-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1979099562542550252885024678663', 'a10': 0, 'a2': 0, 'a3': 1, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 62.28331357659873, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [5, [1]], [13, [1, 1]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '7800.1', 'coefficient_field': '1.1.1.1', 'conductor': 7800, 'conductor_radical': 390, 'degree': 2, 'euler_factors': [[1], [1, -1], [1], [1, 0, 7], [1, -4, 11], [1, 1], [1, -2, 17], [1, 4, 19], [1, 4, 23], [1, 6, 29], [1, 4, 31], [1, 6, 37], [1, 2, 41], [1, 12, 43], [1, 8, 47], [1, 14, 53], [1, -12, 59], [1, 2, 61], [1, 0, 67], [1, -8, 71], [1, -2, 73], [1, -8, 79], [1, 12, 83], [1, -6, 89], [1, -10, 97], [1, -10, 101], [1, 8, 103], [1, -4, 107], [1, -2, 109], [1, -2, 113]], 'euler_factors_factorization': [[1], [[[1, -1], 1]], [1], [[[1, 0, 7], 1]], [[[1, -4, 11], 1]], [[[1, 1], 1]], [[[1, -2, 17], 1]], [[[1, 4, 19], 1]], [[[1, 4, 23], 1]], [[[1, 6, 29], 1]], [[[1, 4, 31], 1]], [[[1, 6, 37], 1]], [[[1, 2, 41], 1]], [[[1, 12, 43], 1]], [[[1, 8, 47], 1]], [[[1, 14, 53], 1]], [[[1, -12, 59], 1]], [[[1, 2, 61], 1]], [[[1, 0, 67], 1]], [[[1, -8, 71], 1]], [[[1, -2, 73], 1]], [[[1, -8, 79], 1]], [[[1, 12, 83], 1]], [[[1, -6, 89], 1]], [[[1, -10, 97], 1]], [[[1, -10, 101], 1]], [[[1, 8, 103], 1]], [[[1, -4, 107], 1]], [[[1, -2, 109], 1]], [[[1, -2, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 110, 'label': '2-7800-1.1-c1-0-110', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/7800/2/a/u', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [8.393778029083798e-60, 0.246180855085658, 0.4911646560628051, 0.7337090094328914, 0.9724843764953767, 1.2060390745457776, 1.432773871265495, 1.6509283030050315, 1.8585800964934018, 2.053658299327319, 2.2339699888643043, 2.3972397752534707, 2.541160765860074, 2.663455221503372, 2.7619428035810647, 2.8346140724228914, 2.8797067364709306, 2.8957820562775134, 2.8817987677172097, 2.8371819003762844, 2.761883928800188, 2.656435807960535, 2.521985613333043, 2.3603227340610005, 2.1738858577266744, 1.9657533384839239, 1.7396149555743445, 1.4997245426033288, 1.250833492392522, 0.99810570765589, 0.7470151610937029, 0.5032278339776941, 0.2724704018218631, 0.06038860942926143, -0.12760119553587446, -0.2864634427104846, -0.41169333592405, -0.49946090971568907, -0.546744455208978, -0.5514486336812185, -0.5125027576337602, -0.42993504012251194, -0.3049190950526267, -0.13978960999137907, 0.06197510119335194, 0.2958050419417048, 0.556125323417144, 0.8364770454590036, 1.1296703562666772, 1.4279666115959344, 1.723285414968394, 2.0074312512030708, 2.272333468952018, 2.51029256531593, 2.7142251158341857, 2.8778993106862107, 2.9961529313866953, 3.0650857527571156, 3.082218794897291, 3.0466135817913553, 2.9589455789377626, 2.8215272627781847, 2.6382777893748166, 2.414637937678817, 2.157430852888054, 1.874671048260071, 1.5753260729036567, 1.2690371473351714, 0.9658068344517676, 0.6756633779254255, 0.4083126329958091, 0.1727894725584239, -0.022878880305716005, -0.17198500647410084, -0.26941667014919246, -0.31188396108479444, -0.29808800488474163, -0.22882275897181695, -0.10700352667689927, 0.062381721210288545, 0.2723994063130672, 0.5143740779566763, 0.7781641534008522, 1.052502070313216, 1.3253884948445622, 1.584527738870401, 1.8177894352412225, 2.0136799014933797, 2.161805577348652, 2.2533105177760704, 