-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1096153860906835421639093055149', 'a10': [20.475478405713993, 0.0], 'a2': [1.3275017126704596, 0.0], 'a3': [0.0, 0.0], 'a4': [-6.2377392028569965, 0.0], 'a5': [15.424069295191071, 0.0], 'a6': [0.0, 0.0], 'a7': [7.965010276022757, 0.0], 'a8': [-18.900623176348006, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 89.74190511873151, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 13], 'central_character': '1521.1', 'coefficient_field': 'CDF', 'conductor': 1521, 'conductor_radical': 39, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.3275017126704596, 0], [8.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-15.424069295191071, 0], [125.0, 0]], [[1.0, 0], [-7.965010276022757, 0], [343.0, 0]], [[1.0, 0], [-12.769065869850152, 0], [1331.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-54.0, 0], [4913.0, 0]], [[1.0, 0], [-84.57940549512367, 0], [6859.0, 0]], [[1.0, 0], [122.85287043428396, 0], [12167.0, 0]], [[1.0, 0], [140.85287043428397, 0], [24389.0, 0]], [[1.0, 0], [-116.43944659921469, 0], [29791.0, 0]], [[1.0, 0], [-433.89774529276775, 0], [50653.0, 0]], [[1.0, 0], [205.82290768816577, 0], [68921.0, 0]], [[1.0, 0], [418.85287043428394, 0], [79507.0, 0]], [[1.0, 0], [-485.86066414480854, 0], [103823.0, 0]], [[1.0, 0], [-674.5586113028519, 0], [148877.0, 0]], [[1.0, 0], [-186.22598119707044, 0], [205379.0, 0]], [[1.0, 0], [671.901913622856, 0], [226981.0, 0]], [[1.0, 0], [14.036425358276075, 0], [300763.0, 0]], [[1.0, 0], [346.78858351337186, 0], [357911.0, 0]], [[1.0, 0], [-832.8997419403178, 0], [389017.0, 0]], [[1.0, 0], [335.6076544914239, 0], [493039.0, 0]], [[1.0, 0], [-568.7969687283002, 0], [571787.0, 0]], [[1.0, 0], [236.6710462785479, 0], [704969.0, 0]], [[1.0, 0], [-1278.9403173975923, 0], [912673.0, 0]], [[1.0, 0], [632.2643521714198, 0], [1030301.0, 0]], [[1.0, 0], [-1506.26435217142, 0], [1092727.0, 0]], [[1.0, 0], [-1268.558611302852, 0], [1225043.0, 0]], [[1.0, 0], [347.4247446038747, 0], [1295029.0, 0]], [[1.0, 0], [659.7057408685679, 0], [1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 79, 'label': '2-39e2-1.1-c3-0-79', 'leading_term': '3.28476991311664005933435535788', '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/1521/4/a/x/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [3.28476991311664, 3.265017090334606, 3.2060268239788132, 3.108602877246955, 2.974081887737795, 2.8043283710634803, 2.6017266714869764, 2.369168885351141, 2.110037614617408, 1.8281823140398596, 1.5278879849949834, 1.2138350464671712, 0.8910493798317731, 0.564841795625171, 0.24073650048748696, -0.07561145941676664, -0.3785093492431212, -0.6623295693528998, -0.9216207179111996, -1.151224943076282, -1.3463991397035386, -1.5029370894253904, -1.6172892478249068, -1.6866765685716387, -1.7091945409035492, -1.6839035207880968, -1.6109014718258345, -1.4913754103732972, -1.3276281772157437, -1.1230776373857743, -0.8822260370397144, -0.610598012562444, -0.3146466371761685, -0.0016278831543549625, 0.3205550536701733, 0.643535008407875, 0.9586880035199864, 1.2573595459115712, 1.5311042968284625, 1.7719324616036713, 1.972555526279848, 2.126623454158569, 2.2289451840303585, 2.2756842736196776, 2.2645218289894804, 2.194779465952473, 2.0674959645075757, 1.8854524913928539, 1.653142755666283, 1.376686191493579, 1.0636841821726297, 0.7230213893768954, 0.36461636109702616, -0.000872317730037452, -0.3623760802593226, -0.7087725881033871, -1.0292565218367158, -1.3137122054096975, -1.55307457224651, -1.7396647186266307, -1.867486554419824, -1.9324718761509632, -1.9326625549913758, -1.8683204316452475, -1.741957896194887, -1.5582849348798022, -1.3240715559979765, -1.0479278519047024, -0.7400073849890497, -0.41164296185988775, -0.07492703429475718, 0.2577482103664881, 0.5741736750058397, 0.862809990549159, 1.1132578838893936, 1.3166920323986375, 1.4662388690754176, 1.5572803961394728, 1.5876685229514884, 1.5578377040802336, 1.470807612501392, 1.3320721005702398, 1.1493756029206945, 0.932383218264657, 0.6922557485148062, 0.44114574013923646, 0.1916348300405238, -0.04386377708096518, -0.2537112827885824, -0.42762981678582573, -0.5572413463681575, -0.6365318613389309, -0.6622160919826028, -0.6339816635231128, -0.5545964033316569, -0.4298683258046709, -0.2684543958682944, -0.08152123769625623, 0.11773180582905206, 0.31466978650433475, 0.4939154088397454, 0.6401087156484153, 0.7386989772781242, 0.7767315130929987, 0.7435908049601472, 0.6316617194743718, 0.43687300236283455, 