Properties

Label 6035.2.a.a.1.17
Level $6035$
Weight $2$
Character 6035.1
Self dual yes
Analytic conductor $48.190$
Analytic rank $1$
Dimension $36$
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] = [6035,2,Mod(1,6035)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6035, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("6035.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6035 = 5 \cdot 17 \cdot 71 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6035.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: \(48.1897176198\)
Analytic rank: \(1\)
Dimension: \(36\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) \(=\) 6035.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.256013 q^{2} +0.196473 q^{3} -1.93446 q^{4} +1.00000 q^{5} -0.0502997 q^{6} +2.99337 q^{7} +1.00727 q^{8} -2.96140 q^{9} +O(q^{10})\) \(q-0.256013 q^{2} +0.196473 q^{3} -1.93446 q^{4} +1.00000 q^{5} -0.0502997 q^{6} +2.99337 q^{7} +1.00727 q^{8} -2.96140 q^{9} -0.256013 q^{10} -4.51326 q^{11} -0.380069 q^{12} +1.63393 q^{13} -0.766343 q^{14} +0.196473 q^{15} +3.61104 q^{16} +1.00000 q^{17} +0.758157 q^{18} -3.34601 q^{19} -1.93446 q^{20} +0.588117 q^{21} +1.15545 q^{22} +4.80598 q^{23} +0.197902 q^{24} +1.00000 q^{25} -0.418307 q^{26} -1.17125 q^{27} -5.79055 q^{28} -5.40684 q^{29} -0.0502997 q^{30} +0.0151487 q^{31} -2.93902 q^{32} -0.886734 q^{33} -0.256013 q^{34} +2.99337 q^{35} +5.72870 q^{36} +2.16222 q^{37} +0.856624 q^{38} +0.321023 q^{39} +1.00727 q^{40} +5.25049 q^{41} -0.150566 q^{42} +4.32978 q^{43} +8.73071 q^{44} -2.96140 q^{45} -1.23039 q^{46} +0.863753 q^{47} +0.709472 q^{48} +1.96029 q^{49} -0.256013 q^{50} +0.196473 q^{51} -3.16076 q^{52} -10.0463 q^{53} +0.299856 q^{54} -4.51326 q^{55} +3.01514 q^{56} -0.657401 q^{57} +1.38422 q^{58} +9.17402 q^{59} -0.380069 q^{60} -4.43046 q^{61} -0.00387827 q^{62} -8.86457 q^{63} -6.46965 q^{64} +1.63393 q^{65} +0.227015 q^{66} -12.2700 q^{67} -1.93446 q^{68} +0.944245 q^{69} -0.766343 q^{70} -1.00000 q^{71} -2.98294 q^{72} +8.55982 q^{73} -0.553557 q^{74} +0.196473 q^{75} +6.47272 q^{76} -13.5099 q^{77} -0.0821860 q^{78} +1.73861 q^{79} +3.61104 q^{80} +8.65408 q^{81} -1.34419 q^{82} -15.4341 q^{83} -1.13769 q^{84} +1.00000 q^{85} -1.10848 q^{86} -1.06230 q^{87} -4.54608 q^{88} +2.45612 q^{89} +0.758157 q^{90} +4.89096 q^{91} -9.29696 q^{92} +0.00297631 q^{93} -0.221132 q^{94} -3.34601 q^{95} -0.577438 q^{96} -12.4758 q^{97} -0.501859 q^{98} +13.3656 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q - 3 q^{2} - 8 q^{3} + 23 q^{4} + 36 q^{5} - 10 q^{6} - 7 q^{7} - 9 q^{8} + 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 36 q - 3 q^{2} - 8 q^{3} + 23 q^{4} + 36 q^{5} - 10 q^{6} - 7 q^{7} - 9 q^{8} + 10 q^{9} - 3 q^{10} - 20 q^{11} - 8 q^{12} - 29 q^{13} - 12 q^{14} - 8 q^{15} + q^{16} + 36 q^{17} - 8 q^{18} - 19 q^{19} + 23 q^{20} - 19 q^{21} - 10 q^{22} - 10 q^{23} - 23 q^{24} + 36 q^{25} - 32 q^{26} - 23 q^{27} - 20 q^{28} - 52 q^{29} - 10 q^{30} - 15 q^{31} - 16 q^{32} - 19 q^{33} - 3 q^{34} - 7 q^{35} + 9 q^{36} - 52 q^{37} + 7 q^{38} - 10 q^{39} - 9 q^{40} - 51 q^{41} - 2 q^{42} - 13 q^{43} - 27 q^{44} + 10 q^{45} + 12 q^{46} - 24 q^{47} + 12 q^{48} - 15 q^{49} - 3 q^{50} - 8 q^{51} - 49 q^{52} - 13 q^{53} - 48 q^{54} - 20 q^{55} - 12 q^{56} - 20 q^{57} - 20 q^{58} - 14 q^{59} - 8 q^{60} - 75 q^{61} - 7 q^{62} + 16 q^{63} - 41 q^{64} - 29 q^{65} - q^{66} - 5 q^{67} + 23 q^{68} - 37 q^{69} - 12 q^{70} - 36 q^{71} - 23 q^{72} - 21 q^{73} + q^{74} - 8 q^{75} - 40 q^{76} - 31 q^{77} + 84 q^{78} - 49 q^{79} + q^{80} - 56 q^{81} - 51 q^{82} + 6 q^{83} + 10 q^{84} + 36 q^{85} - 41 q^{86} - 4 q^{87} - 21 q^{88} - 78 q^{89} - 8 q^{90} - 25 q^{91} - 24 q^{92} - 36 q^{93} + 6 q^{94} - 19 q^{95} - 71 q^{96} - 48 q^{97} + 51 q^{98} - 17 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.256013 −0.181029 −0.0905143 0.995895i \(-0.528851\pi\)
−0.0905143 + 0.995895i \(0.528851\pi\)
\(3\) 0.196473 0.113434 0.0567169 0.998390i \(-0.481937\pi\)
0.0567169 + 0.998390i \(0.481937\pi\)
\(4\) −1.93446 −0.967229
\(5\) 1.00000 0.447214
\(6\) −0.0502997 −0.0205348
\(7\) 2.99337 1.13139 0.565695 0.824615i \(-0.308608\pi\)
0.565695 + 0.824615i \(0.308608\pi\)
\(8\) 1.00727 0.356125
\(9\) −2.96140 −0.987133
\(10\) −0.256013 −0.0809585
\(11\) −4.51326 −1.36080 −0.680400 0.732841i \(-0.738194\pi\)
−0.680400 + 0.732841i \(0.738194\pi\)
\(12\) −0.380069 −0.109716
\(13\) 1.63393 0.453170 0.226585 0.973991i \(-0.427244\pi\)
0.226585 + 0.973991i \(0.427244\pi\)
\(14\) −0.766343 −0.204814
\(15\) 0.196473 0.0507291
\(16\) 3.61104 0.902760
\(17\) 1.00000 0.242536
\(18\) 0.758157 0.178699
\(19\) −3.34601 −0.767628 −0.383814 0.923410i \(-0.625390\pi\)
−0.383814 + 0.923410i \(0.625390\pi\)
\(20\) −1.93446 −0.432558
\(21\) 0.588117 0.128338
\(22\) 1.15545 0.246344
\(23\) 4.80598 1.00212 0.501058 0.865414i \(-0.332944\pi\)
0.501058 + 0.865414i \(0.332944\pi\)
\(24\) 0.197902 0.0403965
\(25\) 1.00000 0.200000
\(26\) −0.418307 −0.0820367
\(27\) −1.17125 −0.225408
\(28\) −5.79055 −1.09431
\(29\) −5.40684 −1.00403 −0.502013 0.864860i \(-0.667407\pi\)
−0.502013 + 0.864860i \(0.667407\pi\)
\(30\) −0.0502997 −0.00918342
\(31\) 0.0151487 0.00272079 0.00136039 0.999999i \(-0.499567\pi\)
0.00136039 + 0.999999i \(0.499567\pi\)
\(32\) −2.93902 −0.519550
\(33\) −0.886734 −0.154361
\(34\) −0.256013 −0.0439059
\(35\) 2.99337 0.505973
