-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_115.88', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.7557495743542583, 0.6548607339452851], 'a3': [0.5406408174555976, 0.8412535328311812], 'a4': [0.14231483827328514, 0.9898214418809327], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [-0.14231483827328514, 0.9898214418809327], 'a7': [-0.28173255684142967, -0.9594929736144974], 'a8': [-0.5406408174555976, 0.8412535328311812], 'a9': [-0.41541501300188644, 0.9096319953545183], 'algebraic': True, 'analytic_conductor': 0.5340577547741961, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [23, [1]]], 'bad_primes': [5, 23], 'central_character': '115.88', 'coeff_info': ['x^44 - 1', '0.989821441880933 + 0.142314838273285*I', '\\\\zeta_{44}'], 'conductor': 115, 'conductor_radical': 115, 'conjugate': 'dirichlet_L_115.17', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^5', 'a^7', 'a^10', 0, 'a^12', 'a^31', 'a^15', 'a^14', 0, 'a^6', 'a^17', 'a^35', 'a^36', 0, 'a^20', 'a^23', 'a^19', 'a^32', 0, 'a^38', 'a^11', 0, 'a^22', 0, 'a^40', 'a^21', 'a^41', 'a^34', 0, 'a^4', 'a^25', 'a^13', 'a^28', 0, 'a^24', 'a^3', 'a^37', 'a^42', 0, 'a^8', 'a^43', 'a^29', 'a^16', 0, 0, 'a^33', 'a^27', 'a^18', 0, 'a^30', 'a^1', 'a^9', 'a^26', 0, 'a^2', 'a^39', 'a^39', 'a^2', 0, 'a^26', 'a^9', 'a^1', 'a^30', 0, 'a^18', 'a^27', 'a^33', 0, 0, 'a^16', 'a^29', 'a^43', 'a^8', 0, 'a^42', 'a^37', 'a^3', 'a^24', 0, 'a^28', 'a^13', 'a^25', 'a^4', 0, 'a^34', 'a^41', 'a^21', 'a^40', 0, 'a^22', 0, 'a^11', 'a^38', 0, 'a^32', 'a^19', 'a^23', 'a^20', 0], 'euler_factors': [[1, 'a^5'], [1, 'a^7'], [0], [1, 'a^31'], [1, 'a^6'], [1, 'a^35'], [1, 'a^23'], [1, 'a^32'], [0], [1, 'a^34'], [1, 'a^4'], [1, 'a^3'], [1, 'a^8'], [1, 'a^29'], [1, 'a^33'], [1, 'a^9'], [1, 'a^2'], [1, 'a^26'], [1, 'a^27'], [1, 'a^16'], [1, 'a^43'], [1, 'a^24'], [1, 'a^25'], [1, 'a^40'], [1, 'a^19'], [1, 'a^36']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-115-115.88-r0-0-0', 'leading_term': '1.09630245339501563583198979534+1.30542707512711602990815213447*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/115/88', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.7047049356985118, 2.271462636515095, 3.2302208199575335, 4.165231172259796, 4.716081673910031, 4.643034797952631, 3.8787130172392406, 2.5664716179343943, 1.0392741307304127, -0.27961219707009854, -1.0321598116835349, -1.0780655463819873, -0.570441414020134, 0.09677952011532903, 0.46518957218868334, 0.2408014661299292, -0.5375446128456381, -1.4903504615502146, -2.0777856324755675, -1.8934204964212575, -0.9189514519972669, 0.41410810880200555, 1.419739678792204, 1.5297762316736165, 0.6442581732105866, -0.7554243008029259, -1.8315242094184843, -1.8595252722193107, -0.6841496387790356, 1.1221643774817174, 2.532269972106305, 2.6481674154544437, 1.265404491019267, -0.9359694228825381, -2.727687458308542, -3.0310832475448883, -1.5676909781455424, 0.9460040560350239, 3.2031571103426644, 4.077499495556682, 3.2821356094387597, 1.4964405512539192, -0.11767708239392727, -0.6837073628973409, -0.14355729258801356, 0.8002419446612818, 1.2720010293236714, 0.8985252118640287, 0.06694325465199683, -0.4294715670133591, -0.08172685357153796, 0.8605389299731028, 1.5402240468036614, 1.199725782312756, -0.08894912446795666, -1.2812626261842308, -1.0099087699798528, 1.3794761646935858, 5.16879697575337, 8.54055315210091, 9.682329472417209, 7.984710846086422, 4.472037899062548, 1.1263528625913932, -0.43291517221651565, 0.03141885827517322, 1.3811042757174117, 2.0897876324019355, 