Properties

Label 6047.2.a.b.1.10
Level $6047$
Weight $2$
Character 6047.1
Self dual yes
Analytic conductor $48.286$
Analytic rank $0$
Dimension $287$
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] = [6047,2,Mod(1,6047)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6047, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("6047.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6047 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6047.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(48.2855381023\)
Analytic rank: \(0\)
Dimension: \(287\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) \(=\) 6047.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.65477 q^{2} +2.03227 q^{3} +5.04782 q^{4} -0.522833 q^{5} -5.39521 q^{6} +4.81464 q^{7} -8.09128 q^{8} +1.13010 q^{9} +O(q^{10})\) \(q-2.65477 q^{2} +2.03227 q^{3} +5.04782 q^{4} -0.522833 q^{5} -5.39521 q^{6} +4.81464 q^{7} -8.09128 q^{8} +1.13010 q^{9} +1.38800 q^{10} +3.60821 q^{11} +10.2585 q^{12} +4.41348 q^{13} -12.7818 q^{14} -1.06253 q^{15} +11.3849 q^{16} -2.41333 q^{17} -3.00017 q^{18} +2.25640 q^{19} -2.63917 q^{20} +9.78463 q^{21} -9.57898 q^{22} -1.20092 q^{23} -16.4436 q^{24} -4.72665 q^{25} -11.7168 q^{26} -3.80012 q^{27} +24.3035 q^{28} -1.24365 q^{29} +2.82079 q^{30} -1.42425 q^{31} -14.0417 q^{32} +7.33285 q^{33} +6.40683 q^{34} -2.51725 q^{35} +5.70457 q^{36} -8.07978 q^{37} -5.99023 q^{38} +8.96936 q^{39} +4.23038 q^{40} -1.38721 q^{41} -25.9760 q^{42} +6.93078 q^{43} +18.2136 q^{44} -0.590855 q^{45} +3.18818 q^{46} -3.62546 q^{47} +23.1371 q^{48} +16.1808 q^{49} +12.5482 q^{50} -4.90452 q^{51} +22.2784 q^{52} +9.49752 q^{53} +10.0885 q^{54} -1.88649 q^{55} -38.9566 q^{56} +4.58561 q^{57} +3.30161 q^{58} +2.47468 q^{59} -5.36349 q^{60} -0.360298 q^{61} +3.78106 q^{62} +5.44105 q^{63} +14.5078 q^{64} -2.30751 q^{65} -19.4670 q^{66} +4.70398 q^{67} -12.1820 q^{68} -2.44060 q^{69} +6.68273 q^{70} -5.24469 q^{71} -9.14399 q^{72} +10.8620 q^{73} +21.4500 q^{74} -9.60580 q^{75} +11.3899 q^{76} +17.3722 q^{77} -23.8116 q^{78} +14.8876 q^{79} -5.95238 q^{80} -11.1132 q^{81} +3.68272 q^{82} +10.4213 q^{83} +49.3911 q^{84} +1.26177 q^{85} -18.3996 q^{86} -2.52743 q^{87} -29.1950 q^{88} +11.1368 q^{89} +1.56859 q^{90} +21.2493 q^{91} -6.06205 q^{92} -2.89445 q^{93} +9.62477 q^{94} -1.17972 q^{95} -28.5364 q^{96} -10.2611 q^{97} -42.9563 q^{98} +4.07766 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 287 q + 21 q^{2} + 29 q^{3} + 319 q^{4} + 19 q^{5} + 15 q^{6} + 52 q^{7} + 60 q^{8} + 352 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 287 q + 21 q^{2} + 29 q^{3} + 319 q^{4} + 19 q^{5} + 15 q^{6} + 52 q^{7} + 60 q^{8} + 352 q^{9} + 38 q^{10} + 32 q^{11} + 80 q^{12} + 86 q^{13} + 14 q^{14} + 41 q^{15} + 375 q^{16} + 59 q^{17} + 93 q^{18} + 39 q^{19} + 27 q^{20} + 51 q^{21} + 99 q^{22} + 68 q^{23} + 31 q^{24} + 492 q^{25} + 19 q^{26} + 107 q^{27} + 142 q^{28} + 39 q^{29} + 12 q^{30} + 104 q^{31} + 131 q^{32} + 139 q^{33} + 71 q^{34} - 5 q^{35} + 410 q^{36} + 298 q^{37} + 19 q^{38} + 37 q^{39} + 98 q^{40} + 90 q^{41} + 32 q^{42} + 105 q^{43} + 85 q^{44} + 73 q^{45} + 97 q^{46} + 66 q^{47} + 161 q^{48} + 473 q^{49} + 85 q^{50} + 34 q^{51} + 179 q^{52} + 95 q^{53} + 28 q^{54} + 62 q^{55} + 16 q^{56} + 247 q^{57} + 247 q^{58} + 32 q^{59} + 51 q^{60} + 106 q^{61} + 22 q^{62} + 104 q^{63} + 480 q^{64} + 150 q^{65} - 27 q^{66} + 232 q^{67} + 88 q^{68} + 57 q^{69} + 123 q^{70} + 46 q^{71} + 240 q^{72} + 372 q^{73} + 13 q^{74} + 81 q^{75} + 82 q^{76} + 65 q^{77} + 154 q^{78} + 143 q^{79} + 17 q^{80} + 519 q^{81} + 98 q^{82} + 49 q^{83} + 79 q^{84} + 236 q^{85} + 61 q^{86} + 31 q^{87} + 254 q^{88} + 114 q^{89} + 36 q^{90} + 96 q^{91} + 151 q^{92} + 189 q^{93} + 8 q^{94} + 30 q^{95} + 23 q^{96} + 503 q^{97} + 91 q^{98} + 130 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.65477 −1.87721 −0.938604 0.344996i \(-0.887880\pi\)
−0.938604 + 0.344996i \(0.887880\pi\)
\(3\) 2.03227 1.17333 0.586665 0.809830i \(-0.300441\pi\)
0.586665 + 0.809830i \(0.300441\pi\)
\(4\) 5.04782 2.52391
\(5\) −0.522833 −0.233818 −0.116909 0.993143i \(-0.537299\pi\)
−0.116909 + 0.993143i \(0.537299\pi\)
\(6\) −5.39521 −2.20258
\(7\) 4.81464 1.81976 0.909882 0.414867i \(-0.136172\pi\)
0.909882 + 0.414867i \(0.136172\pi\)
\(8\) −8.09128 −2.86070
\(9\) 1.13010 0.376701
\(10\) 1.38800 0.438925
\(11\) 3.60821 1.08792 0.543958 0.839112i \(-0.316925\pi\)
0.543958 + 0.839112i \(0.316925\pi\)
\(12\) 10.2585 2.96138
\(13\) 4.41348 1.22408 0.612039 0.790828i \(-0.290350\pi\)
0.612039 + 0.790828i \(0.290350\pi\)
\(14\) −12.7818 −3.41608
\(15\) −1.06253 −0.274345
\(16\) 11.3849 2.84622
\(17\) −2.41333 −0.585318 −0.292659 0.956217i \(-0.594540\pi\)
−0.292659 + 0.956217i \(0.594540\pi\)
\(18\) −3.00017 −0.707147
\(19\) 2.25640 0.517654 0.258827 0.965924i \(-0.416664\pi\)
0.258827 + 0.965924i \(0.416664\pi\)
\(20\) −2.63917 −0.590135
\(21\) 9.78463 2.13518
\(22\) −9.57898 −2.04225
\(23\) −1.20092 −0.250410 −0.125205 0.992131i \(-0.539959\pi\)
−0.125205 + 0.992131i \(0.539959\pi\)
\(24\) −16.4436 −3.35654
\(25\) −4.72665 −0.945329
\(26\) −11.7168 −2.29785
\(27\) −3.80012 −0.731334
\(28\) 24.3035 4.59292
\(29\) −1.24365 −0.230940 −0.115470 0.993311i \(-0.536837\pi\)
−0.115470 + 0.993311i \(0.536837\pi\)
