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lfunc_lfunctions • Show schema
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{'A10': 2, 'A2': 2, 'A3': 0, 'A4': 2, 'A5': 1, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 0, 'Lhash': '2044134155702736754', 'a10': [0.6324555320336759, 0], 'a2': [1.414213562373095, 0], 'a3': [0.0, 0], 'a4': [1.0, 0], 'a5': [0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 334.5332592681543, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1, -1]], [7, [1]], [19, [1, -1]]], 'bad_primes': [3, 5, 7, 19], 'central_character': '41895.1', 'coefficient_field': '1.1.1.1', 'conductor': 41895, 'conductor_radical': 1995, 'degree': 2, 'euler_factors': [[1, -2, 2], [1], [1, -1], [1], [1, -3, 11], [1, -1, 13], [1, -3, 17], [1, -1], [1, 4, 23], [1, 5, 29], [1, -8, 31], [1, 12, 37], [1, 8, 41], [1, -4, 43], [1, 7, 47], [1, 4, 53], [1, 10, 59], [1, 2, 61], [1, 12, 67], [1, -8, 71], [1, -6, 73], [1, 15, 79], [1, -4, 83], [1, -10, 89], [1, -7, 97]], 'gamma_factors': [[], [0]], 'index': 52, 'label': '2-41895-1.1-c1-0-52', 'leading_term': '13.5183675478', 'load_key': 'Cremona', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'EllipticCurve/Q/41895/cb', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 3.218783891429359, 5.441871906268574, 5.736168353799273, 3.863405616572795, 0.8949125647276871, -1.194394058281166, -1.016022090731379, 0.9167703163238105, 2.532319333188321, 2.178156261244817, 0.2945014170774237, -1.147963140887762, -0.9506243148600441, -0.02066733372899571, -0.02901215898650664, -1.099354358899983, -1.675011530838153, -0.8323405830040568, 0.2600970839471558, 0.02432028085568409, -1.07797418172087, -1.177212167282481, 0.01715267749611109, 0.6300597172019069, -0.2178563549116845, -0.5360272736450273, 1.32097644595957, 2.97341673287326, 0.7561208807879835, -3.906518515163358, -4.781824196537624, 0.5788992763125852, 6.120257317041535, 4.972641890648406, -0.5994272317544866, -2.288740121338561, 1.909474309793935, 4.878619813184796, 1.736190783240478, -2.458403483563194, -0.9570645213394605, 3.811830112671696, 4.269837771234319, -0.328579223054873, -3.435169384274332, -1.950027489063958, 0.1123721941694693, -0.3345842793505208, -0.8929612597442828, 0.4611509548913522, 1.333106451005994, -0.06970618500933747, -1.336496649959905, -0.5724526407988128, 0.2686306277138282, -0.1994476580286109, -0.1497428402041549, 0.8748359653607232, 0.3216311493779736, -1.734920921870979, -1.677241211109875, 0.3075086565528521, -0.4787411693673177, -3.765120274055259, -3.23403390993731, 1.519382257544061, 2.627214575042433, -1.799068324905786, -3.237388540351723, 1.351335287829602, 2.770097093848666, -3.345029022235547, -7.156755451881924, -2.226559479634716, 2.203548942390386, -1.890705666609593, -6.547481929370964, -2.774781238733677, 3.315543647456092, 2.594468607253247, -1.332811031296355, -1.13080417638613, 1.004280200469198, 0.3527616652793776, -0.7725913042663881, 0.3641681496872724, 0.9082448247965619, -0.5864769611389232, -1.044977641884767, -0.03286725906717764, -0.1758331190612565, -0.3948407345909009, 1.499613773101876, 2.576028413790122, 0.4131008117152885, -1.207784464176954, -0.2059142045511882, -0.447794577010794, -2.164299487242086, -0.7525588637581124, 1.57999038879324, -1.287512791933789, -5.049350588387918, -2.246615015949637, 0.4514115711582415, -6.054005842463487, -12.68434083537494, -7.343305031223095, 