Properties

Label 8018.2.a.h.1.7
Level $8018$
Weight $2$
Character 8018.1
Self dual yes
Analytic conductor $64.024$
Analytic rank $0$
Dimension $41$
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] = [8018,2,Mod(1,8018)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8018, 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("8018.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8018 = 2 \cdot 19 \cdot 211 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8018.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: \(64.0240523407\)
Analytic rank: \(0\)
Dimension: \(41\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) \(=\) 8018.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -2.09909 q^{3} +1.00000 q^{4} +1.36520 q^{5} +2.09909 q^{6} +4.01442 q^{7} -1.00000 q^{8} +1.40618 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -2.09909 q^{3} +1.00000 q^{4} +1.36520 q^{5} +2.09909 q^{6} +4.01442 q^{7} -1.00000 q^{8} +1.40618 q^{9} -1.36520 q^{10} +3.20824 q^{11} -2.09909 q^{12} +6.79975 q^{13} -4.01442 q^{14} -2.86567 q^{15} +1.00000 q^{16} +1.85135 q^{17} -1.40618 q^{18} -1.00000 q^{19} +1.36520 q^{20} -8.42662 q^{21} -3.20824 q^{22} -5.09179 q^{23} +2.09909 q^{24} -3.13624 q^{25} -6.79975 q^{26} +3.34558 q^{27} +4.01442 q^{28} +4.18921 q^{29} +2.86567 q^{30} +0.712068 q^{31} -1.00000 q^{32} -6.73438 q^{33} -1.85135 q^{34} +5.48047 q^{35} +1.40618 q^{36} -6.50946 q^{37} +1.00000 q^{38} -14.2733 q^{39} -1.36520 q^{40} +2.46268 q^{41} +8.42662 q^{42} +10.2541 q^{43} +3.20824 q^{44} +1.91971 q^{45} +5.09179 q^{46} -5.38403 q^{47} -2.09909 q^{48} +9.11555 q^{49} +3.13624 q^{50} -3.88615 q^{51} +6.79975 q^{52} +8.52058 q^{53} -3.34558 q^{54} +4.37987 q^{55} -4.01442 q^{56} +2.09909 q^{57} -4.18921 q^{58} +10.3430 q^{59} -2.86567 q^{60} +1.41889 q^{61} -0.712068 q^{62} +5.64498 q^{63} +1.00000 q^{64} +9.28299 q^{65} +6.73438 q^{66} +12.7000 q^{67} +1.85135 q^{68} +10.6881 q^{69} -5.48047 q^{70} +4.06966 q^{71} -1.40618 q^{72} -10.9181 q^{73} +6.50946 q^{74} +6.58325 q^{75} -1.00000 q^{76} +12.8792 q^{77} +14.2733 q^{78} -2.13278 q^{79} +1.36520 q^{80} -11.2412 q^{81} -2.46268 q^{82} -1.07045 q^{83} -8.42662 q^{84} +2.52746 q^{85} -10.2541 q^{86} -8.79352 q^{87} -3.20824 q^{88} -1.39280 q^{89} -1.91971 q^{90} +27.2970 q^{91} -5.09179 q^{92} -1.49469 q^{93} +5.38403 q^{94} -1.36520 q^{95} +2.09909 q^{96} +6.73244 q^{97} -9.11555 q^{98} +4.51135 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 41 q - 41 q^{2} + 8 q^{3} + 41 q^{4} - 9 q^{5} - 8 q^{6} + 7 q^{7} - 41 q^{8} + 43 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 41 q - 41 q^{2} + 8 q^{3} + 41 q^{4} - 9 q^{5} - 8 q^{6} + 7 q^{7} - 41 q^{8} + 43 q^{9} + 9 q^{10} - 9 q^{11} + 8 q^{12} + 13 q^{13} - 7 q^{14} + 26 q^{15} + 41 q^{16} - 16 q^{17} - 43 q^{18} - 41 q^{19} - 9 q^{20} + 2 q^{21} + 9 q^{22} + 10 q^{23} - 8 q^{24} + 60 q^{25} - 13 q^{26} + 47 q^{27} + 7 q^{28} - 14 q^{29} - 26 q^{30} + 49 q^{31} - 41 q^{32} + 12 q^{33} + 16 q^{34} - 8 q^{35} + 43 q^{36} + 54 q^{37} + 41 q^{38} + 16 q^{39} + 9 q^{40} - 18 q^{41} - 2 q^{42} + 29 q^{43} - 9 q^{44} - 13 q^{45} - 10 q^{46} - 8 q^{47} + 8 q^{48} + 44 q^{49} - 60 q^{50} - 16 q^{51} + 13 q^{52} + 7 q^{53} - 47 q^{54} + 19 q^{55} - 7 q^{56} - 8 q^{57} + 14 q^{58} - 5 q^{59} + 26 q^{60} - 6 q^{61} - 49 q^{62} + 24 q^{63} + 41 q^{64} - 26 q^{65} - 12 q^{66} + 66 q^{67} - 16 q^{68} + 12 q^{69} + 8 q^{70} + 27 q^{71} - 43 q^{72} - q^{73} - 54 q^{74} + 62 q^{75} - 41 q^{76} - 8 q^{77} - 16 q^{78} + 87 q^{79} - 9 q^{80} + 73 q^{81} + 18 q^{82} - 41 q^{83} + 2 q^{84} + 14 q^{85} - 29 q^{86} + 35 q^{87} + 9 q^{88} - 4 q^{89} + 13 q^{90} + 39 q^{91} + 10 q^{92} + 17 q^{93} + 8 q^{94} + 9 q^{95} - 8 q^{96} + 64 q^{97} - 44 q^{98} + 40 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −2.09909 −1.21191 −0.605955 0.795499i \(-0.707209\pi\)
−0.605955 + 0.795499i \(0.707209\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.36520 0.610534 0.305267 0.952267i \(-0.401254\pi\)
0.305267 + 0.952267i \(0.401254\pi\)
\(6\) 2.09909 0.856950
\(7\) 4.01442 1.51731 0.758654 0.651494i \(-0.225858\pi\)
0.758654 + 0.651494i \(0.225858\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.40618 0.468726
\(10\) −1.36520 −0.431713
\(11\) 3.20824 0.967320 0.483660 0.875256i \(-0.339307\pi\)
0.483660 + 0.875256i \(0.339307\pi\)
\(12\) −2.09909 −0.605955
\(13\) 6.79975 1.88591 0.942956 0.332918i \(-0.108033\pi\)
0.942956 + 0.332918i \(0.108033\pi\)
\(14\) −4.01442 −1.07290
\(15\) −2.86567 −0.739913
\(16\) 1.00000 0.250000
\(17\) 1.85135 0.449019 0.224509 0.974472i \(-0.427922\pi\)
0.224509 + 0.974472i \(0.427922\pi\)
\(18\) −1.40618 −0.331439
\(19\) −1.00000 −0.229416
\(20\) 1.36520 0.305267
\(21\) −8.42662 −1.83884
\(22\) −3.20824 −0.683998
\(23\) −5.09179 −1.06171 −0.530856 0.847462i \(-0.678130\pi\)
−0.530856 + 0.847462i \(0.678130\pi\)
\(24\) 2.09909 0.428475
\(25\) −3.13624 −0.627248
\(26\) −6.79975 −1.33354
\(27\) 3.34558 0.643856
\(28\) 4.01442 0.758654
\(29\) 4.18921 0.777916 0.388958 0.921255i \(-0.372835\pi\)
0.388958 + 0.921255i \(0.372835\pi\)
\(30\) 2.86567 0.523197
\(31\) 0.712068 0.127891 0.0639456 0.997953i \(-0.479632\pi\)
0.0639456 + 0.997953i \(0.479632\pi\)
\(32\) −1.00000 −0.176777
\(33\) −6.73438 −1.17230
\(34\) −1.85135 −0.317504
