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lfunc_lfunctions • Show schema
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{'Lhash': '1758222777206104560468834517399', 'a10': [0.0, 0.0], 'a2': [0.9659258262890683, 0.25881904510252074], 'a3': [0.07498942048610055, 0.2798643272842737], 'a4': [0.8660254037844386, 0.5], 'a5': [0.0, 0.0], 'a6': [-9.176731798894091e-62, 0.28973687178390023], 'a7': [-0.12633392610430919, 2.6427333840391602], 'a8': [0.7071067811865476, 0.7071067811865476], 'a9': [2.5253755828518782, -1.45802627256444], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.7947640707448147, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.9659258262890683, -0.25881904510252074]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0.12633392610430919, -2.6427333840391602]]]], 'bad_primes': [2, 5, 7], 'central_character': '350.143', 'coefficient_field': 'CDF', 'conductor': 350, 'conductor_radical': 70, 'conjugate': '2689201120870390551809744517920', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.9659258262890683, -0.25881904510252074]], 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'5.41239453496756022547601575966063', '6.40806292605335077734280888461723', '7.57379922323973288094017070500309', '8.256622643382096537314474461625778', '9.886988122205710352106758029468183', '10.58275611248157217323502909765928', '11.25833646977148951114504544241257'], 'prelabel': '2-350-35.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6717547878635834, 'root_angle': -0.2846824359177289, 'root_number': '0.6260209468979342 - 0.7798062413478196*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.142341217959', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.38699321160700900540241658913', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.20793234310624120223114350449', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.15637958391626481628815408827', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.7947640707448147, 'bad_primes': [2, 5, 7], 'central_character': '35.3', 'conductor': 350, 'conductor_radical': 70, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/350/2/o/c/143/4'], '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': '2-350-35.3-c1-0-3', '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': '2-350-35.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6717547878635834, 'root_angle': -0.14234121795886445, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.38699321160700900540241658913', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1758222777206104560468834517399', 'Lhash_array': ['1758222777206104560468834517399'], 'label': '2-350-35.3-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/350/2/o/c/143/4'}