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lfunc_lfunctions • Show schema
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{'Lhash': '1379030612637217841603158283698', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, -3.3208844994474864], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, 1.3208844994474864], 'a8': [0, 0], 'a9': [-8.028273858670582, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 23.15661658617132, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [29, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 5, 29], 'central_character': '2900.349', 'coefficient_field': 'CDF', 'conductor': 2900, 'conductor_radical': 290, 'conjugate': '947122481688856490436532731500', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 3.3208844994474864], [-3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -1.3208844994474864], [-7.0, 0]], [[1.0, 0], [-5.320884499447486, 0], [11.0, 0]], [[1.0, 0], [0, -5.028273858670582], [-13.0, 0]], [[1.0, 0], [0, 6.349158358118069], [-17.0, 0]], [[1.0, 0], [-4.349158358118069, 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'4.31737817361596095833677590013682', '4.85959900155327462509477696746848', '5.95006218842075434436456532675676', '6.35892965880746102328801111307875', '7.81726887498035459006856975824038', '8.419290309315023821305993803093483', '9.168808684696348936758518713465393'], 'prelabel': '2-2900-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.812132228666552, 'root_angle': 0.32379180882521663, 'root_number': '-0.4472135954999579392818347337462552470881236719223051449 + 0.8944271909999158785636694674925104941762473438446102897*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.32379180882521663', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.08786333741248214862620771551', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.97110453432116412779188712728', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.51865179567782703564229555589', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 23.15661658617132, 'bad_primes': [2, 5, 29], 'central_character': '5.4', 'conductor': 2900, 'conductor_radical': 290, 'degree': 2, 'index': 25, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2900/2/c/f/349/1'], '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': '2-2900-5.4-c1-0-25', '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': '2-2900-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.812132228666552, 'root_angle': 0.32379180882521663, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.08786333741248214862620771551', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1379030612637217841603158283698', 'Lhash_array': ['1379030612637217841603158283698'], 'factors': ['2-2900-5.4-c1-0-25'], 'label': '2-2900-5.4-c1-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2900/2/c/f/349/1'}