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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': 1, 'Lhash': '287791997452670306,717858818600636415', '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': [0.3333333333333333, 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, 3]], [17, [1, 0, -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, 3], [1, 0, 10, 0, 25], [1, 0, -2, 0, 49], [1, 0, -14, 0, 121], [1, 0, 22, 0, 169], [1, 0, -1], [1, 8, 54, 152, 361], [1, 0, 46, 0, 529], [1, 0, 58, 0, 841], [1, 0, 46, 0, 961], [1, 0, 58, 0, 1369], [1, 0, 46, 0, 1681], [1, -16, 150, -688, 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-0.14005642417112904, -0.654104874388605, -1.1142676507358351, -1.4294904870064309, -1.5263202506414897, -1.3619199017070833], 'positive_zeros': ['0.984825652924800667366751863258871', '2.18485014981353314837233550044604', '2.43284679117287849237620685834639', '3.63156167971905155642785987994977', '4.09840146621603381404148858714252', '4.61798148851481694877863510515379', '5.47429037678013332061015433309093', '5.66883563130032604301217732019776', '6.35150301548018653136035247694595', '6.41629415296385744943735530690562', '7.25002689502959545343122319948388', '7.47968504825111737277392388245613', '8.241072165068691921287501783547819', '8.425519687930285964215233261880586'], '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': 1005650816053306721, 'z1': {'__RealLiteral__': 0, 'data': '0.984825652924800667366751863258871', 'prec': 117}, 'z2': {'__RealLiteral__': 0, 'data': '2.18485014981353314837233550044604', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.43284679117287849237620685834639', '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, 1, 0, 0, -2, 0, 0, 0, 1, 0, -1, -8, 0, 0, 0, 0, 2, -10, 0, 4, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 8, 0, 0, 0, 0, 16, 0, 0, 0, 0, -2, 2, 10, 0, 0, 12, -4, 0, 0, 16, 0, 0, 0, 0, 0, 0, 1, 0, 0, 16, 0, 0, 0, 0, -1, 4, 0, 20, -8, 0, 0, 0, 0, -11, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 28, -2, 0, -10], 'euler11': [1, 0, -14, 0, 121], 'euler13': [1, 0, 22, 0, 169], 'euler17': [1, 0, -1, 0, 0], 'euler19': [1, 8, 54, 152, 361], 'euler2': [1, 1, 0, 0, 0], 'euler23': [1, 0, 46, 0, 529], 'euler29': [1, 0, 58, 0, 841], 'euler3': [1, 2, 3, 0, 0], 'euler31': [1, 0, 46, 0, 961], 'euler37': [1, 0, 58, 0, 1369], 'euler41': [1, 0, 46, 0, 1681], 'euler43': [1, -16, 150, -688, 1849], 'euler47': [1, 0, 94, 0, 2209], 'euler5': [1, 0, 10, 0, 25], 'euler53': [1, -12, 142, -636, 2809], 'euler59': [1, 0, 118, 0, 3481], 'euler61': [1, 0, 106, 0, 3721], 'euler67': [1, -16, 198, -1072, 4489], 'euler7': [1, 0, -2, 0, 49], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, -4, 150, -292, 5329], 'euler79': [1, 0, 94, 0, 6241], 'euler83': [1, 0, 166, 0, 6889], 'euler89': [1, 0, 142, 0, 7921], 'euler97': [1, -28, 390, -2716, 9409], 'euler_factors': [[1, 1, 0, 0, 0], [1, 2, 3, 0, 0], [1, 0, 10, 0, 25], [1, 0, -2, 0, 49], [1, 0, -14, 0, 121], [1, 0, 22, 0, 169], [1, 0, -1, 0, 0], [1, 8, 54, 152, 361], [1, 0, 46, 0, 529], [1, 0, 58, 0, 841], [1, 0, 46, 0, 961], [1, 0, 58, 0, 1369], [1, 0, 46, 0, 1681], [1, -16, 150, -688, 1849], [1, 0, 94, 0, 2209], [1, -12, 142, -636, 2809], [1, 0, 118, 0, 3481], [1, 0, 106, 0, 3721], [1, -16, 198, -1072, 4489], [1, 0, 142, 0, 5041], [1, -4, 150, -292, 5329], [1, 0, 94, 0, 6241], [1, 0, 166, 0, 6889], [1, 0, 142, 0, 7921], [1, -28, 390, -2716, 9409]], 'index': 14, 'instance_types': ['HMF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/TotallyReal/2.2.24.1/holomorphic/2.2.24.1-578.1-d', 'EllipticCurve/2.2.24.1/578.1/d'], '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': '4-332928-1.1-c1e2-0-14', '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': 1005650816053306721, 'z1': {'__RealLiteral__': 0, 'data': '0.984825652924800667366751863258871', 'prec': 117}}
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lfunc_instances • Show schema
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id: 9512624
{'Lhash': '287791997452670306,717858818600636415', 'Lhash_array': ['287791997452670306', '717858818600636415'], 'label': '4-332928-1.1-c1e2-0-14', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.24.1/578.1/d'}
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id: 9512894
{'Lhash': '287791997452670306,717858818600636415', 'Lhash_array': ['287791997452670306', '717858818600636415'], 'label': '4-332928-1.1-c1e2-0-14', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.24.1/holomorphic/2.2.24.1-578.1-d'}