\(30\) 2.82079 0.515003
\(31\) −1.42425 −0.255803 −0.127901 0.991787i \(-0.540824\pi\)
−0.127901 + 0.991787i \(0.540824\pi\)
\(32\) −14.0417 −2.48224
\(33\) 7.33285 1.27648
\(34\) 6.40683 1.09876
\(35\) −2.51725 −0.425493
\(36\) 5.70457 0.950761
\(37\) −8.07978 −1.32831 −0.664154 0.747596i \(-0.731208\pi\)
−0.664154 + 0.747596i \(0.731208\pi\)
\(38\) −5.99023 −0.971744
\(39\) 8.96936 1.43625
\(40\) 4.23038 0.668882
\(41\) −1.38721 −0.216645 −0.108323 0.994116i \(-0.534548\pi\)
−0.108323 + 0.994116i \(0.534548\pi\)
\(42\) −25.9760 −4.00818
\(43\) 6.93078 1.05693 0.528467 0.848954i \(-0.322767\pi\)
0.528467 + 0.848954i \(0.322767\pi\)
\(44\) 18.2136 2.74581
\(45\) −0.590855 −0.0880795
\(46\) 3.18818 0.470071
\(47\) −3.62546 −0.528827 −0.264414 0.964409i \(-0.585178\pi\)
−0.264414 + 0.964409i \(0.585178\pi\)
\(48\) 23.1371 3.33955
\(49\) 16.1808 2.31154
\(50\) 12.5482 1.77458
\(51\) −4.90452 −0.686770
\(52\) 22.2784 3.08946
\(53\) 9.49752 1.30458 0.652292 0.757967i \(-0.273807\pi\)
0.652292 + 0.757967i \(0.273807\pi\)
\(54\) 10.0885 1.37287
\(55\) −1.88649 −0.254374
\(56\) −38.9566 −5.20580
\(57\) 4.58561 0.607378
\(58\) 3.30161 0.433523
\(59\) 2.47468 0.322175 0.161088 0.986940i \(-0.448500\pi\)
0.161088 + 0.986940i \(0.448500\pi\)
\(60\) −5.36349 −0.692423
\(61\) −0.360298 −0.0461314 −0.0230657 0.999734i \(-0.507343\pi\)
−0.0230657 + 0.999734i \(0.507343\pi\)
\(62\) 3.78106 0.480195
\(63\) 5.44105 0.685508
\(64\) 14.5078 1.81347
\(65\) −2.30751 −0.286211
\(66\) −19.4670 −2.39623
\(67\) 4.70398 0.574682 0.287341 0.957828i \(-0.407229\pi\)
0.287341 + 0.957828i \(0.407229\pi\)
\(68\) −12.1820 −1.47729
\(69\) −2.44060 −0.293813
\(70\) 6.68273 0.798739
\(71\) −5.24469 −0.622430 −0.311215 0.950339i \(-0.600736\pi\)
−0.311215 + 0.950339i \(0.600736\pi\)
\(72\) −9.14399 −1.07763
\(73\) 10.8620 1.27130 0.635651 0.771976i \(-0.280732\pi\)
0.635651 + 0.771976i \(0.280732\pi\)
\(74\) 21.4500 2.49351
\(75\) −9.60580 −1.10918
\(76\) 11.3899 1.30651
\(77\) 17.3722 1.97975
\(78\) −23.8116 −2.69613
\(79\) 14.8876 1.67499 0.837495 0.546446i \(-0.184019\pi\)
0.837495 + 0.546446i \(0.184019\pi\)
\(80\) −5.95238 −0.665496
\(81\) −11.1132 −1.23480
\(82\) 3.68272 0.406688
\(83\) 10.4213 1.14389 0.571945 0.820292i \(-0.306189\pi\)
0.571945 + 0.820292i \(0.306189\pi\)
\(84\) 49.3911 5.38901
\(85\) 1.26177 0.136858
\(86\) −18.3996 −1.98408
\(87\) −2.52743 −0.270969
\(88\) −29.1950 −3.11220
\(89\) 11.1368 1.18049 0.590247 0.807223i \(-0.299030\pi\)
0.590247 + 0.807223i \(0.299030\pi\)
\(90\) 1.56859 0.165344
\(91\) 21.2493 2.22753
\(92\) −6.06205 −0.632012
\(93\) −2.89445 −0.300141
\(94\) 9.62477 0.992719
\(95\) −1.17972 −0.121037
\(96\) −28.5364 −2.91249
\(97\) −10.2611 −1.04185 −0.520927 0.853601i \(-0.674414\pi\)
−0.520927 + 0.853601i \(0.674414\pi\)
\(98\) −42.9563 −4.33924
\(99\) 4.07766 0.409820
\(100\) −23.8593 −2.38593
\(101\) −4.84754 −0.482348 −0.241174 0.970482i \(-0.577532\pi\)
−0.241174 + 0.970482i \(0.577532\pi\)
\(102\) 13.0204 1.28921
\(103\) 5.34844 0.526997 0.263499 0.964660i \(-0.415124\pi\)
0.263499 + 0.964660i \(0.415124\pi\)
\(104\) −35.7107 −3.50172
\(105\) −5.11572 −0.499244
\(106\) −25.2138 −2.44898
\(107\) −8.84373 −0.854956 −0.427478 0.904026i \(-0.640598\pi\)
−0.427478 + 0.904026i \(0.640598\pi\)
\(108\) −19.1824 −1.84582
\(109\) −3.69398 −0.353819 −0.176909 0.984227i \(-0.556610\pi\)
−0.176909 + 0.984227i \(0.556610\pi\)
\(110\) 5.00821 0.477514
\(111\) −16.4203 −1.55854
\(112\) 54.8140 5.17944
\(113\) 8.84350 0.831927 0.415963 0.909381i \(-0.363444\pi\)
0.415963 + 0.909381i \(0.363444\pi\)
\(114\) −12.1737 −1.14018
\(115\) 0.627882 0.0585503
\(116\) −6.27773 −0.582873
\(117\) 4.98769 0.461112
\(118\) −6.56970 −0.604790
\(119\) −11.6193 −1.06514
\(120\) 8.59726 0.784819
\(121\) 2.01919 0.183563
\(122\) 0.956509 0.0865983
\(123\) −2.81917 −0.254196
\(124\) −7.18936 −0.645624
\(125\) 5.08541 0.454853
\(126\) −14.4448 −1.28684
\(127\) 14.6220 1.29749 0.648745 0.761006i \(-0.275294\pi\)
0.648745 + 0.761006i \(0.275294\pi\)
\(128\) −10.4314 −0.922017
\(129\) 14.0852 1.24013
\(130\) 6.12591 0.537278
\(131\) 3.34402 0.292168 0.146084 0.989272i \(-0.453333\pi\)
0.146084 + 0.989272i \(0.453333\pi\)
\(132\) 37.0149 3.22173
\(133\) 10.8638 0.942008
\(134\) −12.4880 −1.07880
\(135\) 1.98683 0.170999
\(136\) 19.5269 1.67442
\(137\) 13.0448 1.11449 0.557247 0.830347i \(-0.311858\pi\)
0.557247 + 0.830347i \(0.311858\pi\)
\(138\) 6.47923 0.551548
\(139\) 21.5263 1.82583 0.912917 0.408144i \(-0.133824\pi\)
0.912917 + 0.408144i \(0.133824\pi\)
\(140\) −12.7066 −1.07391
\(141\) −7.36789 −0.620489
\(142\) 13.9235 1.16843
\(143\) 15.9248 1.33169
\(144\) 12.8661 1.07217
\(145\) 0.650221 0.0539980
\(146\) −28.8362 −2.38650
\(147\) 32.8836 2.71220
\(148\) −40.7853 −3.35253
\(149\) −12.2235 −1.00139 −0.500694 0.865624i \(-0.666922\pi\)
−0.500694 + 0.865624i \(0.666922\pi\)
\(150\) 25.5012 2.08217
\(151\) 2.05134 0.166935 0.0834676 0.996510i \(-0.473400\pi\)
0.0834676 + 0.996510i \(0.473400\pi\)
\(152\) −18.2572 −1.48085
\(153\) −2.72731 −0.220490
\(154\) −46.1194 −3.71641
\(155\) 0.744644 0.0598113
\(156\) 45.2757 3.62496
\(157\) 1.72793 0.137904 0.0689520 0.997620i \(-0.478034\pi\)
0.0689520 + 0.997620i \(0.478034\pi\)
\(158\) −39.5233 −3.14430
