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lfunc_lfunctions • Show schema
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{'Lhash': '1512819515415621279090888908401', 'a10': [14.354470960042633, -8.28755767285528], 'a2': [-3.0840347288729144, -1.7805682809049317], 'a3': [0.0, 0.0], 'a4': [4.340846805929487, 7.51856721574295], 'a5': [-2.3272226518163417, 4.030867873471079], 'a6': [0.0, 0.0], 'a7': [-10.681693611858973, 0.0], 'a8': [0.0, -16.672150292382668], '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], [3.886427158706753, 18.598270993295763]]]], 'bad_primes': [3, 19], 'central_character': '171.46', 'coefficient_field': 'CDF', 'conductor': 171, 'conductor_radical': 57, 'conjugate': '674908799105022138229050796018', 'degree': 2, 'euler_factors': [[[1.0, 0], [3.0840347288729144, 1.7805682809049317], [2.0, 3.4641016151377544]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.3272226518163417, -4.030867873471079], [-12.5, 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[0]], 'group': 'GL2', 'index': 5, 'label': '2-171-19.8-c2-0-5', '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/c/46/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.4473369815522556, 0.5138829537215623, 0.5632977933217846, 0.5931380473657146, 0.6000370735676158, 0.5797350219951101, 0.5272301133103601, 0.43704556088831764, 0.30360186831753, 0.1216811042805264, -0.11303371289185069, -0.40336601835388736, -0.7500286380421639, -1.1510190940747054, -1.6010723150280777, -2.091222721453821, -2.6085318783823515, -3.1360380607797866, -3.652979023309763, -4.135328200847273, -4.556667161641816, -4.889393659439292, -5.106236051202261, -5.182012881010029, -5.095543529514224, -4.831585072881113, -4.382645396024296, -3.7505068071778527, -2.947291307426651, 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'10.30202773764148125688410939728158', '11.64622378979675992567997531111331', '12.71425953568062580007847002853784'], 'prelabel': '2-171-19.8-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.158567237905986, 'root_angle': 0.5699338684367, 'root_number': '-0.21794048175245895 + 0.975962061974494*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.284966934218', 'prec': 47}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.19340417236677942572499899424', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.85246548139193151892848726746', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.98589215592205723275501559495', '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': '19.8', 'conductor': 171, 'conductor_radical': 57, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/171/3/p/c/46/1'], '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': '2-171-19.8-c2-0-5', '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': '2-171-19.8-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.158567237905986, 'root_angle': 0.28496693421835, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.19340417236677942572499899424', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1512819515415621279090888908401', 'Lhash_array': ['1512819515415621279090888908401'], 'label': '2-171-19.8-c2-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/171/3/p/c/46/1'}