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lfunc_lfunctions • Show schema
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{'Lhash': '466559028841146854952856068311', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, -27.0], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, 504.0], 'a8': [0, 0], 'a9': [-729.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 187.43101529047314, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 27.0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '600.49', 'coefficient_field': 'CDF', 'conductor': 600, 'conductor_radical': 30, 'conjugate': '1238098532808652958079907071593', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 27.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -504.0], [-823543.0, 0]], [[1.0, 0], [-3812.0, 0], [19487171.0, 0]], [[1.0, 0], [0, 9574.0], [-62748517.0, 0]], [[1.0, 0], [0, -26098.0], [-410338673.0, 0]], [[1.0, 0], [-38308.0, 0], [893871739.0, 0]], [[1.0, 0], [0, -71128.0], [-3404825447.0, 0]], [[1.0, 0], [74262.0, 0], 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0], [0, 2048274.0], [-235260548044817.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 18, 'label': '2-600-5.4-c7-0-18', 'leading_term': '1.798715280293229955638804476543209956763643297462779536', 'load_key': 'CMFs-workshop', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/600/8/f/d/49/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.79871528029323, 1.5766442173753938, 1.3218314134053128, 1.0396464318009124, 0.7361471608982967, 0.41794925263735816, 0.09208249143158852, -0.23416303211041165, -0.5533978421706203, -0.858297817561981, -1.1417693534584061, -1.39711148478099, -1.6181715086428583, -1.7994907042563297, -1.9364368748070744, -2.0253206278691915, -2.063492568831694, -2.049418904238493, -1.9827333363347721, -1.8642635724875272, -1.6960312680429406, -1.4812247615873484, 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'4.61499403499016270572858525092978', '5.69061744073418056884554134960793', '6.85463506165866628274147531397488', '7.43916251976490443872808580599230', '8.827910671563776059768094543270254', '9.367300472474562533358670088482011'], 'prelabel': '2-600-5.4-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 13.69054474045767, 'root_angle': -0.17620819117478337, 'root_number': '0.4472135954999579392818347337462552470881236719223051449 - 0.8944271909999158785636694674925104941762473438446102897*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.17620819117478337', 'prec': 67}, 'spectral_label': 'c7-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.36805017783066326253133837463', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.50637904505272312793679358633', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.84001941120699009691344812448', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 187.43101529047314, 'bad_primes': [2, 3, 5], 'central_character': '5.4', 'conductor': 600, 'conductor_radical': 30, 'degree': 2, 'index': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/600/8/f/d/49/1'], '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': '2-600-5.4-c7-0-18', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7], 'order_of_vanishing': 0, 'prelabel': '2-600-5.4-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 13.69054474045767, 'root_angle': -0.17620819117478337, 'self_dual': False, 'spectral_label': 'c7-0', 'z1': {'__RealLiteral__': 0, 'data': '0.36805017783066326253133837463', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '466559028841146854952856068311', 'Lhash_array': ['466559028841146854952856068311'], 'factors': ['2-600-5.4-c7-0-18'], 'label': '2-600-5.4-c7-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/600/8/f/d/49/1'}