\(159\) 19.3015 1.53071
\(160\) 7.34145 0.580392
\(161\) −5.78202 −0.455687
\(162\) 29.5030 2.31797
\(163\) −15.1929 −1.19000 −0.594999 0.803727i \(-0.702847\pi\)
−0.594999 + 0.803727i \(0.702847\pi\)
\(164\) −7.00237 −0.546793
\(165\) −3.83385 −0.298465
\(166\) −27.6663 −2.14732
\(167\) −19.1259 −1.48001 −0.740004 0.672603i \(-0.765176\pi\)
−0.740004 + 0.672603i \(0.765176\pi\)
\(168\) −79.1702 −6.10811
\(169\) 6.47877 0.498367
\(170\) −3.34970 −0.256910
\(171\) 2.54997 0.195001
\(172\) 34.9853 2.66761
\(173\) 18.1718 1.38158 0.690789 0.723056i \(-0.257263\pi\)
0.690789 + 0.723056i \(0.257263\pi\)
\(174\) 6.70975 0.508665
\(175\) −22.7571 −1.72028
\(176\) 41.0790 3.09645
\(177\) 5.02920 0.378018
\(178\) −29.5656 −2.21603
\(179\) −16.0253 −1.19778 −0.598892 0.800829i \(-0.704392\pi\)
−0.598892 + 0.800829i \(0.704392\pi\)
\(180\) −2.98253 −0.222305
\(181\) 12.5306 0.931391 0.465695 0.884945i \(-0.345804\pi\)
0.465695 + 0.884945i \(0.345804\pi\)
\(182\) −56.4121 −4.18154
\(183\) −0.732221 −0.0541274
\(184\) 9.71700 0.716347
\(185\) 4.22437 0.310582
\(186\) 7.68412 0.563427
\(187\) −8.70779 −0.636777
\(188\) −18.3007 −1.33471
\(189\) −18.2962 −1.33086
\(190\) 3.13189 0.227211
\(191\) −5.05883 −0.366044 −0.183022 0.983109i \(-0.558588\pi\)
−0.183022 + 0.983109i \(0.558588\pi\)
\(192\) 29.4836 2.12780
\(193\) −9.52018 −0.685278 −0.342639 0.939467i \(-0.611321\pi\)
−0.342639 + 0.939467i \(0.611321\pi\)
\(194\) 27.2408 1.95578
\(195\) −4.68947 −0.335820
\(196\) 81.6777 5.83412
\(197\) 11.7235 0.835264 0.417632 0.908616i \(-0.362860\pi\)
0.417632 + 0.908616i \(0.362860\pi\)
\(198\) −10.8253 −0.769317
\(199\) 1.94989 0.138224 0.0691119 0.997609i \(-0.477983\pi\)
0.0691119 + 0.997609i \(0.477983\pi\)
\(200\) 38.2446 2.70430
\(201\) 9.55973 0.674292
\(202\) 12.8691 0.905467
\(203\) −5.98774 −0.420257
\(204\) −24.7571 −1.73335
\(205\) 0.725277 0.0506555
\(206\) −14.1989 −0.989284
\(207\) −1.35717 −0.0943297
\(208\) 50.2468 3.48399
\(209\) 8.14157 0.563164
\(210\) 13.5811 0.937184
\(211\) 11.4882 0.790883 0.395442 0.918491i \(-0.370592\pi\)
0.395442 + 0.918491i \(0.370592\pi\)
\(212\) 47.9418 3.29266
\(213\) −10.6586 −0.730316
\(214\) 23.4781 1.60493
\(215\) −3.62364 −0.247130
\(216\) 30.7479 2.09213
\(217\) −6.85725 −0.465501
\(218\) 9.80667 0.664192
\(219\) 22.0745 1.49166
\(220\) −9.52267 −0.642018
\(221\) −10.6512 −0.716474
\(222\) 43.5921 2.92571
\(223\) 15.6030 1.04486 0.522428 0.852684i \(-0.325027\pi\)
0.522428 + 0.852684i \(0.325027\pi\)
\(224\) −67.6057 −4.51709
\(225\) −5.34160 −0.356107
\(226\) −23.4775 −1.56170
\(227\) 6.56721 0.435881 0.217940 0.975962i \(-0.430066\pi\)
0.217940 + 0.975962i \(0.430066\pi\)
\(228\) 23.1473 1.53297
\(229\) 1.86678 0.123360 0.0616802 0.998096i \(-0.480354\pi\)
0.0616802 + 0.998096i \(0.480354\pi\)
\(230\) −1.66688 −0.109911
\(231\) 35.3050 2.32290
\(232\) 10.0627 0.660650
\(233\) −21.8503 −1.43146 −0.715732 0.698375i \(-0.753907\pi\)
−0.715732 + 0.698375i \(0.753907\pi\)
\(234\) −13.2412 −0.865603
\(235\) 1.89551 0.123649
\(236\) 12.4917 0.813142
\(237\) 30.2556 1.96531
\(238\) 30.8466 1.99949
\(239\) 13.4085 0.867321 0.433661 0.901076i \(-0.357222\pi\)
0.433661 + 0.901076i \(0.357222\pi\)
\(240\) −12.0968 −0.780846
\(241\) 5.48297 0.353189 0.176595 0.984284i \(-0.443492\pi\)
0.176595 + 0.984284i \(0.443492\pi\)
\(242\) −5.36050 −0.344586
\(243\) −11.1846 −0.717490
\(244\) −1.81872 −0.116432
\(245\) −8.45984 −0.540479
\(246\) 7.48426 0.477179
\(247\) 9.95857 0.633649
\(248\) 11.5240 0.731775
\(249\) 21.1789 1.34216
\(250\) −13.5006 −0.853853
\(251\) 4.52226 0.285443 0.142721 0.989763i \(-0.454415\pi\)
0.142721 + 0.989763i \(0.454415\pi\)
\(252\) 27.4654 1.73016
\(253\) −4.33318 −0.272425
\(254\) −38.8180 −2.43566
\(255\) 2.56424 0.160579
\(256\) −1.32241 −0.0826507
\(257\) 14.3919 0.897742 0.448871 0.893597i \(-0.351826\pi\)
0.448871 + 0.893597i \(0.351826\pi\)
\(258\) −37.3930 −2.32798
\(259\) −38.9012 −2.41721
\(260\) −11.6479 −0.722372
\(261\) −1.40546 −0.0869955
\(262\) −8.87761 −0.548461
\(263\) −2.92231 −0.180197 −0.0900987 0.995933i \(-0.528718\pi\)
−0.0900987 + 0.995933i \(0.528718\pi\)
\(264\) −59.3321 −3.65164
\(265\) −4.96561 −0.305035
\(266\) −28.8408 −1.76834
\(267\) 22.6328 1.38511
\(268\) 23.7448 1.45045
\(269\) 14.6405 0.892645 0.446323 0.894872i \(-0.352733\pi\)
0.446323 + 0.894872i \(0.352733\pi\)
\(270\) −5.27458 −0.321001
\(271\) 4.83669 0.293808 0.146904 0.989151i \(-0.453069\pi\)
0.146904 + 0.989151i \(0.453069\pi\)
\(272\) −27.4754 −1.66594
\(273\) 43.1842 2.61363
\(274\) −34.6310 −2.09214
\(275\) −17.0547 −1.02844
\(276\) −12.3197 −0.741558
\(277\) −25.9166 −1.55718 −0.778590 0.627534i \(-0.784065\pi\)
−0.778590 + 0.627534i \(0.784065\pi\)
\(278\) −57.1474 −3.42747
\(279\) −1.60955 −0.0963613
\(280\) 20.3678 1.21721
\(281\) 21.7773 1.29912 0.649561 0.760309i \(-0.274953\pi\)
0.649561 + 0.760309i \(0.274953\pi\)
\(282\) 19.5601 1.16479
\(283\) 17.3429 1.03093 0.515464 0.856911i \(-0.327620\pi\)
0.515464 + 0.856911i \(0.327620\pi\)
\(284\) −26.4743 −1.57096
\(285\) −2.39750 −0.142016
\(286\) −42.2766 −2.49987
\(287\) −6.67890 −0.394243
\(288\) −15.8686 −0.935064
\(289\) −11.1759 −0.657403
\(290\) −1.72619 −0.101365
\(291\) −20.8532 −1.22244
\(292\) 54.8295 3.20865
