-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1132192226239878315680977440991', 'a10': [1.3660254037844386, -0.36602540378443865], 'a2': [-0.8660254037844386, 0.5], 'a3': [0.0, 0.0], 'a4': [0.5, -0.8660254037844386], 'a5': [-1.3660254037844386, -0.36602540378443865], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [-3.9689140359382235e-80, 1.0], 'a9': [-0.8660254037844386, 0.5], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.6628846220931641, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.8660254037844386, -0.5]]], [7, [[1.0, 0], [0, 0]]], [17, [[1.0, 0], [0.5, -0.8660254037844386]]]], 'bad_primes': [2, 7, 17], 'central_character': '3332.2027', 'coefficient_field': 'CDF', 'conductor': 3332, 'conductor_radical': 238, 'conjugate': '573038978172906606318596297187', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.8660254037844386, -0.5]], [[1.0, 0], [0, 0], [0.8660254037844386, -0.5]], [[1.0, 0], [1.3660254037844386, 0.36602540378443865], [0.8660254037844386, 0.5]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-0.8660254037844386, 0.5]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [0.8660254037844386, 0.5]], [[1.0, 0], [-1.0, 1.0], [0, -1.0]], [[1.0, 0], [0, 0], [0.8660254037844386, -0.5]], [[1.0, 0], [-1.3660254037844386, -0.36602540378443865], [0.8660254037844386, 0.5]], [[1.0, 0], [1.0, 1.0], [0, 1.0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [-0.36602540378443865, 1.3660254037844386], [-0.8660254037844386, -0.5]], [[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [0, 1.0]], [[1.0, 0], [0.36602540378443865, 1.3660254037844386], [-0.8660254037844386, 0.5]], [[1.0, 0], [0, 0], [0.8660254037844386, 0.5]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [-1.0, 1.0], [0, -1.0]], [[1.0, 0], [0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [-0.8660254037844386, -0.5]], [[1.0, 0], [-1.3660254037844386, 0.36602540378443865], [0.8660254037844386, -0.5]], [[1.0, 0], [1.0, 1.0], [0, 1.0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-3332-476.123-c0-0-0', 'leading_term': '0.42304641417338748336197436261195', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/3332/1/bc/b/2027/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [0.4230464141733875, 0.44923538703151705, 0.4746188111036704, 0.4991101824412196, 0.5221659419495832, 0.5428441204853366, 0.5598882317890987, 0.5718194778038859, 0.5770254706695629, 0.5738397837408278, 0.5606112477700704, 0.535764369865548, 0.49785301462291903, 0.44560926327046185, 0.3779887288414498, 0.2942128917922353, 0.19380838934508648, 0.0766426965978413, -0.057044717632067615, -0.20661690571353444, -0.3710208909266821, -0.5487773394205425, -0.7379796813770535, -0.9363037730297745, -1.1410289883782463, -1.3490713660621214, -1.5570291201403306, -1.7612404615781554, -1.9578532794595538, -2.1429058081475403, -2.312416971137086, -2.4624846579000166, -2.5893897714987446, -2.689703497877244, -2.7603949086742947, -2.7989357342108065, -2.8033989473906367, -2.7725476967660083, -2.705911130194444, -2.603843769057408, -2.4675653334824696, -2.299178284279566, -2.1016608360778997, -1.8788338026286846, -1.6353003488808528, -1.3763585299054568, -1.1078873740199686, -0.8362081921456351, -0.5679237392370022, -0.30973878508095304, -0.06826653709164165, 0.15017383811514134, 0.33976265971033176, 0.49538167182917187, 0.6128056482747845, 0.688876686484354, 0.721654297479338, 0.7105347273411775, 0.6563335278828631, 0.5613262283930704, 0.4292430360060993, 0.2652147890498558, 0.0756688755400423, -0.13182453168204752, -0.34875382897536183, -0.5659110404729094, -0.7736749200309675, -0.9623247383469614, -1.1223758470491658, -1.2449267755568665, -1.3220065582428961, -1.346910266779968, -1.3145103848660389, -1.2215317480999843, -1.0667783055941855, -0.8513009517100916, -0.5784971191519833, -0.2541346940493325, 0.11370493272918412, 0.5147672856742324, 0.9368484771254837, 1.3660989282016418, 1.787400893068442, 2.184810554625356, 2.542052642487826, 2.8430529923145835, 3.072492330795596, 3.216362935982129, 3.2625087777941357, 3.2011293604888076, 3.0252278180273025, 2.7309848801649808, 2.3180421298970173, 1.7896804809499065, 1.1528829573933916, 0.41827456773262467, -0.4000637819166752, -1.2849059350464944, -2.2163096895358114, -3.1721539794061377, -4.128769078154322, -5.0616408753390285, -5.946166839321351, -6.758438552627946, -7.476023829276073, -8.078720504640895, -8.549254103404097, -8.873892776724576, -9.042955151201612, -9.051190001187674, -8.898010850867367, -8.58757360004391, -8.128690876784392, -7.534582847754918, -6.822470434952328, -6.013023050854802, -5.1296788212050295, -4.197860567727507, -3.244115338364411, -2.295208791199641, -1.3772080859410163, -0.5145879829589468, 