-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2229542945791468366886443546038', 'a10': [0.0, 0.0], 'a2': [-0.4843509486627027, -0.8748737957725903], 'a3': [0.40438055936863865, -1.6818685272460054], 'a4': [-0.5308083170590799, 0.8474919058851873], 'a5': [0.0, 0.0], 'a6': [-1.6672848099731232, 0.46083266178606114], 'a7': [0.0, 0.0], 'a8': [0.9985459725139387, 0.05390677857368543], 'a9': [-1.7744578473347266, -0.905638792831353], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.864506887196897, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.4843509486627027, 0.8748737957725903]]], [467, [[1.0, 0], [-0.3997448975026382, 0.9166264325888739]]]], 'bad_primes': [2, 467], 'central_character': '3736.163', 'coefficient_field': 'CDF', 'conductor': 3736, 'conductor_radical': 934, 'conjugate': '669375350417322163947139114609', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.4843509486627027, 0.8748737957725903]], [[1.0, 0], [-0.40438055936863865, 1.6818685272460054], [-0.8907002588106275, -0.45459107883314326]], [[1.0, 0], [0, 0], [-0.8137456150878302, 0.5812211919100412]], [[1.0, 0], [0, 0], [-0.4243147359028965, -0.9055147734276097]], [[1.0, 0], [-0.2974190078360529, 0.2064341768408205], [0.349751279297901, -0.9368425922370747]], [[1.0, 0], [0, 0], [-0.47251115500051594, -0.8813246895441421]], [[1.0, 0], [0.8746646689239129, 1.141212119751665], [-0.25990419819209926, 0.9656344068860233]], [[1.0, 0], [0.32416704697076704, 0.2590257363600004], [0.22064263981865348, 0.9753547177790529]], [[1.0, 0], [0, 0], [0.8058351460275219, 0.5921399475012663]], [[1.0, 0], [0, 0], [-0.19426374323110576, -0.980949335116671]], [[1.0, 0], [0, 0], [-0.6502166707879502, 0.7597488275933266]], [[1.0, 0], [0, 0], [0.5757220656897896, -0.8176454629470414]], [[1.0, 0], [-0.1911805978206683, 1.2230714384143881], [-0.9522986965988745, -0.3051674826322177]], [[1.0, 0], [1.3744961580743786, 0.4817000538366387], [0.7812306445022025, 0.6242424850093697]], [[1.0, 0], [0, 0], [0.5077642422115294, -0.8614960675077695]], [[1.0, 0], [0, 0], [-0.8438941686914587, -0.5365096756336756]], [[1.0, 0], [1.0552812672479706, -0.40209440185645173], [0.7464438122564557, -0.6654484466463567]], [[1.0, 0], [0, 0], [0.07408981496867606, 0.9972515727327319]], [[1.0, 0], [-0.6363743338945296, -0.34672759880998255], [0.542186650271374, 0.8402580771807593]], [[1.0, 0], [0, 0], [0.6604011258111099, 0.7509130129565066]], [[1.0, 0], [0.4027190579900682, 0.5719450933557044], [-0.3370882061557633, 0.94147306985951]], [[1.0, 0], [0, 0], [0.10095196391651615, -0.9948913010884146]], [[1.0, 0], [1.1364052470217145, -0.18549043703110224], [0.9480976163805078, -0.31797941727979734]], [[1.0, 0], [-0.029078246529855793, -0.028114231067513998], [0.03370169266593337, 0.9994319366077167]], [[1.0, 0], [0.5417864130076588, -1.9099355094750705], [-0.8510511252476587, -0.5250828336697877]], [[1.0, 0], [0, 0], [0.5757220656897896, 0.8176454629470414]], [[1.0, 0], [0, 0], [-0.9822366849055603, -0.18764619587333795]], [[1.0, 0], [0.8998182079834096, 0.1971878829998086], [0.9083547409431929, 0.41820050765873645]], [[1.0, 0], [0, 0], [-0.3997448975026382, -0.9166264325888739]], [[1.0, 0], [-1.5590728261393427, 1.14563047537923], [0.2987405651463953, -0.9543343621268242]], [[1.0, 0], [0, 0], [-0.6902268496974199, 0.7235930458184181]], [[1.0, 0], [0.23994282147501916, 0.08773935466004133], [0.7641150399493669, 0.6450799994753964]], [[1.0, 0], [-0.3363283035427683, 0.8317241796347105], [-0.7189233939252268, -0.6950893134461451]], [[1.0, 0], [0.13459286682528274, -0.6346120031360839], [-0.913910696780706, -0.40591530928237285]], [[1.0, 0], [0, 0], [-0.9996364270358346, -0.02696319237461772]], [[1.0, 0], [0, 0], [-0.939179173520518, 0.34342754698089745]], [[1.0, 0], [0, 0], [-0.797778180372801, -0.6029510551620775]], [[1.0, 0], [-0.4183815217679366, 