\(35\) 5.48047 0.926368
\(36\) 1.40618 0.234363
\(37\) −6.50946 −1.07015 −0.535074 0.844805i \(-0.679716\pi\)
−0.535074 + 0.844805i \(0.679716\pi\)
\(38\) 1.00000 0.162221
\(39\) −14.2733 −2.28555
\(40\) −1.36520 −0.215856
\(41\) 2.46268 0.384605 0.192303 0.981336i \(-0.438404\pi\)
0.192303 + 0.981336i \(0.438404\pi\)
\(42\) 8.42662 1.30026
\(43\) 10.2541 1.56373 0.781866 0.623447i \(-0.214268\pi\)
0.781866 + 0.623447i \(0.214268\pi\)
\(44\) 3.20824 0.483660
\(45\) 1.91971 0.286173
\(46\) 5.09179 0.750744
\(47\) −5.38403 −0.785341 −0.392671 0.919679i \(-0.628449\pi\)
−0.392671 + 0.919679i \(0.628449\pi\)
\(48\) −2.09909 −0.302978
\(49\) 9.11555 1.30222
\(50\) 3.13624 0.443531
\(51\) −3.88615 −0.544170
\(52\) 6.79975 0.942956
\(53\) 8.52058 1.17039 0.585196 0.810892i \(-0.301018\pi\)
0.585196 + 0.810892i \(0.301018\pi\)
\(54\) −3.34558 −0.455275
\(55\) 4.37987 0.590582
\(56\) −4.01442 −0.536449
\(57\) 2.09909 0.278031
\(58\) −4.18921 −0.550070
\(59\) 10.3430 1.34654 0.673271 0.739396i \(-0.264889\pi\)
0.673271 + 0.739396i \(0.264889\pi\)
\(60\) −2.86567 −0.369956
\(61\) 1.41889 0.181670 0.0908350 0.995866i \(-0.471046\pi\)
0.0908350 + 0.995866i \(0.471046\pi\)
\(62\) −0.712068 −0.0904327
\(63\) 5.64498 0.711201
\(64\) 1.00000 0.125000
\(65\) 9.28299 1.15141
\(66\) 6.73438 0.828945
\(67\) 12.7000 1.55155 0.775773 0.631012i \(-0.217360\pi\)
0.775773 + 0.631012i \(0.217360\pi\)
\(68\) 1.85135 0.224509
\(69\) 10.6881 1.28670
\(70\) −5.48047 −0.655041
\(71\) 4.06966 0.482980 0.241490 0.970403i \(-0.422364\pi\)
0.241490 + 0.970403i \(0.422364\pi\)
\(72\) −1.40618 −0.165720
\(73\) −10.9181 −1.27787 −0.638935 0.769261i \(-0.720625\pi\)
−0.638935 + 0.769261i \(0.720625\pi\)
\(74\) 6.50946 0.756709
\(75\) 6.58325 0.760168
\(76\) −1.00000 −0.114708
\(77\) 12.8792 1.46772
\(78\) 14.2733 1.61613
\(79\) −2.13278 −0.239957 −0.119978 0.992777i \(-0.538283\pi\)
−0.119978 + 0.992777i \(0.538283\pi\)
\(80\) 1.36520 0.152634
\(81\) −11.2412 −1.24902
\(82\) −2.46268 −0.271957
\(83\) −1.07045 −0.117497 −0.0587486 0.998273i \(-0.518711\pi\)
−0.0587486 + 0.998273i \(0.518711\pi\)
\(84\) −8.42662 −0.919420
\(85\) 2.52746 0.274141
\(86\) −10.2541 −1.10573
\(87\) −8.79352 −0.942764
\(88\) −3.20824 −0.341999
\(89\) −1.39280 −0.147636 −0.0738182 0.997272i \(-0.523518\pi\)
−0.0738182 + 0.997272i \(0.523518\pi\)
\(90\) −1.91971 −0.202355
\(91\) 27.2970 2.86151
\(92\) −5.09179 −0.530856
\(93\) −1.49469 −0.154993
\(94\) 5.38403 0.555320
\(95\) −1.36520 −0.140066
\(96\) 2.09909 0.214237
\(97\) 6.73244 0.683576 0.341788 0.939777i \(-0.388968\pi\)
0.341788 + 0.939777i \(0.388968\pi\)
\(98\) −9.11555 −0.920809
\(99\) 4.51135 0.453408
\(100\) −3.13624 −0.313624
\(101\) 4.93140 0.490693 0.245346 0.969435i \(-0.421098\pi\)
0.245346 + 0.969435i \(0.421098\pi\)
\(102\) 3.88615 0.384787
\(103\) −11.4164 −1.12489 −0.562446 0.826834i \(-0.690140\pi\)
−0.562446 + 0.826834i \(0.690140\pi\)
\(104\) −6.79975 −0.666770
\(105\) −11.5040 −1.12267
\(106\) −8.52058 −0.827592
\(107\) −2.69435 −0.260472 −0.130236 0.991483i \(-0.541574\pi\)
−0.130236 + 0.991483i \(0.541574\pi\)
\(108\) 3.34558 0.321928
\(109\) 11.5555 1.10682 0.553408 0.832911i \(-0.313327\pi\)
0.553408 + 0.832911i \(0.313327\pi\)
\(110\) −4.37987 −0.417605
\(111\) 13.6639 1.29692
\(112\) 4.01442 0.379327
\(113\) 3.46399 0.325865 0.162932 0.986637i \(-0.447905\pi\)
0.162932 + 0.986637i \(0.447905\pi\)
\(114\) −2.09909 −0.196598
\(115\) −6.95130 −0.648212
\(116\) 4.18921 0.388958
\(117\) 9.56166 0.883976
\(118\) −10.3430 −0.952149
\(119\) 7.43210 0.681299
\(120\) 2.86567 0.261599
\(121\) −0.707214 −0.0642922
\(122\) −1.41889 −0.128460
\(123\) −5.16938 −0.466107
\(124\) 0.712068 0.0639456
\(125\) −11.1076 −0.993491
\(126\) −5.64498 −0.502895
\(127\) 12.7725 1.13337 0.566687 0.823933i \(-0.308225\pi\)
0.566687 + 0.823933i \(0.308225\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −21.5242 −1.89510
\(130\) −9.28299 −0.814172
\(131\) −2.47248 −0.216022 −0.108011 0.994150i \(-0.534448\pi\)
−0.108011 + 0.994150i \(0.534448\pi\)
\(132\) −6.73438 −0.586152
\(133\) −4.01442 −0.348094
\(134\) −12.7000 −1.09711
\(135\) 4.56737 0.393096
\(136\) −1.85135 −0.158752
\(137\) −6.95851 −0.594506 −0.297253 0.954799i \(-0.596070\pi\)
−0.297253 + 0.954799i \(0.596070\pi\)
\(138\) −10.6881 −0.909834
\(139\) 2.69155 0.228294 0.114147 0.993464i \(-0.463587\pi\)
0.114147 + 0.993464i \(0.463587\pi\)
\(140\) 5.48047 0.463184
\(141\) 11.3016 0.951763
\(142\) −4.06966 −0.341518
\(143\) 21.8152 1.82428
\(144\) 1.40618 0.117181
\(145\) 5.71909 0.474945
\(146\) 10.9181 0.903590
\(147\) −19.1344 −1.57817
\(148\) −6.50946 −0.535074
\(149\) −20.5376 −1.68251 −0.841253 0.540642i \(-0.818181\pi\)
−0.841253 + 0.540642i \(0.818181\pi\)
\(150\) −6.58325 −0.537520
\(151\) 3.78224 0.307795 0.153897 0.988087i \(-0.450818\pi\)
0.153897 + 0.988087i \(0.450818\pi\)
\(152\) 1.00000 0.0811107
\(153\) 2.60333 0.210467
\(154\) −12.8792 −1.03784
\(155\) 0.972113 0.0780820
\(156\) −14.2733 −1.14278
\(157\) 1.21829 0.0972299 0.0486150 0.998818i \(-0.484519\pi\)
0.0486150 + 0.998818i \(0.484519\pi\)
\(158\) 2.13278 0.169675
\(159\) −17.8855 −1.41841
\(160\) −1.36520 −0.107928
\(161\) −20.4406 −1.61094
\(162\) 11.2412 0.883192
\(163\) 9.20183 0.720743 0.360371 0.932809i \(-0.382650\pi\)
