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lfunc_lfunctions • Show schema
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{'Lhash': '1356201270723263718366972212857', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-0.7720782153751133, -1.5504500086565771], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [2.6023579819230793, 0.4772137193346791], 'a8': [0, 0], 'a9': [-1.8077904586863602, 2.3941373514237982], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 16.768584424468887, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0.7720782153751133, 1.5504500086565771]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-2.6023579819230793, -0.4772137193346791]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '2100.1601', 'coefficient_field': 'CDF', 'conductor': 2100, 'conductor_radical': 210, 'conjugate': '789546916357224404133006019143', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.7720782153751133, 1.5504500086565771]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.6023579819230793, -0.4772137193346791]], [[1.0, 0], 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[[1.0, 0], [-5.5841424047304065, -9.672018361692912], [-33.5, 58.023702053557386]], [[1.0, 0], [0, 7.970774206603549], [-71.0, 0]], [[1.0, 0], [-10.737719886970684, 6.199425467225322], [36.5, -63.21985447626402]], [[1.0, 0], [-1.1212661956073273, 1.9420900196013537], [-39.5, -68.41600689897065]], [[1.0, 0], [-5.264863306536947, 0], [83.0, 0]], [[1.0, 0], [-7.657226149001477, 13.262704735115532], [-44.5, -77.07626093681505]], [[1.0, 0], [0, 15.901647187088042], [-97.0, 0]], [[1.0, 0], [3.8329471132941375, 6.638859142949908], [-50.5, 87.4685657822283]], [[1.0, 0], [0.9600316980824254, 0.5542745593184618], [51.5, 89.20061658979718]], [[1.0, 0], [1.2743552977121273, 0.7357493741773223], [53.5, 92.66471820493493]], [[1.0, 0], [-4.668983411087224, -8.086916487699316], [-54.5, 94.39676901250381]], [[1.0, 0], [0, -11.977257444833068], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 30, 'label': '2-2100-21.5-c1-0-30', 'leading_term': 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'8.403297092128204918208725396904375', '9.242759155586900206346562164290668'], 'prelabel': '2-2100-21.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.0949462053205155, 'root_angle': 0.4510089972966299, 'root_number': '0.1533028520805735170683702046131854047949140059985802875 + 0.9881792527390775957734683105119945756087269169174683799*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.22550449864831495', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.06985416208464031276886379526', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.58896265673921202010236145739', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.65209372903049708836873725762', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 16.768584424468887, 'bad_primes': [2, 3, 5, 7], 'central_character': '21.5', 'conductor': 2100, 'conductor_radical': 210, 'degree': 2, 'index': 30, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2100/2/bi/n/1601/7'], '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': '2-2100-21.5-c1-0-30', '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': '2-2100-21.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.0949462053205155, 'root_angle': 0.22550449864831495, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.06985416208464031276886379526', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1356201270723263718366972212857', 'Lhash_array': ['1356201270723263718366972212857'], 'label': '2-2100-21.5-c1-0-30', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2100/2/bi/n/1601/7'}