1.849462966103606], [-0.9026336509877119, -0.430409679380696]], [[1.0, 0], [0, 0], [-0.939179173520518, -0.34342754698089745]], [[1.0, 0], [0, 0], [0.15443656205886863, -0.9880027066255624]], [[1.0, 0], [-0.7071408295335264, 0.37300908772336216], [0.5646455660431551, -0.825333499106758]], [[1.0, 0], [0, 0], [0.41206727253501346, -0.9111534244602031]], [[1.0, 0], [0, 0], [-0.6083156260560387, 0.793695218012588]], [[1.0, 0], [-1.7683005115126693, 0.2156411490539504], [0.9706930838367515, -0.24032256862703813]], [[1.0, 0], [0, 0], [-0.9768200297248191, 0.21406220948220528]], [[1.0, 0], [0, 0], [-0.5193334856844527, 0.8545716650151913]], [[1.0, 0], [-0.9774346479062943, 1.2402998440257824], [-0.23377311777594578, -0.972291175217236]], [[1.0, 0], [0, 0], [0.864899615524244, -0.5019448725368304]], [[1.0, 0], [-1.7283842947084638, 1.0030685861459734], [0.49610268986797007, -0.8682638545429406]], [[1.0, 0], [0, 0], [-0.37488438622778975, 0.9270715705718806]], [[1.0, 0], [-0.9665013861742705, 1.745772850608369], [-0.5308083170590799, -0.8474919058851873]], [[1.0, 0], [0, 0], [0.9796174019627969, -0.20087246145666687]], [[1.0, 0], [-0.40084357586699043, -0.18454572796664925], [0.6502166707879502, 0.7597488275933266]], [[1.0, 0], [1.0179518584506135, -1.0671605807216862], [-0.04717379191355071, -0.9988866969564151]], [[1.0, 0], [-1.1950095281466766, 0.016113565126778202], [0.9996364270358346, -0.02696319237461772]], [[1.0, 0], [0, 0], [0.9601807560796713, 0.27937951903149705]], [[1.0, 0], [0, 0], [0.2858462903287812, -0.9582754814275872]], [[1.0, 0], [0, 0], [-0.9706930838367515, -0.24032256862703813]], [[1.0, 0], [0, 0], [0.9601807560796713, -0.27937951903149705]], [[1.0, 0], [-0.7221057601594815, 0.6096149912397035], [0.1677435885536452, -0.9858306591393602]], [[1.0, 0], [-0.5953482202162054, 1.5313598712520837], [-0.7374038396918787, -0.6754521279910768]], [[1.0, 0], [0, 0], [-0.6704655233803912, -0.7419406862804183]], [[1.0, 0], [0.4065309611197418, -1.2986735339236366], [-0.8215081494720247, -0.5701967733607842]], [[1.0, 0], [0, 0], [0.8907002588106275, -0.45459107883314326]], [[1.0, 0], [0.10485547061491086, 0.17254137578138143], [-0.46058546129367267, 0.8876153631190116]], [[1.0, 0], [0, 0], [0.20747205018904832, 0.9782409459792373]], [[1.0, 0], [-1.0606067120968712, -1.5502720671397645], [-0.3623507694956099, 0.9320418015550265]], [[1.0, 0], [-0.542627974781435, -1.9129022297112408], [-0.8510511252476587, 0.5250828336697877]], [[1.0, 0], [0.03470562719110985, 1.715755760428128], [-0.9991820227951157, 0.04043866124219408]], [[1.0, 0], [0, 0], [-0.1677435885536452, -0.9858306591393602]], [[1.0, 0], [-0.7801455049223891, -0.3339834899613599], [0.6902268496974199, 0.7235930458184181]], [[1.0, 0], [0, 0], [0.8215081494720247, -0.5701967733607842]], [[1.0, 0], [0, 0], [0.9926462320073429, -0.12105146872972786]], [[1.0, 0], [0, 0], [0.46058546129367267, 0.8876153631190116]], [[1.0, 0], [1.6996273470390104, -1.0486386975943456], [0.4485760355706122, -0.8937446728858041]], [[1.0, 0], [0, 0], [0.913910696780706, -0.40591530928237285]], [[1.0, 0], [0, 0], [-0.8580533651820602, -0.5135605344063561]], [[1.0, 0], [0, 0], [0.8781191975669858, -0.47844192423356147]], [[1.0, 0], [-0.3326326752534034, 0.399444955288305], [-0.18102012014561342, -0.9834793928204433]], [[1.0, 0], [0.10815610599033784, -0.5876103792420257], [-0.9344634322049353, -0.3560591156981831]], [[1.0, 0], [1.953462478701995, -0.42808550357974884], [0.9083547409431929, -0.41820050765873645]], [[1.0, 0], [0, 0], [-0.9295778103485298, 0.36862595473953375]], [[1.0, 0], [0, 0], [-0.47251115500051594, 0.8813246895441421]], [[1.0, 0], [-0.46905578751328975, 1.0755582769899747], [-0.6804080338412106, -0.7328334786868965]], [[1.0, 0], [0, 0], [-0.6294950157908129, 0.7770045206396963]], [[1.0, 0], [-0.3658340916565229, 