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lfunc_lfunctions • Show schema
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{'Lhash': '927343948875644401262699200224,1372473800985002581139668013498', 'a10': 0, 'a2': -13, 'a3': -18, 'a4': 71, 'a5': 0, 'a6': 234, 'a7': -146, 'a8': -65, 'a9': 243, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 17507.696223341933, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 18, 81]], [5, [1]], [11, [1, 242, 14641]]], 'bad_primes': [3, 5, 11], 'central_character': '825.1', 'coefficient_field': '1.1.1.1', 'conductor': 680625, 'conductor_radical': 165, 'degree': 4, 'euler_factors': [[1, 13, 98, 416, 1024], [1, 18, 81], [1], [1, 146, 7230, 2453822, 282475249], [1, 242, 14641], [1, -130, 701634, -48268090, 137858491849], [1, -728, 1830542, -1033655896, 2015993900449], [1, 828, -865114, 2050209972, 6131066257801], [1, -238, 11988422, -1531849634, 41426511213649], [1, -696, 22778374, -14275759704, 420707233300201], [1, 10480, 63595902, 300033502480, 819628286980801], [1, -1908, 74176718, -132308269956, 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{'algebraic': True, 'analytic_conductor': 17507.696223341933, 'bad_primes': [3, 5, 11], 'central_character': '1.1', 'conductor': 680625, 'conductor_radical': 165, 'degree': 4, 'dirichlet_coefficients': [1, -13, -18, 71, 0, 234, -146, -65, 243, 0, -242, -1278, 130, 1898, 0, -1729, 728, -3159, -828, 0, 2628, 3146, 238, 1170, 0, -1690, -2916, -10366, 696, 0, -10480, 12623, 4356, -9464, 0, 17253, 1908, 10764, -2340, 0, 36484, -34164, -9768, -17182, 0, -3094, -43742, 31122, 14086, 0, -13104, 9230, 12174, 37908, 0, 9490, 14904, -9048, -2788, 0, -25302, 136240, -35478, -40321, 0, -56628, 40520, 51688, -4284, 0, 31386, -15795, 46780, -24804, 0, -58788, 35332, 30420, -16850, 0, 32805, -474292, -79440, 186588, 0, 126984, -12528, 15730, -54204, 0, -18980, 16898, 188640, 568646, 0, -227214, 241568, -183118, -58806, 0], 'euler11': [1, 242, 14641, 0, 0], 'euler13': [1, -130, 701634, -48268090, 137858491849], 'euler17': [1, -728, 1830542, -1033655896, 2015993900449], 'euler19': [1, 828, -865114, 2050209972, 6131066257801], 'euler2': [1, 13, 98, 416, 1024], 'euler23': [1, -238, 11988422, -1531849634, 41426511213649], 'euler29': [1, -696, 22778374, -14275759704, 420707233300201], 'euler3': [1, 18, 81, 0, 0], 'euler31': [1, 10480, 63595902, 300033502480, 819628286980801], 'euler37': [1, -1908, 74176718, -132308269956, 4808584372417849], 'euler41': [1, -36484, 564482438, -4226897637284, 13422659310152401], 'euler43': [1, 9768, 237972854, 1435978471224, 21611482313284249], 'euler47': [1, 43742, 935775830, 10032009296194, 52599132235830049], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, -12174, 457325722, -5091111931782, 174887470365513049], 'euler59': [1, 2788, 1399448534, 1993208945612, 511116753300641401], 'euler61': [1, 25302, 1815376826, 21369975607902, 713342911662882601], 'euler67': [1, -40520, 1779236982, -54707069335640, 1822837804551761449], 'euler7': [1, 146, 7230, 2453822, 282475249], 'euler71': [1, -31386, 3698331094, -56627542410486, 3255243551009881201], 'euler73': [1, -46780, 4437463638, -96978289120540, 4297625829703557649], 'euler79': [1, 16850, 5148027246, 51848400323150, 9468276082626847201], 'euler83': [1, 79440, 5477266486, 312917388679920, 15516041187205853449], 'euler89': [1, 54204, 6019532470, 302678358373596, 31181719929966183601], 'euler97': [1, -241568, 30950947518, -2074426611202976, 73742412689492826049], 'euler_factors': [[1, 13, 98, 416, 1024], [1, 18, 81, 0, 0], [1, 0, 0, 0, 0], [1, 146, 7230, 2453822, 282475249], [1, 242, 14641, 0, 0], [1, -130, 701634, -48268090, 137858491849], [1, -728, 1830542, -1033655896, 2015993900449], [1, 828, -865114, 2050209972, 6131066257801], [1, -238, 11988422, -1531849634, 41426511213649], [1, -696, 22778374, -14275759704, 420707233300201], [1, 10480, 63595902, 300033502480, 819628286980801], [1, -1908, 74176718, -132308269956, 4808584372417849], [1, -36484, 564482438, -4226897637284, 13422659310152401], [1, 9768, 237972854, 1435978471224, 21611482313284249], [1, 43742, 935775830, 10032009296194, 52599132235830049], [1, -12174, 457325722, -5091111931782, 174887470365513049], [1, 2788, 1399448534, 1993208945612, 511116753300641401], [1, 25302, 1815376826, 21369975607902, 713342911662882601], [1, -40520, 1779236982, -54707069335640, 1822837804551761449], [1, -31386, 3698331094, -56627542410486, 3255243551009881201], [1, -46780, 4437463638, -96978289120540, 4297625829703557649], [1, 16850, 5148027246, 51848400323150, 9468276082626847201], [1, 79440, 5477266486, 312917388679920, 15516041187205853449], [1, 54204, 6019532470, 302678358373596, 31181719929966183601], [1, -241568, 30950947518, -2074426611202976, 73742412689492826049]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/825/6/a/c'], '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': '4-825e2-1.1-c5e2-0-1', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5, 5], 'order_of_vanishing': 2, 'prelabel': '4-825e2-1.1-c5e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 11.502897519569105, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5e2-0', 'trace_hash': 1265376769508165723, 'z1': {'__RealLiteral__': 0, 'data': '0.73154538696126853521692391709', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '927343948875644401262699200224,1372473800985002581139668013498', 'Lhash_array': ['927343948875644401262699200224', '1372473800985002581139668013498'], 'label': '4-825e2-1.1-c5e2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/825/6/a/c'}