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lfunc_lfunctions • Show schema
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{'Lhash': '2053139833664172154751154994820', 'a10': [0.0045830756932046055, -0.5517356370350801], 'a2': [-0.7172555650348209, 1.2188291325803546], 'a3': [-1.7061709674439542, -0.29829621159404834], 'a4': [-0.9710889088531597, -1.7484239563396458], 'a5': [-0.3378793522235315, 0.19507473495987226], 'a6': [1.5873327341292003, -1.8655762624888637], 'a7': [1.3952565872118234, -2.2479455188776294], 'a8': [2.8275489781066834, 0.07047536028890983], 'a9': [2.8220387402972773, 1.017888671840568], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.341486753957511, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.7172555650348209, -1.2188291325803546]]], [3, [[1.0, 0], [1.7061709674439542, 0.29829621159404834]]], [7, [[1.0, 0], [-1.3952565872118234, 2.2479455188776294]]]], 'bad_primes': [2, 3, 7], 'central_character': '168.101', 'coefficient_field': 'CDF', 'conductor': 168, 'conductor_radical': 42, 'conjugate': 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'3.75258944043369683701359388556693', '5.02281358765731706418371080211200', '6.34984069846076668684867046969041', '7.926629982766824190912419071242470', '8.877502414929634347340475378566245', '10.07407845236782371137751570671392', '10.86392954440857818498906186993128', '11.84160304078136917418903246230994', '12.31527626664874980570604868187214'], 'prelabel': '2-168-168.101-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': 0.03283107204478732, 'root_number': '0.9946855927362147 + 0.10295907732203698*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0164155360224', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.61964174772963645347365094880', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.75258944043369683701359388557', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.02281358765731706418371080211', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.341486753957511, 'bad_primes': [2, 3, 7], 'central_character': '168.101', 'conductor': 168, 'conductor_radical': 42, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/168/2/ba/c/101/9'], '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': '2-168-168.101-c1-0-8', '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': '2-168-168.101-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': 0.01641553602239366, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.61964174772963645347365094880', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2053139833664172154751154994820', 'Lhash_array': ['2053139833664172154751154994820'], 'label': '2-168-168.101-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/168/2/ba/c/101/9'}