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lfunc_lfunctions • Show schema
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{'Lhash': '784365709359284093323240864008', 'a10': [0.6176537911712761, 0.0], 'a2': [0.8701045374410886, 0.0], 'a3': [0.0, 0.0], 'a4': [-1.2429180939244293, 0.0], 'a5': [0.7098615908701603, 0.0], 'a6': [0.0, 0.0], 'a7': [1.0, 0.0], 'a8': [-2.8216777480734523, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 60.86996146082207, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-1.0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 7, 11], 'central_character': '7623.1', 'coefficient_field': 'CDF', 'conductor': 7623, 'conductor_radical': 231, 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8701045374410886, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.7098615908701603, 0], [5.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.471820311010336, 0], [13.0, 0]], [[1.0, 0], [-1.3468223201732537, 0], [17.0, 0]], [[1.0, 0], [-0.5031485904829708, 0], [19.0, 0]], 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[109.0, 0]], [[1.0, 0], [-8.679265702023077, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 62, 'label': '2-7623-1.1-c1-0-62', 'leading_term': '1.9173132012743211945138086256685', '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/7623/2/a/da/1/8', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [1.9173132012743213, 1.9061187663819135, 1.8725144286602313, 1.8164443371967047, 1.7378390909959576, 1.6366496402762967, 1.5128916520813775, 1.366697574329495, 1.1983732537370932, 1.008455804068717, 0.7977694589982148, 0.5674763400700233, 0.31911938070822654, 0.054655030455559216, -0.22352621384986746, -0.512592964752923, -0.8092808626120375, -1.1099158922921772, -1.4104533017346013, -1.7065318963755503, -1.9935430557573548, -2.266713393372869, 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'4.25531867038386567997530274404223', '5.09304705758359895369339684097791', '5.72035188494029480709499622722524', '6.12830456263722290743194225436020', '7.35958180872271100968756659708553', '7.72059264867164308780943390733288'], 'prelabel': '2-7623-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.80192037006416, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.61875544350948590153962278466', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.97955967923853686672077331736', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.72353192529947398231592323220', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 60.86996146082207, 'bad_primes': [3, 7, 11], 'central_character': '1.1', 'conductor': 7623, 'conductor_radical': 231, 'degree': 2, 'index': 62, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/7623/2/a/da/1/8'], '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': '2-7623-1.1-c1-0-62', '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': '2-7623-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.80192037006416, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.61875544350948590153962278466', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '784365709359284093323240864008', 'Lhash_array': ['784365709359284093323240864008'], 'label': '2-7623-1.1-c1-0-62', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7623/2/a/da/1/8'}