1.2264278116100515], [-0.8365837966105482, -0.5478389829582054]], [[1.0, 0], [0.02777472915332886, 0.8236663844046566], [-0.997728391822902, 0.06736509593614375]], [[1.0, 0], [1.2789451545325454, 1.2036081556056653], [0.06063731521372403, 0.9981598649533407]], [[1.0, 0], [0, 0], [-0.8580533651820602, 0.5135605344063561]], [[1.0, 0], [0, 0], [0.4364850610818145, 0.8997115045682169]], [[1.0, 0], [-0.3997448975026382, 0.9166264325888739]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-3736-3736.163-c0-0-0', 'leading_term': '0.82553648597437455393521501903949', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/3736/1/l/a/163/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.8255364859743746, 0.938045503569144, 1.0657000399530872, 1.2108168695164547, 1.3746782616844115, 1.5574502665116543, 1.7582068073001564, 1.9750075376274105, 2.2049898989844343, 2.444455975693633, 2.688950612844028, 2.933335777800506, 3.171868972755694, 3.398293172474501, 3.605944080389462, 3.7878784245913644, 3.9370249528464143, 4.046357858014642, 4.1090905926575525, 4.118886410182394, 4.070080501890579, 3.9579073014141146, 3.778725430082866, 3.530231897728179, 3.211656596632001, 2.8239278748774392, 2.3698000878228322, 1.8539345329335273, 1.2829260919256464, 0.6652692382732142, 0.011258803347530773, -0.6671770025940306, -1.3567114010505745, -2.042919115625945, -2.7106363225972516, -3.34437225388309, -3.928761456909117, -4.449043158898217, -4.891551970192352, -5.244202422866418, -5.4969486982207965, -5.642200454587471, -5.675176007137292, -5.594175286711507, -5.4007570332062755, -5.099807540046357, -4.699491897770601, -4.211082982598349, -3.6486682551791647, -3.0287395934770402, -2.369676668433068, -1.691139544763633, -1.0133910014837624, -0.3565732648808025, 0.26003281145302315, 0.8187358178582008, 1.3041177991702482, 1.7036432723430168, 2.008164162227972, 2.212294879525201, 2.3146364799731067, 2.3178348182501107, 2.2284646275307955, 2.0567392322603646, 1.816053795939465, 1.5223782322117243, 1.193523754451788, 0.8483140879424466, 0.505698216441047, 0.18384581612080048, -0.10073106088326005, -0.33398617888058957, -0.5050352247243762, -0.6067020183683867, -0.635883310082135, -0.5937088532076368, -0.4854832241246077, -0.32040677642875653, -0.11108463448538233, 0.12715583916126827, 0.3771077518186831, 0.6206465340919096, 0.8397620545734448, 1.017606600135406, 1.1395015707871008, 1.1938460186878437, 1.1728736006491551, 1.073211062884323, 0.8962008073382934, 0.6479619965657691, 0.33917847319211747, -0.015383202344755206, -0.39760686205115187, -0.7869772903548377, -1.1617009180474689, -1.4999379082143114, -1.781078412161857, -1.9869908560861653, -2.1031691993159716, -2.11970940030992, -2.032052814866916, -1.8414456595705642, -1.5550784839651801, -1.1858870631326022, -0.7520153128355315, -0.27596066386095736, 0.21655835135678725, 0.6979549265732093, 1.140275049723617, 1.5167636507626585, 1.8034063000701754, 1.9803557262175908, 2.0331566403387495, 1.9536919216130728, 1.7407877291369862, 1.4004338325502976, 0.9455973810113841, 0.3956322050133796, -0.22468985053654036, -0.8864756316594277, -1.5582645198252758, -2.207751395479947, -2.8035786137862724, -3.3170907373858123, -3.7239461136880005, -4.005486371469474, -4.149778273416551, -4.1522614070808945, -4.0159588461666305, -3.751234754783037, -3.3751112770617877, -2.9101851431069004, -2.3832103868905685, -1.8234356591882854, -1.2608012855878603, -0.7241112430190196, -0.2392977982391765, 0.17210866068025815, 0.4942048742883691, 0.7175550054647962, 0.8395913105458429, 0.8645499562542672, 0.8029483076619209, 0.6706415536404484, 0.48752587098950756, 0.2759803644618035, 0.05915891377213496, -0.1407456466641851, -0.3041398497446338, -0.415451440121835, -0.4642306160966068, -0.44584917898238907, -0.36174504294384374, -0.2191928396863771, -0.030616632929635644, 