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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': -4, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 0, 'Lhash': '49423681071508381,2140124914231022951', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [-2.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.2278938933735533, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1]]], 'bad_primes': [3, 5], 'central_character': '50625.1', 'coefficient_field': '1.1.1.1', 'conductor': 50625, 'conductor_radical': 15, 'degree': 4, 'euler_factors': [[1, 0, 4, 0, 4], [1], [1], [1, 0, -11, 0, 49], [1, 0, 22, 0, 121], [1, 0, 1, 0, 169], [1, 0, 34, 0, 289], [1, 2, 39, 38, 361], [1, 0, 46, 0, 529], [1, 0, 58, 0, 841], [1, 14, 111, 434, 961], [1, 0, -26, 0, 1369], [1, 0, 82, 0, 1681], [1, 0, 61, 0, 1849], [1, 0, 94, 0, 2209], [1, 0, 106, 0, 2809], [1, 0, 118, 0, 3481], [1, 26, 291, 1586, 3721], [1, 0, 109, 0, 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'positive_zeros': ['1.51470298744943699034589542417554', '2.93248946372060750659719660133387', '3.80273248963840130172861112355645', '4.14585724745469274814887485348397', '4.83022728068118968978622921639430', '5.46981299804941090347456591941950', '5.77556571014558049232659651532133', '6.62145632893118011347307968766284', '7.51612763708038261050643932551709', '7.75954149302713039814888795826148', '8.459962290175805266187907432816961', '8.995186005196822049947024673067958', '9.206590206514279856778701903578240', '9.599576350131101649309623215929682'], 'prelabel': '4-15e4-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.3403857823323886, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'N(U(1))', 'symmetry_type': 'symplectic', 'trace_hash': 2189548595302531332, 'z1': {'__RealLiteral__': 0, 'data': '1.51470298744943699034589542417554', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.93248946372060750659719660133387', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '3.80273248963840130172861112355645', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.2278938933735533, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 50625, 'conductor_radical': 15, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -26, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 0, 22, 0, 121], 'euler13': [1, 0, 1, 0, 169], 'euler17': [1, 0, 34, 0, 289], 'euler19': [1, 2, 39, 38, 361], 'euler2': [1, 0, 4, 0, 4], 'euler23': [1, 0, 46, 0, 529], 'euler29': [1, 0, 58, 0, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 14, 111, 434, 961], 'euler37': [1, 0, -26, 0, 1369], 'euler41': [1, 0, 82, 0, 1681], 'euler43': [1, 0, 61, 0, 1849], 'euler47': [1, 0, 94, 0, 2209], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 0, 106, 0, 2809], 'euler59': [1, 0, 118, 0, 3481], 'euler61': [1, 26, 291, 1586, 3721], 'euler67': [1, 0, 109, 0, 4489], 'euler7': [1, 0, -11, 0, 49], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, 0, 46, 0, 5329], 'euler79': [1, 8, 174, 632, 6241], 'euler83': [1, 0, 166, 0, 6889], 'euler89': [1, 0, 178, 0, 7921], 'euler97': [1, 0, 169, 0, 9409], 'euler_factors': [[1, 0, 4, 0, 4], [1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 0, -11, 0, 49], [1, 0, 22, 0, 121], [1, 0, 1, 0, 169], [1, 0, 34, 0, 289], [1, 2, 39, 38, 361], [1, 0, 46, 0, 529], [1, 0, 58, 0, 841], [1, 14, 111, 434, 961], [1, 0, -26, 0, 1369], [1, 0, 82, 0, 1681], [1, 0, 61, 0, 1849], [1, 0, 94, 0, 2209], [1, 0, 106, 0, 2809], [1, 0, 118, 0, 3481], [1, 26, 291, 1586, 3721], [1, 0, 109, 0, 4489], [1, 0, 142, 0, 5041], [1, 0, 46, 0, 5329], [1, 8, 174, 632, 6241], [1, 0, 166, 0, 6889], [1, 0, 178, 0, 7921], [1, 0, 169, 0, 9409]], 'index': 2, 'instance_types': ['ECNF', 'HMF'], 'instance_urls': ['EllipticCurve/2.2.5.1/2025.1/d', 'ModularForm/GL2/TotallyReal/2.2.5.1/holomorphic/2.2.5.1-2025.1-d'], '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': '4-15e4-1.1-c1e2-0-2', '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': '4-15e4-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.3403857823323886, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 2189548595302531332, 'z1': {'__RealLiteral__': 0, 'data': '1.51470298744943699034589542417554', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9517270
{'Lhash': '49423681071508381,2140124914231022951', 'Lhash_array': ['49423681071508381', '2140124914231022951'], 'label': '4-15e4-1.1-c1e2-0-2', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.5.1/holomorphic/2.2.5.1-2025.1-d'}
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id: 9517134
{'Lhash': '49423681071508381,2140124914231022951', 'Lhash_array': ['49423681071508381', '2140124914231022951'], 'label': '4-15e4-1.1-c1e2-0-2', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.5.1/2025.1/d'}