-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1585942866448741238419199368879', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [2.0, 1.0], 'a6': [0.0, 0.0], 'a7': [2.8284271247461903, 2.8284271247461903], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.749228945532191, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-2.0, -1.0]]]], 'bad_primes': [2, 3, 5], 'central_character': '720.703', 'coefficient_field': 'CDF', 'conductor': 720, 'conductor_radical': 30, 'conjugate': '2026491064182983360826110527834', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.0, -1.0]], [[1.0, 0], [-2.8284271247461903, -2.8284271247461903], [0, 7.0]], [[1.0, 0], [0, 5.656854249492381], [-11.0, 0]], [[1.0, 0], [-3.0, -3.0], [0, 13.0]], [[1.0, 0], [-1.0, 1.0], [0, -17.0]], [[1.0, 0], [5.656854249492381, 0], [19.0, 0]], [[1.0, 0], [2.8284271247461903, -2.8284271247461903], [0, -23.0]], [[1.0, 0], [0, -4.0], [-29.0, 0]], [[1.0, 0], [0, 0], [-31.0, 0]], [[1.0, 0], [-5.0, 5.0], [0, -37.0]], [[1.0, 0], [0, 0], [41.0, 0]], [[1.0, 0], [-2.8284271247461903, 2.8284271247461903], [0, -43.0]], [[1.0, 0], [2.8284271247461903, 2.8284271247461903], [0, 47.0]], [[1.0, 0], [1.0, 1.0], [0, 53.0]], [[1.0, 0], [-11.313708498984761, 0], [59.0, 0]], [[1.0, 0], [-4.0, 0], [61.0, 0]], [[1.0, 0], [2.8284271247461903, 2.8284271247461903], [0, 67.0]], [[1.0, 0], [0, -5.656854249492381], [-71.0, 0]], [[1.0, 0], [3.0, 3.0], [0, 73.0]], [[1.0, 0], [5.656854249492381, 0], [79.0, 0]], [[1.0, 0], [2.8284271247461903, -2.8284271247461903], [0, -83.0]], [[1.0, 0], [0, -8.0], [-89.0, 0]], [[1.0, 0], [3.0, -3.0], [0, -97.0]], [[1.0, 0], [18.0, 0], [101.0, 0]], [[1.0, 0], [2.8284271247461903, -2.8284271247461903], [0, -103.0]], [[1.0, 0], [8.48528137423857, 8.48528137423857], [0, 107.0]], [[1.0, 0], [0, 10.0], [-109.0, 0]], [[1.0, 0], [11.0, 11.0], [0, 113.0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 8, 'label': '2-720-20.3-c1-0-8', '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/720/2/x/e/703/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.9895127368404228, 1.9159762583211633, 1.8286196513285358, 1.7209991233459399, 1.585110029407914, 1.4134272866843052, 1.200851326830389, 0.9463317996660335, 0.654060714030419, 0.33417107459614437, 0.0028741390470172538, -0.31803944526755823, -0.6023950532774264, -0.8215407666241684, -0.946905501880257, -0.9530545802995493, -0.8209882450190308, -0.5413377658012052, -0.11704969328579835, 0.4348720170632563, 1.0829606179884377, 1.7825129321686508, 2.47857991400361, 3.1106394045362995, 3.6186243781036955, 3.9497361135028584, 4.06526609174974, 3.9465219437860184, 3.5989357229874575, 3.053550129383623, 2.365335613692264, 1.6081723212856818, 0.8667961900642015, 0.22649794943117138, -0.23819731904449032, -0.47433272321541436, -0.45915640318262513, -0.20508120930779528, 0.24014795970002764, 0.7985673120987821, 1.372091456043273, 1.856467646564663, 2.157217735994412, 2.2051836103423064, 1.969121137032292, 1.4630326688461164, 0.746595491660054, -0.08193535968113427, -0.8997380164132489, -1.5784878025425546, -2.0055732745694717, -2.10394196320232, -1.847008632276318, -1.2656569762666396, -0.4455594460973192, 0.48533610740885963, 1.3775149855995692, 2.085530663363969, 2.494151014158487, 2.5402014179179555, 2.225780888278353, 1.619887175270842, 0.8475212882530795, 0.06770387754826503, -0.5559183850679281, -0.8865276372194657, -0.8415870771746927, -0.4106838454535315, 0.3402230790486085, 1.2796004726570036, 2.2346463443836275, 3.02471640526342, 3.4973815264643515, 3.5597629872480385, 3.198433298345555, 2.483274609502677, 1.5538929858762192, 0.5908683226015423, -0.22249787938000162, -0.7399519144749362, -0.884902671192212, -0.6684080340880489, -0.18798373899006943, 0.39322126450986755, 0.8829357988205717, 1.1042867441979003, 0.9384842666681555, 0.3558064419131307, -0.5727356628196208, -1.6865556974670333, -2.7678499062843316, -3.588542087582658, -3.9615261667856765, -3.784487811589505, -3.065854429181541, -1.9262172488024616, -0.5741039213467329, 0.7389915044959757, 1.7743222306086874, 2.3594651055949174, 2.427003817861307, 2.02879144649495, 1.321932758560897, 0.5294338221481697, -0.11523049996664438, -0.4261736434192089, -0.31134642251824995, 0.20482841538685334, 0.9885446298630194, 1.8320985506269838, 2.5091166782310603, 2.8355324730524836, 2.720434311321304, 2.193092959044966, 1.3983204618030367, 0.5604222173969666, -0.07566585177606054, -0.3111035461195113, -0.05015699442468795, 0.6681373383924015, 1.6731030931114244, 