-
lfunc_lfunctions • Show schema
Hide schema
{'A10': 0, 'A2': 0, 'A3': 2, 'A4': 1, 'A5': 6, 'A6': 0, 'A7': 1, 'A8': 0, 'A9': 2, 'Lhash': '229614574950928079', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.020618556701030927, 0.0], 'a4': [0.010309278350515464, 0.0], 'a5': [0.061855670103092786, 0.0], 'a6': [0.0, 0.0], 'a7': [0.010309278350515464, 0.0], 'a8': [0.0, 0.0], 'a9': [0.020618556701030927, 0.0], 'algebraic': True, 'analytic_conductor': 27.389691889038694, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.500000000000000', 'prec': 57}, 'bad_lfactors': [[7, [1, -1, 5, 7]], [109, [1, 3, 105, -109]], [563, [1, -24, 586, -563]]], 'bad_primes': [7, 109, 563], 'central_character': '429569.1', 'coefficient_field': '1.1.1.1', 'conductor': 429569, 'conductor_radical': 429569, 'degree': 4, 'euler_factors': [[1, 0, -1, 0, 4], [1, -2, 2, -6, 9], [1, -6, 19, -30, 25], [1, -1, 5, 7], [1, 6, 23, 66, 121], [1, -2, 14, -26, 169], [1, -2, 14, -34, 289], [1, -13, 78, -247, 361], [1, 8, 41, 184, 529], [1, 3, 8, 87, 841], [1, -1, 24, -31, 961], [1, 6, 38, 222, 1369], [1, 1, -8, 41, 1681], [1, -6, 54, -258, 1849], [1, 1, -54, 47, 2209], [1, 0, 30, 0, 2809], [1, 0, 62, 0, 3481], [1, 5, -14, 305, 3721], [1, 1, 106, 67, 4489], [1, 6, -2, 426, 5041], [1, 18, 175, 1314, 5329], [1, 0, 94, 0, 6241], [1, 3, 28, 249, 6889], [1, -4, -7, -356, 7921], [1, 21, 240, 2037, 9409]], 'gamma_factors': [[], [0, 0]], 'index': 0, 'label': '4-429569-1.1-c1e2-0-0', 'leading_term': '5.47964873171', 'load_key': 'G2Q', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'origin': 'Genus2Curve/Q/429569/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.1875', 'prec': 20}, 'plot_values': [5.479648731714092, 5.448966600463729, 5.303114699178382, 4.911918564706639, 4.153466594210976, 3.020901166493753, 1.695102977518804, 0.5188665928161478, -0.1552638977260957, -0.1850591263736039, 0.2210535031786611, 0.5945984957323224, 0.5373794900308344, 0.07111269360101381, -0.3340242573611063, -0.2079427131531831, 0.2887113398615125, 0.1935565566938349, -1.541365611392129, -4.831924486269605, -7.88379816854921, -8.180415188014951, -4.600415945854614, 1.16726728032256, 5.562606874835541, 6.017555460067292, 3.16398773360696, 0.0724665301573924, -0.8613978023259964, -0.1015520197868265, 0.1982973799846058, -0.730334455347257, -1.185915748684705, 0.5433338832304319, 3.301544153649216, 3.88436979985891, 1.038215645248714, -2.486444837419702, -2.98715688775781, -0.3915334970712519, 1.739541889897149, 1.037827538275735, -0.5357506496455068, 0.2976924033609805, 3.186378887830322, 4.465355157900129, 2.401179254961956, -0.3281841616949201, -0.581536910903186, 0.8946361840339341, 1.214837600784726, 0.03542861652693039, -0.458785598660979, 0.2243052864652724, 0.162152898352939, -0.8224170640741888, -0.1232783355563294, 2.40235331058564, 2.009626493814037, -4.037725614587639, -10.0476176730579, -8.235745400664365, -0.5330947382222534, 2.717355206410566, -2.790228920319139, -9.026258905126541, -7.408802649499472, -0.7492420746453584, 2.271249714100069, -0.06988414486925922, -2.276324316358496, -1.482268546564417, -0.1603649406316189, -0.001759412431074584, 0.03893818458768391, -0.1719467175223824, -1.612844884099336, -2.362652411144149, -0.4607809438759813, 0.5905367656847464, -3.546779515963931, -9.119958542113695, -8.513538067459994, -2.568719110059235, 0.8664347864104686, 0.01120818497911975, -0.1983162582410487, -0.216953863958536, -5.720262136559252, -14.03924606383737, -14.58099716611339, -5.818802523815008, 1.468806317133322, 1.210070580019157, -0.8750874528013614, -0.1097033428452992, 0.6401673902516062, -0.0840412264790806, 0.02122257327653091, -0.7898782808481036, -5.271010558735032, -7.31505382675561, 0.3188556930242781, 10.74573306679104, 11.10508462295164, 2.857775703769294, -1.888870711322787, -0.1586170788208574, 1.328826533589094, 0.3921542490718604, -0.006754694137930125, 0.09476944145180734, -0.1808026491657749, 0.7991053650641053, 1.896138092845493, 0.01923736019282861, -1.983391327283302, -0.2168253303618613, 0.9698974752366706, -1.123505470842145, 1.898488060103052, 11.90389860069702, 12.9109575338452, -2.242118466121005, -13.8954937949557, -6.318515575985348, 6.248714130248927, 5.893068468114271, -1.087557634982891, -2.110405717910736, 0.2265968447741667, 0.1529165653729968, 0.1800947810728121, 1.363561206235044, 0.5807189303422956, -0.888286969871872, -0.3069235497307975, 