-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '804655893140868502625491164038', 'a10': [-3.202798497030311, 0.0], 'a2': [1.505081032691909, 0.0], 'a3': [0.0, 0.0], 'a4': [0.26526891496894367, 0.0], 'a5': [-2.1279907376827105, 0.0], 'a6': [0.0, 0.0], 'a7': [1.0, 0.0], 'a8': [-2.610910852901298, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 63.888306657226465, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-1.0, 0]]], [127, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 7, 127], 'central_character': '8001.1', 'coefficient_field': 'CDF', 'conductor': 8001, 'conductor_radical': 2667, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.505081032691909, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.1279907376827105, 0], [5.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.6309317049210816, 0], [11.0, 0]], [[1.0, 0], [-2.773381328193069, 0], [13.0, 0]], [[1.0, 0], [4.813105780248937, 0], [17.0, 0]], [[1.0, 0], [-1.8210211135360066, 0], [19.0, 0]], [[1.0, 0], [-4.2179569531941095, 0], [23.0, 0]], [[1.0, 0], [2.1754193882112625, 0], [29.0, 0]], [[1.0, 0], [5.016397032069677, 0], [31.0, 0]], [[1.0, 0], [4.8071573917675865, 0], [37.0, 0]], [[1.0, 0], [0.8030085611086643, 0], [41.0, 0]], [[1.0, 0], [-11.289518006977703, 0], [43.0, 0]], [[1.0, 0], [7.138339014909956, 0], [47.0, 0]], [[1.0, 0], [-7.357690591204255, 0], [53.0, 0]], [[1.0, 0], [-1.9997162043080072, 0], [59.0, 0]], [[1.0, 0], [-1.6471285211395874, 0], [61.0, 0]], [[1.0, 0], [-10.783175067544347, 0], [67.0, 0]], [[1.0, 0], [-4.48471332368514, 0], [71.0, 0]], [[1.0, 0], [-5.532940916483518, 0], [73.0, 0]], [[1.0, 0], [0.5832822198989737, 0], [79.0, 0]], [[1.0, 0], [4.31083381668332, 0], [83.0, 0]], [[1.0, 0], [0.15719856789475992, 0], [89.0, 0]], [[1.0, 0], [-2.3300521246199675, 0], [97.0, 0]], [[1.0, 0], [-5.25621108813014, 0], [101.0, 0]], [[1.0, 0], [-12.185329866830665, 0], [103.0, 0]], [[1.0, 0], [10.144336809865438, 0], [107.0, 0]], [[1.0, 0], [-5.6300465219389215, 0], [109.0, 0]], [[1.0, 0], [10.050005733598415, 0], [113.0, 0]], [[1.0, 0], [1.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 70, 'label': '2-8001-1.1-c1-0-70', 'leading_term': '2.32022985118170704260863611473', '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/8001/2/a/ba/1/30', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [2.320229851181707, 2.3073984383056914, 2.268874545479329, 2.2045775776447174, 2.114400559140723, 1.9982493105508308, 1.856093776209075, 1.688028359481982, 1.4943376945819824, 1.27556410540715, 1.0325730470872185, 0.766613050110502, 0.4793670392679787, 0.17299233247696175, -0.14985290057539344, -0.4859984497357388, -0.8317673850555201, -1.1829986423146406, -1.5350871520935208, -1.8830413195491797, -2.221557193781205, -2.545108200395946, -2.8480488510426083, -3.1247303948685587, -3.3696259476022945, -3.577462235475881, -3.7433547365221997, -3.8629427051547482, -3.932520341910898, -3.9491602328523885, -3.9108251450823395, -3.8164643367780333, -3.6660907298875567, -3.4608356056342737, -3.202977917755968, -2.895945872239313, -2.544289086947237, -2.1536204071380944, -1.7305272961020268, -1.282453622418752, -0.8175536013141276, -0.3445205887412156, 0.12760565775141575, 0.5896487798863732, 1.0325174430513484, 1.447432901814987, 1.8261561322980902, 2.161207844122878, 2.44607457251231, 2.675394156187002, 2.8451142387239536, 2.9526179922321765, 2.9968120467108035, 2.978172602002561, 2.8987468790868087, 2.762108402630341, 2.573266058717642, 2.338528395384026, 2.065326178501593, 1.7619977274755874, 1.4375429779095275, 1.1013534957837174, 0.7629267458929552, 0.431573746882567, 0.11612978341185401, -0.17532194134982979, -0.43570396610793344, -0.6591662949460383, -0.8412677900986159, -0.9791100393088888, -1.071418015764483, -1.1185636313333147, -1.1225302803842536, -1.0868186144267364, -1.0162960005576298, -0.9169943161246891, -0.7958628314163922, -0.6604848446560884, -0.5187683755056066, -0.3786225179565278, -0.24763193459820018, -0.13274238917119846, -0.03997012697731728, 0.025852694031572823, 0.061285441383805365, 0.06442984909121392, 0.03501685349819849, -0.025575548303523554, -0.11437566259216647, -0.22694201428823504, -0.35755415098482757, -0.4994637308447065, -0.6451965220391832, -0.7868934737573874, -0.9166769684099803, -1.0270268362385766, -1.1111497940080426, -1.163325723187529, -1.1792146680104123, -1.1561096187218487, -1.0931220277642624, -0.9912895326280133, -0.8535984439340787, -0.6849170879644934, -0.49183993156717143, -0.2824464066696142, -0.06598232046623254, 0.14752449196573522, 0.3476992199019695, 