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lfunc_lfunctions • Show schema
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{'Lhash': '628488428801481438314029494785', 'a10': [0.0, 0.0], 'a2': [-0.4546644402030934, -0.16548432281323164], 'a3': [-0.3464503588673212, -1.9648176216442699], 'a4': [-0.5867097510307396, -0.4923079356980074], 'a5': [0.0, 0.0], 'a6': [-0.167627855096735, 0.9506648070716249], 'a7': [-0.374606593415912, 0.6488376526466565], 'a8': [0.4272087107591905, 0.7399471924709148], 'a9': [-2.800787814378641, 1.0194033969293188], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.3559596393238675, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[11, [[1.0, 0], [-0.5, -0.8660254037844386]]], [13, [[1.0, 0], [0.17364817766693036, -0.984807753012208]]], [19, [[1.0, 0], [0.4383711467890774, 0.898794046299167]]]], 'bad_primes': [11, 13, 19], 'central_character': '2717.1429', 'coefficient_field': 'CDF', 'conductor': 2717, 'conductor_radical': 2717, 'conjugate': '1305352318478202684325939245155', 'degree': 2, 'euler_factors': [[[1.0, 0], 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[0.17364817766693036, -0.984807753012208]], [[1.0, 0], [1.4386796006773024, 0], [1.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-2717-2717.1429-c0-0-0', 'leading_term': '0.50122008572872886198561473788939', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/2717/1/db/c/1429/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.5012200857287289, 0.47816936688266226, 0.4520123765980992, 0.42030288270089455, 0.37995387440356915, 0.32746066918145966, 0.2591150858877177, 0.1711849010730189, 0.06005531123118748, -0.07765845868196385, -0.24501541823643713, -0.44466034788308917, -0.6787369314896257, -0.9488003879143188, -1.2557301734171802, -1.599645116290783, -1.979824456446806, -2.394638886048716, -2.8414959554807537, -3.316804202061625, 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'4.12975793999769132857785119070818', '5.17221357849990826170892452502925', '5.74736129601734474784136026960891', '6.77407785624348404453264288126124', '7.932574801070789870499977312782541', '8.560476631770979592767267451964692', '9.202112376306712815126115846073862'], 'prelabel': '2-2717-2717.1429-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1644568001106212, 'root_angle': 0.20129438331361713, 'root_number': '0.80662012738588439391456608638474 + 0.59107019049853938070297630212255*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.10064719165680856', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.49578995086526807509890301990', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.08279526297958980866602926486', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.68612722877817369030602721808', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.3559596393238675, 'bad_primes': [11, 13, 19], 'central_character': '2717.1429', 'conductor': 2717, 'conductor_radical': 2717, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2717/1/db/c/1429/3'], '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': '2-2717-2717.1429-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-2717-2717.1429-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1644568001106212, 'root_angle': 0.10064719165680856, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.49578995086526807509890301990', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '628488428801481438314029494785', 'Lhash_array': ['628488428801481438314029494785'], 'label': '2-2717-2717.1429-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2717/1/db/c/1429/3'}