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lfunc_lfunctions • Show schema
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{'Lhash': '394330714436865268083192380237', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.9902680687415704, 0.13917310096006544], 'a4': [0.03489949670250097, 0.9993908270190958], 'a5': [-0.6637213667384003, 0.16548432281323164], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [0.9612616959383189, -0.27563735581699916], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.630445396272019, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.9902680687415704, -0.13917310096006544]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 11], 'central_character': '3267.608', 'coefficient_field': 'CDF', 'conductor': 3267, 'conductor_radical': 33, 'conjugate': '1975993027274250692038685619137', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [-0.03489949670250097, -0.9993908270190958]], [[1.0, 0], [0.9902680687415704, -0.13917310096006544]], [[1.0, 0], [0.6637213667384003, -0.16548432281323164], [0.882947592858927, 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'4.23799905652438875176905332396994', '4.54850656894304302038756499881822', '5.57251119587918491108831307307805', '6.09857393584215489460560895307084', '6.86817424538423577013830040743508', '7.55177775625253933474770519691529', '8.465115423942366338454973351464408'], 'prelabel': '2-3267-297.14-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.27688895220846, 'root_angle': -0.9517628436947595, 'root_number': '-0.98853954499855418491740441530067 - 0.15096214086336834196441362432901*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.47588142184737975', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.31107208434711384387016312711', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.45050175155305111811924097416', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.64709461768174517553248449546', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.630445396272019, 'bad_primes': [3, 11], 'central_character': '297.14', 'conductor': 3267, 'conductor_radical': 33, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3267/1/be/a/608/1'], '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': '2-3267-297.14-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': '2-3267-297.14-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.27688895220846, 'root_angle': -0.47588142184737975, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.31107208434711384387016312711', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '394330714436865268083192380237', 'Lhash_array': ['394330714436865268083192380237'], 'label': '2-3267-297.14-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3267/1/be/a/608/1'}