-
lfunc_lfunctions • Show schema
Hide schema
{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': -1, 'A8': 0, 'A9': -6, 'Lhash': '549355224370905856,914597623939667325', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [-2.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 89.57942739416335, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1, 1]]], 'bad_primes': [2, 7], 'central_character': '1404928.1', 'coefficient_field': '1.1.1.1', 'conductor': 1404928, 'conductor_radical': 14, 'degree': 4, 'euler_factors': [[1], [1, 0, 6, 0, 9], [1, 0, 6, 0, 25], [1, 1], [1, -8, 38, -88, 121], [1, 0, 22, 0, 169], [1, 0, -2, 0, 289], [1, 0, -26, 0, 361], [1, 0, 46, 0, 529], [1, 12, 94, 348, 841], [1, 0, -2, 0, 961], [1, -4, 78, -148, 1369], [1, 0, 78, 0, 1681], [1, -8, 102, -344, 1849], [1, 0, 30, 0, 2209], [1, 12, 142, 636, 2809], [1, 0, 118, 0, 3481], [1, 0, 86, 0, 3721], [1, -8, 150, -536, 4489], [1, 16, 206, 1136, 5041], [1, 0, 46, 0, 5329], [1, -32, 414, -2528, 6241], [1, 0, 102, 0, 6889], [1, 0, 142, 0, 7921], [1, 0, 158, 0, 9409], [1, 0, 198, 0, 10201], [1, 0, -50, 0, 10609], [1, -24, 358, -2568, 11449], [1, -20, 318, -2180, 11881], [1, -4, 230, -452, 12769]], 'gamma_factors': [[], [0, 0]], 'index': 21, 'label': '4-112e3-1.1-c1e2-0-21', 'load_key': 'Costa', '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': 1, 'origin': 'EllipticCurve/2.0.7.1/28672.7/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-2.723578258925985e-74, 0.19804106765326604, 0.3944396334188745, 0.5874537084668463, 0.7751491765109955, 0.9553206583178969, 1.125432157231335, 1.2825831717514429, 1.423505148147261, 1.5445920944849116, 1.6419678764796146, 1.711591163669081, 1.7493972040185244, 1.7514736070277024, 1.7142651623987943, 1.6348004900617923, 1.5109311090539554, 1.3415714514758146, 1.1269265764292353, 0.8686930128367991, 0.570217438275722, 0.23659793494626657, -0.12528651493618242, -0.5068307259851874, -0.8978516892129603, -1.2868361584952717, -1.6612880573783964, -2.0081706232328247, -2.314431962778492, -2.567596220094712, -2.7563962399378776, -2.871417881744458, -2.9057214680001087, -2.855402699234087, -2.720054167019426, -2.503089705184657, -2.2118974886254006, -1.8577941257005681, -1.455760928051503, -1.023954820509205, -0.582999509979059, -0.15507690410327463, 0.2371464804696819, 0.5717092315058376, 0.8285995003607682, 0.9909830822103499, 1.0463379947523614, 0.9874170479996423, 0.8129637524767389, 0.5281163194125685, 0.14444939833871762, -0.32037691134496477, -0.843367267811609, -1.3973202907135733, -1.9522887713243968, -2.47729603860588, -2.94220978028801, -3.319655869296956, -3.5868430128624373, -3.7271658856427563, -3.7314608726709206, -3.598805017497419, -3.3367748696469293, -2.9611164677101733, -2.4948186984156275, -1.9666270432308297, -1.409080007511266, -0.8561927247568076, -0.3409476681053785, 0.10722235926965076, 0.46476164064295594, 0.7159350615692299, 0.8542125252725893, 0.8829539437273604, 0.8153034182311221, 0.6732611670485391, 0.4859684496791703, 0.2873089856411425, 0.11299442196269796, -0.002644574724019523, -0.02990146205670651, 0.05330755975125025, 0.2589638363113451, 0.5872312074214415, 1.025699325308861, 1.5497065942899753, 2.1237761765162793, 2.7041021825565457, 3.2419264194435664, 3.6875576176970646, 3.9947134702313747, 4.124818698664001, 4.050875582237161, 3.760540385583687, 3.258090427378113, 2.5650494889819826, 1.7193480711552223, 0.7730210607927931, -0.2114221101794889, -1.1656928017447368, -2.0211128991486036, -2.7142478686003493, -3.1922903261927926, -3.4177037705907325, -3.3716847866464184, -3.056094492082304, -2.4936394678913985, -1.7262380820419119, -0.8116760333749345, 