)
\(432\) 66.3708 3.19327
\(433\) −35.0983 −1.68672 −0.843358 0.537352i \(-0.819425\pi\)
−0.843358 + 0.537352i \(0.819425\pi\)
\(434\) −4.45025 −0.213619
\(435\) −24.7274 −1.18559
\(436\) 25.5881 1.22545
\(437\) 6.55953 0.313785
\(438\) −57.1953 −2.73290
\(439\) 34.2094 1.63273 0.816363 0.577539i \(-0.195987\pi\)
0.816363 + 0.577539i \(0.195987\pi\)
\(440\) −22.8610 −1.08985
\(441\) 7.89132 0.375777
\(442\) 45.8073 2.17883
\(443\) 0.739407 0.0351303 0.0175651 0.999846i \(-0.494409\pi\)
0.0175651 + 0.999846i \(0.494409\pi\)
\(444\) 27.0826 1.28528
\(445\) 13.0073 0.616604
\(446\) −47.3573 −2.24243
\(447\) 45.8519 2.16872
\(448\) −7.77473 −0.367322
\(449\) −11.9280 −0.562917 −0.281459 0.959573i \(-0.590818\pi\)
−0.281459 + 0.959573i \(0.590818\pi\)
\(450\) −19.3595 −0.912618
\(451\) −55.8452 −2.62965
\(452\) 32.3437 1.52132
\(453\) −24.0861 −1.13166
\(454\) −46.8375 −2.19819
\(455\) 4.15190 0.194644
\(456\) −19.9159 −0.932647
\(457\) −17.4706 −0.817241 −0.408620 0.912704i \(-0.633990\pi\)
−0.408620 + 0.912704i \(0.633990\pi\)
\(458\) −2.45327 −0.114634
\(459\) −72.5952 −3.38845
\(460\) 21.6304 1.00852
\(461\) −25.5743 −1.19111 −0.595556 0.803314i \(-0.703068\pi\)
−0.595556 + 0.803314i \(0.703068\pi\)
\(462\) −37.3763 −1.73890
\(463\) 23.0794 1.07259 0.536296 0.844030i \(-0.319823\pi\)
0.536296 + 0.844030i \(0.319823\pi\)
\(464\) −30.8070 −1.43018
\(465\) 5.98658 0.277621
\(466\) 15.1281 0.700794
\(467\) −11.9470 −0.552841 −0.276421 0.961037i \(-0.589148\pi\)
−0.276421 + 0.961037i \(0.589148\pi\)
\(468\) 131.664 6.08615
\(469\) −13.1845 −0.608805
\(470\) 4.46284 0.205856
\(471\) 48.0224 2.21275
\(472\) 65.8930 3.03297
\(473\) −15.5792 −0.716331
\(474\) −55.0170 −2.52702
\(475\) 1.21864 0.0559151
\(476\) −18.0722 −0.828337
\(477\) 11.3613 0.520198
\(478\) 54.5255 2.49394
\(479\) 16.4726 0.752652 0.376326 0.926487i \(-0.377187\pi\)
0.376326 + 0.926487i \(0.377187\pi\)
\(480\) −0.603289 −0.0275362
\(481\) 8.47869 0.386595
\(482\) −9.82818 −0.447662
\(483\) 17.7638 0.808283
\(484\) 41.4387 1.88358
\(485\) −9.66911 −0.439052
\(486\) −120.837 −5.48128
\(487\) 24.8391 1.12557 0.562783 0.826605i \(-0.309731\pi\)
0.562783 + 0.826605i \(0.309731\pi\)
\(488\) −57.6634 −2.61030
\(489\) −42.8376 −1.93719
\(490\) −2.45327 −0.110828
\(491\) −14.4555 −0.652366 −0.326183 0.945307i \(-0.605763\pi\)
−0.326183 + 0.945307i \(0.605763\pi\)
\(492\) −160.429 −7.23271
\(493\) 33.6962 1.51760
\(494\) −12.4128 −0.558477
\(495\) 36.4301 1.63741
\(496\) 7.45846 0.334895
\(497\) 16.7367 0.750745
\(498\) −83.6728 −3.74947
\(499\) 29.5204 1.32151 0.660757 0.750600i \(-0.270235\pi\)
0.660757 + 0.750600i \(0.270235\pi\)
