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lfunc_lfunctions • Show schema
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{'Lhash': '315197848144539829795221138552', 'a10': [0.0, 0.0], 'a2': [0.15154111639879467, -0.08749230434614051], 'a3': [0.15154111639879467, 5.193942172381265], 'a4': [-3.9846901933604046, 6.9016858673216746], 'a5': [0.0, 0.0], 'a6': [0.4773946792616288, 0.7738371138365203], 'a7': [-7.329791853564224, 4.2318572997592305], 'a8': [0.0, 2.7943957780285285], 'a9': [-26.954070580081215, 1.5741915906268753], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.275429751291645, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.15154111639879467, -5.193942172381265]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '225.49', 'coefficient_field': 'CDF', 'conductor': 225, 'conductor_radical': 15, 'conjugate': '3420055642432657906020490962301', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.15154111639879467, 0.08749230434614051], [4.0, -6.928203230275509]], [[1.0, 0], [-0.15154111639879467, 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[1173.44658137021, 677.4896996337368], [721448.5, 1249585.457044355]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 5, 'label': '2-15e2-45.4-c3-0-5', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/225/4/k/c/49/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.608606319249388, 0.2891406316632107, -0.0029934747908525483, -0.2616829373383759, -0.48078389306838115, -0.6541327646749269, -0.7757013657740099, -0.8399006187859419, -0.8420208774058549, -0.7787807934969783, -0.6489420088803287, -0.4539343756865352, -0.19842664704012553, 0.10922846269403148, 0.456747191200837, 0.8279332641321655, 1.2030180921536242, 1.559359569154032, 1.8725099111941568, 2.1176300191832786, 2.27119036406119, 2.312859306364403, 2.227442876916847, 2.0067097867638055, 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'6.09781793798776392416313321258006', '6.98891329831373009289037037674464', '8.193146318074060130786082076703748', '9.281555409490229578038431149253633', '10.10139220135524420658805582175199', '11.43014263132938619238284570160786'], 'prelabel': '2-15e2-45.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6435463152389933, 'root_angle': 0.7782917502285019, 'root_number': '-0.7670813481004576 + 0.6415498463848187*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.389145875114', 'prec': 47}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.24864725981101670642112071851', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.58271606894664532010706372383', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.36045552467544379144734660864', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 13.275429751291645, 'bad_primes': [3, 5], 'central_character': '45.4', 'conductor': 225, 'conductor_radical': 15, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/225/4/k/c/49/4'], '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': '2-15e2-45.4-c3-0-5', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-15e2-45.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6435463152389933, 'root_angle': 0.38914587511425097, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.24864725981101670642112071851', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '315197848144539829795221138552', 'Lhash_array': ['315197848144539829795221138552'], 'label': '2-15e2-45.4-c3-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/225/4/k/c/49/4'}