1.4270365515038588, -0.07318760567851634, -1.185067447587974, -1.091863198200262, -0.08752737839433714, 0.7007119424923793, 0.3200308910086205, -1.1405432274053966, -2.5807838678350716, -2.8110704969833082, -1.5828943177497756, 0.17023088434904426, 1.1139949281923827, 0.6564215755392849, -0.5506146431729136, -1.2211351641614605, -0.6469043081524992, 0.5715660435707447, 0.9894246441441102, -0.3472782041767929, -2.842880178764715, -4.572343729017733, -3.731191227022383, -0.1767233495236941, 4.248582599159655, 6.96919244783038, 6.555628419146294, 3.7312808769183974, 0.707352501082805, -0.577202994266659, 0.14958445937144182, 1.560366344951668, 2.074434615594784, 1.2280230975277984, -0.1131844553809883, -0.7674504283824131, -0.4245390413871315, 0.14361779325581708, 0.008104515192237208, -0.8264626952333444, -1.3137743347824196, -0.42210091005103845, 1.6566653513602425, 3.4051219572278066, 3.2438549631054627, 1.0709880131685197, -1.4048114420105844, -2.0015684157469913, 0.01750011319018195, 3.170403719229557, 4.911107379000176, 3.770169892673617, 0.6052391389162224, -2.1576553867744046, -2.6148895534504173, -0.9346050263503024, 0.9933452691795998, 1.408563029200121, 0.2719927777641443, -0.8614101176981557, -0.487735256697064, 1.3168780251333803, 2.9589379836941108, 2.8839159963343732, 1.0790319070418464, -0.9410767294842287, -1.613089972031565, -0.7759033388004236, 0.33343799888686404, 0.4719036637476852, -0.3059407475748319, -0.797700204307585, -0.08776303800789921, 1.2886606676281818, 1.7864078566575379, 0.5614117918616531, -1.3155191250191116, -1.5723577959434507, 1.0834062282945311, 5.376015274745484, 8.158920736081695, 6.98548881086114, 2.2846444834099926, -2.882517146440776, -5.317321209237756, -4.1905212914960766, -1.360607374604946, 0.6018754755608079, 0.6831935910127038, -0.10742631084510562, -0.25409394394057533, 0.5322714916671443, 1.1660983347443896, 0.6220033515395884, -0.7488108970748903, -1.5292161739322372, -0.8453997609589052, 0.5340661509108315, 0.9160426894832288, -0.4582733917725219, -2.42084321737421, -2.940728621826485, -1.2510983614719393, 1.1945837154060586, 2.0649112545781603, 0.5253678215045928, -1.8028451468180768, -2.3919377679719576, -0.3756937184516906, 2.4857316769993876, 3.5019524129666824, 1.7472482153090538, -0.9798087698414082, -1.9360495725762992, -0.16787999200953044, 2.5617905339162466, 3.5640454064990275, 1.876086090992683, -0.9043176372421584, -2.3460809830940312, -1.5866774085135302, 0.05842339410704086, 0.7432029303996186, 0.07888133407401625, -0.6746983881378111, -0.26364929035121454, 1.0478214332471323, 1.838387252240049, 1.2792804608033328, 0.15145783842705873, -0.15611323004631944, 0.447254629489528, 0.2756158047747821, -2.3295990987276523, -6.715714004162436, -9.806532251538677, -8.705660682535479, -3.6022625246381628, 2.0304429521447553, 4.3671844792533125, 2.5380968715152092, -0.8780503949011698, -2.544008826469171, -1.448918708546095, 0.6252193861049524, 1.4137454989927754, 0.5794287804006168, -0.2945577959400323, 0.1720362465635365, 1.5049779562683487, 2.0625024706154456, 1.1378504194146022, -0.07753469994797973, 0.14347009468875702, 1.9473996336146602, 3.5442150119266103, 3.1289048360589558, 0.9365081248877707, -0.9492352525209571, -0.8804945845274472, 0.5633734473209715, 1.360712314073522, 0.5382031372926334, -0.5489521409397691, 0.229043113774219, 3.042794863804357, 5.382745544624644, 4.452008328949282, 0.25643050715899957, -4.019588879091437, -4.9752260571257425, -2.3038922937065207, 0.9987124343179705, 1.7204337170237092, -0.45291367469255117, -2.9708057678444217, -3.3151977881334482, -1.499652136748029, 0.38594468386109654, 