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lfunc_lfunctions • Show schema
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{'Lhash': '205767165538164210294110214315', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 1.4142135623730951], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [-4.242640687119285, 0], 'a8': [0, 0], 'a9': [1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 25.552128646809734, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5], 'central_character': '3200.1601', 'coefficient_field': 'CDF', 'conductor': 3200, 'conductor_radical': 10, 'conjugate': '2220360860496812224367919591461', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, -1.4142135623730951], [-3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [4.242640687119285, 0], [7.0, 0]], [[1.0, 0], [0, -5.656854249492381], [-11.0, 0]], [[1.0, 0], [0, -2.0], [-13.0, 0]], [[1.0, 0], [6.0, 0], [17.0, 0]], [[1.0, 0], [0, -2.8284271247461903], [-19.0, 0]], [[1.0, 0], [-7.0710678118654755, 0], [23.0, 0]], [[1.0, 0], 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'0.486931688995323228231229573800017986648807537950254316', '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/3200/2/d/s/1601/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [0.48693168899532324, 0.3266615712600619, 0.17338921412067052, 0.02768525692368311, -0.10980018945236962, -0.23830808813267415, -0.3569516043777911, -0.4647088875454775, -0.560427860498277, -0.6428427144363392, -0.7106012598710241, -0.7623018654144215, -0.796538422161036, -0.8119515842137965, -0.8072844299654058, -0.7814406388743848, -0.7335432642850821, -0.6629921908829419, -0.5695183892576774, -0.45323311930349036, -0.3146702925864317, -0.15482028758148236, 0.02484637206677022, 0.2223669106505496, 0.4352869991935448, 0.6606752461195006, 0.8951521686930388, 1.134933989195827, 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'6.85587097202252289816848869101814', '7.06595783243019650090753817115997', '8.357979040210222510042235318109345'], 'prelabel': '2-3200-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.054911339164094, 'root_angle': 0.75, 'root_number': '-0.70710678118654752440084436210484903928483593768847403659 + 0.7071067811865475244008443621048490392848359376884740366*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.375', 'prec': 17}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.16232167247119800372126578819', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.11046800699204804839025176366', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.66687396725846354100161100346', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 25.552128646809734, 'bad_primes': [2, 5], 'central_character': '8.5', 'conductor': 3200, 'conductor_radical': 10, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3200/2/d/s/1601/3'], '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': '2-3200-8.5-c1-0-6', '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': '2-3200-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.054911339164094, 'root_angle': 0.375, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.16232167247119800372126578819', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '205767165538164210294110214315', 'Lhash_array': ['205767165538164210294110214315'], 'label': '2-3200-8.5-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3200/2/d/s/1601/3'}