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lfunc_lfunctions • Show schema
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{'Lhash': '1973360183227203627189343991430', 'a10': [0.49454149163357086, -0.270040084784612], 'a2': [0.7557495743542583, -0.6548607339452851], 'a3': [0.0, 0.0], 'a4': [0.14231483827328514, -0.9898214418809327], 'a5': [0.5505881699192892, 0.11977312504299793], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [-0.5406408174555976, -0.8412535328311812], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.5990043004761398, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.7557495743542583, 0.6548607339452851]]], [3, [[1.0, 0], [0, 0]]], [89, [[1.0, 0], [-0.21256528955297668, -0.9771468659711595]]]], 'bad_primes': [2, 3, 89], 'central_character': '3204.1475', 'coefficient_field': 'CDF', 'conductor': 3204, 'conductor_radical': 534, 'conjugate': '1467267380511027946599301610966', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.7557495743542583, 0.6548607339452851]], [[1.0, 0], [0, 0]], [[1.0, 0], 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'positive_zeros': ['1.55670670046771357078653226320976', '2.80055285425460696869023113605140', '3.56762363806097269611569354961776', '4.49073986428972093168753009786317', '5.38130949067644478335627821049408', '5.86748277281505812121086521915988', '6.62826946521136586778637374012438', '7.47178033504516117020392849260404', '8.122866004474904979895095891032748', '8.785808250287553235201786020327329'], 'prelabel': '2-3204-1068.407-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2645174180200682, 'root_angle': 0.4471384652417727, 'root_number': '0.16530712178442278137398166489525 + 0.98624213836529516597259286599080*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.22356923262088635', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.55670670046771357078653226321', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.80055285425460696869023113605', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.56762363806097269611569354962', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.5990043004761398, 'bad_primes': [2, 3, 89], 'central_character': '1068.407', 'conductor': 3204, 'conductor_radical': 534, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3204/1/cd/b/1475/1'], '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': '2-3204-1068.407-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3204-1068.407-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2645174180200682, 'root_angle': 0.22356923262088635, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.55670670046771357078653226321', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1973360183227203627189343991430', 'Lhash_array': ['1973360183227203627189343991430'], 'label': '2-3204-1068.407-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3204/1/cd/b/1475/1'}