0.7287373154531671, -0.004056166837156426, -0.26927628738866244, 0.443410014592607, 1.0702967430108132, 0.5735357079102007, -0.47296825065574416, -0.4694392773398549, 1.0498631110119838, 2.42361070828811, 1.5673501989141543, -1.3856334013284861, -3.703907070465922, -2.7744308898018506, 0.88124959121866, 3.751663492617694, 2.781431488098436, -1.4500658104399355, -5.255900279633631, -5.550283037704151, -2.782384198673284, -0.06500480163200716, 0.3149936791648179, -0.9360955929427347, -1.4834607089042715, -0.37328886093830427, 0.9221286835108728, 0.5162519762794375, -1.3981834670703286, -2.6370971295739123, -1.583979370176365, 0.8704552427629378, 2.3307786652025486, 1.6211927584820545, -0.02243348169190404, -0.640744707804142, 0.035974169621042155, 0.43388241807602573, -0.6281076185894574, -2.204674716825491, -2.307047329855258, -0.5571452533951187, 0.9961227143546267, 0.24420360886728285, -2.066520232764399, -2.5552045859977195, 1.198948198662049, 7.534637777522228, 11.753171051187465, 10.536436328439285, 5.132725936034538, -0.037873797210785085, -1.7449890500979037, -0.5925895973329746, 0.5485320837108424, 0.06078721929103253, -1.0408324041230632, -1.0240754296133907, 0.1399877268777734, 0.89247164976812, 0.32768282974675905, -0.5408877615684439, -0.19456192561861754, 1.1818316112464038, 1.7171688508410359, 0.2758491363809279, -1.7780852397703701, -1.9524334756327748, 0.2812743930777569, 2.486978843442083, 1.8798490705790858, -1.3272405172793333, -3.8806558291451902, -3.0343850755887374, 0.33047084994974185, 2.688015162287328, 1.8727585514309204, -0.5406370389224533, -1.2330633324005658, 0.8912767942666726, 3.452982838617826, 3.4653733098101274, 0.8387694416163304, -1.6145714280612113, -1.5423236351685283, 0.32251187758156996, 1.313925829179221, 0.15795585328569275, -1.636985378117577, -1.85420598451771, -0.3362690570487391, 0.9998958914868157, 0.7166256274375188, -0.4285654214514323, -0.7608571801792356, -0.10926036393350987, -0.011348316584407214, -1.3435014401993648, -2.6359957321409175, -1.7034662755604448, 1.123501403006808, 2.421372950576626, -0.8432139449478903, -7.453839451411425, -12.407053484278807, -11.686012750958097, -6.2673645262168645, -0.9515450181348756, 0.6110149121215993, -0.837695748231854, -1.924718969797065, -0.8489465177678147, 0.9857041040804586, 1.353959615432126, 0.15722560238672062, -0.766831498031249, -0.3455504268141909, 0.322094743267296, -0.2900367830860562, -1.7131809385406633, -1.813061358696403, 0.38195783284795704, 3.0704773206402187, 3.604248729638032, 1.6896274161115854, -0.21728599045105065, 0.05649033322545552, 1.7405633055585799, 2.276075044807842, 0.8667557041160008, -0.2012038048694725, 1.6020158269389846, 5.493130427976031, 7.741559879834673, 5.867550866021607, 1.691100859446481, -0.5973167269877769, 0.800682412009053, 3.3315082302617194, 3.228143907085011, -0.06546611458738857, -3.4125018369133953, -3.778202134512077, -1.5665438837439767, 0.33690910184261724, 0.2074954066112052, -0.8481285773248385, -0.9218478804175233, 0.04257372756062052, 0.5020218752790443, -0.18698218635383218, -0.7274478783677707, 0.16276926480418688, 1.60136322099434, 1.4795178136776355, -0.46636109348583465, -1.6878214548109838, 0.18826231528720663, 3.8817416480897875, 5.191699545455686, 1.6917920337871868, -4.042060410295526, -6.8005666744560465, -4.260638145561535, 0.6615254351177444, 3.2509388388101303, 2.050098713897935, -0.282090515165778, -0.7772622252490904, 0.42309769009655784, 1.0519184954859204, 0.24423157444120788, -0.2880614221916521, 1.146706680917814, 3.5685917932130264, 