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lfunc_lfunctions • Show schema
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{'Lhash': '2304840467250250277113079637723', 'a10': [1.694688102640594, 2.9352858967560094], 'a2': [0.8660254037844386, -0.5], 'a3': [0.23327250386328402, 0.40403982870001515], 'a4': [0.5, -0.8660254037844386], 'a5': [0.0, 3.389376205281188], 'a6': [0.40403982870001515, 0.23327250386328402], 'a7': [0.8660254037844386, 0.5], 'a8': [0.0, -1.0], 'a9': [1.3911678778827083, -2.409573446350626], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.4532773167873037, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8660254037844386, 0.5]]], [7, [[1.0, 0], [-0.8660254037844386, -0.5]]], [13, [[1.0, 0], [2.7498679914150155, -2.332000435203893]]]], 'bad_primes': [2, 7, 13], 'central_character': '182.127', 'coefficient_field': 'CDF', 'conductor': 182, 'conductor_radical': 182, 'conjugate': '3070269705824075603938398175349', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8660254037844386, 0.5]], [[1.0, 0], [-0.23327250386328402, 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[[1.0, 0], [-1.5078971689898824, -0.8705848364265832], [29.5, 51.09549882328188]], [[1.0, 0], [1.1897244612970965, -2.0606632139740837], [-30.5, -52.827549630850754]], [[1.0, 0], [-0.25263575145564, 0.14585931910983713], [33.5, -58.023702053557386]], [[1.0, 0], [-9.481583291048155, -5.4741946654305105], [35.5, 61.48780366869514]], [[1.0, 0], [0, -12.718677581210072], [-73.0, 0]], [[1.0, 0], [-9.956022172658084, 0], [79.0, 0]], [[1.0, 0], [0, 3.2355336229623086], [-83.0, 0]], [[1.0, 0], [-6.965141037942373, 4.021326053199738], [44.5, -77.07626093681505]], [[1.0, 0], [-12.794542943680865, -7.386932812692375], [48.5, 84.00446416709055]], [[1.0, 0], [4.119880949103848, 7.135843124982952], [-50.5, 87.4685657822283]], [[1.0, 0], [13.323114955637946, 0], [103.0, 0]], [[1.0, 0], [-4.513246610720067, -7.8171724368551905], [-53.5, 92.66471820493493]], [[1.0, 0], [0, -0.3971916305908907], [-109.0, 0]], [[1.0, 0], [2.236608337780384, -3.873919277667799], [-56.5, -97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-182-13.10-c1-0-2', '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/182/2/m/b/127/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.68830099443467, 1.6711023819828703, 1.6663645742856517, 1.669359112882447, 1.6736125331227127, 1.6715178715085843, 1.6549160934049125, 1.6155983825196147, 1.545745401173748, 1.4383432416197668, 1.2876076493614685, 1.089426836906844, 0.8418112567175287, 0.545321139926293, 0.20343054482831094, -0.17722001481628807, -0.5867317060702588, -1.0120616798988238, -1.4373794699902733, -1.844686405227972, -2.214698789395167, -2.527971221825025, -2.7662094133792845, -2.9136944063066013, -2.958714988917739, -2.8948854118225436, -2.7222144354293927, -2.447792154491799, 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'12.18521114961169340473950518398220', '12.63271699982723686166685513293930'], 'prelabel': '2-182-13.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2055195215289147, 'root_angle': -0.05313646718886412, 'root_number': '0.9860989904936663 - 0.16615890270272043*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0265682335944', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.81819853738505224793291464958', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.08189916177612932704119178990', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.97311401959823166801224759110', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.4532773167873037, 'bad_primes': [2, 7, 13], 'central_character': '13.10', 'conductor': 182, 'conductor_radical': 182, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/182/2/m/b/127/5'], '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': '2-182-13.10-c1-0-2', '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': '2-182-13.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2055195215289147, 'root_angle': -0.02656823359443206, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.81819853738505224793291464958', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2304840467250250277113079637723', 'Lhash_array': ['2304840467250250277113079637723'], 'label': '2-182-13.10-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/182/2/m/b/127/5'}