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lfunc_lfunctions • Show schema
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{'Lhash': '2027189731992608200223312143046', 'a10': [1.144393965901711, 0.0], 'a2': [1.0, 0.0], 'a3': [3.234966843879627, 0.0], 'a4': [1.0, 0.0], 'a5': [1.144393965901711, 0.0], 'a6': [3.234966843879627, 0.0], 'a7': [0.0, 0.0], 'a8': [1.0, 0.0], 'a9': [7.4650104810005145, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 22.693484254447895, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [7, [[1.0, 0], [0, 0]]], [29, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 7, 29], 'central_character': '2842.1', 'coefficient_field': 'CDF', 'conductor': 2842, 'conductor_radical': 406, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [-3.234966843879627, 0], [3.0, 0]], [[1.0, 0], [-1.144393965901711, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.8506828273395497, 0], [11.0, 0]], [[1.0, 0], [-3.661357863123305, 0], [13.0, 0]], [[1.0, 0], [-0.19424817097498398, 0], [17.0, 0]], [[1.0, 0], 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[-3.6418965755334383, 0], [109.0, 0]], [[1.0, 0], [17.77179979661704, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 73, 'label': '2-2842-1.1-c1-0-73', 'leading_term': '6.31737577017509999491617901202', '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/2842/2/a/z/1/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [6.3173757701751, 6.313056544902616, 6.299928736830532, 6.277491266197367, 6.244939448349354, 6.2012086144167915, 6.145031338815301, 6.075004985377404, 5.989666003704529, 5.887567435368027, 5.767356355505676, 5.627848389920692, 5.46809692456516, 5.287455094735963, 5.085629061542566, 4.862721433618889, 4.619263972423857, 4.356238942266383, 4.0750886500857675, 3.7777128848318386, 3.4664541295633047, 3.1440705945277694, 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'4.02051015909853678767452257115215', '4.42412907431500064197406313921220', '5.88151342065053772216879035898017', '6.37807566676285403218576807719022', '7.61178987260962602942689875005472', '7.85813859639467170165538767343655', '8.945663807851769701499427745328870'], 'prelabel': '2-2842-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.763767863199035, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.59917072703442922071838772416', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.28474739110343067598633447042', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.08692442400018980411452511376', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 22.693484254447895, 'bad_primes': [2, 7, 29], 'central_character': '1.1', 'conductor': 2842, 'conductor_radical': 406, 'degree': 2, 'index': 73, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2842/2/a/z/1/5'], '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': '2-2842-1.1-c1-0-73', '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': '2-2842-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.763767863199035, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.59917072703442922071838772416', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2027189731992608200223312143046', 'Lhash_array': ['2027189731992608200223312143046'], 'label': '2-2842-1.1-c1-0-73', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2842/2/a/z/1/5'}