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lfunc_lfunctions • Show schema
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{'Lhash': '858407491619566705429130636818', 'a10': [140.38475772933683, 0], 'a2': [4.898979485566356, 2.8284271247461903], 'a3': [0, 0], 'a4': [16.0, 27.712812921102035], 'a5': [21.4919390063195, -12.408376770705582], 'a6': [0, 0], 'a7': [3.098076211353316, -5.366025403784438], 'a8': [0, 181.01933598375618], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 37.26876154641587, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-4.898979485566356, -2.8284271247461903]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '162.107', 'coefficient_field': 'CDF', 'conductor': 162, 'conductor_radical': 6, 'conjugate': '1849216079183591578070110780270', 'degree': 2, 'euler_factors': [[[1.0, 0], [-4.898979485566356, -2.8284271247461903]], [[1.0, 0], [0, 0]], [[1.0, 0], [-21.4919390063195, 12.408376770705582], [7812.5, -13531.646934131853]], [[1.0, 0], [-3.098076211353316, 5.366025403784438], 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[[1.0, 0], [-1094192.1879687298, 631732.1542689317], [1040975876304.5, -1803023107212.929]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 11, 'label': '2-162-9.2-c6-0-11', 'leading_term': '2.777272627657934319614942996825850994080044524513497668', 'load_key': 'CMFs-workshop', 'motivic_weight': 6, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [6], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/162/7/d/f/107/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0703125', 'prec': 30}, 'plot_values': [2.7772726276579345, 2.552778835001404, 2.3034905938811217, 2.0329918722574902, 1.7451302374205762, 1.4439690787115407, 1.133737146698324, 0.8187756536089181, 0.503483212963861, 0.19225894351811734, -0.11055587703266918, -0.40073715114651826, -0.6742377544822462, -0.9272471560255097, -1.1562501471535245, -1.3580838708371528, -1.5299922563433332, -1.6696768882714663, -1.775343276148596, 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'2.27057662456083825419372236582880', '3.51229886318853810924615294046392', '4.84613263066478634688569853068099', '5.93981266219915084449713402762599', '7.08897515640434676701653885923034', '8.405935909361931091511213521824410', '9.716868235526161498573887970795058', '10.53304759754674894293455595804807', '11.69877763219302206542862469519370'], 'prelabel': '2-162-9.2-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.104814620151529, 'root_angle': -0.5277777777777778, 'root_number': '-0.0871557427476581735580642708374735513777011561497026726 - 0.9961946980917455322950104024738880461835626726458509745*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.2638888888888889', 'prec': 64}, 'spectral_label': 'c6-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.67716411088750949645448610336', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.27057662456083825419372236583', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.51229886318853810924615294046', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 37.26876154641587, 'bad_primes': [2, 3], 'central_character': '9.2', 'conductor': 162, 'conductor_radical': 6, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/162/7/d/f/107/3'], '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': '2-162-9.2-c6-0-11', 'motivic_weight': 6, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [6], 'order_of_vanishing': 0, 'prelabel': '2-162-9.2-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.104814620151529, 'root_angle': -0.2638888888888889, 'self_dual': False, 'spectral_label': 'c6-0', 'z1': {'__RealLiteral__': 0, 'data': '0.67716411088750949645448610336', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '858407491619566705429130636818', 'Lhash_array': ['858407491619566705429130636818'], 'label': '2-162-9.2-c6-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/162/7/d/f/107/3'}