\(36\) 5.72870 0.954783
\(37\) 2.16222 0.355467 0.177733 0.984079i \(-0.443124\pi\)
0.177733 + 0.984079i \(0.443124\pi\)
\(38\) 0.856624 0.138963
\(39\) 0.321023 0.0514047
\(40\) 1.00727 0.159264
\(41\) 5.25049 0.819989 0.409994 0.912088i \(-0.365531\pi\)
0.409994 + 0.912088i \(0.365531\pi\)
\(42\) −0.150566 −0.0232328
\(43\) 4.32978 0.660285 0.330142 0.943931i \(-0.392903\pi\)
0.330142 + 0.943931i \(0.392903\pi\)
\(44\) 8.73071 1.31620
\(45\) −2.96140 −0.441459
\(46\) −1.23039 −0.181412
\(47\) 0.863753 0.125991 0.0629957 0.998014i \(-0.479935\pi\)
0.0629957 + 0.998014i \(0.479935\pi\)
\(48\) 0.709472 0.102403
\(49\) 1.96029 0.280041
\(50\) −0.256013 −0.0362057
\(51\) 0.196473 0.0275117
\(52\) −3.16076 −0.438319
\(53\) −10.0463 −1.37997 −0.689985 0.723824i \(-0.742383\pi\)
−0.689985 + 0.723824i \(0.742383\pi\)
\(54\) 0.299856 0.0408053
\(55\) −4.51326 −0.608568
\(56\) 3.01514 0.402916
\(57\) −0.657401 −0.0870749
\(58\) 1.38422 0.181757
\(59\) 9.17402 1.19436 0.597178 0.802109i \(-0.296289\pi\)
0.597178 + 0.802109i \(0.296289\pi\)
\(60\) −0.380069 −0.0490666
\(61\) −4.43046 −0.567263 −0.283631 0.958933i \(-0.591539\pi\)
−0.283631 + 0.958933i \(0.591539\pi\)
\(62\) −0.00387827 −0.000492541 0
\(63\) −8.86457 −1.11683
\(64\) −6.46965 −0.808706
\(65\) 1.63393 0.202664
\(66\) 0.227015 0.0279437
\(67\) −12.2700 −1.49902 −0.749509 0.661994i \(-0.769710\pi\)
−0.749509 + 0.661994i \(0.769710\pi\)
\(68\) −1.93446 −0.234587
\(69\) 0.944245 0.113674
\(70\) −0.766343 −0.0915955
\(71\) −1.00000 −0.118678
\(72\) −2.98294 −0.351542
\(73\) 8.55982 1.00185 0.500926 0.865490i \(-0.332993\pi\)
0.500926 + 0.865490i \(0.332993\pi\)
\(74\) −0.553557 −0.0643496
\(75\) 0.196473 0.0226867
\(76\) 6.47272 0.742472
\(77\) −13.5099 −1.53959
\(78\) −0.0821860 −0.00930573
\(79\) 1.73861 0.195609 0.0978045 0.995206i \(-0.468818\pi\)
0.0978045 + 0.995206i \(0.468818\pi\)
\(80\) 3.61104 0.403726
\(81\) 8.65408 0.961564
\(82\) −1.34419 −0.148441
\(83\) −15.4341 −1.69412 −0.847059 0.531499i \(-0.821629\pi\)
−0.847059 + 0.531499i \(0.821629\pi\)
\(84\) −1.13769 −0.124132
\(85\) 1.00000 0.108465
\(86\) −1.10848 −0.119530
\(87\) −1.06230 −0.113890
\(88\) −4.54608 −0.484614
\(89\) 2.45612 0.260348 0.130174 0.991491i \(-0.458446\pi\)
0.130174 + 0.991491i \(0.458446\pi\)
\(90\) 0.758157 0.0799168
\(91\) 4.89096 0.512711
\(92\) −9.29696 −0.969275
\(93\) 0.00297631 0.000308629 0
\(94\) −0.221132 −0.0228080
\(95\) −3.34601 −0.343294
\(96\) −0.577438 −0.0589345
\(97\) −12.4758 −1.26672 −0.633361 0.773857i \(-0.718325\pi\)
−0.633361 + 0.773857i \(0.718325\pi\)
\(98\) −0.501859 −0.0506955
\(99\) 13.3656 1.34329
\(100\) −1.93446 −0.193446
\(101\) 6.45187 0.641985 0.320993 0.947082i \(-0.395984\pi\)
0.320993 + 0.947082i \(0.395984\pi\)
\(102\) −0.0502997 −0.00498041
\(103\) −1.85979 −0.183250 −0.0916251 0.995794i \(-0.529206\pi\)
−0.0916251 + 0.995794i \(0.529206\pi\)
\(104\) 1.64581 0.161385
\(105\) 0.588117 0.0573943
\(106\) 2.57199 0.249814
\(107\) −19.2296 −1.85899 −0.929496 0.368831i \(-0.879758\pi\)
−0.929496 + 0.368831i \(0.879758\pi\)
\(108\) 2.26574 0.218021
\(109\) −15.1606 −1.45213 −0.726063 0.687628i \(-0.758652\pi\)
−0.726063 + 0.687628i \(0.758652\pi\)
\(110\) 1.15545 0.110168
\(111\) 0.424818 0.0403219
\(112\) 10.8092 1.02137
\(113\) 9.00544 0.847161 0.423580 0.905859i \(-0.360773\pi\)
0.423580 + 0.905859i \(0.360773\pi\)
\(114\) 0.168303 0.0157631
\(115\) 4.80598 0.448160
\(116\) 10.4593 0.971122
\(117\) −4.83871 −0.447339
\(118\) −2.34867 −0.216213
\(119\) 2.99337 0.274402
\(120\) 0.197902 0.0180659
\(121\) 9.36952 0.851775
\(122\) 1.13426 0.102691
\(123\) 1.03158 0.0930144
\(124\) −0.0293045 −0.00263163
\(125\) 1.00000 0.0894427
\(126\) 2.26945 0.202178
\(127\) 4.78000 0.424156 0.212078 0.977253i \(-0.431977\pi\)
0.212078 + 0.977253i \(0.431977\pi\)
\(128\) 7.53435 0.665949
\(129\) 0.850684 0.0748986
\(130\) −0.418307 −0.0366879
\(131\) 21.1983 1.85210 0.926052 0.377397i \(-0.123181\pi\)
0.926052 + 0.377397i \(0.123181\pi\)
\(132\) 1.71535 0.149302
\(133\) −10.0159 −0.868486
\(134\) 3.14128 0.271365
\(135\) −1.17125 −0.100805
\(136\) 1.00727 0.0863729
\(137\) −0.387209 −0.0330815 −0.0165408 0.999863i \(-0.505265\pi\)
−0.0165408 + 0.999863i \(0.505265\pi\)
\(138\) −0.241739 −0.0205782
\(139\) −12.2334 −1.03762 −0.518812 0.854889i \(-0.673625\pi\)
−0.518812 + 0.854889i \(0.673625\pi\)
\(140\) −5.79055 −0.489391
\(141\) 0.169704 0.0142917
\(142\) 0.256013 0.0214841
\(143\) −7.37434 −0.616673
\(144\) −10.6937 −0.891144
\(145\) −5.40684 −0.449014
\(146\) −2.19143 −0.181364
\(147\) 0.385144 0.0317661
\(148\) −4.18272 −0.343818
\(149\) −2.41173 −0.197577 −0.0987885 0.995108i \(-0.531497\pi\)
−0.0987885 + 0.995108i \(0.531497\pi\)
\(150\) −0.0502997 −0.00410695
\(151\) −17.9563 −1.46127 −0.730633 0.682770i \(-0.760775\pi\)
−0.730633 + 0.682770i \(0.760775\pi\)
\(152\) −3.37035 −0.273371
\(153\) −2.96140 −0.239415
\(154\) 3.45871 0.278710
\(155\) 0.0151487 0.00121677
\(156\) −0.621004 −0.0497201
\(157\) 4.14213 0.330578 0.165289 0.986245i \(-0.447144\pi\)
0.165289 + 0.986245i \(0.447144\pi\)
\(158\) −0.445107 −0.0354108
\(159\) −1.97383 −0.156535
\(160\) −2.93902 −0.232350
\(161\) 14.3861 1.13378
\(162\) −2.21556 −0.174071
\(163\) 9.73141 0.762223 0.381111 0.924529i \(-0.375541\pi\)
0.381111 + 0.924529i \(0.375541\pi\)
\(164\) −10.1568 −0.793117
\(165\) −0.886734 −0.0690321