0.360371 + 0.932809i \(0.382650\pi\)
\(164\) 2.46268 0.192303
\(165\) −9.19375 −0.715732
\(166\) 1.07045 0.0830831
\(167\) −0.544945 −0.0421691 −0.0210846 0.999778i \(-0.506712\pi\)
−0.0210846 + 0.999778i \(0.506712\pi\)
\(168\) 8.42662 0.650128
\(169\) 33.2366 2.55666
\(170\) −2.52746 −0.193847
\(171\) −1.40618 −0.107533
\(172\) 10.2541 0.781866
\(173\) 7.18185 0.546026 0.273013 0.962010i \(-0.411980\pi\)
0.273013 + 0.962010i \(0.411980\pi\)
\(174\) 8.79352 0.666635
\(175\) −12.5902 −0.951728
\(176\) 3.20824 0.241830
\(177\) −21.7109 −1.63189
\(178\) 1.39280 0.104395
\(179\) −12.2753 −0.917498 −0.458749 0.888566i \(-0.651702\pi\)
−0.458749 + 0.888566i \(0.651702\pi\)
\(180\) 1.91971 0.143087
\(181\) −2.93286 −0.217997 −0.108999 0.994042i \(-0.534764\pi\)
−0.108999 + 0.994042i \(0.534764\pi\)
\(182\) −27.2970 −2.02339
\(183\) −2.97837 −0.220168
\(184\) 5.09179 0.375372
\(185\) −8.88669 −0.653362
\(186\) 1.49469 0.109596
\(187\) 5.93958 0.434345
\(188\) −5.38403 −0.392671
\(189\) 13.4305 0.976928
\(190\) 1.36520 0.0990417
\(191\) 0.334793 0.0242248 0.0121124 0.999927i \(-0.496144\pi\)
0.0121124 + 0.999927i \(0.496144\pi\)
\(192\) −2.09909 −0.151489
\(193\) −7.21710 −0.519498 −0.259749 0.965676i \(-0.583640\pi\)
−0.259749 + 0.965676i \(0.583640\pi\)
\(194\) −6.73244 −0.483361
\(195\) −19.4858 −1.39541
\(196\) 9.11555 0.651110
\(197\) 1.72510 0.122908 0.0614542 0.998110i \(-0.480426\pi\)
0.0614542 + 0.998110i \(0.480426\pi\)
\(198\) −4.51135 −0.320608
\(199\) 7.92046 0.561466 0.280733 0.959786i \(-0.409422\pi\)
0.280733 + 0.959786i \(0.409422\pi\)
\(200\) 3.13624 0.221766
\(201\) −26.6584 −1.88034
\(202\) −4.93140 −0.346972
\(203\) 16.8172 1.18034
\(204\) −3.88615 −0.272085
\(205\) 3.36204 0.234815
\(206\) 11.4164 0.795419
\(207\) −7.15997 −0.497652
\(208\) 6.79975 0.471478
\(209\) −3.20824 −0.221918
\(210\) 11.5040 0.793851
\(211\) 1.00000 0.0688428
\(212\) 8.52058 0.585196
\(213\) −8.54258 −0.585328
\(214\) 2.69435 0.184182
\(215\) 13.9988 0.954712
\(216\) −3.34558 −0.227638
\(217\) 2.85854 0.194050
\(218\) −11.5555 −0.782637
\(219\) 22.9181 1.54866
\(220\) 4.37987 0.295291
\(221\) 12.5887 0.846810
\(222\) −13.6639 −0.917064
\(223\) 9.60089 0.642923 0.321461 0.946923i \(-0.395826\pi\)
0.321461 + 0.946923i \(0.395826\pi\)
\(224\) −4.01442 −0.268225
\(225\) −4.41011 −0.294007
\(226\) −3.46399 −0.230421
\(227\) −24.5848 −1.63175 −0.815875 0.578229i \(-0.803744\pi\)
−0.815875 + 0.578229i \(0.803744\pi\)
\(228\) 2.09909 0.139016
\(229\) 5.87183 0.388022 0.194011 0.980999i \(-0.437850\pi\)
0.194011 + 0.980999i \(0.437850\pi\)
\(230\) 6.95130 0.458355
\(231\) −27.0346 −1.77875
\(232\) −4.18921 −0.275035
\(233\) −28.7383 −1.88271 −0.941354 0.337421i \(-0.890445\pi\)
−0.941354 + 0.337421i \(0.890445\pi\)
\(234\) −9.56166 −0.625065
\(235\) −7.35026 −0.479478
\(236\) 10.3430 0.673271
\(237\) 4.47690 0.290806
\(238\) −7.43210 −0.481751
\(239\) −18.0598 −1.16819 −0.584096 0.811684i \(-0.698551\pi\)
−0.584096 + 0.811684i \(0.698551\pi\)
\(240\) −2.86567 −0.184978
\(241\) 6.33711 0.408209 0.204105 0.978949i \(-0.434572\pi\)
0.204105 + 0.978949i \(0.434572\pi\)
\(242\) 0.707214 0.0454614
\(243\) 13.5596 0.869846
\(244\) 1.41889 0.0908350
\(245\) 12.4445 0.795051
\(246\) 5.16938 0.329587
\(247\) −6.79975 −0.432658
\(248\) −0.712068 −0.0452164
\(249\) 2.24697 0.142396
\(250\) 11.1076 0.702504
\(251\) 10.5272 0.664470 0.332235 0.943197i \(-0.392197\pi\)
0.332235 + 0.943197i \(0.392197\pi\)
\(252\) 5.64498 0.355601
\(253\) −16.3357 −1.02702
\(254\) −12.7725 −0.801417
\(255\) −5.30536 −0.332235
\(256\) 1.00000 0.0625000
\(257\) 13.4516 0.839087 0.419544 0.907735i \(-0.362190\pi\)
0.419544 + 0.907735i \(0.362190\pi\)
\(258\) 21.5242 1.34004
\(259\) −26.1317 −1.62374
\(260\) 9.28299 0.575707
\(261\) 5.89077 0.364629
\(262\) 2.47248 0.152750
\(263\) −27.4111 −1.69024 −0.845122 0.534574i \(-0.820472\pi\)
−0.845122 + 0.534574i \(0.820472\pi\)
\(264\) 6.73438 0.414472
\(265\) 11.6323 0.714564
\(266\) 4.01442 0.246140
\(267\) 2.92361 0.178922
\(268\) 12.7000 0.775773
\(269\) −15.0893 −0.920011 −0.460005 0.887916i \(-0.652153\pi\)
−0.460005 + 0.887916i \(0.652153\pi\)
\(270\) −4.56737 −0.277961
\(271\) −11.0613 −0.671926 −0.335963 0.941875i \(-0.609062\pi\)
−0.335963 + 0.941875i \(0.609062\pi\)
\(272\) 1.85135 0.112255
\(273\) −57.2989 −3.46789
\(274\) 6.95851 0.420379
\(275\) −10.0618 −0.606749
\(276\) 10.6881 0.643350
\(277\) −9.23931 −0.555136 −0.277568 0.960706i \(-0.589528\pi\)
−0.277568 + 0.960706i \(0.589528\pi\)
\(278\) −2.69155 −0.161428
\(279\) 1.00129 0.0599459
\(280\) −5.48047 −0.327521
\(281\) −1.98630 −0.118493 −0.0592464 0.998243i \(-0.518870\pi\)
−0.0592464 + 0.998243i \(0.518870\pi\)
\(282\) −11.3016 −0.672998
\(283\) 22.3346 1.32765 0.663827 0.747886i \(-0.268931\pi\)
0.663827 + 0.747886i \(0.268931\pi\)
\(284\) 4.06966 0.241490
\(285\) 2.86567 0.169748
\(286\) −21.8152 −1.28996
\(287\) 9.88621 0.583564
\(288\) −1.40618 −0.0828598
\(289\) −13.5725 −0.798382
\(290\) −5.71909 −0.335836
\(291\) −14.1320 −0.828433
\(292\) −10.9181 −0.638935
\(293\) 7.92357 0.462900 0.231450 0.972847i \(-0.425653\pi\)
0.231450 + 0.972847i \(0.425653\pi\)
\(294\) 19.1344 1.11594
\(295\) 14.1202 0.822111
\(296\) 6.50946 0.378355
\(297\) 10.7334 0.622815
\(298\) 20.5376 1.18971
