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lfunc_lfunctions • Show schema
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{'Lhash': '1266669233954953996504305485807', 'a10': [-2.146710027160044, 0.6258083247213347], 'a2': [0.8660254037844386, 0.5], 'a3': [-0.25881904510252074, -0.9659258262890683], 'a4': [0.5, 0.8660254037844386], 'a5': [-1.5462012557187128, 1.615320920688479], 'a6': [0.25881904510252074, -0.9659258262890683], 'a7': [0.9549853233246136, 1.6540831004808225], 'a8': [0.0, 1.0], 'a9': [-0.8660254037844386, 0.5], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.1141656788299366, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8660254037844386, -0.5]]], [3, [[1.0, 0], [0.25881904510252074, 0.9659258262890683]]], [5, [[1.0, 0], [1.5462012557187128, -1.615320920688479]]], [13, [[1.0, 0], [-2.3314683271995076, -2.750319152255885]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '390.7', 'coefficient_field': 'CDF', 'conductor': 390, 'conductor_radical': 390, 'conjugate': '2628928982673477641049404362428', 'degree': 2, 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[-37.239092362730865, -21.5]], [[1.0, 0], [10.850645840115888, 0], [47.0, 0]], [[1.0, 0], [1.545497221776126, -1.545497221776126], [0, -53.0]], [[1.0, 0], [-3.7520700418028694, 14.00291602956539], [-51.09549882328188, -29.5]], [[1.0, 0], [2.85745080827323, 4.949249980057989], [-30.5, 52.827549630850754]], [[1.0, 0], [-5.071548524576071, -2.928059905872244], [33.5, 58.023702053557386]], [[1.0, 0], [1.7805350269663391, -6.645047185294399], [-61.48780366869514, -35.5]], [[1.0, 0], [0, 2.1526709416533136], [-73.0, 0]], [[1.0, 0], [0, 5.114182030570077], [-79.0, 0]], [[1.0, 0], [3.842610194688176, 0], [83.0, 0]], [[1.0, 0], [-0.804635993525295, 0.21560156466611688], [77.07626093681505, -44.5]], [[1.0, 0], [-15.870657999896475, 9.162928668456717], [48.5, -84.00446416709055]], [[1.0, 0], [-14.650798617255445, -8.458642525515428], [50.5, 87.4685657822283]], [[1.0, 0], [3.600865473515809, 3.600865473515809], [0, 103.0]], [[1.0, 0], [9.215659143469793, -2.4693284252132233], [92.66471820493493, 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'4.10888949798702989035699935258800', '5.04628447247929584882977555491489', '5.99606628984974526688938850937782', '7.45001271405898834862997580037918', '8.391393504115563886854442066007332', '9.382103814131145031663482359187920', '10.51124390334064627206470911036807', '11.22438044431778019762083290845759'], 'prelabel': '2-390-65.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7646998835014231, 'root_angle': -0.4151989057642927, 'root_number': '0.26327026499050077 - 0.9647221193544966*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.207599452882', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.999225838513310593171628839774', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '3.23977752423170540651702040217', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.10888949798702989035699935259', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.1141656788299366, 'bad_primes': [2, 3, 5, 13], 'central_character': '65.7', 'conductor': 390, 'conductor_radical': 390, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/390/2/bd/b/7/1'], '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': '2-390-65.7-c1-0-0', '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': '2-390-65.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7646998835014231, 'root_angle': -0.20759945288214635, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.999225838513310593171628839774', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1266669233954953996504305485807', 'Lhash_array': ['1266669233954953996504305485807'], 'label': '2-390-65.7-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/390/2/bd/b/7/1'}