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lfunc_lfunctions • Show schema
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{'Lhash': '1400304704587661235830908203530', 'a10': [84.98081888480202, 147.19109597728584], 'a2': [-4.0, 6.928203230275509], 'a3': [38.43869881969987, 66.57777933255802], 'a4': [-32.0, -55.42562584220407], 'a5': [10.622602360600252, -18.39888699716073], 'a6': [-615.019181115198, -1.5447077027395315e-59], 'a7': [-642.2835669515964, 641.1043749842408], 'a8': [512.0, 0.0], 'a9': [-1861.5671339031928, 3224.3288576207055], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.373390356777707, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [4.0, -6.928203230275509]]], [7, [[1.0, 0], [642.2835669515964, -641.1043749842408]]]], 'bad_primes': [2, 7], 'central_character': '14.9', 'coefficient_field': 'CDF', 'conductor': 14, 'conductor_radical': 14, 'conjugate': '4427082197670472667101820127073', 'degree': 2, 'euler_factors': [[[1.0, 0], [4.0, -6.928203230275509]], [[1.0, 0], [-38.43869881969987, -66.57777933255802], [-1093.5, 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['1.10464563684626396521844490984673', '3.08486100807694147698516493362869', '6.90797301692274462850428231175614', '8.220474736804353486517114638871141', '9.964668166660463024184031814781919', '12.02578565215134253898458953301126', '13.22334667468482983806600491607644', '14.09016188798609979329841345143199', '16.35152115238444363179806765881990', '18.22178061001384319633236580876546'], 'prelabel': '2-14-7.2-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.091265252610894, 'root_angle': -0.38494024313057434, 'root_number': '-0.7498627183067041 - 0.6615934580191075*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.384940243131', 'prec': 50}, 'spectral_label': 'c7-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.10464563684626396521844490985', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.08486100807694147698516493363', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.90797301692274462850428231176', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.373390356777707, 'bad_primes': [2, 7], 'central_character': '7.2', 'conductor': 14, 'conductor_radical': 14, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/14/8/c/a/9/2'], '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': '2-14-7.2-c7-0-0', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7], 'order_of_vanishing': 0, 'prelabel': '2-14-7.2-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.091265252610894, 'root_angle': -0.38494024313057434, 'self_dual': False, 'spectral_label': 'c7-0', 'z1': {'__RealLiteral__': 0, 'data': '1.10464563684626396521844490985', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1400304704587661235830908203530', 'Lhash_array': ['1400304704587661235830908203530'], 'factors': ['2-14-7.2-c7-0-0'], 'label': '2-14-7.2-c7-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/14/8/c/a/9/2'}