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lfunc_lfunctions • Show schema
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{'Lhash': '860498328668680289882134984360', 'a10': [0, 0], 'a2': [0.7071067811865476, 1.224744871391589], 'a3': [-1.5, -0.8660254037844386], 'a4': [-1.0, 1.7320508075688772], 'a5': [0, 0], 'a6': [0, -2.449489742783178], 'a7': [-3.9757071695483304, -5.761401956295186], 'a8': [-2.8284271247461903, 0], 'a9': [1.5, 2.598076211353316], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 28.61042775783118, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.7071067811865476, -1.224744871391589]]], [3, [[1.0, 0], [1.5, 0.8660254037844386]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [3.9757071695483304, 5.761401956295186]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '1050.451', 'coefficient_field': 'CDF', 'conductor': 1050, 'conductor_radical': 210, 'conjugate': '986057792852614545457138339554', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.7071067811865476, -1.224744871391589]], [[1.0, 0], [1.5, 0.8660254037844386]], 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'5.29029498948690758790231830890149', '6.02066390415674446366576353858252', '6.79533916147062242076225615179904', '8.205395481324137311055481743241877', '8.960079938669140677252344541958807', '9.814098274830373722087866955835013'], 'prelabel': '2-1050-7.3-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.348871634076778, 'root_angle': -0.23261237787348163, 'root_number': '0.7446584642995938191866801179630713399621349682441249846 - 0.6674457068158956683779039174939820737973972431953629805*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.11630618893674081', 'prec': 67}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.67881349049474286780492336722', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.33041053714926577434407029990', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.23742037180951737946421089918', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 28.61042775783118, 'bad_primes': [2, 3, 5, 7], 'central_character': '7.3', 'conductor': 1050, 'conductor_radical': 210, 'degree': 2, 'index': 22, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1050/3/p/c/451/3'], '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': '2-1050-7.3-c2-0-22', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-1050-7.3-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.348871634076778, 'root_angle': -0.11630618893674081, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.67881349049474286780492336722', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '860498328668680289882134984360', 'Lhash_array': ['860498328668680289882134984360'], 'label': '2-1050-7.3-c2-0-22', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1050/3/p/c/451/3'}