Properties

Label 6017.2.a.d.1.3
Level $6017$
Weight $2$
Character 6017.1
Self dual yes
Analytic conductor $48.046$
Analytic rank $1$
Dimension $107$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

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

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(48.0459868962\)
Analytic rank: \(1\)
Dimension: \(107\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) \(=\) 6017.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.62131 q^{2} +1.98857 q^{3} +4.87127 q^{4} -3.39892 q^{5} -5.21266 q^{6} -2.62575 q^{7} -7.52650 q^{8} +0.954412 q^{9} +O(q^{10})\) \(q-2.62131 q^{2} +1.98857 q^{3} +4.87127 q^{4} -3.39892 q^{5} -5.21266 q^{6} -2.62575 q^{7} -7.52650 q^{8} +0.954412 q^{9} +8.90963 q^{10} -1.00000 q^{11} +9.68687 q^{12} -4.77883 q^{13} +6.88290 q^{14} -6.75899 q^{15} +9.98676 q^{16} +6.37974 q^{17} -2.50181 q^{18} +1.24752 q^{19} -16.5571 q^{20} -5.22149 q^{21} +2.62131 q^{22} +0.341368 q^{23} -14.9670 q^{24} +6.55267 q^{25} +12.5268 q^{26} -4.06780 q^{27} -12.7907 q^{28} +7.39206 q^{29} +17.7174 q^{30} +5.53910 q^{31} -11.1254 q^{32} -1.98857 q^{33} -16.7233 q^{34} +8.92471 q^{35} +4.64920 q^{36} -7.86385 q^{37} -3.27013 q^{38} -9.50303 q^{39} +25.5820 q^{40} +3.54712 q^{41} +13.6871 q^{42} +11.7515 q^{43} -4.87127 q^{44} -3.24397 q^{45} -0.894831 q^{46} +2.90410 q^{47} +19.8594 q^{48} -0.105445 q^{49} -17.1766 q^{50} +12.6866 q^{51} -23.2790 q^{52} -12.8682 q^{53} +10.6630 q^{54} +3.39892 q^{55} +19.7627 q^{56} +2.48078 q^{57} -19.3769 q^{58} +7.24949 q^{59} -32.9249 q^{60} -3.35498 q^{61} -14.5197 q^{62} -2.50605 q^{63} +9.18962 q^{64} +16.2429 q^{65} +5.21266 q^{66} -6.74590 q^{67} +31.0774 q^{68} +0.678834 q^{69} -23.3944 q^{70} -4.38121 q^{71} -7.18338 q^{72} -16.0706 q^{73} +20.6136 q^{74} +13.0304 q^{75} +6.07700 q^{76} +2.62575 q^{77} +24.9104 q^{78} +10.9589 q^{79} -33.9442 q^{80} -10.9523 q^{81} -9.29812 q^{82} +17.2970 q^{83} -25.4353 q^{84} -21.6842 q^{85} -30.8043 q^{86} +14.6996 q^{87} +7.52650 q^{88} +18.5041 q^{89} +8.50346 q^{90} +12.5480 q^{91} +1.66290 q^{92} +11.0149 q^{93} -7.61255 q^{94} -4.24022 q^{95} -22.1236 q^{96} +1.40907 q^{97} +0.276405 q^{98} -0.954412 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 107 q - 3 q^{2} - 18 q^{3} + 91 q^{4} - 15 q^{5} - 54 q^{7} - 3 q^{8} + 95 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 107 q - 3 q^{2} - 18 q^{3} + 91 q^{4} - 15 q^{5} - 54 q^{7} - 3 q^{8} + 95 q^{9} - 14 q^{10} - 107 q^{11} - 50 q^{12} - 24 q^{13} - 17 q^{14} - 47 q^{15} + 63 q^{16} + 25 q^{17} - 37 q^{18} - 55 q^{19} - 31 q^{20} + 15 q^{21} + 3 q^{22} - 38 q^{23} + 4 q^{24} + 62 q^{25} - 16 q^{26} - 57 q^{27} - 101 q^{28} + 27 q^{29} - 14 q^{30} - 112 q^{31} - 4 q^{32} + 18 q^{33} - 66 q^{34} + 8 q^{35} + 35 q^{36} - 60 q^{37} - 45 q^{38} - 58 q^{39} - 50 q^{40} - 14 q^{41} - 36 q^{42} - 78 q^{43} - 91 q^{44} - 68 q^{45} - 18 q^{46} - 109 q^{47} - 99 q^{48} + 61 q^{49} - 32 q^{50} - 10 q^{51} - 111 q^{52} - 30 q^{53} - 3 q^{54} + 15 q^{55} - 44 q^{56} + q^{57} - 98 q^{58} - 48 q^{59} - 119 q^{60} - 30 q^{61} + 32 q^{62} - 126 q^{63} + 3 q^{64} + 43 q^{65} - 77 q^{67} + 53 q^{68} - 51 q^{69} - 87 q^{70} - 40 q^{71} - 82 q^{72} - 83 q^{73} + 11 q^{74} - 69 q^{75} - 108 q^{76} + 54 q^{77} - 53 q^{78} - 66 q^{79} - 96 q^{80} + 51 q^{81} - 133 q^{82} - 32 q^{83} + 27 q^{84} - 66 q^{85} - 46 q^{86} - 136 q^{87} + 3 q^{88} - 56 q^{89} + 9 q^{90} - 86 q^{91} - 94 q^{92} - 33 q^{93} - 93 q^{94} - 25 q^{95} - 4 q^{96} - 109 q^{97} - 38 q^{98} - 95 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.62131 −1.85355 −0.926774 0.375621i \(-0.877430\pi\)
−0.926774 + 0.375621i \(0.877430\pi\)
\(3\) 1.98857 1.14810 0.574051 0.818820i \(-0.305371\pi\)
0.574051 + 0.818820i \(0.305371\pi\)
\(4\) 4.87127 2.43564
\(5\) −3.39892 −1.52004 −0.760022 0.649897i \(-0.774812\pi\)
−0.760022 + 0.649897i \(0.774812\pi\)
\(6\) −5.21266 −2.12806
\(7\) −2.62575 −0.992440 −0.496220 0.868197i \(-0.665279\pi\)
−0.496220 + 0.868197i \(0.665279\pi\)
\(8\) −7.52650 −2.66102
\(9\) 0.954412 0.318137
\(10\) 8.90963 2.81747
\(11\) −1.00000 −0.301511
\(12\) 9.68687 2.79636
\(13\) −4.77883 −1.32541 −0.662704 0.748881i \(-0.730591\pi\)
−0.662704 + 0.748881i \(0.730591\pi\)
\(14\) 6.88290 1.83953
\(15\) −6.75899 −1.74516
\(16\) 9.98676 2.49669
\(17\) 6.37974 1.54731 0.773657 0.633605i \(-0.218425\pi\)
0.773657 + 0.633605i \(0.218425\pi\)
\(18\) −2.50181 −0.589682
\(19\) 1.24752 0.286200 0.143100 0.989708i \(-0.454293\pi\)
0.143100 + 0.989708i \(0.454293\pi\)
\(20\) −16.5571 −3.70227
\(21\) −5.22149 −1.13942
\(22\) 2.62131 0.558865
\(23\) 0.341368 0.0711801 0.0355900 0.999366i \(-0.488669\pi\)
0.0355900 + 0.999366i \(0.488669\pi\)
\(24\) −14.9670 −3.05512
\(25\) 6.55267 1.31053
\(26\) 12.5268 2.45671
\(27\) −4.06780 −0.782848
\(28\) −12.7907 −2.41722
\(29\) 7.39206 1.37267 0.686336 0.727285i \(-0.259218\pi\)
0.686336 + 0.727285i \(0.259218\pi\)
\(30\) 17.7174 3.23474
\(31\) 5.53910 0.994851 0.497426 0.867507i \(-0.334279\pi\)
0.497426 + 0.867507i \(0.334279\pi\)
\(32\) −11.1254 −1.96671
\(33\) −1.98857 −0.346166
\(34\) −16.7233 −2.86802
\(35\) 8.92471 1.50855
\(36\) 4.64920 0.774867
\(37\) −7.86385 −1.29281 −0.646404 0.762995i \(-0.723728\pi\)
