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lfunc_lfunctions • Show schema
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{'Lhash': '1892752412184918983253776169439', 'a10': [1.605655361921802, 0.0], 'a2': [1.0, 0.0], 'a3': [3.3059401904118144, 0.0], 'a4': [1.0, 0.0], 'a5': [1.605655361921802, 0.0], 'a6': [3.3059401904118144, 0.0], 'a7': [-1.0, 0.0], 'a8': [1.0, 0.0], 'a9': [7.9292405425801045, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 40.35639318155513, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [7, [[1.0, 0], [1.0, 0]]], [19, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 7, 19], 'central_character': '5054.1', 'coefficient_field': 'CDF', 'conductor': 5054, 'conductor_radical': 266, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [-3.3059401904118144, 0], [3.0, 0]], [[1.0, 0], [-1.605655361921802, 0], [5.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [1.004974142140079, 0], [11.0, 0]], [[1.0, 0], [-3.9940744343647916, 0], [13.0, 0]], [[1.0, 0], [-4.170470059436472, 0], [17.0, 0]], [[1.0, 0], [0, 0]], 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[109.0, 0]], [[1.0, 0], [-5.832411338862538, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 141, 'label': '2-5054-1.1-c1-0-141', 'leading_term': '7.56116902487473801419809038770', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/5054/2/a/bk/1/9', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [7.561169024874738, 7.554044744579236, 7.53253328909008, 7.496227276336271, 7.444475442614778, 7.37642250670801, 7.291061767127061, 7.1872976031908, 7.064014713376075, 6.920150828475617, 6.7547697472099575, 6.567131804819079, 6.356759242591093, 6.123494345679807, 5.8675486175693825, 5.589541636463467, 5.290528579736392, 4.97201570618711, 4.635963358036229, 4.2847762947484345, 3.9212814088125336, 3.54869310815347, 3.1705668869122956, 2.790741848874275, 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'5.27134265900891318835413628684904', '6.12330256913384526812218484523568', '6.76788488215794018538707287503091', '7.84044152751627568278844797111514', '7.988840782203004016375910317530074'], 'prelabel': '2-5054-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.352668193881617, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.49311838123544884429564688706', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.05934266055957602405599695513', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.08373349665684541916723743671', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 40.35639318155513, 'bad_primes': [2, 7, 19], 'central_character': '1.1', 'conductor': 5054, 'conductor_radical': 266, 'degree': 2, 'index': 141, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5054/2/a/bk/1/9'], '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': '2-5054-1.1-c1-0-141', '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': '2-5054-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.352668193881617, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.49311838123544884429564688706', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1892752412184918983253776169439', 'Lhash_array': ['1892752412184918983253776169439'], 'label': '2-5054-1.1-c1-0-141', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5054/2/a/bk/1/9'}