-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '4626140503306636917906089402275', 'a10': [-0.17364817766693036, -0.3007674663608706], 'a2': [0.17364817766693036, -0.984807753012208], 'a3': [-0.23887785891483007, -1.35474365837288], 'a4': [-0.9396926207859084, -0.3420201433256687], 'a5': [0.266044443118978, -0.22323779409789932], 'a6': [-1.3756427629952728, 1.064664768090358e-60], 'a7': [-0.3659821128117296, 0.307095455877804], 'a8': [-0.5, 0.8660254037844386], 'a9': [1.040810113935924, -0.378823900995891], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.5908929749574752, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.17364817766693036, 0.984807753012208]]], [37, [[1.0, 0], [-2.4232242061012816, 5.579245867226574]]]], 'bad_primes': [2, 37], 'central_character': '74.33', 'coefficient_field': 'CDF', 'conductor': 74, 'conductor_radical': 74, 'conjugate': '2319068993710819417939700846288', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.17364817766693036, 0.984807753012208]], [[1.0, 0], [0.23887785891483007, 1.35474365837288], [-2.8190778623577253, 1.0260604299770062]], [[1.0, 0], [-0.266044443118978, 0.22323779409789932], [0.8682408883346517, -4.924038765061041]], [[1.0, 0], [0.3659821128117296, -0.307095455877804], [1.2155372436685123, -6.893654271085456]], [[1.0, 0], [1.292681353224196, -2.2389897817811977], [-5.5, -9.526279441628825]], [[1.0, 0], [-4.212876708731937, -1.5333617226117906], [9.958577760546714, 8.35623892592501]], [[1.0, 0], [1.8886361433687147, -0.687407339545528], [13.022755533022627, -10.927389364671168]], [[1.0, 0], [-0.6116313008966447, -3.46873347708427], [-17.854159794932258, 6.498382723187706]], [[1.0, 0], [2.6048599717265595, 4.511749817632831], [-11.5, 19.91858428704209]], [[1.0, 0], [0.11411087352345758, -0.19764583063869473], [-14.5, -25.11473670974872]], [[1.0, 0], [6.746582210107473, 0], [31.0, 0]], [[1.0, 0], [-2.4232242061012816, 5.579245867226574]], [[1.0, 0], [10.070081554646903, 3.665209942524596], [31.4078221678781, 26.354291997148113]], [[1.0, 0], [-8.858892514609277, 0], [43.0, 0]], [[1.0, 0], [3.7288989396989196, 6.458642419848244], [-23.5, 40.703193977868615]], [[1.0, 0], [-3.3519368236663, -2.812608952467936], [9.203353416347309, 52.194810909647025]], [[1.0, 0], [-3.4301598852876416, -2.8782458946239613], [10.24524248234889, 58.10365742772028]], [[1.0, 0], [-1.351752869782227, -0.4919978086846485], [46.728711030257664, 39.2100441908789]], [[1.0, 0], [8.061112486551373, -6.764076514343824], [11.634427903684333, -65.98211945181794]], [[1.0, 0], [-1.5419334903055724, -8.744739370629672], [-66.71817607579949, 24.28343017612248]], [[1.0, 0], [-7.186671375875246, 0], [73.0, 0]], [[1.0, 0], [-2.708569937830729, 2.2727600358516327], [13.718206035687498, -77.79981248796443]], [[1.0, 0], [1.3293242258389948, -0.48383444989435703], [63.581688778875176, -53.35137160398276]], [[1.0, 0], [-2.9295443541550417, -2.4581795870889787], [15.4546878123568, 87.64789001808651]], [[1.0, 0], [9.24175279049228, 16.007185384124078], [-48.5, 84.00446416709055]], [[1.0, 0], [8.56430568716119, 14.833812581714266], [-50.5, 87.4685657822283]], [[1.0, 0], [-6.710115302403755, 11.622260628408705], [-51.5, -89.20061658979718]], [[1.0, 0], [-19.226125918475933, -6.99773755457919], [81.96675541373065, 68.77827423645971]], [[1.0, 0], [-1.8508694864954485, 10.496802469246802], [-102.42649566566402, -37.28019562249789]], [[1.0, 0], [-2.1206301868270474, 