−0.646404 + 0.762995i \(0.723728\pi\)
\(38\) −3.27013 −0.530486
\(39\) −9.50303 −1.52170
\(40\) 25.5820 4.04487
\(41\) 3.54712 0.553968 0.276984 0.960875i \(-0.410665\pi\)
0.276984 + 0.960875i \(0.410665\pi\)
\(42\) 13.6871 2.11197
\(43\) 11.7515 1.79208 0.896042 0.443970i \(-0.146430\pi\)
0.896042 + 0.443970i \(0.146430\pi\)
\(44\) −4.87127 −0.734372
\(45\) −3.24397 −0.483583
\(46\) −0.894831 −0.131936
\(47\) 2.90410 0.423606 0.211803 0.977312i \(-0.432066\pi\)
0.211803 + 0.977312i \(0.432066\pi\)
\(48\) 19.8594 2.86645
\(49\) −0.105445 −0.0150636
\(50\) −17.1766 −2.42913
\(51\) 12.6866 1.77647
\(52\) −23.2790 −3.22821
\(53\) −12.8682 −1.76758 −0.883789 0.467886i \(-0.845016\pi\)
−0.883789 + 0.467886i \(0.845016\pi\)
\(54\) 10.6630 1.45105
\(55\) 3.39892 0.458310
\(56\) 19.7627 2.64090
\(57\) 2.48078 0.328587
\(58\) −19.3769 −2.54431
\(59\) 7.24949 0.943804 0.471902 0.881651i \(-0.343568\pi\)
0.471902 + 0.881651i \(0.343568\pi\)
\(60\) −32.9249 −4.25059
\(61\) −3.35498 −0.429561 −0.214781 0.976662i \(-0.568904\pi\)
−0.214781 + 0.976662i \(0.568904\pi\)
\(62\) −14.5197 −1.84400
\(63\) −2.50605 −0.315732
\(64\) 9.18962 1.14870
\(65\) 16.2429 2.01468
\(66\) 5.21266 0.641634
\(67\) −6.74590 −0.824143 −0.412072 0.911152i \(-0.635195\pi\)
−0.412072 + 0.911152i \(0.635195\pi\)
\(68\) 31.0774 3.76869
\(69\) 0.678834 0.0817220
\(70\) −23.3944 −2.79617
\(71\) −4.38121 −0.519954 −0.259977 0.965615i \(-0.583715\pi\)
−0.259977 + 0.965615i \(0.583715\pi\)
\(72\) −7.18338 −0.846570
\(73\) −16.0706 −1.88092 −0.940460 0.339904i \(-0.889605\pi\)
−0.940460 + 0.339904i \(0.889605\pi\)
\(74\) 20.6136 2.39628
\(75\) 13.0304 1.50463
\(76\) 6.07700 0.697080
\(77\) 2.62575 0.299232
\(78\) 24.9104 2.82055
\(79\) 10.9589 1.23297 0.616485 0.787367i \(-0.288556\pi\)
0.616485 + 0.787367i \(0.288556\pi\)
\(80\) −33.9442 −3.79508
\(81\) −10.9523 −1.21693
\(82\) −9.29812 −1.02681
\(83\) 17.2970 1.89859 0.949295 0.314388i \(-0.101799\pi\)
0.949295 + 0.314388i \(0.101799\pi\)
\(84\) −25.4353 −2.77522
\(85\) −21.6842 −2.35198
\(86\) −30.8043 −3.32171
\(87\) 14.6996 1.57597
\(88\) 7.52650 0.802328
\(89\) 18.5041 1.96143 0.980716 0.195440i \(-0.0626136\pi\)
0.980716 + 0.195440i \(0.0626136\pi\)
\(90\) 8.50346 0.896343
\(91\) 12.5480 1.31539
\(92\) 1.66290 0.173369
\(93\) 11.0149 1.14219
\(94\) −7.61255 −0.785175
\(95\) −4.24022 −0.435037
\(96\) −22.1236 −2.25798
\(97\) 1.40907 0.143070 0.0715349 0.997438i \(-0.477210\pi\)
0.0715349 + 0.997438i \(0.477210\pi\)
\(98\) 0.276405 0.0279211
\(99\) −0.954412 −0.0959220
\(100\) 31.9198 3.19198
\(101\) 1.21753 0.121149 0.0605745 0.998164i \(-0.480707\pi\)
0.0605745 + 0.998164i \(0.480707\pi\)
\(102\) −33.2554 −3.29278
\(103\) 0.446152 0.0439607 0.0219803 0.999758i \(-0.493003\pi\)
0.0219803 + 0.999758i \(0.493003\pi\)
\(104\) 35.9679 3.52694
\(105\) 17.7474 1.73197
\(106\) 33.7315 3.27629
\(107\) 4.34871 0.420406 0.210203 0.977658i \(-0.432588\pi\)
0.210203 + 0.977658i \(0.432588\pi\)
\(108\) −19.8153 −1.90673
\(109\) −15.1620 −1.45226 −0.726129 0.687558i \(-0.758683\pi\)
−0.726129 + 0.687558i \(0.758683\pi\)
\(110\) −8.90963 −0.849500
\(111\) −15.6378 −1.48428
\(112\) −26.2227 −2.47781
\(113\) −5.47251 −0.514810 −0.257405 0.966304i \(-0.582867\pi\)
−0.257405 + 0.966304i \(0.582867\pi\)
\(114\) −6.50289 −0.609052
\(115\) −1.16028 −0.108197
\(116\) 36.0088 3.34333
\(117\) −4.56097 −0.421662
\(118\) −19.0032 −1.74938
\(119\) −16.7516 −1.53562
\(120\) 50.8716 4.64392
\(121\) 1.00000 0.0909091
\(122\) 8.79445 0.796212
\(123\) 7.05371 0.636011
\(124\) 26.9825 2.42310
\(125\) −5.27739 −0.472024
\(126\) 6.56912 0.585224
\(127\) 14.5050 1.28711 0.643556 0.765399i \(-0.277458\pi\)
0.643556 + 0.765399i \(0.277458\pi\)
\(128\) −1.83806 −0.162463
\(129\) 23.3686 2.05749
\(130\) −42.5776 −3.73430
\(131\) 12.0882 1.05615 0.528077 0.849196i \(-0.322913\pi\)
0.528077 + 0.849196i \(0.322913\pi\)
\(132\) −9.68687 −0.843134
\(133\) −3.27567 −0.284037
\(134\) 17.6831 1.52759
\(135\) 13.8261 1.18996
\(136\) −48.0171 −4.11743
\(137\) −17.9901 −1.53700 −0.768500 0.639850i \(-0.778996\pi\)
−0.768500 + 0.639850i \(0.778996\pi\)
\(138\) −1.77943 −0.151475
\(139\) 11.4626 0.972245 0.486123 0.873891i \(-0.338411\pi\)
0.486123 + 0.873891i \(0.338411\pi\)
\(140\) 43.4747 3.67428
\(141\) 5.77501 0.486343
\(142\) 11.4845 0.963760
\(143\) 4.77883 0.399626
\(144\) 9.53148 0.794290
\(145\) −25.1250 −2.08652
\(146\) 42.1260 3.48637
\(147\) −0.209685 −0.0172946
\(148\) −38.3070 −3.14881
\(149\) 6.78579 0.555913 0.277957 0.960594i \(-0.410343\pi\)
0.277957 + 0.960594i \(0.410343\pi\)
\(150\) −34.1568 −2.78889
\(151\) −6.75010 −0.549315 −0.274658 0.961542i \(-0.588565\pi\)
−0.274658 + 0.961542i \(0.588565\pi\)
\(152\) −9.38945 −0.761585
\(153\) 6.08890 0.492258
\(154\) −6.88290 −0.554640
\(155\) −18.8270 −1.51222
\(156\) −46.2919 −3.70632
\(157\) 17.0875 1.36373 0.681866 0.731477i \(-0.261169\pi\)
0.681866 + 0.731477i \(0.261169\pi\)
\(158\) −28.7266 −2.28537
\(159\) −25.5892 −2.02936
\(160\) 37.8144 2.98949
\(161\) −0.896346 −0.0706419
\(162\) 28.7095 2.25563
\(163\) −17.2817 −1.35361 −0.676803 0.736164i \(-0.736635\pi\)
−0.676803 + 0.736164i \(0.736635\pi\)
\(164\) 17.2790 1.34926
\(165\) 6.75899 0.526187
