-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '375660177334580202035334538783', 'a10': [0, 0], 'a2': [1.4142135623730951, 0], 'a3': [0, 1.7320508075688772], 'a4': [2.0, 0], 'a5': [0, 0], 'a6': [0, 2.449489742783178], 'a7': [-1.5788140895207694, 6.819629467260718], 'a8': [2.8284271247461903, 0], 'a9': [-3.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 28.61042775783118, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.4142135623730951, 0]]], [3, [[1.0, 0], [0, -1.7320508075688772]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [1.5788140895207694, -6.819629467260718]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '1050.601', 'coefficient_field': 'CDF', 'conductor': 1050, 'conductor_radical': 210, 'conjugate': '2456741285322563388758924454117', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.4142135623730951, 0]], [[1.0, 0], [0, -1.7320508075688772]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.5788140895207694, -6.819629467260718]], [[1.0, 0], [8.159645398410072, 0], [121.0, 0]], [[1.0, 0], [0, 14.606399484311634], [-169.0, 0]], [[1.0, 0], [0, -5.814206934070593], [-289.0, 0]], [[1.0, 0], [0, -33.77357749110363], [-361.0, 0]], [[1.0, 0], [37.25755188514298, 0], [529.0, 0]], [[1.0, 0], [-9.253045072210545, 0], [841.0, 0]], [[1.0, 0], [0, -19.255782220461345], [-961.0, 0]], [[1.0, 0], [63.43504885190463, 0], [1369.0, 0]], [[1.0, 0], [0, 8.2587979020984], [-1681.0, 0]], [[1.0, 0], [-42.089324923896044, 0], [1849.0, 0]], [[1.0, 0], [0, -23.33795233822333], [-2209.0, 0]], [[1.0, 0], [71.34968042172235, 0], [2809.0, 0]], [[1.0, 0], [0, 42.93497866769416], [-3481.0, 0]], [[1.0, 0], [0, -34.2864066868949], [-3721.0, 0]], [[1.0, 0], [4.998885547903991, 0], [4489.0, 0]], [[1.0, 0], [38.812005341743024, 0], [5041.0, 0]], [[1.0, 0], [0, 124.62942583410266], [-5329.0, 0]], [[1.0, 0], [-56.184166263674555, 0], [6241.0, 0]], [[1.0, 0], [0, -90.39796171489257], [-6889.0, 0]], [[1.0, 0], [0, -16.228899130715437], [-7921.0, 0]], [[1.0, 0], [0, -82.7605252932962], [-9409.0, 0]], [[1.0, 0], [0, -87.20546222808694], [-10201.0, 0]], [[1.0, 0], [0, -187.56739053821812], [-10609.0, 0]], [[1.0, 0], [157.8576726252988, 0], [11449.0, 0]], [[1.0, 0], [-112.07303861429182, 0], [11881.0, 0]], [[1.0, 0], [-141.9874507639, 0], [12769.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 7, 'label': '2-1050-7.6-c2-0-7', 'leading_term': '1.3605685442731775963161148388256305975727674762826781503', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1050/3/f/e/601/14', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.3605685442731776, 1.0899926424212922, 0.8185682168904396, 0.5478641601900361, 0.2794807926524052, 0.015072605441560609, -0.2436331677237935, -0.49482366916792514, -0.7365944794812356, -0.9669515647051997, -1.1838217098120893, -1.3850716885946994, -1.568536071760914, -1.7320532404076245, -1.8735088586916782, -1.9908857723151843, -2.08231904146338, -2.146154590209324, -2.1810097611165347, -2.1858339062280194, -2.159967026942477, -2.1031943993221285, -2.0157950926228536, -1.8985823120255516, -1.7529335762573623, -1.5808088809638987, -1.384755202148226, -1.1678959619713767, -0.9339044109790373, -0.6869602733467016, -0.4316894494570575, -0.17308706481489763, 0.083575314933473, 0.33285692975213255, 0.5692675984878018, 0.7873975373480704, 0.9820542226475295, 1.1484028290466624, 1.2821063781028552, 1.3794614271687429, 1.4375249344310836, 1.4542278689878494, 1.428471209148985, 1.360200197665179, 1.2504531048423404, 1.1013812897933706, 0.9162380410086938, 0.6993345085387281, 0.4559619937376732, 0.19228091499616937, -0.08482211026888595, -0.36790647048289316, -0.6491753022086161, -0.9206939139371453, -1.174623018758834, -1.4034600204303254, -1.6002808908505115, -1.7589746861208948, -1.8744625074318273, -1.9428927493861903, -1.9618048109599246, -1.9302540820835032, -1.8488919596883213, -1.719995876964099, -1.5474458221835843, -1.3366455402179438, -1.0943885006176204, -0.8286707202006638, -0.5484545759620235, -0.2633897595922849, 0.01650057231233715, 0.28115868954336004, 0.5208450228477411, 0.7264924550670079, 0.8900492052405944, 1.0047971289926154, 1.0656325461264056, 1.069297513444413, 1.0145507861157597, 0.9022695317308618, 0.735475132879431, 0.5192790704980856, 0.26074783501625254, -0.031311038696296485, -0.34663649215447445, -0.6738665287269079, -1.0009443903427404, -1.3155641929567656, -1.605639681438101, -1.85977812717854, -2.067740423498443, -2.220868211456529, -2.312459440677399, -2.33807515330437, -2.295762456760917, -2.186181569536253, -2.012628395074159, -1.7809481797583093, -1.4993402895066221, -1.1780588180857372, -0.8290184228757906, -0.4653192636640151, -0.10070898837203832, 0.2509968348898489, 0.5765117816593642, 0.8636673695815984, 1.1019672042505833, 1.283080616545521, 1.401251655210572, 1.45360218433737, 