-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1818884641494410574270438840483', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 14.0], 'a4': [0.0, 0.0], 'a5': [55.0, -10.0], 'a6': [0.0, 0.0], 'a7': [0.0, -158.0], 'a8': [0.0, 0.0], 'a9': [47.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.830705585038453, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-55.0, 10.0]]]], 'bad_primes': [2, 5], 'central_character': '80.49', 'coefficient_field': 'CDF', 'conductor': 80, 'conductor_radical': 10, 'conjugate': '1552231794357287030470256248907', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, -14.0], [-243.0, 0]], [[1.0, 0], [-55.0, 10.0]], [[1.0, 0], [0, 158.0], [-16807.0, 0]], [[1.0, 0], [-148.0, 0], [161051.0, 0]], [[1.0, 0], [0, 684.0], [-371293.0, 0]], [[1.0, 0], [0, -2048.0], [-1419857.0, 0]], [[1.0, 0], [-2220.0, 0], [2476099.0, 0]], [[1.0, 0], [0, 1246.0], [-6436343.0, 0]], [[1.0, 0], [-270.0, 0], [20511149.0, 0]], [[1.0, 0], [-2048.0, 0], [28629151.0, 0]], [[1.0, 0], [0, 4372.0], [-69343957.0, 0]], [[1.0, 0], [2398.0, 0], [115856201.0, 0]], [[1.0, 0], [0, -2294.0], [-147008443.0, 0]], [[1.0, 0], [0, -10682.0], [-229345007.0, 0]], [[1.0, 0], [0, 2964.0], [-418195493.0, 0]], [[1.0, 0], [39740.0, 0], [714924299.0, 0]], [[1.0, 0], [42298.0, 0], [844596301.0, 0]], [[1.0, 0], [0, 32098.0], [-1350125107.0, 0]], [[1.0, 0], [-4248.0, 0], [1804229351.0, 0]], [[1.0, 0], [0, 30104.0], [-2073071593.0, 0]], [[1.0, 0], [-35280.0, 0], [3077056399.0, 0]], [[1.0, 0], [0, 27826.0], [-3939040643.0, 0]], [[1.0, 0], [-85210.0, 0], [5584059449.0, 0]], [[1.0, 0], [0, 97232.0], [-8587340257.0, 0]], [[1.0, 0], [4298.0, 0], [10510100501.0, 0]], [[1.0, 0], [0, -124114.0], [-11592740743.0, 0]], [[1.0, 0], [0, -42342.0], [-14025517307.0, 0]], [[1.0, 0], [-35990.0, 0], [15386239549.0, 0]], [[1.0, 0], [0, -228816.0], [-18424351793.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 8, 'label': '2-80-5.4-c5-0-8', 'load_key': 'CMFs-workshop', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/80/6/c/c/49/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.2574824199999615, 2.2427139946761874, 2.1795522809855603, 2.070271331306245, 1.9180749244956916, 1.727129406951811, 1.5025998922317507, 1.2506785543361503, 0.9785921823686331, 0.6945754882570767, 0.40779698535376363, 0.12822566130515406, -0.13357080819659953, -0.3667019264605708, -0.5603052724913923, -0.7039677999617395, -0.7882066509738163, -0.8049919622137356, -0.7482875317011193, -0.6145791145704061, -0.40335507601560144, -0.11750073428566873, 0.2364334437000145, 0.6481280543739038, 1.103588906214728, 1.5854645198284323, 2.0736009039280816, 2.545832958586124, 2.97899481290345, 3.3501128296596216, 3.6377261549883744, 3.8232620639893673, 3.8923786295953975, 3.8361771449987794, 3.6521828789261557, 3.344996484214678, 2.9265306109707017, 2.4157672803036103, 1.8380008893400017, 1.2235680453447884, 0.6061066166877824, 0.020429502821463212, -0.4998599091085006, -0.924847781790173, -1.230696333889726, -1.4017349405106523, -1.432057438487952, -1.326448896634089, -1.100505255696641, -0.7798664556467105, -0.3985546525198614, 0.003511216217254534, 0.3836715657078461, 0.7001240179714383, 0.9156717524663319, 1.0012904058340708, 0.9391688706739681, 0.7248990680500556, 0.3685434980784833, -0.10560467721196724, -0.6606414720090178, -1.2499934879850503, -1.8214854923833337, -2.3222091727862564, -2.7037604032953695, -2.927340207558206, -2.968189167162853, -2.818853523220254, -2.4908656558310347, -2.01455797543888, -1.4369072742110103, -0.8175103049659854, -0.22300034954881362, 0.27959418289619214, 0.6298976498010456, 0.7809010395754783, 0.7045889273180869, 0.3957986665220029, -0.12621419040924273, -0.8188040818314682, -1.6195805794322882, -2.4523958029162305, -3.2351136688651656, -3.8883621162942474, -4.344310485564639, -4.55445961560683, -4.495495910215184, -4.172442907757952, -3.618630250254524, -2.892361680247821, -2.070560434835677, -1.2400544142906893, -0.487485272442344, 0.11095983580211044, 0.4987218358033425, 0.6457626445210378, 0.552234962884791, 0.24836485641682615, -0.20954598429245944, -0.7465851324919895, -1.2792724989192963, -1.7269131501651829, -2.0227651165053158, -2.1234936502051522, -2.015557373995048, -1.7175408217388417, -1.277971330329354, -0.7687712669245212, -0.27511780316317724, 0.11697551178543882, 0.3336595604620707, 0.324979022984473, 0.07357662750147469, -0.401023792910694, -1.043374636511581, -1.7683976292542518, -2.472335228684053, -3.0469717657258286, -3.3951940906437326, -3.445677854964427, -3.1645149674856676, -2.5619514237997194, -1.69304581373453, -0.6519053486428508, 