\(293\) 1.49021 0.0870589 0.0435295 0.999052i \(-0.486140\pi\)
0.0435295 + 0.999052i \(0.486140\pi\)
\(294\) −87.2986 −5.09136
\(295\) −1.29384 −0.0753303
\(296\) 65.3757 3.79989
\(297\) −13.7117 −0.795631
\(298\) 32.4506 1.87981
\(299\) −5.30025 −0.306521
\(300\) −48.4884 −2.79948
\(301\) 33.3692 1.92337
\(302\) −5.44583 −0.313372
\(303\) −9.85148 −0.565953
\(304\) 25.6888 1.47335
\(305\) 0.188376 0.0107864
\(306\) 7.24039 0.413906
\(307\) 21.4206 1.22254 0.611270 0.791422i \(-0.290659\pi\)
0.611270 + 0.791422i \(0.290659\pi\)
\(308\) 87.6920 4.99672
\(309\) 10.8694 0.618341
\(310\) −1.97686 −0.112278
\(311\) −23.7181 −1.34493 −0.672466 0.740128i \(-0.734765\pi\)
−0.672466 + 0.740128i \(0.734765\pi\)
\(312\) −72.5735 −4.10867
\(313\) −9.15550 −0.517499 −0.258750 0.965944i \(-0.583310\pi\)
−0.258750 + 0.965944i \(0.583310\pi\)
\(314\) −4.58727 −0.258874
\(315\) −2.84476 −0.160284
\(316\) 75.1501 4.22752
\(317\) −23.6848 −1.33027 −0.665137 0.746721i \(-0.731627\pi\)
−0.665137 + 0.746721i \(0.731627\pi\)
\(318\) −51.2411 −2.87346
\(319\) −4.48736 −0.251244
\(320\) −7.58512 −0.424021
\(321\) −17.9728 −1.00314
\(322\) 15.3499 0.855419
\(323\) −5.44543 −0.302992
\(324\) −56.0973 −3.11652
\(325\) −20.8609 −1.15716
\(326\) 40.3336 2.23387
\(327\) −7.50714 −0.415146
\(328\) 11.2243 0.619757
\(329\) −17.4553 −0.962341
\(330\) 10.1780 0.560281
\(331\) −18.8800 −1.03774 −0.518868 0.854854i \(-0.673647\pi\)
−0.518868 + 0.854854i \(0.673647\pi\)
\(332\) 52.6051 2.88708
\(333\) −9.13099 −0.500375
\(334\) 50.7749 2.77828
\(335\) −2.45939 −0.134371
\(336\) 111.397 6.07719
\(337\) −32.3827 −1.76400 −0.881999 0.471251i \(-0.843803\pi\)
−0.881999 + 0.471251i \(0.843803\pi\)
\(338\) −17.1997 −0.935538
\(339\) 17.9723 0.976124
\(340\) 6.36917 0.345417
\(341\) −5.13900 −0.278292
\(342\) −6.76959 −0.366057
\(343\) 44.2022 2.38669
\(344\) −56.0788 −3.02357
\(345\) 1.27602 0.0686987
\(346\) −48.2421 −2.59351
\(347\) 13.0596 0.701075 0.350537 0.936549i \(-0.385999\pi\)
0.350537 + 0.936549i \(0.385999\pi\)
\(348\) −12.7580 −0.683902
\(349\) 6.31506 0.338037 0.169019 0.985613i \(-0.445940\pi\)
0.169019 + 0.985613i \(0.445940\pi\)
\(350\) 60.4150 3.22932
\(351\) −16.7718 −0.895210
\(352\) −50.6654 −2.70047
\(353\) −35.1580 −1.87127 −0.935637 0.352965i \(-0.885174\pi\)
−0.935637 + 0.352965i \(0.885174\pi\)
\(354\) −13.3514 −0.709618
\(355\) 2.74210 0.145535
\(356\) 56.2163 2.97946
\(357\) −23.6135 −1.24976
\(358\) 42.5435 2.24849
\(359\) −3.15282 −0.166400 −0.0831998 0.996533i \(-0.526514\pi\)
−0.0831998 + 0.996533i \(0.526514\pi\)
\(360\) 4.78077 0.251969
\(361\) −13.9087 −0.732034
\(362\) −33.2659 −1.74841
\(363\) 4.10353 0.215380
\(364\) 107.263 5.62209
\(365\) −5.67901 −0.297253
\(366\) 1.94388 0.101608
\(367\) −4.52578 −0.236244 −0.118122 0.992999i \(-0.537687\pi\)
−0.118122 + 0.992999i \(0.537687\pi\)
\(368\) −13.6723 −0.712720
\(369\) −1.56769 −0.0816106
\(370\) −11.2147 −0.583027
\(371\) 45.7272 2.37404
\(372\) −14.6107 −0.757529
\(373\) −28.8487 −1.49373 −0.746866 0.664975i \(-0.768442\pi\)
−0.746866 + 0.664975i \(0.768442\pi\)
\(374\) 23.1172 1.19536
\(375\) 10.3349 0.533692
\(376\) 29.3346 1.51282
\(377\) −5.48883 −0.282689
\(378\) 48.5724 2.49829
\(379\) −0.655969 −0.0336949 −0.0168474 0.999858i \(-0.505363\pi\)
−0.0168474 + 0.999858i \(0.505363\pi\)
\(380\) −5.95502 −0.305486
\(381\) 29.7157 1.52238
\(382\) 13.4300 0.687141
\(383\) −13.9227 −0.711415 −0.355707 0.934597i \(-0.615760\pi\)
−0.355707 + 0.934597i \(0.615760\pi\)
\(384\) −21.1994 −1.08183
\(385\) −9.08278 −0.462901
\(386\) 25.2739 1.28641
\(387\) 7.83250 0.398148
\(388\) −51.7961 −2.62955
\(389\) 12.2774 0.622491 0.311246 0.950330i \(-0.399254\pi\)
0.311246 + 0.950330i \(0.399254\pi\)
\(390\) 12.4495 0.630404
\(391\) 2.89822 0.146569
\(392\) −130.923 −6.61262
\(393\) 6.79593 0.342810
\(394\) −31.1232 −1.56796
\(395\) −7.78374 −0.391642
\(396\) 20.5833 1.03435
\(397\) −22.7736 −1.14297 −0.571486 0.820612i \(-0.693633\pi\)
−0.571486 + 0.820612i \(0.693633\pi\)
\(398\) −5.17651 −0.259475
\(399\) 22.0781 1.10529
\(400\) −53.8122 −2.69061
\(401\) −38.3309 −1.91416 −0.957078 0.289830i \(-0.906401\pi\)
−0.957078 + 0.289830i \(0.906401\pi\)
\(402\) −25.3789 −1.26579
\(403\) −6.28589 −0.313123
\(404\) −24.4695 −1.21740
\(405\) 5.81033 0.288718
\(406\) 15.8961 0.788909
\(407\) −29.1536 −1.44509
\(408\) 39.6838 1.96464
\(409\) 4.26725 0.211002 0.105501 0.994419i \(-0.466355\pi\)
0.105501 + 0.994419i \(0.466355\pi\)
\(410\) −1.92545 −0.0950910
\(411\) 26.5105 1.30767
\(412\) 26.9980 1.33009
\(413\) 11.9147 0.586283
\(414\) 3.60297 0.177077
\(415\) −5.44862 −0.267462
\(416\) −61.9726 −3.03846
\(417\) 43.7471 2.14231
\(418\) −21.6140 −1.05718
\(419\) −4.44115 −0.216965 −0.108482 0.994098i \(-0.534599\pi\)
−0.108482 + 0.994098i \(0.534599\pi\)
\(420\) −25.8233 −1.26005
\(421\) 9.01192 0.439214 0.219607 0.975588i \(-0.429523\pi\)
0.219607 + 0.975588i \(0.429523\pi\)
\(422\) −30.4987 −1.48465
\(423\) −4.09715 −0.199210
\(424\) −76.8471 −3.73202
\(425\) 11.4069 0.553318
\(426\) 28.2962 1.37095
\(427\) −1.73471 −0.0839483
\(428\) −44.6416 −2.15783
\(429\) 32.3633 1.56252
\(430\) 9.61993 0.463914
\(431\) 5.67668 0.273436 0.136718 0.990610i \(-0.456345\pi\)
0.136718 + 0.990610i \(0.456345\pi\)
\(432\) −43.2639 −2.08154
