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['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.49747825090964987213239593180', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.795404227159861550504585360639', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '1.77606892777127041953409347500', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 38689.2590686159, 'bad_primes': [2], 'central_character': '1.1', 'conductor': 65536, 'conductor_radical': 2, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 33488, 0, 290790, 0, 0, 0, 0, 0, 0, 0, -13811868, 0, 0, 0, 0, 0, -37286544, 0, 74327350, 0, 0, 0, 0, 0, -105686336, 0, 0, 0, 0, 0, 0, 0, 0, 0, -616240884, 0, 0, 0, 0, 0, 5374696992, 0, -3113568878, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9737975520, 0, 0, 0, 0, 0, 0, 0, -19582970544, 0, -2927582644, 0, 0, 0, 0, 0, 76233691360, 0, 53177764491, 0, 0, 0, 0, 0, 0, 0, 49985834220, 0, 0, 0, 0, 0, 0, 0, 150027137092, 0, 0, 0], 'euler11': [1, 0, -284813350678, 0, 81402749386839761113321], 'euler13': [1, 0, -3250539591430, 0, 3211838877954855105157369], 'euler17': [1, 13811868, 116235717027622, 473358907910714388444, 1174562876521148458974062689], 'euler19': [1, 0, -119314641380038, 0, 13569980418174090907801371961], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 37286544, 2253191106693838, 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'euler67': [1, 0, -4573302143790884710, 0, 14915769363385151583217201855136979828889], 'euler7': [1, -33488, 4235015022, -66216717969584, 3909821048582988049], 'euler71': [1, 19582970544, 558117768075196044526, 4526061038681045015860686377424, 53417513915589153425653513253411473303441], 'euler73': [1, 2927582644, 629596056171081924438, 918460799629575157793406608788, 98424433237708439716398638596388483974129], 'euler79': [1, -76233691360, 2948881545647976520158, -57022329290945349278102196785440, 559494740587480879172162808385362976196641], 'euler83': [1, 0, -1715114764544677962310, 0, 1658509762573818415340429240403156732495289], 'euler89': [1, -49985834220, 6174992053201311433078, -138719341197124610068024507733580, 7701585589361325209940623087797432152759121], 'euler97': [1, -150027137092, 19933063527767048807622, -1073146216631953922235571675822276, 51165609725977649453468030598885114890323009], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, -290790, 0, 31381059609], [1, 0, -74327350, 0, 2384185791015625], [1, -33488, 4235015022, -66216717969584, 3909821048582988049], [1, 0, -284813350678, 0, 81402749386839761113321], [1, 0, -3250539591430, 0, 3211838877954855105157369], [1, 13811868, 116235717027622, 473358907910714388444, 1174562876521148458974062689], [1, 0, -119314641380038, 0, 13569980418174090907801371961], [1, 37286544, 2253191106693838, 35526982962086987298288, 907846434775996175406740561329], [1, 0, -7912756903454758, 0, 148852438543083302439338564577241], [1, 105686336, 53609354197085886, 2685328826521678161089216, 645590698195138073036733040138561], [1, 0, -322633551760058230, 0, 31654680139659126296833481434130569], [1, 616240884, 1195596270210772246, 339135248995684976445461844, 302862043149743582494593171234930481], [1, 0, -1858294189067944150, 0, 863586854220408743801513785592407849], [1, -5374696992, 12166160369121486622, -13287106697057121952225092576, 6111571184724799803076702357055363809], [1, 0, -15990678067626115990, 0, 85915027059992607611268303810877410409], [1, 0, -33383941434245697718, 0, 909377607891473342964601076981440190281], [1, 0, -38635239848010367078, 0, 1893461025894826042494075073080422272921], [1, 0, -4573302143790884710, 0, 14915769363385151583217201855136979828889], [1, 19582970544, 558117768075196044526, 4526061038681045015860686377424, 53417513915589153425653513253411473303441], [1, 2927582644, 629596056171081924438, 918460799629575157793406608788, 98424433237708439716398638596388483974129], [1, -76233691360, 2948881545647976520158, -57022329290945349278102196785440, 559494740587480879172162808385362976196641], [1, 0, -1715114764544677962310, 0, 1658509762573818415340429240403156732495289], [1, -49985834220, 6174992053201311433078, -138719341197124610068024507733580, 7701585589361325209940623087797432152759121], [1, -150027137092, 19933063527767048807622, -1073146216631953922235571675822276, 51165609725977649453468030598885114890323009]], 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/256/12/b/e'], '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': '4-2e16-1.1-c11e2-0-4', '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': '4-2e16-1.1-c11e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 14.024829917801313, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c11e2-0', 'trace_hash': 2194372479696807771, 'z1': {'__RealLiteral__': 0, 'data': '0.49747825090964987213239593180', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '630628603366107369661291119652,1008294645983269421126710897280', 'Lhash_array': ['630628603366107369661291119652', '1008294645983269421126710897280'], 'label': '4-2e16-1.1-c11e2-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/256/12/b/e'}