-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2272587930322393544549454593462', 'a10': [-1.8117328370634385, 9.834511890638298], 'a2': [-1.3763519190769355, 1.4510876592588182], 'a3': [-2.018968504088679, 1.0287158345608787], 'a4': [-0.21131078970647282, -3.994414569139466], 'a5': [4.191080201621577, -2.72669153803206], 'a6': [1.2860543227429162, -4.345575293798016], 'a7': [-2.6314228219461078, 5.16445807477744], 'a8': [6.087083698176076, 5.191089678612677], 'a9': [-2.272089718406465, 3.127263210103098], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.994565815926532, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.3763519190769355, -1.4510876592588182]]], [5, [[1.0, 0], [-4.191080201621577, 2.72669153803206]]], [11, [[1.0, 0], [9.843711958664098, 4.909311038715454]]]], 'bad_primes': [2, 5, 11], 'central_character': '220.7', 'coefficient_field': 'CDF', 'conductor': 220, 'conductor_radical': 110, 'conjugate': '158225511360635336582212309010', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.3763519190769355, -1.4510876592588182]], [[1.0, 0], [2.018968504088679, -1.0287158345608787], [5.2900672706322585, -7.281152949374527]], [[1.0, 0], [-4.191080201621577, 2.72669153803206]], [[1.0, 0], [2.6314228219461078, -5.16445807477744], [-28.801477362331184, -39.64183272437242]], [[1.0, 0], [9.843711958664098, 4.909311038715454]], [[1.0, 0], [2.392879319579775, 15.10804542843139], [-160.72855125388097, 52.223872049366115]], [[1.0, 0], [1.9145864117977336, -12.088222857464197], [-274.8553332092994, -89.30591137435981]], [[1.0, 0], [24.29779395883707, 7.894831832235087], [292.055134969356, 212.1904760775828]], [[1.0, 0], [-11.427300574192818, -11.427300574192818], [0, 529.0]], [[1.0, 0], [16.045368432488743, 49.3825662725821], [-680.3832922693308, 494.3273971779699]], [[1.0, 0], [-7.8445262886530855, 10.797064158362941], [-296.9653315943245, -913.9653121596426]], [[1.0, 0], [-4.000766936748142, 7.851947220139564], [-804.6780103883957, -1107.544265299303]], [[1.0, 0], [75.72587972331506, 24.60482983666913], [1359.9575675442866, 988.0670091036474]], [[1.0, 0], [54.598852304791606, -54.598852304791606], [0, -1849.0]], [[1.0, 0], [22.45818564789053, 44.076671087134955], [-1298.4176223140732, 1787.1185405742588]], [[1.0, 0], [21.886094608031183, -3.46641684538287], [2671.517754273086, -868.0287371992273]], [[1.0, 0], [15.090050934735238, 46.44240133697069], [-2816.188157419192, 2046.080463230099]], [[1.0, 0], [-55.4322288955801, -76.29591766329622], [-1149.8522360691793, 3538.8812971342663]], [[1.0, 0], [5.117910573166063, -5.117910573166063], [0, -4489.0]], [[1.0, 0], [-10.760619188693676, -14.810721704393163], [-1557.7546686441099, 4794.275898643869]], [[1.0, 0], [46.576206832217856, -91.41095283549153], [-3132.3076094665894, -4311.251563024095]], [[1.0, 0], [-47.7369486877707, 65.7042731123077], [-1928.575061894047, -5935.543718198053]], [[1.0, 0], [-9.70085829000902, 61.2488087221924], [-6551.828340757313, -2128.8180742490126]], [[1.0, 0], [0, 11.225010113077268], [-7921.0, 0]], [[1.0, 0], [-7.980920331667552, -50.389547832566855], [-8948.4907618211, 2907.5409000738805]], [[1.0, 0], [46.90621162253038, -64.56086163504564], [-3152.2823596188387, -9701.727522726862]], [[1.0, 0], [17.452918200196283, -34.25328061142727], [-6235.813741570847, -8582.861293323816]], [[1.0, 0], [2.1363578451735283, -1.0885286913429912], [6729.553353496525, -9262.435568598774]], [[1.0, 0], [-35.31564537612318, 0], [11881.0, 0]], [[1.0, 0], [-70.37923754705037, -138.12703097928357], [-7505.429886522589, 10330.338001173704]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 