\(166\) −45.3407 −3.51912
\(167\) −1.87154 −0.144824 −0.0724122 0.997375i \(-0.523070\pi\)
−0.0724122 + 0.997375i \(0.523070\pi\)
\(168\) 39.2995 3.03202
\(169\) 9.83719 0.756707
\(170\) 56.8411 4.35951
\(171\) 1.19065 0.0910510
\(172\) 57.2447 4.36486
\(173\) −6.51135 −0.495049 −0.247524 0.968882i \(-0.579617\pi\)
−0.247524 + 0.968882i \(0.579617\pi\)
\(174\) −38.5323 −2.92113
\(175\) −17.2057 −1.30062
\(176\) −9.98676 −0.752780
\(177\) 14.4161 1.08358
\(178\) −48.5050 −3.63560
\(179\) 8.03685 0.600702 0.300351 0.953829i \(-0.402896\pi\)
0.300351 + 0.953829i \(0.402896\pi\)
\(180\) −15.8023 −1.17783
\(181\) −23.1805 −1.72299 −0.861495 0.507765i \(-0.830472\pi\)
−0.861495 + 0.507765i \(0.830472\pi\)
\(182\) −32.8922 −2.43813
\(183\) −6.67162 −0.493180
\(184\) −2.56930 −0.189412
\(185\) 26.7286 1.96513
\(186\) −28.8734 −2.11710
\(187\) −6.37974 −0.466533
\(188\) 14.1467 1.03175
\(189\) 10.6810 0.776929
\(190\) 11.1149 0.806362
\(191\) −16.9709 −1.22797 −0.613985 0.789318i \(-0.710435\pi\)
−0.613985 + 0.789318i \(0.710435\pi\)
\(192\) 18.2742 1.31883
\(193\) −13.5002 −0.971768 −0.485884 0.874023i \(-0.661502\pi\)
−0.485884 + 0.874023i \(0.661502\pi\)
\(194\) −3.69362 −0.265187
\(195\) 32.3001 2.31306
\(196\) −0.513653 −0.0366895
\(197\) 18.4072 1.31146 0.655730 0.754996i \(-0.272361\pi\)
0.655730 + 0.754996i \(0.272361\pi\)
\(198\) 2.50181 0.177796
\(199\) 22.8795 1.62188 0.810942 0.585127i \(-0.198955\pi\)
0.810942 + 0.585127i \(0.198955\pi\)
\(200\) −49.3186 −3.48736
\(201\) −13.4147 −0.946200
\(202\) −3.19153 −0.224555
\(203\) −19.4097 −1.36229
\(204\) 61.7997 4.32684
\(205\) −12.0564 −0.842055
\(206\) −1.16950 −0.0814832
\(207\) 0.325805 0.0226450
\(208\) −47.7250 −3.30913
\(209\) −1.24752 −0.0862927
\(210\) −46.5215 −3.21029
\(211\) −21.0055 −1.44608 −0.723040 0.690806i \(-0.757256\pi\)
−0.723040 + 0.690806i \(0.757256\pi\)
\(212\) −62.6843 −4.30518
\(213\) −8.71235 −0.596960
\(214\) −11.3993 −0.779241
\(215\) −39.9423 −2.72405
\(216\) 30.6163 2.08317
\(217\) −14.5443 −0.987330
\(218\) 39.7444 2.69183
\(219\) −31.9575 −2.15949
\(220\) 16.5571 1.11628
\(221\) −30.4877 −2.05082
\(222\) 40.9916 2.75118
\(223\) −1.81138 −0.121299 −0.0606493 0.998159i \(-0.519317\pi\)
−0.0606493 + 0.998159i \(0.519317\pi\)
\(224\) 29.2125 1.95184
\(225\) 6.25394 0.416929
\(226\) 14.3451 0.954225
\(227\) −12.9529 −0.859713 −0.429856 0.902897i \(-0.641436\pi\)
−0.429856 + 0.902897i \(0.641436\pi\)
\(228\) 12.0845 0.800319
\(229\) −19.9258 −1.31673 −0.658366 0.752698i \(-0.728752\pi\)
−0.658366 + 0.752698i \(0.728752\pi\)
\(230\) 3.04146 0.200548
\(231\) 5.22149 0.343549
\(232\) −55.6364 −3.65271
\(233\) −7.91408 −0.518468 −0.259234 0.965814i \(-0.583470\pi\)
−0.259234 + 0.965814i \(0.583470\pi\)
\(234\) 11.9557 0.781570
\(235\) −9.87081 −0.643900
\(236\) 35.3143 2.29876
\(237\) 21.7925 1.41557
\(238\) 43.9111 2.84634
\(239\) −6.61194 −0.427691 −0.213846 0.976867i \(-0.568599\pi\)
−0.213846 + 0.976867i \(0.568599\pi\)
\(240\) −67.5004 −4.35713
\(241\) −20.4680 −1.31846 −0.659231 0.751940i \(-0.729118\pi\)
−0.659231 + 0.751940i \(0.729118\pi\)
\(242\) −2.62131 −0.168504
\(243\) −9.57610 −0.614307
\(244\) −16.3430 −1.04626
\(245\) 0.358400 0.0228974
\(246\) −18.4900 −1.17888
\(247\) −5.96168 −0.379332
\(248\) −41.6900 −2.64732
\(249\) 34.3962 2.17977
\(250\) 13.8337 0.874918
\(251\) −11.4223 −0.720968 −0.360484 0.932765i \(-0.617389\pi\)
−0.360484 + 0.932765i \(0.617389\pi\)
\(252\) −12.2076 −0.769009
\(253\) −0.341368 −0.0214616
\(254\) −38.0222 −2.38572
\(255\) −43.1206 −2.70032
\(256\) −13.5611 −0.847570
\(257\) −9.98222 −0.622673 −0.311337 0.950300i \(-0.600777\pi\)
−0.311337 + 0.950300i \(0.600777\pi\)
\(258\) −61.2565 −3.81366
\(259\) 20.6485 1.28303
\(260\) 79.1234 4.90703
\(261\) 7.05507 0.436698
\(262\) −31.6870 −1.95763
\(263\) −31.6669 −1.95267 −0.976333 0.216275i \(-0.930609\pi\)
−0.976333 + 0.216275i \(0.930609\pi\)
\(264\) 14.9670 0.921154
\(265\) 43.7379 2.68680
\(266\) 8.58655 0.526475
\(267\) 36.7967 2.25192
\(268\) −32.8611 −2.00731
\(269\) 5.99065 0.365257 0.182628 0.983182i \(-0.441540\pi\)
0.182628 + 0.983182i \(0.441540\pi\)
\(270\) −36.2426 −2.20565
\(271\) −8.45587 −0.513658 −0.256829 0.966457i \(-0.582678\pi\)
−0.256829 + 0.966457i \(0.582678\pi\)
\(272\) 63.7129 3.86316
\(273\) 24.9526 1.51020
\(274\) 47.1577 2.84890
\(275\) −6.55267 −0.395141
\(276\) 3.30678 0.199045
\(277\) −2.10986 −0.126769 −0.0633847 0.997989i \(-0.520189\pi\)
−0.0633847 + 0.997989i \(0.520189\pi\)
\(278\) −30.0470 −1.80210
\(279\) 5.28658 0.316499
\(280\) −67.1719 −4.01429
\(281\) −19.1822 −1.14432 −0.572158 0.820144i \(-0.693894\pi\)
−0.572158 + 0.820144i \(0.693894\pi\)
\(282\) −15.1381 −0.901460
\(283\) 3.99261 0.237336 0.118668 0.992934i \(-0.462138\pi\)
0.118668 + 0.992934i \(0.462138\pi\)
\(284\) −21.3421 −1.26642
\(285\) −8.43197 −0.499467
\(286\) −12.5268 −0.740725
\(287\) −9.31386 −0.549780
\(288\) −10.6182 −0.625684
\(289\) 23.7011 1.39418
\(290\) 65.8606 3.86747
\(291\) 2.80204 0.164259
\(292\) −78.2842 −4.58124
\(293\) 4.68195 0.273523 0.136761 0.990604i \(-0.456331\pi\)
0.136761 + 0.990604i \(0.456331\pi\)
\(294\) 0.549651 0.0320563
\(295\) −24.6405 −1.43462
\(296\) 59.1873 3.44019
\(297\) 4.06780 0.236037
