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{'Lhash': '1540910815675155798104648442994,1760539696944841414705405721344,2836599502513982723700806112240', 'a10': 3, 'a2': 1, 'a3': 0, 'a4': 0, 'a5': 3, 'a6': 0, 'a7': 5, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 33.82177458141172, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1, -3, 3, -1]]], 'bad_primes': [3, 5], 'central_character': '405.1', 'coefficient_field': '1.1.1.1', 'conductor': 66430125, 'conductor_radical': 15, 'degree': 6, 'euler_factors': [[1, -1, 1, -1, 2, -4, 8], [1], [1, -3, 3, -1], [1, -5, 24, -67, 168, -245, 343], [1, 2, 25, 32, 275, 242, 1331], [1, -4, 35, -100, 455, -676, 2197], [1, 2, 43, 56, 731, 578, 4913], [1, -4, 53, -148, 1007, -1444, 6859], [1, -3, 36, -21, 828, -1587, 12167], [1, 7, 58, 355, 1682, 5887, 24389], [1, -8, 33, -28, 1023, -7688, 29791], [1, -6, 99, -440, 3663, -8214, 50653], [1, 13, 142, 1069, 5822, 21853, 68921], [1, -10, 125, -856, 5375, -18490, 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828, -1587, 12167], 1]], [[[1, 7, 58, 355, 1682, 5887, 24389], 1]], [[[1, -8, 33, -28, 1023, -7688, 29791], 1]], [[[1, -6, 99, -440, 3663, -8214, 50653], 1]], [[[1, 13, 142, 1069, 5822, 21853, 68921], 1]], [[[1, -10, 125, -856, 5375, -18490, 79507], 1]], [[[1, -13, 130, -853, 6110, -28717, 103823], 1]], [[[1, 2, 139, 188, 7367, 5618, 148877], 1]], [[[1, 2, 157, 212, 9263, 6962, 205379], 1]], [[[1, -1, 146, -193, 8906, -3721, 226981], 1]], [[[1, -11, 162, -967, 10854, -49379, 300763], 1]], [[[1, 10, 121, 712, 8591, 50410, 357911], 1]], [[[1, 8, 155, 1040, 11315, 42632, 389017], 1]], [[[1, -2, 153, -340, 12087, -12482, 493039], 1]], [[[1, 15, 276, 2409, 22908, 103335, 571787], 1]], [[[1, 3, 89], 3]], [[[1, 18, 255, 2188, 24735, 169362, 912673], 1]], [[[1, -6, 243, -1284, 24543, -61206, 1030301], 1]], [[[1, -6, 297, -1232, 30591, -63654, 1092727], 1]], [[[1, -15, 360, -3237, 38520, -171735, 1225043], 1]], [[[1, -3, 78, 649, 8502, -35643, 1295029], 1]], [[[1, -16, 163, -1744, 18419, 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'8.281294856092912784424661004140563', '8.603754952090573020173189531992563', '8.617418563560361078466997369064225', '9.257898121091855577726697204487699', '9.392007957938456349797394014402046', '9.699823814832895875174538969105986', '10.23480782368015375175878622131674', '10.36556769895641939681826832139535', '10.71476474098541103720363091295427', '10.96848225593364782425800684114978', '11.43647010305502459602123780381801', '11.45116164807663356741459537137922'], 'prelabel': '6-405e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.7983162352216746, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e3-0', 'trace_hash': 2275373870602684034, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.21556430091835107025965573141', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.38882093900943339040678353578', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.23768245130265216385360926189', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 33.82177458141172, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 66430125, 'conductor_radical': 15, 'degree': 6, 'dirichlet_coefficients': [1, 1, 0, 0, 3, 0, 5, 0, 0, 3, -2, 0, 4, 5, 0, -1, -2, 