12.02669142468474], [-106.18526614880764, -38.64827619580057]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-74-37.33-c1-0-2', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/74/2/f/b/33/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.9332819039859231, 0.9882094536805135, 1.0594436189448146, 1.1480964070887052, 1.2543800225066304, 1.377701780918839, 1.5167621674934433, 1.66961623235004, 1.8336908679262531, 2.0057719217117818, 2.1819827480404568, 2.3577749729869333, 2.5279482364809014, 2.6867112774023876, 2.827792766602328, 2.9446066832351634, 3.030473450837871, 3.0788942412754037, 3.0838717052150084, 3.040265938488441, 2.9441699192878983, 2.793284235316674, 2.587267029674059, 2.3280321509667545, 2.0199669399033344, 1.6700413469485598, 1.287782517415111, 0.8850938566942704, 0.47590499808486364, 0.07564893879352155, -0.2994254462959455, -0.6330838418822363, -0.910044062898453, -1.1169711661100181, -1.243468334552722, -1.2829925087193181, -1.2336187023855136, -1.0985772919686434, -0.8864951959588722, -0.6112852436844762, -0.291648116321525, 0.049822650804393125, 0.38791133647801435, 0.6963716612189415, 0.9497511446510095, 1.125329384635758, 1.2050270311534326, 1.177127108520958, 1.0376472576677713, 0.7912124240897312, 0.45130344786819837, 0.03979754323275009, -0.41423007346303453, -0.8764115176633802, -1.3095994376744657, -1.6768231152394315, -1.9444645392760758, -2.085388153784376, -2.0817352730697056, -1.927096879428585, -1.6278094382304504, -1.203177688825391, -0.6845133756634187, -0.1129838290443634, 0.4636193511081828, 0.9949642828231698, 1.4327827452265767, 1.7355796443086324, 1.8729867646821385, 1.829296297880972, 1.6057547294626737, 1.2212911865991156, 0.7114910261447133, 0.12579466435407527, -0.4769119471488058, -1.0339640875787781, -1.4853287683625562, -1.7801255386884862, -1.882564029478097, -1.776616482562534, -1.4688323118525193, -0.9888641343258997, -0.3874984132971758, 0.26775170061920056, 0.8991557846529944, 1.426782021724026, 1.7772130632355951, 1.8920229372125812, 1.7350435068410017, 1.297527760634598, 0.6005061768343531, -0.30608311480668426, -1.3475571647336855, -2.4316283257237625, -3.4578380290473216, -4.328293246659817, -4.958509725998514, -5.287095387401777, -5.283087919695272, -4.949991606172792, -4.325919480751224, -3.479699731014867, -2.5032972112774585, -1.5013710271217717, -0.5791755811226019, 0.16973925134169413, 0.6745023613640785, 0.8951682338875344, 0.8271472782629894, 0.5011983319641201, -0.021071169103900854, -0.6556584068908263, -1.3074925968652733, -1.8831468977893173, -2.3032265235583296, -2.5127363841960637, -2.4879809366580883, -2.2390099954781544, -1.8072393707238135, -1.2585616902355843, -0.6729236661171936, -0.1318836333693906, 0.2940066870128512, 0.5560867719628274, 0.635048253438121, 0.5437649806947061, 0.32496826695434333, 0.044031190850859846, -0.22209879378751293, -0.3981373314212742, -0.4237857028507938, -0.2649628752709959, 0.07897750358379295, 0.5734008643467299, 1.1524602337539545, 1.728686472686576, 2.2067883660721557, 2.499598317493524, 2.5436429333983224, 2.3117460860956323, 1.820416811054078, 1.1305018216880085, 0.34059501991188285, -0.426154799984196, -1.0400908736461156, -1.385321383803428, -1.3790876591938657, -0.9870754342382828, -0.23200411079728642, 0.8062287417513518, 1.9993036809539, 3.1871917163621752, 4.200564757642609, 4.8856388076586645, 5.127660770587575, 4.869316296373261, 4.121006923760446, 2.961134633451736, 1.526065919241484, -0.008913560992974252, -1.4548649803241478, -2.6368273214024116, -3.4194917863588636, -3.7268293854930254, -3.552492127038114, -2.959265125112447, -2.0676200093075408, -1.0352182357079545, -0.030732187173771252, 