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lfunc_lfunctions • Show schema
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{'Lhash': '2288679698424338913086461405900', 'a10': 6823600, 'a2': 140, 'a3': 729, 'a4': 11408, 'a5': 48740, 'a6': 102060, 'a7': 487486, 'a8': 450240, 'a9': 531441, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 35.386206554131206, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '6.5', 'prec': 10}, 'bad_lfactors': [[3, [1, -729]], [11, [1, 1771561]]], 'bad_primes': [3, 11], 'central_character': '33.1', 'coefficient_field': '1.1.1.1', 'conductor': 33, 'conductor_radical': 33, 'degree': 2, 'euler_factors': [[1, -140, 8192], [1, -729], [1, -48740, 1220703125], [1, -487486, 96889010407], [1, 1771561], [1, 18388304, 302875106592253], [1, 96233254, 9904578032905937], [1, 14954652, 42052983462257059], [1, -153804394, 504036361936467383], [1, -5219010534, 10260628712958602189], [1, -1183811728, 24417546297445042591], [1, 17672200362, 243569224216081305397], [1, 19461739306, 925103102315013629321], [1, 3412304904, 1718264124282290785243], [1, 100327719050, 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42052983462257059], 1]], [[[1, -153804394, 504036361936467383], 1]], [[[1, -5219010534, 10260628712958602189], 1]], [[[1, -1183811728, 24417546297445042591], 1]], [[[1, 17672200362, 243569224216081305397], 1]], [[[1, 19461739306, 925103102315013629321], 1]], [[[1, 3412304904, 1718264124282290785243], 1]], [[[1, 100327719050, 5460999706120583177327], 1]], [[[1, -275469097716, 26036721925606486195973], 1]], [[[1, 267676863080, 104972647676132430295979], 1]], [[[1, -563486626260, 161915287432152755657581], 1]], [[[1, -1080842815700, 548242166610401428685587], 1]], [[[1, 1150562265222, 1165087474585497590531111], 1]], [[[1, 345914515454, 1671849507393788885941033], 1]], [[[1, 2004080959294, 4668229371502258117133839], 1]], [[[1, 3336732240564, 8871870642308873326043363], 1]], [[[1, 5696238036294, 21982145917308330487013369], 1]], [[[1, 6550114593202, 67302709016557486028618977], 1]], [[[1, -20022479158390, 113809328043328941786781301], 1]], [[[1, -8502303668252, 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['1.80544993865997630116203589564292', '2.63112862577717729411360416363277', '4.57250189909968270950748693319704', '5.32476514760438560927958477870921', '6.84789568417933628640424568078936', '8.599698246917419019228463224903795', '10.21821014168884657375674165635641', '11.67272570689685354473724827355928', '12.98653630925601026572263765168336', '13.94300358636676800050025533610162'], 'prelabel': '2-33-1.1-c13-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.948630645294025, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c13-0', 'trace_hash': 1413168950634057792, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.80544993865997630116203589564', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.63112862577717729411360416363', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.57250189909968270950748693320', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 35.386206554131206, 'bad_primes': [3, 11], 'central_character': '1.1', 'conductor': 33, 'conductor_radical': 33, 'degree': 2, 'dirichlet_coefficients': [1, 140, 729, 11408, 48740, 102060, 487486, 450240, 531441, 6823600, -1771561, 8316432, -18388304, 68248040, 35531460, -30420736, -96233254, 74401740, -14954652, 556025920, 355377294, -248018540, 153804394, 328224960, 1154884475, -2574362560, 387420489, 5561240288, 5219010534, 4974404400, 1183811728, -7947269120, -1291467969, -13472655560, 23760067640, 6062678928, -17672200362, -2093651280, -13405073616, 21944697600, -19461739306, 49752821160, -3412304904, -20209967888, 25902434340, 21532615160, -100327719050, -22176716544, 140753589789, 161683826500, -70154042166, -209773772032, 275469097716, 54238868460, -86345883140, 219485696640, -10901941308, 730661474760, -267676863080, 