0, 4, 0, 0, -2, 3, 0, 6, 4, 0, 0, -7, 0, 8, 1, 0, -2, 15, 0, 6, 4, 0, 0, -13, 0, 10, 0, 0, 3, 13, 0, 1, 6, 0, 0, -2, 0, -6, 0, 0, -7, -2, 0, 1, 8, 0, -2, 12, 0, 11, 0, 0, 15, -10, 0, -8, 6, 0, 0, -10, 0, 2, -3, 0, -13, -15, 0, -6, 10, 0, 0, -9, 0, 20, 0, 0, 13, 12, 0, -18, 1, 0, 0], 'euler11': [1, 2, 25, 32, 275, 242, 1331], 'euler13': [1, -4, 35, -100, 455, -676, 2197], 'euler17': [1, 2, 43, 56, 731, 578, 4913], 'euler19': [1, -4, 53, -148, 1007, -1444, 6859], 'euler2': [1, -1, 1, -1, 2, -4, 8], 'euler23': [1, -3, 36, -21, 828, -1587, 12167], 'euler29': [1, 7, 58, 355, 1682, 5887, 24389], 'euler3': [1, 0, 0, 0, 0, 0, 0], 'euler31': [1, -8, 33, -28, 1023, -7688, 29791], 'euler37': [1, -6, 99, -440, 3663, -8214, 50653], 'euler41': [1, 13, 142, 1069, 5822, 21853, 68921], 'euler43': [1, -10, 125, -856, 5375, -18490, 79507], 'euler47': [1, -13, 130, -853, 6110, -28717, 103823], 'euler5': [1, -3, 3, -1, 0, 0, 0], 'euler53': [1, 2, 139, 188, 7367, 5618, 148877], 'euler59': [1, 2, 157, 212, 9263, 6962, 205379], 'euler61': [1, -1, 146, -193, 8906, -3721, 226981], 'euler67': [1, -11, 162, -967, 10854, -49379, 300763], 'euler7': [1, -5, 24, -67, 168, -245, 343], 'euler71': [1, 10, 121, 712, 8591, 50410, 357911], 'euler73': [1, 8, 155, 1040, 11315, 42632, 389017], 'euler79': [1, -2, 153, -340, 12087, -12482, 493039], 'euler83': [1, 15, 276, 2409, 22908, 103335, 571787], 'euler89': [1, 9, 294, 1629, 26166, 71289, 704969], 'euler97': [1, 18, 255, 2188, 24735, 169362, 912673], 'euler_factors': [[1, -1, 1, -1, 2, -4, 8], [1, 0, 0, 0, 0, 0, 0], [1, -3, 3, -1, 0, 0, 0], [1, -5, 24, -67, 168, -245, 343], [1, 2, 25, 32, 275, 242, 1331], [1, -4, 35, -100, 455, -676, 2197], [1, 2, 43, 56, 731, 578, 4913], [1, -4, 53, -148, 1007, -1444, 6859], [1, -3, 36, -21, 828, -1587, 12167], [1, 7, 58, 355, 1682, 5887, 24389], [1, -8, 33, -28, 1023, -7688, 29791], [1, -6, 99, -440, 3663, -8214, 50653], [1, 13, 142, 1069, 5822, 21853, 68921], [1, -10, 125, -856, 5375, -18490, 79507], [1, -13, 130, -853, 6110, -28717, 103823], [1, 2, 139, 188, 7367, 5618, 148877], [1, 2, 157, 212, 9263, 6962, 205379], [1, -1, 146, -193, 8906, -3721, 226981], [1, -11, 162, -967, 10854, -49379, 300763], [1, 10, 121, 712, 8591, 50410, 357911], [1, 8, 155, 1040, 11315, 42632, 389017], [1, -2, 153, -340, 12087, -12482, 493039], [1, 15, 276, 2409, 22908, 103335, 571787], [1, 9, 294, 1629, 26166, 71289, 704969], [1, 18, 255, 2188, 24735, 169362, 912673]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/405/2/a/j'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '6-405e3-1.1-c1e3-0-1', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '6-405e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.7983162352216746, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e3-0', 'trace_hash': 2275373870602684034, 'z1': {'__RealLiteral__': 0, 'data': '1.21556430091835107025965573141', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1540910815675155798104648442994,1760539696944841414705405721344,2836599502513982723700806112240', 'Lhash_array': ['1540910815675155798104648442994', '1760539696944841414705405721344', '2836599502513982723700806112240'], 'label': '6-405e3-1.1-c1e3-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/405/2/a/j'}