1.440311810753136, 1.36466230003821, 1.2329398499356066, 1.0541948490207058, 0.8398652925144489, 0.6032765654925041, 0.3590365318620291, 0.12235048040001374, -0.09171481394502731, -0.26898511650178236, -0.39691589884389816, -0.46527709639181036, -0.46675095972595176, -0.39741122523975303, -0.2570561729812954, -0.04937396536363139, 0.21807424272642334, 0.5340598476111615, 0.8840786920053457, 1.2509180297332878, 1.6153784670628104, 1.957122577164168, 2.255614695718072, 2.4911106299033885, 2.645651988706505, 2.704017837655247, 2.654586576303117, 2.490063412479371, 2.208033535214451, 1.8113079280195494, 1.3080374655299423, 0.7115811468361007, 0.04012559651665533, -0.6839352028510821, -1.4348391553616024, -2.1844822419828462, -2.9035895470243367, -3.5629806361908285, -4.134872603175998, -4.594160464017366, -4.919613770586279, -5.09493047343047, -5.1095941820348445, -4.959488890170677, -4.647235651019414, -4.1822281599286875, -3.5803581715119677, -2.863436487229751, -2.0583301802938605, -1.195851028184974, -0.3094430592732756, 0.566272003763326, 1.3970244126995905, 2.1504291317544446, 2.7974480461442637, 3.3137101515481966, 3.6806239916839187, 3.8862258087032777, 3.9257191170676693, 3.8016761439375784, 3.5238880909712664, 3.1088686453669636, 2.5790327126411614, 1.9615890453067344, 1.287200408620583, 0.5884773368406705, -0.10161931137643007, -0.7513864352718376, -1.3319156462199324, -1.8184804125919214, -2.1917019916237983, -2.4384338925570157, -2.5523190934385296, -2.5339913100966145, -2.390910401566538, -2.1368414928153494, -1.7910065468819505, -1.3769548687532434, -0.9212143761718904, -0.45179754855042054, 0.0033559466200259735, 0.4179143485564332, 0.7685821558434973, 1.0363431409412298, 1.2074497477370045, 1.274104823123301, 1.234799006580609, 1.094286656646943, 0.8632038287946576, 0.5573523560167942, 0.1966933307048374, -0.19588988801113774, -0.5959856195525692, -0.979122086579471, -1.322222920109044, -1.6049637471429103, -1.810949591025945, -1.928643564174678, -1.9519923044752792, -1.880711939274363, -1.7202189783549442, -1.481212210123344, -1.178933092669081, -0.8321519799179314, -0.46194456695646713, -0.09033609690188271, 0.26110071209318736, 0.572604962151696, 0.8274575071096351, 1.013002884888879, 1.1213976111522777, 1.1500364759755417, 1.1016290117770169, 0.983920809766854, 0.8090774446866976, 0.592770954523215, 0.35302867611541505, 0.10892044615825693, -0.1208283625802652, -0.31920460540865264, -0.472162710903078, -0.5696806655011695, -0.6065418038870883, -0.5827848235648944, -0.5037858035707353, -0.3799601552239895, -0.22609783474853354, -0.0603701567434795, 0.09693049263137717, 0.22483739164411268, 0.3032476286358775, 0.31444825379942093, 0.24452538240319416, 0.08455651871827521, -0.16850152245105812, -0.5112984719307816, -0.9339962917703242, -1.4206137681968962, -1.9498001674210872, -2.4959991109874347, -3.0309366757794636, -3.525344268400099, -3.950808714643424, -4.281630579248857, -4.4965679165383445, -4.580346894764267, -4.5248329584782505], 'positive_zeros': ['0.29634362754764275998668253145905', '1.85579593192500491104401919014867', '2.91195914652740602728697228910820', '4.09803891980171431983522324301174', '4.85725194752407330075475102115411', '5.99302538150008474094884922098896', '6.88793713887072282348245377340893', '7.33602087452560147530225100724832', '8.323655476974638286462001455286898', '9.395504453898209785634169808623646'], 'prelabel': '2-1050-7.6-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.348871634076778, 'root_angle': -0.9275837748113132, 'root_number': '-0.97423278103724542408416752102162482443858454224605160674 - 0.2255448699315384846124853009205852794555244997074533136*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.46379188740565663', 'prec': 67}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.29634362754764275998668253146', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.85579593192500491104401919015', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.91195914652740602728697228911', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 28.61042775783118, 'bad_primes': [2, 3, 5, 7], 'central_character': '7.6', 'conductor': 1050, 'conductor_radical': 210, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1050/3/f/e/601/14'], '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': '2-1050-7.6-c2-0-7', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-1050-7.6-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.348871634076778, 'root_angle': -0.4637918874056566, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.29634362754764275998668253146', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '375660177334580202035334538783', 'Lhash_array': ['375660177334580202035334538783'], 'label': '2-1050-7.6-c2-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1050/3/f/e/601/14'}