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lfunc_lfunctions • Show schema
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{'Lhash': '1265583538633115904061144268169', 'a10': [-3.2273419692066114, -5.589920264065242], 'a2': [-1.7989949133342362, 3.1159505924528665], 'a3': [-1.5, -2.598076211353316], 'a4': [-2.4727653964049128, -4.282955301771504], 'a5': [-0.8969847400027089, 1.5536231432986514], 'a6': [10.793969480005417, 0], 'a7': [18.495872287725422, -0.9501096337532863], 'a8': [-10.989949133342362, 0], 'a9': [-4.5, 7.794228634059948], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 16.107521431567196, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.5, 2.598076211353316]]], [7, [[1.0, 0], [-18.495872287725422, 0.9501096337532863]]], [13, [[1.0, 0], [13.0, 0]]]], 'bad_primes': [3, 7, 13], 'central_character': '273.79', 'coefficient_field': 'CDF', 'conductor': 273, 'conductor_radical': 273, 'conjugate': '971945400127423779776083929498', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.7989949133342362, -3.1159505924528665], [-4.0, 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['0.998369375918931177820236516061045', '2.32921773197100663825721697200152', '3.82377742425709016171828819844850', '5.02729836551228304951942489615770', '6.23541029955581734749235761919453', '7.893803922185535250947617531452787', '8.718816505743106320180475756978397', '9.748002692790984002701463986492572', '10.46843046144854626138259856079712', '11.27695028117184206334439228252601'], 'prelabel': '2-273-7.2-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.013417674696616, 'root_angle': -0.1015882188317265, 'root_number': '0.803111258258469821896154107023011187084225020567813430 - 0.595829091987372993442993355356459656826279980870623213*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.1015882188317265', 'prec': 64}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.998369375918931177820236516061', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.32921773197100663825721697200', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.82377742425709016171828819845', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 16.107521431567196, 'bad_primes': [3, 7, 13], 'central_character': '7.2', 'conductor': 273, 'conductor_radical': 273, 'degree': 2, 'index': 27, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/273/4/i/b/79/1'], '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': '2-273-7.2-c3-0-27', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-273-7.2-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.013417674696616, 'root_angle': -0.1015882188317265, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.998369375918931177820236516061', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1265583538633115904061144268169', 'Lhash_array': ['1265583538633115904061144268169'], 'factors': ['2-273-7.2-c3-0-27'], 'label': '2-273-7.2-c3-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/273/4/i/b/79/1'}