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lfunc_lfunctions • Show schema
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{'Lhash': '777794688204747006405390808190', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-121.5, -210.4441731196186], 'a4': [0, 0], 'a5': [-1339.8135663286714, 2320.625169551313], 'a6': [0, 0], 'a7': [-28039.678887915696, 34512.362290381905], 'a8': [0, 0], 'a9': [-29524.5, 51137.93406806732], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 64.54082716700547, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '5.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [121.5, 210.4441731196186]]], [7, [[1.0, 0], [28039.678887915696, -34512.362290381905]]]], 'bad_primes': [2, 3, 7], 'central_character': '84.37', 'coefficient_field': 'CDF', 'conductor': 84, 'conductor_radical': 42, 'conjugate': '541342464400513032796715627752', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [121.5, 210.4441731196186]], [[1.0, 0], [1339.8135663286714, -2320.625169551313], [-24414062.5, -42286396.66916204]], [[1.0, 0], [28039.678887915696, -34512.362290381905]], [[1.0, 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-1.1043565477243067], 'positive_zeros': ['0.61357182181329135704878102634056', '2.46384640657069877254269844663690', '4.04418648804151586905649076267444', '4.88937455620651909520757648475067', '6.44302623848961521662122648600378', '7.54119226123494703418355903315588', '8.976926500973895813905923876603971', '10.08575954714741442846747630456720', '10.80665935757954457824798054982608', '12.27865769262502136028403614432371'], 'prelabel': '2-84-7.2-c11-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.033730588400726, 'root_angle': 0.1970061768348983, 'root_number': '0.8145094693505517 + 0.5801502601380808*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.09850308841744915', 'prec': 64}, 'spectral_label': 'c11-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.61357182181329135704878102634056', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.46384640657069877254269844663690', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '4.04418648804151586905649076267444', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 64.54082716700547, 'bad_primes': [2, 3, 7], 'central_character': '7.2', 'conductor': 84, 'conductor_radical': 42, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/84/12/i/b/37/3'], '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': '2-84-7.2-c11-0-8', 'motivic_weight': 11, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [11], 'order_of_vanishing': 0, 'prelabel': '2-84-7.2-c11-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.033730588400726, 'root_angle': 0.09850308841744915, 'self_dual': False, 'spectral_label': 'c11-0', 'z1': {'__RealLiteral__': 0, 'data': '0.61357182181329135704878102634056', 'prec': 113}}
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lfunc_instances • Show schema
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{'Lhash': '777794688204747006405390808190', 'Lhash_array': ['777794688204747006405390808190'], 'label': '2-84-7.2-c11-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/84/12/i/b/37/3'}