\(166\) 3.95134 0.306684
\(167\) 13.8227 1.06963 0.534815 0.844969i \(-0.320381\pi\)
0.534815 + 0.844969i \(0.320381\pi\)
\(168\) 0.592394 0.0457042
\(169\) −10.3303 −0.794637
\(170\) −0.256013 −0.0196353
\(171\) 9.90888 0.757751
\(172\) −8.37577 −0.638647
\(173\) −15.0969 −1.14780 −0.573898 0.818927i \(-0.694569\pi\)
−0.573898 + 0.818927i \(0.694569\pi\)
\(174\) 0.271962 0.0206174
\(175\) 2.99337 0.226278
\(176\) −16.2976 −1.22848
\(177\) 1.80245 0.135480
\(178\) −0.628798 −0.0471304
\(179\) 7.12064 0.532221 0.266111 0.963942i \(-0.414261\pi\)
0.266111 + 0.963942i \(0.414261\pi\)
\(180\) 5.72870 0.426992
\(181\) −2.58241 −0.191949 −0.0959745 0.995384i \(-0.530597\pi\)
−0.0959745 + 0.995384i \(0.530597\pi\)
\(182\) −1.25215 −0.0928155
\(183\) −0.870466 −0.0643467
\(184\) 4.84093 0.356878
\(185\) 2.16222 0.158970
\(186\) −0.000761975 0 −5.58707e−5 0
\(187\) −4.51326 −0.330042
\(188\) −1.67089 −0.121862
\(189\) −3.50600 −0.255024
\(190\) 0.856624 0.0621460
\(191\) −1.16811 −0.0845215 −0.0422608 0.999107i \(-0.513456\pi\)
−0.0422608 + 0.999107i \(0.513456\pi\)
\(192\) −1.27111 −0.0917346
\(193\) 21.7456 1.56528 0.782642 0.622472i \(-0.213872\pi\)
0.782642 + 0.622472i \(0.213872\pi\)
\(194\) 3.19396 0.229313
\(195\) 0.321023 0.0229889
\(196\) −3.79209 −0.270864
\(197\) −14.5883 −1.03937 −0.519685 0.854358i \(-0.673951\pi\)
−0.519685 + 0.854358i \(0.673951\pi\)
\(198\) −3.42176 −0.243174
\(199\) −14.1428 −1.00256 −0.501278 0.865286i \(-0.667137\pi\)
−0.501278 + 0.865286i \(0.667137\pi\)
\(200\) 1.00727 0.0712249
\(201\) −2.41072 −0.170039
\(202\) −1.65176 −0.116218
\(203\) −16.1847 −1.13594
\(204\) −0.380069 −0.0266101
\(205\) 5.25049 0.366710
\(206\) 0.476130 0.0331735
\(207\) −14.2324 −0.989222
\(208\) 5.90018 0.409104
\(209\) 15.1014 1.04459
\(210\) −0.150566 −0.0103900
\(211\) −23.8139 −1.63942 −0.819709 0.572780i \(-0.805865\pi\)
−0.819709 + 0.572780i \(0.805865\pi\)
\(212\) 19.4342 1.33475
\(213\) −0.196473 −0.0134621
\(214\) 4.92302 0.336531
\(215\) 4.32978 0.295288
\(216\) −1.17977 −0.0802733
\(217\) 0.0453458 0.00307827
\(218\) 3.88132 0.262876
\(219\) 1.68177 0.113644
\(220\) 8.73071 0.588624
\(221\) 1.63393 0.109910
\(222\) −0.108759 −0.00729942
\(223\) −22.9150 −1.53450 −0.767252 0.641345i \(-0.778377\pi\)
−0.767252 + 0.641345i \(0.778377\pi\)
\(224\) −8.79758 −0.587813
\(225\) −2.96140 −0.197427
\(226\) −2.30551 −0.153360
\(227\) 0.447454 0.0296985 0.0148493 0.999890i \(-0.495273\pi\)
0.0148493 + 0.999890i \(0.495273\pi\)
\(228\) 1.27171 0.0842214
\(229\) −11.1238 −0.735085 −0.367542 0.930007i \(-0.619801\pi\)
−0.367542 + 0.930007i \(0.619801\pi\)
\(230\) −1.23039 −0.0811298
\(231\) −2.65433 −0.174642
\(232\) −5.44617 −0.357558
\(233\) −21.3732 −1.40020 −0.700102 0.714043i \(-0.746862\pi\)
−0.700102 + 0.714043i \(0.746862\pi\)
\(234\) 1.23877 0.0809811
\(235\) 0.863753 0.0563450
\(236\) −17.7468 −1.15522
\(237\) 0.341590 0.0221887
\(238\) −0.766343 −0.0496746
\(239\) 9.88287 0.639270 0.319635 0.947541i \(-0.396440\pi\)
0.319635 + 0.947541i \(0.396440\pi\)
\(240\) 0.709472 0.0457962
\(241\) −6.69227 −0.431087 −0.215543 0.976494i \(-0.569152\pi\)
−0.215543 + 0.976494i \(0.569152\pi\)
\(242\) −2.39872 −0.154196
\(243\) 5.21405 0.334482
\(244\) 8.57054 0.548673
\(245\) 1.96029 0.125238
\(246\) −0.264098 −0.0168383
\(247\) −5.46714 −0.347866
\(248\) 0.0152589 0.000968940 0
\(249\) −3.03239 −0.192170
\(250\) −0.256013 −0.0161917
\(251\) −18.8833 −1.19191 −0.595953 0.803019i \(-0.703226\pi\)
−0.595953 + 0.803019i \(0.703226\pi\)
\(252\) 17.1481 1.08023
\(253\) −21.6906 −1.36368
\(254\) −1.22374 −0.0767845
\(255\) 0.196473 0.0123036
\(256\) 11.0104 0.688151
\(257\) 0.360589 0.0224929 0.0112465 0.999937i \(-0.496420\pi\)
0.0112465 + 0.999937i \(0.496420\pi\)
\(258\) −0.217786 −0.0135588
\(259\) 6.47233 0.402171
\(260\) −3.16076 −0.196022
\(261\) 16.0118 0.991107
\(262\) −5.42704 −0.335284
\(263\) −4.23386 −0.261071 −0.130536 0.991444i \(-0.541670\pi\)
−0.130536 + 0.991444i \(0.541670\pi\)
\(264\) −0.893183 −0.0549716
\(265\) −10.0463 −0.617141
\(266\) 2.56420 0.157221
\(267\) 0.482560 0.0295322
\(268\) 23.7358 1.44989
\(269\) −0.951881 −0.0580372 −0.0290186 0.999579i \(-0.509238\pi\)
−0.0290186 + 0.999579i \(0.509238\pi\)
\(270\) 0.299856 0.0182487
\(271\) −0.535008 −0.0324994 −0.0162497 0.999868i \(-0.505173\pi\)
−0.0162497 + 0.999868i \(0.505173\pi\)
\(272\) 3.61104 0.218951
\(273\) 0.960941 0.0581588
\(274\) 0.0991306 0.00598870
\(275\) −4.51326 −0.272160
\(276\) −1.82660 −0.109949
\(277\) −29.1825 −1.75341 −0.876704 0.481030i \(-0.840263\pi\)
−0.876704 + 0.481030i \(0.840263\pi\)
\(278\) 3.13191 0.187839
\(279\) −0.0448614 −0.00268578
\(280\) 3.01514 0.180189
\(281\) 27.3061 1.62894 0.814471 0.580204i \(-0.197027\pi\)
0.814471 + 0.580204i \(0.197027\pi\)
\(282\) −0.0434465 −0.00258720
\(283\) 25.1454 1.49474 0.747369 0.664409i \(-0.231317\pi\)
0.747369 + 0.664409i \(0.231317\pi\)
\(284\) 1.93446 0.114789
\(285\) −0.657401 −0.0389411
\(286\) 1.88793 0.111636
\(287\) 15.7167 0.927726
\(288\) 8.70361 0.512865
\(289\) 1.00000 0.0588235
\(290\) 1.38422 0.0812844
\(291\) −2.45115 −0.143689
\(292\) −16.5586 −0.969019
\(293\) 5.68827 0.332312 0.166156 0.986099i \(-0.446864\pi\)
0.166156 + 0.986099i \(0.446864\pi\)
\(294\) −0.0986018 −0.00575057
\(295\) 9.17402 0.534132
\(296\) 2.17794 0.126590
\(297\) 5.28617 0.306735
\(298\) 0.617435 0.0357671
