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lfunc_lfunctions • Show schema
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{'Lhash': '1931318386982238785053536617325', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, -3.0574039924192435], 'a6': [0, 0], 'a7': [0, -1.354656691727707], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 42.54429419693821, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [37, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 37], 'central_character': '5328.2591', 'coefficient_field': 'CDF', 'conductor': 5328, 'conductor_radical': 222, 'conjugate': '372242371857156384257702926353', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 3.0574039924192435], [-5.0, 0]], [[1.0, 0], [0, 1.354656691727707], [-7.0, 0]], [[1.0, 0], [5.122699898036546, 0], [11.0, 0]], [[1.0, 0], [-5.325207147708513, 0], [13.0, 0]], [[1.0, 0], [0, 4.544034792573752], [-17.0, 0]], [[1.0, 0], [0, -1.1101686445229872], [-19.0, 0]], 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[[1.0, 0], [0, 7.30200330306247], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 67, 'label': '2-5328-12.11-c1-0-67', 'leading_term': '1.0609195369795586108710079617462329895298555726317568501', '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/5328/2/e/f/2591/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.0609195369795585, 1.2582349041437677, 1.4565747301813143, 1.6546477138673705, 1.8510101391439364, 2.0440251417474657, 2.2318343605523525, 2.4123444327484433, 2.5832298004084837, 2.741952322354317, 2.885797307155853, 3.0119248440194877, 3.117434719832899, 3.1994427611118725, 3.2551661050312606, 3.282014657458353, 3.2776858155078283, 3.2402594029812914, 3.1682896831532568, 3.0608912763100005, 2.917815826360851, 2.7395163420192543, 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'3.93180877241895177337462611097478', '5.03691748377801945070274282013656', '5.85308703972917083948698306887641', '6.34685961616927096768618389408763', '7.05745671297242265418914087500989', '7.964966775691913381916661609612901', '8.330683475319353821774534487116039'], 'prelabel': '2-5328-12.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.522598730332735, 'root_angle': -0.48537669532568156, 'root_number': '-0.995781915781360406655418752355827767108636813323537474598 - 0.09175170953613698363378598754901810133900875322388831193*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.48537669532568156', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.52354157102479327043524541480', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.59321152093798013419804373004', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.13483572610161280783394354898', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 42.54429419693821, 'bad_primes': [2, 3, 37], 'central_character': '12.11', 'conductor': 5328, 'conductor_radical': 222, 'degree': 2, 'index': 67, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5328/2/e/f/2591/3'], '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': '2-5328-12.11-c1-0-67', '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': '2-5328-12.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.522598730332735, 'root_angle': -0.48537669532568156, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.52354157102479327043524541480', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1931318386982238785053536617325', 'Lhash_array': ['1931318386982238785053536617325'], 'factors': ['2-5328-12.11-c1-0-67'], 'label': '2-5328-12.11-c1-0-67', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5328/2/e/f/2591/3'}