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lfunc_lfunctions • Show schema
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{'Lhash': '3466916130860755504681610294917', 'a10': [-3.2613872124741694, -1.8829627850535648], 'a2': [3.0590716208171305, -1.766155823749115], 'a3': [0.0, 0.0], 'a4': [4.23861278752583, -7.341492701605885], 'a5': [-0.5330681358161528, -0.9233010951296033], 'a6': [0.0, 0.0], 'a7': [0.47722557505166113, 0.0], 'a8': [0.0, -15.814956047231945], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.6594125205610775, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [6.522774424948339, -17.84526306338015]]]], 'bad_primes': [3, 19], 'central_character': '171.145', 'coefficient_field': 'CDF', 'conductor': 171, 'conductor_radical': 57, 'conjugate': '2118083825456253011226008028891', 'degree': 2, 'euler_factors': [[[1.0, 0], [-3.0590716208171305, 1.766155823749115], [2.0, -3.4641016151377544]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.5330681358161528, 0.9233010951296033], [-12.5, 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 12, 'label': '2-171-19.12-c2-0-12', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/171/3/p/f/145/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [3.252472451307542, 3.4236553472453264, 3.5937271310645666, 3.761413564140575, 3.9236471190200484, 4.075614108687884, 4.210941996797433, 4.322007502243477, 4.400345352112485, 4.437139758106044, 4.423782221197379, 4.352477911954309, 4.216878229681384, 4.012710118516402, 3.7383648652117794, 3.395402130991208, 2.9889204761147288, 2.5277449762217503, 2.024386739029775, 1.4947388453022366, 0.9574886096615679, 0.4332466612771608, -0.056581881759763336, -0.4911316511882287, -0.8515368603790144, -1.1224123004148592, -1.2932322815110626, -1.3594744102054372, -1.3233968063049963, 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'11.30604362630941493385148390855007', '12.09169331568405685298591842387347', '12.85779396983088886822758878485179'], 'prelabel': '2-171-19.12-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.158567237905986, 'root_angle': 0.47603950664612127, 'root_number': '0.07520304377850638 + 0.9971682416756201*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.238019753323', 'prec': 47}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.73491459731614340969944701637', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.19481637671908257042329553979', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.02183892025749073444846638835', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.6594125205610775, 'bad_primes': [3, 19], 'central_character': '19.12', 'conductor': 171, 'conductor_radical': 57, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/171/3/p/f/145/4'], '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': '2-171-19.12-c2-0-12', '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': '2-171-19.12-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.158567237905986, 'root_angle': 0.23801975332306063, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '2.73491459731614340969944701637', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3466916130860755504681610294917', 'Lhash_array': ['3466916130860755504681610294917'], 'label': '2-171-19.12-c2-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/171/3/p/f/145/4'}