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lfunc_lfunctions • Show schema
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{'Lhash': '619304880370764635506724680247', 'a10': [0.41421356237309503, 0.0], 'a2': [-0.41421356237309503, 0.0], 'a3': [0.0, 0.0], 'a4': [-1.82842712474619, 0.0], 'a5': [-1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-4.82842712474619, 0.0], 'a8': [1.5857864376269049, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.420477463777095, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [29, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 5, 29], 'central_character': '1305.1', 'coefficient_field': 'CDF', 'conductor': 1305, 'conductor_radical': 435, 'degree': 2, 'euler_factors': [[[1.0, 0], [0.41421356237309503, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [4.82842712474619, 0], [7.0, 0]], [[1.0, 0], [0.8284271247461901, 0], [11.0, 0]], [[1.0, 0], [2.0, 0], [13.0, 0]], [[1.0, 0], [2.8284271247461903, 0], [17.0, 0]], [[1.0, 0], [4.82842712474619, 0], 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[0]], 'group': 'GL2', 'index': 0, 'label': '2-1305-1.1-c1-0-0', 'leading_term': '0.44629927902657797664070152326438', '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/1305/2/a/n/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.44629927902657796, 0.4402768940852728, 0.422125169189976, 0.39159777675533447, 0.3483082491168182, 0.2917643216335993, 0.22141273658800512, 0.1366917896774483, 0.037088754602437594, -0.0778005757314477, -0.2082127318295965, -0.3541599689645196, -0.5153780854166427, -0.6912802505664839, -0.8809182358369955, -1.0829522985393085, -1.295630862046172, -1.5167810402706359, -1.7438109462515845, -1.9737245842565136, -2.2031499384791697, -2.4283806313331002, -2.645431228209155, -2.8501059158951336, -3.038079885321434, -3.204992316100531, 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'7.13012654704060293700489516664289', '8.228094159143384664934506081670572', '8.935221445141604486704813754802181', '9.569735796860283104887902752783032'], 'prelabel': '2-1305-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.2280764340047923, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.48854540853707181561886723604', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.55173832700983347070171173196', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.61131050761625910666601968286', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 10.420477463777095, 'bad_primes': [3, 5, 29], 'central_character': '1.1', 'conductor': 1305, 'conductor_radical': 435, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1305/2/a/n/1/1'], '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': '2-1305-1.1-c1-0-0', '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': '2-1305-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.2280764340047923, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.48854540853707181561886723604', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '619304880370764635506724680247', 'Lhash_array': ['619304880370764635506724680247'], 'label': '2-1305-1.1-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1305/2/a/n/1/1'}