\(433\) −9.64897 −0.463700 −0.231850 0.972752i \(-0.574478\pi\)
−0.231850 + 0.972752i \(0.574478\pi\)
\(434\) 18.2045 0.873842
\(435\) 1.32142 0.0633574
\(436\) −18.6465 −0.893007
\(437\) −2.70976 −0.129626
\(438\) −58.6028 −2.80015
\(439\) 8.83641 0.421739 0.210869 0.977514i \(-0.432371\pi\)
0.210869 + 0.977514i \(0.432371\pi\)
\(440\) 15.2641 0.727688
\(441\) 18.2860 0.870760
\(442\) 28.2764 1.34497
\(443\) 34.6655 1.64701 0.823504 0.567310i \(-0.192016\pi\)
0.823504 + 0.567310i \(0.192016\pi\)
\(444\) −82.8865 −3.93362
\(445\) −5.82266 −0.276020
\(446\) −41.4225 −1.96141
\(447\) −24.8414 −1.17496
\(448\) 69.8496 3.30008
\(449\) 11.9749 0.565130 0.282565 0.959248i \(-0.408815\pi\)
0.282565 + 0.959248i \(0.408815\pi\)
\(450\) 14.1807 0.668487
\(451\) −5.00533 −0.235692
\(452\) 44.6404 2.09971
\(453\) 4.16886 0.195870
\(454\) −17.4344 −0.818239
\(455\) −11.1098 −0.520837
\(456\) −37.1034 −1.73753
\(457\) −21.8291 −1.02112 −0.510560 0.859842i \(-0.670562\pi\)
−0.510560 + 0.859842i \(0.670562\pi\)
\(458\) −4.95588 −0.231573
\(459\) 9.17094 0.428063
\(460\) 3.16944 0.147776
\(461\) 11.8226 0.550634 0.275317 0.961354i \(-0.411217\pi\)
0.275317 + 0.961354i \(0.411217\pi\)
\(462\) −93.7268 −4.36057
\(463\) 9.71467 0.451479 0.225740 0.974188i \(-0.427520\pi\)
0.225740 + 0.974188i \(0.427520\pi\)
\(464\) −14.1588 −0.657306
\(465\) 1.51332 0.0701783
\(466\) 58.0077 2.68715
\(467\) −17.4011 −0.805228 −0.402614 0.915370i \(-0.631898\pi\)
−0.402614 + 0.915370i \(0.631898\pi\)
\(468\) 25.1770 1.16381
\(469\) 22.6480 1.04579
\(470\) −5.03214 −0.232115
\(471\) 3.51162 0.161807
\(472\) −20.0233 −0.921647
\(473\) 25.0077 1.14986
\(474\) −80.3218 −3.68930
\(475\) −10.6652 −0.489353
\(476\) −58.6522 −2.68832
\(477\) 10.7332 0.491439
\(478\) −35.5964 −1.62814
\(479\) −24.6594 −1.12672 −0.563358 0.826213i \(-0.690491\pi\)
−0.563358 + 0.826213i \(0.690491\pi\)
\(480\) 14.9198 0.680991
\(481\) −35.6599 −1.62595
\(482\) −14.5561 −0.663010
\(483\) −11.7506 −0.534670
\(484\) 10.1925 0.463296
\(485\) 5.36483 0.243604
\(486\) 29.6925 1.34688
\(487\) 16.7779 0.760280 0.380140 0.924929i \(-0.375876\pi\)
0.380140 + 0.924929i \(0.375876\pi\)
\(488\) 2.91527 0.131968
\(489\) −30.8759 −1.39626
\(490\) 22.4590 1.01459
\(491\) 13.8578 0.625396 0.312698 0.949853i \(-0.398767\pi\)
0.312698 + 0.949853i \(0.398767\pi\)
\(492\) −14.2307 −0.641569
\(493\) 3.00134 0.135173
\(494\) −26.4377 −1.18949
\(495\) −2.13193 −0.0958232
\(496\) −16.2149 −0.728070
\(497\) −25.2513 −1.13268
\(498\) −56.2253 −2.51952
\(499\) −29.3963 −1.31596 −0.657979 0.753036i \(-0.728589\pi\)
−0.657979 + 0.753036i \(0.728589\pi\)
\(500\) 25.6702 1.14801
\(501\) −38.8689 −1.73654
\(502\) −12.0056 −0.535835
\(503\) 2.86864 0.127906 0.0639532 0.997953i \(-0.479629\pi\)
0.0639532 + 0.997953i \(0.479629\pi\)
\(504\) −44.0250 −1.96103
\(505\) 2.53445 0.112782
\(506\) 11.5036 0.511398
\(507\) 13.1666 0.584748
\(508\) 73.8091 3.27475
\(509\) −5.52853 −0.245048 −0.122524 0.992466i \(-0.539099\pi\)
−0.122524 + 0.992466i \(0.539099\pi\)
\(510\) −6.80748 −0.301440
\(511\) 52.2967 2.31347
\(512\) 24.3736 1.07717
\(513\) −8.57461 −0.378578
\(514\) −38.2072 −1.68525
\(515\) −2.79634 −0.123221
\(516\) 71.0995 3.12998
\(517\) −13.0814 −0.575320
\(518\) 103.274 4.53760
\(519\) 36.9300 1.62105
\(520\) 18.6707 0.818764
\(521\) 32.4592 1.42206 0.711031 0.703161i \(-0.248229\pi\)
0.711031 + 0.703161i \(0.248229\pi\)
\(522\) 3.73117 0.163309
\(523\) −39.8265 −1.74149 −0.870745 0.491735i \(-0.836363\pi\)
−0.870745 + 0.491735i \(0.836363\pi\)
\(524\) 16.8800 0.737407
\(525\) −46.2485 −2.01845
\(526\) 7.75807 0.338268
\(527\) 3.43718 0.149726
\(528\) 83.4834 3.63315
\(529\) −21.5578 −0.937295
\(530\) 13.1826 0.572615
\(531\) 2.79664 0.121364
\(532\) 54.8383 2.37754
\(533\) −6.12240 −0.265191
\(534\) −60.0851 −2.60014
\(535\) 4.62379 0.199904
\(536\) −38.0612 −1.64399
\(537\) −32.5676 −1.40540
\(538\) −38.8671 −1.67568
\(539\) 58.3837 2.51476
\(540\) 10.0292 0.431586
\(541\) −12.9623 −0.557294 −0.278647 0.960394i \(-0.589886\pi\)
−0.278647 + 0.960394i \(0.589886\pi\)
\(542\) −12.8403 −0.551539
\(543\) 25.4655 1.09283
\(544\) 33.8872 1.45290
\(545\) 1.93133 0.0827292
\(546\) −114.644 −4.90633
\(547\) 7.27574 0.311088 0.155544 0.987829i \(-0.450287\pi\)
0.155544 + 0.987829i \(0.450287\pi\)
\(548\) 65.8479 2.81288
\(549\) −0.407174 −0.0173778
\(550\) 45.2765 1.93060
\(551\) −2.80618 −0.119547
\(552\) 19.7475 0.840511
\(553\) 71.6786 3.04808
\(554\) 68.8028 2.92315
\(555\) 8.58505 0.364415
\(556\) 108.661 4.60825
\(557\) 9.87120 0.418256 0.209128 0.977888i \(-0.432937\pi\)
0.209128 + 0.977888i \(0.432937\pi\)
\(558\) 4.27299 0.180890
\(559\) 30.5888 1.29377
\(560\) −28.6586 −1.21105
\(561\) −17.6965 −0.747149
\(562\) −57.8137 −2.43872
\(563\) 22.7966 0.960763 0.480382 0.877060i \(-0.340498\pi\)
0.480382 + 0.877060i \(0.340498\pi\)
\(564\) −37.1918 −1.56606
\(565\) −4.62367 −0.194519
\(566\) −46.0415 −1.93527
\(567\) −53.5060 −2.24704
\(568\) 42.4363 1.78059
\(569\) −36.3099 −1.52219 −0.761094 0.648641i \(-0.775338\pi\)
−0.761094 + 0.648641i \(0.775338\pi\)
\(570\) 6.36483 0.266593
\(571\) −43.1428 −1.80547 −0.902734 0.430198i \(-0.858444\pi\)
−0.902734 + 0.430198i \(0.858444\pi\)
\(572\) 80.3853 3.36108
\(573\) −10.2809 −0.429490
\(574\) 17.7310 0.740076
