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  • lfunc_lfunctions • Show schema
    {'Lhash': '856149716393284034487367143658,2241099982375399440089216300791', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 48, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1302.2253389262594, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1]]], 'bad_primes': [3, 5], 'central_character': '225.1', 'coefficient_field': '1.1.1.1', 'conductor': 50625, 'conductor_radical': 15, 'degree': 4, 'euler_factors': [[1, 0, -48, 0, 1024], [1], [1], [1, 0, 17011, 0, 282475249], [1, -868, 510458, -139792268, 25937424601], [1, 0, -366817, 0, 137858491849], [1, 0, -2068830, 0, 2015993900449], [1, -1462, 5486559, -3620056738, 6131066257801], [1, 0, -4750186, 0, 41426511213649], [1, 15164, 98509022, 311031063436, 420707233300201], [1, -4350, 61988927, -124536806850, 819628286980801], [1, 0, -52011814, 0, 4808584372417849], [1, -24080, 376674002, -2789817320080, 13422659310152401], [1, 0, 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1]], [[[1, -434, 161051], 2]], [[[1, 0, -366817, 0, 137858491849], 1]], [[[1, 0, -2068830, 0, 2015993900449], 1]], [[[1, -731, 2476099], 2]], [[[1, 0, -4750186, 0, 41426511213649], 1]], [[[1, 7582, 20511149], 2]], [[[1, -2175, 28629151], 2]], [[[1, 0, -52011814, 0, 4808584372417849], 1]], [[[1, -12040, 115856201], 2]], [[[1, 0, -292760245, 0, 21611482313284249], 1]], [[[1, 0, 434004870, 0, 52599132235830049], 1]], [[[1, 0, -803443386, 0, 174887470365513049], 1]], [[[1, 5174, 714924299], 2]], [[[1, 38717, 844596301], 2]], [[[1, 0, -1694916365, 0, 1822837804551761449], 1]], [[[1, 64472, 1804229351], 2]], [[[1, 0, -3754499086, 0, 4297625829703557649], 1]], [[[1, -105000, 3077056399], 2]], [[[1, 0, -7867072162, 0, 15516041187205853449], 1]], [[[1, 65376, 5584059449], 2]], [[[1, 0, -9228206065, 0, 73742412689492826049], 1]], [[[1, -94644, 10510100501], 2]], [[[1, 0, -10199511550, 0, 134391637934412192049], 1]], [[[1, 0, -27681933670, 0, 196715135728956532249], 1]], [[[1, -152791, 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'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c5e2-0', 'trace_hash': 394633250149443840, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.67538304027871857389057474475', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.63860312880416090180511276353', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.76791616078745120525825255003', 'prec': 103}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 1302.2253389262594, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 50625, 'conductor_radical': 15, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 48, 0, 0, 0, 0, 0, 0, 868, 0, 0, 0, 0, 1280, 0, 0, 1462, 0, 0, 0, 0, 0, 0, 0, 0, 0, -15164, 0, 4350, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24080, 0, 0, 41664, 0, 0, 0, 0, -17011, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10348, 0, -77434, 0, 0, 12288, 0, 0, 0, 0, 0, 0, -128944, 0, 0, 0, 0, 70176, 0, 0, 210000, 0, 0, 0, 0, 0, 0, 0, 0, 0, -130752, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, -868, 510458, -139792268, 25937424601], 'euler13': [1, 0, -366817, 0, 137858491849], 'euler17': [1, 0, -2068830, 0, 2015993900449], 'euler19': [1, -1462, 5486559, -3620056738, 6131066257801], 'euler2': [1, 0, -48, 0, 1024], 'euler23': [1, 0, -4750186, 0, 41426511213649], 'euler29': [1, 15164, 98509022, 311031063436, 420707233300201], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -4350, 61988927, -124536806850, 819628286980801], 'euler37': [1, 0, -52011814, 0, 4808584372417849], 'euler41': [1, -24080, 376674002, -2789817320080, 13422659310152401], 'euler43': [1, 0, -292760245, 0, 21611482313284249], 'euler47': [1, 0, 434004870, 0, 52599132235830049], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 0, -803443386, 0, 174887470365513049], 'euler59': [1, 10348, 1456618874, 7398036646052, 511116753300641401], 'euler61': [1, 77434, 3188198691, 65400469971634, 713342911662882601], 'euler67': [1, 0, -1694916365, 0, 1822837804551761449], 'euler7': [1, 0, 17011, 0, 282475249], 'euler71': [1, 128944, 7765097486, 232644549435344, 3255243551009881201], 'euler73': [1, 0, -3754499086, 0, 4297625829703557649], 'euler79': [1, -210000, 17179112798, -646181843790000, 9468276082626847201], 'euler83': [1, 0, -7867072162, 0, 15516041187205853449], 'euler89': [1, 130752, 15442140274, 730126941075648, 31181719929966183601], 'euler97': [1, 0, -9228206065, 0, 73742412689492826049], 'euler_factors': [[1, 0, -48, 0, 1024], [1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 0, 17011, 0, 282475249], [1, -868, 510458, -139792268, 25937424601], [1, 0, -366817, 0, 137858491849], [1, 0, -2068830, 0, 2015993900449], [1, -1462, 5486559, -3620056738, 6131066257801], [1, 0, -4750186, 0, 41426511213649], [1, 15164, 98509022, 311031063436, 420707233300201], [1, -4350, 61988927, -124536806850, 819628286980801], [1, 0, -52011814, 0, 4808584372417849], [1, -24080, 376674002, -2789817320080, 13422659310152401], [1, 0, -292760245, 0, 21611482313284249], [1, 0, 434004870, 0, 52599132235830049], [1, 0, -803443386, 0, 174887470365513049], [1, 10348, 1456618874, 7398036646052, 511116753300641401], [1, 77434, 3188198691, 65400469971634, 713342911662882601], [1, 0, -1694916365, 0, 1822837804551761449], [1, 128944, 7765097486, 232644549435344, 3255243551009881201], [1, 0, -3754499086, 0, 4297625829703557649], [1, -210000, 17179112798, -646181843790000, 9468276082626847201], [1, 0, -7867072162, 0, 15516041187205853449], [1, 130752, 15442140274, 730126941075648, 31181719929966183601], [1, 0, -9228206065, 0, 73742412689492826049]], 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/225/6/b/c'], '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': '4-15e4-1.1-c5e2-0-6', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5, 5], 'order_of_vanishing': 0, 'prelabel': '4-15e4-1.1-c5e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.007192310715602, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5e2-0', 'trace_hash': 394633250149443840, 'z1': {'__RealLiteral__': 0, 'data': '0.67538304027871857389057474475', 'prec': 103}}
  • lfunc_instances • Show schema
    {'Lhash': '856149716393284034487367143658,2241099982375399440089216300791', 'Lhash_array': ['856149716393284034487367143658', '2241099982375399440089216300791'], 'factors': ['2-15e2-5.4-c5-0-11', '2-15e2-5.4-c5-0-31'], 'label': '4-15e4-1.1-c5e2-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/225/6/b/c'}