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lfunc_lfunctions • Show schema
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{'Lhash': '507804319936739445643425493564', 'a10': [0, 0], 'a2': [0, 1271.9551395599815], 'a3': [0, 59049.0], 'a4': [479282.12294694775, 0], 'a5': [0, 0], 'a6': [-75107679.03587735, 0], 'a7': [0, -632075570.6821496], 'a8': [0, 3277108624.4200835], 'a9': [-3486784401.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 209.6080082152966, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '10.5', 'prec': 14}, 'bad_lfactors': [[3, [[1.0, 0], [0, -59049.0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '75.49', 'coefficient_field': 'CDF', 'conductor': 75, 'conductor_radical': 15, 'conjugate': '1587747940459791559783866634984', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -1271.9551395599815], [-2097152.0, 0]], [[1.0, 0], [0, -59049.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 632075570.6821496], [-558545864083284030, 0]], [[1.0, 0], [-59758476606.34392, 0], [7400249944258161000000, 0]], [[1.0, 0], [0, -738499392407.168], [-247064529073450400000000, 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'4.35021964433810738816001787368632', '5.86240543607005187397095327083898', '6.69224736344413004036323096692023', '7.972715030782159659530768488031336', '9.065795659541318787051725766843117', '10.26949938714632504980686518589100'], 'prelabel': '2-75-5.4-c21-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 14.477845427248372, 'root_angle': 0.8524163823495667, 'root_number': '-0.89442719099991587856366946749251049417624734384461028971 + 0.4472135954999579392818347337462552470881236719223051449*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.42620819117478337', 'prec': 64}, 'spectral_label': 'c21-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.40058697550043657138456475694', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.17307038601411434892283850991', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.47537815326291899209478447555', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 209.6080082152966, 'bad_primes': [3, 5], 'central_character': '5.4', 'conductor': 75, 'conductor_radical': 15, 'degree': 2, 'index': 19, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/75/22/b/d/49/3'], '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': '2-75-5.4-c21-0-19', 'motivic_weight': 21, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [21], 'order_of_vanishing': 0, 'prelabel': '2-75-5.4-c21-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 14.477845427248372, 'root_angle': 0.42620819117478337, 'self_dual': False, 'spectral_label': 'c21-0', 'z1': {'__RealLiteral__': 0, 'data': '0.40058697550043657138456475694', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '507804319936739445643425493564', 'Lhash_array': ['507804319936739445643425493564'], 'label': '2-75-5.4-c21-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/75/22/b/d/49/3'}