4.3303778284831145, 2.497009456423425, 0.08651802659642449, -0.509624035313583, 0.4793332074322438, 0.7398832520634976, -0.84529338181368, -2.627598208271551, -2.4555682936509347, -0.6663721235199164, 0.35223901944147806, -0.47046032839092594, -1.24351236592434, 0.27257591015759314, 3.0879793436128353, 3.4811891268385713, -0.44355668508734747, -5.70798436550314, -7.145674806518927, -3.0763306183518364, 2.698381767089639, 5.012901368428887, 2.7395489621407845, -0.6931646588181024, -1.7480603456552024, -0.5024719781706675, 0.4983153715959152, 0.01405410777407052, -0.6172603158347771, 0.08332711642824497, 1.4181684263196477, 1.5874299205263191, 0.4190695702695965, -0.3211881636603916, 0.4304569450176473, 1.2937016166605315, 0.37016800994956245, -1.633641064774285, -1.6651501088605238, 1.7840278436201835, 6.104149188594152, 7.098817330651357, 3.9131780084098686, 0.20853404358913866, -0.1298674599718667, 2.43627090170647, 3.9041667420079142, 1.8348209415390642, -1.6915548706588526, -2.8589351507243244, -0.8894854744422624, 1.2857864859536492, 1.045268916423114, -0.6488189898134704, -0.8903483449615488, 1.0641743302213071, 2.7882838922361586, 1.9986299949336817, -0.3837998994293891, -1.4986998596082781, -0.2992137153084936, 1.2857718256531525, 1.164098833138918, -0.15755486891660214, -0.6018112578562691, 0.346153803306482, 0.999331178706501, 0.23513249674966624, -0.49535943488685785, 0.7852030655102517, 3.0685492360324442, 2.6634691471645433, -2.189037206922692, -8.10213282114907, -9.466269056661107, -4.658469184794453, 1.8739310546958872, 4.384248672687737, 1.883585779083762, -1.540989021279912, -2.01131271208717, -0.0010692447967436576, 1.3022870505483124, 0.48270008614253707, -0.779301800093429, -0.6517924806797029, 0.2615943025983691, 0.2370259130474388, -0.6655695495394086, -0.6072189731169839, 1.0513406030583063, 2.276404805968526, 0.8953643118190193, -2.1833383750293187, -3.7329844635331657, -2.275288831161392, -0.011582842215966144, 0.17415972893670628, -1.2993267490562947, -1.2526629959276134, 1.713180550509381, 4.821692573899983, 4.392577485100736, 0.683336831668911, -2.167277687109954, -1.2515125130771578, 1.5125244861818605, 1.9949635208657928, -0.7454947056071973, -3.3118411585348255, -2.458196583276865, 0.7516319002941791, 2.4514755599728035, 0.9231829013993829, -1.5401199274557136, -1.9517228242239764, -0.3659686607250686, 0.8051864294521351, 0.39604110309601254, -0.23319442083098724, 0.28315957862781854, 1.0712682031747112, 0.4783580041300193, -1.048921779645481, -1.2588993722492858, 0.5151152341166796, 1.8879027288360262, 0.6118202903058797, -1.6385213061349329, -0.5892472944738603, 5.057694509494716, 10.89786802822222, 11.113768652263097, 5.04695303311875, -1.9528464735087707, -4.468460481600308, -2.4848972507215787, -0.1028517460730588, 0.05947289511423737, -0.6213284772681248, 0.1309427884120346, 1.8324200834449749, 2.130785819079722, 0.5012022569692556, -0.8694929961550132, -0.28612933851815653, 0.9227683676777214, 0.33078537521321394, -1.9206261756306202, -3.0603453007674304, -1.474016146319253, 0.9904526996918711, 1.5365805723376558, 0.24758761950722383, -0.22107281462877124, 1.331830138691707, 2.7353007089881944, 1.5672906541721816, -1.0666615277976272, -1.7614870448888849, 0.2493970291444124, 1.3666359591003803, -1.9035144117607286, -7.847508335321302, -10.808875990469371, -7.7056534615198915, -1.6835416779110957, 1.6690018867180396, 0.6437104501334506, -1.538899270805552, -1.571774259710537, -0.004840288111482247, 0.477309619587463, -0.7708929469651883, -1.7349553298207934, -1.020231943244732, 