0.4399090779967116, 1.4493311316508661, 2.249911421997436, 2.7395326993178326, 2.8551079928859915, 2.582017264004974, 1.9567579487607378, 1.0622624777414185, 0.01643046697157067, -1.04453079453109, -1.9855318046130428, -2.691886579980459, -3.085513604965518, -3.135529830138073, -2.861549253583304, -2.3291224584505814, -1.6379979404057832, -0.9050524464332005, -0.24463326519511372, 0.25047508482426223, 0.5242951567001383, 0.566521190181311, 0.4134347886462146, 0.14061475524234673, -0.15142400579290916, -0.35628928409369476, -0.38222570619354707, -0.1705030194058118, 0.2916348857208578, 0.96592406979918, 1.7670965712634619, 2.575566652405509, 3.2568603542820687, 3.684609903532898, 3.7631958459175916, 3.446042286339057, 2.74619218906979, 1.7370265492034214, 0.5426476965114102, -0.6807544642630339, -1.7696071499280015, -2.579622825096644, -3.0098505188313727, -3.0198539199932366, -2.6368494323855987, -1.9513233668578527, -1.1016471645257886, -0.25017385004260423, 0.44512689583125215, 0.8585495014548178, 0.9190824466070502, 0.6232954733785709, 0.036228787071720794, -0.7200503390595977, -1.488328661989221, -2.1047391496685766, -2.4287669948894757, -2.3693137455668705, -1.9020057965208446, -1.0744796615021965, 0.0014415131805629246, 1.1693429260329178, 2.256034635059102, 3.102459735526903, 3.5919301435677635, 3.6703776657617087, 3.3547811334773927, 2.728162063857575, 1.9221157150551038, 1.090268935899268, 0.3778553286208341, -0.10659305240454, -0.3117995992328831, -0.2523897533620172, -0.003816078996642229, 0.31550654518424665, 0.5713102872397602, 0.6443290452018707, 0.4585149445085923, 0.0006248414079682691, -0.673192168103403, -1.445616125153001, -2.1599939358873166, -2.6517527739956663, -2.7832389715477395, -2.474913328525239, -1.7263290322428397, -0.6221700797355588, 0.6784997550804779, 1.968289125136878, 3.0282059704888025, 3.668139195413022, 3.7632177304686634, 3.278779125671151, 2.2787734829939237, 0.9156167976935482, -0.5968335019477882, -2.0221151571646003, -3.14431629716382, -3.8071090350974788, -3.9409770387022274, -3.5732844567116544, -2.819284937309363, -1.8560421609036848, -0.8847282973563707, -0.08915017284700551, 0.40088786256645775, 0.5338184429195315, 0.3432214896557006, -0.06381054532505537, -0.5340953803426086, -0.9054100434170633, -1.044914877240102, -0.8803934676079372, -0.4173138670248351, 0.26216502187365437, 1.0181084658279862, 1.6854790231225512, 2.1132460236871835, 2.2010393396024877, 1.924852681340428, 1.3456171359498117, 0.5982218282041617, -0.1370541977014938, -0.6746860446880887, -0.8668169779165652, -0.6392571648516202, -0.01216240131981963, 0.8998042441984329, 1.9085611203938628, 2.790930623300985, 3.3362032452334844, 3.3926603935613207], 'positive_zeros': ['1.43484698478187625651289244073855', '2.66908325633065254032997145100591', '5.12958350681591005540140504081372', '6.37389826249377757064204605115081', '7.34926583302124053202932681555237', '9.051773555324886597155218867365150', '9.723601451032213785933466091870297', '11.59846747118026925394831266567235', '12.19671509682654663964408871947670', '13.58248784421289701729257868103208'], 'prelabel': '2-80-5.4-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.5819974295130996, 'root_angle': -0.05724914704870018, 'root_number': '0.9838699100999074 - 0.17888543819998318*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0286245735244', 'prec': 54}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.43484698478187625651289244074', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.66908325633065254032997145101', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.12958350681591005540140504081', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 12.830705585038453, 'bad_primes': [2, 5], 'central_character': '5.4', 'conductor': 80, 'conductor_radical': 10, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/80/6/c/c/49/2'], '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': '2-80-5.4-c5-0-8', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-80-5.4-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.5819974295130996, 'root_angle': -0.02862457352435009, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '1.43484698478187625651289244074', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1818884641494410574270438840483', 'Lhash_array': ['1818884641494410574270438840483'], 'label': '2-80-5.4-c5-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/80/6/c/c/49/2'}