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lfunc_lfunctions • Show schema
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{'Lhash': '843609176633779189782252768528', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-2.8284271247461903, 0.0], 'a4': [0.0, 0.0], 'a5': [1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-2.0, 0.0], 'a8': [0.0, 0.0], 'a9': [5.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 28.10734151149071, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-1.0, 0]]], [11, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 5, 11], 'central_character': '3520.1', 'coefficient_field': 'CDF', 'conductor': 3520, 'conductor_radical': 110, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [2.8284271247461903, 0], [3.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [2.0, 0], [7.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-6.82842712474619, 0], [13.0, 0]], [[1.0, 0], [-1.17157287525381, 0], [17.0, 0]], [[1.0, 0], [0, 0], [19.0, 0]], [[1.0, 0], [-2.8284271247461903, 0], [23.0, 0]], [[1.0, 0], [7.656854249492381, 0], [29.0, 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'0.99795204202158894455575987823315', '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/3520/2/a/bn/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [0.9979520420215889, 0.9920316665731698, 0.9742516385091201, 0.9445609750495854, 0.9028933885759504, 0.8491939859772468, 0.7834541378849518, 0.7057523112919173, 0.6162983960356906, 0.5154789738909865, 0.4039010474768889, 0.2824319228641771, 0.15223318258090582, 0.014786960193480442, -0.12808698934126614, -0.27422464942394015, -0.42112248299185756, -0.5659542335397933, -0.7056001864751373, -0.836689001604377, -0.9556519209884125, -1.0587888306894007, -1.1423453110307433, -1.2025994521562215, -1.2359568471701023, -1.2390518138063864, -1.2088525492874702, -1.1427676051146487, -1.0387507931452846, -0.8954014158243704, 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'7.60462515660041835347924566116849', '8.724492246229974815332020431449487'], 'prelabel': '2-3520-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.301635739230932, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.66549029873207549241152803058', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.66409038449636696386426825227', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.16511995193899276948389951815', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 28.10734151149071, 'bad_primes': [2, 5, 11], 'central_character': '1.1', 'conductor': 3520, 'conductor_radical': 110, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3520/2/a/bn/1/1'], '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': '2-3520-1.1-c1-0-11', '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': '2-3520-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.301635739230932, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.66549029873207549241152803058', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '843609176633779189782252768528', 'Lhash_array': ['843609176633779189782252768528'], 'label': '2-3520-1.1-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3520/2/a/bn/1/1'}