Formats: - HTML - YAML - JSON - 2026-08-26T12:41:13.493519
Query: /api/lfunc_lfunctions/?_offset=0
Show schema

{'Lhash': '906895654119057069362359161028', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-4.3778021186334675, 0.0], 'a6': [0.0, 0.0], 'a7': [1.0, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 72.4402847137056, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '9072.1', 'coefficient_field': 'CDF', 'conductor': 9072, 'conductor_radical': 42, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [4.3778021186334675, 0], [5.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-2.6457513110645907, 0], [11.0, 0]], [[1.0, 0], [-4.0, 0], [13.0, 0]], [[1.0, 0], [-3.4641016151377544, 0], [17.0, 0]], [[1.0, 0], [-3.58257569495584, 0], [19.0, 0]], [[1.0, 0], [-3.4641016151377544, 0], [23.0, 0]], [[1.0, 0], [-1.8274010069914266, 0], [29.0, 0]], [[1.0, 0], [9.16515138991168, 0], [31.0, 0]], [[1.0, 0], [-3.0, 0], [37.0, 0]], [[1.0, 0], [-4.3778021186334675, 0], [41.0, 0]], [[1.0, 0], [-8.58257569495584, 0], [43.0, 0]], [[1.0, 0], [2.7411015104871397, 0], [47.0, 0]], [[1.0, 0], [8.660254037844387, 0], [53.0, 0]], [[1.0, 0], [3.4641016151377544, 0], [59.0, 0]], [[1.0, 0], [-2.41742430504416, 0], [61.0, 0]], [[1.0, 0], [-0.58257569495584, 0], [67.0, 0]], [[1.0, 0], [11.401355548331527, 0], [71.0, 0]], [[1.0, 0], [3.16515138991168, 0], [73.0, 0]], [[1.0, 0], [-8.58257569495584, 0], [79.0, 0]], [[1.0, 0], [6.2052031256248945, 0], [83.0, 0]], [[1.0, 0], [-8.755604237266935, 0], [89.0, 0]], [[1.0, 0], [-7.58257569495584, 0], [97.0, 0]], [[1.0, 0], [1.8274010069914266, 0], [101.0, 0]], [[1.0, 0], [3.58257569495584, 0], [103.0, 0]], [[1.0, 0], [11.210655149486428, 0], [107.0, 0]], [[1.0, 0], [-6.0, 0], [109.0, 0]], [[1.0, 0], [-13.951756659973567, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 22650368, 'index': 39, 'label': '2-9072-1.1-c1-0-39', 'leading_term': '1.743683202535176286939830430986', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/9072/2/a/ci/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 17}, 'plot_values': [1.7436832025351763, 1.7350951000957027, 1.709351801669273, 1.6665225798687284, 1.606743245685572, 1.5302451050490706, 1.4373924875921802, 1.3287261545238283, 1.2050095204130788, 1.0672744669087326, 0.9168635657686187, 0.7554657298706725, 0.5851426339441532, 0.4083436530376718, 0.22790752425128513, 0.04704942266080318, -0.1306673593622676, -0.3013754375878626, -0.46096287170489125, -0.6051475173140205, -0.7295650062510731, -0.8298686842745543, -0.9018393698312474, -0.9415023596754779, -0.9452487084772101, -0.9099574638956875, -0.833115260650215, -0.7129294818381281, -0.5484310974263592, -0.33956330124121925, -0.08725219929699407, 0.20654393880452138, 0.5388099639602657, 0.9054762460891157, 1.3014501222504635, 1.7206775722732421, 2.1562354449473387, 2.600453626137858, 3.04506555707465, 3.481384506026157, 3.900502002382296, 4.293503894002746, 4.651698622931289, 4.9668515676035465, 5.231418706454595, 5.438772450502127, 5.583412298901662, 5.6611530138339585, 5.66928330462204, 5.60668856283507, 5.473931998488802, 5.273289580871772, 5.008735464701863, 4.685876052128801, 4.311832463082228, 3.8950729116890233, 3.44519825881599, 2.9726857685560724, 2.48859777443762, 2.0042634927958307, 1.5309435408316474, 1.0794877639820253, 0.6599976964432217, 0.28150532424124786, -0.0483202421414046, -0.3234270695509616, -0.5395854872355579, -0.6945351117485007, -0.788066710361069, -0.8220338929245267, -0.8002920008461999, -0.7285641515359921, -0.6142371081704513, -0.46609237890790634, -0.2939806013474251, -0.10844972911142736, 0.07966029827618405, 0.2596419536138462, 0.42134785863674773, 0.5556054091020188, 0.6546017349034527, 0.7122229885804542, 0.7243331615925424, 0.6889794753145286, 0.6065138380378712, 0.47962282870471706, 0.31326206577440213, 0.11449452613254109, -0.10776374377257762, -0.3430831862427072, -0.5799344667816718, -0.8061618393075566, -1.009498604316114, -1.1781047341434014, -1.301105081807876, -1.3691057635239547, -1.3746663801267296, -1.3127067544246993, -1.180828806625955, -0.9795370251225184, -0.7123446316474423, -0.38575686638669804, -0.009127673469905902, 