-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2646465555777475625478752115419', 'a10': [-0.5, -0.8660254037844386], 'a2': [-0.5, 0.8660254037844386], 'a3': [0.0, 0.0], 'a4': [-0.5, -0.8660254037844386], 'a5': [-0.5, 0.8660254037844386], 'a6': [0.0, 0.0], 'a7': [-1.0, 0.0], 'a8': [1.0, -3.9689140359382235e-80], 'a9': [-0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.3792894096010818, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, -0.8660254037844386]]], [5, [[1.0, 0], [0.5, -0.8660254037844386]]], [19, [[1.0, 0], [0.5, -0.8660254037844386]]]], 'bad_primes': [2, 5, 19], 'central_character': '760.619', 'coefficient_field': 'CDF', 'conductor': 760, 'conductor_radical': 190, 'conjugate': '113678120481623908859908027599', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [1.0, 0], [1.0, 0]], [[1.0, 0], [1.0, 0], [1.0, 0]], [[1.0, 0], [1.0, 1.7320508075688772], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [-0.5, -0.8660254037844386], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [1.0, 0], [1.0, 0]], [[1.0, 0], [-0.5, 0.8660254037844386], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [1.0, 1.7320508075688772], [-0.5, 0.8660254037844386]], [[1.0, 0], [-0.5, -0.8660254037844386], [-0.5, 0.8660254037844386]], [[1.0, 0], [1.0, -1.7320508075688772], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-0.5, -0.8660254037844386], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [-1.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-760-760.619-c0-0-0', 'leading_term': '0.078075082404146686727866993902602', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/760/1/bm/a/619/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [0.07807508240414669, 0.13106023752408505, 0.18546588579085022, 0.24310781200529707, 0.30527695328050886, 0.3727177767340006, 0.4456665751788449, 0.5239179681972521, 0.6068948521738914, 0.6937091706524633, 0.7832104488098749, 0.8740241650454605, 0.9645838111432306, 1.0531604803968966, 1.1378931009319824, 1.216821551678781, 1.2879240808927908, 1.3491597496486436, 1.3985160398696044, 1.4340612756468978, 1.454001086419763, 1.4567377761803717, 1.440931146432522, 1.4055590502358288, 1.3499757327462851, 1.2739658456251597, 1.1777919156842838, 1.0622330100173913, 0.928612378265371, 0.778811974177304, 0.6152719681024615, 0.4409736619299819, 0.2594046077890071, 0.0745052076512808, -0.10940337475426701, -0.2877095370966929, -0.4556186713333788, -0.608275876011548, -0.7409014031131088, -0.8489355961750904, -0.9281894221491823, -0.9749961187325953, -0.9863590015027263, -0.9600901301345364, -0.8949343472385407, -0.7906732005202437, -0.6482034579109175, -0.46958533894316257, -0.25805621966371656, -0.018006420344997744, 0.24508525619775962, 0.5247573235219724, 0.8137124356547264, 1.1040034084035748, 1.3872550260080736, 1.6549166248001406, 1.8985388977909765, 2.110066930172, 2.2821402222261518, 2.4083894485810187, 2.4837190026002256, 2.5045640365672774, 2.469110776845371, 2.3774694003957735, 2.2317897217125937, 2.0363113569118196, 1.797341885121699, 1.523158777533696, 1.22383345284849, 0.9109786668310706, 0.5974234584922145, 0.2968229466418461, 0.023213277672366486, -0.2094751589877283, -0.3879306366097575, -0.49998145898286733, -0.5351066465829253, -0.484915977652906, -0.3435793468953559, -0.1081861316297038, 0.22098319155460566, 0.6402885659214991, 1.1426772516968315, 1.7177545064104178, 2.3519820397327047, 3.0290033917258543, 3.7300902899242514, 4.43469889579868, 5.121119869998587, 5.767201590017964, 6.351121862441421, 6.852180290636257, 7.251581270540333, 7.533176542093298, 7.684136430159639, 7.695520425475678, 7.562720587134907, 7.285755338711918, 6.869396465990534, 6.323118333181936, 5.660865290946226, 4.900640681986292, 4.063928451084555, 3.174965805267329, 2.2598923060372518, 1.3458068752038883, 0.4597691469272689, -0.37221487244930795, -1.126180988756409, -1.7811269105163168, -2.319824090726192, -2.729484813241112, -3.0022534338401523, -3.135497686603974, -3.13188428247826, -2.9992323165314034, -2.750147860233623, -2.4014530980363116, -1.973433002807415, -1.4889313599950196, -0.9723354954162136, -0.44849493136862967, 0.058376946957146125, 0.525767537859419, 0.9338461189483414, 1.2663147818518181, 1.5110881964799956, 1.6607689326463009, 1.7128946117169175, 1.6699440823357259, 1.5391015962093793, 1.3317900254848278, 1.0629959023446782, 0.7504198617332737, 0.4134953471923818, 0.07232567708664306, -0.25340566472793735, -0.5454946643211633, -0.7881904577375369, -0.9690311149209618, -1.0794963602506455, -1.1154413718634126, -1.0772872044151567, -0.9699563058423848, -0.8025553788452339, -0.5878217371592528, -0.34136256288020606, -0.08072833613394026, 