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lfunc_lfunctions • Show schema
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{'Lhash': '3056020728907725279939282845586', 'a10': [0.0, -3.3722813232690143], 'a2': [1.0, 0.0], 'a3': [-1.2621688994810694, 1.1861406616345072], 'a4': [1.0, 0.0], 'a5': [0.0, -3.3722813232690143], 'a6': [-1.2621688994810694, 1.1861406616345072], 'a7': [-2.5243377989621387, 0.7922869913932613], 'a8': [1.0, 0.0], 'a9': [0.18614066163450715, -2.9942197070499468], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.359831950361911, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [3, [[1.0, 0], [1.2621688994810694, -1.1861406616345072]]], [7, [[1.0, 0], [2.5243377989621387, -0.7922869913932613]]], [13, [[1.0, 0], [3.4641016151377544, 1.0]]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '546.545', 'coefficient_field': 'CDF', 'conductor': 546, 'conductor_radical': 546, 'conjugate': '353221451248235449868264968577', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [1.2621688994810694, 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1.584204744183309, 0.10464978767520194], 'positive_zeros': ['2.41077527858032448449584408337109', '3.08042349620092918697449558193784', '4.68760980684225302994677591388455', '5.77962603249298552100666725784150', '6.59831927981876178044498715161742', '7.21319606024449331364592477595018', '7.929091169055220540171156304923121', '9.895117890142454645671157933293011', '10.53184796441221626792589205602362', '11.02215353678094656668092574255311'], 'prelabel': '2-546-273.272-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': 0.7525323130190174, 'root_number': '-0.7127097307550488 + 0.7014590791251232*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.37626615651', 'prec': 44}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.41077527858032448449584408337', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.08042349620092918697449558194', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.68760980684225302994677591388', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.359831950361911, 'bad_primes': [2, 3, 7, 13], 'central_character': '273.272', 'conductor': 546, 'conductor_radical': 546, 'degree': 2, 'index': 36, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/546/2/e/g/545/2'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, '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': '2-546-273.272-c1-0-36', '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': '2-546-273.272-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': 0.3762661565095087, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.41077527858032448449584408337', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3056020728907725279939282845586', 'Lhash_array': ['3056020728907725279939282845586'], 'label': '2-546-273.272-c1-0-36', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/546/2/e/g/545/2'}