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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': -4, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': -6, 'Lhash': '1485208795141819780,1485208795141819780', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [-1.788854381999832, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [-2.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.06529112783831148, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]]], 'bad_primes': [2], 'central_character': '1024.1', 'coefficient_field': '1.1.1.1', 'conductor': 1024, 'conductor_radical': 2, 'degree': 4, 'euler_factors': [[1], [1, 0, 6, 0, 9], [1, 4, 14, 20, 25], [1, 0, 14, 0, 49], [1, 0, 22, 0, 121], [1, -12, 62, -156, 169], [1, -4, 38, -68, 289], [1, 0, 38, 0, 361], [1, 0, 46, 0, 529], [1, 20, 158, 580, 841], [1, 0, 62, 0, 961], [1, 4, 78, 148, 1369], [1, -20, 182, -820, 1681], [1, 0, 86, 0, 1849], [1, 0, 94, 0, 2209], [1, -28, 302, -1484, 2809], [1, 0, 118, 0, 3481], [1, 20, 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'3.67478222653086463350186782835361', '5.87146418848833687506982135025618', '5.87146418848833687506982135025618', '7.77199473906097062385997282225311', '7.77199473906097062385997282225311', '8.955386231165229198073332132052119', '8.955386231165229198073332132052119', '10.90769214371221130983350005998246', '10.90769214371221130983350005998246', '11.76661268274493420855693255102103', '11.76661268274493420855693255102103', '13.27687552535142704095990346642387', '13.27687552535142704095990346642387', '14.57652563978276046331230069556564', '14.57652563978276046331230069556564', '15.74882074786535250024495459074091', '15.74882074786535250024495459074091', '16.73856366990991880815681244917426', '16.73856366990991880815681244917426', '18.11836294614508901336437330214268', '18.11836294614508901336437330214268', '19.18872457828343982814861254090794', '19.18872457828343982814861254090794', '20.20845899367360484082674298843252', '20.20845899367360484082674298843252', '21.12487395960335905160798320961912', '21.12487395960335905160798320961912', '22.72990404500935799562639007722915', '22.72990404500935799562639007722915'], 'prelabel': '4-2e10-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.5054911339164094, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'N(U(1))', 'symmetry_type': 'symplectic', 'trace_hash': 664574581069945609, 'z1': {'__RealLiteral__': 0, 'data': '3.67478222653086463350186782835361', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '3.67478222653086463350186782835361', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '5.87146418848833687506982135025618', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.06529112783831148, 'bad_primes': [2], 'central_character': '1.1', 'conductor': 1024, 'conductor_radical': 2, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, -4, 0, 0, 0, -6, 0, 0, 0, 12, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -20, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 20, 0, 0, 0, 24, 0, 0, 0, -14, 0, 0, 0, 28, 0, 0, 0, 0, 0, 0, 0, -20, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 27, 0, 0, 0, -16, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0], 'euler11': [1, 0, 22, 0, 121], 'euler13': [1, -12, 62, -156, 169], 'euler17': [1, -4, 38, -68, 289], 'euler19': [1, 0, 38, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 46, 0, 529], 'euler29': [1, 20, 158, 580, 841], 'euler3': [1, 0, 6, 0, 9], 'euler31': [1, 0, 62, 0, 961], 'euler37': [1, 4, 78, 148, 1369], 'euler41': [1, -20, 182, -820, 1681], 'euler43': [1, 0, 86, 0, 1849], 'euler47': [1, 0, 94, 0, 2209], 'euler5': [1, 4, 14, 20, 25], 'euler53': [1, -28, 302, -1484, 2809], 'euler59': [1, 0, 118, 0, 3481], 'euler61': [1, 20, 222, 1220, 3721], 'euler67': [1, 0, 134, 0, 4489], 'euler7': [1, 0, 14, 0, 49], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, 12, 182, 876, 5329], 'euler79': [1, 0, 158, 0, 6241], 'euler83': [1, 0, 166, 0, 6889], 'euler89': [1, -20, 278, -1780, 7921], 'euler97': [1, -36, 518, -3492, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 6, 0, 9], [1, 4, 14, 20, 25], [1, 0, 14, 0, 49], [1, 0, 22, 0, 121], [1, -12, 62, -156, 169], [1, -4, 38, -68, 289], [1, 0, 38, 0, 361], [1, 0, 46, 0, 529], [1, 20, 158, 580, 841], [1, 0, 62, 0, 961], [1, 4, 78, 148, 1369], [1, -20, 182, -820, 1681], [1, 0, 86, 0, 1849], [1, 0, 94, 0, 2209], [1, -28, 302, -1484, 2809], [1, 0, 118, 0, 3481], [1, 20, 222, 1220, 3721], [1, 0, 134, 0, 4489], [1, 0, 142, 0, 5041], [1, 12, 182, 876, 5329], [1, 0, 158, 0, 6241], [1, 0, 166, 0, 6889], [1, -20, 278, -1780, 7921], [1, -36, 518, -3492, 9409]], 'index': 0, 'instance_types': ['ECNF'], 'instance_urls': ['EllipticCurve/2.0.4.1/64.1/CMa'], 'is_instance_Artin': False, 'is_instance_BMF': False, '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': '4-2e10-1.1-c1e2-0-0', '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': 0, 'prelabel': '4-2e10-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.5054911339164094, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 664574581069945609, 'z1': {'__RealLiteral__': 0, 'data': '3.67478222653086463350186782835361', 'prec': 113}}
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lfunc_instances • Show schema
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{'Lhash': '1485208795141819780,1485208795141819780', 'Lhash_array': ['1485208795141819780', '1485208795141819780'], 'label': '4-2e10-1.1-c1e2-0-0', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.4.1/64.1/CMa'}