-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1879039122298276701333916825007', 'a10': [0.5, 0.8660254037844386], 'a2': [0.8660254037844386, 0.5], 'a3': [0.0, 0.0], 'a4': [0.5, 0.8660254037844386], 'a5': [0.8660254037844386, 0.5], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [3.9689140359382235e-80, 1.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.808485320465464, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8660254037844386, -0.5]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-0.8660254037844386, -0.5]]]], 'bad_primes': [2, 3, 5], 'central_character': '1620.919', 'coefficient_field': 'CDF', 'conductor': 1620, 'conductor_radical': 30, 'conjugate': '2566118484894460081789657376817', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8660254037844386, -0.5]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.8660254037844386, -0.5]], [[1.0, 0], [0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 1.0], [-1.0, 0]], [[1.0, 0], [0, 1.7320508075688772], [-1.0, 0]], [[1.0, 0], [0.8660254037844386, -1.5], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [1.5, 0.8660254037844386], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, -1.0], [-1.0, 0]], [[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0.5, 0.8660254037844386], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-1.5, 0.8660254037844386], [0.5, -0.8660254037844386]], [[1.0, 0], [-0.8660254037844386, -1.5], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [1.0, 0], [1.0, 0]], [[1.0, 0], [1.7320508075688772, 1.0], [0.5, 0.8660254037844386]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 7, 'label': '2-1620-180.139-c0-0-7', 'leading_term': '2.05969365742356204064118751934', '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/1620/1/p/d/919/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [2.059693657423562, 2.0222431917204653, 2.005300290504584, 2.005046870579249, 2.016830622333179, 2.0356495322367634, 2.056559094531349, 2.0749530255455526, 2.086723202871391, 2.0883317117560085, 2.0768311323759567, 2.049860780944698, 2.005635933725625, 1.9429384036556288, 1.8611111092278416, 1.7600559753947216, 1.6402328538651507, 1.5026565004496923, 1.3488885699826445, 1.1810218286566383, 1.0016541976014928, 0.8138507556570658, 0.621092405108244, 0.4272105208614967, 0.2363075475399927, 0.05266416830165725, -0.11936566921444933, -0.2754699358432018, -0.41150136104847224, -0.52360481164874, -0.6083455958413052, -0.6628346790062344, -0.6848465136244872, -0.6729250377737553, -0.6264734025536243, -0.5458231620774988, -0.4322790090564702, -0.28813566728440404, -0.11666425559118408, 0.07793369516613996, 0.2906053786127678, 0.5155586791226412, 0.7464054292439065, 0.9763331607112956, 1.1983012944216234, 1.4052565098461116, 1.590360934282273, 1.747225850232903, 1.8701428863735865, 1.9543041812017248, 1.996002829133641, 1.9928050681715486, 1.9436861668077021, 1.8491228230511378, 1.7111360933199091, 1.533280400915465, 1.3205759945063698, 1.079384282577055, 0.8172276917346969, 0.5425580040157539, 0.26447942964522986, -0.007565131096591614, -0.26413419142831124, -0.4961420152208279, -0.6952137693272022, -0.8540272695662361, -0.9666268478217843, -1.0286952178828057, -1.0377701948239884, -0.993394726494875, -0.8971908973705512, -0.7528513068459362, -0.5660444196226605, -0.344234021958042, -0.09641665752549702, 0.16721529508843613, 0.43567357318661415, 0.6976223057289321, 0.9418570049659813, 1.157794389231068, 1.335951650862288, 1.468393173641779, 1.5491230695788685, 1.574403288088819, 1.5429794490058963, 1.4561999134168284, 1.3180178327868177, 1.1348708593470465, 0.9154386675520293, 0.6702841985909602, 0.41139033979824696, 0.15160931277293552, -0.09595291308701966, -0.3185906144028818, -0.5046609410471403, -0.6442234557426759, -0.7296243446135585, -0.7559940707756916, -0.7216298284560115, -0.6282382751350181, -0.48101955841284005, -0.28858042016145363, -0.06267188832489318, 0.18224457148809986, 0.42958995516536164, 0.6613987205750693, 0.8591590656958932, 1.004726795342907, 1.08127162700477, 1.074211078098927, 0.9720853989672028, 0.7673275587581762, 0.45688514347777465, 0.04265616313500537, -0.46829195301097826, -1.0637417250849495, -1.726594218103975, -2.4353859817085093, -3.1650411900013484, -3.887833654494385, -4.574521898743588, -5.195610311758901, -5.722681115465695, -6.129735996445447, -6.394483171341092, -6.499505660285303, -6.433249768419627, -6.190779196168118, -5.7742496215803545, -5.1930706653683325, -4.463736350611447, -3.609320860763876, -2.6586528329475203, -1.6451977802240454, -0.6056936691505164, 