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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 1, 'A6': 0, 'A7': -1, 'A8': 0, 'A9': 0, 'Lhash': '302767622776852554', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [-0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 442.6906288059787, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, -1]], [7, [1, 1]], [11, [1, 1]]], 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '55440.1', 'coefficient_field': '1.1.1.1', 'conductor': 55440, 'conductor_radical': 2310, 'degree': 2, 'euler_factors': [[1], [1], [1, -1], [1, 1], [1, 1], [1, -2, 13], [1, -6, 17], [1, 8, 19], [1, 6, 23], [1, 6, 29], [1, 2, 31], [1, -2, 37], [1, 0, 41], [1, 8, 43], [1, 12, 47], [1, 6, 53], [1, -6, 59], [1, -8, 61], [1, 2, 67], [1, 0, 71], [1, 10, 73], [1, 8, 79], [1, -12, 83], [1, 6, 89], [1, -2, 97]], 'gamma_factors': [[], [0]], 'index': 6, 'label': '2-55440-1.1-c1-0-6', 'leading_term': '1.33977322975', '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': 0, 'origin': 'EllipticCurve/Q/55440/db', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [1.339773229746919, 0.7404508896565697, -0.8051044816680665, -2.484609344613174, -3.15842343351463, -2.220927426830881, -0.4099400654828561, 0.5660310645094494, -0.3266331160357949, -2.113660682902167, -2.591828227587298, -0.8249668937274904, 1.474616786282163, 1.774701591781931, -0.05748244776578416, -1.329719442893638, 0.01989835542575161, 2.3842510915916, 2.32707168098636, -0.6839310511519299, -3.223590101700537, -2.470749948509918, -0.09550144512849008, 0.3518202730972613, -1.201849398130614, -1.529923103650725, 0.3002948616905659, 0.9780876256433859, -1.670036577993566, -4.483807251605861, -3.405370954545735, 0.0488264286418475, 1.050799202898106, -0.7857517166123993, -1.007865511071518, 1.831429647956164, 3.437573548023185, 1.083654949708831, -1.634520572788365, -1.01896095895093, 0.5503014292467545, -0.4478600803345149, -1.818527530535183, 0.1087430392638483, 2.82975754127909, 1.522724093597424, -1.856051754857608, -1.384586692145807, 2.327212607535266, 3.086639096899035, 0.04257589697170091, -1.461047060010005, -0.1945664717717024, -0.5907174701137922, -3.011086772450804, -2.485741232016457, 1.179230370381293, 2.243717663105806, -0.1466014369359973, -0.5467079379882505, 1.563736593869143, 0.4535247944297095, -3.982063091839811, -4.913648019771417, -1.211530828428959, 0.7840351656915828, -0.304137511068781, 0.6399797254104568, 3.450490253976428, 2.66351795903284, -0.5415086904359362, 0.06462577614306617, 3.169409065342184, 2.553265134270864, -0.2610357336445798, 0.2701363066184159, 1.817565003234784, -0.2354110382555396, -1.809536269656143, 1.720228684544999, 4.856420648694828, 2.261008763364313, -0.7485343479361203, 0.6220136394010636, 1.520345562722186, -0.999990899736567, -1.752776122672367, 0.2527875053090409, -0.7811801630149426, -3.901848021231616, -2.357121616988497, 1.772846441014808, 1.404403495187513, -1.007911848313813, 0.182836880380032, 1.204084545112538, -1.570808176898153, -1.825037113788356, 3.286915133118473, 5.613376528184061, 2.021884130603965, -0.120277510784676, 1.215733939205709, 0.8204410257424528, -0.1824685608994954, 1.746400263312369, 1.55537291127286, -3.697489169304122, -5.621333736342049, -0.5998346951412225, 2.42315251202171, 0.05691599615231061, -0.7867116067765472, 0.1239594607726483, -2.575347691821788, -4.870613106647152, -1.255912813399826, 2.234302716499581, 0.6418345178156387, -0.3899289780847168, 0.9384685644515718], 'positive_zeros': ['0.3826578840254059', '1.566199002557290', '1.947346509218819', '2.830969318681183', '3.493187363492930', '3.997948351062312', '4.701466171768155', '5.513388292909876', '5.820205553640217', '6.463141669711482', '6.873862271193050', '7.745796472705043', '8.153855386592378', '8.606839254106936', '9.328790593331576', '9.881103268952037', '10.19086538357776', '10.74169391225169', '11.35350970815807', '11.84694727570040', '12.50338107849826', '13.05424532469851', '13.14265670240400', '13.91974607651316', '14.48439723550094', '14.81924691979337', '15.27917343116430', '16.09032349312470', '16.43329317694934', '16.68041974329360', '17.44559751858707', '17.74446102024535', '18.46559114917334', '18.71688210293978', '19.23122535225247', '19.65887502960183'], 'prelabel': '2-55440-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 21.040214561785692, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 302767622776852554, 'z1': {'__RealLiteral__': 0, 'data': '0.3826578840254059', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.566199002557290', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.947346509218819', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 442.6906288059787, 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '1.1', 'conductor': 55440, 'conductor_radical': 2310, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 1, 0, -1, 0, 0, 0, -1, 0, 2, 0, 0, 0, 6, 0, -8, 0, 0, 0, -6, 0, 1, 0, 0, 0, -6, 0, -2, 0, 0, 0, -1, 0, 2, 0, 0, 0, 0, 0, -8, 0, 0, 0, -12, 0, 1, 0, 0, 0, -6, 0, -1, 0, 0, 0, 6, 0, 8, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, -10, 0, 0, 0, 1, 0, -8, 0, 0, 0, 12, 0, 6, 0, 0, 0, -6, 0, -2, 0, 0, 0, -8, 0, 2, 0, 0, 0], 'euler11': [1, 1, 0], 'euler13': [1, -2, 13], 'euler17': [1, -6, 17], 'euler19': [1, 8, 19], 'euler2': [1, 0, 0], 'euler23': [1, 6, 23], 'euler29': [1, 6, 29], 'euler3': [1, 0, 0], 'euler31': [1, 2, 31], 'euler37': [1, -2, 37], 'euler41': [1, 0, 41], 'euler43': [1, 8, 43], 'euler47': [1, 12, 47], 'euler5': [1, -1, 0], 'euler53': [1, 6, 53], 'euler59': [1, -6, 59], 'euler61': [1, -8, 61], 'euler67': [1, 2, 67], 'euler7': [1, 1, 0], 'euler71': [1, 0, 71], 'euler73': [1, 10, 73], 'euler79': [1, 8, 79], 'euler83': [1, -12, 83], 'euler89': [1, 6, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, -1, 0], [1, 1, 0], [1, 1, 0], [1, -2, 13], [1, -6, 17], [1, 8, 19], [1, 6, 23], [1, 6, 29], [1, 2, 31], [1, -2, 37], [1, 0, 41], [1, 8, 43], [1, 12, 47], [1, 6, 53], [1, -6, 59], [1, -8, 61], [1, 2, 67], [1, 0, 71], [1, 10, 73], [1, 8, 79], [1, -12, 83], [1, 6, 89], [1, -2, 97]], 'index': 6, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/55440/db'], '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': '2-55440-1.1-c1-0-6', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-55440-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 21.040214561785692, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 302767622776852554, 'z1': {'__RealLiteral__': 0, 'data': '0.3826578840254059', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '302767622776852554', 'Lhash_array': ['302767622776852554'], 'label': '2-55440-1.1-c1-0-6', 'type': 'ECQ', 'url': 'EllipticCurve/Q/55440/db'}