\(299\) −34.6229 −2.00230
\(300\) 6.58325 0.380084
\(301\) 41.1641 2.37266
\(302\) −3.78224 −0.217644
\(303\) −10.3515 −0.594675
\(304\) −1.00000 −0.0573539
\(305\) 1.93706 0.110916
\(306\) −2.60333 −0.148822
\(307\) 5.90593 0.337069 0.168535 0.985696i \(-0.446097\pi\)
0.168535 + 0.985696i \(0.446097\pi\)
\(308\) 12.8792 0.733861
\(309\) 23.9641 1.36327
\(310\) −0.972113 −0.0552123
\(311\) −0.881378 −0.0499783 −0.0249892 0.999688i \(-0.507955\pi\)
−0.0249892 + 0.999688i \(0.507955\pi\)
\(312\) 14.2733 0.808066
\(313\) −21.3977 −1.20947 −0.604734 0.796428i \(-0.706720\pi\)
−0.604734 + 0.796428i \(0.706720\pi\)
\(314\) −1.21829 −0.0687519
\(315\) 7.70651 0.434213
\(316\) −2.13278 −0.119978
\(317\) 2.33800 0.131315 0.0656577 0.997842i \(-0.479085\pi\)
0.0656577 + 0.997842i \(0.479085\pi\)
\(318\) 17.8855 1.00297
\(319\) 13.4400 0.752494
\(320\) 1.36520 0.0763168
\(321\) 5.65567 0.315669
\(322\) 20.4406 1.13911
\(323\) −1.85135 −0.103012
\(324\) −11.2412 −0.624511
\(325\) −21.3256 −1.18293
\(326\) −9.20183 −0.509642
\(327\) −24.2560 −1.34136
\(328\) −2.46268 −0.135979
\(329\) −21.6137 −1.19160
\(330\) 9.19375 0.506099
\(331\) 3.12286 0.171648 0.0858240 0.996310i \(-0.472648\pi\)
0.0858240 + 0.996310i \(0.472648\pi\)
\(332\) −1.07045 −0.0587486
\(333\) −9.15346 −0.501606
\(334\) 0.544945 0.0298181
\(335\) 17.3379 0.947273
\(336\) −8.42662 −0.459710
\(337\) 8.89853 0.484734 0.242367 0.970185i \(-0.422076\pi\)
0.242367 + 0.970185i \(0.422076\pi\)
\(338\) −33.2366 −1.80783
\(339\) −7.27122 −0.394919
\(340\) 2.52746 0.137071
\(341\) 2.28448 0.123712
\(342\) 1.40618 0.0760374
\(343\) 8.49269 0.458562
\(344\) −10.2541 −0.552863
\(345\) 14.5914 0.785574
\(346\) −7.18185 −0.386099
\(347\) −5.82350 −0.312622 −0.156311 0.987708i \(-0.549960\pi\)
−0.156311 + 0.987708i \(0.549960\pi\)
\(348\) −8.79352 −0.471382
\(349\) −22.3662 −1.19724 −0.598618 0.801035i \(-0.704283\pi\)
−0.598618 + 0.801035i \(0.704283\pi\)
\(350\) 12.5902 0.672973
\(351\) 22.7491 1.21426
\(352\) −3.20824 −0.171000
\(353\) −14.8098 −0.788246 −0.394123 0.919058i \(-0.628952\pi\)
−0.394123 + 0.919058i \(0.628952\pi\)
\(354\) 21.7109 1.15392
\(355\) 5.55588 0.294876
\(356\) −1.39280 −0.0738182
\(357\) −15.6006 −0.825674
\(358\) 12.2753 0.648769
\(359\) 30.4912 1.60927 0.804633 0.593773i \(-0.202362\pi\)
0.804633 + 0.593773i \(0.202362\pi\)
\(360\) −1.91971 −0.101178
\(361\) 1.00000 0.0526316
\(362\) 2.93286 0.154148
\(363\) 1.48451 0.0779164
\(364\) 27.2970 1.43075
\(365\) −14.9054 −0.780183
\(366\) 2.97837 0.155682
\(367\) 33.5656 1.75211 0.876054 0.482213i \(-0.160167\pi\)
0.876054 + 0.482213i \(0.160167\pi\)
\(368\) −5.09179 −0.265428
\(369\) 3.46296 0.180274
\(370\) 8.88669 0.461997
\(371\) 34.2052 1.77584
\(372\) −1.49469 −0.0774963
\(373\) 12.1478 0.628991 0.314495 0.949259i \(-0.398165\pi\)
0.314495 + 0.949259i \(0.398165\pi\)
\(374\) −5.93958 −0.307128
\(375\) 23.3158 1.20402
\(376\) 5.38403 0.277660
\(377\) 28.4856 1.46708
\(378\) −13.4305 −0.690792
\(379\) 6.92608 0.355769 0.177884 0.984051i \(-0.443075\pi\)
0.177884 + 0.984051i \(0.443075\pi\)
\(380\) −1.36520 −0.0700331
\(381\) −26.8106 −1.37355
\(382\) −0.334793 −0.0171295
\(383\) −9.79457 −0.500479 −0.250239 0.968184i \(-0.580509\pi\)
−0.250239 + 0.968184i \(0.580509\pi\)
\(384\) 2.09909 0.107119
\(385\) 17.5826 0.896094
\(386\) 7.21710 0.367341
\(387\) 14.4191 0.732962
\(388\) 6.73244 0.341788
\(389\) 34.1871 1.73335 0.866676 0.498871i \(-0.166252\pi\)
0.866676 + 0.498871i \(0.166252\pi\)
\(390\) 19.4858 0.986704
\(391\) −9.42670 −0.476729
\(392\) −9.11555 −0.460405
\(393\) 5.18996 0.261799
\(394\) −1.72510 −0.0869094
\(395\) −2.91167 −0.146502
\(396\) 4.51135 0.226704
\(397\) 16.0565 0.805852 0.402926 0.915233i \(-0.367993\pi\)
0.402926 + 0.915233i \(0.367993\pi\)
\(398\) −7.92046 −0.397017
\(399\) 8.42662 0.421859
\(400\) −3.13624 −0.156812
\(401\) −12.0767 −0.603084 −0.301542 0.953453i \(-0.597501\pi\)
−0.301542 + 0.953453i \(0.597501\pi\)
\(402\) 26.6584 1.32960
\(403\) 4.84189 0.241191
\(404\) 4.93140 0.245346
\(405\) −15.3464 −0.762571
\(406\) −16.8172 −0.834625
\(407\) −20.8839 −1.03518
\(408\) 3.88615 0.192393
\(409\) −9.59680 −0.474531 −0.237266 0.971445i \(-0.576251\pi\)
−0.237266 + 0.971445i \(0.576251\pi\)
\(410\) −3.36204 −0.166039
\(411\) 14.6065 0.720487
\(412\) −11.4164 −0.562446
\(413\) 41.5211 2.04312
\(414\) 7.15997 0.351893
\(415\) −1.46138 −0.0717361
\(416\) −6.79975 −0.333385
\(417\) −5.64980 −0.276672
\(418\) 3.20824 0.156920
\(419\) −17.7597 −0.867620 −0.433810 0.901004i \(-0.642831\pi\)
−0.433810 + 0.901004i \(0.642831\pi\)
\(420\) −11.5040 −0.561337
\(421\) −32.4693 −1.58245 −0.791227 0.611522i \(-0.790558\pi\)
−0.791227 + 0.611522i \(0.790558\pi\)
\(422\) −1.00000 −0.0486792
\(423\) −7.57090 −0.368110
\(424\) −8.52058 −0.413796
\(425\) −5.80628 −0.281646
\(426\) 8.54258 0.413889
\(427\) 5.69601 0.275649
\(428\) −2.69435 −0.130236
\(429\) −45.7921 −2.21086
\(430\) −13.9988 −0.675083
\(431\) −26.6865 −1.28544 −0.642721 0.766100i \(-0.722194\pi\)
−0.642721 + 0.766100i \(0.722194\pi\)
\(432\) 3.34558 0.160964
\(433\) 2.53135 0.121649 0.0608246 0.998148i \(-0.480627\pi\)
0.0608246 + 0.998148i \(0.480627\pi\)
\(434\) −2.85854 −0.137214
\(435\) −12.0049 −0.575590
\(436\) 11.5555 0.553408
\(437\) 5.09179 0.243574