\(500\) 4.01854 0.179715
\(501\) −37.0735 −1.65632
\(502\) −64.9877 −2.90054
\(503\) −25.8441 −1.15233 −0.576165 0.817333i \(-0.695451\pi\)
−0.576165 + 0.817333i \(0.695451\pi\)
\(504\) −39.0781 −1.74068
\(505\) −5.59560 −0.249001
\(506\) −60.9611 −2.71005
\(507\) 13.9873 0.621196
\(508\) −43.2989 −1.92108
\(509\) −27.9714 −1.23981 −0.619905 0.784677i \(-0.712829\pi\)
−0.619905 + 0.784677i \(0.712829\pi\)
\(510\) 36.4106 1.61229
\(511\) 7.06439 0.312510
\(512\) 39.9699 1.76644
\(513\) 19.6717 0.868527
\(514\) 27.8781 1.22965
\(515\) 1.33116 0.0586579
\(516\) −44.7551 −1.97023
\(517\) −8.39801 −0.369344
\(518\) −5.00988 −0.220121
\(519\) −78.2899 −3.43655
\(520\) −20.5604 −0.901632
\(521\) −27.9086 −1.22270 −0.611350 0.791360i \(-0.709373\pi\)
−0.611350 + 0.791360i \(0.709373\pi\)
\(522\) 145.055 6.34890
\(523\) −10.7976 −0.472146 −0.236073 0.971735i \(-0.575860\pi\)
−0.236073 + 0.971735i \(0.575860\pi\)
\(524\) −53.6684 −2.34451
\(525\) 3.30020 0.144033
\(526\) −14.8284 −0.646548
\(527\) −8.15793 −0.355365
\(528\) 62.6415 2.72612
\(529\) 5.97298 0.259695
\(530\) −3.53203 −0.153421
\(531\) −105.004 −4.55678
\(532\) 4.89716 0.212319
\(533\) −50.2253 −2.17550
\(534\) −105.311 −4.55723
\(535\) −0.787195 −0.0340334
\(536\) 65.2903 2.82011
\(537\) 33.6667 1.45282
\(538\) −7.52830 −0.324568
\(539\) 4.61648 0.198846
\(540\) 64.8686 2.79150
\(541\) −19.7792 −0.850376 −0.425188 0.905105i \(-0.639792\pi\)
−0.425188 + 0.905105i \(0.639792\pi\)
\(542\) 25.0755 1.07709
\(543\) 18.6853 0.801861
\(544\) 0.822104 0.0352474
\(545\) 6.36750 0.272754
\(546\) −33.6150 −1.43859
\(547\) −16.2242 −0.693697 −0.346848 0.937921i \(-0.612748\pi\)
−0.346848 + 0.937921i \(0.612748\pi\)
\(548\) −73.9850 −3.16048
\(549\) 91.8895 3.92175
\(550\) −11.3255 −0.482920
\(551\) −9.13092 −0.388990
\(552\) −87.9671 −3.74413
\(553\) 6.79534 0.288967
\(554\) 43.6069 1.85268
\(555\) 6.73941 0.286072
\(556\) 9.45464 0.400966
\(557\) −23.3585 −0.989732 −0.494866 0.868969i \(-0.664783\pi\)
−0.494866 + 0.868969i \(0.664783\pi\)
\(558\) −35.1183 −1.48668
\(559\) −14.0114 −0.592618
\(560\) 4.11160 0.173747
\(561\) −68.5161 −2.89275
\(562\) −7.74415 −0.326667
\(563\) 0.640294 0.0269852 0.0134926 0.999909i \(-0.495705\pi\)
0.0134926 + 0.999909i \(0.495705\pi\)
\(564\) −24.1254 −1.01586
\(565\) 8.04862 0.338608
\(566\) 24.2963 1.02125
\(567\) 29.5989 1.24304
\(568\) −82.8809 −3.47760
\(569\) 45.2633 1.89754 0.948768 0.315974i \(-0.102331\pi\)
0.948768 + 0.315974i \(0.102331\pi\)
\(570\) −9.86647 −0.413261
\(571\) −32.3691 −1.35460 −0.677302 0.735705i \(-0.736851\pi\)
−0.677302 + 0.735705i \(0.736851\pi\)
\(572\) 77.0241 3.22054