\(298\) −17.7877 −1.03041
\(299\) −1.63134 −0.0943427
\(300\) 63.4748 3.66472
\(301\) −30.8564 −1.77853
\(302\) 17.6941 1.01818
\(303\) 2.42115 0.139091
\(304\) 12.4587 0.714554
\(305\) 11.4033 0.652952
\(306\) −15.9609 −0.912424
\(307\) 11.5554 0.659501 0.329750 0.944068i \(-0.393035\pi\)
0.329750 + 0.944068i \(0.393035\pi\)
\(308\) 12.7907 0.728820
\(309\) 0.887205 0.0504713
\(310\) 49.3513 2.80297
\(311\) −0.388501 −0.0220299 −0.0110149 0.999939i \(-0.503506\pi\)
−0.0110149 + 0.999939i \(0.503506\pi\)
\(312\) 71.5246 4.04928
\(313\) 16.0482 0.907096 0.453548 0.891232i \(-0.350158\pi\)
0.453548 + 0.891232i \(0.350158\pi\)
\(314\) −44.7917 −2.52774
\(315\) 8.51785 0.479926
\(316\) 53.3837 3.00307
\(317\) 0.917078 0.0515082 0.0257541 0.999668i \(-0.491801\pi\)
0.0257541 + 0.999668i \(0.491801\pi\)
\(318\) 67.0774 3.76151
\(319\) −7.39206 −0.413876
\(320\) −31.2348 −1.74608
\(321\) 8.64771 0.482668
\(322\) 2.34960 0.130938
\(323\) 7.95884 0.442842
\(324\) −53.3518 −2.96399
\(325\) −31.3141 −1.73699
\(326\) 45.3007 2.50897
\(327\) −30.1507 −1.66734
\(328\) −26.6974 −1.47412
\(329\) −7.62543 −0.420404
\(330\) −17.7174 −0.975312
\(331\) 20.0616 1.10268 0.551342 0.834280i \(-0.314116\pi\)
0.551342 + 0.834280i \(0.314116\pi\)
\(332\) 84.2583 4.62427
\(333\) −7.50535 −0.411291
\(334\) 4.90590 0.268439
\(335\) 22.9288 1.25273
\(336\) −52.1457 −2.84478
\(337\) −2.64737 −0.144211 −0.0721056 0.997397i \(-0.522972\pi\)
−0.0721056 + 0.997397i \(0.522972\pi\)
\(338\) −25.7863 −1.40259
\(339\) −10.8825 −0.591054
\(340\) −105.630 −5.72858
\(341\) −5.53910 −0.299959
\(342\) −3.12106 −0.168767
\(343\) 18.6571 1.00739
\(344\) −88.4475 −4.76877
\(345\) −2.30730 −0.124221
\(346\) 17.0683 0.917596
\(347\) −32.0944 −1.72292 −0.861458 0.507828i \(-0.830448\pi\)
−0.861458 + 0.507828i \(0.830448\pi\)
\(348\) 71.6060 3.83848
\(349\) −12.3599 −0.661612 −0.330806 0.943699i \(-0.607321\pi\)
−0.330806 + 0.943699i \(0.607321\pi\)
\(350\) 45.1014 2.41077
\(351\) 19.4393 1.03759
\(352\) 11.1254 0.592986
\(353\) 19.7893 1.05328 0.526639 0.850089i \(-0.323452\pi\)
0.526639 + 0.850089i \(0.323452\pi\)
\(354\) −37.7892 −2.00847
\(355\) 14.8914 0.790353
\(356\) 90.1386 4.77733
\(357\) −33.3117 −1.76304
\(358\) −21.0671 −1.11343
\(359\) −12.0187 −0.634323 −0.317161 0.948372i \(-0.602730\pi\)
−0.317161 + 0.948372i \(0.602730\pi\)
\(360\) 24.4157 1.28682
\(361\) −17.4437 −0.918089
\(362\) 60.7632 3.19364
\(363\) 1.98857 0.104373
\(364\) 61.1247 3.20381
\(365\) 54.6227 2.85908
\(366\) 17.4884 0.914132
\(367\) −36.9937 −1.93106 −0.965528 0.260299i \(-0.916179\pi\)
−0.965528 + 0.260299i \(0.916179\pi\)
\(368\) 3.40916 0.177715
\(369\) 3.38542 0.176238
\(370\) −70.0640 −3.64245
\(371\) 33.7886 1.75421
\(372\) 53.6565 2.78196
\(373\) −9.41821 −0.487656 −0.243828 0.969818i \(-0.578403\pi\)
−0.243828 + 0.969818i \(0.578403\pi\)
\(374\) 16.7233 0.864740
\(375\) −10.4945 −0.541931
\(376\) −21.8577 −1.12723
\(377\) −35.3254 −1.81935
\(378\) −27.9982 −1.44007
\(379\) 26.4154 1.35687 0.678433 0.734662i \(-0.262659\pi\)
0.678433 + 0.734662i \(0.262659\pi\)
\(380\) −20.6553 −1.05959
\(381\) 28.8442 1.47774
\(382\) 44.4860 2.27610
\(383\) 25.8275 1.31972 0.659862 0.751387i \(-0.270615\pi\)
0.659862 + 0.751387i \(0.270615\pi\)
\(384\) −3.65511 −0.186524
\(385\) −8.92471 −0.454845
\(386\) 35.3883 1.80122
\(387\) 11.2157 0.570129
\(388\) 6.86399 0.348466
\(389\) −11.2536 −0.570581 −0.285291 0.958441i \(-0.592090\pi\)
−0.285291 + 0.958441i \(0.592090\pi\)
\(390\) −84.6685 −4.28736
\(391\) 2.17784 0.110138
\(392\) 0.793635 0.0400846
\(393\) 24.0383 1.21257
\(394\) −48.2510 −2.43085
\(395\) −37.2483 −1.87417
\(396\) −4.64920 −0.233631
\(397\) −2.18903 −0.109864 −0.0549320 0.998490i \(-0.517494\pi\)
−0.0549320 + 0.998490i \(0.517494\pi\)
\(398\) −59.9743 −3.00624
\(399\) −6.51390 −0.326103
\(400\) 65.4399 3.27199
\(401\) 4.99967 0.249672 0.124836 0.992177i \(-0.460160\pi\)
0.124836 + 0.992177i \(0.460160\pi\)
\(402\) 35.1641 1.75383
\(403\) −26.4704 −1.31858
\(404\) 5.93093 0.295075
\(405\) 37.2261 1.84978
\(406\) 50.8789 2.52508
\(407\) 7.86385 0.389797
\(408\) −95.4854 −4.72723
\(409\) 22.0928 1.09242 0.546209 0.837649i \(-0.316070\pi\)
0.546209 + 0.837649i \(0.316070\pi\)
\(410\) 31.6036 1.56079
\(411\) −35.7746 −1.76463
\(412\) 2.17333 0.107072
\(413\) −19.0353 −0.936668
\(414\) −0.854037 −0.0419736
\(415\) −58.7910 −2.88594
\(416\) 53.1664 2.60670
\(417\) 22.7942 1.11624
\(418\) 3.27013 0.159948
\(419\) 11.0473 0.539697 0.269849 0.962903i \(-0.413026\pi\)
0.269849 + 0.962903i \(0.413026\pi\)
\(420\) 86.4525 4.21845
\(421\) −4.06262 −0.198000 −0.0990000 0.995087i \(-0.531564\pi\)
−0.0990000 + 0.995087i \(0.531564\pi\)
\(422\) 55.0620 2.68038
\(423\) 2.77171 0.134765
\(424\) 96.8522 4.70356
\(425\) 41.8043 2.02781
\(426\) 22.8378 1.10649
\(427\) 8.80934 0.426314
\(428\) 21.1837 1.02396
\(429\) 9.50303 0.458811
\(430\) 104.701 5.04915
\(431\) 4.48615 0.216090 0.108045 0.994146i \(-0.465541\pi\)
0.108045 + 0.994146i \(0.465541\pi\)
\(432\) −40.6241 −1.95453
\(433\) −21.5501 −1.03563 −0.517817 0.855492i \(-0.673255\pi\)
−0.517817 + 0.855492i \(0.673255\pi\)
\(434\) 38.1251 1.83006
\(435\) −49.9629 −2.39554
\(436\) −73.8584 −3.53717
\(437\) 0.425862 0.0203718
