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lfunc_lfunctions • Show schema
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{'Lhash': '2058276986234443398507112566361', 'a10': [2.4600468171151584, 0.0], 'a2': [1.0, 0.0], 'a3': [2.1009199237645135, 0.0], 'a4': [1.0, 0.0], 'a5': [2.4600468171151584, 0.0], 'a6': [2.1009199237645135, 0.0], 'a7': [3.0999525358618203, 0.0], 'a8': [1.0, 0.0], 'a9': [1.4138645260706886, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 36.715214849384736, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [11, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 11, 19], 'central_character': '4598.1', 'coefficient_field': 'CDF', 'conductor': 4598, 'conductor_radical': 418, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [-2.1009199237645135, 0], [3.0, 0]], [[1.0, 0], [-2.4600468171151584, 0], [5.0, 0]], [[1.0, 0], [-3.0999525358618203, 0], [7.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.9783219546573068, 0], [13.0, 0]], [[1.0, 0], [-2.14576363532013, 0], [17.0, 0]], 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[-3.380800202583594, 0], [109.0, 0]], [[1.0, 0], [-11.366805290176472, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 140, 'label': '2-4598-1.1-c1-0-140', 'leading_term': '6.90189720589165906468676389015', '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/4598/2/a/cd/1/8', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [6.901897205891659, 6.894659517936756, 6.872774691624901, 6.835739689204194, 6.782756104273008, 6.712787301929885, 6.624633073278363, 6.517017198528658, 6.38868287918668, 6.238490986878533, 6.065516397196568, 5.869138218916815, 5.649120381528023, 5.405679718366025, 5.139539320449239, 4.851965509351865, 4.544787282316613, 4.220397531183645, 3.8817357479213945, 3.5322523237930117, 3.1758549431751586, 2.816837977564302, 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'3.63477536425187220689369549234425', '4.53835474699350940327572077775726', '5.45656698477550974392222984190763', '5.90591304512157596283846012616691', '6.84414443540140530781052228949128', '7.79988593305413301805084337576046', '8.237847919962720763508139663562481'], 'prelabel': '2-4598-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.059308116392889, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.62369424655647907428268238721', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.84388136967659744760366264769', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.98376173536696584685277487745', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 36.715214849384736, 'bad_primes': [2, 11, 19], 'central_character': '1.1', 'conductor': 4598, 'conductor_radical': 418, 'degree': 2, 'index': 140, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4598/2/a/cd/1/8'], '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': '2-4598-1.1-c1-0-140', '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': '2-4598-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.059308116392889, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.62369424655647907428268238721', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2058276986234443398507112566361', 'Lhash_array': ['2058276986234443398507112566361'], 'label': '2-4598-1.1-c1-0-140', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4598/2/a/cd/1/8'}