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lfunc_lfunctions • Show schema
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{'Lhash': '114250111817582093281189771147', 'a10': [-4.152502793914358, -1.7692160991030954], 'a2': [-2.5395684886324386, -0.10234111149557822], 'a3': [-0.27821746391645263, 0.9605181116313724], 'a4': [4.445419789084277, 0.3588713862581271], 'a5': [1.6604992319287886, 0.6297442928704645], 'a6': [0.8048527955054441, -2.410828444565077], 'a7': [-2.0505960052472716, -4.812925704946757], 'a8': [-6.206523893605819, -0.7536084400779649], 'a9': [-0.8451900855437947, -0.5344658261278011], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.048415382478917, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.27821746391645263, -0.9605181116313724]]], [13, [[1.0, 0], [3.481673582557205, -0.936989362011799]]]], 'bad_primes': [3, 13], 'central_character': '507.4', 'coefficient_field': 'CDF', 'conductor': 507, 'conductor_radical': 39, 'conjugate': '2090222946072899345404073182485', 'degree': 2, 'euler_factors': [[[1.0, 0], 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[34.03923941537649, -14.502764564822778]], [[1.0, 0], [9.647800972517187, 2.7945196310619433], [34.652793507295584, 21.913098871239846]], [[1.0, 0], [1.807726544024027, -8.85483027628693], [-39.55911607732944, -16.85456422398323]], [[1.0, 0], [7.017116155575578, -4.843565562942913], [16.666429690999173, -43.945763406214496]], [[1.0, 0], [-0.5322373548102878, 4.383368980525033], [-51.45991632358076, -12.683730207240561]], [[1.0, 0], [-0.7398251293741677, -4.552326895902177], [-55.963650074881585, 18.683411634286877]], [[1.0, 0], [0.7809925557069657, -0.586877832593004], [16.97126529890361, -58.59160480951371]], [[1.0, 0], [0.24524042918387465, 3.037847816023334], [-66.13236759674017, 10.747555817469935]], [[1.0, 0], [-5.056861852153822, 4.857181738944713], [2.8588817477684754, -70.94241887018144]], [[1.0, 0], [-1.4200019124253018, 2.705587595872335], [-41.46872651137437, -60.07782221023692]], [[1.0, 0], [6.955518421677082, 10.076808097854803], [-28.013786076360315, 73.86628317214777]], [[1.0, 0], [-2.33385457013852, 9.468820207337366], [-73.49285012921642, -38.57202327963279]], [[1.0, 0], [14.674206426089114, 8.472157030246686], [44.5, 77.07626093681505]], [[1.0, 0], [-10.963642757552856, -8.951537239490095], [19.40249229627631, 95.03969324809997]], [[1.0, 0], [4.358239514586088, -1.4549941389254317], [80.74371910375362, -60.67496868803587]], [[1.0, 0], [-4.912085055884679, 1.2107202276057676], [91.20197064228061, -47.86648672050816]], [[1.0, 0], [3.894378731286178, 4.76974803658033], [-21.402749234036754, 104.83759976852265]], [[1.0, 0], [3.77270553083423, -4.258504221535065], [-13.138498147830212, -108.20526727668789]], [[1.0, 0], [-3.091534707373706, -10.67321597058752], [-95.50647966644881, 60.394638352441525]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-507-169.4-c1-0-1', 'load_key': 'CMFs-workshop', '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': 'ModularForm/GL2/Q/holomorphic/507/2/t/b/4/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.0901498834963785, -0.03534337467563204, -0.16469894297167229, -0.2985929842304894, -0.4360704461585935, -0.5739609945753985, -0.7066911191420153, -0.8264780139108211, -0.9238719413825569, -0.9886191065721573, -1.0108177805743075, -0.9823237578866021, -0.8983279117361033, -0.758985579791189, -0.5709335296147154, -0.3484942267358837, -0.11434754277537551, 0.10054557487915197, 0.2579488389173403, 0.3144003413882371, 0.2243222798466314, -0.055918003481029474, -0.5632445927690556, -1.3227964616547858, -2.3430486032030173, -3.6117235757820203, -5.093109030356934, -6.727344961437086, -8.432109847912608, -10.106919561867372, -11.639970928687159, -12.917139423523672, -13.832414770841252, -14.2987735292585, -14.258290376535475, -13.690221302672043, -12.615881907702045, -11.09940362445042, -9.243867776194008, -7.18285453759253, 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'root_number': '-0.9750200497877611 - 0.22211686678834586*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.464351674288', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.090127446630019628498889466138', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.06380389028709035727884689809', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.60617978875754033109245059941', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.048415382478917, 'bad_primes': [3, 13], 'central_character': '169.4', 'conductor': 507, 'conductor_radical': 39, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/507/2/t/b/4/2'], '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': '2-507-169.4-c1-0-1', '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': '2-507-169.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0120674398436345, 'root_angle': -0.46435167428819346, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.090127446630019628498889466138', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '114250111817582093281189771147', 'Lhash_array': ['114250111817582093281189771147'], 'label': '2-507-169.4-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/507/2/t/b/4/2'}