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lfunc_lfunctions • Show schema
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{'Lhash': '1684556254151793988392691181132', 'a10': 0, 'a2': 0, 'a3': -4, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': -7, 'a8': 0, 'a9': -11, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 41.30133700401845, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1]], [7, [1, 7]]], 'bad_primes': [2, 5, 7], 'central_character': '700.1', 'coefficient_field': '1.1.1.1', 'conductor': 700, 'conductor_radical': 70, 'degree': 2, 'euler_factors': [[1], [1, 4, 27], [1], [1, 7], [1, 12, 1331], [1, -82, 2197], [1, -30, 4913], [1, -68, 6859], [1, 216, 12167], [1, -246, 24389], [1, 112, 29791], [1, 110, 50653], [1, 246, 68921], [1, -172, 79507], [1, 192, 103823], [1, 558, 148877], [1, -540, 205379], [1, -110, 226981], [1, 140, 300763], [1, 840, 357911], [1, -550, 389017], [1, 208, 493039], [1, 516, 571787], [1, 1398, 704969], [1, 1586, 912673], [1, 1242, 1030301], [1, 680, 1092727], [1, 996, 1225043], [1, -1382, 1295029], [1, -750, 1442897]], 'euler_factors_factorization': [[1], [[[1, 4, 27], 1]], [1], [[[1, 7], 1]], [[[1, 12, 1331], 1]], [[[1, -82, 2197], 1]], [[[1, -30, 4913], 1]], [[[1, -68, 6859], 1]], [[[1, 216, 12167], 1]], [[[1, -246, 24389], 1]], [[[1, 112, 29791], 1]], [[[1, 110, 50653], 1]], [[[1, 246, 68921], 1]], [[[1, -172, 79507], 1]], [[[1, 192, 103823], 1]], [[[1, 558, 148877], 1]], [[[1, -540, 205379], 1]], [[[1, -110, 226981], 1]], [[[1, 140, 300763], 1]], [[[1, 840, 357911], 1]], [[[1, -550, 389017], 1]], [[[1, 208, 493039], 1]], [[[1, 516, 571787], 1]], [[[1, 1398, 704969], 1]], [[[1, 1586, 912673], 1]], [[[1, 1242, 1030301], 1]], [[[1, 680, 1092727], 1]], [[[1, 996, 1225043], 1]], [[[1, -1382, 1295029], 1]], [[[1, -750, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 18, 'label': '2-700-1.1-c3-0-18', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/700/4/a/e', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [-1.1534456052129343e-60, 0.17012769148721288, 0.3378204234209215, 0.5006554857456899, 0.6562352993742006, 0.80220152837503, 0.9362509564746107, 1.0561535669271367, 1.1597731444818513, 1.2450905765703335, 1.310229873109521, 1.3534867560644963, 1.373359496949416, 1.368581508603306, 1.3381550325724876, 1.2813851107362038, 1.1979128945787623, 1.0877472325141992, 0.9512933892602511, 0.7893776953260276, 0.6032669025994103, 0.3946810366001924, 0.1657985893576056, -0.08074700951227555, -0.3418805715480806, -0.6141087312200868, -0.8935544702161947, -1.176002873643678, -1.4569581250142951, -1.7317114370019537, -1.9954192841668004, -2.243190959802385, -2.4701841306246877, -2.6717067200508375, -2.843323124010365, -2.9809624638745227, -3.0810263207440975, -3.1404931855051017, -3.1570167108011318, -3.129014774581009, -3.055746369078312, 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0.043759447670779175, 0.29268609513052307, 0.42829937951590175, 0.4367687519644169, 0.310939040729693, 0.05084683117293593, -0.3361484107883562, -0.8356315023743308, -1.4267879049177064, -2.0834182274962436, -2.775259267604375, -3.4695420466546527, -4.132703048263085, -4.732155183297516, -5.238020518323189, -5.624727854037194, -5.872384852483693, -5.967846287869343, -5.905416525147126, -5.687144620533437, -5.3226933611626075], 