\(575\) 5.67634 0.236720
\(576\) 16.3953 0.683136
\(577\) 35.5300 1.47913 0.739567 0.673083i \(-0.235030\pi\)
0.739567 + 0.673083i \(0.235030\pi\)
\(578\) 29.6694 1.23408
\(579\) −19.3475 −0.804057
\(580\) 3.28220 0.136286
\(581\) 50.1750 2.08161
\(582\) 55.3606 2.29477
\(583\) 34.2691 1.41928
\(584\) −87.8876 −3.63681
\(585\) −2.60773 −0.107816
\(586\) −3.95617 −0.163428
\(587\) −1.37204 −0.0566300 −0.0283150 0.999599i \(-0.509014\pi\)
−0.0283150 + 0.999599i \(0.509014\pi\)
\(588\) 165.991 6.84534
\(589\) −3.21368 −0.132417
\(590\) 3.43486 0.141411
\(591\) 23.8252 0.980039
\(592\) −91.9872 −3.78065
\(593\) 9.07464 0.372651 0.186326 0.982488i \(-0.440342\pi\)
0.186326 + 0.982488i \(0.440342\pi\)
\(594\) 36.4013 1.49357
\(595\) 6.07495 0.249049
\(596\) −61.7021 −2.52741
\(597\) 3.96269 0.162182
\(598\) 14.0710 0.575404
\(599\) 13.8286 0.565022 0.282511 0.959264i \(-0.408833\pi\)
0.282511 + 0.959264i \(0.408833\pi\)
\(600\) 77.7232 3.17304
\(601\) −21.5366 −0.878498 −0.439249 0.898365i \(-0.644755\pi\)
−0.439249 + 0.898365i \(0.644755\pi\)
\(602\) −88.5877 −3.61056
\(603\) 5.31599 0.216484
\(604\) 10.3548 0.421330
\(605\) −1.05570 −0.0429203
\(606\) 26.1535 1.06241
\(607\) −12.7145 −0.516066 −0.258033 0.966136i \(-0.583074\pi\)
−0.258033 + 0.966136i \(0.583074\pi\)
\(608\) −31.6837 −1.28494
\(609\) −12.1687 −0.493099
\(610\) −0.500094 −0.0202482
\(611\) −16.0009 −0.647326
\(612\) −13.7670 −0.556497
\(613\) −20.2443 −0.817659 −0.408830 0.912611i \(-0.634063\pi\)
−0.408830 + 0.912611i \(0.634063\pi\)
\(614\) −56.8670 −2.29496
\(615\) 1.47395 0.0594356
\(616\) −140.564 −5.66347
\(617\) −27.4499 −1.10509 −0.552546 0.833482i \(-0.686344\pi\)
−0.552546 + 0.833482i \(0.686344\pi\)
\(618\) −28.8559 −1.16076
\(619\) 26.1234 1.04999 0.524995 0.851105i \(-0.324067\pi\)
0.524995 + 0.851105i \(0.324067\pi\)
\(620\) 3.75883 0.150958
\(621\) 4.56366 0.183133
\(622\) 62.9663 2.52472
\(623\) 53.6195 2.14822
\(624\) 102.115 4.08787
\(625\) 20.9744 0.838977
\(626\) 24.3058 0.971454
\(627\) 16.5458 0.660777
\(628\) 8.72229 0.348057
\(629\) 19.4991 0.777482
\(630\) 7.55219 0.300886
\(631\) 27.9930 1.11438 0.557192 0.830384i \(-0.311879\pi\)
0.557192 + 0.830384i \(0.311879\pi\)
\(632\) −120.460 −4.79164
\(633\) 23.3472 0.927966
\(634\) 62.8779 2.49720
\(635\) −7.64484 −0.303376
\(636\) 97.4305 3.86337
\(637\) 71.4135 2.82951
\(638\) 11.9129 0.471637
\(639\) −5.92705 −0.234470
\(640\) 5.45389 0.215584
\(641\) −24.8962 −0.983342 −0.491671 0.870781i \(-0.663614\pi\)
−0.491671 + 0.870781i \(0.663614\pi\)
\(642\) 47.7138 1.88311
\(643\) 7.39794 0.291746 0.145873 0.989303i \(-0.453401\pi\)
0.145873 + 0.989303i \(0.453401\pi\)
\(644\) −29.1866 −1.15011
\(645\) −7.36419 −0.289965
\(646\) 14.4564 0.568779
\(647\) −44.9537 −1.76731 −0.883657 0.468136i \(-0.844926\pi\)
−0.883657 + 0.468136i \(0.844926\pi\)
\(648\) 89.9198 3.53238
\(649\) 8.92916 0.350500
\(650\) 55.3811 2.17222
\(651\) −13.9358 −0.546186
\(652\) −76.6909 −3.00345
\(653\) −33.4300 −1.30822 −0.654108 0.756401i \(-0.726956\pi\)
−0.654108 + 0.756401i \(0.726956\pi\)
\(654\) 19.9298 0.779316
\(655\) −1.74836 −0.0683141
\(656\) −15.7932 −0.616619
\(657\) 12.2752 0.478901
\(658\) 46.3398 1.80651
\(659\) 6.93984 0.270338 0.135169 0.990823i \(-0.456842\pi\)
0.135169 + 0.990823i \(0.456842\pi\)
\(660\) −19.3526 −0.753299
\(661\) −34.1413 −1.32794 −0.663972 0.747758i \(-0.731130\pi\)
−0.663972 + 0.747758i \(0.731130\pi\)
\(662\) 50.1220 1.94805
\(663\) −21.6460 −0.840660
\(664\) −84.3220 −3.27233
\(665\) −5.67993 −0.220258
\(666\) 24.2407 0.939309
\(667\) 1.49353 0.0578297
\(668\) −96.5442 −3.73541
\(669\) 31.7095 1.22596
\(670\) 6.52913 0.252242
\(671\) −1.30003 −0.0501872
\(672\) −137.393 −5.30004
\(673\) 15.7571 0.607393 0.303697 0.952769i \(-0.401779\pi\)
0.303697 + 0.952769i \(0.401779\pi\)
\(674\) 85.9688 3.31139
\(675\) 17.9618 0.691352
\(676\) 32.7037 1.25783
\(677\) 41.4036 1.59127 0.795634 0.605778i \(-0.207138\pi\)
0.795634 + 0.605778i \(0.207138\pi\)
\(678\) −47.7125 −1.83239
\(679\) −49.4034 −1.89593
\(680\) −10.2093 −0.391509
\(681\) 13.3463 0.511432
\(682\) 13.6429 0.522412
\(683\) 49.4339 1.89154 0.945769 0.324841i \(-0.105311\pi\)
0.945769 + 0.324841i \(0.105311\pi\)
\(684\) 12.8718 0.492165
\(685\) −6.82025 −0.260588
\(686\) −117.347 −4.48032
\(687\) 3.79379 0.144742
\(688\) 78.9060 3.00826
\(689\) 41.9171 1.59691
\(690\) −3.38755 −0.128962
\(691\) 2.17090 0.0825849 0.0412925 0.999147i \(-0.486852\pi\)
0.0412925 + 0.999147i \(0.486852\pi\)
\(692\) 91.7281 3.48698
\(693\) 19.6325 0.745775
\(694\) −34.6702 −1.31606
\(695\) −11.2546 −0.426913
\(696\) 20.4501 0.775160
\(697\) 3.34778 0.126806
\(698\) −16.7651 −0.634567
\(699\) −44.4057 −1.67958
\(700\) −114.874 −4.34182
\(701\) 14.8442 0.560658 0.280329 0.959904i \(-0.409556\pi\)
0.280329 + 0.959904i \(0.409556\pi\)
\(702\) 44.5252 1.68050
\(703\) −18.2312 −0.687603
\(704\) 52.3470 1.97290
\(705\) 3.85218 0.145081
\(706\) 93.3366 3.51277
\(707\) −23.3392 −0.877759
\(708\) 25.3865 0.954083
\(709\) −22.4308 −0.842408 −0.421204 0.906966i \(-0.638392\pi\)
−0.421204 + 0.906966i \(0.638392\pi\)
\(710\) −7.27964 −0.273200
\(711\) 16.8246 0.630971
\(712\) −90.1105 −3.37704
\(713\) 1.71041 0.0640555
\(714\) 62.6885 2.34606
\(715\) −8.32598 −0.311374
