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lfunc_lfunctions • Show schema
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{'Lhash': '1815574450055122372420851477174', 'a10': [-9.367996366518437, -16.225845671930568], 'a2': [1.0, -1.7320508075688772], 'a3': [0, 0], 'a4': [-2.0, -3.4641016151377544], 'a5': [4.683998183259218, -8.112922835965284], 'a6': [0, 0], 'a7': [29.990435002924873, 0], 'a8': [-8.0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 20.178653221963298, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 1.7320508075688772]]], [3, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-68.54369704893811, 46.48399288855672]]]], 'bad_primes': [2, 3, 19], 'central_character': '342.163', 'coefficient_field': 'CDF', 'conductor': 342, 'conductor_radical': 114, 'conjugate': '1549372421175227144520168322758', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 1.7320508075688772]], [[1.0, 0], [0, 0]], [[1.0, 0], [-4.683998183259218, 8.112922835965284], [-62.5, -108.25317547305482]], [[1.0, 0], [-29.990435002924873, 0], [343.0, 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[0]], 'group': 'GL2', 'index': 15, 'label': '2-342-19.11-c3-0-15', 'leading_term': '3.022720869344368549600970776557492339410346255485918959', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/342/4/g/j/163/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0703125', 'prec': 30}, 'plot_values': [3.0227208693443686, 3.1034788419084665, 3.1632772591018306, 3.200953280430441, 3.2154308167334977, 3.205732848920564, 3.1709998970268867, 3.110514380028782, 3.0237302921694407, 2.9103073244599957, 2.7701482899669028, 2.603438476090737, 2.4106853521973193, 2.192756911186017, 1.9509168223532638, 1.6868545230595955, 1.4027083806904483, 1.101080116433901, 0.785038800442841, 0.45811290553025014, 0.12426914445778939, -0.2121228861959259, -0.5463408764932525, -0.8733749982842829, -1.1880078764258577, -1.484908588546833, 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'8.259134908367587425527152271370210', '9.288143868383581697984581111962437', '10.46520018428397695744979903911699', '11.41923245615561210846489144357567'], 'prelabel': '2-342-19.11-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.492065585225053, 'root_angle': 0.40922571643577893, 'root_number': '0.2813261769446322224164298261982281563485154040142538414 + 0.95961220405209389009988290323654204141869760962090563681*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.20461285821788947', 'prec': 64}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.43223570416662452165974874566', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.04792981582120552302930602357', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.43011554421061593968892904989', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 20.178653221963298, 'bad_primes': [2, 3, 19], 'central_character': '19.11', 'conductor': 342, 'conductor_radical': 114, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/342/4/g/j/163/4'], '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': '2-342-19.11-c3-0-15', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-342-19.11-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.492065585225053, 'root_angle': 0.20461285821788947, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.43223570416662452165974874566', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1815574450055122372420851477174', 'Lhash_array': ['1815574450055122372420851477174'], 'label': '2-342-19.11-c3-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/342/4/g/j/163/4'}