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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 1, 'A3': 0, 'A4': 1, 'A5': 0, 'A6': 0, 'A7': -2, 'A8': 1, 'A9': -6, 'Lhash': '1244793531549715028,1338735293501548123', 'a10': [0.0, 0], 'a2': [0.7071067811865476, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-0.7559289460184544, 0], 'a8': [0.3535533905932738, 0], 'a9': [-2.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.997703950241446, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [5, [1, 0, -1]], [7, [1, 2, 1]]], 'bad_primes': [2, 5, 7], 'central_character': '156800.1', 'coefficient_field': '1.1.1.1', 'conductor': 156800, 'conductor_radical': 70, 'degree': 4, 'euler_factors': [[1, -1], [1, 0, 6, 0, 9], [1, 0, -1], [1, 2, 1], [1, 0, 6, 0, 121], [1, 0, -10, 0, 169], [1, -4, 38, -68, 289], [1, 0, 38, 0, 361], [1, 0, 46, 0, 529], [1, 0, 22, 0, 841], [1, -16, 126, -496, 961], [1, 0, -26, 0, 1369], [1, -4, 86, -164, 1681], [1, 0, 70, 0, 1849], [1, -16, 158, -752, 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1.393656919640385, 1.9640087687923882, 2.387380021362305, 2.6057896823374214, 2.5951001754674543], 'positive_zeros': ['0.837608542604674414323310984226177', '2.34423344984301921891298897661732', '3.00381372509091040158022668794666', '3.11732069850814337090071774580729', '4.07505442753619333270812979660164', '4.63923341949934829303628265618552', '5.35297783463712406492518278139300', '5.82344169953684002039972565231392', '6.17616144092315208416665412995313', '6.50661147582867110066747443110687', '7.45420248729985818641828193490952', '7.63810043151096799752774274090886', '8.342925504546681427970604924894861', '8.910824986105461683565850952843142', '8.977646092372605556420891081567740'], 'prelabel': '4-156800-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.778177325798607, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 277685815837569200, 'z1': {'__RealLiteral__': 0, 'data': '0.837608542604674414323310984226177', 'prec': 117}, 'z2': {'__RealLiteral__': 0, 'data': '2.34423344984301921891298897661732', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '3.00381372509091040158022668794666', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.997703950241446, 'bad_primes': [2, 5, 7], 'central_character': '1.1', 'conductor': 156800, 'conductor_radical': 70, 'degree': 4, 'dirichlet_coefficients': [1, 1, 0, 1, 0, 0, -2, 1, -6, 0, 0, 0, 0, -2, 0, 1, 4, -6, 0, 0, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 16, 1, 0, 4, 0, -6, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 16, 0, 3, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 16, 12, 1, 0, 0, 0, 4, 0, 0, -32, -6, 4, 0, 0, 0, 0, 0, -16, 0, 27, 4, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 16, 0, 0, 4, 3, 0, 1], 'euler11': [1, 0, 6, 0, 121], 'euler13': [1, 0, -10, 0, 169], 'euler17': [1, -4, 38, -68, 289], 'euler19': [1, 0, 38, 0, 361], 'euler2': [1, -1, 0, 0, 0], 'euler23': [1, 0, 46, 0, 529], 'euler29': [1, 0, 22, 0, 841], 'euler3': [1, 0, 6, 0, 9], 'euler31': [1, -16, 126, -496, 961], 'euler37': [1, 0, -26, 0, 1369], 'euler41': [1, -4, 86, -164, 1681], 'euler43': [1, 0, 70, 0, 1849], 'euler47': [1, -16, 158, -752, 2209], 'euler5': [1, 0, -1, 0, 0], 'euler53': [1, 0, 102, 0, 2809], 'euler59': [1, 0, 54, 0, 3481], 'euler61': [1, 0, -74, 0, 3721], 'euler67': [1, 0, -10, 0, 4489], 'euler7': [1, 2, 1, 0, 0], 'euler71': [1, 32, 398, 2272, 5041], 'euler73': [1, -4, 150, -292, 5329], 'euler79': [1, 16, 222, 1264, 6241], 'euler83': [1, 0, 102, 0, 6889], 'euler89': [1, -20, 278, -1780, 7921], 'euler97': [1, -4, 198, -388, 9409], 'euler_factors': [[1, -1, 0, 0, 0], [1, 0, 6, 0, 9], [1, 0, -1, 0, 0], [1, 2, 1, 0, 0], [1, 0, 6, 0, 121], [1, 0, -10, 0, 169], [1, -4, 38, -68, 289], [1, 0, 38, 0, 361], [1, 0, 46, 0, 529], [1, 0, 22, 0, 841], [1, -16, 126, -496, 961], [1, 0, -26, 0, 1369], [1, -4, 86, -164, 1681], [1, 0, 70, 0, 1849], [1, -16, 158, -752, 2209], [1, 0, 102, 0, 2809], [1, 0, 54, 0, 3481], [1, 0, -74, 0, 3721], [1, 0, -10, 0, 4489], [1, 32, 398, 2272, 5041], [1, -4, 150, -292, 5329], [1, 16, 222, 1264, 6241], [1, 0, 102, 0, 6889], [1, -20, 278, -1780, 7921], [1, -4, 198, -388, 9409]], 'index': 5, 'instance_types': ['HMF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/TotallyReal/2.2.8.1/holomorphic/2.2.8.1-2450.1-i', 'EllipticCurve/2.2.8.1/2450.1/i'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': True, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-156800-1.1-c1e2-0-5', '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': '4-156800-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.778177325798607, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 277685815837569200, 'z1': {'__RealLiteral__': 0, 'data': '0.837608542604674414323310984226177', 'prec': 117}}
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lfunc_instances • Show schema
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id: 9556098
{'Lhash': '1244793531549715028,1338735293501548123', 'Lhash_array': ['1244793531549715028', '1338735293501548123'], 'label': '4-156800-1.1-c1e2-0-5', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.8.1/2450.1/i'}
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id: 9556242
{'Lhash': '1244793531549715028,1338735293501548123', 'Lhash_array': ['1244793531549715028', '1338735293501548123'], 'label': '4-156800-1.1-c1e2-0-5', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.8.1/holomorphic/2.2.8.1-2450.1-i'}