0.14844978288648622, 0.03474749507080029, -0.8752688726987939, -0.8033673499468487, 0.204897059148718, 0.03184123838119726, -2.0627590075794378, -3.4163123253571186, -1.0568151333419733, 3.794946255739543, 6.337326062149597, 3.9290510058135393, -0.33408989139305706, -1.2245551912695336, 2.183792642234783, 5.522584097528293, 4.789560427476891, 1.2060369091849032, -0.8646388103519296, 0.27215801203962126, 1.9475317461780974, 1.3371774809606805, -0.6735784939779237, -1.2117797811723863, 0.16997449219978228, 0.890114612919488, -0.717619861287832, -2.774945503154765, -2.409819449730506, 0.17779851037168715, 1.9535587416717144, 1.1847924375544587, -0.4523869668149552, -0.6223772738954827, 0.30907222030583115, 0.23815220474533758, -1.0702396618456447, -1.4640357428026152, -0.01976537115787372, 0.7625779779641175, -1.8140671978913372, -6.048254312088627, -6.827801695959644], 'positive_zeros': ['2.73650659871433570460212993716', '4.012998955306845276900652955', '4.80460818146367243207747519598', '6.46507095765335245585825446458', '7.64751020405258639263030247997', '8.87236459469221358408858680182', '10.18326863054071338417378072000', '11.45025930605688427089256162878', '13.095103378235224895879809483754', '13.79838932105669492951194856630', '15.02683539828321720364555277183', '15.6574649916933962158965245838', '16.85616228545197675318165667236', '17.66507691922650845555884611817', '19.85825349558143224269094579061', '20.30403530033552153291835830416', '21.54747969619697107131290246924', '22.52492517467040131220948081103', '23.2092148719247993682317319628', '24.653994572296354415372745917672', '25.48532075967508763095188535353', '26.41450577599437543637839246900', '27.13437750860762792452474674811', '28.44994122793916477370051747433', '30.110145591484343899334742113598', '30.5896787772761697028127687900', '31.84519278641499256305910864085', '32.709706046898400636918011014428', '33.12923875224870343515511793773', '34.13598835614291398019537855397', '35.435554446477863513033792421106', '36.24816820984902961057680487885', '37.55655743931736202097093202577', '38.57285084915657082056400977510', '39.43385988837846673598558806392', '40.10176752308713895969138510522', '41.40291398544232878228940165186', '42.38743534087853114480979609891', '43.01784106154161514404141207905', '43.77130933132387719407947203809', '44.77660486526866782063616841643', '45.53087578644895472737617884765', '47.00370732769392417432693631059', '48.306111721453583324141811650550', '49.015335070645012112406888576213', '49.50425400417681920515744125335', '50.460071173235430955248724944573', '51.43592297640395715416812259969', '52.112206123066323225071816150065', '53.27743715648219435949712768369', '54.12978255104577651145004401217', '55.039734674463021657376618143570', '56.12933926632099986124252133826', '56.89410990156337622649733193451', '58.01872774161354279415161472760', '59.04964281888404196133235722415', '59.712385046622423227011215199', '60.38387819317021591328260487573', '61.621654242496199265158927209898', '61.97943542220220195439802064428', '62.55749898066365058988225776831', '64.250177174577842009794776496333', '65.22705399297144499423868663118', '66.147558106196576456347738719778', '67.04056070092913254858214259300', '67.44892299269573539594723139317', '68.71915525853149141345978482481', '69.02020255063397323504143246180', '70.43969964474537114986235031474', '71.1358271023888677828303221622', '72.00044026238761415463873803358', '72.46194862977936877696779241258', '73.76628708986170495339619855049', '74.88948548226917735230594582697', '75.57523847695071388075031