-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1978406813546851995214028251905', 'a10': [-10.0, 0.0], 'a2': [2.0, 0.0], 'a3': [5.501478533601825, 0.0], 'a4': [4.0, 0.0], 'a5': [-5.0, 0.0], 'a6': [11.00295706720365, 0.0], 'a7': [0.05005263684548753, 0.0], 'a8': [8.0, 0.0], 'a9': [3.2662660556816805, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.570439301320347, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-2.0, 0]]], [5, [[1.0, 0], [5.0, 0]]], [23, [[1.0, 0], [-23.0, 0]]]], 'bad_primes': [2, 5, 23], 'central_character': '230.1', 'coefficient_field': 'CDF', 'conductor': 230, 'conductor_radical': 230, 'conjugate': '1978406813546851995214028251905', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.0, 0]], [[1.0, 0], [-5.501478533601825, 0], [27.0, 0]], [[1.0, 0], [5.0, 0]], [[1.0, 0], [-0.05005263684548753, 0], [343.0, 0]], [[1.0, 0], [-35.17566031153268, 0], [1331.0, 0]], [[1.0, 0], [-86.10996776087492, 0], [2197.0, 0]], [[1.0, 0], [-8.827925083601997, 0], [4913.0, 0]], [[1.0, 0], [-106.31668165016914, 0], [6859.0, 0]], [[1.0, 0], [-23.0, 0]], [[1.0, 0], [280.7536764243028, 0], [24389.0, 0]], [[1.0, 0], [117.0772554491833, 0], [29791.0, 0]], [[1.0, 0], [-93.30884085455727, 0], [50653.0, 0]], [[1.0, 0], [58.057851755045874, 0], [68921.0, 0]], [[1.0, 0], [508.1011046045329, 0], [79507.0, 0]], [[1.0, 0], [407.91408211057586, 0], [103823.0, 0]], [[1.0, 0], [-316.2505000363448, 0], [148877.0, 0]], [[1.0, 0], [-129.50038411928057, 0], [205379.0, 0]], [[1.0, 0], [-299.00804699999657, 0], [226981.0, 0]], [[1.0, 0], [-596.3264180318284, 0], [300763.0, 0]], [[1.0, 0], [692.1080349124094, 0], [357911.0, 0]], [[1.0, 0], [-842.097711181253, 0], [389017.0, 0]], [[1.0, 0], [1161.0597963647963, 0], [493039.0, 0]], [[1.0, 0], [-1121.694600893448, 0], [571787.0, 0]], [[1.0, 0], [-409.09162442149176, 0], [704969.0, 0]], [[1.0, 0], [1123.621857898209, 0], [912673.0, 0]], [[1.0, 0], [981.8235523218466, 0], [1030301.0, 0]], [[1.0, 0], [28.95745514987959, 0], [1092727.0, 0]], [[1.0, 0], [187.8737193886722, 0], [1225043.0, 0]], [[1.0, 0], [-2142.021027023657, 0], [1295029.0, 0]], [[1.0, 0], [1668.6727390985504, 0], [1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 12, 'label': '2-230-1.1-c3-0-12', '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/230/4/a/i/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [3.8442518510003896, 3.815889653991876, 3.730804604050863, 3.589078309351966, 3.391094187516693, 3.137877380852865, 2.8315117919058084, 2.4755828380382354, 2.075588785738922, 1.6392623626849205, 1.1767475192095334, 0.700583538562554, 0.22546013689577882, -0.23227724498225671, -0.6553732314774922, -1.0266377170966747, -1.330103582708056, -1.552294256609537, -1.6835045553528705, -1.7189790630457398, -1.6598609182598985, -1.5137831943974032, -1.2949874451441836, -1.0238808146274672, -0.7259843639391756, -0.43027922036467636, -0.16702022688947563, 0.034846449173745714, 0.15046173549147768, 0.16177567901530496, 0.05992748786380575, -0.15300861511540131, -0.46317858819713964, -0.8452118879204156, -1.2637070743672107, -1.6759335272577498, -2.0356053988624963, -2.297442860020871, -2.4221079882918075, -2.3810060769393755, -2.1603943571197974, -1.7642522474152091, -1.2154475470643404, -0.5548809711923658, 0.16150235430406143, 0.8676998666369529, 1.4942431844653752, 1.9757599421066272, 2.2586833341966073, 2.308182719428434, 2.11339261984342, 1.690142175254681, 1.0806301918919923, 0.34983329990977885, -0.42115885412761744, -1.144265549960495, -1.7349974043362624, -2.1232202193249305, -2.262687359799771, -2.1379767482206007, -1.767712261081399, -1.2033725430049051, -0.5235499778485425, 0.17584890853726493, 0.7943579057282213, 1.2410516138467909, 1.4480697009043784, 1.381584697934446, 1.0484620438444905, 0.4973676351044772, -0.1861903367179964, -0.8905340360630815, -1.492975485123955, -1.8774803981632278, -1.9523465877545225, -1.6652455001102586, -1.0132108186509352, -0.0457831821955141, 1.1395352369477068, 2.4092251598288144, 3.6116401077930123, 4.5983851631367365, 5.246055936185978, 5.4749979522508, 5.262059333136103, 4.645126552753486, 3.7184493818143287, 2.6191984599551548, 1.5071304057624382, 0.5404213131478018, -0.14854218637981204, -0.4735002722416495, -0.407400313064322, 0.014043648130691139, 0.6990293696540637, 1.5155785064942304, 2.314076362672647, 2.952638919393367, 3.3209476271812473, 3.358392542366193, 3.0633151172898203, 2.4916967339815876, 1.745533313839357, 0.9530308419616663, 0.24429768437512717, -0.27290475484913795, -0.532751007806584, -0.5225184473332014, -0.28315840292464756, 