\(299\) 7.85262 0.454129
\(300\) −0.380069 −0.0219433
\(301\) 12.9606 0.747039
\(302\) 4.59706 0.264531
\(303\) 1.26762 0.0728228
\(304\) −12.0826 −0.692984
\(305\) −4.43046 −0.253688
\(306\) 0.758157 0.0433409
\(307\) −19.3064 −1.10187 −0.550937 0.834547i \(-0.685729\pi\)
−0.550937 + 0.834547i \(0.685729\pi\)
\(308\) 26.1343 1.48914
\(309\) −0.365398 −0.0207868
\(310\) −0.00387827 −0.000220271 0
\(311\) 24.4576 1.38686 0.693432 0.720522i \(-0.256098\pi\)
0.693432 + 0.720522i \(0.256098\pi\)
\(312\) 0.323357 0.0183065
\(313\) 15.8703 0.897041 0.448520 0.893773i \(-0.351951\pi\)
0.448520 + 0.893773i \(0.351951\pi\)
\(314\) −1.06044 −0.0598440
\(315\) −8.86457 −0.499462
\(316\) −3.36327 −0.189199
\(317\) 12.6273 0.709218 0.354609 0.935015i \(-0.384614\pi\)
0.354609 + 0.935015i \(0.384614\pi\)
\(318\) 0.505327 0.0283373
\(319\) 24.4025 1.36628
\(320\) −6.46965 −0.361665
\(321\) −3.77809 −0.210872
\(322\) −3.68303 −0.205247
\(323\) −3.34601 −0.186177
\(324\) −16.7409 −0.930052
\(325\) 1.63393 0.0906340
\(326\) −2.49137 −0.137984
\(327\) −2.97866 −0.164720
\(328\) 5.28868 0.292018
\(329\) 2.58554 0.142545
\(330\) 0.227015 0.0124968
\(331\) 16.0187 0.880470 0.440235 0.897883i \(-0.354895\pi\)
0.440235 + 0.897883i \(0.354895\pi\)
\(332\) 29.8567 1.63860
\(333\) −6.40319 −0.350893
\(334\) −3.53878 −0.193634
\(335\) −12.2700 −0.670381
\(336\) 2.12371 0.115858
\(337\) −26.1625 −1.42516 −0.712580 0.701591i \(-0.752474\pi\)
−0.712580 + 0.701591i \(0.752474\pi\)
\(338\) 2.64469 0.143852
\(339\) 1.76933 0.0960966
\(340\) −1.93446 −0.104911
\(341\) −0.0683701 −0.00370245
\(342\) −2.53680 −0.137175
\(343\) −15.0857 −0.814554
\(344\) 4.36127 0.235144
\(345\) 0.944245 0.0508364
\(346\) 3.86500 0.207784
\(347\) −1.80176 −0.0967235 −0.0483617 0.998830i \(-0.515400\pi\)
−0.0483617 + 0.998830i \(0.515400\pi\)
\(348\) 2.05497 0.110158
\(349\) −2.04186 −0.109298 −0.0546492 0.998506i \(-0.517404\pi\)
−0.0546492 + 0.998506i \(0.517404\pi\)
\(350\) −0.766343 −0.0409628
\(351\) −1.91374 −0.102148
\(352\) 13.2646 0.707003
\(353\) −12.9105 −0.687155 −0.343578 0.939124i \(-0.611639\pi\)
−0.343578 + 0.939124i \(0.611639\pi\)
\(354\) −0.461450 −0.0245258
\(355\) −1.00000 −0.0530745
\(356\) −4.75125 −0.251816
\(357\) 0.588117 0.0311265
\(358\) −1.82298 −0.0963473
\(359\) 7.21644 0.380869 0.190435 0.981700i \(-0.439010\pi\)
0.190435 + 0.981700i \(0.439010\pi\)
\(360\) −2.98294 −0.157215
\(361\) −7.80419 −0.410747
\(362\) 0.661131 0.0347483
\(363\) 1.84086 0.0966200
\(364\) −9.46134 −0.495909
\(365\) 8.55982 0.448041
\(366\) 0.222851 0.0116486
\(367\) 12.2122 0.637472 0.318736 0.947844i \(-0.396742\pi\)
0.318736 + 0.947844i \(0.396742\pi\)
\(368\) 17.3546 0.904670
\(369\) −15.5488 −0.809438
\(370\) −0.553557 −0.0287780
\(371\) −30.0724 −1.56128
\(372\) −0.00575755 −0.000298515 0
\(373\) −32.6907 −1.69266 −0.846331 0.532658i \(-0.821193\pi\)
−0.846331 + 0.532658i \(0.821193\pi\)
\(374\) 1.15545 0.0597471
\(375\) 0.196473 0.0101458
\(376\) 0.870035 0.0448686
\(377\) −8.83439 −0.454994
\(378\) 0.897582 0.0461666
\(379\) −27.5902 −1.41721 −0.708607 0.705603i \(-0.750676\pi\)
−0.708607 + 0.705603i \(0.750676\pi\)
\(380\) 6.47272 0.332044
\(381\) 0.939141 0.0481136
\(382\) 0.299052 0.0153008
\(383\) −23.8612 −1.21925 −0.609625 0.792690i \(-0.708680\pi\)
−0.609625 + 0.792690i \(0.708680\pi\)
\(384\) 1.48030 0.0755411
\(385\) −13.5099 −0.688527
\(386\) −5.56716 −0.283361
\(387\) −12.8222 −0.651789
\(388\) 24.1338 1.22521
\(389\) −11.1355 −0.564591 −0.282295 0.959328i \(-0.591096\pi\)
−0.282295 + 0.959328i \(0.591096\pi\)
\(390\) −0.0821860 −0.00416165
\(391\) 4.80598 0.243049
\(392\) 1.97454 0.0997295
\(393\) 4.16489 0.210091
\(394\) 3.73479 0.188156
\(395\) 1.73861 0.0874790
\(396\) −25.8551 −1.29927
\(397\) −26.2598 −1.31794 −0.658970 0.752169i \(-0.729008\pi\)
−0.658970 + 0.752169i \(0.729008\pi\)
\(398\) 3.62074 0.181491
\(399\) −1.96785 −0.0985156
\(400\) 3.61104 0.180552
\(401\) −29.2301 −1.45968 −0.729842 0.683616i \(-0.760406\pi\)
−0.729842 + 0.683616i \(0.760406\pi\)
\(402\) 0.617176 0.0307819
\(403\) 0.0247519 0.00123298
\(404\) −12.4809 −0.620947
\(405\) 8.65408 0.430024
\(406\) 4.14350 0.205638
\(407\) −9.75866 −0.483719
\(408\) 0.197902 0.00979760
\(409\) 23.6621 1.17002 0.585009 0.811027i \(-0.301091\pi\)
0.585009 + 0.811027i \(0.301091\pi\)
\(410\) −1.34419 −0.0663850
\(411\) −0.0760761 −0.00375256
\(412\) 3.59768 0.177245
\(413\) 27.4613 1.35128
\(414\) 3.64369 0.179077
\(415\) −15.4341 −0.757632
\(416\) −4.80214 −0.235444
\(417\) −2.40353 −0.117701
\(418\) −3.86617 −0.189100
\(419\) −21.0903 −1.03033 −0.515164 0.857092i \(-0.672269\pi\)
−0.515164 + 0.857092i \(0.672269\pi\)
\(420\) −1.13769 −0.0555135
\(421\) −3.26477 −0.159115 −0.0795576 0.996830i \(-0.525351\pi\)
−0.0795576 + 0.996830i \(0.525351\pi\)
\(422\) 6.09668 0.296782
\(423\) −2.55792 −0.124370
\(424\) −10.1194 −0.491441
\(425\) 1.00000 0.0485071
\(426\) 0.0502997 0.00243703
\(427\) −13.2620 −0.641795
\(428\) 37.1988 1.79807
\(429\) −1.44886 −0.0699516
\(430\) −1.10848 −0.0534557
\(431\) 13.0823 0.630152 0.315076 0.949066i \(-0.397970\pi\)
0.315076 + 0.949066i \(0.397970\pi\)
\(432\) −4.22944 −0.203489
\(433\) −16.3046 −0.783547 −0.391773 0.920062i \(-0.628138\pi\)
−0.391773 + 0.920062i \(0.628138\pi\)
\(434\) −0.0116091 −0.000557255 0
\(435\) −1.06230 −0.0509333
\(436\) 29.3276 1.40454
