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lfunc_lfunctions • Show schema
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{'Lhash': '1613177532555396414724645728275', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 1024, 'a5': 6243, 'a6': 0, 'a7': -16807, 'a8': 0, 'a9': 59049, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 57.817509993308924, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '5.0', 'prec': 10}, 'bad_lfactors': [[7, [1, 16807]], [13, [1, -371293]]], 'bad_primes': [7, 13], 'central_character': '91.90', 'coefficient_field': '1.1.1.1', 'conductor': 91, 'conductor_radical': 91, 'degree': 2, 'euler_factors': [[1, 0, -1024], [1, 0, -59049], [1, -6243, 9765625], [1, 16807], [1, 0, -25937424601], [1, -371293], [1, 0, -2015993900449], [1, -2147375, 6131066257801], [1, 6466725, 41426511213649], [1, 4721673, 420707233300201], [1, 42179225, 819628286980801], [1, 0, -4808584372417849], [1, 221229150, 13422659310152401], [1, 84317525, 21611482313284249], [1, -406710639, 52599132235830049], [1, -545143575, 174887470365513049], [1, 1330532550, 511116753300641401], [1, 0, -713342911662882601], [1, 0, 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'c10-0', 'trace_hash': 1365742841919360929, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.27257268861384825727314505014568', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.10369014234273439765813355288268', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '3.41928952876231657969455093576109', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 57.817509993308924, 'bad_primes': [7, 13], 'central_character': '91.90', 'conductor': 91, 'conductor_radical': 91, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 1024, 6243, 0, -16807, 0, 59049, 0, 0, 0, 371293, 0, 0, 1048576, 0, 0, 2147375, 6392832, 0, 0, -6466725, 0, 29209424, 0, 0, -17210368, -4721673, 0, -42179225, 0, 0, 0, -104926101, 60466176, 0, 0, 0, 0, -221229150, 0, -84317525, 0, 368642907, 0, 406710639, 0, 282475249, 0, 0, 380204032, 545143575, 0, 0, 0, 0, 0, -1330532550, 0, 0, 0, -992436543, 1073741824, 2317982199, 0, 0, 0, 0, 0, 0, 0, -3488411189, 0, 0, 2198912000, 0, 0, 5013092827, 6546259968, 3486784401, 0, 893026839, 0, 0, 0, 0, 0, 3850158675, 0, -6240321451, -6621926400, 0, 0, 13406062125, 0, -9195272389, 0, 0, 29910450176], 'euler11': [1, 0, -25937424601], 'euler13': [1, -371293, 0], 'euler17': [1, 0, -2015993900449], 'euler19': [1, -2147375, 6131066257801], 'euler2': [1, 0, -1024], 'euler23': [1, 6466725, 41426511213649], 'euler29': [1, 4721673, 420707233300201], 'euler3': [1, 0, -59049], 'euler31': [1, 42179225, 819628286980801], 'euler37': [1, 0, -4808584372417849], 'euler41': [1, 221229150, 13422659310152401], 'euler43': [1, 84317525, 21611482313284249], 'euler47': [1, -406710639, 52599132235830049], 'euler5': [1, -6243, 9765625], 'euler53': [1, -545143575, 174887470365513049], 'euler59': [1, 1330532550, 511116753300641401], 'euler61': [1, 0, -713342911662882601], 'euler67': [1, 0, -1822837804551761449], 'euler7': [1, 16807, 0], 'euler71': [1, 0, -3255243551009881201], 'euler73': [1, 3488411189, 4297625829703557649], 'euler79': [1, -5013092827, 9468276082626847201], 'euler83': [1, -893026839, 15516041187205853449], 'euler89': [1, -3850158675, 31181719929966183601], 'euler97': [1, 9195272389, 73742412689492826049], 'euler_factors': [[1, 0, -1024], [1, 0, -59049], [1, -6243, 9765625], [1, 16807, 0], [1, 0, -25937424601], [1, -371293, 0], [1, 0, -2015993900449], [1, -2147375, 6131066257801], [1, 6466725, 41426511213649], [1, 4721673, 420707233300201], [1, 42179225, 819628286980801], [1, 0, -4808584372417849], [1, 221229150, 13422659310152401], [1, 84317525, 21611482313284249], [1, -406710639, 52599132235830049], [1, -545143575, 174887470365513049], [1, 1330532550, 511116753300641401], [1, 0, -713342911662882601], [1, 0, -1822837804551761449], [1, 0, -3255243551009881201], [1, 3488411189, 4297625829703557649], [1, -5013092827, 9468276082626847201], [1, -893026839, 15516041187205853449], [1, -3850158675, 31181719929966183601], [1, 9195272389, 73742412689492826049]], 'index': 63, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/91/11/b/b', 'ModularForm/GL2/Q/holomorphic/91/11/b/b/90/1'], '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': '2-91-91.90-c10-0-63', 'motivic_weight': 10, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [10], 'order_of_vanishing': 0, 'prelabel': '2-91-91.90-c10-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.60378261086605, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c10-0', 'trace_hash': 1365742841919360929, 'z1': {'__RealLiteral__': 0, 'data': '1.27257268861384825727314505014568', 'prec': 113}}
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lfunc_instances • Show schema
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id: 24578777
{'Lhash': '1613177532555396414724645728275', 'Lhash_array': ['1613177532555396414724645728275'], 'label': '2-91-91.90-c10-0-63', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/91/11/b/b/90/1'}
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id: 23374019
{'Lhash': '1613177532555396414724645728275', 'Lhash_array': ['1613177532555396414724645728275'], 'label': '2-91-91.90-c10-0-63', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/91/11/b/b'}