\(716\) −80.8927 −3.02310
\(717\) 27.2496 1.01765
\(718\) 8.37003 0.312367
\(719\) −3.79952 −0.141698 −0.0708491 0.997487i \(-0.522571\pi\)
−0.0708491 + 0.997487i \(0.522571\pi\)
\(720\) −6.72681 −0.250693
\(721\) 25.7508 0.959010
\(722\) 36.9243 1.37418
\(723\) 11.1429 0.414407
\(724\) 63.2521 2.35075
\(725\) 5.87830 0.218315
\(726\) −10.8940 −0.404313
\(727\) 44.2672 1.64178 0.820890 0.571086i \(-0.193478\pi\)
0.820890 + 0.571086i \(0.193478\pi\)
\(728\) −171.934 −6.37230
\(729\) 10.6095 0.392946
\(730\) 15.0765 0.558006
\(731\) −16.7262 −0.618642
\(732\) −3.69612 −0.136613
\(733\) 21.0691 0.778207 0.389103 0.921194i \(-0.372785\pi\)
0.389103 + 0.921194i \(0.372785\pi\)
\(734\) 12.0149 0.443479
\(735\) −17.1926 −0.634160
\(736\) 16.8630 0.621578
\(737\) 16.9729 0.625207
\(738\) 4.16186 0.153200
\(739\) 37.7493 1.38863 0.694315 0.719671i \(-0.255708\pi\)
0.694315 + 0.719671i \(0.255708\pi\)
\(740\) 21.3239 0.783881
\(741\) 20.2385 0.743479
\(742\) −121.395 −4.45656
\(743\) 31.1083 1.14125 0.570626 0.821210i \(-0.306700\pi\)
0.570626 + 0.821210i \(0.306700\pi\)
\(744\) 23.4198 0.858613
\(745\) 6.39084 0.234142
\(746\) 76.5869 2.80404
\(747\) 11.7772 0.430905
\(748\) −43.9554 −1.60717
\(749\) −42.5794 −1.55582
\(750\) −27.4368 −1.00185
\(751\) 13.2161 0.482261 0.241130 0.970493i \(-0.422482\pi\)
0.241130 + 0.970493i \(0.422482\pi\)
\(752\) −41.2753 −1.50516
\(753\) 9.19044 0.334918
\(754\) 14.5716 0.530666
\(755\) −1.07250 −0.0390324
\(756\) −92.3562 −3.35896
\(757\) 45.8183 1.66529 0.832647 0.553805i \(-0.186825\pi\)
0.832647 + 0.553805i \(0.186825\pi\)
\(758\) 1.74145 0.0632523
\(759\) −8.80618 −0.319644
\(760\) 9.54544 0.346250
\(761\) −18.9676 −0.687574 −0.343787 0.939048i \(-0.611710\pi\)
−0.343787 + 0.939048i \(0.611710\pi\)
\(762\) −78.8885 −2.85783
\(763\) −17.7852 −0.643867
\(764\) −25.5361 −0.923863
\(765\) 1.42593 0.0515545
\(766\) 36.9615 1.33547
\(767\) 10.9219 0.394368
\(768\) −2.68749 −0.0969765
\(769\) −51.1167 −1.84331 −0.921657 0.388006i \(-0.873164\pi\)
−0.921657 + 0.388006i \(0.873164\pi\)
\(770\) 24.1127 0.868962
\(771\) 29.2482 1.05335
\(772\) −48.0562 −1.72958
\(773\) 10.8544 0.390406 0.195203 0.980763i \(-0.437464\pi\)
0.195203 + 0.980763i \(0.437464\pi\)
\(774\) −20.7935 −0.747408
\(775\) 6.73193 0.241818
\(776\) 83.0253 2.98043
\(777\) −79.0577 −2.83618
\(778\) −32.5938 −1.16855
\(779\) −3.13009 −0.112147
\(780\) −23.6716 −0.847580
\(781\) −18.9240 −0.677152
\(782\) −7.69412 −0.275141
\(783\) 4.72603 0.168895
\(784\) 184.216 6.57914
\(785\) −0.903419 −0.0322444
\(786\) −18.0417 −0.643525
\(787\) 52.0046 1.85376 0.926882 0.375353i \(-0.122479\pi\)
0.926882 + 0.375353i \(0.122479\pi\)
\(788\) 59.1781 2.10813
\(789\) −5.93891 −0.211431
\(790\) 20.6641 0.735194
\(791\) 42.5783 1.51391
\(792\) −32.9934 −1.17237
\(793\) −1.59017 −0.0564685
\(794\) 60.4587 2.14560
\(795\) −10.0914 −0.357907
\(796\) 9.84269 0.348865
\(797\) −30.4897 −1.08000 −0.540000 0.841665i \(-0.681576\pi\)
−0.540000 + 0.841665i \(0.681576\pi\)
\(798\) −58.6122 −2.07485
\(799\) 8.74941 0.309532
\(800\) 66.3701 2.34654
\(801\) 12.5857 0.444694
\(802\) 101.760 3.59327
\(803\) 39.1924 1.38307
\(804\) 48.2558 1.70185
\(805\) 3.02303 0.106548
\(806\) 16.6876 0.587796
\(807\) 29.7533 1.04737
\(808\) 39.2228 1.37985
\(809\) 10.8070 0.379953 0.189976 0.981789i \(-0.439159\pi\)
0.189976 + 0.981789i \(0.439159\pi\)
\(810\) −15.4251 −0.541983
\(811\) −27.6590 −0.971240 −0.485620 0.874170i \(-0.661406\pi\)
−0.485620 + 0.874170i \(0.661406\pi\)
\(812\) −30.2250 −1.06069
\(813\) 9.82944 0.344733
\(814\) 77.3961 2.71273
\(815\) 7.94333 0.278243
\(816\) −55.8373 −1.95470
\(817\) 15.6386 0.547126
\(818\) −11.3286 −0.396095
\(819\) 24.0139 0.839115
\(820\) 3.66107 0.127850
\(821\) 35.7352 1.24717 0.623583 0.781757i \(-0.285676\pi\)
0.623583 + 0.781757i \(0.285676\pi\)
\(822\) −70.3794 −2.45476
\(823\) −32.3160 −1.12646 −0.563232 0.826299i \(-0.690442\pi\)
−0.563232 + 0.826299i \(0.690442\pi\)
\(824\) −43.2757 −1.50758
\(825\) −34.6598 −1.20670
\(826\) −31.6308 −1.10058
\(827\) −19.6875 −0.684603 −0.342301 0.939590i \(-0.611206\pi\)
−0.342301 + 0.939590i \(0.611206\pi\)
\(828\) −6.85075 −0.238080
\(829\) −40.7168 −1.41415 −0.707076 0.707138i \(-0.749986\pi\)
−0.707076 + 0.707138i \(0.749986\pi\)
\(830\) 14.4648 0.502082
\(831\) −52.6695 −1.82708
\(832\) 64.0296 2.21983
\(833\) −39.0495 −1.35298
\(834\) −116.139 −4.02155
\(835\) 9.99965 0.346052
\(836\) 41.0972 1.42138
\(837\) 5.41233 0.187077
\(838\) 11.7903 0.407288
\(839\) 13.6771 0.472184 0.236092 0.971731i \(-0.424133\pi\)
0.236092 + 0.971731i \(0.424133\pi\)
\(840\) 41.3927 1.42819
\(841\) −27.4533 −0.946667
\(842\) −23.9246 −0.824496
\(843\) 44.2572 1.52430
\(844\) 57.9906 1.99612
\(845\) −3.38731 −0.116527
\(846\) 10.8770 0.373959
\(847\) 9.72169 0.334041
\(848\) 108.128 3.71313
\(849\) 35.2454 1.20962
\(850\) −30.2828 −1.03869
\(851\) 9.70319 0.332621
\(852\) −53.8028 −1.84325
\(853\) −40.0027 −1.36967 −0.684833 0.728700i \(-0.740125\pi\)
−0.684833 + 0.728700i \(0.740125\pi\)
\(854\) 4.60525 0.157588
\(855\) −1.33321 −0.0455947
\(856\) 71.5571 2.44577
\(857\) −31.5976 −1.07935 −0.539677 0.841872i \(-0.681454\pi\)
−0.539677 + 0.841872i \(0.681454\pi\)
\(858\) −85.9173 −2.93317
\(859\) 8.52813 0.290976 0.145488 0.989360i \(-0.453525\pi\)
