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lfunc_lfunctions • Show schema
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{'Lhash': '801830407084792807364301127341', 'a10': [16.488192217990587, 28.558386646521477], 'a2': [-4.21476282560816, 0.0], 'a3': [0.0, 0.0], 'a4': [9.764225676128481, 0.0], 'a5': [-3.9120095009406515, -6.775799215321376], 'a6': [0.0, 0.0], 'a7': [-15.900183057475832, 9.496535091219245], 'a8': [-7.435792795729741, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.151360991084982, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [15.900183057475832, -9.496535091219245]]]], 'bad_primes': [3, 7], 'central_character': '189.37', 'coefficient_field': 'CDF', 'conductor': 189, 'conductor_radical': 21, 'conjugate': '986924416475342867286844292301', 'degree': 2, 'euler_factors': [[[1.0, 0], [4.21476282560816, 0], [8.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.9120095009406515, 6.775799215321376], [-62.5, 108.25317547305482]], [[1.0, 0], [15.900183057475832, -9.496535091219245]], 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 7, 'label': '2-189-63.58-c3-0-7', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/189/4/h/a/37/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.5492957081761415, 0.5093930446906793, 0.4340148637325625, 0.3244110067086243, 0.18252049655323604, 0.011184729622715153, -0.18560391227592007, -0.4024548854721928, -0.6323743489383408, -0.8666434970600727, -1.0948197009276803, -1.304894749098764, -1.4836363225348177, -1.617127423690081, -1.691503795651432, -1.6938717018540759, -1.6133685045945916, -1.4423074921680339, -1.1773280667509418, -0.8204548444165446, -0.37995682875401376, 0.12910695959483146, 0.6847639759732267, 1.2585188276040584, 1.8163214030272707, 2.3201350316059104, 2.7300763949752596, 3.007041120266884, 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'10.13742304606455604098645629035472', '10.73041456725548331497856326254240', '11.62399793064738780629699349393325'], 'prelabel': '2-189-63.58-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.339365357532024, 'root_angle': -0.06274135261336208, 'root_number': '0.9806370748368234 - 0.19583392825421853*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0313706763067', 'prec': 54}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.63253266076664205165872458152', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.59458503834065716607451833788', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.18808599673220062320430392235', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 11.151360991084982, 'bad_primes': [3, 7], 'central_character': '63.58', 'conductor': 189, 'conductor_radical': 21, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/189/4/h/a/37/3'], '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': '2-189-63.58-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': '2-189-63.58-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.339365357532024, 'root_angle': -0.03137067630668104, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.63253266076664205165872458152', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '801830407084792807364301127341', 'Lhash_array': ['801830407084792807364301127341'], 'label': '2-189-63.58-c3-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/189/4/h/a/37/3'}