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lfunc_lfunctions • Show schema
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{'Lhash': '2773699844170045711379343333447', 'a10': [19.79898987322333, -34.292856398964496], 'a2': [1.0, 1.7320508075688772], 'a3': [-3.5355339059327378, 6.123724356957945], 'a4': [-2.0, 3.4641016151377544], 'a5': [-9.899494936611665, -17.146428199482248], 'a6': [-14.142135623730951, -5.804825213226668e-61], 'a7': [0.0, 0.0], 'a8': [-8.0, 0.0], 'a9': [-11.5, -19.91858428704209], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.782187180562583, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, -1.7320508075688772]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 7], 'central_character': '98.67', 'coefficient_field': 'CDF', 'conductor': 98, 'conductor_radical': 14, 'conjugate': '80190318118192862590290170594', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, -1.7320508075688772]], [[1.0, 0], [3.5355339059327378, -6.123724356957945], [-13.5, -23.382685902179844]], [[1.0, 0], [9.899494936611665, 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'2-98-7.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4046178866012338, 'root_angle': 0.5634637625061879, 'root_number': '-0.1980589951144843 + 0.9801901011815212*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.281731881253', 'prec': 47}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.18806336988336164400032956730', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.79113970056088417285437527670', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.76271804229069354324198601339', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.782187180562583, 'bad_primes': [2, 7], 'central_character': '7.4', 'conductor': 98, 'conductor_radical': 14, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/98/4/c/h/67/1'], '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': '2-98-7.4-c3-0-7', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-98-7.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4046178866012338, 'root_angle': 0.28173188125309395, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '2.18806336988336164400032956730', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2773699844170045711379343333447', 'Lhash_array': ['2773699844170045711379343333447'], 'label': '2-98-7.4-c3-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/98/4/c/h/67/1'}