0.3284372113877492, -0.03303334153716059, 0.3590293310614302, 0.3492604184188595, -0.04812786614116924, 2.892506720193218, 4.69066312670584, -3.827890632629269, -13.78917061853689, -7.210522922573017, 8.463702150824878, 10.13696575256979, -0.0001047149728806034, -1.989912480488634, 3.847688087253255, 3.88706082116861, -0.1903798009663196, -0.4541362146400223, 0.2907681409799331, -0.4382304318569097, 0.4424240290353976, 0.7957240579967597, -1.348492251979077, -0.2895815724317491], 'positive_zeros': [1.436933422967416, 1.785746622363006, 2.462650888796994, 2.892551610873603, 3.22479125779506, 4.274893386130168, 5.068805393950029, 5.460499389724272, 5.683325390401386, 6.147719635374605, 6.79930324210848, 7.336997400699762, 7.794107710750812, 8.036604228189336, 8.781474998950982, 9.078334587947662, 9.568112818282142, 9.881075047099792, 10.15791340017397, 10.51077207571892, 10.95444277456198, 11.63925124212134, 11.92932230643491, 12.58711680093121, 12.93351736313007, 13.56723819490178, 13.68425481373967, 13.82600156299269, 14.01090360599174, 14.66122685271454, 14.86364168445964, 15.66560047985626, 15.93915203439395, 16.17003231914484, 16.28856559301522, 17.19158201104489, 17.52333019943819, 17.82649035132852, 18.16334958535373, 18.36601388982453, 18.47708208949269, 19.11975246975333, 19.76323426241825], 'prelabel': '4-429569-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.287687961023143, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'USp(4)', 'trace_hash': 229614574950928079, 'z1': {'__RealLiteral__': 0, 'data': '1.43693342297', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.78574662236', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.4626508888', 'prec': 40}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 27.389691889038694, 'bad_primes': [7, 109, 563], 'central_character': '1.1', 'conductor': 429569, 'conductor_radical': 429569, 'degree': 4, 'dirichlet_coefficients': [1, 0, 2, 1, 6, 0, 1, 0, 2, 0, -6, 2, 2, 0, 12, -3, 2, 0, 13, 6, 2, 0, -8, 0, 17, 0, 6, 1, -3, 0, 1, 0, -12, 0, 6, 2, -6, 0, 4, 0, -1, 0, 6, -6, 12, 0, -1, -6, -4, 0, 4, 2, 0, 0, -36, 0, 26, 0, 0, 12, -5, 0, 2, -7, 12, 0, -1, 2, -16, 0, -6, 0, -18, 0, 34, 13, -6, 0, 0, -18, 11, 0, -3, 2, 12, 0, -6, 0, 4, 0, 2, -8, 2, 0, 78, 0, -21, 0, -12, 17], 'euler11': [1, 6, 23, 66, 121], 'euler13': [1, -2, 14, -26, 169], 'euler17': [1, -2, 14, -34, 289], 'euler19': [1, -13, 78, -247, 361], 'euler2': [1, 0, -1, 0, 4], 'euler23': [1, 8, 41, 184, 529], 'euler29': [1, 3, 8, 87, 841], 'euler3': [1, -2, 2, -6, 9], 'euler31': [1, -1, 24, -31, 961], 'euler37': [1, 6, 38, 222, 1369], 'euler41': [1, 1, -8, 41, 1681], 'euler43': [1, -6, 54, -258, 1849], 'euler47': [1, 1, -54, 47, 2209], 'euler5': [1, -6, 19, -30, 25], 'euler53': [1, 0, 30, 0, 2809], 'euler59': [1, 0, 62, 0, 3481], 'euler61': [1, 5, -14, 305, 3721], 'euler67': [1, 1, 106, 67, 4489], 'euler7': [1, -1, 5, 7, 0], 'euler71': [1, 6, -2, 426, 5041], 'euler73': [1, 18, 175, 1314, 5329], 'euler79': [1, 0, 94, 0, 6241], 'euler83': [1, 3, 28, 249, 6889], 'euler89': [1, -4, -7, -356, 7921], 'euler97': [1, 21, 240, 2037, 9409], 'euler_factors': [[1, 0, -1, 0, 4], [1, -2, 2, -6, 9], [1, -6, 19, -30, 25], [1, -1, 5, 7, 0], [1, 6, 23, 66, 121], [1, -2, 14, -26, 169], [1, -2, 14, -34, 289], [1, -13, 78, -247, 361], [1, 8, 41, 184, 529], [1, 3, 8, 87, 841], [1, -1, 24, -31, 961], [1, 6, 38, 222, 1369], [1, 1, -8, 41, 1681], [1, -6, 54, -258, 1849], [1, 1, -54, 47, 2209], [1, 0, 30, 0, 2809], [1, 0, 62, 0, 3481], [1, 5, -14, 305, 3721], [1, 1, 106, 67, 4489], [1, 6, -2, 426, 5041], [1, 18, 175, 1314, 5329], [1, 0, 94, 0, 6241], [1, 3, 28, 249, 6889], [1, -4, -7, -356, 7921], [1, 21, 240, 2037, 9409]], 'index': 0, 'instance_types': ['G2Q'], 'instance_urls': ['Genus2Curve/Q/429569/a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': True, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-429569-1.1-c1e2-0-0', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-429569-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.287687961023143, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 229614574950928079, 'z1': {'__RealLiteral__': 0, 'data': '1.43693342297', 'prec': 44}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '229614574950928079', 'Lhash_array': ['229614574950928079'], 'label': '4-429569-1.1-c1e2-0-0', 'type': 'G2Q', 'url': 'Genus2Curve/Q/429569/a'}