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lfunc_lfunctions • Show schema
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{'Lhash': '980353324116178026522886734871', 'a10': [-0.5, -0.8660254037844386], 'a2': [-1.0, 0.0], 'a3': [1.2148504480934026, 1.2345599980427273], 'a4': [1.0, 0.0], 'a5': [0.5, 0.8660254037844386], 'a6': [-1.2148504480934026, -1.2345599980427273], 'a7': [-1.095944365924365, -2.4080917646133506], 'a8': [-1.0, 0.0], 'a9': [-0.048276777534517375, 2.999611533640795], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.030575327340666, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [3, [[1.0, 0], [-1.2148504480934026, -1.2345599980427273]]], [5, [[1.0, 0], [-0.5, -0.8660254037844386]]], [7, [[1.0, 0], [1.095944365924365, 2.4080917646133506]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '630.121', 'coefficient_field': 'CDF', 'conductor': 630, 'conductor_radical': 210, 'conjugate': '2237244130439827636062429196986', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [-1.2148504480934026, 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'8.157934905585564057174533529954406', '8.360057356716816650586045993379775', '9.568261038265502533741354219232381', '9.847468808106683104547834039951908'], 'prelabel': '2-630-63.58-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2428944084242275, 'root_angle': -0.5398876931900537, 'root_number': '-0.12498318563034579 - 0.9921588599159363*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.269943846595', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.77336241069871618124826443583', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.43552873561276168320235241440', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.05968718923128761716192659330', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.030575327340666, 'bad_primes': [2, 3, 5, 7], 'central_character': '63.58', 'conductor': 630, 'conductor_radical': 210, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/630/2/i/i/121/7'], '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': '2-630-63.58-c1-0-9', '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': '2-630-63.58-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2428944084242275, 'root_angle': -0.26994384659502685, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.77336241069871618124826443583', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '980353324116178026522886734871', 'Lhash_array': ['980353324116178026522886734871'], 'label': '2-630-63.58-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/630/2/i/i/121/7'}