-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2963136491442966349378183422587', 'a10': [0, 0], 'a2': [0, 0], 'a3': [3.6213203435596424, -2.0907702751760278], 'a4': [0, 0], 'a5': [-2.742640687119285, -1.5834643389987395], 'a6': [0, 0], 'a7': [-2.242640687119285, -6.631030293135233], 'a8': [0, 0], 'a9': [4.242640687119285, -7.3484692283495345], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.207115843341303, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [2.242640687119285, 6.631030293135233]]]], 'bad_primes': [2, 7], 'central_character': '448.257', 'coefficient_field': 'CDF', 'conductor': 448, 'conductor_radical': 14, 'conjugate': '741715533636589659035236077202', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-3.6213203435596424, 2.0907702751760278], [4.5, -7.794228634059948]], [[1.0, 0], [2.742640687119285, 1.5834643389987395], [12.5, 21.650635094610966]], [[1.0, 0], [2.242640687119285, 6.631030293135233]], [[1.0, 0], [6.621320343559643, 11.468463248234714], [-60.5, 104.78907385791707]], [[1.0, 0], [0, -5.493325359846907], [-169.0, 0]], [[1.0, 0], [11.742640687119286, -6.7796167617053715], [144.5, -250.28134169370276]], [[1.0, 0], [-0.6213203435596426, -0.3587194676071504], [180.5, 312.63517076618234]], [[1.0, 0], [-1.1360389693210722, 1.9676772142422783], [-264.5, -458.12743860196804]], [[1.0, 0], [20.48528137423857, 0], [841.0, 0]], [[1.0, 0], [-21.31980515339464, 12.308995244382766], [480.5, -832.2504130368455]], [[1.0, 0], [-32.47056274847714, 56.24066443071573], [-684.5, -1185.5887777808964]], [[1.0, 0], [0, 21.030795812694027], [-1681.0, 0]], [[1.0, 0], [6.48528137423857, 0], [1849.0, 0]], [[1.0, 0], [-41.378679656440355, -23.889991838357133], [1104.5, 1913.050116959825]], [[1.0, 0], [-11.01471862576143, -19.07805229089404], [-1404.5, 2432.6653592304883]], [[1.0, 0], [-72.53300858899107, 41.87695203398743], [1740.5, -3014.634430573631]], [[1.0, 0], [57.38225099390856, 33.12965805803978], [1860.5, 3222.4805274818964]], [[1.0, 0], [-46.31980515339464, -80.22825592237022], [-2244.5, 3887.5880375883453]], [[1.0, 0], [48.42640687119285, 0], [5041.0, 0]], [[1.0, 0], [-113.44112549695429, 65.49526434284067], [2664.5, -4615.049376767273]], [[1.0, 0], [-38.10660171779821, 66.00257027901796], [-3120.5, -5404.864545018681]], [[1.0, 0], [0, 107.98149594355094], [-6889.0, 0]], [[1.0, 0], [145.41168824543144, 83.95347735181777], [3960.5, 6859.787223376538]], [[1.0, 0], [0, -25.58161554584733], [-9409.0, 0]], [[1.0, 0], [24.683766184073566, -14.251179050988656], [5100.5, -8834.325144005059]], [[1.0, 0], [-48.922835533724644, -28.245612264915714], [5304.5, 9187.66350874911]], [[1.0, 0], [-23.805086527633208, 41.2316193444341], [-5724.5, -9915.124847928038]], [[1.0, 0], [-37.654328932550705, -65.21921083608859], [-5940.5, 10289.247822362915]], [[1.0, 0], [-85.45584412271572, 0], [12769.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 29, 'label': '2-448-7.5-c2-0-29', 'leading_term': '1.6983318648604097525118391078939029264986463003103122432', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/448/3/s/d/257/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0703125', 'prec': 30}, 'plot_values': [1.6983318648604098, 1.8916961930355656, 2.0805109576058203, 2.264005757096399, 2.4412692221173042, 2.611223449435342, 2.772609010627156, 2.923981542183133, 3.0637203963533315, 3.1900493356113917, 3.3010688111072684, 3.394798985469888, 3.469232339686147, 3.5223944320699414, 3.552411141571821, 3.5575805164708614, 3.536447155766824, 3.4878768728917793, 3.411129233864357, 3.3059254336910295, 3.1725088881094807, 3.011695887030553, 2.824913696039983, 2.6142236168569246, 2.382326738289577, 2.1325504342982473, 1.868814099466941, 1.5955731538718894, 1.3177409930632364, 1.0405892930332497, 0.7696278872513644, 0.5104662900730768, 0.2686598197661399, 0.04954414209320594, -0.1419371248291335, -0.3014063710154035, -0.42522154181208577, -0.5106348550447649, -0.5559340375583299, -0.5605594340027227, -0.5251906077178616, -0.45179660219089385, -0.3436448696321228, -0.20526499684262503, -0.04236475090659686, 0.13830240212463343, 0.3291173277442187, 0.5218198638230602, 0.7077731051929437, 0.878260351174601, 1.0248058223401415, 1.1395085336290884, 1.215377278665217, 1.2466536244230886, 1.2291092179214094, 1.1603036363675545, 1.0397895209551993, 0.86925285278878, 0.6525779627242551, 0.39582919318734666, 0.10714399787666357, -0.2034644063868793, -0.524393042270428, -0.8428181415547212, -1.14513744328646, -1.417472348373314, -1.6462129264471947, -1.8185857258822304, -1.9232219584370809, -1.950702077875258, -1.8940521829447776, -1.7491681502903806, -1.5151450004969926, -1.1944917295682898, -0.7932156540082599, -0.32076511960406795, 0.2101749441970748, 0.7840338891373939, 1.3828452765065953, 1.9868618164288916, 2.5752748080953016, 3.127011679565422, 3.621580221939564, 4.039924296245243, 4.365253423392008, 4.583807954208558, 4.685522594579998, 4.664553985252101, 4.519642772089677, 4.254287021094293, 3.8767117097267643, 3.3996280496309064, 2.8397861749992828, 2.2173348120355034, 1.5550114319107804, 0.8771955668287359, 