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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 1, 'A3': 2, 'A4': -1, 'A5': 0, 'A6': 2, 'A7': 0, 'A8': -3, 'A9': 3, 'Lhash': '1174233585972169502680671115267', 'a10': [0.0, 0], 'a2': [0.7071067811865476, 0], 'a3': [1.1547005383792515, 0], 'a4': [-0.5, 0], 'a5': [0.0, 0], 'a6': [0.8164965809277259, 0], 'a7': [0.0, 0], 'a8': [-1.0606601717798214, 0], 'a9': [1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 19.42819122738756, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1, 2]], [3, [1, -2, 1]], [23, [1, 0, 23]]], 'bad_primes': [2, 3, 23], 'central_character': '304704.1', 'coefficient_field': '1.1.1.1', 'conductor': 304704, 'conductor_radical': 138, 'degree': 4, 'euler_factors': [[1, -1, 2], [1, -2, 1], [1, 0, -6, 0, 25], [1, 0, -2, 0, 49], [1, 0, -22, 0, 121], [1, 0, 22, 0, 169], [1, 0, -18, 0, 289], [1, 0, -22, 0, 361], [1, 0, 23], [1, 0, 54, 0, 841], [1, 0, -2, 0, 961], [1, 0, 10, 0, 1369], [1, -12, 118, -492, 1681], [1, 0, -70, 0, 1849], [1, 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-2.0802599288848365, -2.073236976070385, -1.8869218723547603, -1.5546063827217598, -1.1326565212365545], 'positive_zeros': ['0.926306969570920423508871513209475', '2.04919469679826535599177793431624', '2.83074343481662872937191278964296', '3.12205759743206158519825507722956', '3.91624558429943130112244988038032', '4.20883043135713897973718086472068', '4.85154726517137833091566815759086', '5.25903998055197925567753027283274', '5.94699188325599470659884992821324', '6.42863197942740220204602984579245', '6.92478978405668928717286262994431', '7.60397505367903767130862241085460', '7.85392252500592886735780157959150', '8.454348571562701433984302858901121', '8.920790519114965671257010703910222'], 'prelabel': '4-552e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.0994623577417815, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1579719788892835537, 'z1': {'__RealLiteral__': 0, 'data': '0.926306969570920423508871513209475', 'prec': 117}, 'z2': {'__RealLiteral__': 0, 'data': '2.04919469679826535599177793431624', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.83074343481662872937191278964296', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 19.42819122738756, 'bad_primes': [2, 3, 23], 'central_character': '1.1', 'conductor': 304704, 'conductor_radical': 138, 'degree': 4, 'dirichlet_coefficients': [1, 1, 2, -1, 0, 2, 0, -3, 3, 0, 0, -2, 0, 0, 0, -1, 0, 3, 0, 0, 0, 0, 0, -6, 6, 0, 4, 0, 0, 0, 0, 5, 0, 0, 0, -3, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, -2, 2, 6, 0, 0, 0, 4, 0, 0, 0, 0, -8, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, -9, 12, 0, 12, 0, 0, 0, 0, 0, 5, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 2, 0, -6], 'euler11': [1, 0, -22, 0, 121], 'euler13': [1, 0, 22, 0, 169], 'euler17': [1, 0, -18, 0, 289], 'euler19': [1, 0, -22, 0, 361], 'euler2': [1, -1, 2, 0, 0], 'euler23': [1, 0, 23, 0, 0], 'euler29': [1, 0, 54, 0, 841], 'euler3': [1, -2, 1, 0, 0], 'euler31': [1, 0, -2, 0, 961], 'euler37': [1, 0, 10, 0, 1369], 'euler41': [1, -12, 118, -492, 1681], 'euler43': [1, 0, -70, 0, 1849], 'euler47': [1, 0, 94, 0, 2209], 'euler5': [1, 0, -6, 0, 25], 'euler53': [1, 0, 90, 0, 2809], 'euler59': [1, 8, 134, 472, 3481], 'euler61': [1, 0, 58, 0, 3721], 'euler67': [1, 0, 10, 0, 4489], 'euler7': [1, 0, -2, 0, 49], 'euler71': [1, 0, 78, 0, 5041], 'euler73': [1, -12, 182, -876, 5329], 'euler79': [1, 0, 142, 0, 6241], 'euler83': [1, 0, -166, 0, 6889], 'euler89': [1, 0, -34, 0, 7921], 'euler97': [1, 0, -130, 0, 9409], 'euler_factors': [[1, -1, 2, 0, 0], [1, -2, 1, 0, 0], [1, 0, -6, 0, 25], [1, 0, -2, 0, 49], [1, 0, -22, 0, 121], [1, 0, 22, 0, 169], [1, 0, -18, 0, 289], [1, 0, -22, 0, 361], [1, 0, 23, 0, 0], [1, 0, 54, 0, 841], [1, 0, -2, 0, 961], [1, 0, 10, 0, 1369], [1, -12, 118, -492, 1681], [1, 0, -70, 0, 1849], [1, 0, 94, 0, 2209], [1, 0, 90, 0, 2809], [1, 8, 134, 472, 3481], [1, 0, 58, 0, 3721], [1, 0, 10, 0, 4489], [1, 0, 78, 0, 5041], [1, -12, 182, -876, 5329], [1, 0, 142, 0, 6241], [1, 0, -166, 0, 6889], [1, 0, -34, 0, 7921], [1, 0, -130, 0, 9409]], 'index': 6, 'instance_types': ['HMF', 'HMF', 'ECNF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/TotallyReal/2.2.184.1/holomorphic/2.2.184.1-9.1-a', 'ModularForm/GL2/TotallyReal/2.2.184.1/holomorphic/2.2.184.1-9.1-b', 'EllipticCurve/2.2.184.1/9.1/b', 'EllipticCurve/2.2.184.1/9.1/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': '4-552e2-1.1-c1e2-0-6', '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': '4-552e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.0994623577417815, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1579719788892835537, 'z1': {'__RealLiteral__': 0, 'data': '0.926306969570920423508871513209475', 'prec': 117}}
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lfunc_instances • Show schema
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id: 9462354
{'Lhash': '1174233585972169502680671115267', 'Lhash_array': ['1174233585972169502680671115267'], 'label': '4-552e2-1.1-c1e2-0-6', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.184.1/9.1/a'}
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id: 9462334
{'Lhash': '1174233585972169502680671115267', 'Lhash_array': ['1174233585972169502680671115267'], 'label': '4-552e2-1.1-c1e2-0-6', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.184.1/9.1/b'}
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id: 9462285
{'Lhash': '1174233585972169502680671115267', 'Lhash_array': ['1174233585972169502680671115267'], 'label': '4-552e2-1.1-c1e2-0-6', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.184.1/holomorphic/2.2.184.1-9.1-b'}
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id: 9462283
{'Lhash': '1174233585972169502680671115267', 'Lhash_array': ['1174233585972169502680671115267'], 'label': '4-552e2-1.1-c1e2-0-6', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.184.1/holomorphic/2.2.184.1-9.1-a'}