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lfunc_lfunctions • Show schema
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{'Lhash': '1221591244454354605019043161438', 'a10': [0.0, 0.0], 'a2': [0.7922869913932613, 0.0], 'a3': [1.0, 0.0], 'a4': [-1.3722813232690143, 0.0], 'a5': [0.0, 0.0], 'a6': [0.7922869913932613, 0.0], 'a7': [2.5243377989621387, 0.0], 'a8': [-2.6718146237444933, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 72.46423983431198, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.0, 0]]], [5, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5, 11], 'central_character': '9075.1', 'coefficient_field': 'CDF', 'conductor': 9075, 'conductor_radical': 165, 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.7922869913932613, 0], [2.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.5243377989621387, 0], [7.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-6.780726405493154, 0], [13.0, 0]], [[1.0, 0], [-6.6332495807108, 0], [17.0, 0]], [[1.0, 0], [-7.72049022166877, 0], [19.0, 0]], 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0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 178, 'label': '2-9075-1.1-c1-0-178', 'leading_term': '3.95438180322642875279002452628', '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/9075/2/a/db/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [3.9543818032264286, 3.9435156632570023, 3.9108833155801057, 3.8563915703456857, 3.7799131688454546, 3.6813268714064393, 3.560569776123239, 3.417698481242219, 3.252955255500095, 3.06683520866707, 2.860150529404895, 2.6340881301044288, 2.3902574522745654, 2.1307256883606267, 1.8580382237498472, 1.5752226661734874, 1.2857753909750795, 0.9936300816145749, 0.7031082832739481, 0.4188525142177785, 0.14574299533811494, -0.11120043811532973, -0.3469291913718899, -0.5564870167539477, -0.735138427873798, 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'5.60277180387910321010177120332864', '6.03299592709311692153319260170745', '7.20209108529280376900961613578106', '7.900662207555534813715588379273584'], 'prelabel': '2-9075-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.512593014723068, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.963665574910324491318257092373', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.62515702012049602368677664633', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.94595695000723963534878952943', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 72.46423983431198, 'bad_primes': [3, 5, 11], 'central_character': '1.1', 'conductor': 9075, 'conductor_radical': 165, 'degree': 2, 'index': 178, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9075/2/a/db/1/3'], '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': '2-9075-1.1-c1-0-178', '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': '2-9075-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.512593014723068, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.963665574910324491318257092373', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1221591244454354605019043161438', 'Lhash_array': ['1221591244454354605019043161438'], 'label': '2-9075-1.1-c1-0-178', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9075/2/a/db/1/3'}