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lfunc_lfunctions • Show schema
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{'Lhash': '2441558004508633348996587168284', 'a10': [-1.945826201310958, 3.898493749924725], 'a2': [0.08572422190793073, 1.4116130340069406], 'a3': [1.6927283552396108, 0.36697508821145], 'a4': [-1.9853027155565597, 0.2420188579506767], 'a5': [2.6681800766564447, 1.5404744855039947], 'a6': [-0.3729189965207225, 2.420936063185886], 'a7': [-1.463066402379498, -2.204413006273623], 'a8': [-0.5118255049014375, -2.7817323114441455], 'a9': [2.730658569264397, 1.2423782749641579], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.341486753957511, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.08572422190793073, -1.4116130340069406]]], [3, [[1.0, 0], [-1.6927283552396108, -0.36697508821145]]], [7, [[1.0, 0], [1.463066402379498, 2.204413006273623]]]], 'bad_primes': [2, 3, 7], 'central_character': '168.5', 'coefficient_field': 'CDF', 'conductor': 168, 'conductor_radical': 42, 'conjugate': 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'4.66693758864834600289615720872052', '5.83199516111567949942628110754216', '7.66147835900374497053093603160835', '8.993503056162948148264820729289658', '9.564077373432417894210749854087272', '10.09465571923622014919948980214285', '11.97008737398970704778166157661807', '12.67430146798281752823836461251235'], 'prelabel': '2-168-168.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': -0.46946288223554394, 'root_number': '0.09578809500113883 - 0.9954017484694573*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.234731441118', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.92604965758628772659653896428', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.85720545392912396130966329342', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.66693758864834600289615720872', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.341486753957511, 'bad_primes': [2, 3, 7], 'central_character': '168.5', 'conductor': 168, 'conductor_radical': 42, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/168/2/ba/c/5/13'], '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': '2-168-168.5-c1-0-12', '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': '2-168-168.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': -0.23473144111777197, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.92604965758628772659653896428', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2441558004508633348996587168284', 'Lhash_array': ['2441558004508633348996587168284'], 'label': '2-168-168.5-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/168/2/ba/c/5/13'}