-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '247732642019297911529603849566', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-6.245489833067524, 0.0], 'a4': [0.0, 0.0], 'a5': [-5.777762177032807, 0.0], 'a6': [0.0, 0.0], 'a7': [10.327322327596148, 0.0], 'a8': [0.0, 0.0], 'a9': [12.00614325494982, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 109.50754497065464, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [29, [[1.0, 0], [29.0, 0]]]], 'bad_primes': [2, 29], 'central_character': '1856.1', 'coefficient_field': 'CDF', 'conductor': 1856, 'conductor_radical': 58, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [6.245489833067524, 0], [27.0, 0]], [[1.0, 0], [5.777762177032807, 0], [125.0, 0]], [[1.0, 0], [-10.327322327596148, 0], [343.0, 0]], [[1.0, 0], [21.955463745945572, 0], [1331.0, 0]], [[1.0, 0], [61.70735569449365, 0], [2197.0, 0]], [[1.0, 0], [-41.92082562744584, 0], [4913.0, 0]], [[1.0, 0], [141.82687931722262, 0], [6859.0, 0]], [[1.0, 0], [193.5790377025645, 0], [12167.0, 0]], [[1.0, 0], [29.0, 0]], [[1.0, 0], [-115.13757031178989, 0], [29791.0, 0]], [[1.0, 0], [-99.16340925886308, 0], [50653.0, 0]], [[1.0, 0], [-244.67447682497493, 0], [68921.0, 0]], [[1.0, 0], [-385.33289389880315, 0], [79507.0, 0]], [[1.0, 0], [108.2878823240903, 0], [103823.0, 0]], [[1.0, 0], [515.2625631655134, 0], [148877.0, 0]], [[1.0, 0], [856.2688889965823, 0], [205379.0, 0]], [[1.0, 0], [402.6775753625724, 0], [226981.0, 0]], [[1.0, 0], [758.7166522704475, 0], [300763.0, 0]], [[1.0, 0], [696.4092928791995, 0], [357911.0, 0]], [[1.0, 0], [1103.520351024807, 0], [389017.0, 0]], [[1.0, 0], [817.7399792662388, 0], [493039.0, 0]], [[1.0, 0], [1083.6688795386128, 0], [571787.0, 0]], [[1.0, 0], [-119.41682321545426, 0], [704969.0, 0]], [[1.0, 0], [-1609.7939837312317, 0], [912673.0, 0]], [[1.0, 0], [-660.4472108728954, 0], [1030301.0, 0]], [[1.0, 0], [-486.2443089942967, 0], [1092727.0, 0]], [[1.0, 0], [791.1688159106956, 0], [1225043.0, 0]], [[1.0, 0], [-2200.751629836524, 0], [1295029.0, 0]], [[1.0, 0], [-1877.7778272831795, 0], [1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 7, 'label': '2-1856-1.1-c3-0-7', 'leading_term': '0.16607029028800248730614713150993', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1856/4/a/bj/1/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [0.1660702902880025, 0.15465587754422705, 0.12058784392417712, 0.06439067921575953, -0.013065260574985568, -0.1105696047425422, -0.22658047210927976, -0.3592359171212917, -0.5063686578888102, -0.6655244552047681, -0.8339845155972817, -1.0087922685753112, -1.186784817484299, -1.3646292849517323, -1.5388641689872211, -1.705945696641879, -1.8622990119075329, -2.004373867280759, -2.1287043089079316, -2.231971658867748, -2.311069910833664, -2.3631724733430306, -2.38579902464514, -2.376881091125912, -2.334824834026854, -2.2585694327313077, -2.147639392975393, -2.0021890900221146, -1.8230378843770838, -1.6116942243038135, -1.3703672773464954, -1.1019648131155557, -0.810076291125756, -0.49894038834402477, -0.17339652753438548, 0.1611796659378925, 0.4989566515133648, 0.833742253587598, 1.1590927443913512, 1.4684340979893002, 1.7551933515088731, 2.012937599900174, 2.235517776741691, 2.4172140494420327, 2.552879395865489, 2.6380777433307903, 2.669212951228296, 2.6436449145775214, 2.5597891649514497, 2.4171965520116703, 2.2166099051983728, 1.9599949994673667, 1.6505436765169994, 1.2926475953318588, 0.8918417911881855, 0.45471799519861245, -0.0111915114871771, -0.4975578849061464, -0.9954250691420425, -1.4954012005647734, -1.987867970653972, -2.463203142821629, -2.912010809853383, -3.325353495567818, -3.694979869447559, -4.013541675443942, -4.274793490883129, -4.473769138481499, -4.606928978417721, -4.672272906625773, -4.669414671952636, -4.599614083971539, -4.465764793951345, -4.272336566438361, -4.025272285115619, -3.7318413161644086, -3.4004522434416216, -3.0404293478526196, -2.661758482424668, -2.2748091489833486, -1.890040567935656, -1.5177003087460599, -1.1675245794870588, -0.8484495300700715, -0.5683428840099464, -0.3337648655131353, -0.14976672998375828, -0.01973424503805505, 0.05471777493578806, 0.07379527464025558, 0.03951620763157037, -0.04435779441754693, -0.17244838067049698, -0.3379430992898467, -0.5328287180640428, -0.748168403204564, -0.9744141956056951, -1.201744746621817, -1.4204170998670687, -1.6211204860743016, -1.7953196785312575, -1.9355754682361168, -2.035830277424553, -2.0916478384822845, -2.1003972068661394, -2.061373119133129, -1.9758468017928745, -1.8470437194514735, -1.6800473440437353, -1.4816307420600388, -1.2600205164076839, -1.0246003017275152, -0.7855634931160633, -0.5535270873922118, -0.33912033903501676, -0.15256329602767735, -0.0032511147023750746, 