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lfunc_lfunctions • Show schema
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{'Lhash': '2775935076592601615670249331184', 'a10': [-4.432401972969639, 5.509429439607595], 'a2': [-1.3660254037844386, -0.36602540378443865], 'a3': [1.6730326074756159, -0.4482877360840268], 'a4': [1.7320508075688772, 1.0], 'a5': [2.019091279803275, -4.574196148376497], 'a6': [-2.449489742783178, 5.755272054005115e-61], 'a7': [-6.190562945983681, -3.2675572545578837], 'a8': [-2.0, -2.0], 'a9': [2.598076211353316, -1.5], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.722085551566235, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.3660254037844386, 0.36602540378443865]]], [3, [[1.0, 0], [-1.6730326074756159, 0.4482877360840268]]], [5, [[1.0, 0], [-2.019091279803275, 4.574196148376497]]], [7, [[1.0, 0], [6.190562945983681, 3.2675572545578837]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '210.193', 'coefficient_field': 'CDF', 'conductor': 210, 'conductor_radical': 210, 'conjugate': 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['2.18982665735559844982557096810229', '3.28133201487084882574399895793656', '5.23278031303048188020393075050020', '6.80891442503891660693369329510502', '7.14205538116095982709013081960486', '8.707885317153530331023194179135386', '9.740789884745215096110651890718501', '9.928440891083431920332445496322848', '11.41608768586843697918282045904804', '12.27173957410459601431085897699381'], 'prelabel': '2-210-35.18-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.392088115343211, 'root_angle': 0.6499560099124143, 'root_number': '-0.4538673592509656 + 0.8910692566835391*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.324978004956', 'prec': 47}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.18982665735559844982557096810', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.28133201487084882574399895794', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.23278031303048188020393075050', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.722085551566235, 'bad_primes': [2, 3, 5, 7], 'central_character': '35.18', 'conductor': 210, 'conductor_radical': 210, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/210/3/v/a/193/7'], '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': '2-210-35.18-c2-0-15', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-210-35.18-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.392088115343211, 'root_angle': 0.32497800495620716, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '2.18982665735559844982557096810', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2775935076592601615670249331184', 'Lhash_array': ['2775935076592601615670249331184'], 'label': '2-210-35.18-c2-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/210/3/v/a/193/7'}