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lfunc_lfunctions • Show schema
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{'Lhash': '1244904966306220919873840092643', 'a10': [0.52869086730227, 0.0], 'a2': [-1.1462144370921823, 0.0], 'a3': [0.0, 0.0], 'a4': [-0.6861924642014515, 0.0], 'a5': [-0.46124952730790897, 0.0], 'a6': [0.0, 0.0], 'a7': [-3.032324931243616, 0.0], 'a8': [3.078952583275929, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 47.934196333374636, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [23, [[1.0, 0], [1.0, 0]]], [29, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 23, 29], 'central_character': '6003.1', 'coefficient_field': 'CDF', 'conductor': 6003, 'conductor_radical': 2001, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.1462144370921823, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.46124952730790897, 0], [5.0, 0]], [[1.0, 0], [3.032324931243616, 0], [7.0, 0]], [[1.0, 0], [1.2402209707502194, 0], [11.0, 0]], [[1.0, 0], [-3.028118212089834, 0], [13.0, 0]], [[1.0, 0], 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'4.05551646897873037495244478953128', '4.66241421069803401228728911980929', '5.86622756322773088128940692720286', '6.24628146160713662711227142045218', '7.30005532296840427709642244855081', '7.73797642166803545091649396840670'], 'prelabel': '2-6003-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.923452630976444, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.982056858634458636150974985228', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.21731160953064931084625872091', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.23729207210556060952426666471', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 47.934196333374636, 'bad_primes': [3, 23, 29], 'central_character': '1.1', 'conductor': 6003, 'conductor_radical': 2001, 'degree': 2, 'index': 121, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6003/2/a/u/1/7'], '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': '2-6003-1.1-c1-0-121', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-6003-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.923452630976444, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.982056858634458636150974985228', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1244904966306220919873840092643', 'Lhash_array': ['1244904966306220919873840092643'], 'factors': ['2-6003-1.1-c1-0-121'], 'label': '2-6003-1.1-c1-0-121', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6003/2/a/u/1/7'}