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lfunc_lfunctions • Show schema
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{'Lhash': '347049132316077518639058484379,523984062499672530665171038216', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': -1576, 'a5': 0, 'a6': 0, 'a7': -116200, '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, 1576, 0, 4194304], [1], [1], [1, 116200, 7330263486, 229765367536600, 3909821048582988049], [1, 0, 544818541222, 0, 81402749386839761113321], [1, 1525300, 4165955810574, 2733582249024636100, 3211838877954855105157369], [1, 0, -11975946694814, 0, 1174562876521148458974062689], [1, 20603408, 339105623100054, 2400096332105636530352, 13569980418174090907801371961], [1, 0, 1797531507451534, 0, 907846434775996175406740561329], [1, 0, 4519838782611658, 0, 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True, 'sign_arg': 0, 'spectral_label': 'c11e2-0', 'trace_hash': 2225217007547424347, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.27377349267502761270351220858', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.41335054186487489840419172138', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.53092399206508955062576061958', '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, -1576, 0, 0, -116200, 0, 0, 0, 0, 0, -1525300, 0, 0, -1710528, 0, 0, -20603408, 0, 0, 0, 0, 0, 0, 0, 0, 183131200, 0, 0, 212319016, 0, 0, 0, 0, 0, 19148900, 0, 0, 0, 0, 0, -3181394800, 0, 0, 0, 0, 0, 6172176514, 0, 0, 2403872800, 0, 0, 0, 0, 0, 0, 0, 0, -6185242196, 0, 0, 9306015232, 0, 0, 18227640800, 0, 0, 0, 0, 0, -1240285900, 0, 0, 32470971008, 0, 0, 21236972968, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 177239860000, 0, 0, 0, 0, 0, -263745804700, 0, 0, 0], 'euler11': [1, 0, 544818541222, 0, 81402749386839761113321], 'euler13': [1, 1525300, 4165955810574, 2733582249024636100, 3211838877954855105157369], 'euler17': [1, 0, -11975946694814, 0, 1174562876521148458974062689], 'euler19': [1, 20603408, 339105623100054, 2400096332105636530352, 13569980418174090907801371961], 'euler2': [1, 0, 1576, 0, 4194304], 'euler23': [1, 0, 1797531507451534, 0, 907846434775996175406740561329], 'euler29': [1, 0, 4519838782611658, 0, 148852438543083302439338564577241], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -212319016, 62086794931611726, -5394702812703407655566296, 645590698195138073036733040138561], 'euler37': [1, -19148900, 355926913651723326, -3406926747692709502495700, 31654680139659126296833481434130569], 'euler41': [1, 0, 1088883326741296882, 0, 302862043149743582494593171234930481], 'euler43': [1, 3181394800, 4388905697309205414, 2956450270426302669691723600, 863586854220408743801513785592407849], 'euler47': [1, 0, 2869299998598432286, 0, 6111571184724799803076702357055363809], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 0, 17432708152043665114, 0, 85915027059992607611268303810877410409], 'euler59': [1, 0, 26931896409526885318, 0, 909377607891473342964601076981440190281], 'euler61': [1, 6185242196, 96592140478666402926, 269144119323520481432665339556, 1893461025894826042494075073080422272921], 'euler67': [1, -18227640800, 327321988093392194166, -2226144193448017550877187786400, 14915769363385151583217201855136979828889], 'euler7': [1, 116200, 7330263486, 229765367536600, 3909821048582988049], 'euler71': [1, 0, 451020199785470330542, 0, 53417513915589153425653513253411473303441], 'euler73': [1, 1240285900, 627837948415154119254, 389110784564170032428104984300, 98424433237708439716398638596388483974129], 'euler79': [1, -21236972968, 1608739876265932540014, -15885124334404275786657573542872, 559494740587480879172162808385362976196641], 'euler83': [1, 0, -1024696094999093064746, 0, 1658509762573818415340429240403156732495289], 'euler89': [1, 0, 1778791077346460680978, 0, 7701585589361325209940623087797432152759121], 'euler97': [1, 263745804700, 31696490435974243776006, 1886577441605048334193550783139100, 51165609725977649453468030598885114890323009], 'euler_factors': [[1, 0, 1576, 0, 4194304], [1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 116200, 7330263486, 229765367536600, 3909821048582988049], [1, 0, 544818541222, 0, 81402749386839761113321], [1, 1525300, 4165955810574, 2733582249024636100, 3211838877954855105157369], [1, 0, -11975946694814, 0, 1174562876521148458974062689], [1, 20603408, 339105623100054, 2400096332105636530352, 13569980418174090907801371961], [1, 0, 1797531507451534, 0, 907846434775996175406740561329], [1, 0, 4519838782611658, 0, 148852438543083302439338564577241], [1, -212319016, 62086794931611726, -5394702812703407655566296, 645590698195138073036733040138561], [1, -19148900, 355926913651723326, -3406926747692709502495700, 31654680139659126296833481434130569], [1, 0, 1088883326741296882, 0, 302862043149743582494593171234930481], [1, 3181394800, 4388905697309205414, 2956450270426302669691723600, 863586854220408743801513785592407849], [1, 0, 2869299998598432286, 0, 6111571184724799803076702357055363809], [1, 0, 17432708152043665114, 0, 85915027059992607611268303810877410409], [1, 0, 26931896409526885318, 0, 909377607891473342964601076981440190281], [1, 6185242196, 96592140478666402926, 269144119323520481432665339556, 1893461025894826042494075073080422272921], [1, -18227640800, 327321988093392194166, -2226144193448017550877187786400, 14915769363385151583217201855136979828889], [1, 0, 451020199785470330542, 0, 53417513915589153425653513253411473303441], [1, 1240285900, 627837948415154119254, 389110784564170032428104984300, 98424433237708439716398638596388483974129], [1, -21236972968, 1608739876265932540014, -15885124334404275786657573542872, 559494740587480879172162808385362976196641], [1, 0, -1024696094999093064746, 0, 1658509762573818415340429240403156732495289], [1, 0, 1778791077346460680978, 0, 7701585589361325209940623087797432152759121], [1, 263745804700, 31696490435974243776006, 1886577441605048334193550783139100, 51165609725977649453468030598885114890323009]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/225/12/a/j'], '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-c11e2-0-2', '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': 2225217007547424347, 'z1': {'__RealLiteral__': 0, 'data': '0.27377349267502761270351220858', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '347049132316077518639058484379,523984062499672530665171038216', 'Lhash_array': ['347049132316077518639058484379', '523984062499672530665171038216'], 'label': '4-15e4-1.1-c11e2-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/225/12/a/j'}