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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '906508457447502756,2110014172124380148', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 21.22777793843102, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 0, -1]], [17, [1, 2, 1]]], 'bad_primes': [2, 3, 17], 'central_character': '332928.1', 'coefficient_field': '1.1.1.1', 'conductor': 332928, 'conductor_radical': 102, 'degree': 4, 'euler_factors': [[1], [1, 0, -1], [1, 0, 10, 0, 25], [1, 0, 10, 0, 49], [1, 0, 22, 0, 121], [1, -4, 30, -52, 169], [1, 2, 1], [1, 0, 22, 0, 361], [1, 0, 42, 0, 529], [1, 0, 58, 0, 841], [1, 0, 26, 0, 961], [1, 0, 74, 0, 1369], [1, 20, 182, 820, 1681], [1, 0, 70, 0, 1849], [1, 0, 78, 0, 2209], [1, 4, 110, 212, 2809], [1, 0, 102, 0, 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-6.776750110621369], 'positive_zeros': ['1.56214672992889030308430941458241', '1.86322179819912387769835446844751', '3.04403834504276039976899251672031', '3.38688660560456486653785466781824', '4.27397030413758079313764720862603', '4.32146836767987654020354473359521', '5.36989365154370802259795523402236', '5.53399853944419593600376639580512', '6.29392484047154187578719849324004', '6.62723952041019147822559271931636', '7.03118715673001635895164549850479', '7.73801571262467689165588307382279', '8.139884873932014733298462713742626', '8.407090090052685003442827550966005'], 'prelabel': '4-332928-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.1464764795303726, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 710679620358188953, 'z1': {'__RealLiteral__': 0, 'data': '1.56214672992889030308430941458241', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.86322179819912387769835446844751', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '3.04403834504276039976899251672031', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 21.22777793843102, 'bad_primes': [2, 3, 17], 'central_character': '1.1', 'conductor': 332928, 'conductor_radical': 102, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 4, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -28, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0], 'euler11': [1, 0, 22, 0, 121], 'euler13': [1, -4, 30, -52, 169], 'euler17': [1, 2, 1, 0, 0], 'euler19': [1, 0, 22, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 42, 0, 529], 'euler29': [1, 0, 58, 0, 841], 'euler3': [1, 0, -1, 0, 0], 'euler31': [1, 0, 26, 0, 961], 'euler37': [1, 0, 74, 0, 1369], 'euler41': [1, 20, 182, 820, 1681], 'euler43': [1, 0, 70, 0, 1849], 'euler47': [1, 0, 78, 0, 2209], 'euler5': [1, 0, 10, 0, 25], 'euler53': [1, 4, 110, 212, 2809], 'euler59': [1, 0, 102, 0, 3481], 'euler61': [1, 0, 122, 0, 3721], 'euler67': [1, 0, 118, 0, 4489], 'euler7': [1, 0, 10, 0, 49], 'euler71': [1, 0, 138, 0, 5041], 'euler73': [1, 28, 342, 2044, 5329], 'euler79': [1, 0, 122, 0, 6241], 'euler83': [1, 0, 22, 0, 6889], 'euler89': [1, 4, 182, 356, 7921], 'euler97': [1, 4, 198, 388, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, -1, 0, 0], [1, 0, 10, 0, 25], [1, 0, 10, 0, 49], [1, 0, 22, 0, 121], [1, -4, 30, -52, 169], [1, 2, 1, 0, 0], [1, 0, 22, 0, 361], [1, 0, 42, 0, 529], [1, 0, 58, 0, 841], [1, 0, 26, 0, 961], [1, 0, 74, 0, 1369], [1, 20, 182, 820, 1681], [1, 0, 70, 0, 1849], [1, 0, 78, 0, 2209], [1, 4, 110, 212, 2809], [1, 0, 102, 0, 3481], [1, 0, 122, 0, 3721], [1, 0, 118, 0, 4489], [1, 0, 138, 0, 5041], [1, 28, 342, 2044, 5329], [1, 0, 122, 0, 6241], [1, 0, 22, 0, 6889], [1, 4, 182, 356, 7921], [1, 4, 198, 388, 9409]], 'index': 28, 'instance_types': ['BMF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/20808.2/b', 'EllipticCurve/2.0.4.1/20808.2/b'], 'is_instance_Artin': False, 'is_instance_BMF': True, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, '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': '4-332928-1.1-c1e2-0-28', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 1, 'prelabel': '4-332928-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.1464764795303726, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 710679620358188953, 'z1': {'__RealLiteral__': 0, 'data': '1.56214672992889030308430941458241', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9656643
{'Lhash': '906508457447502756,2110014172124380148', 'Lhash_array': ['906508457447502756', '2110014172124380148'], 'label': '4-332928-1.1-c1e2-0-28', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.4.1/20808.2/b'}
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id: 9656767
{'Lhash': '906508457447502756,2110014172124380148', 'Lhash_array': ['906508457447502756', '2110014172124380148'], 'label': '4-332928-1.1-c1e2-0-28', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/20808.2/b'}