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lfunc_lfunctions • Show schema
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{'Lhash': '1599402350471718485910136086361', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.0, 0.0], 'a4': [0.0, 0.0], 'a5': [1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [3.4313369051005815, 0.0], 'a8': [0.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.456662715319746, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.0, 0]]], [5, [[1.0, 0], [-1.0, 0]]], [13, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '1560.1', 'coefficient_field': 'CDF', 'conductor': 1560, 'conductor_radical': 390, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-3.4313369051005815, 0], [7.0, 0]], [[1.0, 0], [2.636746766506401, 0], [11.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-7.84215662791222, 0], [17.0, 0]], [[1.0, 0], [-0.7945901385941807, 0], [19.0, 0]], [[1.0, 0], [3.4313369051005815, 0], [23.0, 0]], 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[113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 12, 'label': '2-1560-1.1-c1-0-12', 'leading_term': '2.65819172571063076059898005022', '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/1560/2/a/q/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [2.6581917257106307, 2.6542856456772084, 2.642418013047734, 2.622151337968144, 2.592791235203497, 2.553435700256658, 2.5030388297758073, 2.4404846915301706, 2.3646669129380573, 2.274569843400714, 2.169347691072749, 2.0483986738368407, 1.9114318295494284, 1.7585246287695602, 1.5901699021268587, 1.4073108494457107, 1.2113630744869477, 1.0042227298444641, 0.788260000124392, 0.566297328760385, 0.3415720253471772, 0.11768318701351488, -0.10147676879802718, -0.31180523689529704, -0.5090860221284624, 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'6.02078879345166859751202156638428', '7.41644598289367513556424409481945', '7.83284790028976280581249569926030', '8.488176953244069843852140818609989', '9.472317953188781602547058671510403'], 'prelabel': '2-1560-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.5293997670028463, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.26170598600573382275781644085', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.29421508134718927524124795597', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.29129373650755031170999303490', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.456662715319746, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 1560, 'conductor_radical': 390, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1560/2/a/q/1/3'], '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': '2-1560-1.1-c1-0-12', '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': '2-1560-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.5293997670028463, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.26170598600573382275781644085', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1599402350471718485910136086361', 'Lhash_array': ['1599402350471718485910136086361'], 'label': '2-1560-1.1-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1560/2/a/q/1/3'}