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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': 1, 'A9': -3, 'Lhash': '747129475622322621,977379866071001924', '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': [0.3535533905932738, 0], 'a9': [-1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.100869362368084, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [5, [1]]], 'bad_primes': [2, 5], 'central_character': '80000.1', 'coefficient_field': '1.1.1.1', 'conductor': 80000, 'conductor_radical': 10, 'degree': 4, 'euler_factors': [[1, -1], [1, 2, 7, 6, 9], [1], [1, 0, 10, 0, 49], [1, 6, 31, 66, 121], [1, 0, 10, 0, 169], [1, -6, 43, -102, 289], [1, -10, 63, -190, 361], [1, 0, 10, 0, 529], [1, 0, 58, 0, 841], [1, 0, 58, 0, 961], [1, 0, 70, 0, 1369], [1, 6, 91, 246, 1681], [1, -8, 102, -344, 1849], [1, 0, -50, 0, 2209], [1, 0, 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2.5241685269172147, 3.2141025813435524, 3.5557207504297432, 3.437497824088504, 2.8141184184983135, 1.7171705110442923], 'positive_zeros': ['0.806837847292090646690279005746159', '2.37228414250853175167766648204125', '3.27747260558597777923671030480632', '3.29699975126484092788987476481791', '4.78507259529948280984941273758728', '5.22748830252304089500003968022490', '5.34945783064988058695168525193373', '5.91956414482903908532570774167511', '6.35306147256574072432179047412320', '7.23606762344534562872845833638270', '7.63971798893296337235505790724414', '8.071729218562685355881418106439985', '8.592914531793421630007930470901086', '9.429239826768018761346169045309084', '9.930723730317650982781533521356298'], 'prelabel': '4-80000-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.5028341325604684, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1724509341693324545, 'z1': {'__RealLiteral__': 0, 'data': '0.806837847292090646690279005746159', 'prec': 117}, 'z2': {'__RealLiteral__': 0, 'data': '2.37228414250853175167766648204125', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '3.27747260558597777923671030480632', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.100869362368084, 'bad_primes': [2, 5], 'central_character': '1.1', 'conductor': 80000, 'conductor_radical': 10, 'degree': 4, 'dirichlet_coefficients': [1, 1, -2, 1, 0, -2, 0, 1, -3, 0, -6, -2, 0, 0, 0, 1, 6, -3, 10, 0, 0, -6, 0, -2, 0, 0, 14, 0, 0, 0, 0, 1, 12, 6, 0, -3, 0, 10, 0, 0, -6, 0, 8, -6, 0, 0, 0, -2, -10, 0, -12, 0, 0, 14, 0, 0, -20, 0, 0, 0, 0, 0, 0, 1, 0, 12, 26, 6, 0, 0, 0, -3, -22, 0, 0, 10, 0, 0, 0, 0, -4, -6, 18, 0, 0, 8, 0, -6, 30, 0, 0, 0, 0, 0, 0, -2, -4, -10, 18, 0], 'euler11': [1, 6, 31, 66, 121], 'euler13': [1, 0, 10, 0, 169], 'euler17': [1, -6, 43, -102, 289], 'euler19': [1, -10, 63, -190, 361], 'euler2': [1, -1, 0, 0, 0], 'euler23': [1, 0, 10, 0, 529], 'euler29': [1, 0, 58, 0, 841], 'euler3': [1, 2, 7, 6, 9], 'euler31': [1, 0, 58, 0, 961], 'euler37': [1, 0, 70, 0, 1369], 'euler41': [1, 6, 91, 246, 1681], 'euler43': [1, -8, 102, -344, 1849], 'euler47': [1, 0, -50, 0, 2209], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 0, 70, 0, 2809], 'euler59': [1, 0, 118, 0, 3481], 'euler61': [1, 0, 118, 0, 3721], 'euler67': [1, -26, 303, -1742, 4489], 'euler7': [1, 0, 10, 0, 49], 'euler71': [1, 0, -2, 0, 5041], 'euler73': [1, 22, 267, 1606, 5329], 'euler79': [1, 0, 58, 0, 6241], 'euler83': [1, -18, 247, -1494, 6889], 'euler89': [1, -30, 403, -2670, 7921], 'euler97': [1, 4, 198, 388, 9409], 'euler_factors': [[1, -1, 0, 0, 0], [1, 2, 7, 6, 9], [1, 0, 0, 0, 0], [1, 0, 10, 0, 49], [1, 6, 31, 66, 121], [1, 0, 10, 0, 169], [1, -6, 43, -102, 289], [1, -10, 63, -190, 361], [1, 0, 10, 0, 529], [1, 0, 58, 0, 841], [1, 0, 58, 0, 961], [1, 0, 70, 0, 1369], [1, 6, 91, 246, 1681], [1, -8, 102, -344, 1849], [1, 0, -50, 0, 2209], [1, 0, 70, 0, 2809], [1, 0, 118, 0, 3481], [1, 0, 118, 0, 3721], [1, -26, 303, -1742, 4489], [1, 0, -2, 0, 5041], [1, 22, 267, 1606, 5329], [1, 0, 58, 0, 6241], [1, -18, 247, -1494, 6889], [1, -30, 403, -2670, 7921], [1, 4, 198, 388, 9409]], 'index': 0, 'instance_types': ['BMF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/1250.1/b', 'EllipticCurve/2.0.8.1/1250.1/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': '4-80000-1.1-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': '4-80000-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.5028341325604684, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1724509341693324545, 'z1': {'__RealLiteral__': 0, 'data': '0.806837847292090646690279005746159', 'prec': 117}}
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lfunc_instances • Show schema
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id: 9817576
{'Lhash': '747129475622322621,977379866071001924', 'Lhash_array': ['747129475622322621', '977379866071001924'], 'label': '4-80000-1.1-c1e2-0-0', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.8.1/1250.1/b'}
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id: 9817984
{'Lhash': '747129475622322621,977379866071001924', 'Lhash_array': ['747129475622322621', '977379866071001924'], 'label': '4-80000-1.1-c1e2-0-0', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/1250.1/b'}