'positive_zeros': ['1.32888057154590103210472452355619', '2.98433511020767117727399390021707', '3.98996572450602387798519540015539', '5.32073503935097225800223353302756', '5.99223084513934842475474184116213', '6.69982066208537100979911062295291', '8.022326298776415156122080265755807', '8.632013842436056915010106690352487', '9.824534535444736393360971976686410'], 'prelabel': '2-700-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.426611626978749, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'trace_hash': 1518557510505095589, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.32888057154590103210472452356', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.98433511020767117727399390022', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.98996572450602387798519540016', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 41.30133700401845, 'bad_primes': [2, 5, 7], 'central_character': '1.1', 'conductor': 700, 'conductor_radical': 70, 'degree': 2, 'dirichlet_coefficients': [1, 0, -4, 0, 0, 0, -7, 0, -11, 0, -12, 0, 82, 0, 0, 0, 30, 0, 68, 0, 28, 0, -216, 0, 0, 0, 152, 0, 246, 0, -112, 0, 48, 0, 0, 0, -110, 0, -328, 0, -246, 0, 172, 0, 0, 0, -192, 0, 49, 0, -120, 0, -558, 0, 0, 0, -272, 0, 540, 0, 110, 0, 77, 0, 0, 0, -140, 0, 864, 0, -840, 0, 550, 0, 0, 0, 84, 0, -208, 0, -311, 0, -516, 0, 0, 0, -984, 0, -1398, 0, -574, 0, 448, 0, 0, 0, -1586, 0, 132, 0], 'euler11': [1, 12, 1331], 'euler13': [1, -82, 2197], 'euler17': [1, -30, 4913], 'euler19': [1, -68, 6859], 'euler2': [1, 0, 0], 'euler23': [1, 216, 12167], 'euler29': [1, -246, 24389], 'euler3': [1, 4, 27], 'euler31': [1, 112, 29791], 'euler37': [1, 110, 50653], 'euler41': [1, 246, 68921], 'euler43': [1, -172, 79507], 'euler47': [1, 192, 103823], 'euler5': [1, 0, 0], 'euler53': [1, 558, 148877], 'euler59': [1, -540, 205379], 'euler61': [1, -110, 226981], 'euler67': [1, 140, 300763], 'euler7': [1, 7, 0], 'euler71': [1, 840, 357911], 'euler73': [1, -550, 389017], 'euler79': [1, 208, 493039], 'euler83': [1, 516, 571787], 'euler89': [1, 1398, 704969], 'euler97': [1, 1586, 912673], 'euler_factors': [[1, 0, 0], [1, 4, 27], [1, 0, 0], [1, 7, 0], [1, 12, 1331], [1, -82, 2197], [1, -30, 4913], [1, -68, 6859], [1, 216, 12167], [1, -246, 24389], [1, 112, 29791], [1, 110, 50653], [1, 246, 68921], [1, -172, 79507], [1, 192, 103823], [1, 558, 148877], [1, -540, 205379], [1, -110, 226981], [1, 140, 300763], [1, 840, 357911], [1, -550, 389017], [1, 208, 493039], [1, 516, 571787], [1, 1398, 704969], [1, 1586, 912673]], 'index': 18, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/700/4/a/e/1/1', 'ModularForm/GL2/Q/holomorphic/700/4/a/e'], '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': '2-700-1.1-c3-0-18', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-700-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.426611626978749, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 1518557510505095589, 'z1': {'__RealLiteral__': 0, 'data': '1.32888057154590103210472452356', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20423959
{'Lhash': '1684556254151793988392691181132', 'Lhash_array': ['1684556254151793988392691181132'], 'factors': ['2-700-1.1-c3-0-18'], 'label': '2-700-1.1-c3-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/700/4/a/e'}
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id: 24569177
{'Lhash': '1684556254151793988392691181132', 'Lhash_array': ['1684556254151793988392691181132'], 'factors': ['2-700-1.1-c3-0-18'], 'label': '2-700-1.1-c3-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/700/4/a/e/1/1'}