0.15909141792320894, -0.19765914290106515, -0.625171784595378, -1.1112334551511602, -1.640004465471044, -2.192590665869703, -2.7477883769198, -3.2829728534942997, -3.77509280600846, -4.2017267736946255, -4.542152346730812, -4.778376692340428, -4.896076778728334, -4.8854002166365875, -4.741582729630036, -4.46534576588675, -4.063047389874242, -3.5465709331525117, -2.932948424647222, -2.243728963129053, -1.5041152833461844, -0.7419041235130444, 0.013723041928679293, 0.7335034046086507, 1.3894284827964931, 1.956046768672643, 2.4116679601103392, 2.7394066272686546, 2.928009743007415, 2.972422174346523, 2.8740565790546224, 2.640748607465992, 2.286394171492663, 1.8302820066805658, 1.296150954847574, 0.711016454921137, 0.10382380125879638, -0.4960039542913312, -1.0600486584843216, -1.5623324206348728, -1.9806289279651328, -2.2975792514533318, -2.5015500029894886, -2.587184647278479, -2.5556147157297135, -2.4143158078592415, -2.1766126442727103, -1.8608570015191408, -1.4893210186958696, -1.086865043631461, -0.6794528891402905, -0.29259724453520475, 0.05017662396676022, 0.32876026789585583, 0.527700503417349, 0.6371723589053921, 0.6536259553257724, 0.5800645299577056, 0.42593144993894666, 0.20660642657547676, -0.05746602605460215, -0.34197086541148414, -0.6201746854313279, -0.8645544838744805, -1.0485097181196692, -1.1480575424177601, -1.143410082843577, -1.0203375208450134, -0.7712314684690491, -0.39579912464553824, 0.0986608298480111, 0.6974258306979229, 1.3789599485189858, 2.1159404544785896, 2.8766483308179356, 3.626648002960395, 4.330662972703894, 4.954540662946261, 5.467192557606845, 5.842395196714278, 6.060343930555457, 6.108864296890954, 5.984204799747588, 5.691358696291427, 5.243889775380704, 4.6632664269819, 3.9777377934395646, 3.2208136541519985, 2.429434183743737, 1.641935276671583, 0.8959284636721709, 0.2262206385038069, -0.3371026208939615, -0.7703154316738873, -1.0573132403847847, -1.1904217824550691, -1.1707048723558313, -1.0077532156074323, -0.7189684675607134, -0.3283881287760289, 0.13487444098343726, 0.6384764495237111, 1.1488620688823066, 1.6333216493455565, 2.061964024856296, 2.409477960063202, 2.6565726136640166, 2.79100793164517, 2.808152817872676, 2.711040031953134, 2.5099200104627215, 2.2213490041636907, 1.8668778528370067, 1.4714342870039285, 1.0615120253004717, 0.6632926957248438, 0.30083081503170855, -0.005572649870192723, -0.24069599997184202, -0.3953308833921049, -0.4667614818422756, -0.4587578031832361, -0.3810867198148168, -0.2485790227322598, -0.07982294599581141, 0.10441794498923414, 0.2829439202499065, 0.43588435149296634, 0.5463550630531564, 0.6018803691165756, 0.5954683710667844, 0.5262524264252318, 0.3996427986012425, 0.22696823562268761, 0.024625113179548165, -0.18721088517111623, -0.38622150492485186, -0.5498137596374078, -0.657081268703336, -0.69071083553887, -0.6386859824899186, -0.495650017347877, -0.26381242482793044, 0.046687328256487075, 0.41800708126977026, 0.825426884307294, 1.2387343981912873, 1.624091478886363, 1.946264984242707, 2.1710745649024963], 'positive_zeros': ['0.864712926976473255208328020718805', '1.93389277118341985675288936184742', '3.10532885501930015910677477838861', '4.11462068124171021169062391522169', '5.08633098353777881636386391771700', '5.70776736150244280323402271040724', '6.29721064039630347016816338798057', '7.55751131997804371363681762160358', '8.388918459351090839192016847280344', '9.307180818851219892079030472775458'], 'prelabel': '2-39e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.473220419621383, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.864712926976473255208328020719', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.93389277118341985675288936185', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.10532885501930015910677477839', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 89.74190511873151, 'bad_primes': [3, 13], 'central_character': '1.1', 'conductor': 1521, 'conductor_radical': 39, 'degree': 2, 'index': 79, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1521/4/a/x/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': '2-39e2-1.1-c3-0-79', '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': '2-39e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.473220419621383, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.864712926976473255208328020719', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1096153860906835421639093055149', 'Lhash_array': ['1096153860906835421639093055149'], 'factors': ['2-39e2-1.1-c3-0-79'], 'label': '2-39e2-1.1-c3-0-79', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1521/4/a/x/1/3'}