0.421401645168819, 1.397581277704208, 2.2860006683135268, 3.0531474091924875, 3.670387364447943, 4.115308956169104, 4.37279568142631, 4.435768949541726, 4.3055586727633655, 3.991876994634546, 3.5123902236639615, 2.8919044585339964, 2.161200477079774, 1.3555721319093048, 0.5131387126140858, -0.3269854366897013, -1.126572091240493, -1.8501152264361977, -2.466527246788677, -2.950606839679251, -3.2842010463340974, -3.456999631620906, -3.4669189329509775, -3.320054091813669, -3.0302017631214397, -2.617978791490324, -2.109584633245547, -1.535275215243817, -0.9276322911814042, -0.3197241953980656, 0.25673954461739634, 0.773156451613802, 1.2055839612136234, 1.5360093862823672, 1.7532653177892707, 1.853538934460547, 1.8404470009247331, 1.724673488620819, 1.5231922998083347, 1.2581220081023985, 0.9552813850300109, 0.642532426635796, 0.34801050547863255, 0.09834831503448654, -0.08299904892299932, -0.17722632745216038, -0.17135811920310665, -0.059064686969563025, 0.15893637617541342, 0.4749172585951951, 0.8746134755521902, 1.3381044842153567, 1.8410466262498753, 2.3561815231193854, 2.8550255829179707, 3.309634625634246, 3.6943325923698125, 3.9872952607080725, 4.171888790065713, 4.2376782693927915, 4.181042316200863, 4.0053548929546485, 3.720723284840593, 3.3432998479482423, 2.894212832968941, 2.3981864984437125, 1.8819411889301876, 1.3724786765083221, 0.8953658243524755, 0.47312994466452424, 0.12387199300520525, -0.13981062823832657, -0.3115205045052905, -0.3913302789886288, -0.3856095628254078, -0.30642203982765764, -0.1705355752113666, 0.0018851196411467151, 0.18881154793821403, 0.36800248347584796, 0.5186566141249079, 0.6229497145249353, 0.6673468145030597, 0.643595113416709, 0.5493254697953626, 0.3882177162666699, 0.16971595865741163, -0.09168771538230773, -0.37755133359753534, -0.6668849478537713, -0.93775536166132, -1.1689766284731102, -1.3417614325370222, -1.4412095511580039, -1.457519700705008, -1.3868296342614665, -1.2316152134224985, -1.0006105979927558, -0.7082465237504794, -0.3736394138390713, -0.019198212022434137, 0.33105418871607645, 0.6533245054605037, 0.9259219679911032, 1.131019324809651, 1.256165400150008, 1.2954275397892085, 1.2500665517945249, 1.1286788656405802, 0.9467784576398346, 0.7258320066688677, 0.491801839075952, 0.2732894891863522, 0.09940525811067083, -0.0024865497214499217, -0.008983013652329288, 0.09734750726953201, 0.3263173802416371, 0.6789685452170189, 1.1470211212643264, 1.7129841505861434, 2.3509444997358404], 'positive_zeros': ['1.48230050296191406741310029785510', '2.26242527132989234558910948549110', '3.57255283615605177361288474574896', '4.35764931623525485525467436163190', '5.36737219805671584897445819349240', '5.99184138148652764590891469837852', '6.62642737977617720361907892094008', '7.88588828543812388200220977460562', '8.766064760443898842999176615245260', '9.641281582971000526324660776284843'], 'prelabel': '2-1620-180.139-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8991581176108371, 'root_angle': -0.38888888888888895, 'root_number': '0.34202014332566873304409961468239 - 0.93969262078590838405410927732446*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.19444444444444445', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.48230050296191406741310029786', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.26242527132989234558910948549', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.57255283615605177361288474575', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.808485320465464, 'bad_primes': [2, 3, 5], 'central_character': '180.139', 'conductor': 1620, 'conductor_radical': 30, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1620/1/p/d/919/2'], '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': '2-1620-180.139-c0-0-7', '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': '2-1620-180.139-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8991581176108371, 'root_angle': -0.19444444444444448, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.48230050296191406741310029786', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1879039122298276701333916825007', 'Lhash_array': ['1879039122298276701333916825007'], 'label': '2-1620-180.139-c0-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1620/1/p/d/919/2'}