44, 'label': '2-220-220.7-c2-0-44', '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/220/3/w/a/7/19', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.1785205960238392, 0.34313628366572385, 0.49276639347960494, 0.6260076484170854, 0.7406362587510787, 0.833538333360646, 0.9008053171434373, 0.9379864899499906, 0.9404797046157314, 0.9040340762119558, 0.8253322382257751, 0.7026133733912229, 0.5362909548753614, 0.32951162164824227, 0.08859530817515045, -0.1767065150569132, -0.4531960211061268, -0.7245111257270571, -0.971742546448951, -1.1744007034475483, -1.3117171176977502, -1.3642293117701791, -1.315559827210132, -1.154262473476731, -0.8755766814801444, -0.48290858370722894, 0.01115020547030976, 0.5844442809125409, 1.205662866329232, 1.8356276360087418, 2.429479185419078, 2.939692668497856, 3.319756337207035, 3.528251480936649, 3.5329897801627834, 3.3148060913806963, 2.8705820445772163, 2.2150970512559542, 1.381372988864379, 0.41929637702006195, -0.6075392708801555, -1.6266407854788965, -2.5627444932594683, -3.344753670071303, -3.912821479886897, -4.22482679354078, -4.26147893519678, -4.02936602636582, -3.561431696413823, -2.914616350115126, -2.164709833163144, -1.398799525502925, -0.7060213516200848, -0.16758759103046508, 0.15276613069386075, 0.21673404484270745, 0.016723336621104867, -0.42234425234259015, -1.0451366675428369, -1.7718712171508582, -2.5075735884746377, -3.153610400106331, -3.62010405960254, -3.837637515839843, -3.766661454485378, -3.4032433742705828, -2.7802315207635773, -1.9634997443596731, -1.043617143194768, -0.12395504780641793, 0.693196604383793, 1.3205726709560246, 1.69791493757462, 1.8001818113235244, 1.6406713984248307, 1.2684687578102505, 0.7604813657833533, 0.2091808908771622, -0.2921124371551756, -0.6641085081333716, -0.8541869657318003, -0.8446767756797641, -0.655300848384137, -0.3392352392512583, 0.026704803558296384, 0.356211690119442, 0.569610689038324, 0.6091623967158141, 0.45076300241160344, 0.10977754198283356, -0.36031160580302163, -0.8765211892498903, -1.3410046081184246, -1.6592896987618537, -1.7588900141514674, -1.6047998051049592, -1.2087478383594004, -0.6300538240126125, 0.03263379993948632, 0.6577723555288107, 1.122979000620823, 1.3289107506624822, 1.220559307942794, 0.8017158623424059, 0.1393362344955804, -0.6438041260790843, -1.3876953239030791, -1.922307450429977, -2.0990196811708692, -1.8207452163979596, -1.0650835230643887, 0.10427178614252003, 1.5407972853172747, 3.0334987153665076, 4.338048822703839, 5.215916708608159, 5.474975385881947, 5.004459128926515, 3.7978125088044705, 1.958868010938315, -0.310388565405856, -2.7389454311554986, -5.0281633204956035, -6.898472443757602, -8.133267863427974, -8.612255569499867, -8.328311767984225, -7.384879922774923, -5.97450250712709, -4.342589348318479, -2.743278072941604, -1.3956918661744444, -0.4487399916856382, 0.039151506413665466, 0.1020127267548653, -0.14967447767937692, -0.559036353316957, -0.9602226243342654, -1.2151062537727622, -1.241527478341887, -1.0273140299004733, -0.6275092442072115, -0.1459828537511818, 0.29392784343927353, 0.5826638110938743, 0.6536493063714579, 0.5014810340642651, 0.18468597357842984, -0.18775883815828084, -0.4831023398909012, -0.5784433822010463, -0.39325079423662473, 0.08721850066743117, 0.8036520848357004, 1.6321714998713097, 2.4100131536992744, 2.971895886752457, 3.188803160704094, 3.0000102608846313, 2.4304405316597806, 1.5886222877046974, 0.6449551968248164, -0.20532678673160076, -0.7862955143827153, -0.9823674286445289, -0.7663931191344721, -0.2076754238650933, 0.5426693551864007, 