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lfunc_lfunctions • Show schema
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{'Lhash': '2788899769864944810690173910107', 'a10': [0.11545054030166584, 0.27872226017958324], 'a2': [0.213324782404157, -0.213324782404157], 'a3': [0.9802489884462678, 0.4060324255169515], 'a4': [0.0, 1.908985074424438], 'a5': [-0.3826834323650898, 0.9238795325112867], 'a6': [0.2957281809846309, -0.12249462333975933], 'a7': [-0.960473484064669, -2.318788111528663], 'a8': [0.8338833904226908, 0.8338833904226908], 'a9': [-1.32529459478089, -1.32529459478089], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.6787284171808836, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0.3826834323650898, -0.9238795325112867]]], [17, [[1.0, 0], [-2.761131441206381, -3.06205048364353]]]], 'bad_primes': [5, 17], 'central_character': '85.26', 'coefficient_field': 'CDF', 'conductor': 85, 'conductor_radical': 85, 'conjugate': '4033623811794235761923155274504', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.213324782404157, 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-0.20334261454823918], 'positive_zeros': ['2.20005399702633186438631002513440', '4.52284321921065619763693254787900', '5.90954251001310487501644889957972', '7.16731934356936293449752271708049', '8.965573362980959817892945584534806', '9.311363724320658618405204762104015', '11.04176385105724015416144635445651', '12.06357102849648184375988677131147', '13.38729402654983503156907229570664', '14.24802959558016495347739827000112'], 'prelabel': '2-85-17.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8238497540091176, 'root_angle': -0.06168833592144314, 'root_number': '0.9258191324712028 - 0.3779668423952944*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0616883359214', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.20005399702633186438631002513', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.52284321921065619763693254788', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.90954251001310487501644889958', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.6787284171808836, 'bad_primes': [5, 17], 'central_character': '17.9', 'conductor': 85, 'conductor_radical': 85, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/85/2/l/a/26/4'], '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': '2-85-17.9-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': '2-85-17.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8238497540091176, 'root_angle': -0.06168833592144314, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.20005399702633186438631002513', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2788899769864944810690173910107', 'Lhash_array': ['2788899769864944810690173910107'], 'factors': ['2-85-17.9-c1-0-1'], 'label': '2-85-17.9-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/85/2/l/a/26/4'}