-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '457968909432064281682575401184', 'a10': [4.585786437626905, 7.942815102630085], 'a2': [1.0, -1.7320508075688772], 'a3': [0, 0], 'a4': [-2.0, -3.4641016151377544], 'a5': [-2.2928932188134525, 3.9714075513150426], 'a6': [0, 0], 'a7': [0, 0], 'a8': [-8.0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 52.039684625063245, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 1.7320508075688772]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '882.667', 'coefficient_field': 'CDF', 'conductor': 882, 'conductor_radical': 42, 'conjugate': '1328964122837573748253940838003', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 1.7320508075688772]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.2928932188134525, -3.9714075513150426], [-62.5, -108.25317547305482]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.242640687119285, 5.616418420780657], [-665.5, 1152.6798124370878]], [[1.0, 0], [45.21320343559643, 0], [2197.0, 0]], [[1.0, 0], [40.77817459305202, 70.62987023508043], [-2456.5, 4254.782808792947]], [[1.0, 0], [2.526911934581186, -4.376739856946777], [-3429.5, -5940.068244557465]], [[1.0, 0], [-53.12489168102785, 92.01501153813341], [-6083.5, -10536.931087845265]], [[1.0, 0], [-268.13203435596427, 0], [24389.0, 0]], [[1.0, 0], [-146.18376618407356, -253.19771027258454], [-14895.5, 25799.76280414221]], [[1.0, 0], [57.27922061357855, -99.21052032066461], [-25326.5, -43866.78477789317]], [[1.0, 0], [161.60512242138307, 0], [68921.0, 0]], [[1.0, 0], [471.29350596345137, 0], [79507.0, 0]], [[1.0, 0], [173.00209204105306, -299.6484132308112], [-51911.5, -89913.35549711177]], [[1.0, 0], [-202.7645019878171, -351.19841941429985], [-74438.5, 128931.26403921588]], [[1.0, 0], [-126.71782079359116, -219.48170383890783], [-102689.5, 177863.43140384424]], [[1.0, 0], [375.6086937588513, -650.5733413549094], [-113490.5, -196571.31217639567]], [[1.0, 0], [5.823376490862843, 10.086383953776602], [-150381.5, 260468.39851841913]], [[1.0, 0], [-681.6610383315985, 0], [357911.0, 0]], [[1.0, 0], [-342.72853480599576, -593.6232354876231], [-194508.5, 336898.604504011]], [[1.0, 0], [0.13203435596425733, -0.2286902128747285], [-246519.5, -426984.29905647587]], [[1.0, 0], [437.1370849898476, 0], [571787.0, 0]], [[1.0, 0], [-29.256313292354182, 50.673421064510144], [-352484.5, -610521.062880512]], [[1.0, 0], [-1280.0904037956216, 0], [912673.0, 0]], [[1.0, 0], [-653.1944801964781, -1131.366026923843], [-515150.5, 892266.8395445109]], [[1.0, 0], [379.48737341529164, -657.291411586148], [-546363.5, -946329.3414011582]], [[1.0, 0], [-631.2569260369921, 1093.3690685258193], [-612521.5, -1060918.3587283]], [[1.0, 0], [-1052.76363543604, -1823.44010493614], [-647514.5, 1121528.0126375577]], [[1.0, 0], [1535.7627688842626, 0], [1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 9, 'label': '2-882-7.2-c3-0-9', 'leading_term': '1.394014384043075321050707325291811581759116262269542524', '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/882/4/g/be/667/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.3940143840430754, 1.2234255359125303, 1.0285539177055885, 0.8112029597491656, 0.5734416416994426, 0.3176013351924616, 0.046271652125851055, -0.23770557503372367, -0.5312451104130164, -0.831030869495124, -1.1335331155967576, -1.435031119816765, -1.7316419794147977, -2.019356121661408, -2.2940798157202407, -2.5516847796842494, -2.7880647099719638, -2.999198283103629, -3.1812178932248463, -3.3304831009159033, -3.4436574884842948, -3.517787353015333, -3.5503804300128796, -3.5394826365347116, -3.4837506621337115, -3.382518127032777, -3.235852977462442, -3.044603804662259, -2.8104328620851717, -2.535833718642669, -2.224131726279457, -1.8794657974826163, -1.5067503798083097, -1.1116169748486293, -0.7003350702554519, -0.27971292474984794, 0.14302074592065492, 0.560352505234715, 0.9646350458596412, 1.348250230248883, 1.7037808224538975, 2.0241868954344255, 2.302982463707542, 2.5344075595973976, 2.7135907620453725, 2.836697116885732, 2.901056470387885, 2.9052674833593692, 2.849273006070898, 2.7344030742110683, 2.563382526677667, 2.3403011348249256, 2.070545151177997, 1.7606903089164683, 1.4183575012769039, 1.052033607065159, 0.670861165195562, 0.28440179505354996, -0.09762063371901111, -0.4655901031126236, -0.8102740405782288, -1.1230960385050355, -1.396396995676188, -1.623675917113873, -1.799801846394546, -1.9211889503358244, -1.985927629827186, -1.9938656809431137, -1.946634953941032, -1.8476206191084834, -1.701872001201873, -1.515955931650754, -1.2977556242357944, -1.0562201331975336, -0.8010714258440066, -0.5424779161043691, -0.29070488377905535, -0.055753473525438586, 0.15299913744498006, 0.32714534801752376, 0.45956546725869923, 0.5447062219192047, 0.578807885832134, 0.5600699688952463, 0.4887473481015993, 0.3671710700756234, 0.1996907312002294, -0.0074617423099090805, -0.2463840408552932, -0.5077852007955118, -0.7813282071572185, -1.0560218238890275, -1.3206476218491152, -1.5642062575399611, -1.77636570635374, -1.9478934553450737, -2.071054671803588, -2.1399591177225643, -2.150841079380677, -2.1022587967919844, -1.9952027487591388, -1.8331055835110912, -1.6217503613735909, -1.3690779484360152, -1.0848987025200127, -0.7805178449164769, -0.4682879267801207, -0.16110539258731102, 