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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': -4, 'A5': 3, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': -2, 'Lhash': '409437620317032020,2118555155025302141', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [-2.0, 0], 'a5': [1.3416407864998738, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [-0.6666666666666666, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.5754418249421496, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [1, -3, 5]], [19, [1, -2, 1]]], 'bad_primes': [5, 19], 'central_character': '9025.1', 'coefficient_field': '1.1.1.1', 'conductor': 9025, 'conductor_radical': 95, 'degree': 4, 'euler_factors': [[1, 0, 4, 0, 4], [1, 0, 2, 0, 9], [1, -3, 5], [1, 0, 13, 0, 49], [1, -6, 31, -66, 121], [1, 0, 10, 0, 169], [1, 0, 25, 0, 289], [1, -2, 1], [1, 0, 46, 0, 529], [1, -12, 94, -348, 841], [1, 8, 78, 248, 961], [1, 0, 70, 0, 1369], [1, 12, 118, 492, 1681], [1, 0, 85, 0, 1849], [1, 0, 85, 0, 2209], [1, 0, -38, 0, 2809], 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-0.6175052086741831, -4.01838128078105, -7.108394263530273, -9.64392405838754, -11.441527453624515], 'positive_zeros': ['1.43009506463758030263279983978222', '3.23182893022898332662250292694322', '3.94480584782122104516168200312560', '5.03912355415234199771433602491991', '5.15254746234400988386261721370913', '6.36395749589543487340848898302544', '6.39084306102520193435942181608554', '7.79259928613141419667093336123668', '8.415277882855381679327851057926848', '9.093042453849772655367942297607846', '9.180168549070062598241568188032870', '9.774569434898319390985970077664394', '10.24320445923116880350231460909254', '10.91480268940863095584089699097963', '11.99055989369382628931438537309342'], 'prelabel': '4-95e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.8709643042066444, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 222149766128640210, 'z1': {'__RealLiteral__': 0, 'data': '1.43009506463758030263279983978222', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '3.23182893022898332662250292694322', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '3.94480584782122104516168200312560', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.5754418249421496, 'bad_primes': [5, 19], 'central_character': '1.1', 'conductor': 9025, 'conductor_radical': 95, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, -4, 3, 0, 0, 0, -2, 0, 6, 0, 0, 0, 0, 12, 0, 0, 2, -12, 0, 0, 0, 0, 4, 0, 0, 0, 12, 0, -8, 0, 0, 0, 0, 8, 0, 0, 0, 0, -12, 0, 0, -24, -6, 0, 0, 0, -13, 0, 0, 0, 0, 0, 18, 0, 0, 0, -12, 0, -2, 0, 0, -32, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, -8, 0, 0, 16, 36, -5, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 6, 0, 0, 0, -12, -16], 'euler11': [1, -6, 31, -66, 121], 'euler13': [1, 0, 10, 0, 169], 'euler17': [1, 0, 25, 0, 289], 'euler19': [1, -2, 1, 0, 0], 'euler2': [1, 0, 4, 0, 4], 'euler23': [1, 0, 46, 0, 529], 'euler29': [1, -12, 94, -348, 841], 'euler3': [1, 0, 2, 0, 9], 'euler31': [1, 8, 78, 248, 961], 'euler37': [1, 0, 70, 0, 1369], 'euler41': [1, 12, 118, 492, 1681], 'euler43': [1, 0, 85, 0, 1849], 'euler47': [1, 0, 85, 0, 2209], 'euler5': [1, -3, 5, 0, 0], 'euler53': [1, 0, -38, 0, 2809], 'euler59': [1, 12, 154, 708, 3481], 'euler61': [1, 2, 123, 122, 3721], 'euler67': [1, 0, 118, 0, 4489], 'euler7': [1, 0, 13, 0, 49], 'euler71': [1, -12, 178, -852, 5041], 'euler73': [1, 0, 97, 0, 5329], 'euler79': [1, -16, 222, -1264, 6241], 'euler83': [1, 0, 22, 0, 6889], 'euler89': [1, -24, 322, -2136, 7921], 'euler97': [1, 0, 130, 0, 9409], 'euler_factors': [[1, 0, 4, 0, 4], [1, 0, 2, 0, 9], [1, -3, 5, 0, 0], [1, 0, 13, 0, 49], [1, -6, 31, -66, 121], [1, 0, 10, 0, 169], [1, 0, 25, 0, 289], [1, -2, 1, 0, 0], [1, 0, 46, 0, 529], [1, -12, 94, -348, 841], [1, 8, 78, 248, 961], [1, 0, 70, 0, 1369], [1, 12, 118, 492, 1681], [1, 0, 85, 0, 1849], [1, 0, 85, 0, 2209], [1, 0, -38, 0, 2809], [1, 12, 154, 708, 3481], [1, 2, 123, 122, 3721], [1, 0, 118, 0, 4489], [1, -12, 178, -852, 5041], [1, 0, 97, 0, 5329], [1, -16, 222, -1264, 6241], [1, 0, 22, 0, 6889], [1, -24, 322, -2136, 7921], [1, 0, 130, 0, 9409]], 'index': 0, 'instance_types': ['HMF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/TotallyReal/2.2.5.1/holomorphic/2.2.5.1-361.1-a', 'EllipticCurve/2.2.5.1/361.1/a'], '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': True, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-95e2-1.1-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': '4-95e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.8709643042066444, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 222149766128640210, 'z1': {'__RealLiteral__': 0, 'data': '1.43009506463758030263279983978222', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9525620
{'Lhash': '409437620317032020,2118555155025302141', 'Lhash_array': ['409437620317032020', '2118555155025302141'], 'label': '4-95e2-1.1-c1e2-0-0', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.5.1/361.1/a'}
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id: 9525509
{'Lhash': '409437620317032020,2118555155025302141', 'Lhash_array': ['409437620317032020', '2118555155025302141'], 'label': '4-95e2-1.1-c1e2-0-0', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.5.1/holomorphic/2.2.5.1-361.1-a'}