\(437\) −16.0809 −0.769253
\(438\) −0.430556 −0.0205728
\(439\) −5.74066 −0.273987 −0.136993 0.990572i \(-0.543744\pi\)
−0.136993 + 0.990572i \(0.543744\pi\)
\(440\) −4.54608 −0.216726
\(441\) −5.80519 −0.276438
\(442\) −0.418307 −0.0198968
\(443\) −4.70047 −0.223326 −0.111663 0.993746i \(-0.535618\pi\)
−0.111663 + 0.993746i \(0.535618\pi\)
\(444\) −0.821791 −0.0390005
\(445\) 2.45612 0.116431
\(446\) 5.86655 0.277789
\(447\) −0.473840 −0.0224119
\(448\) −19.3661 −0.914962
\(449\) 7.27995 0.343562 0.171781 0.985135i \(-0.445048\pi\)
0.171781 + 0.985135i \(0.445048\pi\)
\(450\) 0.758157 0.0357399
\(451\) −23.6968 −1.11584
\(452\) −17.4206 −0.819398
\(453\) −3.52794 −0.165757
\(454\) −0.114554 −0.00537629
\(455\) 4.89096 0.229292
\(456\) −0.662183 −0.0310095
\(457\) 10.6438 0.497895 0.248947 0.968517i \(-0.419915\pi\)
0.248947 + 0.968517i \(0.419915\pi\)
\(458\) 2.84785 0.133071
\(459\) −1.17125 −0.0546694
\(460\) −9.29696 −0.433473
\(461\) 1.28165 0.0596924 0.0298462 0.999555i \(-0.490498\pi\)
0.0298462 + 0.999555i \(0.490498\pi\)
\(462\) 0.679542 0.0316152
\(463\) −14.1688 −0.658482 −0.329241 0.944246i \(-0.606793\pi\)
−0.329241 + 0.944246i \(0.606793\pi\)
\(464\) −19.5243 −0.906394
\(465\) 0.00297631 0.000138023 0
\(466\) 5.47181 0.253477
\(467\) 17.7602 0.821846 0.410923 0.911670i \(-0.365206\pi\)
0.410923 + 0.911670i \(0.365206\pi\)
\(468\) 9.36028 0.432679
\(469\) −36.7287 −1.69597
\(470\) −0.221132 −0.0102001
\(471\) 0.813816 0.0374987
\(472\) 9.24074 0.425340
\(473\) −19.5414 −0.898515
\(474\) −0.0874515 −0.00401678
\(475\) −3.34601 −0.153526
\(476\) −5.79055 −0.265410
\(477\) 29.7512 1.36221
\(478\) −2.53014 −0.115726
\(479\) −23.7082 −1.08326 −0.541628 0.840618i \(-0.682192\pi\)
−0.541628 + 0.840618i \(0.682192\pi\)
\(480\) −0.577438 −0.0263563
\(481\) 3.53291 0.161087
\(482\) 1.71331 0.0780391
\(483\) 2.82648 0.128609
\(484\) −18.1249 −0.823861
\(485\) −12.4758 −0.566495
\(486\) −1.33487 −0.0605508
\(487\) −6.20621 −0.281230 −0.140615 0.990064i \(-0.544908\pi\)
−0.140615 + 0.990064i \(0.544908\pi\)
\(488\) −4.46269 −0.202016
\(489\) 1.91196 0.0864618
\(490\) −0.501859 −0.0226717
\(491\) −33.0432 −1.49122 −0.745610 0.666382i \(-0.767842\pi\)
−0.745610 + 0.666382i \(0.767842\pi\)
\(492\) −1.99555 −0.0899662
\(493\) −5.40684 −0.243512
\(494\) 1.39966 0.0629737
\(495\) 13.3656 0.600737
\(496\) 0.0547026 0.00245622
\(497\) −2.99337 −0.134271
\(498\) 0.776332 0.0347883
\(499\) −34.6230 −1.54994 −0.774970 0.631998i \(-0.782235\pi\)
−0.774970 + 0.631998i \(0.782235\pi\)
\(500\) −1.93446 −0.0865116
\(501\) 2.71578 0.121332
\(502\) 4.83438 0.215769
\(503\) 1.42347 0.0634695 0.0317347 0.999496i \(-0.489897\pi\)
0.0317347 + 0.999496i \(0.489897\pi\)
\(504\) −8.92904 −0.397731
\(505\) 6.45187 0.287105
\(506\) 5.55309 0.246865
\(507\) −2.02962 −0.0901386
\(508\) −9.24671 −0.410256
\(509\) −13.7811 −0.610837 −0.305419 0.952218i \(-0.598796\pi\)
−0.305419 + 0.952218i \(0.598796\pi\)
\(510\) −0.0502997 −0.00222731
\(511\) 25.6227 1.13348
\(512\) −17.8875 −0.790524
\(513\) 3.91903 0.173029
\(514\) −0.0923154 −0.00407186
\(515\) −1.85979 −0.0819520
\(516\) −1.64561 −0.0724440
\(517\) −3.89834 −0.171449
\(518\) −1.65700 −0.0728045
\(519\) −2.96613 −0.130199
\(520\) 1.64581 0.0721736
\(521\) 36.2827 1.58958 0.794788 0.606888i \(-0.207582\pi\)
0.794788 + 0.606888i \(0.207582\pi\)
\(522\) −4.09924 −0.179419
\(523\) 5.89721 0.257867 0.128933 0.991653i \(-0.458845\pi\)
0.128933 + 0.991653i \(0.458845\pi\)
\(524\) −41.0072 −1.79141
\(525\) 0.588117 0.0256675
\(526\) 1.08392 0.0472614
\(527\) 0.0151487 0.000659888 0
\(528\) −3.20203 −0.139350
\(529\) 0.0974419 0.00423660
\(530\) 2.57199 0.111720
\(531\) −27.1679 −1.17899
\(532\) 19.3753 0.840025
\(533\) 8.57892 0.371594
\(534\) −0.123542 −0.00534618
\(535\) −19.2296 −0.831367
\(536\) −12.3592 −0.533837
\(537\) 1.39901 0.0603718
\(538\) 0.243694 0.0105064
\(539\) −8.84729 −0.381080
\(540\) 2.26574 0.0975019
\(541\) −24.2999 −1.04473 −0.522367 0.852721i \(-0.674951\pi\)
−0.522367 + 0.852721i \(0.674951\pi\)
\(542\) 0.136969 0.00588332
\(543\) −0.507374 −0.0217735
\(544\) −2.93902 −0.126009
\(545\) −15.1606 −0.649411
\(546\) −0.246013 −0.0105284
\(547\) 21.3305 0.912026 0.456013 0.889973i \(-0.349277\pi\)
0.456013 + 0.889973i \(0.349277\pi\)
\(548\) 0.749040 0.0319974
\(549\) 13.1204 0.559964
\(550\) 1.15545 0.0492687
\(551\) 18.0914 0.770719
\(552\) 0.951112 0.0404820
\(553\) 5.20431 0.221310
\(554\) 7.47111 0.317417
\(555\) 0.424818 0.0180325
\(556\) 23.6650 1.00362
\(557\) 0.501461 0.0212476 0.0106238 0.999944i \(-0.496618\pi\)
0.0106238 + 0.999944i \(0.496618\pi\)
\(558\) 0.0114851 0.000486203 0
\(559\) 7.07454 0.299221
\(560\) 10.8092 0.456772
\(561\) −0.886734 −0.0374379
\(562\) −6.99071 −0.294885
\(563\) −12.6810 −0.534442 −0.267221 0.963635i \(-0.586105\pi\)
−0.267221 + 0.963635i \(0.586105\pi\)
\(564\) −0.328285 −0.0138233
\(565\) 9.00544 0.378862
\(566\) −6.43755 −0.270590
\(567\) 25.9049 1.08790
\(568\) −1.00727 −0.0422642
\(569\) −31.7105 −1.32937 −0.664686 0.747123i \(-0.731435\pi\)
−0.664686 + 0.747123i \(0.731435\pi\)
\(570\) 0.168303 0.00704945
\(571\) 40.7772 1.70647 0.853237 0.521523i \(-0.174636\pi\)
0.853237 + 0.521523i \(0.174636\pi\)
\(572\) 14.2653 0.596464
\(573\) −0.229502 −0.00958759
\(574\) −4.02368 −0.167945
\(575\) 4.80598 0.200423
\(576\) 19.1592 0.798301
\(577\) −22.4643 −0.935200 −0.467600 0.883940i \(-0.654881\pi\)