0.2706054855013014, 0.9595011480817552, 1.5370291181017304, 1.9924023815527319, 2.3194339312817354, 2.516676255395339, 2.587377080112806, 2.539252738450795, 2.384088074496902, 2.1371790753962765, 1.8166411288750315, 1.4426116294963554, 1.0363803293958265, 0.6194841208720675, 0.21280467685746682, -0.1642925456004309, -0.49474104846661265, -0.7644441591210116, -0.9628051983903402, -1.0830942744751202, -1.1226362608140092, -1.0828125254188676, -0.9688774095614188, -0.7895989228325155, -0.5567412375247366, -0.28441394432081674, 0.011680683567246792, 0.315066291965189, 0.6093375671084373, 0.8789911476706127, 1.110202145634199, 1.291508574889037, 1.414370309973544, 1.473575182039666, 1.4674721987790016, 1.3980203101406607, 1.270650234218836, 1.0939461695632098, 0.8791632938754754, 0.6396053300468151, 0.389893719907111, 0.14516570281127605, -0.07975746277772952, -0.2711889989149884, -0.41733896779607615, -0.5089800981055397, -0.5399812560501538, -0.5076792143084679, -0.4130674507391357, -0.2607900016004483, -0.058938441897999204, 0.18133963921825416, 0.44640228782020736, 0.7208173763050177, 0.9881738545626448, 1.2319584216311579, 1.4364519152274136, 1.5875979995680025, 1.6737974936602307, 1.6865849271734505, 1.6211495121067623, 1.4766704210735238, 1.256445695396439, 0.967804796722802, 0.6218062159483078, 0.23273306500534152, -0.18258941562726763, -0.6056205996492977, -1.0170333930873794, -1.3976971485634324, -1.7296627979449353, -1.9970975744048591, -2.187118687290665, -2.2904800922423294, -2.3020738540230785, -2.221217174127169, -2.0517074635390924, -1.801640291527776, -1.482997967183948, -1.111029204511396, -0.7034520754217143, -0.27952259674170116, 0.14098076792657008, 0.5388011671587779, 0.8962182482947619, 1.197977144284002, 1.4320790564615722, 1.5903881900274568, 1.6690197429970213, 1.6684857610492654, 1.5935893001329866, 1.4530717350789355, 1.2590324044238168, 1.0261532621221976, 0.7707730200579793, 0.5098646932788575, 0.25997690567076964, 0.03620233882001864, -0.1487639396612781, -0.28541789364644876, -0.36804121237376675, -0.3950578779174896, -0.3691268553003895, -0.29696064913576065, -0.1888759393613547, -0.05809900213183612, 0.08013583536836459, 0.2096428115489341, 0.3144336349904032, 0.3798884833788541, 0.3938755087879707, 0.34774619808367346, 0.23713927440956087, 0.06253537501071, -0.17048194010531123, -0.4512868824957052, -0.7646032422559108, -1.0912169172784802, -1.4089789356287248, -1.6940500379241552, -1.9223214599029241, -2.0709334489787885, -2.119804142058121, -2.0530773847637787, -1.8603992787207528, -1.537939801680935, -1.0890875421802764, -0.5247619058367129, 0.13669272199288418, 0.8700434861074203, 1.6441244737403815, 2.4231747185670285, 3.168499223783857, 3.840372834931716, 4.400090133571026], 'positive_zeros': ['0.893142184475783003192371305847826', '2.55430590685711043479117431061286', '3.16736292453920796230399277179864', '3.94578985778106671440609392824655', '4.85075914889955199496866068541488', '6.17715472083869137951955940554307', '6.93425905449879630512231962839036', '7.51366325706378503990873009210378', '8.309394413620756412203976266732268', '8.747501822276882638344351859079340'], 'prelabel': '2-3332-476.123-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2895288372476066, 'root_angle': 0.2030147107378025, 'root_number': '0.80341388350316183956962971841876 + 0.59542097023397479272519192402381*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.10150735536890124', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.893142184475783003192371305848', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.55430590685711043479117431061', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.16736292453920796230399277180', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.6628846220931641, 'bad_primes': [2, 7, 17], 'central_character': '476.123', 'conductor': 3332, 'conductor_radical': 238, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3332/1/bc/b/2027/1'], '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': '2-3332-476.123-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3332-476.123-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2895288372476066, 'root_angle': 0.10150735536890125, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.893142184475783003192371305848', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1132192226239878315680977440991', 'Lhash_array': ['1132192226239878315680977440991'], 'label': '2-3332-476.123-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3332/1/bc/b/2027/1'}