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lfunc_lfunctions • Show schema
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{'Lhash': '4914622021967380170457409809360', 'a10': [-2.980284590371443, 5.162004331537939], 'a2': [-1.3626251538627532, -2.360135998161647], 'a3': [0.6732080041229965, -1.1660304672030684], 'a4': [-2.7134946198789835, 4.699910547695198], 'a5': [-1.0935819663694628, -1.894139527992989], 'a6': [-3.669320640798941, 1.861316211831716e-60], 'a7': [-2.1972854742622236, -1.4737491457491112], 'a8': [9.3394034802224, 0.0], 'a9': [0.5935819663694629, 1.0281141242085503], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.7266386583936518, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [2.1972854742622236, 1.4737491457491112]]], [13, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [7, 13], 'central_character': '91.53', 'coefficient_field': 'CDF', 'conductor': 91, 'conductor_radical': 91, 'conjugate': '1259383272635575981604761983449', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.3626251538627532, 2.360135998161647], [-1.0, 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-13.078192324964544], [-54.5, -94.39676901250381]], [[1.0, 0], [-3.1040846072050194, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 7, 'label': '2-91-7.4-c1-0-7', '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/91/2/e/c/53/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.5608223636160671, 0.6465514304971385, 0.7475560091199984, 0.867209689175028, 1.00826802934028, 1.1727773439815095, 1.3620218439163627, 1.5764675802613701, 1.8156805959599664, 2.0782173243776136, 2.3614988806951356, 2.6616872685193194, 2.9735834221063837, 3.290566747208472, 3.6045945479113994, 3.906277715733626, 4.185046193573297, 4.429413793562024, 4.627346782506615, 4.7667342168932345, 4.8359504365295765, 4.8244917087261925, 4.723660220919297, 4.527260072393828, 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'9.793712328622021252868219679942257', '10.81843645917661457145973265272013', '12.81586648775742280819878436326152', '14.51210292486327522549187062344059', '14.84122740478573587665499507047653'], 'prelabel': '2-91-7.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8524310285258578, 'root_angle': -0.9584365310942283, 'root_number': '-0.9914871265550291 - 0.1302047536599631*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.479218265547', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.87695317706830688773733718277', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.80794956159442223979761458822', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.77671020498878347309174617315', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.7266386583936518, 'bad_primes': [7, 13], 'central_character': '7.4', 'conductor': 91, 'conductor_radical': 91, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/91/2/e/c/53/1'], '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': '2-91-7.4-c1-0-7', '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': '2-91-7.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8524310285258578, 'root_angle': -0.47921826554711416, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.87695317706830688773733718277', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4914622021967380170457409809360', 'Lhash_array': ['4914622021967380170457409809360'], 'label': '2-91-7.4-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/91/2/e/c/53/1'}