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lfunc_lfunctions • Show schema
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{'Lhash': '1047175473521180302807855568581,1702970774511830470362828753116', 'a10': 0, 'a2': 0, 'a3': 10, 'a4': 0, 'a5': -10, 'a6': 0, 'a7': 16, 'a8': 0, 'a9': 39, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 749.4939003437466, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [29, [1, -58, 841]]], 'bad_primes': [2, 29], 'central_character': '464.1', 'coefficient_field': '1.1.1.1', 'conductor': 215296, 'conductor_radical': 58, 'degree': 4, 'euler_factors': [[1], [1, -10, 61, -270, 729], [1, 10, 243, 1250, 15625], [1, -16, 550, -5488, 117649], [1, -26, 93, -34606, 1771561], [1, 26, 3211, 57122, 4826809], [1, -60, 10078, -294780, 24137569], [1, -220, 23770, -1508980, 47045881], [1, 52, 20402, 632684, 148035889], [1, -58, 841], [1, -294, 73253, -8758554, 887503681], [1, -312, 119370, -15803736, 2565726409], [1, -40, 100154, -2756840, 4750104241], [1, -322, 126453, -25601254, 6321363049], [1, -130, 126173, -13496990, 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2.4141096856221154], 'positive_zeros': ['0.826075791967159972326976804706306', '1.34340706674633016349526612836027', '2.56075905492001820411926054466694', '2.57973953734593212920978969946835', '3.58581447039045162228379826295283', '3.68264483548214855602328653688361', '4.41824193807745198649569365538113', '4.95550350079299034817694972693889', '5.66891098212242015395114944740293', '6.13289769561649529171874232600522', '7.25999113088945968858502194409206', '7.28051258209038325958056998713834', '7.918083194474415170445556792178080', '8.017236876011354319051527024497601', '8.481707463687013210237351977198259', '8.954385336525583748073464215367980', '9.617928620828343113349283360001414', '9.723173678106536532632278193006535', '10.07555892973262500665317721605303', '10.95583030356924640425444390546594'], 'prelabel': '4-464e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.232292637330567, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3e2-0', 'trace_hash': 1734794752719442680, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.826075791967159972326976804706', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.34340706674633016349526612836', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.56075905492001820411926054467', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 749.4939003437466, 'bad_primes': [2, 29], 'central_character': '1.1', 'conductor': 215296, 'conductor_radical': 58, 'degree': 4, 'dirichlet_coefficients': [1, 0, 10, 0, -10, 0, 16, 0, 39, 0, 26, 0, -26, 0, -100, 0, 60, 0, 220, 0, 160, 0, -52, 0, -143, 0, 50, 0, 58, 0, 294, 0, 260, 0, -160, 0, 312, 0, -260, 0, 40, 0, 322, 0, -390, 0, 130, 0, -294, 0, 600, 0, 1002, 0, -260, 0, 2200, 0, 900, 0, -948, 0, 624, 0, 260, 0, -320, 0, -520, 0, 660, 0, 648, 0, -1430, 0, 416, 0, -258, 0, 92, 0, -1212, 0, -600, 0, 580, 0, 760, 0, -416, 0, 2940, 0, -2200, 0, 24, 0, 1014, 0], 'euler11': [1, -26, 93, -34606, 1771561], 'euler13': [1, 26, 3211, 57122, 4826809], 'euler17': [1, -60, 10078, -294780, 24137569], 'euler19': [1, -220, 23770, -1508980, 47045881], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 52, 20402, 632684, 148035889], 'euler29': [1, -58, 841, 0, 0], 'euler3': [1, -10, 61, -270, 729], 'euler31': [1, -294, 73253, -8758554, 887503681], 'euler37': [1, -312, 119370, -15803736, 2565726409], 'euler41': [1, -40, 100154, -2756840, 4750104241], 'euler43': [1, -322, 126453, -25601254, 6321363049], 'euler47': [1, -130, 126173, -13496990, 10779215329], 'euler5': [1, 10, 243, 1250, 15625], 'euler53': [1, -1002, 518987, -149174754, 22164361129], 'euler59': [1, -900, 490250, -184841100, 42180533641], 'euler61': [1, 948, 615270, 215177988, 51520374361], 'euler67': [1, 320, 158614, 96244160, 90458382169], 'euler7': [1, -16, 550, -5488, 117649], 'euler71': [1, -660, 822410, -236221260, 128100283921], 'euler73': [1, -648, 63810, -252083016, 151334226289], 'euler79': [1, 258, 770157, 127204062, 243087455521], 'euler83': [1, 1212, 1502618, 693005844, 326940373369], 'euler89': [1, -760, 1009370, -535776440, 496981290961], 'euler97': [1, -24, 1157322, -21904152, 832972004929], 'euler_factors': [[1, 0, 0, 0, 0], [1, -10, 61, -270, 729], [1, 10, 243, 1250, 15625], [1, -16, 550, -5488, 117649], [1, -26, 93, -34606, 1771561], [1, 26, 3211, 57122, 4826809], [1, -60, 10078, -294780, 24137569], [1, -220, 23770, -1508980, 47045881], [1, 52, 20402, 632684, 148035889], [1, -58, 841, 0, 0], [1, -294, 73253, -8758554, 887503681], [1, -312, 119370, -15803736, 2565726409], [1, -40, 100154, -2756840, 4750104241], [1, -322, 126453, -25601254, 6321363049], [1, -130, 126173, -13496990, 10779215329], [1, -1002, 518987, -149174754, 22164361129], [1, -900, 490250, -184841100, 42180533641], [1, 948, 615270, 215177988, 51520374361], [1, 320, 158614, 96244160, 90458382169], [1, -660, 822410, -236221260, 128100283921], [1, -648, 63810, -252083016, 151334226289], [1, 258, 770157, 127204062, 243087455521], [1, 1212, 1502618, 693005844, 326940373369], [1, -760, 1009370, -535776440, 496981290961], [1, -24, 1157322, -21904152, 832972004929]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/464/4/a/f'], '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': '4-464e2-1.1-c3e2-0-2', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3, 3], 'order_of_vanishing': 0, 'prelabel': '4-464e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.232292637330567, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 1734794752719442680, 'z1': {'__RealLiteral__': 0, 'data': '0.826075791967159972326976804706', 'prec': 107}}
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{'Lhash': '1047175473521180302807855568581,1702970774511830470362828753116', 'Lhash_array': ['1047175473521180302807855568581', '1702970774511830470362828753116'], 'label': '4-464e2-1.1-c3e2-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/464/4/a/f'}