-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '4598633802825532940903039220230', 'a10': [-21.740852297878796, 3.258045866607423e-60], 'a2': [1.0, -1.7320508075688772], 'a3': [3.3117376914898995, 4.004047135432493], 'a4': [-2.0, -3.4641016151377544], 'a5': [-5.435213074469699, -9.414065194944163], 'a6': [10.246950765959598, -1.7320508075688772], 'a7': [-12.435213074469699, 21.538420847926304], 'a8': [-8.0, 0.0], 'a9': [-5.064786925530301, 26.520707633827897], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.0620343801033316, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 1.7320508075688772]]], [3, [[1.0, 0], [-3.3117376914898995, -4.004047135432493]]]], 'bad_primes': [2, 3], 'central_character': '18.7', 'coefficient_field': 'CDF', 'conductor': 18, 'conductor_radical': 6, 'conjugate': '4225767501989712439101119577404', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 1.7320508075688772]], [[1.0, 0], [-3.3117376914898995, -4.004047135432493]], [[1.0, 0], [5.435213074469699, 9.414065194944163], [-62.5, 108.25317547305482]], [[1.0, 0], [12.435213074469699, -21.538420847926304], [-171.5, -297.04671349806245]], [[1.0, 0], [-21.370426148939398, 37.014663869361534], [-665.5, -1152.6798124370878]], [[1.0, 0], [7.564786925530301, 13.102595303451242], [-1098.5, 1902.6578121144116]], [[1.0, 0], [13.870426148939398, 0], [4913.0, 0]], [[1.0, 0], [-143.35213074469698, 0], [6859.0, 0]], [[1.0, 0], [9.564786925530301, 16.566696918589], [-6083.5, 10536.931087845265]], [[1.0, 0], [113.04649152128789, -195.80226693227493], [-12194.5, -21121.493572898675]], [[1.0, 0], [29.694360776590905, 51.43214156333587], [-14895.5, 25799.76280414221]], [[1.0, 0], [84.18596608515156, 0], [50653.0, 0]], [[1.0, 0], [101.6295738510606, 176.02758546161036], [-34460.5, 59687.336854227295]], [[1.0, 0], [162.94511378727276, -282.22921592464843], [-39753.5, -68855.08177868936]], [[1.0, 0], [5.471803882954518, -9.477442334329892], [-51911.5, -89913.35549711177]], [[1.0, 0], [140.18596608515156, 0], [148877.0, 0]], [[1.0, 0], [57.370426148939394, 99.36849294184111], [-102689.5, 177863.43140384424]], [[1.0, 0], [-377.52819611704547, 653.8980169645502], [-113490.5, -196571.31217639567]], [[1.0, 0], [-383.7225568936364, -664.6269645500174], [-150381.5, 260468.39851841913]], [[1.0, 0], [-335.85363676606073, 0], [357911.0, 0]], [[1.0, 0], [-167.27894912772734, 0], [389017.0, 0]], [[1.0, 0], [-12.657769968106084, 21.923900695279226], [-246519.5, -426984.29905647587]], [[1.0, 0], [143.86052543613633, -249.17373925894293], [-285893.5, -495182.06755369285]], [[1.0, 0], [860.8170459575759, 0], [704969.0, 0]], [[1.0, 0], [-201.0746876383334, 348.27157510563507], [-456336.5, -790398.003348155]], [[1.0, 0], [-665.714162202197, 1153.050752252354], [-515150.5, -892266.8395445109]], [[1.0, 0], [-259.25225903204563, -449.03808462051035], [-546363.5, 946329.3414011582]], [[1.0, 0], [-1471.8704261489395, 0], [1225043.0, 0]], [[1.0, 0], [643.6676706809092, 0], [1295029.0, 0]], [[1.0, 0], [511.8635374788638, 886.5736534553283], [-721448.5, 1249585.457044355]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-18-9.7-c3-0-1', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/18/4/c/b/7/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.17578125', 'prec': 34}, 'plot_values': [1.2746754581453752, 1.292921897385817, 1.3189242413877322, 1.3521803265999828, 1.3915934222562911, 1.435475176130647, 1.4815534115281421, 1.526984857919219, 1.5683765733452626, 1.6018232079204104, 1.6229694133185684, 1.6271072645885172, 1.6093175653113092, 1.5646615285228278, 1.488425724652517, 1.376418487768057, 1.2253103064202355, 1.0330043043956874, 0.799016078206473, 0.5248354012842051, 0.21423629379357556, -0.12650250255257875, -0.4885066185038403, -0.8603833580927012, -1.2285003562474115, -1.5774885276250363, -1.8909770887556785, -2.1525486374214893, -2.3468787309999195, -2.4609986975704077, -2.4855947930703524, -2.4162341241073237, -2.254391225756279, -2.008142157363343, -1.6923985145283549, -1.3285741716858226, -0.9436139697553718, -0.56836538858446, -0.23533893521525154, 0.02402418274594655, 0.1823843340639944, 0.21957584563928634, 0.12540912018646685, -0.0981324414161759, -0.4356261234167268, -0.8581505022158706, -1.3246190739287587, -1.7845650616252509, -2.182278866375159, -2.4620286018031874, -2.5739278305234805, -2.4798749424204645, -2.158897967079404, -1.6112168125843083, -0.8603959706385224, 0.04689022560543348, 1.0437266782172492, 2.0484131194520576, 2.9721301191739853, 3.7281170606945935, 4.241392064832523, 4.457867411527001, 4.3516700637475, 3.9295890777669764, 3.2318442662356537, 2.3287848053605495, 1.3136403685675817, 0.2919981623351832, -0.6308094767180428, -1.362830693945807, -1.8373567877072023, -2.0217886929680375, -1.9220792497874137, -1.5818712884306065, -1.0761821672379976, -0.5003021161469906, 0.04464461688397, 0.46740909362040856, 0.7011928193864269, 0.7147076313169453, 0.5177542645566945, 0.16012655929979805, -0.2763184339764442, -0.6914431664697985, -0.9844215875098482, -1.0723046351856034, -0.9063634818250744, -0.4831883272221323, 0.15175719921385222, 0.9092373810623005, 