0.12812876078406066, 0.3870619894030233, 0.604433276834701, 0.7705823115545875, 0.8779014725943323, 0.9212090578686537, 0.8980249437178559, 0.8087335630817897, 0.6566236066538135, 0.4477990165709071, 0.19096144856221672, -0.102929810724692, -0.42110872609761507, -0.74954701073604, -1.0735701940054838, -1.3785191875505638, -1.6504282979952904, -1.8766888866464893, -2.0466674913817817, -2.1522482768603326, -2.1882721754315386, -2.1528489639694444, -2.047523664541659, -1.8772848673285825, -1.6504096015153884, -1.3781469232766395, -1.074250111267059, -0.7543748981418084, -0.4353681539990574, -0.1344775177357382, 0.13148268258302157, 0.346970550812032, 0.4985205239111067, 0.57547208132339, 0.570585520502659, 0.48051119373833223, 0.3060845183606645, 0.05242654920615913, -0.27116136635009797, -0.6515107235398344, -1.0720986130989085, -1.513741912313153, -1.9554452584840307, -2.3753666900434327, -2.751857853043146, -3.064530553649805, -3.295298511656309, -3.4293426599128725, -3.4559503518816617, -3.3691833739374513, -3.168336573846723, -2.8581579509180735, -2.448811829523024, -1.9555787776908284, -1.3982986771853056, -0.8005761864724008, -0.1887801228583125, 0.40912060986923715, 0.9648326029997275, 1.4510660763980465, 1.8428523277749096, 2.118786016495579, 2.2621297451330746, 2.261723533457768, 2.112649932266532, 1.8166163723341726, 1.382029412147578, 0.8237502335064449, 0.16253633159693978, -0.5758099171048386, -1.3615500522684625, -2.1623263164517725, -2.9446256277898457, -3.675321343590194, -4.323218176980824, -4.860524086521857, -5.2641752839460985, -5.516946665934634, -5.608289737258771, -5.534853024041593, -5.300655468413125, -4.916900590171061, -4.401437424330575, -3.777892453173229, -3.0745139845572997, -2.322785752793339, -1.5558790845538473, -0.8070220607545041, -0.10786916955633401, 0.5130443542746382, 1.0316830822061493, 1.4296545315458888, 1.6950546733415113, 1.8229710522717173, 1.81561680747652, 1.6820885627882851, 1.4377614125644815, 1.1033539587105796, 0.7037144592712614, 0.2663946049668549, -0.17991064580496946, -0.606971079640909, -0.9885880631896923, -1.302033197382968, -1.5292787077113468, -1.6579509709068587, -1.6819540255427943, -1.6017284895595845, -1.4241319845184666, -1.1619487815555276, -0.8330577037219798, -0.4593071093309973, -0.06516287819088773, 0.3237912950901621, 0.6824131485249099, 0.9875287397310948, 1.2193366940193895, 1.362606488898368, 1.40759937852787, 1.3506568076076104, 1.1944208052741254, 0.9476727480747218, 0.6247997488434656, 0.24492040174072036, -0.16927766518772183, -0.5929182800824253, -1.0004515382813597, -1.3672106354052733, -1.6709154163847009, -1.8930301394753966, -2.019891461515912, -2.043536397585261, -1.962178203341004, -1.7802996945598133, -1.5083571550888877, -1.1621122443959433, -0.761632693224903, -0.3300235987743773, 0.10803154559892304, 0.5278284585308456, 0.9061998710618696, 1.2229744281370882, 1.462243241385317, 1.613352289319263, 1.671555843536776, 1.6382874004923804, 1.5210289090496187, 1.332784883045515, 1.0911936355589715], 'positive_zeros': ['0.36127376845765780076231228750403', '2.08952014264613264108021015364775', '3.38331683814579567936102602662156', '4.52657336495654746081666719397537', '5.09570395837229049823408273627793', '6.30155404260583660587168673292674', '6.95281073799891623302048060597520', '8.055788958127365801970805526398890', '8.506448691744356321990688754379636', '9.627599008287067019858286065857503'], 'prelabel': '2-882-7.2-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.213853659803701, 'root_angle': -0.23013042917285453, 'root_number': '0.7498400306039945301714288520225375404802689692146216792 - 0.6616191718079219523819485086349207591460594151595316938*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.11506521458642727', 'prec': 67}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.36127376845765780076231228750', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.08952014264613264108021015365', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.38331683814579567936102602662', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 52.039684625063245, 'bad_primes': [2, 3, 7], 'central_character': '7.2', 'conductor': 882, 'conductor_radical': 42, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/882/4/g/be/667/2'], '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': '2-882-7.2-c3-0-9', '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': '2-882-7.2-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.213853659803701, 'root_angle': -0.11506521458642727, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.36127376845765780076231228750', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '457968909432064281682575401184', 'Lhash_array': ['457968909432064281682575401184'], 'label': '2-882-7.2-c3-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/882/4/g/be/667/2'}