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lfunc_lfunctions • Show schema
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{'Lhash': '107039993332902006165836675085', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-0.7755292598500868, -2.0972730788136236], 'a6': [0, 0], 'a7': [0, -2.0215794743826665], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 27.308837491277906, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0.7755292598500868, 2.0972730788136236]]], [19, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 5, 19], 'central_character': '3420.1369', 'coefficient_field': 'CDF', 'conductor': 3420, 'conductor_radical': 570, 'conjugate': '1428575592203459874840260534679', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.7755292598500868, 2.0972730788136236]], [[1.0, 0], [0, 2.0215794743826665], [-7.0, 0]], [[1.0, 0], [2.799207836145135, 0], [11.0, 0]], [[1.0, 0], [0, -4.216125632009914], [-13.0, 0]], [[1.0, 0], 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'1.91108777303249248388338149397963', '2.80939387390381738788624046758359', '3.46431045434601477900917835803678', '4.48329934115877437076879189662878', '5.59319934085940549105543007247148', '5.98658749698720476923282733680576', '6.88833956652069101959899626094737', '7.88487228815382380224411807311406', '8.087366861701538327815983959664611'], 'prelabel': '2-3420-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.225785825239866, 'root_angle': -0.6127409809575664, 'root_number': '-0.3468272287129784697074081406772011572334675933194608718 - 0.9379290343215073555573981992036061575068831319962995834*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.3063704904787832', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.084439666035444145038061560743', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.91108777303249248388338149398', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.80939387390381738788624046758', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 27.308837491277906, 'bad_primes': [2, 3, 5, 19], 'central_character': '5.4', 'conductor': 3420, 'conductor_radical': 570, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3420/2/f/e/1369/3'], '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': '2-3420-5.4-c1-0-2', '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': '2-3420-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.225785825239866, 'root_angle': -0.3063704904787832, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.084439666035444145038061560743', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '107039993332902006165836675085', 'Lhash_array': ['107039993332902006165836675085'], 'label': '2-3420-5.4-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3420/2/f/e/1369/3'}