0.18750451289820308, 0.4160557685782902, 0.6349222005260041, 0.8247140793836653, 0.9684458867292375, 1.0530340596503893, 1.0704898770055202, 1.0187050693671365, 0.9017574108409255, 0.7296997249909922, 0.517835850166743, 0.2855282161253171, 0.05462065922188342, -0.15240612759046185, -0.31440334281770593, -0.4134883689772438, -0.4367823427870562, -0.37779773945243983, -0.23734413617224373, -0.02385302536939977, 0.24693552687877324, 0.5529332833359183, 0.8672689845007809, 1.160365605386779, 1.4023915662367132, 1.5659107481438073, 1.6285309116889244, 1.5753390733279338, 1.4009170547111338, 1.110751152176115, 0.7218858439223625, 0.2627206394365536, -0.2280915262929129, -0.7036205430466321, -1.111419321652846, -1.3969138081627461, -1.5072136021773974, -1.3950916890867937, -1.0228560215206426, -0.3658290267603099, 0.5848351280422449, 1.8202316775768341, 3.3128683906837773, 5.0170262248079105, 6.870353873769609, 8.79664764986502, 10.709683392125337, 12.517888665729847, 14.129577295122175, 15.45841943299132, 16.428792975977533, 16.980658816683064, 17.07362410815274, 16.689903548615476, 15.835956021775164, 14.542658464735414, 12.863974933808226, 10.87417987434258, 8.66379344374168, 6.334476267898323, 3.993204652362615, 1.7460994845267763, -0.3076912094554309, -2.0816571058801325, -3.5067678878368755, -4.535178280371553, -5.142558719698277, -5.328909172095328, -5.117818441282649, -4.554238755188801, -3.7009476707456814, -2.6339588851506512, -1.4372138129355059, -0.1969316210717961, 1.003986523055289, 2.0911141817221255, 3.002871536974317, 3.693830559105922, 4.136755448627498, 4.323277638056222, 4.263207804853802, 3.982588420274407, 3.520681577899531, 2.9261612640344596, 2.252831272007045, 1.5552158579304243, 0.8843683320515081, 0.28421366284368743, -0.21131238719159942, -0.5801383474999114, -0.8128437989913755, -0.912348055890481, -0.8925821584568967, -0.7763075089760232, -0.5923105391970481, -0.3722476780245327, -0.1474351525857768, 0.05412750664060831, 0.21024205118889255, 0.3062985821276475, 0.3362290746249583, 0.30257151778997815], 'positive_zeros': ['1.75879926644617898887326798363200', '3.13877178176383525817684258162839', '4.07972890021522839197862886947438', '4.59826851126675387255783556110412', '5.32960212646022490130456639356021', '6.18520810210292377757600793967915', '6.89343267885813186371672333056555', '8.001376295368495409468883211775067', '8.571257576084134316624986221285125', '9.032042099317531471076692859775812'], 'prelabel': '2-3736-3736.163-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3654694750146914, 'root_angle': -0.7461974424619888, 'root_number': '-0.69860936844845821658721452157379 - 0.71550328462980961585175824864709*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.3730987212309944', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.75879926644617898887326798363', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.13877178176383525817684258163', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.07972890021522839197862886947', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.864506887196897, 'bad_primes': [2, 467], 'central_character': '3736.163', 'conductor': 3736, 'conductor_radical': 934, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3736/1/l/a/163/1'], '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': '2-3736-3736.163-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3736-3736.163-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3654694750146914, 'root_angle': -0.3730987212309944, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.75879926644617898887326798363', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2229542945791468366886443546038', 'Lhash_array': ['2229542945791468366886443546038'], 'label': '2-3736-3736.163-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3736/1/l/a/163/1'}