0.18118077021370976, 1.1782035383233813, 2.1063263738187596, 2.8997968096591706, 3.5057609452236087, 3.8886448371611873, 4.0329009046851185, 3.943841681464393, 3.6464692722682326, 3.1824093567484124, 2.605253248130742, 1.9747798391121048, 1.3506526567170578, 0.7862511171514156, 0.32329060264833254, -0.012188652706934703, -0.21202299495299615, -0.2860668896214107, -0.26024748153740057, -0.17273724523033365, -0.06866561591658737, 0.006034609517754141, 0.010937346490193123, -0.08315509042249115, -0.28977592014928266, -0.6042116253935307, -1.0031428369906747, -1.4466292389993642, -1.8822878289253213, -2.251249686729301, -2.4952544109559387, -2.564081303319545, -2.4224435029001787, -2.0554976472570052, -1.4722482886347745, -0.7063425785384055, 0.18596492550282634, 1.13057555687263, 2.0426128521031632, 2.8350799660308215, 3.4281811270813995, 3.7582647927722954, 3.785348330289616, 3.498308045997243, 2.9170543528339024, 2.0913362436770244, 1.0961970415176356, 0.024491915694214255, -1.022768725774437, -1.9472102842674843, -2.6638176396742788, -3.1103639804580743, -3.2544356556219105, -3.0971965809792534, -2.6733966085238587, -2.047557262427969, -1.3067157377218956, -0.5505206429341225, 0.12020011244676691, 0.6150794039499561, 0.8646943657928807, 0.8286477999058133, 0.5002741309170482, -0.09260861017682519, -0.8910077438243266, -1.8117414115322423, -2.7572655326714637, -3.627154367357051, -4.3298375718656805, -4.793159724284575, -4.9724711058422475, -4.855265633450101, -4.461816433937102, -3.8417676331185073, -3.067157912441143, -2.2228102423620366, -1.395362206248911, -0.662386189499867, -0.08303304244335376, 0.3085739581280183, 0.5063410289459938, 0.5312393984946009, 0.4265575552008156, 0.2500793193993955, 0.06433103467567283, -0.07367781530242593, -0.12171032405454722, -0.05916918685448376, 0.1094863031877955, 0.35535294554680286, 0.6297295378033463, 0.872207420361641, 1.0210919971057144, 1.024659618901527, 0.851573847188665, 0.4988383848916153, -0.004048775637186447, -0.5955866207130129, -1.187625836088577, -1.6751200903272105, -1.9491599062914098, -1.9116579842577825, -1.4897446375894043, -0.6478794791239669, 0.6040928993161874, 2.208241016321834, 4.061825884676552, 6.026409434477183, 7.941854474639061, 9.643595916189339, 10.98107947599181, 11.835051642449336, 12.131479362248658, 11.850273991757147, 11.027643815836274, 9.751718782005351, 8.151970552388313, 6.38377052372344, 4.610074262690513, 2.982601405444182, 1.6249398338265117, 0.6197306008678194, 0.0015211391511795675, -0.24391326542547473, -0.17387594809763526, 0.1223422664317481, 0.5382422929049057, 0.9663883303156267, 1.3138088500488252, 1.5143406425277364, 1.5362238268406756, 1.3839950231966132, 1.0946005594017585, 0.7285310076115528, 0.35753016680661326, 0.05094157692220549, -0.13705487214056725, -0.17722531307493303, -0.07048231689491548, 0.1523527802320709, 0.43619598491255424, 0.7118361152210214, 0.9088875901936471, 0.9693931938412632, 0.8597549644669853, 0.5788890173615133, 0.16106347836831802, -0.32729365511000225], 'positive_zeros': ['1.01536704926852438245703233734839', '1.93975903006317803281774950017712', '2.35911554344998475560129433400815', '3.22234166202046004358507312699016', '3.70152283742019411667382089257066', '3.77515777589665000060106383713554', '4.58367495132727840614913978641465', '5.10093822894527537496894350174306', '5.81038841174965326632002876390424', '6.08808818165492598018676693089554', '6.15054397459112152814277916996712', '6.78746217059840482908609994193716', '7.31356679414241138388846467494871', '7.81893808816424475924755874672632'], 