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lfunc_lfunctions • Show schema
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{'Lhash': '2212177781102215198489899067393', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 5, 'a6': 0, 'a7': 18, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 42.481375204133265, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, -5]]], 'bad_primes': [2, 3, 5], 'central_character': '720.1', 'coefficient_field': '1.1.1.1', 'conductor': 720, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[1], [1], [1, -5], [1, -18, 343], [1, 34, 1331], [1, -12, 2197], [1, 102, 4913], [1, 164, 6859], [1, 48, 12167], [1, -146, 24389], [1, 100, 29791], [1, -328, 50653], [1, 288, 68921], [1, 120, 79507], [1, 16, 103823], [1, 126, 148877], [1, 642, 205379], [1, -602, 226981], [1, 436, 300763], [1, 652, 357911], [1, -1062, 389017], [1, 388, 493039], [1, -444, 571787], [1, 820, 704969], [1, 766, 912673], [1, 798, 1030301], [1, -402, 1092727], [1, 1444, 1225043], [1, 198, 1295029], [1, 2010, 1442897]], 'euler_factors_factorization': [[1], [1], [[[1, -5], 1]], [[[1, -18, 343], 1]], [[[1, 34, 1331], 1]], [[[1, -12, 2197], 1]], [[[1, 102, 4913], 1]], [[[1, 164, 6859], 1]], [[[1, 48, 12167], 1]], [[[1, -146, 24389], 1]], [[[1, 100, 29791], 1]], [[[1, -328, 50653], 1]], [[[1, 288, 68921], 1]], [[[1, 120, 79507], 1]], [[[1, 16, 103823], 1]], [[[1, 126, 148877], 1]], [[[1, 642, 205379], 1]], [[[1, -602, 226981], 1]], [[[1, 436, 300763], 1]], [[[1, 652, 357911], 1]], [[[1, -1062, 389017], 1]], [[[1, 388, 493039], 1]], [[[1, -444, 571787], 1]], [[[1, 820, 704969], 1]], [[[1, 766, 912673], 1]], [[[1, 798, 1030301], 1]], [[[1, -402, 1092727], 1]], [[[1, 1444, 1225043], 1]], [[[1, 198, 1295029], 1]], [[[1, 2010, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 28, 'label': '2-720-1.1-c3-0-28', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/720/4/a/z', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [-2.117283713678537e-60, 0.23930126270230984, 0.47617382804211633, 0.7082000754917338, 0.9329852033998426, 1.1481702665705358, 1.3514470713526767, 1.5405753910770241, 1.713402838624467, 1.8678875847369745, 2.0021239458939757, 2.114370690120442, 2.2030817291320495, 2.2669386869294113, 2.3048846643435263, 2.316158361844554, 2.3003275845254394, 2.2573210385027442, 2.187457241508655, 2.0914693161349405, 1.9705244154228163, 1.8262365500385236, 1.6606716461964899, 1.4763437650575542, 1.2762015579049493, 1.0636042163401267, 0.842286401280498, 0.6163118957060588, 0.3900160196326173, 0.16793716610426204, -0.04526184280653553, -0.24488152910258915, -0.42628125592444704, -0.5849806971768721, -0.7167652012444633, -0.817792674103984, -0.884699353686722, -0.9147016483937996, -0.9056910793961364, -0.8563193089382884, -0.7660702640519875, 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2.1665497813070136, 2.4701652593578816, 2.6916293316826017, 2.8161113864485565, 2.834353212439326, 2.7432529897118267, 2.5460933052811514, 2.252395974634844, 1.8774080204177384, 1.4412448035104508, 0.9677367529473094, 0.4830441796230536, 0.014119183228960965, -0.41289624273525893, -0.7742418076148533, -1.0499866082197842, -1.2252653207043833, -1.2912266350394868, -1.2456336842601319, -1.0930760654906573, -0.8447756053356043, -0.5179919889299642], 'positive_zeros': ['1.74510056691010278427860866614266', '2.58216215805839475919722932871855', '4.23803846914387519133137654675202', '4.91871015722656249551079093458212', '6.05164972946561926212109785925212', '6.84643026874068490471649050787342', '8.140087082031022352012151639789447', '8.499274051364086291368336254454571', '9.598023949803419899905638252894040'], 'prelabel': '2-720-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.517773792034613, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'trace_hash': 750439021159304949, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.74510056691010278427860866614', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.58216215805839475919722932872', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.23803846914387519133137654675', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 42.481375204133265, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 720, 'conductor_radical': 30, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 5, 0, 18, 0, 0, 0, -34, 0, 12, 0, 0, 0, -102, 0, -164, 0, 0, 0, -48, 0, 25, 0, 0, 0, 146, 0, -100, 0, 0, 0, 90, 0, 328, 0, 0, 0, -288, 0, -120, 0, 0, 0, -16, 0, -19, 0, 0, 0, -126, 0, -170, 0, 0, 0, -642, 0, 602, 0, 0, 0, 60, 0, -436, 0, 0, 0, -652, 0, 1062, 0, 0, 0, -612, 0, -388, 0, 0, 0, 444, 0, -510, 0, 0, 0, -820, 0, 216, 0, 0, 0, -820, 0, -766, 0, 0, 0], 'euler11': [1, 34, 1331], 'euler13': [1, -12, 2197], 'euler17': [1, 102, 4913], 'euler19': [1, 164, 6859], 'euler2': [1, 0, 0], 'euler23': [1, 48, 12167], 'euler29': [1, -146, 24389], 'euler3': [1, 0, 0], 'euler31': [1, 100, 29791], 'euler37': [1, -328, 50653], 'euler41': [1, 288, 68921], 'euler43': [1, 120, 79507], 'euler47': [1, 16, 103823], 'euler5': [1, -5, 0], 'euler53': [1, 126, 148877], 'euler59': [1, 642, 205379], 'euler61': [1, -602, 226981], 'euler67': [1, 436, 300763], 'euler7': [1, -18, 343], 'euler71': [1, 652, 357911], 'euler73': [1, -1062, 389017], 'euler79': [1, 388, 493039], 'euler83': [1, -444, 571787], 'euler89': [1, 820, 704969], 'euler97': [1, 766, 912673], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, -5, 0], [1, -18, 343], [1, 34, 1331], [1, -12, 2197], [1, 102, 4913], [1, 164, 6859], [1, 48, 12167], [1, -146, 24389], [1, 100, 29791], [1, -328, 50653], [1, 288, 68921], [1, 120, 79507], [1, 16, 103823], [1, 126, 148877], [1, 642, 205379], [1, -602, 226981], [1, 436, 300763], [1, 652, 357911], [1, -1062, 389017], [1, 388, 493039], [1, -444, 571787], [1, 820, 704969], [1, 766, 912673]], 'index': 28, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/720/4/a/z/1/1', 'ModularForm/GL2/Q/holomorphic/720/4/a/z'], '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': '2-720-1.1-c3-0-28', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-720-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.517773792034613, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 750439021159304949, 'z1': {'__RealLiteral__': 0, 'data': '1.74510056691010278427860866614', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20219348
{'Lhash': '2212177781102215198489899067393', 'Lhash_array': ['2212177781102215198489899067393'], 'label': '2-720-1.1-c3-0-28', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/720/4/a/z'}
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id: 24569833
{'Lhash': '2212177781102215198489899067393', 'Lhash_array': ['2212177781102215198489899067393'], 'label': '2-720-1.1-c3-0-28', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/720/4/a/z/1/1'}