\(573\) −44.8267 −1.87266
\(574\) 29.6770 1.23870
\(575\) 5.38266 0.224472
\(576\) −61.3529 −2.55637
\(577\) 14.4879 0.603139 0.301569 0.953444i \(-0.402489\pi\)
0.301569 + 0.953444i \(0.402489\pi\)
\(578\) −7.91122 −0.329063
\(579\) 42.8353 1.78018
\(580\) −30.1098 −1.25024
\(581\) 10.3347 0.428756
\(582\) 78.2839 3.24497
\(583\) 6.64644 0.275268
\(584\) −34.9831 −1.44761
\(585\) 32.7640 1.35462
\(586\) 68.7059 2.83821
\(587\) 6.32770 0.261172 0.130586 0.991437i \(-0.458314\pi\)
0.130586 + 0.991437i \(0.458314\pi\)
\(588\) 13.2620 0.546915
\(589\) 2.21062 0.0910871
\(590\) 32.6438 1.34393
\(591\) −46.2911 −1.90416
\(592\) 8.39639 0.345089
\(593\) −27.5633 −1.13189 −0.565944 0.824444i \(-0.691488\pi\)
−0.565944 + 0.824444i \(0.691488\pi\)
\(594\) −182.820 −7.50118
\(595\) −4.49719 −0.184367
\(596\) 55.8323 2.28698
\(597\) 24.3552 0.996791
\(598\) −54.8264 −2.24202
\(599\) −14.0719 −0.574962 −0.287481 0.957786i \(-0.592818\pi\)
−0.287481 + 0.957786i \(0.592818\pi\)
\(600\) −16.3427 −0.667188
\(601\) 27.9541 1.14027 0.570136 0.821550i \(-0.306891\pi\)
0.570136 + 0.821550i \(0.306891\pi\)
\(602\) 8.27903 0.337428
\(603\) −104.043 −4.23697
\(604\) −29.3288 −1.19337
\(605\) 10.3119 0.419237
\(606\) 45.3036 1.84033
\(607\) 24.5146 0.995016 0.497508 0.867459i \(-0.334249\pi\)
0.497508 + 0.867459i \(0.334249\pi\)
\(608\) −0.222772 −0.00903460
\(609\) −24.7274 −1.00201
\(610\) −28.5668 −1.15664
\(611\) −7.55289 −0.305557
\(612\) −142.613 −5.76480
\(613\) −0.307384 −0.0124151 −0.00620755 0.999981i \(-0.501976\pi\)
−0.00620755 + 0.999981i \(0.501976\pi\)
\(614\) 8.49021 0.342637
\(615\) −39.9223 −1.60982
\(616\) −22.8610 −0.921094
\(617\) 22.9094 0.922298 0.461149 0.887323i \(-0.347437\pi\)
0.461149 + 0.887323i \(0.347437\pi\)
\(618\) −10.7774 −0.433532
\(619\) −12.4559 −0.500645 −0.250323 0.968162i \(-0.580537\pi\)
−0.250323 + 0.968162i \(0.580537\pi\)
\(620\) 7.28966 0.292760
\(621\) 86.8886 3.48672
\(622\) 3.61360 0.144892
\(623\) 13.0073 0.521125
\(624\) 56.3376 2.25531
\(625\) 1.00000 0.0400000
\(626\) 19.2335 0.768727
\(627\) 18.5664 0.741469
\(628\) 58.4752 2.33342
\(629\) −9.18382 −0.366183
\(630\) −19.3595 −0.771303
\(631\) 11.9901 0.477317 0.238658 0.971104i \(-0.423292\pi\)
0.238658 + 0.971104i \(0.423292\pi\)
\(632\) −33.6508 −1.33856
\(633\) −18.9885 −0.754726
\(634\) 41.4488 1.64614
\(635\) −10.7748 −0.427584
\(636\) 19.0936 0.757110
\(637\) 4.15190 0.164504
\(638\) 84.8585 3.35958
\(639\) 132.075 5.22480
\(640\) 19.4391 0.768399
\(641\) −6.08927 −0.240512 −0.120256 0.992743i \(-0.538371\pi\)
−0.120256 + 0.992743i \(0.538371\pi\)
\(642\) 6.37335 0.251536