−0.467600 + 0.883940i \(0.654881\pi\)
\(578\) −0.256013 −0.0106487
\(579\) 4.27243 0.177556
\(580\) 10.4593 0.434299
\(581\) −46.2002 −1.91671
\(582\) 0.627527 0.0260118
\(583\) 45.3417 1.87786
\(584\) 8.62207 0.356784
\(585\) −4.83871 −0.200056
\(586\) −1.45627 −0.0601580
\(587\) −47.4882 −1.96005 −0.980023 0.198883i \(-0.936269\pi\)
−0.980023 + 0.198883i \(0.936269\pi\)
\(588\) −0.745044 −0.0307251
\(589\) −0.0506878 −0.00208856
\(590\) −2.34867 −0.0966932
\(591\) −2.86620 −0.117900
\(592\) 7.80786 0.320901
\(593\) 12.3754 0.508197 0.254099 0.967178i \(-0.418221\pi\)
0.254099 + 0.967178i \(0.418221\pi\)
\(594\) −1.35333 −0.0555278
\(595\) 2.99337 0.122716
\(596\) 4.66540 0.191102
\(597\) −2.77868 −0.113724
\(598\) −2.01037 −0.0822103
\(599\) 0.219599 0.00897256 0.00448628 0.999990i \(-0.498572\pi\)
0.00448628 + 0.999990i \(0.498572\pi\)
\(600\) 0.197902 0.00807931
\(601\) 18.9651 0.773604 0.386802 0.922163i \(-0.373580\pi\)
0.386802 + 0.922163i \(0.373580\pi\)
\(602\) −3.31810 −0.135235
\(603\) 36.3363 1.47973
\(604\) 34.7358 1.41338
\(605\) 9.36952 0.380925
\(606\) −0.324527 −0.0131830
\(607\) 21.4753 0.871654 0.435827 0.900031i \(-0.356456\pi\)
0.435827 + 0.900031i \(0.356456\pi\)
\(608\) 9.83400 0.398821
\(609\) −3.17986 −0.128854
\(610\) 1.13426 0.0459247
\(611\) 1.41131 0.0570955
\(612\) 5.72870 0.231569
\(613\) −16.1815 −0.653563 −0.326782 0.945100i \(-0.605964\pi\)
−0.326782 + 0.945100i \(0.605964\pi\)
\(614\) 4.94269 0.199471
\(615\) 1.03158 0.0415973
\(616\) −13.6081 −0.548287
\(617\) −29.6298 −1.19285 −0.596425 0.802669i \(-0.703413\pi\)
−0.596425 + 0.802669i \(0.703413\pi\)
\(618\) 0.0935467 0.00376300
\(619\) −4.83528 −0.194346 −0.0971732 0.995267i \(-0.530980\pi\)
−0.0971732 + 0.995267i \(0.530980\pi\)
\(620\) −0.0293045 −0.00117690
\(621\) −5.62902 −0.225885
\(622\) −6.26147 −0.251062
\(623\) 7.35207 0.294555
\(624\) 1.15923 0.0464061
\(625\) 1.00000 0.0400000
\(626\) −4.06300 −0.162390
\(627\) 2.96702 0.118492
\(628\) −8.01277 −0.319744
\(629\) 2.16222 0.0862133
\(630\) 2.26945 0.0904169
\(631\) 24.5189 0.976081 0.488040 0.872821i \(-0.337712\pi\)
0.488040 + 0.872821i \(0.337712\pi\)
\(632\) 1.75125 0.0696612
\(633\) −4.67879 −0.185965
\(634\) −3.23275 −0.128389
\(635\) 4.78000 0.189689
\(636\) 3.81830 0.151405
\(637\) 3.20297 0.126906
\(638\) −6.24736 −0.247335
\(639\) 2.96140 0.117151
\(640\) 7.53435 0.297821
\(641\) −42.7514 −1.68858 −0.844290 0.535887i \(-0.819977\pi\)
−0.844290 + 0.535887i \(0.819977\pi\)
\(642\) 0.967241 0.0381740
\(643\) 12.4530 0.491098 0.245549 0.969384i \(-0.421032\pi\)
0.245549 + 0.969384i \(0.421032\pi\)
\(644\) −27.8293 −1.09663
\(645\) 0.850684 0.0334957
\(646\) 0.856624 0.0337034
\(647\) −0.200365 −0.00787716 −0.00393858 0.999992i \(-0.501254\pi\)
−0.00393858 + 0.999992i \(0.501254\pi\)
\(648\) 8.71701 0.342437
\(649\) −41.4047 −1.62528
\(650\) −0.418307 −0.0164073
\(651\) 0.00890922 0.000349180 0
\(652\) −18.8250 −0.737244
\(653\) 17.6841 0.692031 0.346015 0.938229i \(-0.387534\pi\)
0.346015 + 0.938229i \(0.387534\pi\)
\(654\) 0.762575 0.0298191
\(655\) 21.1983 0.828286
\(656\) 18.9597 0.740253
\(657\) −25.3490 −0.988960
\(658\) −0.661931 −0.0258048
\(659\) 34.3116 1.33659 0.668296 0.743896i \(-0.267024\pi\)
0.668296 + 0.743896i \(0.267024\pi\)
\(660\) 1.71535 0.0667699
\(661\) −6.07210 −0.236177 −0.118089 0.993003i \(-0.537677\pi\)
−0.118089 + 0.993003i \(0.537677\pi\)
\(662\) −4.10101 −0.159390
\(663\) 0.321023 0.0124675
\(664\) −15.5464 −0.603317
\(665\) −10.0159 −0.388399
\(666\) 1.63930 0.0635216
\(667\) −25.9852 −1.00615
\(668\) −26.7394 −1.03458
\(669\) −4.50219 −0.174065
\(670\) 3.14128 0.121358
\(671\) 19.9958 0.771931
\(672\) −1.72849 −0.0666778
\(673\) 31.7403 1.22350 0.611748 0.791052i \(-0.290467\pi\)
0.611748 + 0.791052i \(0.290467\pi\)
\(674\) 6.69793 0.257995
\(675\) −1.17125 −0.0450816
\(676\) 19.9835 0.768596
\(677\) 23.1595 0.890093 0.445047 0.895507i \(-0.353187\pi\)
0.445047 + 0.895507i \(0.353187\pi\)
\(678\) −0.452971 −0.0173962
\(679\) −37.3446 −1.43315
\(680\) 1.00727 0.0386271
\(681\) 0.0879126 0.00336882
\(682\) 0.0175036 0.000670249 0
\(683\) −0.336970 −0.0128938 −0.00644690 0.999979i \(-0.502052\pi\)
−0.00644690 + 0.999979i \(0.502052\pi\)
\(684\) −19.1683 −0.732919
\(685\) −0.387209 −0.0147945
\(686\) 3.86215 0.147458
\(687\) −2.18554 −0.0833834
\(688\) 15.6350 0.596079
\(689\) −16.4150 −0.625361
\(690\) −0.241739 −0.00920285
\(691\) −20.5156 −0.780449 −0.390225 0.920720i \(-0.627603\pi\)
−0.390225 + 0.920720i \(0.627603\pi\)
\(692\) 29.2043 1.11018
\(693\) 40.0081 1.51978
\(694\) 0.461274 0.0175097
\(695\) −12.2334 −0.464039
\(696\) −1.07002 −0.0405592
\(697\) 5.25049 0.198876
\(698\) 0.522744 0.0197861
\(699\) −4.19925 −0.158830
\(700\) −5.79055 −0.218862
\(701\) 5.77880 0.218262 0.109131 0.994027i \(-0.465193\pi\)
0.109131 + 0.994027i \(0.465193\pi\)
\(702\) 0.489943 0.0184917
\(703\) −7.23482 −0.272866
\(704\) 29.1992 1.10049
\(705\) 0.169704 0.00639143
\(706\) 3.30525 0.124395
\(707\) 19.3129 0.726335
\(708\) −3.48676 −0.131040
\(709\) 30.9761 1.16333 0.581666 0.813428i \(-0.302401\pi\)
0.581666 + 0.813428i \(0.302401\pi\)
\(710\) 0.256013 0.00960800
\(711\) −5.14872 −0.193092
\(712\) 2.47398 0.0927163
\(713\) 0.0728044 0.00272655
\(714\) −0.150566 −0.00563478
\(715\) −7.37434 −0.275785
\(716\) −13.7746 −0.514780
