-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2503205992082748955840568943470', 'a10': [0.0, 0.0], 'a2': [-1.0809731454762448, -0.911864605497545], 'a3': [0.6190182805250813, 0.0], 'a4': [0.33700588248161334, 1.9714023017062725], 'a5': [0.0, 0.0], 'a6': [-0.6691421378064937, -0.5644608601667719], 'a7': [-1.82372921099509, -1.82372921099509], 'a8': [1.4333576732921949, -2.4383366831539868], 'a9': [-2.6168163683757717, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.194016080851217, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0809731454762448, 0.911864605497545]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5], 'central_character': '400.107', 'coefficient_field': 'CDF', 'conductor': 400, 'conductor_radical': 10, 'conjugate': '595355095136639644914104174006', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0809731454762448, 0.911864605497545]], [[1.0, 0], [-0.6190182805250813, 0], [3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.82372921099509, 1.82372921099509], [0, 7.0]], [[1.0, 0], [0.5678487706660399, -0.5678487706660399], [0, -11.0]], [[1.0, 0], [0, 2.787706822740578], [-13.0, 0]], [[1.0, 0], [3.651928494916384, 3.651928494916384], [0, 17.0]], [[1.0, 0], [-4.510653374078585, 4.510653374078585], [0, -19.0]], [[1.0, 0], [-2.1552040396894827, 2.1552040396894827], [0, -23.0]], [[1.0, 0], [3.2025867342809073, 3.2025867342809073], [0, 29.0]], [[1.0, 0], [0, 3.5408710098938947], [-31.0, 0]], [[1.0, 0], [0, 5.223712062997742], [-37.0, 0]], [[1.0, 0], [0, -8.762871260082791], [-41.0, 0]], [[1.0, 0], [0, -10.860372469737932], [-43.0, 0]], [[1.0, 0], [3.2204962945371656, -3.2204962945371656], [0, -47.0]], [[1.0, 0], [12.86578613278791, 0], [53.0, 0]], [[1.0, 0], [3.7931942309833047, 3.7931942309833047], [0, 59.0]], [[1.0, 0], [-6.633949539749247, 6.633949539749247], [0, -61.0]], [[1.0, 0], [0, -7.787320089756068], [-67.0, 0]], [[1.0, 0], [-13.664995542219883, 0], [71.0, 0]], [[1.0, 0], [1.3438212770785622, 1.3438212770785622], [0, 73.0]], [[1.0, 0], [-16.35281520277162, 0], [79.0, 0]], [[1.0, 0], [-0.39105598952228565, 0], [83.0, 0]], [[1.0, 0], [18.031664098532108, 0], [89.0, 0]], [[1.0, 0], [-6.435165244730758, -6.435165244730758], [0, 97.0]], [[1.0, 0], [5.365156701299929, 5.365156701299929], [0, 101.0]], [[1.0, 0], [-11.564304915889311, 11.564304915889311], [0, -103.0]], [[1.0, 0], [-7.787320089756068, 0], [107.0, 0]], [[1.0, 0], [-4.397714558782862, -4.397714558782862], [0, 109.0]], [[1.0, 0], [-3.7620647547509485, 3.7620647547509485], [0, -113.0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 25, 'label': '2-20e2-80.27-c1-0-25', '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/400/2/s/e/107/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.6141306663025017, 0.7673051760200856, 0.9229833944829113, 1.081747432534085, 1.241260023459562, 1.3961014642007747, 1.537967892308327, 1.6561453738127871, 1.7382053442165128, 1.7709018061447142, 1.741262969545653, 1.6378573879254772, 1.4521854313433347, 1.180110710832754, 0.8232107226592343, 0.3898978767795469, -0.10385336763649408, -0.6343356894164492, -1.1706342050687226, -1.675942461888397, -2.1096965469415, -2.430469182589773, -2.5994684879051255, -2.5843870583013913, -2.3632583707715704, -1.9279127450168216, -1.2865973333188345, -0.46534477272013147, 0.4922501593624752, 1.5270567583537347, 2.568270360456253, 3.538931546100935, 4.362701333246986, 4.97128468597419, 5.31173470009218, 5.352785121010354, 5.089372367110081, 4.544632739225228, 3.768894953173479, 2.8355155764819218, 1.8337924780871422, 0.8595926082334416, 0.004690364064405969, -0.653924951027562, -1.0633989525749434, -1.2017115613438658, -1.0806760019510717, -0.744620141787983, -0.26469463619429245, 0.2706280443842082, 0.7677105305625057, 1.1409451326794824, 1.3251107195935838, 1.28502718912084, 1.020943914504743, 0.568667764172441, -0.005795044868522297, -0.6164494357542263, -1.1709243007599155, -1.585404613472607, -1.7984714252382492, -1.7814950840979216, -1.5436896280801957, -1.1307563194888395, -0.6171056847324706, -0.09278083489030846, 0.3527869855980371, 0.6473685634995676, 0.749827074759131, 0.6585848174877365, 0.4127923872854858, 0.08558719821049471, -0.22970475561330966, -0.438158504825077, -0.46328347510292356, -0.264634537193038, 0.15067400834028344, 0.7253038776133209, 1.3590959641644245, 1.9258631093149252, 2.296977950689351, 2.3676007985562997, 2.080525996879215, 1.4426823685671588, 0.5303697145935876, -0.5187771209139154, -1.5266415669928746, -2.305269353353154, -2.6921012772148556, -2.5832795429992044, -1.9583909852953951, -0.8911958782098457, 0.4567564218081104, 1.8595904248139898, 3.0642703848059156, 3.835200958735254, 3.9981616786423597, 3.475137814380819, 2.3029301376194202, 0.6312337999262339, -1.3003120044134322, -3.2025056452065277, -4.787235325239985, -5.818964923948565, -6.157150851654536, -5.781206592176237, -4.792902529358286, -3.3954998897074637, -1.8535911185801521, -0.4415853787824141, 