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lfunc_lfunctions • Show schema
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{'Lhash': '1969063463571619040993275165655', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -5, 'a6': 0, 'a7': 16, '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, -16, 343], [1, 28, 1331], [1, 26, 2197], [1, -62, 4913], [1, -68, 6859], [1, 208, 12167], [1, -58, 24389], [1, 160, 29791], [1, -270, 50653], [1, 282, 68921], [1, 76, 79507], [1, 280, 103823], [1, -210, 148877], [1, -196, 205379], [1, -742, 226981], [1, 836, 300763], [1, 504, 357911], [1, 1062, 389017], [1, 768, 493039], [1, 1052, 571787], [1, -726, 704969], [1, 1406, 912673], [1, 990, 1030301], [1, 736, 1092727], [1, -1212, 1225043], [1, 1834, 1295029], [1, -2046, 1442897]], 'euler_factors_factorization': [[1], [1], [[[1, 5], 1]], [[[1, -16, 343], 1]], [[[1, 28, 1331], 1]], [[[1, 26, 2197], 1]], [[[1, -62, 4913], 1]], [[[1, -68, 6859], 1]], [[[1, 208, 12167], 1]], [[[1, -58, 24389], 1]], [[[1, 160, 29791], 1]], [[[1, -270, 50653], 1]], [[[1, 282, 68921], 1]], [[[1, 76, 79507], 1]], [[[1, 280, 103823], 1]], [[[1, -210, 148877], 1]], [[[1, -196, 205379], 1]], [[[1, -742, 226981], 1]], [[[1, 836, 300763], 1]], [[[1, 504, 357911], 1]], [[[1, 1062, 389017], 1]], [[[1, 768, 493039], 1]], [[[1, 1052, 571787], 1]], [[[1, -726, 704969], 1]], [[[1, 1406, 912673], 1]], [[[1, 990, 1030301], 1]], [[[1, 736, 1092727], 1]], [[[1, -1212, 1225043], 1]], [[[1, 1834, 1295029], 1]], [[[1, -2046, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 23, 'label': '2-720-1.1-c3-0-23', '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/l', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [-1.3321142079171506e-60, 0.21698034013549108, 0.43147372892336566, 0.6410047309049057, 0.843121605740034, 1.0354097793179717, 1.2155071670740447, 1.3811218108998076, 1.5300521652122177, 1.6602102198219468, 1.769647482688628, 1.8565836703995438, 1.9194377744021263, 1.9568609928167884, 1.967770847061354, 1.9513856452636724, 1.907258315895136, 1.8353085201721622, 1.7358518650234396, 1.6096249837739827, 1.4578052325573057, 1.2820237696147436, 1.0843708441539104, 0.8673922225974983, 0.6340758232379341, 0.3878278148890353, 0.13243765933950918, -0.12796816170161754, -0.3889837011718958, -0.6459920285876622, -0.8942439450950447, -1.128945885516781, -1.3453556069622599, -1.5388839171844702, -1.7052003685694952, -1.8403405471221064, -1.9408123319635804, -2.0036983014241074, -2.026751327966701, -2.008480346101861, -1.948223303883558, 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1.2722771696746897, 1.662715503725986, 1.954671053349449, 2.13675105609358, 2.2039377541909557, 2.1578524966133172, 2.006640919723566, 1.7644828319477002, 1.450752202866638, 1.0888732556945364, 0.7049368613007863, 0.3261561271569875, -0.020749652850716303, -0.3111483466964737, -0.5239715979056895, -0.6429865324462057, -0.6577855398767752, -0.5644329776830221, -0.36572736117326615, -0.071060046627899, 0.3041247039363043], 'positive_zeros': ['1.55331718631072820004742209192202', '2.84483562175671081789187281342425', '4.05367443821206399974325006275723', '5.05455036767600041321342701723995', '5.82590851836972082420520483793313', '7.22828625858627094936085097158048', '7.86523313374082870419126362774114', '8.478744813245837004359988632783311', '9.800095994046997545597161350358884'], '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': 486231862568992217, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.55331718631072820004742209192', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.84483562175671081789187281342', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.05367443821206399974325006276', '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, 16, 0, 0, 0, -28, 0, -26, 0, 0, 0, 62, 0, 68, 0, 0, 0, -208, 0, 25, 0, 0, 0, 58, 0, -160, 0, 0, 0, -80, 0, 270, 0, 0, 0, -282, 0, -76, 0, 0, 0, -280, 0, -87, 0, 0, 0, 210, 0, 140, 0, 0, 0, 196, 0, 742, 0, 0, 0, 130, 0, -836, 0, 0, 0, -504, 0, -1062, 0, 0, 0, -448, 0, -768, 0, 0, 0, -1052, 0, -310, 0, 0, 0, 726, 0, -416, 0, 0, 0, -340, 0, -1406, 0, 0, 0], 'euler11': [1, 28, 1331], 'euler13': [1, 26, 2197], 'euler17': [1, -62, 4913], 'euler19': [1, -68, 6859], 'euler2': [1, 0, 0], 'euler23': [1, 208, 12167], 'euler29': [1, -58, 24389], 'euler3': [1, 0, 0], 'euler31': [1, 160, 29791], 'euler37': [1, -270, 50653], 'euler41': [1, 282, 68921], 'euler43': [1, 76, 79507], 'euler47': [1, 280, 103823], 'euler5': [1, 5, 0], 'euler53': [1, -210, 148877], 'euler59': [1, -196, 205379], 'euler61': [1, -742, 226981], 'euler67': [1, 836, 300763], 'euler7': [1, -16, 343], 'euler71': [1, 504, 357911], 'euler73': [1, 1062, 389017], 'euler79': [1, 768, 493039], 'euler83': [1, 1052, 571787], 'euler89': [1, -726, 704969], 'euler97': [1, 1406, 912673], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 5, 0], [1, -16, 343], [1, 28, 1331], [1, 26, 2197], [1, -62, 4913], [1, -68, 6859], [1, 208, 12167], [1, -58, 24389], [1, 160, 29791], [1, -270, 50653], [1, 282, 68921], [1, 76, 79507], [1, 280, 103823], [1, -210, 148877], [1, -196, 205379], [1, -742, 226981], [1, 836, 300763], [1, 504, 357911], [1, 1062, 389017], [1, 768, 493039], [1, 1052, 571787], [1, -726, 704969], [1, 1406, 912673]], 'index': 23, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/720/4/a/l/1/1', 'ModularForm/GL2/Q/holomorphic/720/4/a/l'], '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-c3-0-23', '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': 486231862568992217, 'z1': {'__RealLiteral__': 0, 'data': '1.55331718631072820004742209192', 'prec': 103}}
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lfunc_instances • Show schema
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id: 19979670
{'Lhash': '1969063463571619040993275165655', 'Lhash_array': ['1969063463571619040993275165655'], 'label': '2-720-1.1-c3-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/720/4/a/l'}
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id: 24569819
{'Lhash': '1969063463571619040993275165655', 'Lhash_array': ['1969063463571619040993275165655'], 'label': '2-720-1.1-c3-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/720/4/a/l/1/1'}