\(438\) −22.9181 −1.09507
\(439\) 3.05361 0.145741 0.0728704 0.997341i \(-0.476784\pi\)
0.0728704 + 0.997341i \(0.476784\pi\)
\(440\) −4.37987 −0.208802
\(441\) 12.8181 0.610385
\(442\) −12.5887 −0.598785
\(443\) −23.5422 −1.11852 −0.559261 0.828992i \(-0.688915\pi\)
−0.559261 + 0.828992i \(0.688915\pi\)
\(444\) 13.6639 0.648462
\(445\) −1.90144 −0.0901371
\(446\) −9.60089 −0.454615
\(447\) 43.1103 2.03905
\(448\) 4.01442 0.189663
\(449\) −28.4555 −1.34290 −0.671448 0.741052i \(-0.734327\pi\)
−0.671448 + 0.741052i \(0.734327\pi\)
\(450\) 4.41011 0.207895
\(451\) 7.90085 0.372036
\(452\) 3.46399 0.162932
\(453\) −7.93927 −0.373019
\(454\) 24.5848 1.15382
\(455\) 37.2658 1.74705
\(456\) −2.09909 −0.0982989
\(457\) −21.6748 −1.01390 −0.506952 0.861974i \(-0.669228\pi\)
−0.506952 + 0.861974i \(0.669228\pi\)
\(458\) −5.87183 −0.274373
\(459\) 6.19384 0.289104
\(460\) −6.95130 −0.324106
\(461\) 38.6715 1.80111 0.900556 0.434740i \(-0.143160\pi\)
0.900556 + 0.434740i \(0.143160\pi\)
\(462\) 27.0346 1.25776
\(463\) 17.3366 0.805702 0.402851 0.915266i \(-0.368019\pi\)
0.402851 + 0.915266i \(0.368019\pi\)
\(464\) 4.18921 0.194479
\(465\) −2.04055 −0.0946283
\(466\) 28.7383 1.33128
\(467\) −22.9253 −1.06086 −0.530429 0.847729i \(-0.677969\pi\)
−0.530429 + 0.847729i \(0.677969\pi\)
\(468\) 9.56166 0.441988
\(469\) 50.9829 2.35417
\(470\) 7.35026 0.339042
\(471\) −2.55729 −0.117834
\(472\) −10.3430 −0.476075
\(473\) 32.8975 1.51263
\(474\) −4.47690 −0.205631
\(475\) 3.13624 0.143901
\(476\) 7.43210 0.340650
\(477\) 11.9814 0.548593
\(478\) 18.0598 0.826037
\(479\) 37.0920 1.69478 0.847388 0.530974i \(-0.178174\pi\)
0.847388 + 0.530974i \(0.178174\pi\)
\(480\) 2.86567 0.130799
\(481\) −44.2627 −2.01821
\(482\) −6.33711 −0.288648
\(483\) 42.9066 1.95232
\(484\) −0.707214 −0.0321461
\(485\) 9.19111 0.417347
\(486\) −13.5596 −0.615074
\(487\) −15.8194 −0.716847 −0.358423 0.933559i \(-0.616686\pi\)
−0.358423 + 0.933559i \(0.616686\pi\)
\(488\) −1.41889 −0.0642301
\(489\) −19.3155 −0.873476
\(490\) −12.4445 −0.562186
\(491\) 29.5626 1.33414 0.667072 0.744994i \(-0.267547\pi\)
0.667072 + 0.744994i \(0.267547\pi\)
\(492\) −5.16938 −0.233054
\(493\) 7.75570 0.349299
\(494\) 6.79975 0.305935
\(495\) 6.15888 0.276821
\(496\) 0.712068 0.0319728
\(497\) 16.3373 0.732829
\(498\) −2.24697 −0.100689
\(499\) −14.7836 −0.661804 −0.330902 0.943665i \(-0.607353\pi\)
−0.330902 + 0.943665i \(0.607353\pi\)
\(500\) −11.1076 −0.496745
\(501\) 1.14389 0.0511052
\(502\) −10.5272 −0.469852
\(503\) −6.57703 −0.293255 −0.146628 0.989192i \(-0.546842\pi\)
−0.146628 + 0.989192i \(0.546842\pi\)
\(504\) −5.64498 −0.251448
\(505\) 6.73233 0.299585
\(506\) 16.3357 0.726210
\(507\) −69.7666 −3.09844
\(508\) 12.7725 0.566687
\(509\) −6.46511 −0.286561 −0.143280 0.989682i \(-0.545765\pi\)
−0.143280 + 0.989682i \(0.545765\pi\)
\(510\) 5.30536 0.234925
\(511\) −43.8299 −1.93892
\(512\) −1.00000 −0.0441942
\(513\) −3.34558 −0.147711
\(514\) −13.4516 −0.593324
\(515\) −15.5856 −0.686785
\(516\) −21.5242 −0.947551
\(517\) −17.2732 −0.759676
\(518\) 26.1317 1.14816
\(519\) −15.0754 −0.661735
\(520\) −9.28299 −0.407086
\(521\) −30.2026 −1.32320 −0.661600 0.749857i \(-0.730122\pi\)
−0.661600 + 0.749857i \(0.730122\pi\)
\(522\) −5.89077 −0.257832
\(523\) 34.8479 1.52379 0.761897 0.647698i \(-0.224268\pi\)
0.761897 + 0.647698i \(0.224268\pi\)
\(524\) −2.47248 −0.108011
\(525\) 26.4279 1.15341
\(526\) 27.4111 1.19518
\(527\) 1.31829 0.0574256
\(528\) −6.73438 −0.293076
\(529\) 2.92637 0.127233
\(530\) −11.6323 −0.505273
\(531\) 14.5441 0.631159
\(532\) −4.01442 −0.174047
\(533\) 16.7456 0.725331
\(534\) −2.92361 −0.126517
\(535\) −3.67831 −0.159027
\(536\) −12.7000 −0.548555
\(537\) 25.7669 1.11193
\(538\) 15.0893 0.650546
\(539\) 29.2448 1.25966
\(540\) 4.56737 0.196548
\(541\) 12.1188 0.521026 0.260513 0.965470i \(-0.416108\pi\)
0.260513 + 0.965470i \(0.416108\pi\)
\(542\) 11.0613 0.475123
\(543\) 6.15633 0.264193
\(544\) −1.85135 −0.0793761
\(545\) 15.7755 0.675749
\(546\) 57.2989 2.45217
\(547\) 14.5532 0.622251 0.311126 0.950369i \(-0.399294\pi\)
0.311126 + 0.950369i \(0.399294\pi\)
\(548\) −6.95851 −0.297253
\(549\) 1.99521 0.0851535
\(550\) 10.0618 0.429037
\(551\) −4.18921 −0.178466
\(552\) −10.6881 −0.454917
\(553\) −8.56188 −0.364088
\(554\) 9.23931 0.392541
\(555\) 18.6540 0.791816
\(556\) 2.69155 0.114147
\(557\) −16.4156 −0.695552 −0.347776 0.937578i \(-0.613063\pi\)
−0.347776 + 0.937578i \(0.613063\pi\)
\(558\) −1.00129 −0.0423882
\(559\) 69.7251 2.94906
\(560\) 5.48047 0.231592
\(561\) −12.4677 −0.526387
\(562\) 1.98630 0.0837870
\(563\) −28.9442 −1.21985 −0.609925 0.792459i \(-0.708801\pi\)
−0.609925 + 0.792459i \(0.708801\pi\)
\(564\) 11.3016 0.475882
\(565\) 4.72902 0.198952
\(566\) −22.3346 −0.938793
\(567\) −45.1269 −1.89515
\(568\) −4.06966 −0.170759
\(569\) −1.36758 −0.0573320 −0.0286660 0.999589i \(-0.509126\pi\)
−0.0286660 + 0.999589i \(0.509126\pi\)
\(570\) −2.86567 −0.120030
\(571\) 33.7948 1.41427 0.707134 0.707079i \(-0.249988\pi\)
0.707134 + 0.707079i \(0.249988\pi\)
\(572\) 21.8152 0.912140
\(573\) −0.702762 −0.0293583
\(574\) −9.88621 −0.412642
\(575\) 15.9691 0.665957
\(576\) 1.40618 0.0585907
\(577\) 13.6874 0.569813 0.284907 0.958555i \(-0.408037\pi\)
