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lfunc_lfunctions • Show schema
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{'Lhash': '565526914396703880607998311770', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.1399477355498853, 0.0], 'a4': [0.0, 0.0], 'a5': [-2.77940736369183, 0.0], 'a6': [0.0, 0.0], 'a7': [1.98760874860765, 0.0], 'a8': [0.0, 0.0], 'a9': [-1.7005191602146887, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 32.16374193417175, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-1.0, 0]]], [53, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 19, 53], 'central_character': '4028.1', 'coefficient_field': 'CDF', 'conductor': 4028, 'conductor_radical': 2014, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.1399477355498853, 0], [3.0, 0]], [[1.0, 0], [2.77940736369183, 0], [5.0, 0]], [[1.0, 0], [-1.98760874860765, 0], [7.0, 0]], [[1.0, 0], [5.0695099913038195, 0], [11.0, 0]], [[1.0, 0], [-4.334846272916146, 0], [13.0, 0]], [[1.0, 0], [2.007022397762547, 0], [17.0, 0]], [[1.0, 0], 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[[1.0, 0], [2.4314403179453112, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 5, 'label': '2-4028-1.1-c1-0-5', 'leading_term': '0.60658379973767139903972281811209', '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/4028/2/a/e/1/7', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [0.6065837997376714, 0.5987554320950332, 0.575250880381735, 0.5360182713333589, 0.48099228210245343, 0.41012433104788404, 0.32342198899059243, 0.22099509683715077, 0.10310577203609758, -0.0297806109416146, -0.17694630590794802, -0.33737658490644423, -0.5097219915471495, -0.6922694958475492, -0.8829242538939233, -1.079203340398667, -1.2782424901000788, -1.4768165518171943, -1.6713740206474257, -1.858085662978608, -2.03290688133532, -2.1916530804106515, 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'4.87170805691284174964412830055793', '5.29438834353710999397435309751039', '6.19256950939755184380846723476067', '7.01592987092415077792024024027072', '7.937157645300486397245450383962779', '8.274582585104682393833663874274325'], 'prelabel': '2-4028-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.671308661514709, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.44612207361782947663317709426', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.89712406792363982687454415042', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.12031151814227417587938693738', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 32.16374193417175, 'bad_primes': [2, 19, 53], 'central_character': '1.1', 'conductor': 4028, 'conductor_radical': 2014, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4028/2/a/e/1/7'], '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': '2-4028-1.1-c1-0-5', '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': '2-4028-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.671308661514709, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.44612207361782947663317709426', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '565526914396703880607998311770', 'Lhash_array': ['565526914396703880607998311770'], 'label': '2-4028-1.1-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4028/2/a/e/1/7'}