\(438\) 83.7706 4.00271
\(439\) −24.3851 −1.16384 −0.581919 0.813247i \(-0.697698\pi\)
−0.581919 + 0.813247i \(0.697698\pi\)
\(440\) −25.5820 −1.21957
\(441\) −0.100638 −0.00479230
\(442\) 79.9177 3.80130
\(443\) −10.5395 −0.500745 −0.250372 0.968150i \(-0.580553\pi\)
−0.250372 + 0.968150i \(0.580553\pi\)
\(444\) −76.1761 −3.61516
\(445\) −62.8940 −2.98146
\(446\) 4.74818 0.224833
\(447\) 13.4940 0.638245
\(448\) −24.1296 −1.14002
\(449\) −29.3277 −1.38406 −0.692030 0.721869i \(-0.743283\pi\)
−0.692030 + 0.721869i \(0.743283\pi\)
\(450\) −16.3935 −0.772798
\(451\) −3.54712 −0.167028
\(452\) −26.6581 −1.25389
\(453\) −13.4230 −0.630670
\(454\) 33.9535 1.59352
\(455\) −42.6497 −1.99945
\(456\) −18.6716 −0.874377
\(457\) −38.3699 −1.79487 −0.897433 0.441150i \(-0.854571\pi\)
−0.897433 + 0.441150i \(0.854571\pi\)
\(458\) 52.2317 2.44063
\(459\) −25.9515 −1.21131
\(460\) −5.65205 −0.263528
\(461\) 14.4851 0.674638 0.337319 0.941390i \(-0.390480\pi\)
0.337319 + 0.941390i \(0.390480\pi\)
\(462\) −13.6871 −0.636783
\(463\) −10.3397 −0.480525 −0.240263 0.970708i \(-0.577234\pi\)
−0.240263 + 0.970708i \(0.577234\pi\)
\(464\) 73.8228 3.42714
\(465\) −37.4387 −1.73618
\(466\) 20.7453 0.961006
\(467\) 10.2825 0.475817 0.237908 0.971288i \(-0.423538\pi\)
0.237908 + 0.971288i \(0.423538\pi\)
\(468\) −22.2177 −1.02701
\(469\) 17.7130 0.817912
\(470\) 25.8745 1.19350
\(471\) 33.9797 1.56570
\(472\) −54.5633 −2.51148
\(473\) −11.7515 −0.540334
\(474\) −57.1249 −2.62383
\(475\) 8.17457 0.375075
\(476\) −81.6016 −3.74020
\(477\) −12.2815 −0.562332
\(478\) 17.3320 0.792745
\(479\) −13.4202 −0.613186 −0.306593 0.951841i \(-0.599189\pi\)
−0.306593 + 0.951841i \(0.599189\pi\)
\(480\) 75.1965 3.43224
\(481\) 37.5800 1.71350
\(482\) 53.6531 2.44383
\(483\) −1.78245 −0.0811041
\(484\) 4.87127 0.221422
\(485\) −4.78933 −0.217472
\(486\) 25.1019 1.13865
\(487\) 30.6858 1.39051 0.695253 0.718765i \(-0.255292\pi\)
0.695253 + 0.718765i \(0.255292\pi\)
\(488\) 25.2513 1.14307
\(489\) −34.3659 −1.55408
\(490\) −0.939479 −0.0424413
\(491\) 27.7664 1.25308 0.626541 0.779389i \(-0.284470\pi\)
0.626541 + 0.779389i \(0.284470\pi\)
\(492\) 34.3605 1.54909
\(493\) 47.1594 2.12395
\(494\) 15.6274 0.703110
\(495\) 3.24397 0.145806
\(496\) 55.3176 2.48383
\(497\) 11.5040 0.516023
\(498\) −90.1633 −4.04031
\(499\) 10.7926 0.483145 0.241573 0.970383i \(-0.422337\pi\)
0.241573 + 0.970383i \(0.422337\pi\)
\(500\) −25.7076 −1.14968
\(501\) −3.72170 −0.166273
\(502\) 29.9414 1.33635
\(503\) 7.82077 0.348711 0.174355 0.984683i \(-0.444216\pi\)
0.174355 + 0.984683i \(0.444216\pi\)
\(504\) 18.8618 0.840169
\(505\) −4.13830 −0.184152
\(506\) 0.894831 0.0397801
\(507\) 19.5619 0.868777
\(508\) 70.6579 3.13494
\(509\) −16.7584 −0.742804 −0.371402 0.928472i \(-0.621123\pi\)
−0.371402 + 0.928472i \(0.621123\pi\)
\(510\) 113.033 5.00517
\(511\) 42.1973 1.86670
\(512\) 39.2240 1.73347
\(513\) −5.07465 −0.224051
\(514\) 26.1665 1.15415
\(515\) −1.51644 −0.0668222
\(516\) 113.835 5.01131
\(517\) −2.90410 −0.127722
\(518\) −54.1261 −2.37817
\(519\) −12.9483 −0.568366
\(520\) −122.252 −5.36110
\(521\) 16.7968 0.735881 0.367940 0.929849i \(-0.380063\pi\)
0.367940 + 0.929849i \(0.380063\pi\)
\(522\) −18.4935 −0.809440
\(523\) 32.6983 1.42980 0.714898 0.699228i \(-0.246473\pi\)
0.714898 + 0.699228i \(0.246473\pi\)
\(524\) 58.8851 2.57241
\(525\) −34.2146 −1.49325
\(526\) 83.0088 3.61936
\(527\) 35.3380 1.53935
\(528\) −19.8594 −0.864268
\(529\) −22.8835 −0.994933
\(530\) −114.651 −4.98010
\(531\) 6.91900 0.300259
\(532\) −15.9567 −0.691810
\(533\) −16.9511 −0.734233
\(534\) −96.4556 −4.17404
\(535\) −14.7809 −0.639035
\(536\) 50.7730 2.19306
\(537\) 15.9818 0.689667
\(538\) −15.7034 −0.677020
\(539\) 0.105445 0.00454185
\(540\) 67.3508 2.89832
\(541\) −6.07192 −0.261052 −0.130526 0.991445i \(-0.541667\pi\)
−0.130526 + 0.991445i \(0.541667\pi\)
\(542\) 22.1655 0.952089
\(543\) −46.0960 −1.97817
\(544\) −70.9771 −3.04312
\(545\) 51.5345 2.20750
\(546\) −65.4085 −2.79922
\(547\) −1.00000 −0.0427569
\(548\) −87.6348 −3.74357
\(549\) −3.20203 −0.136659
\(550\) 17.1766 0.732412
\(551\) 9.22174 0.392859
\(552\) −5.10924 −0.217464
\(553\) −28.7752 −1.22365
\(554\) 5.53061 0.234973
\(555\) 53.1517 2.25616
\(556\) 55.8375 2.36804
\(557\) 22.9557 0.972665 0.486333 0.873774i \(-0.338334\pi\)
0.486333 + 0.873774i \(0.338334\pi\)
\(558\) −13.8578 −0.586646
\(559\) −56.1583 −2.37524
\(560\) 89.1289 3.76639
\(561\) −12.6866 −0.535627
\(562\) 50.2826 2.12104
\(563\) 29.3636 1.23753 0.618764 0.785577i \(-0.287634\pi\)
0.618764 + 0.785577i \(0.287634\pi\)
\(564\) 28.1316 1.18456
\(565\) 18.6006 0.782534
\(566\) −10.4659 −0.439913
\(567\) 28.7581 1.20773
\(568\) 32.9752 1.38361
\(569\) −27.1032 −1.13623 −0.568113 0.822951i \(-0.692326\pi\)
−0.568113 + 0.822951i \(0.692326\pi\)
\(570\) 22.1028 0.925785
\(571\) 35.4328 1.48282 0.741408 0.671055i \(-0.234159\pi\)
0.741408 + 0.671055i \(0.234159\pi\)
\(572\) 23.2790 0.973343
\(573\) −33.7478 −1.40983
\(574\) 24.4145 1.01904
\(575\) 2.23687 0.0932838
\(576\) 8.77068 0.365445
\(577\) −23.5697 −0.981219 −0.490610 0.871380i \(-0.663226\pi\)
−0.490610 + 0.871380i \(0.663226\pi\)
\(578\) −62.1278 −2.58418
\(579\) −26.8462 −1.11569
