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              lfunc_lfunctions •   Show schema
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        {'Lhash': '476561879081958374827590326630', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': -2, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 55.69565540984309, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1]], [31, [1, 1]]], 'bad_primes': [3, 5, 31], 'central_character': '6975.1', 'coefficient_field': '1.1.1.1', 'conductor': 6975, 'conductor_radical': 465, 'degree': 2, 'euler_factors': [[1, 0, 2], [1], [1], [1, 0, 7], [1, 5, 11], [1, 0, 13], [1, 5, 17], [1, 1, 19], [1, 5, 23], [1, 5, 29], [1, 1], [1, -10, 37], [1, 0, 41], [1, 10, 43], [1, 0, 47], [1, 5, 53], [1, -10, 59], [1, -12, 61], [1, 5, 67], [1, 0, 71], [1, 0, 73], [1, 4, 79], [1, -15, 83], [1, 15, 89], [1, 5, 97], [1, -10, 101], [1, -5, 103], [1, 10, 107], [1, -6, 109], [1, 20, 113]], 'euler_factors_factorization': [[[[1, 0, 2], 1]], [1], [1], [[[1, 0, 7], 1]], [[[1, 5, 11], 1]], [[[1, 0, 13], 1]], [[[1, 5, 17], 1]], [[[1, 1, 19], 1]], [[[1, 5, 23], 1]], [[[1, 5, 29], 1]], [[[1, 1], 1]], [[[1, -10, 37], 1]], [[[1, 0, 41], 1]], [[[1, 10, 43], 1]], [[[1, 0, 47], 1]], [[[1, 5, 53], 1]], [[[1, -10, 59], 1]], [[[1, -12, 61], 1]], [[[1, 5, 67], 1]], [[[1, 0, 71], 1]], [[[1, 0, 73], 1]], [[[1, 4, 79], 1]], [[[1, -15, 83], 1]], [[[1, 15, 89], 1]], [[[1, 5, 97], 1]], [[[1, -10, 101], 1]], [[[1, -5, 103], 1]], [[[1, 10, 107], 1]], [[[1, -6, 109], 1]], [[[1, 20, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 18, 'label': '2-6975-1.1-c1-0-18', 'leading_term': '0.584697144786939506633684223975360000000000000000000000000000000000000000000000000000000000', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/6975/2/a/h', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': 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4.353458326603976, 3.9034854685006835, 3.3644448167446006, 2.770471691366974, 2.157061721984551, 1.5587468396108877, 1.0068791044322831, 0.5276701012121522, 0.1406161589690585, -0.14258673255046778, -0.3185680020539122, -0.392215772066463, -0.37602738138962943, -0.28892660808728404], 'positive_zeros': ['0.37594103532642005402513162613298', '1.86404792772923216627969938554240', '2.72333841453887006520886822469969', '3.70848528006472173717751843921064', '4.42079435904286573611721519029756', '5.07474535880573760881544752915519', '5.70017460468149024733356968257543', '6.48756794281593571580354007419899', '7.41395744385447578882794647796721', '8.170393545719501567753713652964587'], 'prelabel': '2-6975-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.462952191314312, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 525222059505001109, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.37594103532642005402513162613', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.86404792772923216627969938554', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.72333841453887006520886822470', 'prec': 103}}
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              lfunc_search •   Show schema
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        {'algebraic': True, 'analytic_conductor': 55.69565540984309, 'bad_primes': [3, 5, 31], 'central_character': '1.1', 'conductor': 6975, 'conductor_radical': 465, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, -2, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 4, -5, 0, -1, 0, 0, 0, -5, 0, 0, 0, 0, 0, -5, 0, -1, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, -10, 10, 0, 0, 0, 0, -7, 0, 0, 0, -5, 0, 0, 0, 0, 0, 10, 0, 12, 0, 0, -8, 0, 0, -5, 10, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -4, 0, 0, 0, 15, 0, 0, 0, 0, 0, -15, 0, 0, 10, 0, 0, 0, 0, -5, 0, 0, 0], 'euler11': [1, 5, 11], 'euler13': [1, 0, 13], 'euler17': [1, 5, 17], 'euler19': [1, 1, 19], 'euler2': [1, 0, 2], 'euler23': [1, 5, 23], 'euler29': [1, 5, 29], 'euler3': [1, 0, 0], 'euler31': [1, 1, 0], 'euler37': [1, -10, 37], 'euler41': [1, 0, 41], 'euler43': [1, 10, 43], 'euler47': [1, 0, 47], 'euler5': [1, 0, 0], 'euler53': [1, 5, 53], 'euler59': [1, -10, 59], 'euler61': [1, -12, 61], 'euler67': [1, 5, 67], 'euler7': [1, 0, 7], 'euler71': [1, 0, 71], 'euler73': [1, 0, 73], 'euler79': [1, 4, 79], 'euler83': [1, -15, 83], 'euler89': [1, 15, 89], 'euler97': [1, 5, 97], 'euler_factors': [[1, 0, 2], [1, 0, 0], [1, 0, 0], [1, 0, 7], [1, 5, 11], [1, 0, 13], [1, 5, 17], [1, 1, 19], [1, 5, 23], [1, 5, 29], [1, 1, 0], [1, -10, 37], [1, 0, 41], [1, 10, 43], [1, 0, 47], [1, 5, 53], [1, -10, 59], [1, -12, 61], [1, 5, 67], [1, 0, 71], [1, 0, 73], [1, 4, 79], [1, -15, 83], [1, 15, 89], [1, 5, 97]], 'index': 18, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/6975/h', 'ModularForm/GL2/Q/holomorphic/6975/2/a/h/1/1', 'ModularForm/GL2/Q/holomorphic/6975/2/a/h'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-6975-1.1-c1-0-18', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-6975-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.462952191314312, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 525222059505001109, 'z1': {'__RealLiteral__': 0, 'data': '0.37594103532642005402513162613', 'prec': 103}}
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              lfunc_instances •   Show schema
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              id: 21798404
              {'Lhash': '476561879081958374827590326630', 'Lhash_array': ['476561879081958374827590326630'], 'factors': ['2-6975-1.1-c1-0-18'], 'label': '2-6975-1.1-c1-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6975/2/a/h'}
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              id: 24577534
              {'Lhash': '476561879081958374827590326630', 'Lhash_array': ['476561879081958374827590326630'], 'factors': ['2-6975-1.1-c1-0-18'], 'label': '2-6975-1.1-c1-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6975/2/a/h/1/1'}
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              id: 87463
              {'Lhash': '525222059505001109', 'Lhash_array': ['525222059505001109'], 'factors': ['2-6975-1.1-c1-0-18'], 'label': '2-6975-1.1-c1-0-18', 'type': 'ECQ', 'url': 'EllipticCurve/Q/6975/h'}