1.2862605062942976, 1.8242875737828028, 2.005774212497467, 1.7656749047235816, 1.1432399721379707, 0.2755095012159428, -0.6333580341091335, -1.3603102991358293, -1.718030330556397, -1.6028151408122495, -1.0236645151050932, -0.10463894264007266, 0.9412474863067674, 1.8614416645930665, 2.4254902529538507, 2.4843439927826516, 2.012692156960215, 1.1231720893656088, 0.0476336031685351, -0.9115990602402242, -1.4501638009865008, -1.3343335764098812, -0.4608389082194885, 1.110820232499803, 3.162207088755135, 5.356275813108808, 7.3059380136249406, 8.655751565913555, 9.158202057601638, 8.726985805116236, 7.454857224552073, 5.591802858522102, 3.488611010189917, 1.5190746330370153, -0.0009056720367262978, -0.8784182424116255, -1.0778836924584438, -0.7172715332740245, -0.028166001575835105, 0.7095419329140427, 1.2415020261178655, 1.40265832196971, 1.1551771107099236, 0.5916673728719956, -0.09615401815612426, -0.6743093278590614, -0.9334220359041527, -0.7477409791280626, -0.11080897874734197, 0.8613528004526543, 1.959937775469447, 2.937563098950711, 3.572195235190028, 3.7235829373297116, 3.367239272967156, 2.5972947837208675, 1.5981269598890788, 0.5931971471654857, -0.21435471219664498, -0.6927854249030134, -0.8105554743581341, -0.6354753575192982, -0.3054089367680736, 0.02002482655446427, 0.2118376531674514, 0.21211596938420052, 0.05011146132309885, -0.17107244119242887, -0.3132438934607645, -0.2553645011877981, 0.057315553141918024, 0.5835352373819397, 1.1867465385429827, 1.668419269472623, 1.826030804882703, 1.5196184122837928, 0.7268929974519617, -0.43122665396008036, -1.705417148527893, -2.7727804831639182, -3.319638140912881, -3.131150993129008, -2.1629948499009406, -0.573488840355138, 1.29596973298778, 2.990881750870783, 4.04889955293572, 4.114780247182804, 3.035478601216507], 'positive_zeros': ['1.79275577190846907475689636508668', '3.24740609759028949517711807274139', '4.92651108274901195019172181114581', '6.67882939830806399650125353834233', '7.00628840599711898371853004105446', '8.642667683411815710789318997544708', '9.674454249669540299447432230168491', '10.49081376579710622179399124728888', '11.15667591845134437994718110352800', '12.24387414421737666653141980649641'], 'prelabel': '2-220-220.7-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4483802433295634, 'root_angle': 0.2963808657073447, 'root_number': '-0.28731223456417 + 0.9578369797986207*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.296380865707', 'prec': 47}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.79275577190846907475689636509', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.24740609759028949517711807274', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.92651108274901195019172181115', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 5.994565815926532, 'bad_primes': [2, 5, 11], 'central_character': '220.7', 'conductor': 220, 'conductor_radical': 110, 'degree': 2, 'index': 44, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/220/3/w/a/7/19'], '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': '2-220-220.7-c2-0-44', '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': '2-220-220.7-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4483802433295634, 'root_angle': 0.2963808657073447, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.79275577190846907475689636509', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2272587930322393544549454593462', 'Lhash_array': ['2272587930322393544549454593462'], 'factors': ['2-220-220.7-c2-0-44'], 'label': '2-220-220.7-c2-0-44', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/220/3/w/a/7/19'}