0.7936727608664778, 1.3265995469343161, 1.5143573498197338, 1.367743995699378, 0.9575801453916031, 0.3998523437085959, -0.1668566135967327, -0.6076026729038276, -0.8162683323903803, -0.7351602015625466, -0.36546138782874815, 0.23337371552514125, 0.9551846479080641, 1.6675153328024384, 2.237100467033422, 2.5556781532780093, 2.561266729015155, 2.2508366361499843, 1.681875579416294, 0.9624083717214631, 0.2312132835792504, -0.36813514946098463, -0.7145350202662633, -0.7327481600413733, -0.4083821235875834, 0.20852948722562184, 1.01219824986797, 1.8605070850167045, 2.6015937286495765, 3.102551300201436, 3.274716812529019, 3.090599666927306, 2.5890633759163277, 1.8676299315427878, 1.0632979757913974, 0.3255600871093802, -0.21308991230721736, -0.4632878936550368, -0.39628139457738804, -0.049136239855060715, 0.48352936089887516, 1.069754367763461, 1.568381634584137, 1.8594171181770462, 1.8702900690125308, 1.5924000541835714, 1.084213385489111, 0.45987792589881193, -0.1346700820601044, -0.5534411086322588, -0.6834902537258918, -0.47237085721625066, 0.05615144462397027, 0.8020043838028018, 1.6051070638040952, 2.2754428545911645, 2.6313076985641164, 2.538191833461843, 1.940289838605911, 0.8778007787989589, -0.5142031227012507, -2.0259797153303754, -3.4091876194337725, -4.422290076411843, -4.876641169759986, -4.674171791126733, -3.828984974735811, -2.468155365330392, -0.8110406511833786, 0.8693375023295261, 2.295659061659343, 3.2369828349542784, 3.550910531970823, 3.2089965481774225, 2.3004266564869194, 1.013288678131324, -0.4027759187075698, -1.6850348724546165, -2.607543803910846, -3.0225320233193553, -2.8852119168670347, -2.2574127150739467, -1.2898544970674728, -0.187294331060514, 0.835740565904784, 1.5991056891265913, 1.9917907790704967, 1.9902123122095252], 'positive_zeros': ['3.64938138511806075628993087681866', '5.10691019732322619661000002747474', '6.38630541976562303954617090625987', '7.899241766303637650717508146373065', '9.150952604979135287796908089040588', '10.32423843176886395918193050457258', '11.33535989188602221652010839108394', '13.09319224226518596399961019960505', '13.74554880250188375278344279023706', '15.15957799162391824025842500136535'], 'prelabel': '2-74-37.33-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7686956321961738, 'root_angle': 0.4751264929559764, 'root_number': '0.07806292522069962 + 0.9969484338249334*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.237563246478', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.64938138511806075628993087682', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.10691019732322619661000002747', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.38630541976562303954617090626', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.5908929749574752, 'bad_primes': [2, 37], 'central_character': '37.33', 'conductor': 74, 'conductor_radical': 74, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/74/2/f/b/33/1'], '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': '2-74-37.33-c1-0-2', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-74-37.33-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7686956321961738, 'root_angle': 0.2375632464779882, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.64938138511806075628993087682', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '4626140503306636917906089402275', 'Lhash_array': ['4626140503306636917906089402275'], 'label': '2-74-37.33-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/74/2/f/b/33/1'}