0.6088190095247624, 1.151546131771357, 1.1507537734197142, 0.6822734365678244, -0.08809223545957229, -0.9444431828973779, -1.6699516601327484, -2.09446828391804, -2.130112440994863, -1.787140706181283, -1.1668840646941265, -0.43379307183348864, 0.22656633671345744, 0.6534843164110755, 0.7500674817993592, 0.5059012495189098, -0.0019564973319244365, -0.629781972584666, -1.2046022713563218, -1.5689177408911765, -1.6215442960597417, -1.3442478879734754, -0.8072836576312072, -0.15217502685760223, 0.44419249052621146, 0.8152619401810983, 0.8487083816772686, 0.5172015934628448, -0.11219592129141767, -0.8928978510346816, -1.6346223935749544, -2.1513503927113127, -2.309200952129339, -2.0617162726166667, -1.4630164624999913, -0.6548508525347803, 0.1696388432090706, 0.8163643620408741, 1.1418057812660363, 1.0917600032598054, 0.7164735564980157, 0.15732753850002412, -0.39219778840037256, -0.7414163470596049, -0.7585579207741058, -0.41248588468997255, 0.21240946703422886, 0.9338004593395913, 1.518495628959191, 1.7476956930205487, 1.483450295796957, 0.7179541743305836, -0.4091543160658109, -1.6325876877887278, -2.6192908607165397, -3.0495305498295613, -2.7013260808692405, -1.516271151868685, 0.3715813649987036, 2.653453459190236, 4.908262405811521, 6.696150188526967, 7.660940500146455, 7.616167366929396, 6.59261352836607, 4.834419624208349, 2.7435688993859633, 0.7856778069391622, -0.6199041832104307, -1.198377740965434, -0.881563372052901, 0.18170525651574881, 1.669090342110078, 3.1705018940046656, 4.293577879723502, 4.761460935593262, 4.477796142532597, 3.5428787787467106, 2.2180973715102756, 0.8496496914665255, -0.2268150116898836, -0.7743588539508877, -0.7121196136136914, -0.12740538083689415, 0.758975977592981, 1.6625272906783646, 2.3188416774157647, 2.55688768675825, 2.341158497886357, 1.771775266930564, 1.0443520514299145, 0.38334625182580045, -0.029798887112047645, -0.11139348070034413, 0.10340739519035702, 0.4788829962937322, 0.8296399534031642, 0.9870661222851344, 0.8593888537388465, 0.4654328701960838, -0.06940762259977216, -0.5542683752482714, -0.7981090313031689, -0.6780748430596174, -0.18818399598677832, 0.5487008976308602, 1.311266561328534, 1.8445565867066018, 1.9397239598897873, 1.5035934856714126, 0.595112961747286, -0.5845470046777554, -1.7471484411560518, -2.6021150085292097, -2.944977538767822, -2.7213561759577063, -2.044910045247683, -1.161510459632357, -0.3688420873987278, 0.08455554368492371, 0.08894366913332488, -0.2781923870457916, -0.7633116654533124, -1.007930983831406, -0.6609700793610904, 0.5005596887359589, 2.480014850771844, 5.02936514061447, 7.691161933168834, 9.906365639906948, 11.15978311474513, 11.12222464452562, 9.747753478239066, 7.29620106981521, 4.272253006838119, 1.296710304813706, -1.0542979560147654, -2.3965329198497227, -2.6293283226867117, -1.945996980528376, -0.7612356916897554, 0.4216363534627017, 1.1631450834026482, 1.2140851843583222, 0.5788138584399436, -0.5017587668523741, -1.6397030957034895], 'positive_zeros': ['1.97468134486905825181986172028033', '3.43752891210564289644411041532115', '5.25076415317958334800372926674972', '6.06205325590259187330082214515124', '6.99880807139023546712348049066320', '8.148626815096626697646579137459638', '8.906933148091299072592838330869394', '9.460903837663264105513741869484663', '10.56396579329467825712523475839928', '11.45930624393083670456894113320323'], 'prelabel': '2-20e2-80.27-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7871810431098514, 'root_angle': 0.8089581637604877, 'root_number': '-0.8252364344423482 + 0.5647874177678537*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.40447908188', 'prec': 44}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.97468134486905825181986172028', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.43752891210564289644411041532', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.25076415317958334800372926675', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 3.194016080851217, 'bad_primes': [2, 5], 'central_character': '80.27', 'conductor': 400, 'conductor_radical': 10, 'degree': 2, 'index': 25, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/400/2/s/e/107/4'], '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': '2-20e2-80.27-c1-0-25', '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': '2-20e2-80.27-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7871810431098514, 'root_angle': 0.40447908188024384, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.97468134486905825181986172028', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2503205992082748955840568943470', 'Lhash_array': ['2503205992082748955840568943470'], 'label': '2-20e2-80.27-c1-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/400/2/s/e/107/4'}