0.208865928098584, -0.4254917667193817, -1.002975183975731, -1.5033011645368441, -1.9097349880912724, -2.209864788161126, -2.3961790505697897, -2.4664138274717753, -2.4236470898794984, -2.276130039391923, -2.0368586071375483, -1.7229021016508639, -1.354519292300062, -0.9541043823582772, -0.5450156155549498, -0.15034702249435425, 0.20829148903768474, 0.5119192523662853, 0.7451911425025487, 0.8972071290108731, 0.9620767221229337, 0.939202588146667, 0.8332627025316447, 0.653887181012773, 0.4150434705576228, 0.13416089635109127, -0.16895837762329408, -0.47338110549831613, -0.7583659095515325, -1.0046891553663264, -1.1958932056313012, -1.3193789998419938, -1.3672722040391045, -1.337004014358711, -1.2315635314832665, -1.0593976326748804, -0.8339554064492871, -0.5728962589739214, -0.2970024203274249, -0.028856412999917425, 0.2086392106928747, 0.3938100671533564, 0.5077289951118826, 0.5356074584671684, 0.46796554320671424, 0.30149765583867444, 0.039567550375506896, -0.30771234649195206, -0.7238373530237778, -1.1866955552977259, -1.6697465870634567, -2.14353283350726, -2.5774382161465295, -2.941590808036982, -3.208792614853158, -3.3563539964726727, -3.3677120361623696, -3.2337218542571087, -2.9535270672311706, -2.5349394631833113, -1.99428718355839, -1.3557235500863962, -0.6500231342810385, 0.08707446716196712, 0.81688165650008, 1.5000231028006066, 2.0988024876227547, 2.579528095260654, 2.9146480769227647, 3.0845544089332337, 3.0789322444129352, 2.897557642372942, 2.550480057065542, 2.057564466010177, 1.4474091815996466, 0.7556965464896304, 0.02307209343265192, -0.7073193025845019, -1.3924866051401936, -1.9922660119107003, -2.4718409998114867, -2.803942578518821, -2.9705817993055676, -2.964195421770778, -2.788123123063549, -2.4563783570796036, -1.9927220536641945, -1.4290956019277752, -0.8035137087404484, -0.1575556239715498, 0.466377895056508, 1.0278568454425336, 1.4910734422436058, 1.8271710230525853, 2.0160897987317683, 2.047801636619849, 1.9228483086704937, 1.6521464677667161, 1.2560746126696243, 0.7629087464083331, 0.20672056975618233, -0.375108633428261, -0.9445767768851538, -1.4657553876651461, -1.9072916721174424, -2.244534017367396, -2.461124399047029, -2.549940897054179, -2.5133224814041264, -2.3625628483361116, -2.11671628938373, -1.800812086384671, -1.4436205854903168, -1.0751501959111842, -0.7240771045742703, -0.41531650162544614, -0.16793474330056743, 0.006423435132593046, 0.10445812074571101, 0.13140430550569654, 0.10046394386120222, 0.031516840093849974, -0.050792730166705734, -0.11944324875647534, -0.14770407415905112, -0.1118635814521236, 0.0062142240666565535, 0.2169283203404473, 0.5213719918624381, 0.9105113790746283, 1.3652090603230598, 1.8571242055430435, 2.3504500806521462, 2.804379991575288, 3.176129767151594, 3.424293839326932, 3.512277322465542, 3.411531465480431, 3.1043262103229803, 2.5858214308385112, 1.865246119626939, 0.9660590736552455, -0.07495917978888023, -1.2096511377307164, -2.381349598776199, -3.5284780350090794, -4.588632340160968, -5.502848208950161, -6.219736587233785, -6.699172288464528, -6.915248346089713, -6.858259324599199, -6.535547103776227, -5.971127383402365, -5.204107857783959, -4.2860024337081315, -3.2771325615370634, -2.242379666687768, -1.2466057408368814, -0.35008781133502564, 0.3956864109713747], 'positive_zeros': ['2.33750253493311133591020494578719', '3.11076421535844472803662783484826', '4.24344168368033718221530382200018', '5.31670947961665835572101300829234', '6.77261337945866564665106813964830', '7.83308971422588216265189749430056', '8.539283544272564776619581434936962', '9.500150553213333548273513028856444', '9.993284898723072282001260494810497', '11.17141808695311884689802404001751'], 'prelabel': '2-448-7.5-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.49386832083599, 'root_angle': 0.7698695708271456, 'root_number': '-0.74984003060399453017142885202253754048026896921462167914 + 0.6616191718079219523819485086349207591460594151595316938*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.3849347854135728', 'prec': 60}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.33750253493311133591020494579', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.11076421535844472803662783485', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.24344168368033718221530382200', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 12.207115843341303, 'bad_primes': [2, 7], 'central_character': '7.5', 'conductor': 448, 'conductor_radical': 14, 'degree': 2, 'index': 29, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/448/3/s/d/257/2'], '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': '2-448-7.5-c2-0-29', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-448-7.5-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.49386832083599, 'root_angle': 0.3849347854135728, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '2.33750253493311133591020494579', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2963136491442966349378183422587', 'Lhash_array': ['2963136491442966349378183422587'], 'label': '2-448-7.5-c2-0-29', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/448/3/s/d/257/2'}