\(643\) −8.48814 −0.334740 −0.167370 0.985894i \(-0.553527\pi\)
−0.167370 + 0.985894i \(0.553527\pi\)
\(644\) 21.6304 0.852358
\(645\) −11.1371 −0.438525
\(646\) 13.4451 0.528989
\(647\) −43.9773 −1.72893 −0.864464 0.502695i \(-0.832342\pi\)
−0.864464 + 0.502695i \(0.832342\pi\)
\(648\) −146.575 −5.75801
\(649\) −61.4280 −2.41126
\(650\) −10.1857 −0.399518
\(651\) 5.98658 0.234633
\(652\) −52.1620 −2.04282
\(653\) −5.71273 −0.223556 −0.111778 0.993733i \(-0.535655\pi\)
−0.111778 + 0.993733i \(0.535655\pi\)
\(654\) −51.5531 −2.01588
\(655\) −13.3552 −0.521830
\(656\) −49.7377 −1.94193
\(657\) 55.7473 2.17491
\(658\) 4.46284 0.173980
\(659\) 25.4529 0.991503 0.495752 0.868464i \(-0.334893\pi\)
0.495752 + 0.868464i \(0.334893\pi\)
\(660\) 61.2237 2.38313
\(661\) 39.8580 1.55030 0.775148 0.631780i \(-0.217675\pi\)
0.775148 + 0.631780i \(0.217675\pi\)
\(662\) −35.3535 −1.37405
\(663\) −61.6211 −2.39316
\(664\) −51.1779 −1.98609
\(665\) 1.21864 0.0472569
\(666\) −39.5346 −1.53193
\(667\) −40.3307 −1.56161
\(668\) −45.1431 −1.74664
\(669\) 63.7062 2.46302
\(670\) 32.3452 1.24961
\(671\) 53.7561 2.07523
\(672\) −0.603289 −0.0232724
\(673\) 14.6574 0.565002 0.282501 0.959267i \(-0.408836\pi\)
0.282501 + 0.959267i \(0.408836\pi\)
\(674\) −70.4566 −2.71389
\(675\) 16.1423 0.621318
\(676\) 17.0318 0.655070
\(677\) −9.06983 −0.348582 −0.174291 0.984694i \(-0.555763\pi\)
−0.174291 + 0.984694i \(0.555763\pi\)
\(678\) −65.1639 −2.50261
\(679\) −9.66911 −0.371066
\(680\) 22.2703 0.854026
\(681\) 63.0070 2.41443
\(682\) −20.5445 −0.786688
\(683\) 47.3216 1.81071 0.905355 0.424655i \(-0.139605\pi\)
0.905355 + 0.424655i \(0.139605\pi\)
\(684\) 38.6451 1.47763
\(685\) −18.4109 −0.703445
\(686\) −2.45327 −0.0936664
\(687\) 3.30020 0.125910
\(688\) −13.8754 −0.528993
\(689\) 5.97759 0.227728
\(690\) −43.5795 −1.65904
\(691\) 24.8451 0.945152 0.472576 0.881290i \(-0.343324\pi\)
0.472576 + 0.881290i \(0.343324\pi\)
\(692\) −95.3310 −3.62394
\(693\) 36.4301 1.38386
\(694\) 36.5781 1.38849
\(695\) 2.35275 0.0892450
\(696\) 122.451 4.64150
\(697\) 54.4022 2.06063
\(698\) 81.1153 3.07026
\(699\) −20.3506 −0.769731
\(700\) 4.01854 0.151887
\(701\) 12.4372 0.469747 0.234874 0.972026i \(-0.424532\pi\)
0.234874 + 0.972026i \(0.424532\pi\)
\(702\) −164.422 −6.20570
\(703\) 2.48861 0.0938599
\(704\) −35.8919 −1.35273
\(705\) −6.00352 −0.226106
\(706\) −82.6829 −3.11181
\(707\) −5.59560 −0.210444
\(708\) −176.467 −6.63205
\(709\) 42.5291 1.59721 0.798607 0.601853i \(-0.205571\pi\)
0.798607 + 0.601853i \(0.205571\pi\)
\(710\) −41.0598 −1.54095
\(711\) 53.6242 2.01106
\(712\) −64.4124 −2.41396
\(713\) 9.76416 0.365671
\(714\) 36.4106 1.36263