0.284907 + 0.958555i \(0.408037\pi\)
\(578\) 13.5725 0.564541
\(579\) 15.1493 0.629585
\(580\) 5.71909 0.237472
\(581\) −4.29724 −0.178279
\(582\) 14.1320 0.585790
\(583\) 27.3360 1.13214
\(584\) 10.9181 0.451795
\(585\) 13.0535 0.539697
\(586\) −7.92357 −0.327320
\(587\) −6.75410 −0.278772 −0.139386 0.990238i \(-0.544513\pi\)
−0.139386 + 0.990238i \(0.544513\pi\)
\(588\) −19.1344 −0.789087
\(589\) −0.712068 −0.0293403
\(590\) −14.1202 −0.581320
\(591\) −3.62114 −0.148954
\(592\) −6.50946 −0.267537
\(593\) 8.99007 0.369178 0.184589 0.982816i \(-0.440905\pi\)
0.184589 + 0.982816i \(0.440905\pi\)
\(594\) −10.7334 −0.440397
\(595\) 10.1463 0.415957
\(596\) −20.5376 −0.841253
\(597\) −16.6257 −0.680447
\(598\) 34.6229 1.41584
\(599\) 23.5439 0.961977 0.480988 0.876727i \(-0.340278\pi\)
0.480988 + 0.876727i \(0.340278\pi\)
\(600\) −6.58325 −0.268760
\(601\) 30.8591 1.25877 0.629385 0.777093i \(-0.283307\pi\)
0.629385 + 0.777093i \(0.283307\pi\)
\(602\) −41.1641 −1.67772
\(603\) 17.8584 0.727250
\(604\) 3.78224 0.153897
\(605\) −0.965486 −0.0392526
\(606\) 10.3515 0.420499
\(607\) 32.0409 1.30050 0.650250 0.759720i \(-0.274664\pi\)
0.650250 + 0.759720i \(0.274664\pi\)
\(608\) 1.00000 0.0405554
\(609\) −35.3009 −1.43046
\(610\) −1.93706 −0.0784293
\(611\) −36.6101 −1.48108
\(612\) 2.60333 0.105233
\(613\) −3.46021 −0.139757 −0.0698784 0.997556i \(-0.522261\pi\)
−0.0698784 + 0.997556i \(0.522261\pi\)
\(614\) −5.90593 −0.238344
\(615\) −7.05721 −0.284574
\(616\) −12.8792 −0.518918
\(617\) −23.6533 −0.952245 −0.476122 0.879379i \(-0.657958\pi\)
−0.476122 + 0.879379i \(0.657958\pi\)
\(618\) −23.9641 −0.963976
\(619\) −37.8759 −1.52236 −0.761180 0.648541i \(-0.775380\pi\)
−0.761180 + 0.648541i \(0.775380\pi\)
\(620\) 0.972113 0.0390410
\(621\) −17.0350 −0.683590
\(622\) 0.881378 0.0353400
\(623\) −5.59128 −0.224010
\(624\) −14.2733 −0.571389
\(625\) 0.517193 0.0206877
\(626\) 21.3977 0.855222
\(627\) 6.73438 0.268945
\(628\) 1.21829 0.0486150
\(629\) −12.0513 −0.480517
\(630\) −7.70651 −0.307035
\(631\) −11.2238 −0.446811 −0.223405 0.974726i \(-0.571717\pi\)
−0.223405 + 0.974726i \(0.571717\pi\)
\(632\) 2.13278 0.0848375
\(633\) −2.09909 −0.0834313
\(634\) −2.33800 −0.0928539
\(635\) 17.4369 0.691964
\(636\) −17.8855 −0.709205
\(637\) 61.9834 2.45587
\(638\) −13.4400 −0.532093
\(639\) 5.72267 0.226385
\(640\) −1.36520 −0.0539641
\(641\) −7.97255 −0.314897 −0.157448 0.987527i \(-0.550327\pi\)
−0.157448 + 0.987527i \(0.550327\pi\)
\(642\) −5.65567 −0.223212
\(643\) 39.9487 1.57542 0.787711 0.616045i \(-0.211266\pi\)
0.787711 + 0.616045i \(0.211266\pi\)
\(644\) −20.4406 −0.805472
\(645\) −29.3848 −1.15702
\(646\) 1.85135 0.0728405
\(647\) 1.94128 0.0763196 0.0381598 0.999272i \(-0.487850\pi\)
0.0381598 + 0.999272i \(0.487850\pi\)
\(648\) 11.2412 0.441596
\(649\) 33.1828 1.30254
\(650\) 21.3256 0.836461
\(651\) −6.00033 −0.235171
\(652\) 9.20183 0.360371
\(653\) −19.3525 −0.757322 −0.378661 0.925535i \(-0.623615\pi\)
−0.378661 + 0.925535i \(0.623615\pi\)
\(654\) 24.2560 0.948485
\(655\) −3.37542 −0.131889
\(656\) 2.46268 0.0961513
\(657\) −15.3528 −0.598970
\(658\) 21.6137 0.842591
\(659\) 19.3530 0.753886 0.376943 0.926236i \(-0.376975\pi\)
0.376943 + 0.926236i \(0.376975\pi\)
\(660\) −9.19375 −0.357866
\(661\) −44.0744 −1.71430 −0.857148 0.515070i \(-0.827766\pi\)
−0.857148 + 0.515070i \(0.827766\pi\)
\(662\) −3.12286 −0.121373
\(663\) −26.4249 −1.02626
\(664\) 1.07045 0.0415416
\(665\) −5.48047 −0.212523
\(666\) 9.15346 0.354689
\(667\) −21.3306 −0.825923
\(668\) −0.544945 −0.0210846
\(669\) −20.1531 −0.779165
\(670\) −17.3379 −0.669823
\(671\) 4.55213 0.175733
\(672\) 8.42662 0.325064
\(673\) −13.7683 −0.530731 −0.265365 0.964148i \(-0.585493\pi\)
−0.265365 + 0.964148i \(0.585493\pi\)
\(674\) −8.89853 −0.342758
\(675\) −10.4925 −0.403858
\(676\) 33.2366 1.27833
\(677\) 37.4217 1.43823 0.719117 0.694889i \(-0.244546\pi\)
0.719117 + 0.694889i \(0.244546\pi\)
\(678\) 7.27122 0.279250
\(679\) 27.0268 1.03719
\(680\) −2.52746 −0.0969236
\(681\) 51.6057 1.97753
\(682\) −2.28448 −0.0874774
\(683\) 11.6717 0.446603 0.223302 0.974749i \(-0.428317\pi\)
0.223302 + 0.974749i \(0.428317\pi\)
\(684\) −1.40618 −0.0537666
\(685\) −9.49973 −0.362966
\(686\) −8.49269 −0.324252
\(687\) −12.3255 −0.470247
\(688\) 10.2541 0.390933
\(689\) 57.9378 2.20725
\(690\) −14.5914 −0.555485
\(691\) 2.80943 0.106876 0.0534379 0.998571i \(-0.482982\pi\)
0.0534379 + 0.998571i \(0.482982\pi\)
\(692\) 7.18185 0.273013
\(693\) 18.1104 0.687959
\(694\) 5.82350 0.221057
\(695\) 3.67449 0.139381
\(696\) 8.79352 0.333318
\(697\) 4.55928 0.172695
\(698\) 22.3662 0.846574
\(699\) 60.3242 2.28167
\(700\) −12.5902 −0.475864
\(701\) 11.3301 0.427934 0.213967 0.976841i \(-0.431362\pi\)
0.213967 + 0.976841i \(0.431362\pi\)
\(702\) −22.7491 −0.858609
\(703\) 6.50946 0.245509
\(704\) 3.20824 0.120915
\(705\) 15.4288 0.581084
\(706\) 14.8098 0.557374
\(707\) 19.7967 0.744532
\(708\) −21.7109 −0.815944
\(709\) −48.9067 −1.83673 −0.918364 0.395736i \(-0.870489\pi\)
−0.918364 + 0.395736i \(0.870489\pi\)
\(710\) −5.55588 −0.208509
\(711\) −2.99907 −0.112474
\(712\) 1.39280 0.0521974
\(713\) −3.62570 −0.135784
\(714\) 15.6006 0.583839
\(715\) 29.7820 1.11379
\(716\) −12.2753 −0.458749
\(717\) 37.9092 1.41574
\(718\) −30.4912 −1.13792
