-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2551707628207715927103078552094', 'a10': [0.0, 0.0], 'a2': [0.0, -1.0], 'a3': [0.0, 0.0], 'a4': [7.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, -24.0], 'a8': [0.0, -15.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.275429751291645, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '225.199', 'coefficient_field': 'CDF', 'conductor': 225, 'conductor_radical': 15, 'conjugate': '869867943412694818632822237243', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1.0], [-8.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 24.0], [-343.0, 0]], [[1.0, 0], [52.0, 0], [1331.0, 0]], [[1.0, 0], [0, 22.0], [-2197.0, 0]], [[1.0, 0], [0, -14.0], [-4913.0, 0]], [[1.0, 0], [-20.0, 0], [6859.0, 0]], [[1.0, 0], [0, 168.0], [-12167.0, 0]], [[1.0, 0], [-230.0, 0], [24389.0, 0]], [[1.0, 0], [288.0, 0], [29791.0, 0]], [[1.0, 0], [0, 34.0], [-50653.0, 0]], [[1.0, 0], [122.0, 0], [68921.0, 0]], [[1.0, 0], [0, -188.0], [-79507.0, 0]], [[1.0, 0], [0, 256.0], [-103823.0, 0]], [[1.0, 0], [0, 338.0], [-148877.0, 0]], [[1.0, 0], [-100.0, 0], [205379.0, 0]], [[1.0, 0], [-742.0, 0], [226981.0, 0]], [[1.0, 0], [0, 84.0], [-300763.0, 0]], [[1.0, 0], [-328.0, 0], [357911.0, 0]], [[1.0, 0], [0, -38.0], [-389017.0, 0]], [[1.0, 0], [-240.0, 0], [493039.0, 0]], [[1.0, 0], [0, -1212.0], [-571787.0, 0]], [[1.0, 0], [-330.0, 0], [704969.0, 0]], [[1.0, 0], [0, -866.0], [-912673.0, 0]], [[1.0, 0], [-1218.0, 0], [1030301.0, 0]], [[1.0, 0], [0, -88.0], [-1092727.0, 0]], [[1.0, 0], [0, 36.0], [-1225043.0, 0]], [[1.0, 0], [-970.0, 0], [1295029.0, 0]], [[1.0, 0], [0, -1042.0], [-1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 18, 'label': '2-15e2-5.4-c3-0-18', '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/225/4/b/e/199/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.7652026655123854, 2.027282850068081, 2.2563183155456015, 2.4466153577774716, 2.592391745426341, 2.6878893806928557, 2.727634294321599, 2.7068360609257667, 2.6219026777325913, 2.4710323858928986, 2.2548314778359027, 1.9768973767418851, 1.6442998476590172, 1.267890950561512, 0.8623772628284372, 0.4460969442997206, 0.04046008962307578, -0.33096630960535545, -0.6437181444184967, -0.8739937375499831, -1.0004312690557198, -1.0059859587046822, -0.8797573412085691, -0.6185944690588085, -0.2282977023953516, 0.27575643779861647, 0.868713600316386, 1.5171619180884706, 2.180906989095256, 2.815553402131091, 3.3757556670606816, 3.818912831140536, 4.109003108322068, 4.22019824656987, 4.139872140260657, 3.8706323007807493, 3.4310606962775876, 2.854951977111724, 2.188976603383439, 1.4888626484847345, 0.8143667340416735, 0.22347152817690785, -0.23361737520060008, -0.5200196097724088, -0.6166047233599747, -0.5246924105626233, -0.2665767303586303, 0.11635503443045253, 0.567863216864368, 1.0231125416265507, 1.416316461344272, 1.688908915897925, 1.7972414477682463, 1.7187805932432223, 1.455892407945274, 1.036546910711599, 0.5116351809327931, -0.050972599314031725, -0.5750422423399847, -0.9862608101639949, -1.2228761102639245, -1.245220903056626, -1.0426956464754489, -0.6370363752041259, -0.08113909003961446, 0.5466990917674643, 1.1526031862964872, 1.6398531135018015, 1.9228553841793266, 1.9403763577910482, 1.6660267709983503, 1.1142564434836213, 0.3406733067123089, -0.5637202318568931, -1.4838812458408885, -2.296289663332767, -2.8866031237876553, -3.1668282607713145, -3.089350090511887, -2.655492910031958, -1.9170097344684642, -0.9699238423785771, 