2.700865551257586, 3.4592261029110447, 3.702734644275265, 3.298458022474022, 2.2647928654348415, 0.7723185317510446, -0.8945048061214008, -2.4055734603513073, -3.4658870104878106, -3.8876857897218104, -3.634822487525644, -2.8274461186839264, -1.7057278454289588, -0.562560462757832, 0.33619074631754364, 0.8217026982645245, 0.8628641461877271, 0.5661615362109769, 0.1349247305546205, -0.20015996551482998, -0.2587957080127725, 0.026201678736556315, 0.5805593384037873, 1.2042281866182638, 1.6279052033475883, 1.5949258496186869, 0.9449347967002536, -0.32568681369209873, -2.045757654427892, -3.900978652392945, -5.508437346899503, -6.51426627063123, -6.687411349499467, -5.9827939650331805, -4.555306604728699, -2.7198716614183955, -0.8682824110936339, 0.6338140052539732, 1.5404574121549424, 1.782714709722128, 1.4736732375908697, 0.8604562833070559, 0.23848533190796725, -0.14539149563077852, -0.17089765644234645, 0.12076384116770462, 0.5459682426034651, 0.8456712063293459, 0.7790698896288107, 0.213807052394484, -0.8168892262281893, -2.1098395945361967, -3.3436413976062687, -4.171947983105646, -4.330035578717128, -3.7212705434596662, -2.4554185424974846, -0.8251090462700019, 0.7741343904687087, 1.957001266042533, 2.4603751140693833, 2.2195322577497194, 1.3844609231045863, 0.27060351395280685, -0.7411249321910736, -1.3240019958637057, -1.3072435565009364, -0.7275697382627642, 0.18592458318314734, 1.088859194523374, 1.6358993177971048, 1.5953894135713784, 0.9269871214213588, -0.20321607791395765, -1.4753317576558884, -2.5190903219149474, -3.034168811462334, -2.887670840655669, -2.156223952550737, -1.0983086976861043, -0.06563279128318092, 0.6170595707474438, 0.7633423014610661, 0.38965086251962583, -0.28966812618429416, -0.9362431054504778, -1.206457098874231, -0.8752992816515277, 0.07709683554091275, 1.4468196666461735, 2.863597437824791, 3.906732677188782, 4.241770752429387, 3.7323121973380906, 2.4889182098169536, 0.8376708219634366, -0.7821570855090743, -1.9577662448260935, -2.433256832150779, -2.186945854454644, -1.429444413631086, -0.5232584893398071, 0.14840834559319974, 0.31833225980881186, -0.07002700151006742, -0.8429396530307455, -1.659095682029308, -2.132986802013407, -1.9759127447817688, -1.1049440385567793, 0.3190328763729409, 1.938451599030039, 3.315725238664786, 4.079054683130602, 4.046327472552723, 3.283380035988831, 2.075871277427048, 0.8246469306563959, -0.0980903675585453, -0.4801335540968528, -0.34054768129106733, 0.08541157372558099, 0.44288059887225667, 0.4007513766886245, -0.21065281842918854, -1.3190330236727883, -2.618361372994042, -3.665852215162679, -4.035200056059141, -3.4723111139636194, -1.997460109883391, 0.08427783968472738, 2.270458956004727, 4.0179408926660605, 4.915174101858287, 4.8104438074264415], 'positive_zeros': ['1.25108832525556024564387860561369', '2.27886909060435536651965762010179', '4.17912950374236370212943521180964', '4.68808491534124084129503227756263', '5.86288057028163082038441799366874', '6.81047690892648088793871774872097', '7.88675247607973060769692218301877', '8.448617636884204419795370340989827', '9.711849828816361933576352486787939', '10.29084235082692176748229223670768'], 'prelabel': '2-720-20.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.397754980295566, 'root_angle': -0.0881040955873917, 'root_number': '0.8506508083520399 - 0.5257311121191337*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0881040955874', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.25108832525556024564387860561', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.27886909060435536651965762010', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.17912950374236370212943521181', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 5.749228945532191, 'bad_primes': [2, 3, 5], 'central_character': '20.3', 'conductor': 720, 'conductor_radical': 30, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/720/2/x/e/703/2'], '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': '2-720-20.3-c1-0-8', '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': '2-720-20.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.397754980295566, 'root_angle': -0.0881040955873917, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.25108832525556024564387860561', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1585942866448741238419199368879', 'Lhash_array': ['1585942866448741238419199368879'], 'factors': ['2-720-20.3-c1-0-8'], 'label': '2-720-20.3-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/720/2/x/e/703/2'}