0.145488 + 0.989360i \(0.453525\pi\)
\(860\) −18.2915 −0.623734
\(861\) −13.5733 −0.462577
\(862\) −15.0703 −0.513297
\(863\) 30.5439 1.03972 0.519862 0.854250i \(-0.325983\pi\)
0.519862 + 0.854250i \(0.325983\pi\)
\(864\) 53.3601 1.81535
\(865\) −9.50082 −0.323038
\(866\) 25.6158 0.870462
\(867\) −22.7123 −0.771351
\(868\) −34.6142 −1.17488
\(869\) 53.7177 1.82225
\(870\) −3.50808 −0.118935
\(871\) 20.7609 0.703456
\(872\) 29.8890 1.01217
\(873\) −11.5961 −0.392468
\(874\) 7.19381 0.243334
\(875\) 24.4844 0.827724
\(876\) 111.428 3.76481
\(877\) −39.3688 −1.32939 −0.664695 0.747115i \(-0.731439\pi\)
−0.664695 + 0.747115i \(0.731439\pi\)
\(878\) −23.4587 −0.791691
\(879\) 3.02850 0.102149
\(880\) −21.4774 −0.724004
\(881\) 54.5669 1.83840 0.919202 0.393786i \(-0.128835\pi\)
0.919202 + 0.393786i \(0.128835\pi\)
\(882\) −48.5451 −1.63460
\(883\) 6.96298 0.234323 0.117161 0.993113i \(-0.462620\pi\)
0.117161 + 0.993113i \(0.462620\pi\)
\(884\) −53.7651 −1.80832
\(885\) −2.62943 −0.0883873
\(886\) −92.0291 −3.09178
\(887\) −3.55517 −0.119371 −0.0596855 0.998217i \(-0.519010\pi\)
−0.0596855 + 0.998217i \(0.519010\pi\)
\(888\) 132.861 4.45852
\(889\) 70.3995 2.36112
\(890\) 15.4578 0.518148
\(891\) −40.0987 −1.34336
\(892\) 78.7612 2.63712
\(893\) −8.18049 −0.273750
\(894\) 65.9483 2.20564
\(895\) 8.37853 0.280063
\(896\) −50.2236 −1.67785
\(897\) −10.7715 −0.359650
\(898\) −31.7906 −1.06087
\(899\) 1.77127 0.0590752
\(900\) −26.9635 −0.898782
\(901\) −22.9206 −0.763596
\(902\) 13.2880 0.442443
\(903\) 67.8151 2.25675
\(904\) −71.5552 −2.37989
\(905\) −6.55140 −0.217776
\(906\) −11.0674 −0.367689
\(907\) −8.90405 −0.295654 −0.147827 0.989013i \(-0.547228\pi\)
−0.147827 + 0.989013i \(0.547228\pi\)
\(908\) 33.1501 1.10012
\(909\) −5.47822 −0.181701
\(910\) 29.4941 0.977719
\(911\) −6.64310 −0.220096 −0.110048 0.993926i \(-0.535100\pi\)
−0.110048 + 0.993926i \(0.535100\pi\)
\(912\) 52.2065 1.72873
\(913\) 37.6024 1.24446
\(914\) 57.9512 1.91686
\(915\) 0.382829 0.0126559
\(916\) 9.42317 0.311350
\(917\) 16.1003 0.531677
\(918\) −24.3468 −0.803563
\(919\) 5.72843 0.188963 0.0944817 0.995527i \(-0.469881\pi\)
0.0944817 + 0.995527i \(0.469881\pi\)
\(920\) −5.08037 −0.167495
\(921\) 43.5324 1.43444
\(922\) −31.3864 −1.03365
\(923\) −23.1473 −0.761903
\(924\) 178.213 5.86279
\(925\) 38.1903 1.25569
\(926\) −25.7903 −0.847520
\(927\) 6.04429 0.198521
\(928\) 17.4630 0.573250
\(929\) 8.36149 0.274332 0.137166 0.990548i \(-0.456201\pi\)
0.137166 + 0.990548i \(0.456201\pi\)
\(930\) −4.01751 −0.131739
\(931\) 36.5103 1.19658
\(932\) −110.297 −3.61289
\(933\) −48.2016 −1.57805
\(934\) 46.1960 1.51158
\(935\) 4.55272 0.148890
\(936\) −40.3568 −1.31910
\(937\) −30.9702 −1.01175 −0.505876 0.862606i \(-0.668831\pi\)
−0.505876 + 0.862606i \(0.668831\pi\)
\(938\) −60.1252 −1.96316
\(939\) −18.6064 −0.607197
\(940\) 9.56818 0.312080
\(941\) −13.1099 −0.427371 −0.213685 0.976903i \(-0.568547\pi\)
−0.213685 + 0.976903i \(0.568547\pi\)
\(942\) −9.32255 −0.303745
\(943\) 1.66593 0.0542501
\(944\) 28.1738 0.916981
\(945\) 9.56587 0.311178
\(946\) −66.3898 −2.15852
\(947\) 50.7977 1.65070 0.825352 0.564618i \(-0.190977\pi\)
0.825352 + 0.564618i \(0.190977\pi\)
\(948\) 152.725 4.96028
\(949\) 47.9392 1.55617
\(950\) 28.3137 0.918618
\(951\) −48.1339 −1.56085
\(952\) 94.0150 3.04704
\(953\) −7.94039 −0.257214 −0.128607 0.991696i \(-0.541051\pi\)
−0.128607 + 0.991696i \(0.541051\pi\)
\(954\) −28.4942 −0.922533
\(955\) 2.64492 0.0855876
\(956\) 67.6835 2.18904
\(957\) −9.11950 −0.294792
\(958\) 65.4651 2.11508
\(959\) 62.8061 2.02811
\(960\) −15.4150 −0.497517
\(961\) −28.9715 −0.934565
\(962\) 94.6690 3.05225
\(963\) −9.99434 −0.322063
\(964\) 27.6771 0.891419
\(965\) 4.97746 0.160230
\(966\) 31.1952 1.00369
\(967\) 23.2056 0.746240 0.373120 0.927783i \(-0.378288\pi\)
0.373120 + 0.927783i \(0.378288\pi\)
\(968\) −16.3378 −0.525118
\(969\) −11.0666 −0.355509
\(970\) −14.2424 −0.457296
\(971\) −3.65287 −0.117226 −0.0586130 0.998281i \(-0.518668\pi\)
−0.0586130 + 0.998281i \(0.518668\pi\)
\(972\) −56.4576 −1.81088
\(973\) 103.641 3.32259
\(974\) −44.5416 −1.42720
\(975\) −42.3950 −1.35773
\(976\) −4.10194 −0.131300
\(977\) 32.1244 1.02775 0.513875 0.857865i \(-0.328210\pi\)
0.513875 + 0.857865i \(0.328210\pi\)
\(978\) 81.9686 2.62107
\(979\) 40.1838 1.28428
\(980\) −42.7038 −1.36412
\(981\) −4.17458 −0.133284
\(982\) −36.7894 −1.17400
\(983\) −3.35423 −0.106983 −0.0534917 0.998568i \(-0.517035\pi\)
−0.0534917 + 0.998568i \(0.517035\pi\)
\(984\) 22.8107 0.727179
\(985\) −6.12942 −0.195300
\(986\) −7.96787 −0.253749
\(987\) −35.4738 −1.12914
\(988\) 50.2691 1.59927
\(989\) −8.32333 −0.264667
\(990\) 5.65979 0.179880
\(991\) −15.1526 −0.481337 −0.240668 0.970607i \(-0.577367\pi\)
−0.240668 + 0.970607i \(0.577367\pi\)
\(992\) 19.9989 0.634964
\(993\) −38.3691 −1.21761
\(994\) 67.0365 2.12627
\(995\) −1.01946 −0.0323192
\(996\) 106.908 3.38749
\(997\) 13.8661 0.439142 0.219571 0.975596i \(-0.429534\pi\)
0.219571 + 0.975596i \(0.429534\pi\)
\(998\) 78.0405 2.47033
\(999\) 30.7042 0.971437
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 6047.2.a.b.1.10 287
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6047.2.a.b.1.10 287 1.1 even 1 trivial