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lfunc_lfunctions • Show schema
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{'Lhash': '1388116210648588953660126748025', 'a10': [3.0, 5.196152422706632], 'a2': [-2.301767435984125, 0.837774832901458], 'a3': [0.0, 0.0], 'a4': [3.064177772475912, -2.5711504387461575], 'a5': [-0.42534943004813686, -2.4122764896167532], 'a6': [0.0, 0.0], 'a7': [1.532088886237956, 1.2855752193730787], 'a8': [-2.449489742783178, 4.242640687119285], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.821094307351343, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '729.163', 'coefficient_field': 'CDF', 'conductor': 729, 'conductor_radical': 3, 'conjugate': '1050487632238668976544019870808', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.301767435984125, -0.837774832901458], [1.532088886237956, -1.2855752193730787]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.42534943004813686, 2.4122764896167532], [-4.698463103929542, 1.7101007166283437]], [[1.0, 0], 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'positive_zeros': ['1.09503061048420658879406261006932', '2.46559426982897407613324545775061', '3.38820118557286355417146479891140', '4.89553094538638744553881560779519', '6.58019164451155533887945876498692', '7.30873288820904026542199547529062', '7.83789058111635691457871960810229', '8.796539406578495929923128529520572', '9.856060553776301871447172107384945', '10.23743720887985471999049886990184'], 'prelabel': '2-3e6-27.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': 0.07407407407407408, 'root_number': '0.9730448705798238 + 0.2306158707424402*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.037037037037', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.09503061048420658879406261007', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.46559426982897407613324545775', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.38820118557286355417146479891', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.821094307351343, 'bad_primes': [3], 'central_character': '27.7', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/2/e/p/163/1'], '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': '2-3e6-27.7-c1-0-15', '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': '2-3e6-27.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': 0.03703703703703704, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.09503061048420658879406261007', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1388116210648588953660126748025', 'Lhash_array': ['1388116210648588953660126748025'], 'label': '2-3e6-27.7-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/2/e/p/163/1'}