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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': -1, 'A3': 2, 'A4': 1, 'A5': 0, 'A6': -2, 'A7': 0, 'A8': -1, 'A9': 3, 'Lhash': '1761240379116786450,1834044102859205000', 'a10': [0.0, 0], 'a2': [-0.7071067811865476, 0], 'a3': [1.1547005383792515, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [-0.8164965809277259, 0], 'a7': [0.0, 0], 'a8': [-0.3535533905932738, 0], 'a9': [1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 21.22777793843102, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1, -2, 1]], [17, [1, 2, 1]]], 'bad_primes': [2, 3, 17], 'central_character': '332928.1', 'coefficient_field': '1.1.1.1', 'conductor': 332928, 'conductor_radical': 102, 'degree': 4, 'euler_factors': [[1, 1], [1, -2, 1], [1, 0, 10, 0, 25], [1, 0, 10, 0, 49], [1, 0, 22, 0, 121], [1, 0, 22, 0, 169], [1, 2, 1], [1, 8, 54, 152, 361], [1, 0, 10, 0, 529], [1, 0, 58, 0, 841], [1, 0, -38, 0, 961], [1, 0, 10, 0, 1369], [1, -12, 118, -492, 1681], [1, 8, 102, 344, 1849], 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5.766711807629816, 4.883691955035571, 3.698466549648751, 2.3608344353935458, 1.0335069325785327, -0.12871978051853214], 'positive_zeros': ['1.60962373150081650216951780831658', '2.04126125287275460099535053656671', '2.70945693922168405804036190722392', '3.33704793748910042211032942690889', '4.05372696693836488551925909573513', '4.37901858420320549126928147503413', '5.05586136129239314554307726555141', '5.96956680213085492365415051586057', '6.30405633057891562651145051325605', '6.65576551455226941276409559472308', '7.50641789037179894281138679970041', '7.64324124944073722179939518359952', '8.251849824429749124017602038072280', '8.367508603382134314146293072792047'], 'prelabel': '4-332928-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.1464764795303726, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1289441472762297499, 'z1': {'__RealLiteral__': 0, 'data': '1.60962373150081650216951780831658', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.04126125287275460099535053656671', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.70945693922168405804036190722392', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 21.22777793843102, 'bad_primes': [2, 3, 17], 'central_character': '1.1', 'conductor': 332928, 'conductor_radical': 102, 'degree': 4, 'dirichlet_coefficients': [1, -1, 2, 1, 0, -2, 0, -1, 3, 0, 0, 2, 0, 0, 0, 1, -2, -3, -8, 0, 0, 0, 0, -2, -10, 0, 4, 0, 0, 0, 0, -1, 0, 2, 0, 3, 0, 8, 0, 0, 12, 0, -8, 0, 0, 0, 0, 2, -10, 10, -4, 0, 0, -4, 0, 0, -16, 0, -24, 0, 0, 0, 0, 1, 0, 0, -8, -2, 0, 0, 0, -3, 4, 0, -20, -8, 0, 0, 0, 0, 5, -12, 24, 0, 0, 8, 0, 0, -36, 0, 0, 0, 0, 0, 0, -2, 28, 10, 0, -10], 'euler11': [1, 0, 22, 0, 121], 'euler13': [1, 0, 22, 0, 169], 'euler17': [1, 2, 1, 0, 0], 'euler19': [1, 8, 54, 152, 361], 'euler2': [1, 1, 0, 0, 0], 'euler23': [1, 0, 10, 0, 529], 'euler29': [1, 0, 58, 0, 841], 'euler3': [1, -2, 1, 0, 0], 'euler31': [1, 0, -38, 0, 961], 'euler37': [1, 0, 10, 0, 1369], 'euler41': [1, -12, 118, -492, 1681], 'euler43': [1, 8, 102, 344, 1849], 'euler47': [1, 0, -50, 0, 2209], 'euler5': [1, 0, 10, 0, 25], 'euler53': [1, 0, 70, 0, 2809], 'euler59': [1, 24, 262, 1416, 3481], 'euler61': [1, 0, 58, 0, 3721], 'euler67': [1, 8, 150, 536, 4489], 'euler7': [1, 0, 10, 0, 49], 'euler71': [1, 0, 106, 0, 5041], 'euler73': [1, -4, 150, -292, 5329], 'euler79': [1, 0, 58, 0, 6241], 'euler83': [1, -24, 310, -1992, 6889], 'euler89': [1, 36, 502, 3204, 7921], 'euler97': [1, -28, 390, -2716, 9409], 'euler_factors': [[1, 1, 0, 0, 0], [1, -2, 1, 0, 0], [1, 0, 10, 0, 25], [1, 0, 10, 0, 49], [1, 0, 22, 0, 121], [1, 0, 22, 0, 169], [1, 2, 1, 0, 0], [1, 8, 54, 152, 361], [1, 0, 10, 0, 529], [1, 0, 58, 0, 841], [1, 0, -38, 0, 961], [1, 0, 10, 0, 1369], [1, -12, 118, -492, 1681], [1, 8, 102, 344, 1849], [1, 0, -50, 0, 2209], [1, 0, 70, 0, 2809], [1, 24, 262, 1416, 3481], [1, 0, 58, 0, 3721], [1, 8, 150, 536, 4489], [1, 0, 106, 0, 5041], [1, -4, 150, -292, 5329], [1, 0, 58, 0, 6241], [1, -24, 310, -1992, 6889], [1, 36, 502, 3204, 7921], [1, -28, 390, -2716, 9409]], 'index': 29, 'instance_types': ['ECNF', 'BMF'], 'instance_urls': ['EllipticCurve/2.0.8.1/5202.5/d', 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/5202.5/d'], 'is_instance_Artin': False, 'is_instance_BMF': True, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, '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': '4-332928-1.1-c1e2-0-29', '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': 1, 'prelabel': '4-332928-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.1464764795303726, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1289441472762297499, 'z1': {'__RealLiteral__': 0, 'data': '1.60962373150081650216951780831658', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9880527
{'Lhash': '1761240379116786450,1834044102859205000', 'Lhash_array': ['1761240379116786450', '1834044102859205000'], 'label': '4-332928-1.1-c1e2-0-29', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/5202.5/d'}
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id: 9881248
{'Lhash': '1761240379116786450,1834044102859205000', 'Lhash_array': ['1761240379116786450', '1834044102859205000'], 'label': '4-332928-1.1-c1e2-0-29', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.8.1/5202.5/d'}