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lfunc_lfunctions • Show schema
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{'Lhash': '446985810410275169268946012508,1770744365949336676577719037921', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 960, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 29886.53168256653, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '5.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1]]], 'bad_primes': [3, 5], 'central_character': '225.1', 'coefficient_field': '1.1.1.1', 'conductor': 50625, 'conductor_radical': 15, 'degree': 4, 'euler_factors': [[1, 0, -960, 0, 4194304], [1], [1], [1, 0, -3171549230, 0, 3909821048582988049], [1, -224056, 583173614006, -63925791670418216, 81402749386839761113321], [1, 0, -2381082913990, 0, 3211838877954855105157369], [1, 0, -68481509426910, 0, 1174562876521148458974062689], [1, -27424840, 421010980052838, -3194726711842232359960, 13569980418174090907801371961], [1, 0, -192013219177870, 0, 907846434775996175406740561329], [1, 9067700, 24421575327234158, 110630562402490745623300, 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'root_analytic_conductor': 13.148278047938732, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c11e2-0', 'trace_hash': 742711031180858507, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.35260963102119723228072847195', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.05813111363330051784176593555', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.39687100343780032407590121781', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 29886.53168256653, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 50625, 'conductor_radical': 15, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 960, 0, 0, 0, 0, 0, 0, 224056, 0, 0, 0, 0, -3272704, 0, 0, 27424840, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9067700, 0, -530678016, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2533939916, 0, 0, 215093760, 0, 0, 0, 0, 3171549230, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14997474440, 0, -8129657716, 0, 0, -7168327680, 0, 0, 0, 0, 0, 0, 26567469296, 0, 0, 0, 0, 26327846400, 0, 0, -54200604480, 0, 0, 0, 0, 0, 0, 0, 0, 0, -127000825260, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, -224056, 583173614006, -63925791670418216, 81402749386839761113321], 'euler13': [1, 0, -2381082913990, 0, 3211838877954855105157369], 'euler17': [1, 0, -68481509426910, 0, 1174562876521148458974062689], 'euler19': [1, -27424840, 421010980052838, -3194726711842232359960, 13569980418174090907801371961], 'euler2': [1, 0, -960, 0, 4194304], 'euler23': [1, 0, -192013219177870, 0, 907846434775996175406740561329], 'euler29': [1, 9067700, 24421575327234158, 110630562402490745623300, 148852438543083302439338564577241], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 530678016, 121221742959233726, 13483720108965953247895296, 645590698195138073036733040138561], 'euler37': [1, 0, -310833159700713910, 0, 31654680139659126296833481434130569], 'euler41': [1, -2533939916, 2705870937907018646, -1394500700399431910422670956, 302862043149743582494593171234930481], 'euler43': [1, 0, -1858387834815761110, 0, 863586854220408743801513785592407849], 'euler47': [1, 0, 2116783152048544290, 0, 6111571184724799803076702357055363809], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 0, -12765108038242661910, 0, 85915027059992607611268303810877410409], 'euler59': [1, -14997474440, 116542836784089013718, -452262166165447147779094135960, 909377607891473342964601076981440190281], 'euler61': [1, 8129657716, 103550668867701261486, 353753256063197655609329758276, 1893461025894826042494075073080422272921], 'euler67': [1, 0, -197042557804441142630, 0, 14915769363385151583217201855136979828889], 'euler7': [1, 0, -3171549230, 0, 3909821048582988049], 'euler71': [1, -26567469296, 638702190441878814446, -6140334399564449030612432419216, 53417513915589153425653513253411473303441], 'euler73': [1, 0, 206361010706558907890, 0, 98424433237708439716398638596388483974129], 'euler79': [1, 54200604480, 2230414002554390875358, 40541716677890222021092888777920, 559494740587480879172162808385362976196641], 'euler83': [1, 0, -1394692076788719335110, 0, 1658509762573818415340429240403156732495289], 'euler89': [1, 127000825260, 9582648551714244197878, 352449270607738630188551391952140, 7701585589361325209940623087797432152759121], 'euler97': [1, 0, -13920514658667639538750, 0, 51165609725977649453468030598885114890323009], 'euler_factors': [[1, 0, -960, 0, 4194304], [1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 0, -3171549230, 0, 3909821048582988049], [1, -224056, 583173614006, -63925791670418216, 81402749386839761113321], [1, 0, -2381082913990, 0, 3211838877954855105157369], [1, 0, -68481509426910, 0, 1174562876521148458974062689], [1, -27424840, 421010980052838, -3194726711842232359960, 13569980418174090907801371961], [1, 0, -192013219177870, 0, 907846434775996175406740561329], [1, 9067700, 24421575327234158, 110630562402490745623300, 148852438543083302439338564577241], [1, 530678016, 121221742959233726, 13483720108965953247895296, 645590698195138073036733040138561], [1, 0, -310833159700713910, 0, 31654680139659126296833481434130569], [1, -2533939916, 2705870937907018646, -1394500700399431910422670956, 302862043149743582494593171234930481], [1, 0, -1858387834815761110, 0, 863586854220408743801513785592407849], [1, 0, 2116783152048544290, 0, 6111571184724799803076702357055363809], [1, 0, -12765108038242661910, 0, 85915027059992607611268303810877410409], [1, -14997474440, 116542836784089013718, -452262166165447147779094135960, 909377607891473342964601076981440190281], [1, 8129657716, 103550668867701261486, 353753256063197655609329758276, 1893461025894826042494075073080422272921], [1, 0, -197042557804441142630, 0, 14915769363385151583217201855136979828889], [1, -26567469296, 638702190441878814446, -6140334399564449030612432419216, 53417513915589153425653513253411473303441], [1, 0, 206361010706558907890, 0, 98424433237708439716398638596388483974129], [1, 54200604480, 2230414002554390875358, 40541716677890222021092888777920, 559494740587480879172162808385362976196641], [1, 0, -1394692076788719335110, 0, 1658509762573818415340429240403156732495289], [1, 127000825260, 9582648551714244197878, 352449270607738630188551391952140, 7701585589361325209940623087797432152759121], [1, 0, -13920514658667639538750, 0, 51165609725977649453468030598885114890323009]], 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/225/12/b/b'], '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': '4-15e4-1.1-c11e2-0-3', 'motivic_weight': 11, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [11, 11], 'order_of_vanishing': 0, 'prelabel': '4-15e4-1.1-c11e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 13.148278047938732, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c11e2-0', 'trace_hash': 742711031180858507, 'z1': {'__RealLiteral__': 0, 'data': '0.35260963102119723228072847195', 'prec': 103}}
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{'Lhash': '446985810410275169268946012508,1770744365949336676577719037921', 'Lhash_array': ['446985810410275169268946012508', '1770744365949336676577719037921'], 'label': '4-15e4-1.1-c11e2-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/225/12/b/b'}