1.669633006106978, 2.3027223844353153, 2.6906631831396175, 2.75017485930654, 2.449791824906923, 1.8186868563378922, 0.9448960173530861, -0.037385071552824674, -0.9697282430527516, -1.6970597242365597, -2.096035253684844, -2.0988688412263077, -1.707818218072199, -0.9970379969587069, -0.10076500630845707, 0.8105924076352009, 1.5624215092163949, 2.010064461606908, 2.0685358362121153, 1.7316778172719938, 1.0764114934915427, 0.25050794867471043, -0.5544483401971604, -1.1401376681598783, -1.3415704979144059, -1.0621281429709786, -0.29621915180494723, 0.8655895534597897, 2.2507028159998805, 3.635690936464703, 4.78869749323523, 5.51463983240001, 5.6938969433550035, 5.306257115710378, 4.4347936102734105, 3.2484972225974693, 1.9670564282718406, 0.8151415961552828, -0.023992451104203446, -0.44543515651489995, -0.44187330123214014, -0.1008251234263684, 0.41952473210649016, 0.9303213239223882, 1.258525321165011, 1.2888829634644183, 0.9912902484208622, 0.42683043539038457, -0.26914084540952776, -0.9228471347161716, -1.3680435543153633, -1.4904634930241873, -1.2592073577514267, -0.7365071817255876, -0.06259263637436582, 0.5812587956891421, 1.0225565056585146, 1.1475727906234872, 0.9380262485348457, 0.48381267488417146, -0.033169623621687745, -0.38173328374792564, -0.34116557141386705, 0.23650791767082854, 1.377879833037056, 2.966732878362342, 4.757229754470604, 6.420672841953349, 7.616147228413863, 8.068766792703343, 7.636505221402775, 6.348606611988477, 4.405028199511214, 2.1357860135471203, -0.070875146266584, -1.8544765604434514, -2.961507150638619, -3.2982376534055273, -2.944030349429575, -2.122049760383698, -1.1352799518692478, -0.28482179331925206, 0.20789537959437288, 0.2544457524590484, -0.08560122704250984, -0.63141148346106, -1.1412036504171217, -1.3886639782273111, -1.2334334661757664, -0.6652847368247247, 0.1909263751037079, 1.1111798791966458, 1.8388173989512637, 2.1622899698426035, 1.9811218668974284, 1.3401461515900466, 0.4210745013203001, -0.5070889714099395, -1.1649851680051395, -1.3448950409526612, -0.9734489773670498, -0.13589047565209736, 0.9461971718266436, 1.9779963248547177, 2.67724643240579, 2.857295063529573, 2.4822294340217708, 1.6768392069463467, 0.687588608931314, -0.19424347236771378, -0.7241218116666518, -0.782203671825052, -0.4128274116773074, 0.18799654601961371, 0.7347037768629435, 0.9457766978788523, 0.640078915111567, -0.1948147627968334, -1.3854274101676547, -2.6142767182676128, -3.510503301998007, -3.763071088813748, -3.222134572714759, -1.9563617568799956, -0.2463514656118855, 1.486693453170928, 2.7978856754173687, 3.3472707538024227, 3.0015296374128, 1.877250186287356, 0.31129478357949153, -1.234267696417096, -2.305086952229311, -2.5857787929630356, -1.9900585577748537, -0.6826488397626429, 0.9732946786193828, 2.526579281072337, 3.571780134716666, 3.8651189771860617, 3.387244218884326, 2.3350416827619527, 1.0474713156837159, -0.10857247178008547, -0.8541031207703877, -1.0777824880077356, -0.8547731364100641, -0.40108288952871185, 0.01807630274083988, 0.19183446254607714, 0.04142823686823864, -0.35584723926656914, -0.8048908412766238, -1.0788320381174548, -1.020499293874076, -0.6204199115493583, -0.03991962793561012, 0.43289771215508116, 0.4820792555499893, -0.1155959776742155, -1.3915966007653673, -3.146211593159029, -4.987622416034863, -6.441502447091291, -7.097744662454399, -6.746011726161307, -5.453138818834314], 'positive_zeros': ['3.62768242447689383205795706977535', '6.83613776844462763888020529733268', '7.49280612897997457221569944910742', '9.659404539468818438178579664216701', '11.83011894895909056258898003511317', '13.34376940576790711248211056618949', '14.30441924306445031095314370466330', '15.43062941847074119135500388071634', '17.04411175449106600726258323842353', '18.30021021962872889399323045359605'], 'prelabel': '2-18-9.7-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0305505228291, 'root_angle': 0.11562146414599488, 'root_number': '0.9347521286397827 + 0.35530051787662104*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.057810732073', 'prec': 47}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.62768242447689383205795706978', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '6.83613776844462763888020529733', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.49280612897997457221569944911', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.0620343801033316, 'bad_primes': [2, 3], 'central_character': '9.7', 'conductor': 18, 'conductor_radical': 6, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/18/4/c/b/7/2'], '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': '2-18-9.7-c3-0-1', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-18-9.7-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0305505228291, 'root_angle': 0.05781073207299744, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '3.62768242447689383205795706978', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '4598633802825532940903039220230', 'Lhash_array': ['4598633802825532940903039220230'], 'label': '2-18-9.7-c3-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/18/4/c/b/7/2'}