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lfunc_lfunctions • Show schema
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{'Lhash': '1054743413164556198136001144515', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [1.838434837902316, -3.184262545651465], 'a6': [0, 0], 'a7': [-1.555754505221257, 2.1400065232339274], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 18.1100711784264, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [1.555754505221257, -2.1400065232339274]]]], 'bad_primes': [2, 3, 7], 'central_character': '2268.865', 'coefficient_field': 'CDF', 'conductor': 2268, 'conductor_radical': 42, 'conjugate': '1466754542413344465340240348060', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.838434837902316, 3.184262545651465], [-2.5, -4.330127018922194]], [[1.0, 0], [1.555754505221257, -2.1400065232339274]], [[1.0, 0], [-0.3015716853316113, -0.5223374811185247], [-5.5, 9.526279441628825]], [[1.0, 0], 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[-1.1381539054979766, 0], [71.0, 0]], [[1.0, 0], [5.335108067200197, -9.240678236261335], [-36.5, -63.21985447626402]], [[1.0, 0], [-4.145507070417902, 0], [79.0, 0]], [[1.0, 0], [-6.240879469243714, 10.809520324643602], [-41.5, -71.88010851410841]], [[1.0, 0], [4.09463978600904, 7.092124148060614], [-44.5, 77.07626093681505]], [[1.0, 0], [-6.77935356197894, 11.742184811820568], [-48.5, -84.00446416709055]], [[1.0, 0], [-7.669748665776395, -13.284394370408323], [-50.5, 87.4685657822283]], [[1.0, 0], [-2.4803317444468904, 4.296060601007959], [-51.5, -89.20061658979718]], [[1.0, 0], [-3.4139876426834164, -5.913200053539979], [-53.5, 92.66471820493493]], [[1.0, 0], [-8.901942115405662, 15.418616029919775], [-54.5, -94.39676901250381]], [[1.0, 0], [4.639464715383152, 8.0357886069667], [-56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 14, 'label': '2-2268-63.25-c1-0-14', 'leading_term': '2.0569340608989986906786031026233732714094825298245008293', 'load_key': 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'prelabel': '2-2268-63.25-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.255592929125905, 'root_angle': -0.05751247975483975, 'root_number': '0.98372158435916846048102568793363760865804447381801997970 - 0.1796993168208699955838966131297018764774562438500055566*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.028756239877419872', 'prec': 70}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.832045843684891462374552495561', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.34184721464260371445664396610', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.24278308681371881729249443225', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 18.1100711784264, 'bad_primes': [2, 3, 7], 'central_character': '63.25', 'conductor': 2268, 'conductor_radical': 42, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2268/2/i/n/865/8'], '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': '2-2268-63.25-c1-0-14', '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': '2-2268-63.25-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.255592929125905, 'root_angle': -0.028756239877419876, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.832045843684891462374552495561', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1054743413164556198136001144515', 'Lhash_array': ['1054743413164556198136001144515'], 'label': '2-2268-63.25-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2268/2/i/n/865/8'}