'prelabel': '4-112e3-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.076465650952455, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1463952848310573181, 'z1': {'__RealLiteral__': 0, 'data': '1.01536704926852438245703233734839', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.93975903006317803281774950017712', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.35911554344998475560129433400815', 'prec': 113}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 89.57942739416335, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 1404928, 'conductor_radical': 14, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, -1, 0, -6, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 1, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 8, 0, 0, 0, -16, 0, 0, 0, 0, 0, -8, 0, 32, 0, 27, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -48, 0], 'euler11': [1, -8, 38, -88, 121], 'euler13': [1, 0, 22, 0, 169], 'euler17': [1, 0, -2, 0, 289], 'euler19': [1, 0, -26, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 46, 0, 529], 'euler29': [1, 12, 94, 348, 841], 'euler3': [1, 0, 6, 0, 9], 'euler31': [1, 0, -2, 0, 961], 'euler37': [1, -4, 78, -148, 1369], 'euler41': [1, 0, 78, 0, 1681], 'euler43': [1, -8, 102, -344, 1849], 'euler47': [1, 0, 30, 0, 2209], 'euler5': [1, 0, 6, 0, 25], 'euler53': [1, 12, 142, 636, 2809], 'euler59': [1, 0, 118, 0, 3481], 'euler61': [1, 0, 86, 0, 3721], 'euler67': [1, -8, 150, -536, 4489], 'euler7': [1, 1, 0, 0, 0], 'euler71': [1, 16, 206, 1136, 5041], 'euler73': [1, 0, 46, 0, 5329], 'euler79': [1, -32, 414, -2528, 6241], 'euler83': [1, 0, 102, 0, 6889], 'euler89': [1, 0, 142, 0, 7921], 'euler97': [1, 0, 158, 0, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 6, 0, 9], [1, 0, 6, 0, 25], [1, 1, 0, 0, 0], [1, -8, 38, -88, 121], [1, 0, 22, 0, 169], [1, 0, -2, 0, 289], [1, 0, -26, 0, 361], [1, 0, 46, 0, 529], [1, 12, 94, 348, 841], [1, 0, -2, 0, 961], [1, -4, 78, -148, 1369], [1, 0, 78, 0, 1681], [1, -8, 102, -344, 1849], [1, 0, 30, 0, 2209], [1, 12, 142, 636, 2809], [1, 0, 118, 0, 3481], [1, 0, 86, 0, 3721], [1, -8, 150, -536, 4489], [1, 16, 206, 1136, 5041], [1, 0, 46, 0, 5329], [1, -32, 414, -2528, 6241], [1, 0, 102, 0, 6889], [1, 0, 142, 0, 7921], [1, 0, 158, 0, 9409]], 'index': 21, 'instance_types': ['ECNF', 'BMF'], 'instance_urls': ['EllipticCurve/2.0.7.1/28672.7/a', 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/28672.7/a'], 'is_instance_Artin': False, 'is_instance_BMF': True, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, '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': '4-112e3-1.1-c1e2-0-21', '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': 1, 'prelabel': '4-112e3-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.076465650952455, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1463952848310573181, 'z1': {'__RealLiteral__': 0, 'data': '1.01536704926852438245703233734839', 'prec': 113}}
-
lfunc_instances • Show schema
Hide schema
-
id: 9620066
{'Lhash': '549355224370905856,914597623939667325', 'Lhash_array': ['549355224370905856', '914597623939667325'], 'label': '4-112e3-1.1-c1e2-0-21', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/28672.7/a'}
-
id: 9620455
{'Lhash': '549355224370905856,914597623939667325', 'Lhash_array': ['549355224370905856', '914597623939667325'], 'label': '4-112e3-1.1-c1e2-0-21', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.7.1/28672.7/a'}