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  • lfunc_lfunctions • Show schema
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True, 'root_analytic_conductor': 7.591161870357474, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c11e4-0', 'trace_hash': 2233059411975744876, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.24972117325237790715009141799624', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '0.61944599774270272998193452695484', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '1.04032624956134079912957134476557', 'prec': 110}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 11027219.456951272, '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, 6283207, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 728375968, 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, -52110458392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -31381059609, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 0, -1141246682444, 0, 488416496321038566679926, 0, -92900617679551232564007071185236524, 0, 6626407607736641103900260617069258125403649041], 'euler13': [1, 0, 0, 0, 6423677755909710210314738, 0, 0, 0, 10315908977942302627204470186314316211062255002161], 'euler17': [1, 0, 0, 0, 2339993563734265350540393218, 0, 0, 0, 1379597950901634641862681879083307429684165246101910721], 'euler19': [1, 0, 226911314282356, 0, 40012146973684716323425971606, 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0, 196848866475416879432797277192776967948258, 0, 0, 0, 9687369058164125853307735924047630443938791496606281580842909489563923061541308641], 'euler79': [1, 0, -2633892617527596163004, 0, 2853337061341554749910797115308861786969286, 0, -1473649066778883408635101949577642871501589852936646576993269564, 0, 313034364745052523839935074823374313377854946907932671365884372878988897965899682881], 'euler83': [1, 0, 0, 0, -1768719249742181378392436843621190716210062, 0, 0, 0, 2750654632552663531244212470741561872330397633217957738144914426656998013516407193521], 'euler89': [1, 0, 11100692295067961361956, 0, 46209513536167951259643738526784592916554726, 0, 85492931811629706974850830723672665993856409129013709906361400676, 0, 59314420590258030980772760544661405787251822601630132400001155963107100089893048692641], 'euler97': [1, 0, 0, 0, 102331219451955298906936061197770229780646018, 0, 0, 0, 2617919618631058636393965401227693956107300157969550698791944746999930276251112354814081], 'euler_factors': [[1, 0, 0, 0, -6283207, 0, 0, 0, 17592186044416], [1, 0, 0, 0, 31381059609, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 7819642097165976098, 0, 0, 0, 15286700631942576193765185769276826401], [1, 0, -1141246682444, 0, 488416496321038566679926, 0, -92900617679551232564007071185236524, 0, 6626407607736641103900260617069258125403649041], [1, 0, 0, 0, 6423677755909710210314738, 0, 0, 0, 10315908977942302627204470186314316211062255002161], [1, 0, 0, 0, 2339993563734265350540393218, 0, 0, 0, 1379597950901634641862681879083307429684165246101910721], [1, 0, 226911314282356, 0, 40012146973684716323425971606, 0, 3079182091473717839598625775036430935420116, 0, 184144368549628275143663229532787625188711914273876985521], [1, 0, 0, 0, -1547514398936113092430568145502, 0, 0, 0, 824185149135487077883465900577270766354751717380230010246241], [1, 0, 48802039062823316, 0, 893114631258499814636031387463446, 0, 7264302520376058289856097686172671267821417751156, 0, 22157048460222391505313258277903605213230926984354560377055172081], [1, -728375968, 300583239120595708, -79672423854430405090694176, 15083010857955592063912194513345670, -2024354940785868082008236670821028509964256, 194053743209621523372656781258786205161581181896188, -11947897957439477805719063084389182824771587368075734593888, 416787349596085853594397793593920583748646209303727133530079150721], [1, 0, 0, 0, 63309360279318252593666962868261138, 0, 0, 0, 1002018774744129923516369294161573737191759373151725198030728940263761], [1, 0, -2201316126864993764, 0, 1817172258898461494967559027409582886, 0, -666695099800812159587186372705774459149435651038520484, 0, 91725417180837143663326189086434787308803478524071148179882832902891361], [1, 0, 0, 0, 1727173708440817487603027571184815698, 0, 0, 0, 745782254782301503355862595418917382807246689177519953982343989556806801], [1, 0, 0, 0, 12090886489402518745578299033987314178, 0, 0, 0, 37351302345958493037830232088788907611014369661290907772288660777346988481], [1, 0, 0, 0, 67011876803156865585493478941250548178, 0, 0, 0, 7381391874719262009044156620311078835772712945516819387010106565605821547281], [1, 0, 120623553778951370636, 0, 5456265647348840057787606461888641141686, 0, 109692358790871287125927865572860747352344874145641595988716, 0, 826967633734418240453603147406490983820063629653592282316619531810805486858961], [1, 52110458392, 1192368123129879564268, 15646712028766287993443670140104, 128786745917728416755586233395173636757270, 680849738109598359740676463086949148944332609760744, 2257702569665790016701838804704780256073571998611421655586828, 4293480045795125093027741547194135644490910926893351999857921309620152, 3585194656582687097035763534929220777070593006222509027099005738447779809872241], [1, 0, 0, 0, 29831538726770303166434403710273959657778, 0, 0, 0, 222480175701699090139272510552932572965903322627160280533457310251712459718974321], [1, 0, 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59314420590258030980772760544661405787251822601630132400001155963107100089893048692641], [1, 0, 0, 0, 102331219451955298906936061197770229780646018, 0, 0, 0, 2617919618631058636393965401227693956107300157969550698791944746999930276251112354814081]], 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/75/12/e/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': '8-75e4-1.1-c11e4-0-3', 'motivic_weight': 11, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0, 0, 0], 'nu_real_doubled': [11, 11, 11, 11], 'order_of_vanishing': 0, 'prelabel': '8-75e4-1.1-c11e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.591161870357474, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c11e4-0', 'trace_hash': 2233059411975744876, 'z1': {'__RealLiteral__': 0, 'data': '0.24972117325237790715009141799624', 'prec': 107}}
  • lfunc_instances • Show schema
    {'Lhash': '316559195163074519338002414857,785241090847511550607582501076,1318770194689616438119775299071,1675834998940063166808937414191', 'Lhash_array': ['316559195163074519338002414857', '785241090847511550607582501076', '1318770194689616438119775299071', '1675834998940063166808937414191'], 'factors': ['2-75-15.2-c11-0-10', '2-75-15.8-c11-0-22', '2-75-15.8-c11-0-40', '2-75-15.2-c11-0-51'], 'label': '8-75e4-1.1-c11e4-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/75/12/e/b'}