405342895680, 563486626260, 165733641920, 259070047326, -863411007488, -896245936960, -180805515660, 1080842815700, -1097828961632, 112123403226, 3326409469600, -1150562265222, 239275995840, -345914515454, -2474108050680, 841910782275, -170602670016, -863611185646, -1876710306240, -2004080959294, -1482706672640, 282429536481, -2724643502840, -3336732240564, 4054144169952, -4690408799960, -477722686560, 3804658679286, -797627624640, -5696238036294, 3626340807600, -8964040763744, 1754600526752, 862998749712, -14045880667000, -728889738480, -5793559188480, -6550114593202, 19705502570460, -941480149401, 13174922090800], 'euler11': [1, 1771561, 0], 'euler13': [1, 18388304, 302875106592253], 'euler17': [1, 96233254, 9904578032905937], 'euler19': [1, 14954652, 42052983462257059], 'euler2': [1, -140, 8192], 'euler23': [1, -153804394, 504036361936467383], 'euler29': [1, -5219010534, 10260628712958602189], 'euler3': [1, -729, 0], 'euler31': [1, -1183811728, 24417546297445042591], 'euler37': [1, 17672200362, 243569224216081305397], 'euler41': [1, 19461739306, 925103102315013629321], 'euler43': [1, 3412304904, 1718264124282290785243], 'euler47': [1, 100327719050, 5460999706120583177327], 'euler5': [1, -48740, 1220703125], 'euler53': [1, -275469097716, 26036721925606486195973], 'euler59': [1, 267676863080, 104972647676132430295979], 'euler61': [1, -563486626260, 161915287432152755657581], 'euler67': [1, -1080842815700, 548242166610401428685587], 'euler7': [1, -487486, 96889010407], 'euler71': [1, 1150562265222, 1165087474585497590531111], 'euler73': [1, 345914515454, 1671849507393788885941033], 'euler79': [1, 2004080959294, 4668229371502258117133839], 'euler83': [1, 3336732240564, 8871870642308873326043363], 'euler89': [1, 5696238036294, 21982145917308330487013369], 'euler97': [1, 6550114593202, 67302709016557486028618977], 'euler_factors': [[1, -140, 8192], [1, -729, 0], [1, -48740, 1220703125], [1, -487486, 96889010407], [1, 1771561, 0], [1, 18388304, 302875106592253], [1, 96233254, 9904578032905937], [1, 14954652, 42052983462257059], [1, -153804394, 504036361936467383], [1, -5219010534, 10260628712958602189], [1, -1183811728, 24417546297445042591], [1, 17672200362, 243569224216081305397], [1, 19461739306, 925103102315013629321], [1, 3412304904, 1718264124282290785243], [1, 100327719050, 5460999706120583177327], [1, -275469097716, 26036721925606486195973], [1, 267676863080, 104972647676132430295979], [1, -563486626260, 161915287432152755657581], [1, -1080842815700, 548242166610401428685587], [1, 1150562265222, 1165087474585497590531111], [1, 345914515454, 1671849507393788885941033], [1, 2004080959294, 4668229371502258117133839], [1, 3336732240564, 8871870642308873326043363], [1, 5696238036294, 21982145917308330487013369], [1, 6550114593202, 67302709016557486028618977]], 'index': 15, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/33/14/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/33/14/a/a'], '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': '2-33-1.1-c13-0-15', 'motivic_weight': 13, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [13], 'order_of_vanishing': 0, 'prelabel': '2-33-1.1-c13-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.948630645294025, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c13-0', 'trace_hash': 1413168950634057792, 'z1': {'__RealLiteral__': 0, 'data': '1.80544993865997630116203589564', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20721396
{'Lhash': '2288679698424338913086461405900', 'Lhash_array': ['2288679698424338913086461405900'], 'label': '2-33-1.1-c13-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/33/14/a/a'}
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id: 24565919
{'Lhash': '2288679698424338913086461405900', 'Lhash_array': ['2288679698424338913086461405900'], 'label': '2-33-1.1-c13-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/33/14/a/a/1/1'}