\(717\) 1.94172 0.0725147
\(718\) −1.84750 −0.0689482
\(719\) 32.1646 1.19954 0.599768 0.800174i \(-0.295259\pi\)
0.599768 + 0.800174i \(0.295259\pi\)
\(720\) −10.6937 −0.398532
\(721\) −5.56704 −0.207327
\(722\) 1.99797 0.0743569
\(723\) −1.31485 −0.0488998
\(724\) 4.99556 0.185659
\(725\) −5.40684 −0.200805
\(726\) −0.471284 −0.0174910
\(727\) −29.7656 −1.10394 −0.551972 0.833863i \(-0.686124\pi\)
−0.551972 + 0.833863i \(0.686124\pi\)
\(728\) 4.92653 0.182589
\(729\) −24.9378 −0.923622
\(730\) −2.19143 −0.0811083
\(731\) 4.32978 0.160143
\(732\) 1.68388 0.0622380
\(733\) 27.9754 1.03329 0.516647 0.856198i \(-0.327180\pi\)
0.516647 + 0.856198i \(0.327180\pi\)
\(734\) −3.12649 −0.115401
\(735\) 0.385144 0.0142062
\(736\) −14.1249 −0.520649
\(737\) 55.3777 2.03986
\(738\) 3.98070 0.146531
\(739\) 33.5438 1.23393 0.616964 0.786992i \(-0.288363\pi\)
0.616964 + 0.786992i \(0.288363\pi\)
\(740\) −4.18272 −0.153760
\(741\) −1.07415 −0.0394597
\(742\) 7.69894 0.282637
\(743\) −49.9137 −1.83116 −0.915579 0.402138i \(-0.868267\pi\)
−0.915579 + 0.402138i \(0.868267\pi\)
\(744\) 0.00299796 0.000109911 0
\(745\) −2.41173 −0.0883591
\(746\) 8.36925 0.306420
\(747\) 45.7067 1.67232
\(748\) 8.73071 0.319226
\(749\) −57.5613 −2.10324
\(750\) −0.0502997 −0.00183668
\(751\) 49.1635 1.79400 0.897000 0.442030i \(-0.145741\pi\)
0.897000 + 0.442030i \(0.145741\pi\)
\(752\) 3.11905 0.113740
\(753\) −3.71007 −0.135202
\(754\) 2.26172 0.0823670
\(755\) −17.9563 −0.653498
\(756\) 6.78221 0.246666
\(757\) 13.9284 0.506237 0.253119 0.967435i \(-0.418544\pi\)
0.253119 + 0.967435i \(0.418544\pi\)
\(758\) 7.06346 0.256556
\(759\) −4.26162 −0.154687
\(760\) −3.37035 −0.122255
\(761\) 29.4978 1.06930 0.534648 0.845075i \(-0.320444\pi\)
0.534648 + 0.845075i \(0.320444\pi\)
\(762\) −0.240432 −0.00870995
\(763\) −45.3815 −1.64292
\(764\) 2.25966 0.0817517
\(765\) −2.96140 −0.107070
\(766\) 6.10878 0.220719
\(767\) 14.9897 0.541246
\(768\) 2.16325 0.0780595
\(769\) −40.4548 −1.45884 −0.729419 0.684067i \(-0.760209\pi\)
−0.729419 + 0.684067i \(0.760209\pi\)
\(770\) 3.45871 0.124643
\(771\) 0.0708459 0.00255145
\(772\) −42.0660 −1.51399
\(773\) −15.0094 −0.539852 −0.269926 0.962881i \(-0.586999\pi\)
−0.269926 + 0.962881i \(0.586999\pi\)
\(774\) 3.28265 0.117992
\(775\) 0.0151487 0.000544158 0
\(776\) −12.5665 −0.451111
\(777\) 1.27164 0.0456198
\(778\) 2.85083 0.102207
\(779\) −17.5682 −0.629447
\(780\) −0.621004 −0.0222355
\(781\) 4.51326 0.161497
\(782\) −1.23039 −0.0439988
\(783\) 6.33278 0.226315
\(784\) 7.07868 0.252810
\(785\) 4.14213 0.147839
\(786\) −1.06627 −0.0380325
\(787\) 52.3683 1.86673 0.933363 0.358933i \(-0.116859\pi\)
0.933363 + 0.358933i \(0.116859\pi\)
\(788\) 28.2204 1.00531
\(789\) −0.831840 −0.0296143
\(790\) −0.445107 −0.0158362
\(791\) 26.9567 0.958468
\(792\) 13.4628 0.478379
\(793\) −7.23906 −0.257066
\(794\) 6.72285 0.238585
\(795\) −1.97383 −0.0700046
\(796\) 27.3586 0.969701
\(797\) 16.3220 0.578155 0.289077 0.957306i \(-0.406652\pi\)
0.289077 + 0.957306i \(0.406652\pi\)
\(798\) 0.503795 0.0178341
\(799\) 0.863753 0.0305574
\(800\) −2.93902 −0.103910
\(801\) −7.27354 −0.256998
\(802\) 7.48330 0.264244
\(803\) −38.6327 −1.36332
\(804\) 4.66344 0.164467
\(805\) 14.3861 0.507043
\(806\) −0.00633681 −0.000223205 0
\(807\) −0.187019 −0.00658338
\(808\) 6.49879 0.228627
\(809\) −30.6249 −1.07671 −0.538357 0.842717i \(-0.680955\pi\)
−0.538357 + 0.842717i \(0.680955\pi\)
\(810\) −2.21556 −0.0778467
\(811\) −20.8972 −0.733799 −0.366899 0.930261i \(-0.619581\pi\)
−0.366899 + 0.930261i \(0.619581\pi\)
\(812\) 31.3086 1.09872
\(813\) −0.105115 −0.00368653
\(814\) 2.49835 0.0875669
\(815\) 9.73141 0.340876
\(816\) 0.709472 0.0248365
\(817\) −14.4875 −0.506853
\(818\) −6.05782 −0.211807
\(819\) −14.4841 −0.506114
\(820\) −10.1568 −0.354693
\(821\) 27.1289 0.946806 0.473403 0.880846i \(-0.343025\pi\)
0.473403 + 0.880846i \(0.343025\pi\)
\(822\) 0.0194765 0.000679321 0
\(823\) −4.36324 −0.152093 −0.0760464 0.997104i \(-0.524230\pi\)
−0.0760464 + 0.997104i \(0.524230\pi\)
\(824\) −1.87331 −0.0652599
\(825\) −0.886734 −0.0308721
\(826\) −7.03045 −0.244621
\(827\) −22.1533 −0.770347 −0.385173 0.922844i \(-0.625858\pi\)
−0.385173 + 0.922844i \(0.625858\pi\)
\(828\) 27.5320 0.956803
\(829\) −11.5838 −0.402321 −0.201161 0.979558i \(-0.564471\pi\)
−0.201161 + 0.979558i \(0.564471\pi\)
\(830\) 3.95134 0.137153
\(831\) −5.73358 −0.198896
\(832\) −10.5709 −0.366481
\(833\) 1.96029 0.0679199
\(834\) 0.615336 0.0213073
\(835\) 13.8227 0.478353
\(836\) −29.2131 −1.01036
\(837\) −0.0177430 −0.000613287 0
\(838\) 5.39939 0.186519
\(839\) 8.64816 0.298567 0.149284 0.988794i \(-0.452303\pi\)
0.149284 + 0.988794i \(0.452303\pi\)
\(840\) 0.592394 0.0204395
\(841\) 0.233954 0.00806737
\(842\) 0.835825 0.0288044
\(843\) 5.36490 0.184777
\(844\) 46.0670 1.58569
\(845\) −10.3303 −0.355372
\(846\) 0.654860 0.0225146
\(847\) 28.0465 0.963689
\(848\) −36.2777 −1.24578
\(849\) 4.94039 0.169554
\(850\) −0.256013 −0.00878118
\(851\) 10.3916 0.356219
\(852\) 0.380069 0.0130209
\(853\) 47.4429 1.62441 0.812207 0.583369i \(-0.198266\pi\)
0.812207 + 0.583369i \(0.198266\pi\)
\(854\) 3.39526 0.116183
\(855\) 9.90888 0.338877
\(856\) −19.3694 −0.662033
\(857\) 4.89427 0.167185 0.0835925 0.996500i \(-0.473361\pi\)
0.0835925 + 0.996500i \(0.473361\pi\)
\(858\) 0.370927 0.0126632
\(859\) 23.4313 0.799466 0.399733 0.916632i \(-0.369103\pi\)