\(715\) 19.1672 0.716812
\(716\) 40.9948 1.53205
\(717\) −73.3490 −2.73927
\(718\) −50.4030 −1.88102
\(719\) −37.5115 −1.39894 −0.699472 0.714660i \(-0.746581\pi\)
−0.699472 + 0.714660i \(0.746581\pi\)
\(720\) 32.4459 1.20919
\(721\) 1.33116 0.0495749
\(722\) 42.9688 1.59913
\(723\) 13.2211 0.491698
\(724\) 22.7524 0.845587
\(725\) −7.49271 −0.278272
\(726\) −83.4879 −3.09853
\(727\) −13.9071 −0.515785 −0.257892 0.966174i \(-0.583028\pi\)
−0.257892 + 0.966174i \(0.583028\pi\)
\(728\) −20.5604 −0.762018
\(729\) 73.7560 2.73170
\(730\) −17.3309 −0.641444
\(731\) 15.1766 0.561328
\(732\) 154.428 5.70781
\(733\) −38.9654 −1.43922 −0.719610 0.694378i \(-0.755680\pi\)
−0.719610 + 0.694378i \(0.755680\pi\)
\(734\) −83.8729 −3.09580
\(735\) 3.30020 0.121730
\(736\) −0.983969 −0.0362696
\(737\) −60.8661 −2.24203
\(738\) 234.191 8.62069
\(739\) 18.8906 0.694903 0.347451 0.937698i \(-0.387047\pi\)
0.347451 + 0.937698i \(0.387047\pi\)
\(740\) 8.20635 0.301672
\(741\) 16.6980 0.613415
\(742\) −3.53203 −0.129665
\(743\) −22.8346 −0.837722 −0.418861 0.908050i \(-0.637571\pi\)
−0.418861 + 0.908050i \(0.637571\pi\)
\(744\) −29.6457 −1.08687
\(745\) 13.8937 0.509025
\(746\) 40.4004 1.47917
\(747\) 81.5545 2.98392
\(748\) −83.4298 −3.05049
\(749\) −0.787195 −0.0287635
\(750\) −8.09629 −0.295635
\(751\) 10.6325 0.387986 0.193993 0.981003i \(-0.437856\pi\)
0.193993 + 0.981003i \(0.437856\pi\)
\(752\) −7.47957 −0.272752
\(753\) 87.4230 3.18587
\(754\) 76.3189 2.77937
\(755\) −7.29837 −0.265615
\(756\) 64.8686 2.35925
\(757\) 5.70148 0.207224 0.103612 0.994618i \(-0.466960\pi\)
0.103612 + 0.994618i \(0.466960\pi\)
\(758\) −31.5374 −1.14549
\(759\) 82.0064 2.97664
\(760\) −6.03475 −0.218903
\(761\) −13.7575 −0.498707 −0.249354 0.968412i \(-0.580218\pi\)
−0.249354 + 0.968412i \(0.580218\pi\)
\(762\) 87.2356 3.16021
\(763\) 6.36750 0.230519
\(764\) −54.5840 −1.97478
\(765\) −35.4888 −1.28310
\(766\) 50.5373 1.82599
\(767\) −55.2463 −1.99483
\(768\) −106.068 −3.82742
\(769\) 44.9301 1.62022 0.810110 0.586278i \(-0.199407\pi\)
0.810110 + 0.586278i \(0.199407\pi\)
\(770\) −11.3255 −0.408142
\(771\) −37.5023 −1.35061
\(772\) 52.1591 1.87725
\(773\) −24.3953 −0.877436 −0.438718 0.898625i \(-0.644567\pi\)
−0.438718 + 0.898625i \(0.644567\pi\)
\(774\) 65.3324 2.34833
\(775\) 1.81401 0.0651610
\(776\) 47.8818 1.71885
\(777\) 6.73941 0.241775
\(778\) 92.9375 3.33197
\(779\) −14.7418 −0.528180
\(780\) 55.0625 1.97155
\(781\) 77.2648 2.76475
\(782\) 59.3860 2.12364
\(783\) −120.950 −4.32239
\(784\) 4.11160 0.146843
\(785\) 14.5514 0.519360
\(786\) 108.127 3.85678
\(787\) −21.6906 −0.773188 −0.386594 0.922250i \(-0.626349\pi\)