2.2812702072937685, 2.241024952968872, 2.13043780601038, 1.9500643189588316, 1.7032244025224348, 1.3959700108299757, 1.0369462389224609, 0.6371475228945745, 0.2095748357083251, -0.23119609622257276, -0.6695216401978862, -1.0892547727810435, -1.4743469582135702, -1.809464886249741, -2.0805981992571856, -2.275633892271366, -2.3848735986477028, -2.4014714939249737, -2.3217730363408604, -2.145538147182253, -1.8760366101308315, -1.5200082904371413, -1.0874860633742611, -0.591484891343964, -0.0475660754789428, 0.5267089043039886, 1.1124155923530399, 1.6899711394853212, 2.239879169126215, 2.7434854404417117, 3.1837136058768145, 3.545750411178901, 3.8176510411390754, 3.9908379563933956, 4.060470421136083, 4.0256668581395045, 3.889568003634386, 3.659235342181358, 3.345386215269107, 2.9619740250203375, 2.5256287897157317, 2.054979643459445, 1.5698864136490356, 1.0906118890641852, 0.6369695801679263, 0.2274834948956693, -0.121403407702716, -0.3960369140809817, -0.5861433253331064, -0.6852778190162445, -0.6911078538898763, -0.6055170924178624, -0.4345231404789483, -0.1880106887557566, 0.1207099843073763, 0.4755011063467485, 0.858126652521504, 1.2490809108349559, 1.6284795258267435, 1.9769727702947948, 2.2766392014598176, 2.5118181901348073, 2.6698420943010532, 2.7416330151336425, 2.722134965576064, 2.6105596542800877, 2.4104326194628247, 2.1294357529693655, 1.7790519031722234, 1.3740267782872706, 0.9316723262840838, 0.4710436984269071, 0.012028405079233011, -0.42560899994501955, -0.8231806817986889, -1.1639812307371906, -1.4341006060289878, -1.6231036384617363, -1.7245415111498414, -1.7362685451919107, -1.660546971350729, -1.5039327308770356, -1.276946217351143, -0.9935427101926911, -0.6704075125300237, -0.3261099621827666, 0.019841949804838062, 0.34799905712738444, 0.6399700597367747, 0.8793708918021846, 1.052675090518469, 1.1499203176052006, 1.1652330456902713, 1.0971423551360058, 0.9486643694956102, 0.7271505714149681, 0.4439054973712252, 0.11359148035794701, -0.2465504431840958, -0.6176242355916847, -0.9800997256577566, -1.3148773428384126, -1.6043402800475373, -1.8333374429035172, -1.9900433420915407, -2.0666467979131364, -2.0598287062390197, -1.9709997700208841, -1.8062815077358694, -1.5762273823873076, -1.29529485105424, -0.9810927766725656, -0.653441232761849, -0.3332915706360032, -0.04156308855849818, 0.20204176139986899, 0.3801793312892083, 0.4789006695946141, 0.4885226268973431, 0.4042832330236319, 0.22674109964962014, -0.038108304075331084, -0.37901182416008145, -0.7799297640177881, -1.2207795870801836, -1.6784175724098023, -2.127810192058807, -2.5433357031665667, -2.900148182324073, -3.175531486284018, -3.3501697315707135, -3.4092639719490276, -3.3434317277758603, -3.1493365806753175, -2.8300086835246545, -2.3948330628747065, -1.859200176865845, -1.2438314022633685, -0.5738099723617538, 0.1226356132315555, 0.8155344666576989, 1.4746901212427777, 2.07123156984445, 2.5791157248422882, 2.976499873649548, 3.2469085711554717, 3.3801295157843527, 3.3727868102502105, 3.2285569057278267, 2.9580115813709553, 2.5780924967545884, 2.111242069233064, 1.5842345477280286, 1.0267680982828415, 0.46989250852813885, -0.05564305693015594, -0.5210325649853933, -0.9009558763344981, -1.1749364394829307, -1.3284380975723074, -1.3536390352403715, -1.2498383564050337, -1.0234709244232032, -0.687727807570785, -0.26180174466084516, 0.23020176966735756, 