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lfunc_lfunctions • Show schema
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{'Lhash': '2226954953625306109499501746034', 'a10': [0.0, 0.0], 'a2': [0.0, -2.6332552711492934], 'a3': [1.557011875385124, 0.7587582091217853], 'a4': [-4.934033323035539, 0.0], 'a5': [0.0, 0.0], 'a6': [1.998004053697739, -4.100009728099924], 'a7': [4.703718547165084, 0.0], 'a8': [0.0, 7.72605871361101], 'a9': [1.8485719601806023, 2.3627910842971382], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.42558224671293, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.557011875385124, -0.7587582091217853]]], [11, [[1.0, 0], [0, 3.3166247903554]]], [13, [[1.0, 0], [-3.605551275463989, 0]]]], 'bad_primes': [3, 11, 13], 'central_character': '429.428', 'coefficient_field': 'CDF', 'conductor': 429, 'conductor_radical': 429, 'conjugate': '1865273219150038216438210608909', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 2.6332552711492934], [-2.0, 0]], [[1.0, 0], [-1.557011875385124, -0.7587582091217853]], [[1.0, 0], [0, 0], 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0], [0, -5.331026038837081], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 33, 'label': '2-429-429.428-c1-0-33', '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/429/2/e/d/428/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.878647287373275, 1.9990265860848593, 2.1265707094730097, 2.2570980069393283, 2.3821659535849435, 2.4895097313346444, 2.563818762904854, 2.5877181071639233, 2.5429041456998562, 2.4114346404910143, 2.1771759532091095, 1.8273794240896724, 1.354313919841399, 0.7568364538320812, 0.04174639585766727, -0.7752529472613675, -1.669164193555022, -2.606036126334499, -3.5441491742506552, -4.4360932919765, -5.23169757355529, -5.881669732584669, -6.341698950426193, -6.576680025034805, -6.564644165340984, -6.299945870327859, 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'7.927068599795247891349769346600703', '8.269775668297176098546385062066457', '9.032585814254404030299023358442712', '10.16700982088128763655503231868571', '11.55911003590685450539023101247995'], 'prelabel': '2-429-429.428-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8508328521811281, 'root_angle': 0.6443375380136824, 'root_number': '-0.43806925628630106 + 0.8989412253850455*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.322168769007', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.75675770060327534331312720937', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.09077564662709769520143162064', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.74287917022030438899352947807', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.42558224671293, 'bad_primes': [3, 11, 13], 'central_character': '429.428', 'conductor': 429, 'conductor_radical': 429, 'degree': 2, 'index': 33, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/429/2/e/d/428/4'], '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': '2-429-429.428-c1-0-33', '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': '2-429-429.428-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8508328521811281, 'root_angle': 0.3221687690068412, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.75675770060327534331312720937', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2226954953625306109499501746034', 'Lhash_array': ['2226954953625306109499501746034'], 'label': '2-429-429.428-c1-0-33', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/429/2/e/d/428/4'}