−0.386594 + 0.922250i \(0.626349\pi\)
\(788\) −56.3672 −2.00800
\(789\) 19.9475 0.710149
\(790\) −16.6708 −0.593121
\(791\) 8.04862 0.286176
\(792\) −180.403 −6.41034
\(793\) 48.3464 1.71683
\(794\) 19.4271 0.689442
\(795\) 4.75137 0.168514
\(796\) 29.6565 1.05115
\(797\) −44.6267 −1.58076 −0.790379 0.612618i \(-0.790116\pi\)
−0.790379 + 0.612618i \(0.790116\pi\)
\(798\) −9.86647 −0.349269
\(799\) 8.18102 0.289424
\(800\) −0.182804 −0.00646309
\(801\) 102.644 3.62676
\(802\) −22.1614 −0.782547
\(803\) 32.6126 1.15087
\(804\) −174.853 −6.16660
\(805\) 5.38266 0.189714
\(806\) −18.4770 −0.650825
\(807\) 10.1272 0.356496
\(808\) 27.7096 0.974821
\(809\) 2.13506 0.0750648 0.0375324 0.999295i \(-0.488050\pi\)
0.0375324 + 0.999295i \(0.488050\pi\)
\(810\) −72.6142 −2.55140
\(811\) 8.28173 0.290811 0.145405 0.989372i \(-0.453551\pi\)
0.145405 + 0.989372i \(0.453551\pi\)
\(812\) −30.1098 −1.05665
\(813\) −33.7322 −1.18304
\(814\) −23.1280 −0.810636
\(815\) −12.9803 −0.454681
\(816\) −61.0229 −2.13623
\(817\) −4.11253 −0.143879
\(818\) 17.8407 0.623786
\(819\) 32.7640 1.14487
\(820\) −48.6120 −1.69760
\(821\) −39.3454 −1.37316 −0.686582 0.727052i \(-0.740890\pi\)
−0.686582 + 0.727052i \(0.740890\pi\)
\(822\) 149.060 5.19906
\(823\) 18.5539 0.646747 0.323373 0.946271i \(-0.395183\pi\)
0.323373 + 0.946271i \(0.395183\pi\)
\(824\) −6.59194 −0.229641
\(825\) 15.2353 0.530425
\(826\) 32.6438 1.13582
\(827\) −41.8382 −1.45486 −0.727429 0.686183i \(-0.759285\pi\)
−0.727429 + 0.686183i \(0.759285\pi\)
\(828\) 170.693 5.93198
\(829\) −3.20690 −0.111380 −0.0556902 0.998448i \(-0.517736\pi\)
−0.0556902 + 0.998448i \(0.517736\pi\)
\(830\) −25.3539 −0.880046
\(831\) −58.6610 −2.03493
\(832\) −32.2799 −1.11911
\(833\) −4.49719 −0.155819
\(834\) −19.0486 −0.659598
\(835\) −11.2337 −0.388758
\(836\) 22.6076 0.781902
\(837\) 29.2823 1.01214
\(838\) −40.4679 −1.39794
\(839\) −5.38819 −0.186021 −0.0930104 0.995665i \(-0.529649\pi\)
−0.0930104 + 0.995665i \(0.529649\pi\)
\(840\) −16.3427 −0.563877
\(841\) 27.1407 0.935886
\(842\) −61.8924 −2.13295
\(843\) 10.4176 0.358802
\(844\) −23.1217 −0.795881
\(845\) 4.23831 0.145802
\(846\) 35.2177 1.21081
\(847\) 10.3119 0.354320
\(848\) 5.91956 0.203278
\(849\) −32.6840 −1.12171
\(850\) 11.0328 0.378423
\(851\) 10.9920 0.376802
\(852\) 221.962 7.60431
\(853\) −50.1428 −1.71686 −0.858429 0.512932i \(-0.828559\pi\)
−0.858429 + 0.512932i \(0.828559\pi\)
\(854\) −28.5668 −0.977537
\(855\) 9.61669 0.328884
\(856\) 3.89821 0.133238
\(857\) 36.0037 1.22986 0.614931 0.788581i \(-0.289184\pi\)
0.614931 + 0.788581i \(0.289184\pi\)
\(858\) −155.183 −5.29786
