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lfunc_lfunctions • Show schema
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{'Lhash': '666611450652996927624138046824', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, -362078.95427392883], 'a4': [0, 0], 'a5': [0, -49711445.358381025], 'a6': [0, 0], 'a7': [7736845736.891514, 0], 'a8': [0, 0], 'a9': [-36957990301.10184, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 214.53058390086642, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '11.5', 'prec': 14}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]]], 'bad_primes': [2], 'central_character': '64.33', 'coefficient_field': 'CDF', 'conductor': 64, 'conductor_radical': 2, 'conjugate': '1086906950294757584891068721239', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 362078.95427392883], [-94143178827.0, 0]], [[1.0, 0], [0, 49711445.358381025], [-11920928955078124, 0]], [[1.0, 0], [-7736845736.891514, 0], [27368747340080914000, 0]], [[1.0, 0], [0, -929842972004.022], [-895430243255237400000000, 0]], [[1.0, 0], [0, -10650656517966.188], [-41753905413413120000000000, 0]], [[1.0, 0], 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'1.89631357069342688497828047470153', '3.18130633609844586665147992860425', '4.16380096682535369391239917442266', '5.10161530017694173578689914378483', '6.07841635495500821618796000205758', '7.80948605759538274824992401200408', '8.487999318399090305014326024012880', '9.829628332210138190404045923899172', '10.93248847272243668514472764055931'], 'prelabel': '2-2e6-8.5-c23-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 14.64686259582121, 'root_angle': 0.08333333333333333, 'root_number': '0.96592582628906828674974319972889736763390483900840455041 + 0.25881904510252076234889883762404832834906890131993051381*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.04166666666666667', 'prec': 64}, 'spectral_label': 'c23-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.52586371239281499750474729527', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.89631357069342688497828047470', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.18130633609844586665147992860', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 214.53058390086642, 'bad_primes': [2], 'central_character': '8.5', 'conductor': 64, 'conductor_radical': 2, 'degree': 2, 'index': 19, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/64/24/b/c/33/9'], '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': '2-2e6-8.5-c23-0-19', 'motivic_weight': 23, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [23], 'order_of_vanishing': 0, 'prelabel': '2-2e6-8.5-c23-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 14.64686259582121, 'root_angle': 0.041666666666666664, 'self_dual': False, 'spectral_label': 'c23-0', 'z1': {'__RealLiteral__': 0, 'data': '0.52586371239281499750474729527', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '666611450652996927624138046824', 'Lhash_array': ['666611450652996927624138046824'], 'label': '2-2e6-8.5-c23-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/64/24/b/c/33/9'}