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lfunc_lfunctions • Show schema
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{'Lhash': '40583467874130895949138777858', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.7390089172206591, 0.6736956436465572], 'a4': [-0.9829730996839018, -0.18374951781657034], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.44573835577653825, 0.8951632913550623], 'a8': [0.0, 0.0], 'a9': [0.092268359463302, -0.9957341762950345], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.0794776223251843, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.7390089172206591, -0.6736956436465572]]], [7, [[1.0, 0], [0.44573835577653825, -0.8951632913550623]]], [103, [[1.0, 0], [0.8502171357296141, -0.5264321628773558]]]], 'bad_primes': [3, 7, 103], 'central_character': '2163.1175', 'coefficient_field': 'CDF', 'conductor': 2163, 'conductor_radical': 2163, 'conjugate': '2377847637747120395628175208054', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [0.9829730996839018, 0.18374951781657034]], [[1.0, 0], [0.7390089172206591, 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'2.90937339736564216089744140203606', '4.12500135896152163601786773122385', '4.66522834283735017518281460046128', '5.64873372742608297625410016063746', '6.53215979252415698780479957593234', '7.13153258193260097501135524003289', '8.006263212966426359232971272398145', '8.702910058532792194847263834216829'], 'prelabel': '2-2163-2163.1175-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0389791250670941, 'root_angle': 0.7786822073166361, 'root_number': '-0.76786773248090589725441604719486 + 0.64060841815779468767727260824048*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.38934110365831803', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.03201471120419475017162900539', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.38630907840325551799705102921', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.90937339736564216089744140204', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.0794776223251843, 'bad_primes': [3, 7, 103], 'central_character': '2163.1175', 'conductor': 2163, 'conductor_radical': 2163, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2163/1/bu/b/1175/1'], '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': '2-2163-2163.1175-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-2163-2163.1175-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0389791250670941, 'root_angle': 0.38934110365831803, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.03201471120419475017162900539', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '40583467874130895949138777858', 'Lhash_array': ['40583467874130895949138777858'], 'label': '2-2163-2163.1175-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2163/1/bu/b/1175/1'}