870864', '76.791488899064368939739295832120', '77.498267715374792661456710453591', '77.966315175387827479956268656977', '78.911672879643168310507109101635', '79.49827779680967792297397281874', '80.491072880609873350122647253142', '81.49381205721713191656603290672', '82.40420919359502967333109483430', '83.76236789794046677178714698912', '84.158501627851812603763495268433', '85.07341072709040504649501004470', '85.72248723677090747177986250323', '86.765566539140986142679801861008', '87.80743659318353353737348263361', '88.42450270648669552992852211724', '88.9274472920733642932950036867', '90.084713581289466150822920359', '90.66209431571877878855636766986', '91.492274458999242782941857429', '93.12179744446078254688463205722', '93.871276102518951204693023540178', '94.39163468282479673737491794934', '95.27802479499420129908299670097', '96.03628625310751769442834447292', '96.61403637024158949587045919766', '97.539052741172214949474423378620', '98.40589325081063311311962895444', '99.25859574038719472204903354822', '100.283207871012247068561706571700', '101.174586359191276258187070415464', '101.77522270312244186231655382569', '102.899039438286256675166765951517', '103.69789329106579509666673777617', '104.40066100177131333911055912081', '105.37190221427605124038825370811', '106.12867922788244385056523712553', '106.931193443127312988795626388985', '107.182004598982593533054813343402', '108.318546335071990664929467112956', '109.01233001708252358781739210456', '110.72309648890450133996126955852', '111.10583056801838416739118772745', '112.00937649621948921385832941746', '112.84823307774650775300285710622', '113.56234935819744403868596886744', '113.98482678493698584152085388807', '114.95858445233668486275500845983', '116.192902478899711503122749893426', '116.54922879952955111372799701063', '117.68029032257200399846361719558', '117.90846516879619321911493852696', '119.54391982764200058819096555216', '119.89432767462018276079298458897', '120.932379401584544883256574136983', '122.10229277576297077691535519397', '122.562377000741798723255164073976', '123.42409817576540849134981030597', '123.999705921386690066468612381653', '124.65275756376184347976066767681', '125.5585360224112328245257190469', '126.23215389393189815901085335990', '127.279778158914439342838549725764', '128.39233159710197176165218301802', '129.32750689237012359290804180342', '129.90257322000049025482293543956', '130.69977422421143463612621106314', '131.05350509698108721030199579455', '132.516031501538050538901497483759', '132.99175903290978896254014153949', '133.61720925100884862683312488317', '134.82262168312086446291436763721', '135.19104772499089288970188761617', '135.90448469322402713296991277983', '136.849274711294092224549630352998', '137.97059701990763830597108331968', '138.987540064165741687990626922681', '139.79711692019852559310793590', '140.31732693753580331953443888837', '140.91738480016657902718321292841', '141.98776172860411025501208781221', '142.37826065785116330610322402835', '143.18350298249702235332469700481', '143.93208457687179836305403593279', '145.34199093800620912724748808665', '145.648316140787715168210819044059', '146.71810756509581904432024722266', '147.60455527361327861366249343885', '148.31422446921539334032133280277', '148.91893001714259487151586197560', '149.94778943272113996659680674745', '150.67475299705602581489877499983', '151.523148472631429122935440710179', '152.09515499480985189733460459714', '152.87639285453533015995217403017', '153.311325939940780231293358091904', '154.26039981480756293720801229566', '155.52504273684666262564422345918