0.17562850915347641, 0.4094515438373875, 0.6037727879993536, 0.7439369765893052, 0.8184979877616654, 0.8199342349625699, 0.7451394481188047, 0.5956575801913306, 0.3776449269309765, 0.10155815823471424, -0.21841704718262814, -0.5651666186560276, -0.9196338197871676, -1.261934257488994, -1.57253571951725, -1.8334333986005098, -2.0292500980770547, -2.1481942303660584, -2.1828157256946117, -2.1305110268185237, -1.9937425835960103, -1.7799548989766247, -1.5011872679068048, -1.1734018305926626, -0.8155633154090984, -0.4485227709832002, -0.09377065861128914, 0.22786598193688623, 0.49750264065909383, 0.6993729500435251, 0.8218258718253029, 0.8580791521618001, 0.8066776766653619, 0.671622849211502, 0.4621591644712747, 0.19222555164346886, -0.12039947759149305, -0.45520969641017506, -0.7902733401009506, -1.103645173875387, -1.3747991114677958, -1.5859886256857227, -1.7234446530346146, -1.7783290500434534, -1.7473755462275264, -1.6331688283532113, -1.4440348212595728, -1.1935400652362123, -0.8996237937381467, -0.5834112467419688, -0.26777926919765915, 0.024236201894906814, 0.2710879011639105, 0.4543104659591167, 0.5599494234280813, 0.5797235158924424, 0.5118322269068069, 0.3613409378284495, 0.14010186672878655, -0.1338016898172296, -0.4370690735850309, -0.7426041142594068, -1.0212663677116187, -1.2438482172684364, -1.3831554305835458, -1.416057221420425, -1.3253686682850954, -1.1014339866672527, -0.7432935738414794, -0.2593403042636908, 0.3325999437971982, 1.0057937899509437, 1.7257242091509755, 2.4517663276437114, 3.1393316712501784, 3.7423644449732767, 4.216046887508074, 4.5195525262080665, 4.618677691211222, 4.4881837724376314, 4.11369559457913, 3.4930244202734126, 2.636816264510009, 1.5684655847944162, 0.3232786522495102, -1.053082720568157, -2.5068008580778205, -3.978627278132511, -5.406979864778347, -6.73123264473892, -7.895003280430026, -8.849240117257212, -9.55491990363823, -9.985188779544366, -10.126811634483046, -9.980836550058582, -9.562429208924218, -8.89988383396492, -8.032869094759514, -7.010016088653156, -5.885997733613446, -4.718281839228299, -3.56376146741966, -2.4754744136446662, -1.4996180487640902, -0.6730465964835884, -0.021406334087568892, 0.4419777987078163, 0.7164003810251452], 'positive_zeros': ['2.08769321396684753097294298472123', '3.06694144039904105032339516368989', '4.50572225206484644566944009496726', '4.96007331081898695259924177902864', '6.65891544052718000998395278507074', '7.61759914191809537237971471387520', '8.451001153632169762611776343665541', '9.206859017586479809392143903734753', '9.833131092178589342708295578636723', '10.89240870297608099267138201498147'], 'prelabel': '2-760-760.619-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6158647656759411, 'root_angle': 0.29945668930219493, 'root_number': '-0.30576855776155245201166452061865 + 0.95210587073309245599954997573793*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.29945668930219493', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.08769321396684753097294298472', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.06694144039904105032339516369', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.50572225206484644566944009497', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.3792894096010818, 'bad_primes': [2, 5, 19], 'central_character': '760.619', 'conductor': 760, 'conductor_radical': 190, 'degree': 2, 'index': 0, 'instance_types': ['CMF', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/760/1/bm/a/619/1', 'ArtinRepresentation/2.760.6t5.a.a'], 'is_instance_Artin': True, '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': '2-760-760.619-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-760-760.619-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6158647656759411, 'root_angle': 0.29945668930219493, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.08769321396684753097294298472', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 24597242
{'Lhash': '2646465555777475625478752115419', 'Lhash_array': ['2646465555777475625478752115419'], 'factors': ['2-760-760.619-c0-0-0'], 'label': '2-760-760.619-c0-0-0', 'type': 'Artin', 'url': 'ArtinRepresentation/2.760.6t5.a.a'}
-
id: 19803822
{'Lhash': '2646465555777475625478752115419', 'Lhash_array': ['2646465555777475625478752115419'], 'factors': ['2-760-760.619-c0-0-0'], 'label': '2-760-760.619-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/760/1/bm/a/619/1'}