\(580\) −122.391 −5.08201
\(581\) −45.4175 −1.88423
\(582\) −7.34503 −0.304461
\(583\) 12.8682 0.532945
\(584\) 120.955 5.00517
\(585\) 15.5024 0.640944
\(586\) −12.2729 −0.506987
\(587\) −26.0626 −1.07572 −0.537859 0.843035i \(-0.680767\pi\)
−0.537859 + 0.843035i \(0.680767\pi\)
\(588\) −1.02144 −0.0421233
\(589\) 6.91013 0.284727
\(590\) 64.5903 2.65914
\(591\) 36.6040 1.50569
\(592\) −78.5344 −3.22774
\(593\) 28.2838 1.16148 0.580739 0.814090i \(-0.302764\pi\)
0.580739 + 0.814090i \(0.302764\pi\)
\(594\) −10.6630 −0.437507
\(595\) 56.9373 2.33420
\(596\) 33.0554 1.35400
\(597\) 45.4975 1.86209
\(598\) 4.27624 0.174869
\(599\) −12.7547 −0.521142 −0.260571 0.965455i \(-0.583911\pi\)
−0.260571 + 0.965455i \(0.583911\pi\)
\(600\) −98.0736 −4.00384
\(601\) 48.1728 1.96501 0.982505 0.186237i \(-0.0596293\pi\)
0.982505 + 0.186237i \(0.0596293\pi\)
\(602\) 80.8843 3.29660
\(603\) −6.43837 −0.262191
\(604\) −32.8816 −1.33793
\(605\) −3.39892 −0.138186
\(606\) −6.34659 −0.257812
\(607\) −46.6140 −1.89200 −0.946002 0.324160i \(-0.894918\pi\)
−0.946002 + 0.324160i \(0.894918\pi\)
\(608\) −13.8791 −0.562874
\(609\) −38.5976 −1.56405
\(610\) −29.8916 −1.21028
\(611\) −13.8782 −0.561452
\(612\) 29.6607 1.19896
\(613\) −28.1114 −1.13541 −0.567704 0.823233i \(-0.692168\pi\)
−0.567704 + 0.823233i \(0.692168\pi\)
\(614\) −30.2903 −1.22242
\(615\) −23.9750 −0.966765
\(616\) −19.7627 −0.796262
\(617\) 10.9689 0.441590 0.220795 0.975320i \(-0.429135\pi\)
0.220795 + 0.975320i \(0.429135\pi\)
\(618\) −2.32564 −0.0935510
\(619\) −19.8238 −0.796785 −0.398392 0.917215i \(-0.630432\pi\)
−0.398392 + 0.917215i \(0.630432\pi\)
\(620\) −91.7113 −3.68321
\(621\) −1.38861 −0.0557232
\(622\) 1.01838 0.0408334
\(623\) −48.5871 −1.94660
\(624\) −94.9045 −3.79922
\(625\) −14.8259 −0.593036
\(626\) −42.0673 −1.68135
\(627\) −2.48078 −0.0990727
\(628\) 83.2380 3.32156
\(629\) −50.1693 −2.00038
\(630\) −22.3279 −0.889566
\(631\) −38.6081 −1.53696 −0.768481 0.639872i \(-0.778987\pi\)
−0.768481 + 0.639872i \(0.778987\pi\)
\(632\) −82.4820 −3.28096
\(633\) −41.7710 −1.66025
\(634\) −2.40395 −0.0954729
\(635\) −49.3014 −1.95647
\(636\) −124.652 −4.94278
\(637\) 0.503905 0.0199654
\(638\) 19.3769 0.767139
\(639\) −4.18148 −0.165417
\(640\) 6.24742 0.246951
\(641\) −44.1434 −1.74356 −0.871779 0.489899i \(-0.837034\pi\)
−0.871779 + 0.489899i \(0.837034\pi\)
\(642\) −22.6683 −0.894648
\(643\) 47.5060 1.87345 0.936727 0.350059i \(-0.113839\pi\)
0.936727 + 0.350059i \(0.113839\pi\)
\(644\) −4.36634 −0.172058
\(645\) −79.4282 −3.12748
\(646\) −20.8626 −0.820828
\(647\) −42.0758 −1.65417 −0.827085 0.562077i \(-0.810003\pi\)
−0.827085 + 0.562077i \(0.810003\pi\)
\(648\) 82.4328 3.23826
\(649\) −7.24949 −0.284568
\(650\) 82.0839 3.21960
\(651\) −28.9223 −1.13355
\(652\) −84.1838 −3.29689
\(653\) −7.61860 −0.298139 −0.149069 0.988827i \(-0.547628\pi\)
−0.149069 + 0.988827i \(0.547628\pi\)
\(654\) 79.0345 3.09049
\(655\) −41.0870 −1.60540
\(656\) 35.4243 1.38309
\(657\) −15.3380 −0.598391
\(658\) 19.9886 0.779238
\(659\) 17.9862 0.700641 0.350321 0.936630i \(-0.386073\pi\)
0.350321 + 0.936630i \(0.386073\pi\)
\(660\) 32.9249 1.28160
\(661\) −21.9803 −0.854934 −0.427467 0.904031i \(-0.640594\pi\)
−0.427467 + 0.904031i \(0.640594\pi\)
\(662\) −52.5876 −2.04388
\(663\) −60.6269 −2.35455
\(664\) −130.186 −5.05218
\(665\) 11.1337 0.431748
\(666\) 19.6739 0.762347
\(667\) 2.52341 0.0977069
\(668\) −9.11680 −0.352740
\(669\) −3.60205 −0.139263
\(670\) −60.1035 −2.32200
\(671\) 3.35498 0.129518
\(672\) 58.0911 2.24091
\(673\) −32.2772 −1.24419 −0.622097 0.782940i \(-0.713719\pi\)
−0.622097 + 0.782940i \(0.713719\pi\)
\(674\) 6.93957 0.267302
\(675\) −26.6549 −1.02595
\(676\) 47.9197 1.84306
\(677\) −15.9664 −0.613637 −0.306819 0.951768i \(-0.599265\pi\)
−0.306819 + 0.951768i \(0.599265\pi\)
\(678\) 28.5263 1.09555
\(679\) −3.69988 −0.141988
\(680\) 163.206 6.25868
\(681\) −25.7577 −0.987038
\(682\) 14.5197 0.555988
\(683\) −34.0716 −1.30371 −0.651856 0.758343i \(-0.726009\pi\)
−0.651856 + 0.758343i \(0.726009\pi\)
\(684\) 5.79996 0.221767
\(685\) 61.1470 2.33631
\(686\) −48.9061 −1.86724
\(687\) −39.6238 −1.51174
\(688\) 117.359 4.47428
\(689\) 61.4947 2.34276
\(690\) 6.04816 0.230249
\(691\) 15.1627 0.576815 0.288407 0.957508i \(-0.406874\pi\)
0.288407 + 0.957508i \(0.406874\pi\)
\(692\) −31.7186 −1.20576
\(693\) 2.50605 0.0951968
\(694\) 84.1294 3.19351
\(695\) −38.9605 −1.47786
\(696\) −110.637 −4.19368
\(697\) 22.6297 0.857162
\(698\) 32.3992 1.22633
\(699\) −15.7377 −0.595254
\(700\) −83.8134 −3.16785
\(701\) −24.3826 −0.920918 −0.460459 0.887681i \(-0.652315\pi\)
−0.460459 + 0.887681i \(0.652315\pi\)
\(702\) −50.9564 −1.92323
\(703\) −9.81030 −0.370002
\(704\) −9.18962 −0.346347
\(705\) −19.6288 −0.739263
\(706\) −51.8739 −1.95230
\(707\) −3.19693 −0.120233
\(708\) 70.2249 2.63921
\(709\) 22.9588 0.862234 0.431117 0.902296i \(-0.358120\pi\)
0.431117 + 0.902296i \(0.358120\pi\)
\(710\) −39.0350 −1.46496
\(711\) 10.4593 0.392254
\(712\) −139.271 −5.21941
\(713\) 1.89087 0.0708136
\(714\) 87.3204 3.26788
\(715\) −16.2429 −0.607448
\(716\) 39.1497 1.46309
\(717\) −13.1483 −0.491033
\(718\) 31.5048 1.17575
\(719\) 12.5563 0.468269 0.234135 0.972204i \(-0.424774\pi\)