0.7606280964635108], 'positive_zeros': ['1.56123427242982466090595067308819', '2.04891969776081833544716378077149', '3.36892009313603717025518168271813', '3.68722841172202400700992394976638', '4.61611270593743150732647425787701', '5.34770733733994876965528529786708', '6.35761349768140561273772871158090', '6.73262641164950051142451665078371', '7.59499942265741132817665548039249'], 'prelabel': '2-7800-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.8919777987902835, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 46697186428733885, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.56123427242982466090595067309', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.04891969776081833544716378077', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.36892009313603717025518168272', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 62.28331357659873, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 7800, 'conductor_radical': 390, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 4, 0, -1, 0, 0, 0, 2, 0, -4, 0, 0, 0, -4, 0, 0, 0, 1, 0, -6, 0, -4, 0, 4, 0, 0, 0, -6, 0, -1, 0, -2, 0, -12, 0, 0, 0, -8, 0, -7, 0, 2, 0, -14, 0, 0, 0, -4, 0, 12, 0, -2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 8, 0, 2, 0, 0, 0, 0, 0, 8, 0, 1, 0, -12, 0, 0, 0, -6, 0, 6, 0, 0, 0, -4, 0, 0, 0, 10, 0, 4, 0], 'euler11': [1, -4, 11], 'euler13': [1, 1, 0], 'euler17': [1, -2, 17], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 4, 23], 'euler29': [1, 6, 29], 'euler3': [1, -1, 0], 'euler31': [1, 4, 31], 'euler37': [1, 6, 37], 'euler41': [1, 2, 41], 'euler43': [1, 12, 43], 'euler47': [1, 8, 47], 'euler5': [1, 0, 0], 'euler53': [1, 14, 53], 'euler59': [1, -12, 59], 'euler61': [1, 2, 61], 'euler67': [1, 0, 67], 'euler7': [1, 0, 7], 'euler71': [1, -8, 71], 'euler73': [1, -2, 73], 'euler79': [1, -8, 79], 'euler83': [1, 12, 83], 'euler89': [1, -6, 89], 'euler97': [1, -10, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, 0, 0], [1, 0, 7], [1, -4, 11], [1, 1, 0], [1, -2, 17], [1, 4, 19], [1, 4, 23], [1, 6, 29], [1, 4, 31], [1, 6, 37], [1, 2, 41], [1, 12, 43], [1, 8, 47], [1, 14, 53], [1, -12, 59], [1, 2, 61], [1, 0, 67], [1, -8, 71], [1, -2, 73], [1, -8, 79], [1, 12, 83], [1, -6, 89], [1, -10, 97]], 'index': 110, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/7800/u', 'ModularForm/GL2/Q/holomorphic/7800/2/a/u/1/1', 'ModularForm/GL2/Q/holomorphic/7800/2/a/u'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-7800-1.1-c1-0-110', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-7800-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.8919777987902835, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 46697186428733885, 'z1': {'__RealLiteral__': 0, 'data': '1.56123427242982466090595067309', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 22147908
{'Lhash': '1979099562542550252885024678663', 'Lhash_array': ['1979099562542550252885024678663'], 'label': '2-7800-1.1-c1-0-110', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7800/2/a/u'}
-
id: 24581217
{'Lhash': '1979099562542550252885024678663', 'Lhash_array': ['1979099562542550252885024678663'], 'label': '2-7800-1.1-c1-0-110', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7800/2/a/u/1/1'}
-
id: 102723
{'Lhash': '46697186428733885', 'Lhash_array': ['46697186428733885'], 'label': '2-7800-1.1-c1-0-110', 'type': 'ECQ', 'url': 'EllipticCurve/Q/7800/u'}