0.399733 + 0.916632i \(0.369103\pi\)
\(860\) −8.37577 −0.285611
\(861\) 3.08790 0.105235
\(862\) −3.34924 −0.114076
\(863\) 33.3022 1.13362 0.566810 0.823849i \(-0.308178\pi\)
0.566810 + 0.823849i \(0.308178\pi\)
\(864\) 3.44234 0.117111
\(865\) −15.0969 −0.513310
\(866\) 4.17418 0.141844
\(867\) 0.196473 0.00667257
\(868\) −0.0877195 −0.00297739
\(869\) −7.84680 −0.266185
\(870\) 0.271962 0.00922039
\(871\) −20.0483 −0.679310
\(872\) −15.2709 −0.517138
\(873\) 36.9457 1.25042
\(874\) 4.11692 0.139257
\(875\) 2.99337 0.101195
\(876\) −3.25332 −0.109919
\(877\) −26.6764 −0.900799 −0.450399 0.892827i \(-0.648718\pi\)
−0.450399 + 0.892827i \(0.648718\pi\)
\(878\) 1.46968 0.0495994
\(879\) 1.11759 0.0376954
\(880\) −16.2976 −0.549391
\(881\) 51.4538 1.73352 0.866762 0.498722i \(-0.166197\pi\)
0.866762 + 0.498722i \(0.166197\pi\)
\(882\) 1.48621 0.0500431
\(883\) 1.61861 0.0544706 0.0272353 0.999629i \(-0.491330\pi\)
0.0272353 + 0.999629i \(0.491330\pi\)
\(884\) −3.16076 −0.106308
\(885\) 1.80245 0.0605886
\(886\) 1.20338 0.0404284
\(887\) 11.9868 0.402479 0.201239 0.979542i \(-0.435503\pi\)
0.201239 + 0.979542i \(0.435503\pi\)
\(888\) 0.427907 0.0143596
\(889\) 14.3083 0.479886
\(890\) −0.628798 −0.0210774
\(891\) −39.0581 −1.30850
\(892\) 44.3282 1.48422
\(893\) −2.89013 −0.0967145
\(894\) 0.121309 0.00405719
\(895\) 7.12064 0.238017
\(896\) 22.5531 0.753447
\(897\) 1.54283 0.0515135
\(898\) −1.86376 −0.0621946
\(899\) −0.0819067 −0.00273174
\(900\) 5.72870 0.190957
\(901\) −10.0463 −0.334692
\(902\) 6.06670 0.201999
\(903\) 2.54642 0.0847394
\(904\) 9.07093 0.301695
\(905\) −2.58241 −0.0858422
\(906\) 0.903198 0.0300067
\(907\) −29.9710 −0.995172 −0.497586 0.867415i \(-0.665780\pi\)
−0.497586 + 0.867415i \(0.665780\pi\)
\(908\) −0.865580 −0.0287253
\(909\) −19.1066 −0.633725
\(910\) −1.25215 −0.0415083
\(911\) 16.4482 0.544954 0.272477 0.962162i \(-0.412157\pi\)
0.272477 + 0.962162i \(0.412157\pi\)
\(912\) −2.37390 −0.0786078
\(913\) 69.6583 2.30535
\(914\) −2.72495 −0.0901332
\(915\) −0.870466 −0.0287767
\(916\) 21.5186 0.710995
\(917\) 63.4544 2.09545
\(918\) 0.299856 0.00989673
\(919\) −21.2572 −0.701212 −0.350606 0.936523i \(-0.614024\pi\)
−0.350606 + 0.936523i \(0.614024\pi\)
\(920\) 4.84093 0.159601
\(921\) −3.79318 −0.124990
\(922\) −0.328119 −0.0108060
\(923\) −1.63393 −0.0537814
\(924\) 5.13468 0.168919
\(925\) 2.16222 0.0710933
\(926\) 3.62741 0.119204
\(927\) 5.50757 0.180892
\(928\) 15.8908 0.521642
\(929\) 51.5700 1.69196 0.845979 0.533216i \(-0.179017\pi\)
0.845979 + 0.533216i \(0.179017\pi\)
\(930\) −0.000761975 0 −2.49862e−5 0
\(931\) −6.55915 −0.214967
\(932\) 41.3455 1.35432
\(933\) 4.80526 0.157317
\(934\) −4.54686 −0.148778
\(935\) −4.51326 −0.147599
\(936\) −4.87390 −0.159308
\(937\) −13.0092 −0.424990 −0.212495 0.977162i \(-0.568159\pi\)
−0.212495 + 0.977162i \(0.568159\pi\)
\(938\) 9.40302 0.307019
\(939\) 3.11808 0.101755
\(940\) −1.67089 −0.0544985
\(941\) 3.94223 0.128513 0.0642566 0.997933i \(-0.479532\pi\)
0.0642566 + 0.997933i \(0.479532\pi\)
\(942\) −0.208348 −0.00678833
\(943\) 25.2338 0.821724
\(944\) 33.1277 1.07822
\(945\) −3.50600 −0.114050
\(946\) 5.00286 0.162657
\(947\) 29.5663 0.960775 0.480387 0.877056i \(-0.340496\pi\)
0.480387 + 0.877056i \(0.340496\pi\)
\(948\) −0.660791 −0.0214615
\(949\) 13.9861 0.454009
\(950\) 0.856624 0.0277925
\(951\) 2.48092 0.0804493
\(952\) 3.01514 0.0977214
\(953\) 11.7629 0.381039 0.190519 0.981683i \(-0.438983\pi\)
0.190519 + 0.981683i \(0.438983\pi\)
\(954\) −7.61670 −0.246600
\(955\) −1.16811 −0.0377992
\(956\) −19.1180 −0.618320
\(957\) 4.79443 0.154982
\(958\) 6.06961 0.196100
\(959\) −1.15906 −0.0374281
\(960\) −1.27111 −0.0410249
\(961\) −30.9998 −0.999993
\(962\) −0.904471 −0.0291613
\(963\) 56.9464 1.83507
\(964\) 12.9459 0.416960
\(965\) 21.7456 0.700016
\(966\) −0.723616 −0.0232820
\(967\) −0.308221 −0.00991173 −0.00495587 0.999988i \(-0.501578\pi\)
−0.00495587 + 0.999988i \(0.501578\pi\)
\(968\) 9.43767 0.303338
\(969\) −0.657401 −0.0211188
\(970\) 3.19396 0.102552
\(971\) −15.2376 −0.488999 −0.244500 0.969649i \(-0.578624\pi\)
−0.244500 + 0.969649i \(0.578624\pi\)
\(972\) −10.0864 −0.323520
\(973\) −36.6191 −1.17396
\(974\) 1.58887 0.0509108
\(975\) 0.321023 0.0102809
\(976\) −15.9986 −0.512102
\(977\) 50.7456 1.62350 0.811748 0.584008i \(-0.198516\pi\)
0.811748 + 0.584008i \(0.198516\pi\)
\(978\) −0.489487 −0.0156521
\(979\) −11.0851 −0.354281
\(980\) −3.79209 −0.121134
\(981\) 44.8967 1.43344
\(982\) 8.45950 0.269954
\(983\) 8.65035 0.275903 0.137952 0.990439i \(-0.455948\pi\)
0.137952 + 0.990439i \(0.455948\pi\)
\(984\) 1.03908 0.0331247
\(985\) −14.5883 −0.464821
\(986\) 1.38422 0.0440826
\(987\) 0.507988 0.0161694
\(988\) 10.5760 0.336466
\(989\) 20.8088 0.661682
\(990\) −3.42176 −0.108751
\(991\) 37.3022 1.18494 0.592472 0.805591i \(-0.298152\pi\)
0.592472 + 0.805591i \(0.298152\pi\)
\(992\) −0.0445224 −0.00141359
\(993\) 3.14725 0.0998750
\(994\) 0.766343 0.0243069
\(995\) −14.1428 −0.448357
\(996\) 5.86603 0.185872
\(997\) 16.4849 0.522082 0.261041 0.965328i \(-0.415934\pi\)
0.261041 + 0.965328i \(0.415934\pi\)
\(998\) 8.86395 0.280584
\(999\) −2.53251 −0.0801250
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 6035.2.a.a.1.17 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6035.2.a.a.1.17 36 1.1 even 1 trivial