0.4056087357570365, 0.8443246340715014, 1.2911917968437567, 1.7292638196160206, 2.1411263901863973, 2.5095905480683927, 2.8184012813855333, 3.0529322200717317, 3.2008367946448733, 3.252627103144903, 3.2021538730212855, 3.0469642717947343, 2.7885188060768873, 2.432253995186941, 1.9874837066026214, 1.4671387479419766, 0.8873512444900583, 0.26689719260472056, -0.3734829395782611, -1.0118598927471731, -1.625957068587431, -2.1940236136179165, -2.6957027727626683, -3.1128584793785485, -3.4303241041831445, -3.636539872736519, -3.7240496095081483, -3.68983303174019, -3.5354565840794114, -3.2670334988683702, -2.8949920593108014, -2.4336595680872652, -1.9006778953983232, -1.3162743068204363, -0.7024181761073536, -0.08189982721072325, 0.5226281704827627, 1.0896046374766029, 1.5994653785169837, 2.035459407204276, 2.384338080277621, 2.636884866870738, 2.788260542250688, 2.8381469750512256, 2.79068199743524, 2.6541876795377366, 2.440704207942816, 2.165351014102971, 1.8455453432795268, 1.5001156614908169, 1.1483527863211116, 0.8090450924437238, 0.499545372742911, 0.23491582570325764, 0.02719419845994346, -0.11518153117525383, -0.18776016120189945, -0.19025541867328172, -0.12650513386184745, -0.004212405594966042, 0.16551904715064306, 0.3688323694902024, 0.5899151334564421, 0.811905969312098, 1.0178629855851888, 1.191742776609798, 1.3193374952413939, 1.389118870855899, 1.3929421632940213, 1.3265697051911873, 1.1899826043351918, 0.987459935418886, 0.7274168215236733, 0.42200558304821706, 0.08649695701141615, -0.26152941423972853, -0.6031451189643218, -0.9191346207569115, -1.1911027054589218, -1.4025682584556727, -1.5399842272162287, -1.5936261507280978, -1.5582973049672784, -1.4338070934305607, -1.22519041480897, -0.9426488326808884, -0.601208801983563, -0.22010723407268082, 0.17807048320623778, 0.5684610499340776, 0.9251513528403107, 1.2225034004928634, 1.436508763945788, 1.546101996750188, 1.5343629995155021, 1.389542527210518, 1.1058528670011953, 0.683976798241581, 0.13126175862240347, -0.5384180030704563, -1.3051314163486927, -2.1436754178140056, -3.024640474972736, -3.9157073265454496, -4.783112488174714, -5.593210203942226, -6.3140523475272925, -6.916905689870921, -7.377628134673194, -7.677831930543847, -7.805772218645344, -7.756913065598337, -7.5341396640586575, -7.147603795974444, -6.614208966641314, -5.956760786488261, -5.202826148956015, -4.383360524166308, -3.531175363994783, -2.679326458748632, -1.859508566483358, -1.100541457488067, -0.42702764045973335, 0.1417473110467976, 0.5926142524111562, 0.9189788201359955, 1.120916669192697, 1.2049039281857588, 1.1832016864577162, 1.0729328186463538, 0.8949068306675442, 0.6722626619107442, 0.4290096552634502, 0.18855258299182698, -0.027712674410934387, -0.20165053973953478, -0.319411162758772, -0.3721702972116622, -0.35654117468088037, -0.27463562630982513, -0.13377287237407792, 0.05414421407601305, 0.27354523260765434, 0.5063425841209316, 0.7332431564260008, 0.9351381659525769, 1.0944825799784346, 1.196575531595536, 1.230658556408371, 1.1907590657751685, 1.076221650588103, 0.8918887202182136, 0.6479135223985474, 0.3592114840522161], 'positive_zeros': ['0.71541452664936098332074175503301', '1.42086187153501670610053224734615', '2.99263690795249172503381424694593', '3.54255488828347524246264408495259', '4.10275699757139131967432156048173', '4.78232419579792413336737874361759', '5.64462297184992318000121241396916', '6.47499132561472873517379985815111', '7.36683482026774018574235930898930', '7.59507708554501066928181989801226'], 'prelabel': '2-9072-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.51118585825181, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.71541452664936098332074175503', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '1.42086187153501670610053224735', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '2.99263690795249172503381424695', 'prec': 100}}