0.234135 + 0.972204i \(0.424774\pi\)
\(720\) −32.3967 −1.20736
\(721\) −1.17148 −0.0436283
\(722\) 45.7254 1.70172
\(723\) −40.7021 −1.51373
\(724\) −112.918 −4.19658
\(725\) 48.4377 1.79893
\(726\) −5.21266 −0.193460
\(727\) −12.7478 −0.472788 −0.236394 0.971657i \(-0.575966\pi\)
−0.236394 + 0.971657i \(0.575966\pi\)
\(728\) −94.4425 −3.50027
\(729\) 13.8143 0.511639
\(730\) −143.183 −5.29944
\(731\) 74.9713 2.77292
\(732\) −32.4993 −1.20121
\(733\) −8.10796 −0.299475 −0.149737 0.988726i \(-0.547843\pi\)
−0.149737 + 0.988726i \(0.547843\pi\)
\(734\) 96.9720 3.57930
\(735\) 0.712704 0.0262885
\(736\) −3.79785 −0.139991
\(737\) 6.74590 0.248488
\(738\) −8.87423 −0.326665
\(739\) −9.52182 −0.350266 −0.175133 0.984545i \(-0.556036\pi\)
−0.175133 + 0.984545i \(0.556036\pi\)
\(740\) 130.202 4.78633
\(741\) −11.8552 −0.435512
\(742\) −88.5703 −3.25152
\(743\) 12.3149 0.451789 0.225895 0.974152i \(-0.427469\pi\)
0.225895 + 0.974152i \(0.427469\pi\)
\(744\) −82.9036 −3.03939
\(745\) −23.0644 −0.845013
\(746\) 24.6881 0.903894
\(747\) 16.5084 0.604012
\(748\) −31.0774 −1.13630
\(749\) −11.4186 −0.417227
\(750\) 27.5092 1.00450
\(751\) 23.7336 0.866053 0.433026 0.901381i \(-0.357446\pi\)
0.433026 + 0.901381i \(0.357446\pi\)
\(752\) 29.0025 1.05761
\(753\) −22.7140 −0.827745
\(754\) 92.5989 3.37225
\(755\) 22.9431 0.834983
\(756\) 52.0301 1.89232
\(757\) 29.1425 1.05920 0.529602 0.848246i \(-0.322341\pi\)
0.529602 + 0.848246i \(0.322341\pi\)
\(758\) −69.2429 −2.51502
\(759\) −0.678834 −0.0246401
\(760\) 31.9140 1.15764
\(761\) 20.5084 0.743430 0.371715 0.928347i \(-0.378770\pi\)
0.371715 + 0.928347i \(0.378770\pi\)
\(762\) −75.6097 −2.73905
\(763\) 39.8117 1.44128
\(764\) −82.6698 −2.99089
\(765\) −20.6957 −0.748254
\(766\) −67.7019 −2.44617
\(767\) −34.6441 −1.25093
\(768\) −26.9672 −0.973096
\(769\) −30.9971 −1.11778 −0.558892 0.829240i \(-0.688773\pi\)
−0.558892 + 0.829240i \(0.688773\pi\)
\(770\) 23.3944 0.843077
\(771\) −19.8503 −0.714892
\(772\) −65.7633 −2.36687
\(773\) −19.9782 −0.718566 −0.359283 0.933229i \(-0.616979\pi\)
−0.359283 + 0.933229i \(0.616979\pi\)
\(774\) −29.4000 −1.05676
\(775\) 36.2959 1.30379
\(776\) −10.6054 −0.380712
\(777\) 41.0610 1.47305
\(778\) 29.4992 1.05760
\(779\) 4.42510 0.158546
\(780\) 157.342 5.63376
\(781\) 4.38121 0.156772
\(782\) −5.70879 −0.204146
\(783\) −30.0694 −1.07459
\(784\) −1.05306 −0.0376092
\(785\) −58.0791 −2.07293
\(786\) −63.0119 −2.24756
\(787\) −5.62379 −0.200466 −0.100233 0.994964i \(-0.531959\pi\)
−0.100233 + 0.994964i \(0.531959\pi\)
\(788\) 89.6665 3.19424
\(789\) −62.9719 −2.24186
\(790\) 97.6395 3.47386
\(791\) 14.3694 0.510918
\(792\) 7.18338 0.255250
\(793\) 16.0329 0.569344
\(794\) 5.73812 0.203638
\(795\) 86.9758 3.08471
\(796\) 111.452 3.95032
\(797\) 46.0882 1.63253 0.816264 0.577679i \(-0.196041\pi\)
0.816264 + 0.577679i \(0.196041\pi\)
\(798\) 17.0750 0.604447
\(799\) 18.5274 0.655452
\(800\) −72.9010 −2.57744
\(801\) 17.6605 0.624004
\(802\) −13.1057 −0.462778
\(803\) 16.0706 0.567119
\(804\) −65.3467 −2.30460
\(805\) 3.04661 0.107379
\(806\) 69.3871 2.44406
\(807\) 11.9128 0.419352
\(808\) −9.16376 −0.322380
\(809\) 43.4188 1.52652 0.763262 0.646089i \(-0.223597\pi\)
0.763262 + 0.646089i \(0.223597\pi\)
\(810\) −97.5812 −3.42866
\(811\) 7.13376 0.250500 0.125250 0.992125i \(-0.460027\pi\)
0.125250 + 0.992125i \(0.460027\pi\)
\(812\) −94.5500 −3.31805
\(813\) −16.8151 −0.589731
\(814\) −20.6136 −0.722506
\(815\) 58.7391 2.05754
\(816\) 126.698 4.43530
\(817\) 14.6602 0.512895
\(818\) −57.9121 −2.02485
\(819\) 11.9760 0.418474
\(820\) −58.7300 −2.05094
\(821\) −26.5981 −0.928280 −0.464140 0.885762i \(-0.653637\pi\)
−0.464140 + 0.885762i \(0.653637\pi\)
\(822\) 93.7764 3.27083
\(823\) −0.831920 −0.0289989 −0.0144995 0.999895i \(-0.504615\pi\)
−0.0144995 + 0.999895i \(0.504615\pi\)
\(824\) −3.35797 −0.116980
\(825\) −13.0304 −0.453662
\(826\) 49.8976 1.73616
\(827\) 22.1773 0.771179 0.385589 0.922670i \(-0.373998\pi\)
0.385589 + 0.922670i \(0.373998\pi\)
\(828\) 1.58709 0.0551551
\(829\) −31.5224 −1.09482 −0.547408 0.836866i \(-0.684386\pi\)
−0.547408 + 0.836866i \(0.684386\pi\)
\(830\) 154.110 5.34922
\(831\) −4.19561 −0.145544
\(832\) −43.9156 −1.52250
\(833\) −0.672714 −0.0233081
\(834\) −59.7507 −2.06900
\(835\) 6.36123 0.220139
\(836\) −6.07700 −0.210178
\(837\) −22.5319 −0.778817
\(838\) −28.9585 −1.00035
\(839\) 16.1003 0.555844 0.277922 0.960604i \(-0.410354\pi\)
0.277922 + 0.960604i \(0.410354\pi\)
\(840\) −133.576 −4.60881
\(841\) 25.6426 0.884228
\(842\) 10.6494 0.367002
\(843\) −38.1452 −1.31379
\(844\) −102.324 −3.52213
\(845\) −33.4358 −1.15023
\(846\) −7.26551 −0.249793
\(847\) −2.62575 −0.0902218
\(848\) −128.511 −4.41309
\(849\) 7.93958 0.272486
\(850\) −109.582 −3.75863
\(851\) −2.68446 −0.0920222
\(852\) −42.4402 −1.45398
\(853\) −9.49455 −0.325087 −0.162544 0.986701i \(-0.551970\pi\)
−0.162544 + 0.986701i \(0.551970\pi\)
\(854\) −23.0920 −0.790192
\(855\) −4.04691 −0.138402
\(856\) −32.7306 −1.11871
\(857\) −53.4992 −1.82750 −0.913750 0.406278i \(-0.866826\pi\)
−0.913750 + 0.406278i \(0.866826\pi\)
\(858\) −24.9104 −0.850427
\(859\) −11.2340 −0.383298 −0.191649 0.981464i \(-0.561383\pi\)