', '156.40336276708174911654459951703', '157.18765381602178708665055295853', '157.91357767208673278802053759558', '158.64913691863765021558866241180', '159.15223537102019122992919737895', '159.825835541402880614600542353134', '160.720394853184414034726268360509', '161.87740587520854855388580956474', '162.23308191978598311650806689286', '162.97336442646259655606462756426', '164.11642741203170288826460415214', '164.825457188812615784971744837397', '165.556285515130794057533549218470', '166.490028957569716984920565668642', '167.294500162492662955120379527294', '168.19172109220262821801381184436', '168.89856836609001384436192541794', '169.27442072834791981945159761929', '170.098705000071996767187207836405', '170.86226776601495879530897423206', '171.63830779300183717331935175911', '172.23345128074512422526892488980', '173.64900613664999563293169529310', '174.71338687266091929792543684887', '175.02438450920842368023598716816', '175.59821037343131968490700632801', '176.64543386457898107580699135167', '177.25137840918955746460293660627', '177.86664578883600292768858554884', '178.92372213711658506221861262104', '179.75052610725501444803020214358', '180.074707299675088731457882059371', '181.11832615090157869064090679101', '181.842733393711727875322126881218', '182.37181698868120294849637076839', '183.85878829654737649097441938961', '184.45714220189086899441788189738', '185.31357131307616108606393651084', '185.77572367777230643721193851112', '186.81774999379138988790734375853', '187.200702002279042799925412960315', '188.055366619080415610530305892938', '188.44494330126216717629941930767', '189.44769365994585349559603474365', '190.594646679307684841916527533473', '191.08169554849898557280935115800', '192.311196902717806196946848397230', '192.77015353465343711879543301925', '193.64023807883507987683211916851', '194.34179726987397731187768541000', '194.89990909003193997947669768245', '195.917349779333581298746203383391', '196.77269661637120535257555831350', '197.39212101668511919406657960413', '197.88165815863741390744652304771', '198.75356992293941230747252930157', '199.208821136360272188153876773305'], 'prelabel': '1-115-115.88-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5340577547741961, 'root_angle': 0.5552926278395918, 'root_number': '-0.172834655713848528806023508986+0.984950852471469992632303979048*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.27764631392', 'prec': 44}, 'spectral_label': 'r0-0', 'st_group': 'mu(44)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.32748513511145905635053711991+0.952479280467404946744483954213*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.73650659871', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '4.01299895531', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.80460818146', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.5340577547741961, 'bad_primes': [5, 23], 'central_character': '115.88', 'conductor': 115, 'conductor_radical': 115, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/115/88'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, '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': '1-115-115.88-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-115-115.88-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5340577547741961, 'root_angle': 0.2776463139197959, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.73650659871', 'prec': 44}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_115.88', 'Lhash_array': ['dirichlet_L_115.88'], 'label': '1-115-115.88-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/115/88'}