\(859\) −26.3962 −0.900628 −0.450314 0.892870i \(-0.648688\pi\)
−0.450314 + 0.892870i \(0.648688\pi\)
\(860\) −13.5613 −0.462437
\(861\) −39.9223 −1.36055
\(862\) −51.6272 −1.75843
\(863\) −36.8111 −1.25306 −0.626532 0.779396i \(-0.715526\pi\)
−0.626532 + 0.779396i \(0.715526\pi\)
\(864\) −2.95088 −0.100391
\(865\) −23.7228 −0.806599
\(866\) 86.1056 2.92599
\(867\) 10.6424 0.361433
\(868\) 7.28966 0.247427
\(869\) 31.3705 1.06417
\(870\) 60.6631 2.05667
\(871\) −54.7409 −1.85483
\(872\) −31.5321 −1.06781
\(873\) −76.3020 −2.58243
\(874\) −16.0923 −0.544330
\(875\) 1.00000 0.0338062
\(876\) 93.6879 3.16542
\(877\) −20.9514 −0.707477 −0.353739 0.935344i \(-0.615090\pi\)
−0.353739 + 0.935344i \(0.615090\pi\)
\(878\) −83.9250 −2.83233
\(879\) −92.4248 −3.11741
\(880\) 18.9811 0.639853
\(881\) 13.5699 0.457182 0.228591 0.973523i \(-0.426588\pi\)
0.228591 + 0.973523i \(0.426588\pi\)
\(882\) −19.3595 −0.651870
\(883\) 22.3686 0.752763 0.376382 0.926465i \(-0.377168\pi\)
0.376382 + 0.926465i \(0.377168\pi\)
\(884\) −75.0339 −2.52366
\(885\) −43.9133 −1.47613
\(886\) −1.81397 −0.0609414
\(887\) −28.7208 −0.964349 −0.482174 0.876075i \(-0.660153\pi\)
−0.482174 + 0.876075i \(0.660153\pi\)
\(888\) −33.3738 −1.11995
\(889\) −10.7748 −0.361374
\(890\) −31.9104 −1.06964
\(891\) 136.643 4.57771
\(892\) 77.5729 2.59733
\(893\) −2.21688 −0.0741850
\(894\) −112.487 −3.76214
\(895\) 10.2014 0.340995
\(896\) 19.4391 0.649416
\(897\) 73.7538 2.46257
\(898\) 29.2626 0.976507
\(899\) −13.5918 −0.453312
\(900\) 31.7116 1.05705
\(901\) −6.47471 −0.215704
\(902\) 137.003 4.56171
\(903\) −11.1371 −0.370621
\(904\) −39.8570 −1.32563
\(905\) 5.66186 0.188207
\(906\) 59.0897 1.96312
\(907\) −25.7259 −0.854215 −0.427107 0.904201i \(-0.640467\pi\)
−0.427107 + 0.904201i \(0.640467\pi\)
\(908\) 76.7215 2.54609
\(909\) −44.1567 −1.46458
\(910\) −10.1857 −0.337654
\(911\) 7.15184 0.236951 0.118476 0.992957i \(-0.462199\pi\)
0.118476 + 0.992957i \(0.462199\pi\)
\(912\) 16.5359 0.547557
\(913\) 47.7100 1.57897
\(914\) 42.8602 1.41769
\(915\) 38.4288 1.27042
\(916\) 4.01854 0.132776
\(917\) −13.3552 −0.441027
\(918\) 178.096 5.87803
\(919\) −22.9002 −0.755408 −0.377704 0.925926i \(-0.623286\pi\)
−0.377704 + 0.925926i \(0.623286\pi\)
\(920\) −26.6551 −0.878792
\(921\) −11.4212 −0.376342
\(922\) 62.7406 2.06625
\(923\) 69.4893 2.28727
\(924\) 61.2237 2.01411
\(925\) 2.04212 0.0671446
\(926\) −56.6201 −1.86065
\(927\) 10.5046 0.345016
\(928\) 1.36969 0.0449624
\(929\) −15.8766 −0.520896 −0.260448 0.965488i \(-0.583870\pi\)
−0.260448 + 0.965488i \(0.583870\pi\)
\(930\) −14.6867 −0.481596
\(931\) 1.21864 0.0399394
\(932\) −24.7803 −0.811705