\(719\) 18.1079 0.675312 0.337656 0.941270i \(-0.390366\pi\)
0.337656 + 0.941270i \(0.390366\pi\)
\(720\) 1.91971 0.0715433
\(721\) −45.8302 −1.70681
\(722\) −1.00000 −0.0372161
\(723\) −13.3022 −0.494713
\(724\) −2.93286 −0.108999
\(725\) −13.1384 −0.487946
\(726\) −1.48451 −0.0550952
\(727\) 9.15818 0.339658 0.169829 0.985474i \(-0.445678\pi\)
0.169829 + 0.985474i \(0.445678\pi\)
\(728\) −27.2970 −1.01170
\(729\) 5.26087 0.194847
\(730\) 14.9054 0.551673
\(731\) 18.9839 0.702145
\(732\) −2.97837 −0.110084
\(733\) −36.0381 −1.33110 −0.665549 0.746354i \(-0.731803\pi\)
−0.665549 + 0.746354i \(0.731803\pi\)
\(734\) −33.5656 −1.23893
\(735\) −26.1221 −0.963530
\(736\) 5.09179 0.187686
\(737\) 40.7445 1.50084
\(738\) −3.46296 −0.127473
\(739\) 17.8157 0.655360 0.327680 0.944789i \(-0.393733\pi\)
0.327680 + 0.944789i \(0.393733\pi\)
\(740\) −8.88669 −0.326681
\(741\) 14.2733 0.524342
\(742\) −34.2052 −1.25571
\(743\) 36.6957 1.34623 0.673117 0.739536i \(-0.264955\pi\)
0.673117 + 0.739536i \(0.264955\pi\)
\(744\) 1.49469 0.0547982
\(745\) −28.0379 −1.02723
\(746\) −12.1478 −0.444764
\(747\) −1.50524 −0.0550740
\(748\) 5.93958 0.217172
\(749\) −10.8162 −0.395216
\(750\) −23.3158 −0.851372
\(751\) 3.91941 0.143021 0.0715106 0.997440i \(-0.477218\pi\)
0.0715106 + 0.997440i \(0.477218\pi\)
\(752\) −5.38403 −0.196335
\(753\) −22.0975 −0.805278
\(754\) −28.4856 −1.03738
\(755\) 5.16350 0.187919
\(756\) 13.4305 0.488464
\(757\) 22.5512 0.819637 0.409818 0.912167i \(-0.365592\pi\)
0.409818 + 0.912167i \(0.365592\pi\)
\(758\) −6.92608 −0.251567
\(759\) 34.2901 1.24465
\(760\) 1.36520 0.0495209
\(761\) 27.4817 0.996210 0.498105 0.867117i \(-0.334029\pi\)
0.498105 + 0.867117i \(0.334029\pi\)
\(762\) 26.8106 0.971245
\(763\) 46.3886 1.67938
\(764\) 0.334793 0.0121124
\(765\) 3.55406 0.128497
\(766\) 9.79457 0.353892
\(767\) 70.3298 2.53946
\(768\) −2.09909 −0.0757444
\(769\) 35.7216 1.28815 0.644077 0.764961i \(-0.277242\pi\)
0.644077 + 0.764961i \(0.277242\pi\)
\(770\) −17.5826 −0.633634
\(771\) −28.2361 −1.01690
\(772\) −7.21710 −0.259749
\(773\) 5.71637 0.205603 0.102802 0.994702i \(-0.467219\pi\)
0.102802 + 0.994702i \(0.467219\pi\)
\(774\) −14.4191 −0.518282
\(775\) −2.23322 −0.0802195
\(776\) −6.73244 −0.241681
\(777\) 54.8528 1.96783
\(778\) −34.1871 −1.22567
\(779\) −2.46268 −0.0882345
\(780\) −19.4858 −0.697705
\(781\) 13.0564 0.467196
\(782\) 9.42670 0.337098
\(783\) 14.0153 0.500866
\(784\) 9.11555 0.325555
\(785\) 1.66320 0.0593622
\(786\) −5.18996 −0.185120
\(787\) −8.51979 −0.303698 −0.151849 0.988404i \(-0.548523\pi\)
−0.151849 + 0.988404i \(0.548523\pi\)
\(788\) 1.72510 0.0614542
\(789\) 57.5385 2.04842
\(790\) 2.91167 0.103592
\(791\) 13.9059 0.494437
\(792\) −4.51135 −0.160304
\(793\) 9.64809 0.342614
\(794\) −16.0565 −0.569823
\(795\) −24.4172 −0.865987
\(796\) 7.92046 0.280733
\(797\) −29.3299 −1.03892 −0.519460 0.854495i \(-0.673867\pi\)
−0.519460 + 0.854495i \(0.673867\pi\)
\(798\) −8.42662 −0.298299
\(799\) −9.96773 −0.352633
\(800\) 3.13624 0.110883
\(801\) −1.95852 −0.0692010
\(802\) 12.0767 0.426445
\(803\) −35.0279 −1.23611
\(804\) −26.6584 −0.940168
\(805\) −27.9054 −0.983537
\(806\) −4.84189 −0.170548
\(807\) 31.6738 1.11497
\(808\) −4.93140 −0.173486
\(809\) 17.5296 0.616307 0.308154 0.951337i \(-0.400289\pi\)
0.308154 + 0.951337i \(0.400289\pi\)
\(810\) 15.3464 0.539219
\(811\) 17.4583 0.613042 0.306521 0.951864i \(-0.400835\pi\)
0.306521 + 0.951864i \(0.400835\pi\)
\(812\) 16.8172 0.590169
\(813\) 23.2187 0.814314
\(814\) 20.8839 0.731980
\(815\) 12.5623 0.440038
\(816\) −3.88615 −0.136043
\(817\) −10.2541 −0.358745
\(818\) 9.59680 0.335544
\(819\) 38.3845 1.34126
\(820\) 3.36204 0.117407
\(821\) 20.5697 0.717886 0.358943 0.933359i \(-0.383137\pi\)
0.358943 + 0.933359i \(0.383137\pi\)
\(822\) −14.6065 −0.509462
\(823\) 47.7009 1.66275 0.831375 0.555712i \(-0.187554\pi\)
0.831375 + 0.555712i \(0.187554\pi\)
\(824\) 11.4164 0.397710
\(825\) 21.1206 0.735326
\(826\) −41.5211 −1.44470
\(827\) −34.8192 −1.21078 −0.605391 0.795928i \(-0.706983\pi\)
−0.605391 + 0.795928i \(0.706983\pi\)
\(828\) −7.15997 −0.248826
\(829\) 5.13640 0.178394 0.0891972 0.996014i \(-0.471570\pi\)
0.0891972 + 0.996014i \(0.471570\pi\)
\(830\) 1.46138 0.0507251
\(831\) 19.3941 0.672775
\(832\) 6.79975 0.235739
\(833\) 16.8761 0.584722
\(834\) 5.64980 0.195636
\(835\) −0.743957 −0.0257457
\(836\) −3.20824 −0.110959
\(837\) 2.38228 0.0823436
\(838\) 17.7597 0.613500
\(839\) −30.2316 −1.04371 −0.521855 0.853034i \(-0.674760\pi\)
−0.521855 + 0.853034i \(0.674760\pi\)
\(840\) 11.5040 0.396925
\(841\) −11.4505 −0.394846
\(842\) 32.4693 1.11896
\(843\) 4.16942 0.143603
\(844\) 1.00000 0.0344214
\(845\) 45.3745 1.56093
\(846\) 7.57090 0.260293
\(847\) −2.83905 −0.0975510
\(848\) 8.52058 0.292598
\(849\) −46.8823 −1.60900
\(850\) 5.80628 0.199154
\(851\) 33.1448 1.13619
\(852\) −8.54258 −0.292664
\(853\) −13.5929 −0.465413 −0.232706 0.972547i \(-0.574758\pi\)
−0.232706 + 0.972547i \(0.574758\pi\)
\(854\) −5.69601 −0.194914
\(855\) −1.91971 −0.0656526
\(856\) 2.69435 0.0920908
\(857\) 24.8412 0.848560 0.424280 0.905531i \(-0.360527\pi\)
0.424280 + 0.905531i \(0.360527\pi\)
\(858\) 45.7921 1.56332
\(859\) 31.0539 1.05955 0.529773 0.848140i \(-0.322277\pi\)
