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lfunc_lfunctions • Show schema
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{'Lhash': '2012753013588779326225207979793', 'a10': [3.4728339089952556, 0.0], 'a2': [2.114907541476756, 0.0], 'a3': [1.0, 0.0], 'a4': [2.4728339089952556, 0.0], 'a5': [1.6420736324815002, 0.0], 'a6': [2.114907541476756, 0.0], 'a7': [0.0, 0.0], 'a8': [1.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.911810006841044, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.0, 0]]], [7, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 7, 11], 'central_character': '1617.1', 'coefficient_field': 'CDF', 'conductor': 1617, 'conductor_radical': 231, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.114907541476756, 0], [2.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.6420736324815002, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-4.587741450472011, 0], [13.0, 0]], [[1.0, 0], [-0.7158527350369995, 0], [17.0, 0]], [[1.0, 0], [-1.6420736324815002, 0], [19.0, 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[[1.0, 0], [13.066818536925044, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 46, 'label': '2-1617-1.1-c1-0-46', 'leading_term': '5.42538074785626169871029770070', '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/1617/2/a/r/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [5.425380747856262, 5.422593068630421, 5.413959981396332, 5.398686911163955, 5.375500184012759, 5.342718650920219, 5.29834610866762, 5.240178201503071, 5.1659173994349405, 5.073290214097948, 4.9601617650588254, 4.824643881131552, 4.665193907937531, 4.480702177803314, 4.270566646759143, 4.034753540865069, 3.7738430376711523, 3.489059105431773, 3.1822826947364233, 2.856047573688983, 2.513518252662349, 2.1584496774698887, 1.7951286876272623, 1.428297636377956, 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'5.46240768225880472051407318514713', '5.79759602624576880994992442727453', '6.74618635002000132020893689461730', '7.57153378145971643248515349006923', '8.779268319986869671551412957382188', '9.249231668232122523465801106157082'], 'prelabel': '2-1617-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.593300711997403, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.58778216428596393451246135794', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.60946159557131001245877039894', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.65665845413847059418412007617', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.911810006841044, 'bad_primes': [3, 7, 11], 'central_character': '1.1', 'conductor': 1617, 'conductor_radical': 231, 'degree': 2, 'index': 46, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1617/2/a/r/1/3'], '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': '2-1617-1.1-c1-0-46', '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': '2-1617-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.593300711997403, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.58778216428596393451246135794', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2012753013588779326225207979793', 'Lhash_array': ['2012753013588779326225207979793'], 'label': '2-1617-1.1-c1-0-46', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1617/2/a/r/1/3'}