−0.191649 + 0.981464i \(0.561383\pi\)
\(860\) −194.570 −6.63479
\(861\) −18.5213 −0.631203
\(862\) −11.7596 −0.400533
\(863\) 3.73858 0.127263 0.0636314 0.997973i \(-0.479732\pi\)
0.0636314 + 0.997973i \(0.479732\pi\)
\(864\) 45.2559 1.53964
\(865\) 22.1316 0.752496
\(866\) 56.4896 1.91960
\(867\) 47.1312 1.60066
\(868\) −70.8492 −2.40478
\(869\) −10.9589 −0.371754
\(870\) 130.968 4.44024
\(871\) 32.2375 1.09233
\(872\) 114.117 3.86449
\(873\) 1.34484 0.0455159
\(874\) −1.11632 −0.0377600
\(875\) 13.8571 0.468455
\(876\) −155.674 −5.25973
\(877\) −0.884778 −0.0298768 −0.0149384 0.999888i \(-0.504755\pi\)
−0.0149384 + 0.999888i \(0.504755\pi\)
\(878\) 63.9210 2.15723
\(879\) 9.31040 0.314032
\(880\) 33.9442 1.14426
\(881\) 12.5963 0.424382 0.212191 0.977228i \(-0.431940\pi\)
0.212191 + 0.977228i \(0.431940\pi\)
\(882\) 0.263804 0.00888275
\(883\) −46.5541 −1.56667 −0.783335 0.621600i \(-0.786483\pi\)
−0.783335 + 0.621600i \(0.786483\pi\)
\(884\) −148.514 −4.99506
\(885\) −48.9993 −1.64709
\(886\) 27.6272 0.928154
\(887\) −27.0479 −0.908180 −0.454090 0.890956i \(-0.650036\pi\)
−0.454090 + 0.890956i \(0.650036\pi\)
\(888\) 117.698 3.94969
\(889\) −38.0865 −1.27738
\(890\) 164.865 5.52628
\(891\) 10.9523 0.366917
\(892\) −8.82371 −0.295440
\(893\) 3.62292 0.121236
\(894\) −35.3720 −1.18302
\(895\) −27.3166 −0.913094
\(896\) 4.82628 0.161235
\(897\) −3.24403 −0.108315
\(898\) 76.8771 2.56542
\(899\) 40.9454 1.36560
\(900\) 30.4647 1.01549
\(901\) −82.0955 −2.73500
\(902\) 9.29812 0.309593
\(903\) −61.3602 −2.04194
\(904\) 41.1888 1.36992
\(905\) 78.7886 2.61902
\(906\) 35.1860 1.16898
\(907\) −35.7723 −1.18780 −0.593899 0.804539i \(-0.702412\pi\)
−0.593899 + 0.804539i \(0.702412\pi\)
\(908\) −63.0970 −2.09395
\(909\) 1.16203 0.0385420
\(910\) 111.798 3.70607
\(911\) 14.9009 0.493688 0.246844 0.969055i \(-0.420606\pi\)
0.246844 + 0.969055i \(0.420606\pi\)
\(912\) 24.7749 0.820380
\(913\) −17.2970 −0.572446
\(914\) 100.579 3.32687
\(915\) 22.6763 0.749655
\(916\) −97.0639 −3.20708
\(917\) −31.7407 −1.04817
\(918\) 68.0269 2.24522
\(919\) −23.0874 −0.761585 −0.380792 0.924661i \(-0.624349\pi\)
−0.380792 + 0.924661i \(0.624349\pi\)
\(920\) 8.73286 0.287914
\(921\) 22.9787 0.757174
\(922\) −37.9700 −1.25047
\(923\) 20.9371 0.689152
\(924\) 25.4353 0.836759
\(925\) −51.5292 −1.69427
\(926\) 27.1035 0.890676
\(927\) 0.425813 0.0139855
\(928\) −82.2397 −2.69965
\(929\) −15.4011 −0.505294 −0.252647 0.967559i \(-0.581301\pi\)
−0.252647 + 0.967559i \(0.581301\pi\)
\(930\) 98.1386 3.21809
\(931\) −0.131545 −0.00431121
\(932\) −38.5516 −1.26280
\(933\) −0.772562 −0.0252925
\(934\) −26.9536 −0.881949
\(935\) 21.6842 0.709150
\(936\) 34.3281 1.12205
\(937\) −21.4605 −0.701083 −0.350542 0.936547i \(-0.614003\pi\)
−0.350542 + 0.936547i \(0.614003\pi\)
\(938\) −46.4314 −1.51604
\(939\) 31.9129 1.04144
\(940\) −48.0834 −1.56831
\(941\) 42.4259 1.38304 0.691522 0.722355i \(-0.256940\pi\)
0.691522 + 0.722355i \(0.256940\pi\)
\(942\) −89.0715 −2.90211
\(943\) 1.21087 0.0394315
\(944\) 72.3990 2.35639
\(945\) −36.3039 −1.18097
\(946\) 30.8043 1.00153
\(947\) −11.2762 −0.366427 −0.183214 0.983073i \(-0.558650\pi\)
−0.183214 + 0.983073i \(0.558650\pi\)
\(948\) 106.157 3.44782
\(949\) 76.7986 2.49299
\(950\) −21.4281 −0.695219
\(951\) 1.82367 0.0591367
\(952\) 126.081 4.08630
\(953\) 14.0789 0.456061 0.228030 0.973654i \(-0.426771\pi\)
0.228030 + 0.973654i \(0.426771\pi\)
\(954\) 32.1937 1.04231
\(955\) 57.6827 1.86657
\(956\) −32.2086 −1.04170
\(957\) −14.6996 −0.475172
\(958\) 35.1786 1.13657
\(959\) 47.2375 1.52538
\(960\) −62.1126 −2.00468
\(961\) −0.318396 −0.0102708
\(962\) −98.5088 −3.17605
\(963\) 4.15046 0.133747
\(964\) −99.7054 −3.21129
\(965\) 45.8862 1.47713
\(966\) 4.67235 0.150330
\(967\) 17.5871 0.565564 0.282782 0.959184i \(-0.408743\pi\)
0.282782 + 0.959184i \(0.408743\pi\)
\(968\) −7.52650 −0.241911
\(969\) 15.8267 0.508427
\(970\) 12.5543 0.403095
\(971\) 22.9942 0.737918 0.368959 0.929446i \(-0.379714\pi\)
0.368959 + 0.929446i \(0.379714\pi\)
\(972\) −46.6478 −1.49623
\(973\) −30.0979 −0.964895
\(974\) −80.4370 −2.57737
\(975\) −62.2702 −1.99424
\(976\) −33.5054 −1.07248
\(977\) −9.49749 −0.303852 −0.151926 0.988392i \(-0.548547\pi\)
−0.151926 + 0.988392i \(0.548547\pi\)
\(978\) 90.0836 2.88056
\(979\) −18.5041 −0.591394
\(980\) 1.74587 0.0557697
\(981\) −14.4708 −0.462018
\(982\) −72.7844 −2.32265
\(983\) −8.67688 −0.276750 −0.138375 0.990380i \(-0.544188\pi\)
−0.138375 + 0.990380i \(0.544188\pi\)
\(984\) −53.0897 −1.69244
\(985\) −62.5646 −1.99348
\(986\) −123.620 −3.93685
\(987\) −15.1637 −0.482666
\(988\) −29.0410 −0.923916
\(989\) 4.01157 0.127561
\(990\) −8.50346 −0.270258
\(991\) 44.4643 1.41246 0.706228 0.707985i \(-0.250395\pi\)
0.706228 + 0.707985i \(0.250395\pi\)
\(992\) −61.6247 −1.95659
\(993\) 39.8938 1.26599
\(994\) −30.1555 −0.956473
\(995\) −77.7656 −2.46533
\(996\) 167.553 5.30914
\(997\) −7.80694 −0.247248 −0.123624 0.992329i \(-0.539452\pi\)
−0.123624 + 0.992329i \(0.539452\pi\)
\(998\) −28.2909 −0.895532
\(999\) 31.9885 1.01207
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 6017.2.a.d.1.3 107
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6017.2.a.d.1.3 107 1.1 even 1 trivial