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lfunc_lfunctions • Show schema
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{'Lhash': '2213995943598684908780697461199', 'a10': [-0.4270509831248423, -0.739674000194466], 'a2': [-0.19098300562505258, 0.33079226912480375], 'a3': [0.0, 0.0], 'a4': [0.9270509831248422, 1.6056994039789048], 'a5': [-1.118033988749895, 1.9364916731037085], 'a6': [0.0, 0.0], 'a7': [-2.0, -1.7320508075688772], 'a8': [-1.4721359549995794, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.5397479255428665, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [2.0, 1.7320508075688772]]], [13, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 7, 13], 'central_character': '819.352', 'coefficient_field': 'CDF', 'conductor': 819, 'conductor_radical': 273, 'conjugate': '3275010137402573462875425269121', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.19098300562505258, -0.33079226912480375], [-1.0, -1.7320508075688772]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.118033988749895, 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[[1.0, 0], [-1.5, -2.598076211353316], [-33.5, 58.023702053557386]], [[1.0, 0], [8.94427190999916, 0], [71.0, 0]], [[1.0, 0], [5.354101966249685, 9.27357663444888], [-36.5, 63.21985447626402]], [[1.0, 0], [5.354101966249685, -9.27357663444888], [-39.5, -68.41600689897065]], [[1.0, 0], [0, 0], [83.0, 0]], [[1.0, 0], [1.118033988749895, -1.9364916731037085], [-44.5, -77.07626093681505]], [[1.0, 0], [17.41640786499874, 0], [97.0, 0]], [[1.0, 0], [4.5, 7.794228634059948], [-50.5, 87.4685657822283]], [[1.0, 0], [5.354101966249685, -9.27357663444888], [-51.5, -89.20061658979718]], [[1.0, 0], [7.118033988749895, -12.328796518516972], [-53.5, -92.66471820493493]], [[1.0, 0], [5.354101966249685, 9.27357663444888], [-54.5, 94.39676901250381]], [[1.0, 0], [-14.94427190999916, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 28, 'label': '2-819-7.2-c1-0-28', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 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0.3535062863872795, 'root_number': '-0.6054643436493675 + 0.7958724323465669*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.353506286387', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.74653484422290677461957236649', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.82323335618506260299832368688', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.37097026767864617643545308797', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.5397479255428665, 'bad_primes': [3, 7, 13], 'central_character': '7.2', 'conductor': 819, 'conductor_radical': 273, 'degree': 2, 'index': 28, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/819/2/j/c/352/2'], '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': '2-819-7.2-c1-0-28', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-819-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5572930855775735, 'root_angle': 0.3535062863872795, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.74653484422290677461957236649', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2213995943598684908780697461199', 'Lhash_array': ['2213995943598684908780697461199'], 'factors': ['2-819-7.2-c1-0-28'], 'label': '2-819-7.2-c1-0-28', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/819/2/j/c/352/2'}