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lfunc_lfunctions • Show schema
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{'Lhash': '2957158976570811985283209175745', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.7071067811865476, -0.7071067811865476], 'a4': [0.0, 0.0], 'a5': [0.7071067811865476, -0.7071067811865476], 'a6': [0.0, 0.0], 'a7': [-1.0, -1.0], 'a8': [0.0, 0.0], 'a9': [0.0, -1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.47910241212768234, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-0.7071067811865476, 0.7071067811865476]]], [5, [[1.0, 0], [-0.7071067811865476, 0.7071067811865476]]]], 'bad_primes': [2, 3, 5], 'central_character': '960.863', 'coefficient_field': 'CDF', 'conductor': 960, 'conductor_radical': 30, 'conjugate': '1603603631147235970791282464861', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.7071067811865476, 0.7071067811865476]], [[1.0, 0], [-0.7071067811865476, 0.7071067811865476]], [[1.0, 0], [1.0, 1.0], [0, 1.0]], [[1.0, 0], [0, -1.4142135623730951], 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'1.2652258198749864525364384690862', '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/960/1/u/a/863/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [1.2652258198749864, 1.3176853473892955, 1.3883116253341687, 1.4771657766681403, 1.5832151872681512, 1.7045974294622503, 1.8388962086632807, 1.9833616956872806, 2.1350561149409666, 2.2909363921311163, 2.4478960352829877, 2.6027866895954643, 2.752434000068735, 2.8936567336745034, 3.023293873814549, 3.1382415950522007, 3.235500266403025, 3.3122305362463504, 3.365816850372776, 3.393936280526341, 3.394630202097156, 3.3663761112455144, 3.3081566960658986, 3.2195231710779435, 3.1006498548450394, 2.9523770256601995, 2.776239239258721, 2.574476543261419, 2.350026380637176, 2.1064944403297057, 1.8481032843637388, 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'9.638969351235205504357373624476700', '10.14315286482335506936605779814860'], 'prelabel': '2-960-120.83-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6921722416622053, 'root_angle': 0.42620819117478337, 'root_number': '0.22975292054736118352393736938184 + 0.97324898946773016378805774830813*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.21310409558739168', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.33278710714009158359677376160', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.00865802169970201021369718166', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.86430967622701641927142908577', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.47910241212768234, 'bad_primes': [2, 3, 5], 'central_character': '120.83', 'conductor': 960, 'conductor_radical': 30, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/960/1/u/a/863/2'], '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': '2-960-120.83-c0-0-3', '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': '2-960-120.83-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6921722416622053, 'root_angle': 0.21310409558739168, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.33278710714009158359677376160', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2957158976570811985283209175745', 'Lhash_array': ['2957158976570811985283209175745'], 'label': '2-960-120.83-c0-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/960/1/u/a/863/2'}