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lfunc_lfunctions • Show schema
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{'Lhash': '1014041192536485016218468189466', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-4.5, -7.794228634059948], 'a4': [0, 0], 'a5': [-38.81286641361127, 67.22585661575836], 'a6': [0, 0], 'a7': [0, 0], 'a8': [0, 0], 'a9': [-40.5, 70.14805770653953], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 94.30568605003263, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [4.5, 7.794228634059948]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '588.373', 'coefficient_field': 'CDF', 'conductor': 588, 'conductor_radical': 42, 'conjugate': '150368892434648637232432194850', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [4.5, 7.794228634059948]], [[1.0, 0], [38.81286641361127, -67.22585661575836], [-1562.5, -2706.329386826371]], [[1.0, 0], [0, 0]], [[1.0, 0], [238.69006489527888, 413.4233196605355], [-80525.5, 139474.25730488764]], [[1.0, 0], [-63.754396963335246, 0], 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'label': '2-588-7.2-c5-0-19', 'leading_term': '0.385659479282515167619826487848590887193660205901007743', 'load_key': 'CMFs-workshop', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/588/6/i/i/373/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [0.38565947928251515, 0.5565946246795114, 0.6998695944336524, 0.8119927950252258, 0.8900914639370856, 0.9319701698930298, 0.9361593020264161, 0.9019526858883146, 0.8294335009716094, 0.719487725736565, 0.5738044080124268, 0.39486215668858654, 0.18590137956256397, -0.04911804427570422, -0.3055737688330017, -0.5782525359785214, -0.8614358803174267, -1.1489992770488209, -1.4345236910358434, -1.7114181300500857, -1.9730514383409208, -2.2128911991131766, -2.424647258433103, -2.602417051924643, -2.7408296235136325, -2.835184986862173, -2.8815853092199366, 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'7.69211452236991929118294298481266', '8.426269252361693004690008995372562', '9.330418730424216858356807112519134', '10.10040851420790273398255029052863'], 'prelabel': '2-588-7.2-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.711111473463408, 'root_angle': 0.5859748544508822, 'root_number': '-0.2668258571384815647106987959345095138142320105440431026 + 0.9637447597586793761438043440821124880542606995232854472*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.2929874272254411', 'prec': 60}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.799937453075725890137391300786', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.33762802900758455706464986772', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.82673394934010298392069978200', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 94.30568605003263, 'bad_primes': [2, 3, 7], 'central_character': '7.2', 'conductor': 588, 'conductor_radical': 42, 'degree': 2, 'index': 19, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/588/6/i/i/373/1'], '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': '2-588-7.2-c5-0-19', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-588-7.2-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.711111473463408, 'root_angle': 0.2929874272254411, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.799937453075725890137391300786', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1014041192536485016218468189466', 'Lhash_array': ['1014041192536485016218468189466'], 'label': '2-588-7.2-c5-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/588/6/i/i/373/1'}