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lfunc_lfunctions • Show schema
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{'Lhash': '1227177468413197791552161136070', 'a10': [883.5030163522312, -510.090704320807], 'a2': [-2.3345207824511163, 4.043508606530783], 'a3': [-32.10031952872917, 18.533128120984788], 'a4': [21.100025432607655, 36.54631609027194], 'a5': [-189.2257766548136, -109.24955308927262], 'a6': [5.457976503530905e-60, -173.06389104907277], 'a7': [0.0, 0.0], 'a8': [-495.8524516844216, 0.0], 'a9': [322.45367589767426, -558.5061497421198], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.2726500973727, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.0', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0, 0]]]], 'bad_primes': [7], 'central_character': '49.19', 'coefficient_field': 'CDF', 'conductor': 49, 'conductor_radical': 7, 'conjugate': '334698141112016968496825286760', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.3345207824511163, -4.043508606530783], [-32.0, -55.42562584220407]], [[1.0, 0], [32.10031952872917, -18.533128120984788], [364.5, -631.3325193588557]], [[1.0, 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'3.27761826627561727562286424894314', '5.61648191739114222315905892379184', '6.79783814678766457062568431506244', '7.972554697502068079463938704782660', '10.21685212449913466118606731937637', '11.15502069381180979427834484059013', '11.71827273438220607997055899023511', '12.69338037104057298051262100689273', '14.74254701483261970221706749865496'], 'prelabel': '2-7e2-7.5-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.357476745619052, 'root_angle': 0.05652399726933656, 'root_number': '0.9375940792147648 + 0.34773171069290965*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0565239972693', 'prec': 50}, 'spectral_label': 'c6-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.968072328599264831642434536656', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '3.27761826627561727562286424894', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.61648191739114222315905892379', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 11.2726500973727, 'bad_primes': [7], 'central_character': '7.5', 'conductor': 49, 'conductor_radical': 7, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/49/7/d/e/19/5'], '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': '2-7e2-7.5-c6-0-8', 'motivic_weight': 6, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [6], 'order_of_vanishing': 0, 'prelabel': '2-7e2-7.5-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.357476745619052, 'root_angle': 0.05652399726933656, 'self_dual': False, 'spectral_label': 'c6-0', 'z1': {'__RealLiteral__': 0, 'data': '0.968072328599264831642434536656', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1227177468413197791552161136070', 'Lhash_array': ['1227177468413197791552161136070'], 'factors': ['2-7e2-7.5-c6-0-8'], 'label': '2-7e2-7.5-c6-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/49/7/d/e/19/5'}