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lfunc_lfunctions • Show schema
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{'Lhash': '1431148258120795978414513679046', 'a10': [-1.0311250970335655, 0.0], 'a2': [1.0, 0.0], 'a3': [2.554821520978613, 0.0], 'a4': [1.0, 0.0], 'a5': [-1.0311250970335655, 0.0], 'a6': [2.554821520978613, 0.0], 'a7': [2.7738448500230684, 0.0], 'a8': [1.0, 0.0], 'a9': [3.5271130040554732, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 63.417189285300914, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [11, [[1.0, 0], [-1.0, 0]]], [19, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 11, 19], 'central_character': '7942.1', 'coefficient_field': 'CDF', 'conductor': 7942, 'conductor_radical': 418, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [-2.554821520978613, 0], [3.0, 0]], [[1.0, 0], [1.0311250970335655, 0], [5.0, 0]], [[1.0, 0], [-2.7738448500230684, 0], [7.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-2.637904485936446, 0], [13.0, 0]], [[1.0, 0], [5.958501071192586, 0], [17.0, 0]], 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[18.13309414118948, 0], [109.0, 0]], [[1.0, 0], [-9.138998571101615, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 168, 'label': '2-7942-1.1-c1-0-168', 'leading_term': '6.44289031436656717025930225501', '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/7942/2/a/cb/1/12', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [6.442890314366567, 6.431367428734082, 6.396692827563082, 6.33855879532652, 6.256485556509664, 6.1498687230436495, 6.018041583489805, 5.860348568587187, 5.676225764423781, 5.465284186541965, 5.227391637534169, 4.962749286759623, 4.6719595661770486, 4.356082508666974, 4.016678215478018, 3.655833694605491, 3.276172844315358, 2.880848859981206, 2.4735188199959106, 2.0583006635289, 1.6397132154806162, 1.2226003463862345, 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'4.21163160197716598272375178712373', '4.64160784728556287845967552537756', '5.75647360842118595995463595665934', '6.47225214335536116114704640512098', '7.43584410776283043267134472652859', '7.76435012223711706062602009496681'], 'prelabel': '2-7942-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.9634910237471175, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.12897691040664537519156137224', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.14722450120192038704259033741', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.64479701902380552011670169060', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 63.417189285300914, 'bad_primes': [2, 11, 19], 'central_character': '1.1', 'conductor': 7942, 'conductor_radical': 418, 'degree': 2, 'index': 168, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/7942/2/a/cb/1/12'], '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': '2-7942-1.1-c1-0-168', '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': '2-7942-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.9634910237471175, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.12897691040664537519156137224', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1431148258120795978414513679046', 'Lhash_array': ['1431148258120795978414513679046'], 'label': '2-7942-1.1-c1-0-168', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7942/2/a/cb/1/12'}