1.288465466887651, 0.07799614807689476, -3.984631835770227, -0.1490547873741879, 3.863288066666267, -0.8638349741365928, -5.511958852484798, -1.678070684567126, 2.920550103508074, 1.505280398767445, -0.4677437099833321, 0.3981246825549135], 'positive_zeros': ['1.333656103569807', '1.894110312271258', '2.787509376225228', '3.507927354984715', '3.739387487634896', '4.668778046367403', '5.006300677475566', '5.746627949035212', '6.200356727100317', '6.602686140272123', '7.292011231707679', '7.979132519611100', '8.720738591718327', '9.156637155947707', '9.833999493348878', '10.30073629810823', '10.98384182880248', '11.72143320919532', '11.92242416053673', '12.43384475260446', '12.99099766273929', '13.62196975361356', '13.92478195705830', '14.29047010526864', '14.79162398306541', '15.45164778116778', '15.70274684387529', '16.42102739273413', '16.90919870750112', '17.43536467667952', '17.88470996456914', '18.58408510143961', '18.92554669035394', '19.59688913624974'], 'prelabel': '2-41895-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 18.29025038833953, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 2044134155702736754, 'z1': {'__RealLiteral__': 0, 'data': '1.333656103569807', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '1.894110312271258', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.787509376225228', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 334.5332592681543, 'bad_primes': [3, 5, 7, 19], 'central_character': '1.1', 'conductor': 41895, 'conductor_radical': 1995, 'degree': 2, 'dirichlet_coefficients': [1, 2, 0, 2, 1, 0, 0, 0, 0, 2, 3, 0, 1, 0, 0, -4, 3, 0, 1, 2, 0, 6, -4, 0, 1, 2, 0, 0, -5, 0, 8, -8, 0, 6, 0, 0, -12, 2, 0, 0, -8, 0, 4, 6, 0, -8, -7, 0, 0, 2, 0, 2, -4, 0, 3, 0, 0, -10, -10, 0, -2, 16, 0, -8, 1, 0, -12, 6, 0, 0, 8, 0, 6, -24, 0, 2, 0, 0, -15, -4, 0, -16, 4, 0, 3, 8, 0, 0, 10, 0, 0, -8, 0, -14, 1, 0, 7, 0, 0, 2], 'euler11': [1, -3, 11], 'euler13': [1, -1, 13], 'euler17': [1, -3, 17], 'euler19': [1, -1, 0], 'euler2': [1, -2, 2], 'euler23': [1, 4, 23], 'euler29': [1, 5, 29], 'euler3': [1, 0, 0], 'euler31': [1, -8, 31], 'euler37': [1, 12, 37], 'euler41': [1, 8, 41], 'euler43': [1, -4, 43], 'euler47': [1, 7, 47], 'euler5': [1, -1, 0], 'euler53': [1, 4, 53], 'euler59': [1, 10, 59], 'euler61': [1, 2, 61], 'euler67': [1, 12, 67], 'euler7': [1, 0, 0], 'euler71': [1, -8, 71], 'euler73': [1, -6, 73], 'euler79': [1, 15, 79], 'euler83': [1, -4, 83], 'euler89': [1, -10, 89], 'euler97': [1, -7, 97], 'euler_factors': [[1, -2, 2], [1, 0, 0], [1, -1, 0], [1, 0, 0], [1, -3, 11], [1, -1, 13], [1, -3, 17], [1, -1, 0], [1, 4, 23], [1, 5, 29], [1, -8, 31], [1, 12, 37], [1, 8, 41], [1, -4, 43], [1, 7, 47], [1, 4, 53], [1, 10, 59], [1, 2, 61], [1, 12, 67], [1, -8, 71], [1, -6, 73], [1, 15, 79], [1, -4, 83], [1, -10, 89], [1, -7, 97]], 'index': 52, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/41895/cb'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-41895-1.1-c1-0-52', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-41895-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 18.29025038833953, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2044134155702736754, 'z1': {'__RealLiteral__': 0, 'data': '1.333656103569807', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '2044134155702736754', 'Lhash_array': ['2044134155702736754'], 'label': '2-41895-1.1-c1-0-52', 'type': 'ECQ', 'url': 'EllipticCurve/Q/41895/cb'}