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lfunc_lfunctions • Show schema
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{'Lhash': '768203143539243307523400177735,1302138328027774185854401207285', 'a10': 0, 'a2': 0, 'a3': -2, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 4, 'a8': 0, 'a9': -1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 652.9112783831148, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1]]], 'bad_primes': [2, 5], 'central_character': '3200.1', 'coefficient_field': '1.1.1.1', 'conductor': 10240000, 'conductor_radical': 10, 'degree': 4, 'euler_factors': [[1], [1, 2, 5, 6, 9], [1], [1, -4, 10, -28, 49], [1, -2, 5, -22, 121], [1, 0, -6, 0, 169], [1, -6, 35, -102, 289], [1, -6, 45, -114, 361], [1, -4, 42, -92, 529], [1, 16, 122, 464, 841], [1, -4, 58, -124, 961], [1, 4, 46, 148, 1369], [1, -10, 75, -410, 1681], [1, 20, 186, 860, 1849], [1, -8, 78, -376, 2209], [1, -4, 78, -212, 2809], [1, -4, 90, -236, 3481], [1, 12, 158, 732, 3721], [1, -14, 165, -938, 4489], [1, 8, 126, 568, 5041], [1, 6, 147, 438, 5329], [1, -20, 250, -1580, 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'3.15978815668361773663467847377583', '3.85383871969369583013552300198649', '4.17038576256479047738542312157029', '4.97880710637258612649134856336352', '5.15976134122521946423128357562977', '5.35221018591912918383327415071314', '5.60792138824045654886823473971741', '6.24994609108507013909849993427322', '6.41030030655787428061247477009553', '7.03676014516620699102890183706324', '7.56887103064768595205763100330053', '7.59489059071052323706659983290251', '7.999074365969824494290242841103695', '8.387793127411064329101240827807676', '9.004226813107531565084218041728691'], 'prelabel': '4-3200e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.054911339164094, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 1438505152133227349, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.60600542720599434226467620275', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.02720602017096475216196914316', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.80009446496141328112468694990', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 652.9112783831148, 'bad_primes': [2, 5], 'central_character': '1.1', 'conductor': 10240000, 'conductor_radical': 10, 'degree': 4, 'dirichlet_coefficients': [1, 0, -2, 0, 0, 0, 4, 0, -1, 0, 2, 0, 0, 0, 0, 0, 6, 0, 6, 0, -8, 0, 4, 0, 0, 0, 6, 0, -16, 0, 4, 0, -4, 0, 0, 0, -4, 0, 0, 0, 10, 0, -20, 0, 0, 0, 8, 0, 6, 0, -12, 0, 4, 0, 0, 0, -12, 0, 4, 0, -12, 0, -4, 0, 0, 0, 14, 0, -8, 0, -8, 0, -6, 0, 0, 0, 8, 0, 20, 0, -4, 0, 6, 0, 0, 0, 32, 0, 18, 0, 0, 0, -8, 0, 0, 0, 12, 0, -2, 0], 'euler11': [1, -2, 5, -22, 121], 'euler13': [1, 0, -6, 0, 169], 'euler17': [1, -6, 35, -102, 289], 'euler19': [1, -6, 45, -114, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -4, 42, -92, 529], 'euler29': [1, 16, 122, 464, 841], 'euler3': [1, 2, 5, 6, 9], 'euler31': [1, -4, 58, -124, 961], 'euler37': [1, 4, 46, 148, 1369], 'euler41': [1, -10, 75, -410, 1681], 'euler43': [1, 20, 186, 860, 1849], 'euler47': [1, -8, 78, -376, 2209], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, -4, 78, -212, 2809], 'euler59': [1, -4, 90, -236, 3481], 'euler61': [1, 12, 158, 732, 3721], 'euler67': [1, -14, 165, -938, 4489], 'euler7': [1, -4, 10, -28, 49], 'euler71': [1, 8, 126, 568, 5041], 'euler73': [1, 6, 147, 438, 5329], 'euler79': [1, -20, 250, -1580, 6241], 'euler83': [1, -6, 157, -498, 6889], 'euler89': [1, -18, 251, -1602, 7921], 'euler97': [1, -12, 102, -1164, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 2, 5, 6, 9], [1, 0, 0, 0, 0], [1, -4, 10, -28, 49], [1, -2, 5, -22, 121], [1, 0, -6, 0, 169], [1, -6, 35, -102, 289], [1, -6, 45, -114, 361], [1, -4, 42, -92, 529], [1, 16, 122, 464, 841], [1, -4, 58, -124, 961], [1, 4, 46, 148, 1369], [1, -10, 75, -410, 1681], [1, 20, 186, 860, 1849], [1, -8, 78, -376, 2209], [1, -4, 78, -212, 2809], [1, -4, 90, -236, 3481], [1, 12, 158, 732, 3721], [1, -14, 165, -938, 4489], [1, 8, 126, 568, 5041], [1, 6, 147, 438, 5329], [1, -20, 250, -1580, 6241], [1, -6, 157, -498, 6889], [1, -18, 251, -1602, 7921], [1, -12, 102, -1164, 9409]], 'index': 22, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3200/2/a/bh'], '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': '4-3200e2-1.1-c1e2-0-22', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-3200e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.054911339164094, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1438505152133227349, 'z1': {'__RealLiteral__': 0, 'data': '0.60600542720599434226467620275', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '768203143539243307523400177735,1302138328027774185854401207285', 'Lhash_array': ['768203143539243307523400177735', '1302138328027774185854401207285'], 'label': '4-3200e2-1.1-c1e2-0-22', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3200/2/a/bh'}