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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '674163433235545958', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 1619.3661529915669, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1]], [13, [1]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '202800.1', 'coefficient_field': '1.1.1.1', 'conductor': 202800, 'conductor_radical': 390, 'degree': 2, 'euler_factors': [[1], [1, 1], [1], [1, 0, 7], [1, -4, 11], [1], [1, -6, 17], [1, -4, 19], [1, -8, 23], [1, -6, 29], [1, 8, 31], [1, 10, 37], [1, -6, 41], [1, -4, 43], [1, 0, 47], [1, -10, 53], [1, -4, 59], [1, 2, 61], [1, -12, 67], [1, -16, 71], [1, -2, 73], [1, -16, 79], [1, -12, 83], [1, 10, 89], [1, 6, 97]], 'gamma_factors': [[], [0]], 'index': 132, 'label': '2-202800-1.1-c1-0-132', 'leading_term': '3.51479346167', '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/202800/dm', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [3.514793461670901, 2.779558595577629, 1.085618784972727, -0.2404408814235557, -0.08522221744112188, 0.989068723265692, 0.8969931202310234, -1.400794492530948, -3.800404834035759, -3.013208880200384, 0.9373995916655264, 3.90111864995616, 2.730519154489315, -0.3342595753926555, -0.9406445826603216, 0.7556000768514536, 0.5086204898756344, -2.767590124311463, -4.766370208671545, -2.746608830999073, -0.03495032469198139, -0.101447678640345, -0.6626925004589557, 1.42178673041973, 3.603695645349307, 2.190738386976978, -0.3681108161834814, 0.08937939939245032, 1.423700888486443, -0.2447419164613293, -1.926099249866606, 0.7999480644795526, 3.901576206251302, 1.289956214527419, -3.225510780230659, -2.251311799251698, 1.714771784843591, 1.785032983058126, -0.02256221484633903, 1.705971748125924, 3.722346910102868, 1.035922557894914, -2.073452798766657, -0.6687844562895507, 0.9235568540882034, -1.068275802032733, -2.023467520376887, 0.213850356020709, 0.6300494467651315, -1.22921289212502, -0.6627755290856342, -0.05171328500210078, -4.23515586435671, -7.567483682345914, -3.733163210314813, 0.6350534332498164, -0.7970532201168342, -1.795498572222451, 1.227542634630699, 1.333838927139763, -1.818012466663279, -0.05073486810929804, 4.531780228541485, 3.199522978589302, -0.7693353885909424, -0.0841161802658645, 1.329157019453789, -0.4172706774481584, -0.490113729478384, 1.186437551588819, -0.541847492963017, -2.222858534075323, 0.4117437292189547, 0.9931177154024393, -2.762438573277686, -2.765533039325339, 0.6528031435423411, -0.1616704844362388, -1.494502613774747, 1.783759424246607, 1.689530658831805, -4.215903247286229, -4.886954383154767, 0.203556481320259, 0.873316614695355, -0.5623188488185863, 2.322318087499517, 3.292737339898215, -0.5077527761779366, -1.109530283878483, 1.139383472171412, 0.1359161375684266, -0.5392669848090332, 0.8483032422058226, -1.707313068943603, -4.782131923096397, -1.558580081707475, 1.108049707786703, -1.222833048040392, -0.6502680974026455, 1.959466182201022, -0.3954567076034088, -1.329750800600778, 2.732838950385189, 1.284094977148094, -4.321687812892123, -1.959591414194555, 3.089515454324516, 0.9773508994052984, -1.438131801540028, 0.04806326662143537, -0.09450555607700196, 0.988583118663024, 5.376174780222615, 4.527639882005401, -0.3502292277427783, -0.2691816414127515, 0.9134855348257461, -0.4433798988769486, 1.684414178953461, 3.770075289950937], 'positive_zeros': ['0.6820380297908390', '1.022796720025815', '1.621532220807796', '2.446375668193335', '3.217004298607233', '3.642482158936525', '4.050924282510209', '5.006201233894822', '5.225949083251928', '5.617200400428240', '6.446393027160450', '6.737276396278512', '7.227514512786232', '7.701973069863633', '8.311464609440231', '8.881307604023878', '9.488372964674504', '9.551925833769569', '10.31139513774492', '10.81271925735716', '11.14789303574106', '11.72688516970023', '12.08474289197322', '12.60266676390723', '12.74189296977842', '13.68257098898636', '13.92789026569174', '14.40713395704255', '14.84963840289326', '15.25262412230588', '15.93130804159755', '16.25866857085145', '16.69884851029316', '17.06232888374778', '17.45477313162849', '17.96810991996824', '18.32654409986474', '18.93773041746796', '19.23495180497217', '19.63493196672120'], 'prelabel': '2-202800-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 40.241348796872686, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 674163433235545958, 'z1': {'__RealLiteral__': 0, 'data': '0.6820380297908390', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.022796720025815', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.621532220807796', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1619.3661529915669, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 202800, 'conductor_radical': 390, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 0, 0, 0, 0, 1, 0, 4, 0, 0, 0, 0, 0, 6, 0, 4, 0, 0, 0, 8, 0, 0, 0, -1, 0, 6, 0, -8, 0, -4, 0, 0, 0, -10, 0, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, -7, 0, -6, 0, 10, 0, 0, 0, -4, 0, 4, 0, -2, 0, 0, 0, 0, 0, 12, 0, -8, 0, 16, 0, 2, 0, 0, 0, 0, 0, 16, 0, 1, 0, 12, 0, 0, 0, -6, 0, -10, 0, 0, 0, 8, 0, 0, 0, -6, 0, 4, 0], 'euler11': [1, -4, 11], 'euler13': [1, 0, 0], 'euler17': [1, -6, 17], 'euler19': [1, -4, 19], 'euler2': [1, 0, 0], 'euler23': [1, -8, 23], 'euler29': [1, -6, 29], 'euler3': [1, 1, 0], 'euler31': [1, 8, 31], 'euler37': [1, 10, 37], 'euler41': [1, -6, 41], 'euler43': [1, -4, 43], 'euler47': [1, 0, 47], 'euler5': [1, 0, 0], 'euler53': [1, -10, 53], 'euler59': [1, -4, 59], 'euler61': [1, 2, 61], 'euler67': [1, -12, 67], 'euler7': [1, 0, 7], 'euler71': [1, -16, 71], 'euler73': [1, -2, 73], 'euler79': [1, -16, 79], 'euler83': [1, -12, 83], 'euler89': [1, 10, 89], 'euler97': [1, 6, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 0, 0], [1, 0, 7], [1, -4, 11], [1, 0, 0], [1, -6, 17], [1, -4, 19], [1, -8, 23], [1, -6, 29], [1, 8, 31], [1, 10, 37], [1, -6, 41], [1, -4, 43], [1, 0, 47], [1, -10, 53], [1, -4, 59], [1, 2, 61], [1, -12, 67], [1, -16, 71], [1, -2, 73], [1, -16, 79], [1, -12, 83], [1, 10, 89], [1, 6, 97]], 'index': 132, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/202800/dm'], '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': '2-202800-1.1-c1-0-132', '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': '2-202800-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 40.241348796872686, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 674163433235545958, 'z1': {'__RealLiteral__': 0, 'data': '0.6820380297908390', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '674163433235545958', 'Lhash_array': ['674163433235545958'], 'label': '2-202800-1.1-c1-0-132', 'type': 'ECQ', 'url': 'EllipticCurve/Q/202800/dm'}