0.529773 + 0.848140i \(0.322277\pi\)
\(860\) 13.9988 0.477356
\(861\) −20.7520 −0.707227
\(862\) 26.6865 0.908945
\(863\) −4.29609 −0.146241 −0.0731203 0.997323i \(-0.523296\pi\)
−0.0731203 + 0.997323i \(0.523296\pi\)
\(864\) −3.34558 −0.113819
\(865\) 9.80464 0.333368
\(866\) −2.53135 −0.0860189
\(867\) 28.4899 0.967567
\(868\) 2.85854 0.0970251
\(869\) −6.84247 −0.232115
\(870\) 12.0049 0.407004
\(871\) 86.3565 2.92608
\(872\) −11.5555 −0.391318
\(873\) 9.46701 0.320410
\(874\) −5.09179 −0.172233
\(875\) −44.5904 −1.50743
\(876\) 22.9181 0.774331
\(877\) 46.7308 1.57799 0.788994 0.614401i \(-0.210602\pi\)
0.788994 + 0.614401i \(0.210602\pi\)
\(878\) −3.05361 −0.103054
\(879\) −16.6323 −0.560993
\(880\) 4.37987 0.147645
\(881\) 51.3965 1.73159 0.865796 0.500398i \(-0.166813\pi\)
0.865796 + 0.500398i \(0.166813\pi\)
\(882\) −12.8181 −0.431607
\(883\) 6.00177 0.201976 0.100988 0.994888i \(-0.467800\pi\)
0.100988 + 0.994888i \(0.467800\pi\)
\(884\) 12.5887 0.423405
\(885\) −29.6396 −0.996324
\(886\) 23.5422 0.790914
\(887\) 26.9133 0.903659 0.451829 0.892104i \(-0.350772\pi\)
0.451829 + 0.892104i \(0.350772\pi\)
\(888\) −13.6639 −0.458532
\(889\) 51.2741 1.71968
\(890\) 1.90144 0.0637366
\(891\) −36.0644 −1.20820
\(892\) 9.60089 0.321461
\(893\) 5.38403 0.180170
\(894\) −43.1103 −1.44182
\(895\) −16.7582 −0.560164
\(896\) −4.01442 −0.134112
\(897\) 72.6766 2.42660
\(898\) 28.4555 0.949571
\(899\) 2.98300 0.0994886
\(900\) −4.41011 −0.147004
\(901\) 15.7746 0.525528
\(902\) −7.90085 −0.263069
\(903\) −86.4072 −2.87545
\(904\) −3.46399 −0.115211
\(905\) −4.00392 −0.133095
\(906\) 7.93927 0.263764
\(907\) 58.5145 1.94294 0.971472 0.237156i \(-0.0762153\pi\)
0.971472 + 0.237156i \(0.0762153\pi\)
\(908\) −24.5848 −0.815875
\(909\) 6.93443 0.230000
\(910\) −37.2658 −1.23535
\(911\) −37.4134 −1.23956 −0.619781 0.784775i \(-0.712779\pi\)
−0.619781 + 0.784775i \(0.712779\pi\)
\(912\) 2.09909 0.0695078
\(913\) −3.43426 −0.113657
\(914\) 21.6748 0.716938
\(915\) −4.06607 −0.134420
\(916\) 5.87183 0.194011
\(917\) −9.92557 −0.327771
\(918\) −6.19384 −0.204427
\(919\) 12.2240 0.403234 0.201617 0.979464i \(-0.435380\pi\)
0.201617 + 0.979464i \(0.435380\pi\)
\(920\) 6.95130 0.229178
\(921\) −12.3971 −0.408497
\(922\) −38.6715 −1.27358
\(923\) 27.6727 0.910857
\(924\) −27.0346 −0.889373
\(925\) 20.4152 0.671248
\(926\) −17.3366 −0.569717
\(927\) −16.0535 −0.527266
\(928\) −4.18921 −0.137517
\(929\) −33.6650 −1.10451 −0.552257 0.833674i \(-0.686233\pi\)
−0.552257 + 0.833674i \(0.686233\pi\)
\(930\) 2.04055 0.0669123
\(931\) −9.11555 −0.298750
\(932\) −28.7383 −0.941354
\(933\) 1.85009 0.0605693
\(934\) 22.9253 0.750140
\(935\) 8.10869 0.265182
\(936\) −9.56166 −0.312533
\(937\) 33.4928 1.09416 0.547081 0.837079i \(-0.315739\pi\)
0.547081 + 0.837079i \(0.315739\pi\)
\(938\) −50.9829 −1.66465
\(939\) 44.9156 1.46577
\(940\) −7.35026 −0.239739
\(941\) −51.1775 −1.66834 −0.834169 0.551509i \(-0.814052\pi\)
−0.834169 + 0.551509i \(0.814052\pi\)
\(942\) 2.55729 0.0833212
\(943\) −12.5394 −0.408340
\(944\) 10.3430 0.336636
\(945\) 18.3353 0.596448
\(946\) −32.8975 −1.06959
\(947\) −3.16912 −0.102982 −0.0514912 0.998673i \(-0.516397\pi\)
−0.0514912 + 0.998673i \(0.516397\pi\)
\(948\) 4.47690 0.145403
\(949\) −74.2405 −2.40995
\(950\) −3.13624 −0.101753
\(951\) −4.90768 −0.159142
\(952\) −7.43210 −0.240876
\(953\) −47.9786 −1.55418 −0.777089 0.629391i \(-0.783304\pi\)
−0.777089 + 0.629391i \(0.783304\pi\)
\(954\) −11.9814 −0.387914
\(955\) 0.457059 0.0147901
\(956\) −18.0598 −0.584096
\(957\) −28.2117 −0.911955
\(958\) −37.0920 −1.19839
\(959\) −27.9344 −0.902048
\(960\) −2.86567 −0.0924891
\(961\) −30.4930 −0.983644
\(962\) 44.2627 1.42709
\(963\) −3.78873 −0.122090
\(964\) 6.33711 0.204105
\(965\) −9.85275 −0.317171
\(966\) −42.9066 −1.38050
\(967\) −11.8867 −0.382251 −0.191126 0.981566i \(-0.561214\pi\)
−0.191126 + 0.981566i \(0.561214\pi\)
\(968\) 0.707214 0.0227307
\(969\) 3.88615 0.124841
\(970\) −9.19111 −0.295109
\(971\) −3.64315 −0.116914 −0.0584571 0.998290i \(-0.518618\pi\)
−0.0584571 + 0.998290i \(0.518618\pi\)
\(972\) 13.5596 0.434923
\(973\) 10.8050 0.346392
\(974\) 15.8194 0.506887
\(975\) 44.7644 1.43361
\(976\) 1.41889 0.0454175
\(977\) 16.9679 0.542852 0.271426 0.962459i \(-0.412505\pi\)
0.271426 + 0.962459i \(0.412505\pi\)
\(978\) 19.3155 0.617640
\(979\) −4.46843 −0.142812
\(980\) 12.4445 0.397525
\(981\) 16.2491 0.518793
\(982\) −29.5626 −0.943382
\(983\) 13.2719 0.423306 0.211653 0.977345i \(-0.432115\pi\)
0.211653 + 0.977345i \(0.432115\pi\)
\(984\) 5.16938 0.164794
\(985\) 2.35510 0.0750398
\(986\) −7.75570 −0.246992
\(987\) 45.3692 1.44412
\(988\) −6.79975 −0.216329
\(989\) −52.2116 −1.66023
\(990\) −6.15888 −0.195742
\(991\) −7.97607 −0.253368 −0.126684 0.991943i \(-0.540433\pi\)
−0.126684 + 0.991943i \(0.540433\pi\)
\(992\) −0.712068 −0.0226082
\(993\) −6.55517 −0.208022
\(994\) −16.3373 −0.518188
\(995\) 10.8130 0.342794
\(996\) 2.24697 0.0711981
\(997\) 4.07981 0.129209 0.0646044 0.997911i \(-0.479421\pi\)
0.0646044 + 0.997911i \(0.479421\pi\)
\(998\) 14.7836 0.467966
\(999\) −21.7779 −0.689022
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 8018.2.a.h.1.7 41
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8018.2.a.h.1.7 41 1.1 even 1 trivial