\(933\) −4.86109 −0.159145
\(934\) 29.3092 0.959028
\(935\) −20.7612 −0.678964
\(936\) −162.248 −5.30325
\(937\) 35.8403 1.17085 0.585425 0.810727i \(-0.300928\pi\)
0.585425 + 0.810727i \(0.300928\pi\)
\(938\) 32.3452 1.05611
\(939\) −25.8734 −0.844347
\(940\) −7.31029 −0.238435
\(941\) −9.15363 −0.298400 −0.149200 0.988807i \(-0.547670\pi\)
−0.149200 + 0.988807i \(0.547670\pi\)
\(942\) −117.812 −3.83852
\(943\) −65.1136 −2.12039
\(944\) −54.7100 −1.78066
\(945\) 16.1423 0.525110
\(946\) 38.2200 1.24264
\(947\) −10.0309 −0.325960 −0.162980 0.986629i \(-0.552111\pi\)
−0.162980 + 0.986629i \(0.552111\pi\)
\(948\) 90.1198 2.92695
\(949\) 29.3307 0.952114
\(950\) −2.98966 −0.0969973
\(951\) −55.7579 −1.80807
\(952\) 22.2703 0.721783
\(953\) 31.2434 1.01207 0.506037 0.862512i \(-0.331110\pi\)
0.506037 + 0.862512i \(0.331110\pi\)
\(954\) −27.8724 −0.902401
\(955\) −13.5830 −0.439536
\(956\) −89.3147 −2.88864
\(957\) −114.154 −3.69006
\(958\) −40.4117 −1.30564
\(959\) −18.4109 −0.594519
\(960\) −25.6582 −0.828114
\(961\) −27.7094 −0.893851
\(962\) −20.8005 −0.670636
\(963\) −6.21200 −0.200179
\(964\) 16.0989 0.518511
\(965\) 12.9796 0.417829
\(966\) −43.5795 −1.40215
\(967\) 58.3287 1.87573 0.937863 0.347006i \(-0.112802\pi\)
0.937863 + 0.347006i \(0.112802\pi\)
\(968\) −51.0647 −1.64128
\(969\) −18.0866 −0.581026
\(970\) 23.7210 0.761634
\(971\) 5.06433 0.162522 0.0812611 0.996693i \(-0.474105\pi\)
0.0812611 + 0.996693i \(0.474105\pi\)
\(972\) 197.935 6.34877
\(973\) 2.35275 0.0754258
\(974\) −60.9370 −1.95255
\(975\) 13.7021 0.438819
\(976\) 47.8771 1.53251
\(977\) −3.00938 −0.0962787 −0.0481393 0.998841i \(-0.515329\pi\)
−0.0481393 + 0.998841i \(0.515329\pi\)
\(978\) 105.092 3.36048
\(979\) 60.0478 1.91914
\(980\) 4.01854 0.128368
\(981\) 50.2479 1.60429
\(982\) 35.4632 1.13168
\(983\) 16.0530 0.512010 0.256005 0.966675i \(-0.417594\pi\)
0.256005 + 0.966675i \(0.417594\pi\)
\(984\) 197.696 6.30233
\(985\) −14.0268 −0.446930
\(986\) −82.6659 −2.63262
\(987\) −6.00352 −0.191094
\(988\) 20.3325 0.646865
\(989\) −18.1648 −0.577607
\(990\) −89.3729 −2.84046
\(991\) 55.8993 1.77570 0.887849 0.460135i \(-0.152199\pi\)
0.887849 + 0.460135i \(0.152199\pi\)
\(992\) −0.331607 −0.0105285
\(993\) 47.5584 1.50922
\(994\) −41.0598 −1.30234
\(995\) 7.37991 0.233959
\(996\) 137.059 4.34288
\(997\) 21.5954 0.683932 0.341966 0.939712i \(-0.388907\pi\)
0.341966 + 0.939712i \(0.388907\pi\)
\(998\) −72.4215 −2.29246
\(999\) 32.9646 1.04295
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 8015.2.a.o.1.7 73
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8015.2.a.o.1.7 73 1.1 even 1 trivial