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lfunc_lfunctions • Show schema
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{'Lhash': '2555830942682868515464907455813', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 66, 'a6': 0, 'a7': -176, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 23.095270053069214, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '144.1', 'coefficient_field': '1.1.1.1', 'conductor': 144, 'conductor_radical': 6, 'degree': 2, 'euler_factors': [[1], [1], [1, -66, 3125], [1, 176, 16807], [1, 60, 161051], [1, 658, 371293], [1, -414, 1419857], [1, 956, 2476099], [1, -600, 6436343], [1, 5574, 20511149], [1, -3592, 28629151], [1, 8458, 69343957], [1, 19194, 115856201], [1, 13316, 147008443], [1, 19680, 229345007], [1, -31266, 418195493], [1, -26340, 714924299], [1, 31090, 844596301], [1, -16804, 1350125107], [1, -6120, 1804229351], [1, 25558, 2073071593], [1, 74408, 3077056399], [1, 6468, 3939040643], [1, -32742, 5584059449], [1, -166082, 8587340257], [1, 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 11, 'label': '2-12e2-1.1-c5-0-11', 'load_key': 'CMFs-workshop', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/144/6/a/j', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0703125', 'prec': 30}, 'plot_values': [-1.474927546813378e-60, 0.23108211023218003, 0.45961361082146, 0.6830631716610844, 0.8989382541783698, 1.1048050730238899, 1.2983091946385779, 1.4771969158664595, 1.6393375090145696, 1.782746351845868, 1.9056088838593854, 2.0063052460962942, 2.083435373098924, 2.135844215240313, 2.1626466802955395, 2.1632517978158807, 2.1373855316251786, 2.085111597620539, 2.0068495890068947, 1.9033896719878642, 1.7759030944472753, 1.625947750699761, 1.4554680690403774, 1.266788537238864, 1.0626002554591907, 0.8459400069104408, 0.6201614637585052, 0.3888982986206955, 0.15601914869960462, 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'10.15489081859172396485728813413290', '11.82779050664734778527052649631568'], 'prelabel': '2-12e2-1.1-c5-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.805753848572481, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c5-0', 'trace_hash': 1637808191158970887, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.01619511103667959607515431165', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.30742614915159950285938965112', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.12418426347401793692091307834', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 23.095270053069214, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 144, 'conductor_radical': 6, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 66, 0, -176, 0, 0, 0, -60, 0, -658, 0, 0, 0, 414, 0, -956, 0, 0, 0, 600, 0, 1231, 0, 0, 0, -5574, 0, 3592, 0, 0, 0, -11616, 0, -8458, 0, 0, 0, -19194, 0, -13316, 0, 0, 0, -19680, 0, 14169, 0, 0, 0, 31266, 0, -3960, 0, 0, 0, 26340, 0, -31090, 0, 0, 0, -43428, 0, 16804, 0, 0, 0, 6120, 0, -25558, 0, 0, 0, 10560, 0, -74408, 0, 0, 0, -6468, 0, 27324, 0, 0, 0, 32742, 0, 115808, 0, 0, 0, -63096, 0, 166082, 0, 0, 0], 'euler11': [1, 60, 161051], 'euler13': [1, 658, 371293], 'euler17': [1, -414, 1419857], 'euler19': [1, 956, 2476099], 'euler2': [1, 0, 0], 'euler23': [1, -600, 6436343], 'euler29': [1, 5574, 20511149], 'euler3': [1, 0, 0], 'euler31': [1, -3592, 28629151], 'euler37': [1, 8458, 69343957], 'euler41': [1, 19194, 115856201], 'euler43': [1, 13316, 147008443], 'euler47': [1, 19680, 229345007], 'euler5': [1, -66, 3125], 'euler53': [1, -31266, 418195493], 'euler59': [1, -26340, 714924299], 'euler61': [1, 31090, 844596301], 'euler67': [1, -16804, 1350125107], 'euler7': [1, 176, 16807], 'euler71': [1, -6120, 1804229351], 'euler73': [1, 25558, 2073071593], 'euler79': [1, 74408, 3077056399], 'euler83': [1, 6468, 3939040643], 'euler89': [1, -32742, 5584059449], 'euler97': [1, -166082, 8587340257], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, -66, 3125], [1, 176, 16807], [1, 60, 161051], [1, 658, 371293], [1, -414, 1419857], [1, 956, 2476099], [1, -600, 6436343], [1, 5574, 20511149], [1, -3592, 28629151], [1, 8458, 69343957], [1, 19194, 115856201], [1, 13316, 147008443], [1, 19680, 229345007], [1, -31266, 418195493], [1, -26340, 714924299], [1, 31090, 844596301], [1, -16804, 1350125107], [1, -6120, 1804229351], [1, 25558, 2073071593], [1, 74408, 3077056399], [1, 6468, 3939040643], [1, -32742, 5584059449], [1, -166082, 8587340257]], 'index': 11, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/144/6/a/j/1/1', 'ModularForm/GL2/Q/holomorphic/144/6/a/j'], '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': '2-12e2-1.1-c5-0-11', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'prelabel': '2-12e2-1.1-c5-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.805753848572481, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c5-0', 'trace_hash': 1637808191158970887, 'z1': {'__RealLiteral__': 0, 'data': '2.01619511103667959607515431165', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20702707
{'Lhash': '2555830942682868515464907455813', 'Lhash_array': ['2555830942682868515464907455813'], 'label': '2-12e2-1.1-c5-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/144/6/a/j'}
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id: 24559234
{'Lhash': '2555830942682868515464907455813', 'Lhash_array': ['2555830942682868515464907455813'], 'label': '2-12e2-1.1-c5-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/144/6/a/j/1/1'}