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lfunc_lfunctions • Show schema
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{'Lhash': '639039282199383066620190618381', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': -19, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 106.20343801033316, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1]]], 'bad_primes': [2, 3, 5], 'central_character': '1800.1', 'coefficient_field': '1.1.1.1', 'conductor': 1800, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[1], [1], [1], [1, 19, 343], [1, 22, 1331], [1, -1, 2197], [1, -58, 4913], [1, 53, 6859], [1, 58, 12167], [1, 22, 24389], [1, 35, 29791], [1, 270, 50653], [1, -468, 68921], [1, 431, 79507], [1, -230, 103823], [1, 0, 148877], [1, 446, 205379], [1, -127, 226981], [1, 811, 300763], [1, 36, 357911], [1, -522, 389017], [1, -1368, 493039], [1, -1138, 571787], [1, 144, 704969], [1, 1079, 912673], [1, -1440, 1030301], [1, -124, 1092727], [1, -432, 1225043], [1, -701, 1295029], [1, -1044, 1442897]], 'euler_factors_factorization': [[1], [1], [1], [[[1, 19, 343], 1]], [[[1, 22, 1331], 1]], [[[1, -1, 2197], 1]], [[[1, -58, 4913], 1]], [[[1, 53, 6859], 1]], [[[1, 58, 12167], 1]], [[[1, 22, 24389], 1]], [[[1, 35, 29791], 1]], [[[1, 270, 50653], 1]], [[[1, -468, 68921], 1]], [[[1, 431, 79507], 1]], [[[1, -230, 103823], 1]], [[[1, 0, 148877], 1]], [[[1, 446, 205379], 1]], [[[1, -127, 226981], 1]], [[[1, 811, 300763], 1]], [[[1, 36, 357911], 1]], [[[1, -522, 389017], 1]], [[[1, -1368, 493039], 1]], [[[1, -1138, 571787], 1]], [[[1, 144, 704969], 1]], [[[1, 1079, 912673], 1]], [[[1, -1440, 1030301], 1]], [[[1, -124, 1092727], 1]], [[[1, -432, 1225043], 1]], [[[1, -701, 1295029], 1]], [[[1, -1044, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 10, 'label': '2-1800-1.1-c3-0-10', 'leading_term': '1.238106820735683165566622607835100000000000000000000000000000000000000000000000000000000000', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1800/4/a/g', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.2381068207356831, 1.2241542727449053, 1.182470406816514, 1.1135757143158185, 1.018334821365016, 0.8979520264723211, 0.7539647168460065, 0.5882343497434862, 0.4029346269914487, 0.20053645436789827, -0.016210734165298286, -0.24430169234534904, -0.4805024798036178, -0.7213822743477916, -0.9633500731344752, -1.2026963561001194, -1.4356396421164965, -1.6583777077872381, -1.8671430651383125, -2.058262112812707, -2.2282171913708777, -2.3737105928852418, -2.491729404373466, -2.57960990998644, -2.6351001444193844, -2.65641908568103, -2.6423109046731064, -2.5920926569751135, -2.50569381304183, -2.3836860800504396, -2.227302074170451, -2.0384415571564363, -1.8196641556279132, -1.574167733505211, -1.3057518845979386, -1.0187663485171135, 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'rational': True, 'root_analytic_conductor': 10.305505228291, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'trace_hash': 1012603067331352868, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.50411310662759094186357961075', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.94545679460177814690827762679', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.02609427807122887681750241964', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 106.20343801033316, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 1800, 'conductor_radical': 30, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, -19, 0, 0, 0, -22, 0, 1, 0, 0, 0, 58, 0, -53, 0, 0, 0, -58, 0, 0, 0, 0, 0, -22, 0, -35, 0, 0, 0, 0, 0, -270, 0, 0, 0, 468, 0, -431, 0, 0, 0, 230, 0, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, -446, 0, 127, 0, 0, 0, 0, 0, -811, 0, 0, 0, -36, 0, 522, 0, 0, 0, 418, 0, 1368, 0, 0, 0, 1138, 0, 0, 0, 0, 0, -144, 0, -19, 0, 0, 0, 0, 0, -1079, 0, 0, 0], 'euler11': [1, 22, 1331], 'euler13': [1, -1, 2197], 'euler17': [1, -58, 4913], 'euler19': [1, 53, 6859], 'euler2': [1, 0, 0], 'euler23': [1, 58, 12167], 'euler29': [1, 22, 24389], 'euler3': [1, 0, 0], 'euler31': [1, 35, 29791], 'euler37': [1, 270, 50653], 'euler41': [1, -468, 68921], 'euler43': [1, 431, 79507], 'euler47': [1, -230, 103823], 'euler5': [1, 0, 0], 'euler53': [1, 0, 148877], 'euler59': [1, 446, 205379], 'euler61': [1, -127, 226981], 'euler67': [1, 811, 300763], 'euler7': [1, 19, 343], 'euler71': [1, 36, 357911], 'euler73': [1, -522, 389017], 'euler79': [1, -1368, 493039], 'euler83': [1, -1138, 571787], 'euler89': [1, 144, 704969], 'euler97': [1, 1079, 912673], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 0, 0], [1, 19, 343], [1, 22, 1331], [1, -1, 2197], [1, -58, 4913], [1, 53, 6859], [1, 58, 12167], [1, 22, 24389], [1, 35, 29791], [1, 270, 50653], [1, -468, 68921], [1, 431, 79507], [1, -230, 103823], [1, 0, 148877], [1, 446, 205379], [1, -127, 226981], [1, 811, 300763], [1, 36, 357911], [1, -522, 389017], [1, -1368, 493039], [1, -1138, 571787], [1, 144, 704969], [1, 1079, 912673]], 'index': 10, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1800/4/a/g/1/1', 'ModularForm/GL2/Q/holomorphic/1800/4/a/g'], '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': '2-1800-1.1-c3-0-10', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-1800-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 10.305505228291, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 1012603067331352868, 'z1': {'__RealLiteral__': 0, 'data': '0.50411310662759094186357961075', 'prec': 103}}
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lfunc_instances • Show schema
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id: 21180943
{'Lhash': '639039282199383066620190618381', 'Lhash_array': ['639039282199383066620190618381'], 'label': '2-1800-1.1-c3-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1800/4/a/g'}
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id: 24592239
{'Lhash': '639039282199383066620190618381', 'Lhash_array': ['639039282199383066620190618381'], 'label': '2-1800-1.1-c3-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1800/4/a/g/1/1'}