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lfunc_lfunctions • Show schema
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{'Lhash': '3065846037384299810600474455144', 'a10': [22.361932527554636, 1.3654466850176456e-60], 'a2': [1.7320508075688772, 1.0], 'a3': [-2.5431189273802683, -4.404811191912691], 'a4': [2.0, 3.4641016151377544], 'a5': [9.683000823287939, -5.590483131888659], 'a6': [-1.0558349532872956e-60, -10.172475709521073], 'a7': [-10.207575908127124, -17.6800400949922], 'a8': [0.0, 8.0], 'a9': [0.5650922424004665, -0.9787684748006358], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.366141340424807, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.7320508075688772, -1.0]]], [37, [[1.0, 0], [-224.5486380923632, -15.195694484454988]]]], 'bad_primes': [2, 37], 'central_character': '74.27', 'coefficient_field': 'CDF', 'conductor': 74, 'conductor_radical': 74, 'conjugate': '1627657154939594910177562926639', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.7320508075688772, -1.0]], [[1.0, 0], [2.5431189273802683, 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'10.00620783039098991623373891545296', '10.85985361551298069620664589838222', '11.95894377901576862936390431481134', '13.18096933349074079481356786083076', '14.18614957682922699976527364090316'], 'prelabel': '2-74-37.27-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0895313686146966, 'root_angle': 0.28182273011825487, 'root_number': '0.6330013921074695 + 0.7741506556155627*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.140911365059', 'prec': 47}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.41852608031923074921831684227', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.20365603955815523861031068065', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.69072951443446091031440877807', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.366141340424807, 'bad_primes': [2, 37], 'central_character': '37.27', 'conductor': 74, 'conductor_radical': 74, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/74/4/e/a/27/7'], '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': '2-74-37.27-c3-0-6', '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': '2-74-37.27-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0895313686146966, 'root_angle': 0.14091136505912744, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '2.41852608031923074921831684227', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3065846037384299810600474455144', 'Lhash_array': ['3065846037384299810600474455144'], 'label': '2-74-37.27-c3-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/74/4/e/a/27/7'}