0.10063969442895065, 0.15250729722367806, 0.14762803049660336, 0.08339413434895163, -0.04052535178929435, -0.22210894826519892, -0.45699769590482736, -0.7386026806048942, -1.0583035102079237, -1.4057325027100298, -1.76913580179582, -2.1357993227128977, -2.492524488710115, -2.8261362763186404, -3.1240042621535786, -3.37455624970396, -3.5677637216610956, -3.6955788526015967, -3.7523041373436627, -3.7348778176083144, -3.643061165517845, -3.479517215997323, -3.2497746100969613, -2.96207466998155, -2.627104504861339, -2.2576236613473566, -1.8679963894177807, -1.4736458038291127, -1.090449895501008, -0.7341023189248435, -0.41946300411595994, -0.15992479949763758, 0.03317753388470278, 0.15109062457432376, 0.18807478167952357, 0.14172503687259097, 0.013164699009041578, -0.19290002648499127, -0.4682703956635911, -0.8014906908303102, -1.1782232328259583, -1.5817511641362578, -1.9935917308778557, -2.394197764116369, -2.7637208297422675, -3.08280628297316, -3.333388393529475, -3.4994529207682312, -3.567735083109323, -3.528322795340368, -3.375138294787666, -3.106275738615756, -2.724177869957114, -2.2356412103651895, -1.6516461880340476, -0.9870158706037758, -0.25991423250121576, 0.5087981640667496, 1.2963268662597611, 2.078794977368636, 2.832149469062406, 3.5330855949331212, 4.1599512918571815, 4.6935937282418925, 5.118112073863615, 5.42148407335928, 5.596038980987131, 5.638755666118329, 5.551371973749062, 5.340299417407651, 5.016345649645892, 4.59425553025583, 4.092089619020216, 3.530466191958995, 2.931699077681846, 2.3188684361005425, 1.714864815090801, 1.1414482510115815, 0.6183637346300341, 0.16255203833377035, -0.21250922592653101, -0.497305209959571, -0.6866021373444151, -0.779570586622551, -0.779708952614371, -0.694571516874907, -0.5353146514122875, -0.3160832066437327, -0.0532666837630439, 0.23533900812858133, 0.5314238713089561, 0.8170672373323324, 1.0756087161078391, 1.292444621475576, 1.4557113853856585, 1.5568229443473267, 1.5908362132964076, 1.556627223166147, 1.4568698881773459, 1.29781923376663, 1.088910771804656, 0.8421970645111828, 0.5716508973241967, 0.2923714499253404, 0.019735043123973083, -0.23146483986879837, -0.44784269388998, -0.6181671971515658, -0.7339881439482703, -0.7901096614908366, -0.7848830275865473, -0.7203016621244666, -0.6018911647942198, -0.43839809902357835, -0.241292025569195, -0.02410550685715437, 0.19835410744489707, 0.4108798369846318, 0.5987804706903613, 0.748786456809208, 0.8498960495930611, 0.8941136510750636, 0.8770370511112473, 0.7982574308586367, 0.6615452291236472, 0.4748058371444038, 0.24980104990704982, 0.0016446562888428138, -0.2519071478721111, -0.49133834083028677, -0.696386394483479, -0.8471359929023692, -0.9251371863369535, -0.914489205956882, -0.8028313793843731, -0.5821858872725647, -0.24960338550119365, 0.1924284742572364, 0.7358422700321909, 1.3671293281745562], 'positive_zeros': ['0.19542659623613621642595570859233', '1.75299680043428732461771447212507', '2.84255941221592549156285613666385', '4.42833554525674082943831469109118', '4.59777969703257899042473828141792', '5.89192229532633671314963214402899', '6.13035523799313724968940764891987', '7.55615151681721210480626859522591', '7.77343216708864775250292176128850', '8.802562065003615790623467336773545'], 'prelabel': '2-1856-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.464585274661134, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.19542659623613621642595570859', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.75299680043428732461771447213', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.84255941221592549156285613666', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 109.50754497065464, 'bad_primes': [2, 29], 'central_character': '1.1', 'conductor': 1856, 'conductor_radical': 58, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1856/4/a/bj/1/4'], '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': '2-1856-1.1-c3-0-7', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-1856-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.464585274661134, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.19542659623613621642595570859', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '247732642019297911529603849566', 'Lhash_array': ['247732642019297911529603849566'], 'label': '2-1856-1.1-c3-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1856/4/a/bj/1/4'}