0.5242879276168685, 0.6676381359976881, 0.7691707252630448, 0.821821319479607, 0.8204298543308449, 0.7620585562938288, 0.6462210456730564, 0.47500864467200493, 0.25310410821653306, -0.012322257160868013, -0.31183395386237167, -0.6340616327768318, -0.9661375803431296, -1.2942154733340057, -1.6040549995100621, -1.881647175976871, -2.1138533908219674, -2.289029515934494, -2.3976060131321564, -2.432595852224515, -2.3900042903045975, -2.269118076665265, -2.072656335652255, -1.8067710695345003, -1.4808916903117366, -1.1074149629741155, -0.7012489180422826, -0.27922634142300135, 0.14058995937421384, 0.5396821076527905, 0.8998996045039186, 1.2042931766349334, 1.4379221203118937, 1.5885971279225861, 1.6475222459097794, 1.6098030335454372, 1.4747930748200813, 1.246257561630583, 0.9323404592266274, 0.5453304602863558, 0.10123015272475844, -0.3808578498906739, -0.8795050762639364, -1.3718607066189692, -1.8346464379805958, -2.2451992569725205, -2.582515087008505, -2.8282448050633584, -2.967594905237601, -2.9900881591454214, -2.8901449145763554, -2.6674530020840725, -2.327103297656642, -1.8794784375763816, -1.3398935390911375, -0.7279995284100111, -0.06697126071944287, 0.6174865296100683, 1.2982728342123426, 1.94811312044086, 2.5408152294695965, 3.052499389190656, 3.462743040927912, 3.7555837748166048, 3.9203290831503756, 3.9521296895689515, 3.8522835750361075, 3.628250056098022, 3.2933668286921547, 2.8662771424769264, 2.3700885347737786, 1.8312981285124779, 1.278531698488719, 0.7411538976432558, 0.24781465553433782, -0.17499862688936957, -0.5043321621593133, -0.7219913750636605, -0.8155578436466201, -0.7791432457874153, -0.6138376890236726, -0.3278238800539992, 0.06385561224720779, 0.5398739779709762, 1.0735177234533047, 1.6338689744696753, 2.1872206017887423, 2.6986597888676114, 3.13374615124984, 3.460204488790713, 3.6495500757308066, 3.6785662530123333, 3.530559964350289, 3.196330550417816, 2.6748001648773045, 1.9732700029615238, 1.107284386426914, 0.10010375968632672, -1.0181931217657008, -2.211939057393276, -3.4413847976841927, -4.664412250031692, -5.838373909447792, -6.921970990600467, -7.877080126671734, -8.670440400247955, -9.275118833948962, -9.671683013714272, -9.849023744652117, -9.804787849483082, -9.545400550623897, -9.085677346349001, -8.448045846935104, -7.661417611117326, -6.759767591224681, -5.780493428634795, -4.762637759005025, -3.745063299571083, -2.7646724339874766, -1.8547601658513657, -1.043581817935, -0.3532050985444247, 0.20129924062204968, 0.612292149135618, 0.8796104817523975, 1.010225543605349, 1.0175413186929338, 0.9203767061750042, 0.7416925589660457, 0.5071373766841406, 0.24349443630094414, -0.022882537985316694, -0.26755859019862743, -0.46935038912447447, -0.6114313093860183, -0.6821510821940582, -0.6755292708666519, -0.5914009188160247, -0.43521290151383624, -0.21748963348144773, 0.04699431698687147, 0.3402805541794581, 0.6424646299265161, 0.9330284573971431, 1.192185794765366, 1.402159297735726, 1.5483125220099818, 1.6200696571733892], 'positive_zeros': ['0.63476157625452727114539011919466', '1.95601989444432438030736771432762', '3.01815322291314880868146597929343', '3.86966085874669773937925452671177', '4.06101529563786555349591192654806', '4.98306290673915462381928502353942', '5.52921236033631342098554143589059', '6.40602160076388133802249070923781', '6.99446145579194312527514453975145', '7.73900314070336575166753567773384'], 'prelabel': '2-8001-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.993016117663373, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.63476157625452727114539011919', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.95601989444432438030736771433', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.01815322291314880868146597929', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 63.888306657226465, 'bad_primes': [3, 7, 127], 'central_character': '1.1', 'conductor': 8001, 'conductor_radical': 2667, 'degree': 2, 'index': 70, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8001/2/a/ba/1/30'], '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': '2-8001-1.1-c1-0-70', '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': '2-8001-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.993016117663373, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.63476157625452727114539011919', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '804655893140868502625491164038', 'Lhash_array': ['804655893140868502625491164038'], 'label': '2-8001-1.1-c1-0-70', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8001/2/a/ba/1/30'}