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lfunc_lfunctions • Show schema
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{'Lhash': '2207992329229049036136532646442', 'a10': [-0.5132047960677143, -0.8888967814773054], 'a2': [0.14335288193054102, -0.24829447491511947], 'a3': [-3.064832682777001, 0.0], 'a4': [0.9588999024844167, 1.6608633504758517], 'a5': [1.790005157749037, -3.1003798790316752], 'a6': [-0.43935259771099466, 0.7609810216728123], 'a7': [2.102092699784959, 1.6066132955726404], 'a8': [1.1232557857383876, 0.0], 'a9': [6.393199373418069, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.0620103468830295, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [-2.102092699784959, -1.6066132955726404]]], [19, [[1.0, 0], [-2.605617132656569, -3.4943896975017767]]]], 'bad_primes': [7, 19], 'central_character': '133.102', 'coefficient_field': 'CDF', 'conductor': 133, 'conductor_radical': 133, 'conjugate': '1966685801422501032186015858614', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.14335288193054102, 0.24829447491511947], [-1.0, 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-133-133.102-c1-0-3', '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/133/2/g/a/102/7', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.9300604108684326, 0.9450268954656206, 0.9650893379965602, 0.98820734665706, 1.0108748959994749, 1.0284200577214921, 1.0353131147597285, 1.0254467545371073, 0.9923935606768247, 0.9296659559825726, 0.8310039886294909, 0.6907064296216596, 0.5040079584157859, 0.2674932058476558, -0.020471887602042743, -0.359319412379651, -0.7459040893873183, -1.1742120204510678, -1.6351941246545718, -2.1167631973616707, -2.6039881925567765, -3.0795099413708176, -3.52418906453026, -3.917979687900268, -4.241002553163274, -4.474769526274944, -4.603490082698254, -4.615371183422614, 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'10.41383191719442953178756380454760', '11.23745847813281092447714269995301', '11.75032680002974128226520775564446', '13.48243211248802222085069878654216'], 'prelabel': '2-133-133.102-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0305388623836704, 'root_angle': 0.09170446605875555, 'root_number': '0.9587860012025538 + 0.2841292028250822*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0458522330294', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.74179882755667794595420274681', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.61747598304907069939802656591', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.71588318412209103097100204403', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.0620103468830295, 'bad_primes': [7, 19], 'central_character': '133.102', 'conductor': 133, 'conductor_radical': 133, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/133/2/g/a/102/7'], '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': '2-133-133.102-c1-0-3', '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': '2-133-133.102-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0305388623836704, 'root_angle': 0.04585223302937778, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.74179882755667794595420274681', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2207992329229049036136532646442', 'Lhash_array': ['2207992329229049036136532646442'], 'label': '2-133-133.102-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/133/2/g/a/102/7'}