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  • lfunc_lfunctions • Show schema
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'8-75e4-1.1-c9e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.215117674854636, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c9e4-0', 'trace_hash': 1318207580352501464, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.17592590938500470586699811319742', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '0.66846494216827235557483573569392', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '0.907401606410959924206216905169890', 'prec': 110}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 2226357.2115213773, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 31640625, 'conductor_radical': 15, 'degree': 8, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -85673, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -32989472, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 791579528, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -387420489, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 0, -9431790764, 0, 33359503880953388886, 0, -52439976765999721468245841484, 0, 30912680532870672635673352936887453361], 'euler13': [1, 0, 0, 0, 224910813903914786258, 0, 0, 0, 12646218552730347184269489080961456410641], 'euler17': [1, 0, 0, 0, -5999735689711595420542, 0, 0, 0, 197770344305988984840145602058543169130838081], 'euler19': [1, 0, 857150912596, 0, 391931622336861390930486, 0, 89252853334057993152482041054565236, 0, 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18701397461209715023927088008788055619800417991632621566284510161], 'euler67': [1, 0, 0, 0, 1480391027713560112434162035465618, 0, 0, 0, 547889398733702676213614311297941818478464344374520135510515030481], 'euler7': [1, 0, 0, 0, 3256827195820898, 0, 0, 0, 2651730845859653471779023381601], 'euler71': [1, 0, -183394002873796124, 0, 12612510108777727870656060869033766, 0, -385509785855827548271225059872289924056884725987164, 0, 4418761423445010359012517479030513507821439762288727229544623559521], 'euler73': [1, 0, 0, 0, 6931727443098214408166945170751138, 0, 0, 0, 12012211336350227316446820100278887925603925639507433655692782073761], 'euler79': [1, 0, -123985600064739644, 0, 32571917375014934968163747045083206, 0, -1780979380885104182920543145205708166471717125809084, 0, 206336132715709669990485567530001552309415935666586885734738159549121], 'euler83': [1, 0, 0, 0, 57568683429868415121343383075018578, 0, 0, 0, 1221268978022589508833760255513684608154133797863046939086649799003281], 'euler89': [1, 0, 1401425614829940836, 0, 736497657713054133014530649722642086, 0, 172024447130221367654923380329451230442203924163937316, 0, 15067466661578195724088403821109198918255739721817916514744422568289761], 'euler97': [1, 0, 0, 0, 1155902525086081958656549590612514178, 0, 0, 0, 334027661875095082935878165689897695724025886105865253311336914562753921], 'euler_factors': [[1, 0, 0, 0, 85673, 0, 0, 0, 68719476736], [1, 0, 0, 0, 387420489, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 3256827195820898, 0, 0, 0, 2651730845859653471779023381601], [1, 0, -9431790764, 0, 33359503880953388886, 0, -52439976765999721468245841484, 0, 30912680532870672635673352936887453361], [1, 0, 0, 0, 224910813903914786258, 0, 0, 0, 12646218552730347184269489080961456410641], [1, 0, 0, 0, -5999735689711595420542, 0, 0, 0, 197770344305988984840145602058543169130838081], [1, 0, 857150912596, 0, 391931622336861390930486, 0, 89252853334057993152482041054565236, 0, 10842505080063916320800450434338728415281531281], [1, 0, 0, 0, 4809080971637743013633378, 0, 0, 0, 10524515126174167358877236351104092889324551536161], [1, 0, 58028583903476, 0, 1262743706191032721981830966, 0, 12212538183882098142981347037959648639636, 0, 44292268542362921407825091617016319887724139383235921], [1, 32989472, 513872962207228, 4860601024622150447264, 30401701776824798970407995270, 128512454564779977879856628720354144, 359224754450595194690689670011319012701948, 609734962224593195396725106531575839080783866592, 488675963633769261467693849486036510107332864779998081], [1, 0, 0, 0, 33780107621126601499906871858, 0, 0, 0, 285273917723723876056171083405292782327767461712708093041], [1, 0, -1309527737575844, 0, 643073585805190706138119617126, 0, -140353782985709462367814671439286096111050724, 0, 11487323243342943712727117998313670374759563626306467569441], [1, 0, 0, 0, 505198667146996121623641613298, 0, 0, 0, 63806423321775344604618774305037646254726223988233042609201], [1, 0, 0, 0, 2254739152546151619355840023938, 0, 0, 0, 1568638556854706336108974223356857608957236560013645822451521], [1, 0, 0, 0, 5248706182068433983596210407538, 0, 0, 0, 118558120445975157028044470669508269904542112710719750776396721], [1, 0, 34651983274619756, 0, 450284979324197740563114894562326, 0, 2600544595392433791184616027102404656188282152076, 0, 5632126739027588519658984775872141857619309476789431335641625841], [1, -791579528, 281750890302100108, -58770681630386315018384216, 7849858386044483826367186097276470, -687272936961181349368370758886633900318456, 38530294389354540781199294116254598468162252551148, -1265902038316081927695460685130723236752576711061600395688, 18701397461209715023927088008788055619800417991632621566284510161], [1, 0, 0, 0, 1480391027713560112434162035465618, 0, 0, 0, 547889398733702676213614311297941818478464344374520135510515030481], [1, 0, -183394002873796124, 0, 12612510108777727870656060869033766, 0, -385509785855827548271225059872289924056884725987164, 0, 4418761423445010359012517479030513507821439762288727229544623559521], [1, 0, 0, 0, 6931727443098214408166945170751138, 0, 0, 0, 12012211336350227316446820100278887925603925639507433655692782073761], [1, 0, -123985600064739644, 0, 32571917375014934968163747045083206, 0, -1780979380885104182920543145205708166471717125809084, 0, 206336132715709669990485567530001552309415935666586885734738159549121], [1, 0, 0, 0, 57568683429868415121343383075018578, 0, 0, 0, 1221268978022589508833760255513684608154133797863046939086649799003281], [1, 0, 1401425614829940836, 0, 736497657713054133014530649722642086, 0, 172024447130221367654923380329451230442203924163937316, 0, 15067466661578195724088403821109198918255739721817916514744422568289761], [1, 0, 0, 0, 1155902525086081958656549590612514178, 0, 0, 0, 334027661875095082935878165689897695724025886105865253311336914562753921]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/75/10/e/c'], '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': '8-75e4-1.1-c9e4-0-2', 'motivic_weight': 9, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0, 0, 0], 'nu_real_doubled': [9, 9, 9, 9], 'order_of_vanishing': 0, 'prelabel': '8-75e4-1.1-c9e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.215117674854636, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c9e4-0', 'trace_hash': 1318207580352501464, 'z1': {'__RealLiteral__': 0, 'data': '0.17592590938500470586699811319742', 'prec': 107}}
  • lfunc_instances • Show schema
    {'Lhash': '223012584627598311401826543896,847379985171139106180446985628,1150268191014912920044285813373,2411307627508062625862882589838', 'Lhash_array': ['223012584627598311401826543896', '847379985171139106180446985628', '1150268191014912920044285813373', '2411307627508062625862882589838'], 'factors': ['2-75-15.8-c9-0-6', '2-75-15.2-c9-0-17', '2-75-15.2-c9-0-27', '2-75-15.8-c9-0-46'], 'label': '8-75e4-1.1-c9e4-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/75/10/e/c'}