0.10085098439053684, 0.5203654994834654, 0.8653604834083439, 1.0487806867684817, 1.0254763250094903, 0.802145455539843, 0.43597386594877585, 0.021979972793577735, -0.32852186328048877, -0.5139275483056865, -0.4672532404328859, -0.17435910697300627, 0.31893458389620555, 0.9130827151649824, 1.473865092028683, 1.8608875458811396, 1.9598978407151613, 1.71207642731177, 1.1336492578227793, 0.32079233103636573, -0.5624019793445137, -1.3116713905488335, -1.721400455111628, -1.6272125408142089, -0.9437607455618415, 0.31041755050162745, 2.006948684166966, 3.9230022387684396, 5.776195095200236, 7.273130792206634, 8.162620030818806, 8.28327091850942, 7.595849260440143, 6.193528758557016, 4.287388489144635, 2.1694379545772833, 0.16004762862036814, -1.4500430257052912, -2.4517106907067747, -2.7530962735612627, -2.3918639095439667, -1.5218229568059543, -0.37699399744159673, 0.7790859876555226, 1.707955546057539, 2.243121529933284, 2.319447224166212, 1.9791737539035048, 1.3539500336728967, 0.6276135395568864, -0.011251121159495642, -0.41573032528447496, -0.5151028362474318, -0.32948791392603016, 0.03858876816009432, 0.43338337294924434, 0.6885424766462446, 0.6725198466113775, 0.3254447773898618, -0.32191050209554245, -1.152105693979212, -1.9873804366823697, -2.6322404708329974, -2.921988429680027, -2.765204488753769, -2.1694108763186306, -1.2430770094634915, -0.17283286243736573, 0.8191138558341131, 1.527326029989677, 1.8125566166363998, 1.6359753903940402, 1.0694343987060644, 0.2787679489166026, -0.5162289677638492, -1.0956125787390971, -1.293732155517238, -1.0407388424246, -0.38060198805837037, 0.5391955621202111, 1.5040420380953687, 2.285777753441979, 2.700078028090208, 2.6530667903172627, 2.1651265134150006, 1.3655540546903318, 0.45914877610954397, -0.32687648796030905, -0.8020019385580177, -0.8620560484835643, -0.5161629464166922, 0.11651735679483795, 0.8398741082503283, 1.4353928333813117, 1.7238304239222457, 1.6173719268445372, 1.1476979178295208, 0.4614435455929611, -0.21692275902421315, -0.6459289943830071, -0.6359793445366417, -0.1077872604954674, 0.8761181689860824, 2.1167748987013155, 3.3215699278018187, 4.174950655401087, 4.419722875310399, 3.9279992555567564, 2.7426617806979285, 1.0771169039496769, -0.7284894238715033, -2.285184878732009, -3.2486267292479276, -3.4048851377987632, -2.7265974660812073, -1.3845173804216142, 0.2894958385235753, 1.8797230593625662, 2.9853805207585387, 3.3165708392002444, 2.7634985597151753, 1.4217169809022423, -0.4326932322248489, -2.4113843808567794, -4.107816099920639, -5.193145786060529, -5.489858004119193, -5.005264906807862, -3.917815957490223, -2.5216334050506903, -1.145473345306981, -0.06851246287098559, 0.5446386822269628, 0.67339241896453, 0.42921450287521146, 0.008075515579286005, -0.3770707897934437, -0.5631300379684947, -0.48340680303371986, -0.1809262128462132, 0.21402290544546895, 0.5337713173036681, 0.6339984502889147, 0.445627220623937, 0.001157003712925548, -0.5731750238308331, -1.09718015979526, -1.395977178002753], 'positive_zeros': ['1.56068778982998718654644880591078', '3.34954089972216128614177621413855', '3.79221102266587888045541856028764', '5.47209119178626565991916149599248', '6.68167572917697175433594143499775', '7.84289999927998245593390808054514', '8.717211303196833470815703803825925', '9.630199338544330494958673907238907', '11.21710880206054870212065473521478', '11.62191604736660636454882356058481'], 'prelabel': '2-230-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.683807717745369, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.56068778982998718654644880591', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.34954089972216128614177621414', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.79221102266587888045541856029', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 13.570439301320347, 'bad_primes': [2, 5, 23], 'central_character': '1.1', 'conductor': 230, 'conductor_radical': 230, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/230/4/a/i/1/3'], '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': '2-230-1.1-c3-0-12', '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': '2-230-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.683807717745369, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.56068778982998718654644880591', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1978406813546851995214028251905', 'Lhash_array': ['1978406813546851995214028251905'], 'factors': ['2-230-1.1-c3-0-12'], 'label': '2-230-1.1-c3-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/230/4/a/i/1/3'}