0.05867022440841358, 1.0290805893891513, 1.8100606950406624, 2.299161524364073, 2.4390860599885285, 2.2272355322873905, 1.7166295585372053, 1.0077331890028434, 0.23222515690303325, -0.4688544119288392, -0.9690789014386414, -1.1787222392562642, -1.0611020044164452, -0.6401539062111328, 0.0023878867315858293, 0.7400795949223937, 1.423191051444839, 1.9049788290617338, 2.0683260369496477, 1.848024865638475, 1.2445758850620092, 0.3267461458973885, -0.7779473106458084, -1.9035082533748298, -2.873169762183911, -3.529761148766537, -3.7633196401295756, -3.530879841882008, -2.864676030767568, -1.8670412577716802, -0.6927226352794944, 0.4782963253055823, 1.4725250895968471, 2.1533518653688004, 2.4443481874779724, 2.3410303121141847, 1.908794250208395, 1.2674210820299128, 0.5652120347795334, -0.05207570771262986, -0.47120463567404697, -0.6341917810358116, -0.5490501904936986, -0.28619978459868967, 0.03882610814067221, 0.29284041985069104, 0.3568422236297667, 0.15536374746420958, -0.32320341918651163, -1.0200749803658058, -1.8152618173160078, -2.5510450105209674, -3.0651269427823693, -3.2265500640497753, -2.9665907847334574, -2.297615319041559, -1.3152265176142477, -0.1824901289812964, 0.9011037769270334, 1.7398429662519816, 2.1828071348905116, 2.156831276022416, 1.6839685695897477, 0.8791076331999105, -0.07242109117995929, -0.9530404155636434, -1.559104821923077, -1.7452309343648376, -1.457038755871936, -0.7448134602403049, 0.24541392456630315, 1.3019724191285258, 2.192710586419497, 2.715565222135488, 2.7434415211062637, 2.2533061470425633, 1.3326973731306568, 0.16178411168929768, -1.0254144770653852, -1.9922396933304105, -2.551628343546059, -2.6075088837519353, -2.1757534261469806, -1.37960570032257, -0.42030937480103076, 0.4705714743277909, 1.0862636130439411, 1.2945113150256877, 1.0701233810423418, 0.5023621790431329, -0.2250223601242119, -0.8768840858036482, -1.2231032058684148, -1.0951864957419395, -0.429588172804533, 0.7128109114072274, 2.1561569782270626, 3.6463093272117963, 4.906549173148107, 5.69944788681516, 5.8803896824839414, 5.430065494685738, 4.458156552078716, 3.177265143929076, 1.8532872960862696, 0.7441155097001583, 0.04139308420965351, -0.17071718988652348, 0.07001072907955232, 0.6193104046578498, 1.2674599026599849, 1.7952327757440854, 2.0303948710779576, 1.890332435326236, 1.4000397961531796, 0.6811272486590566, -0.08490113078071203, -0.7090634031551544, -1.0487732389189264, -1.0484626039880305, -0.75568560049583, -0.30794592907721424, 0.10660121120528313, 0.3041978641071031, 0.16131917985225183, -0.34432109016408863, -1.1196490505457941, -1.9741021727468417, -2.666045412726718, -2.9663663147389245, -2.7227581191929047, -1.9073364646483257, -0.6340071296533103, 0.8604489298633099, 2.268180118812159, 3.2827230668929066, 3.6740064556072185, 3.346545382511114, 2.3653259970424148, 0.9419502638483156, -0.6161425926692572, -1.980818269645704, -2.8835707875950414, -3.1801882475857197, -2.882787049832677, -2.1507070953742993, -1.242644039909891, -0.4428071755866738, 0.01899168584503418, 0.0315825274702354, -0.3666713942736109, -0.9990890286180228, -1.6012875105780733, -1.8975972167177793, -1.6823465747539732, -0.8834068190748745, 0.4100808713105906, 1.9642671093267592, 3.45779980140062, 4.564710635685597, 5.040651293912728, 4.78884188040066, 3.887316450075268, 2.569458714418267, 1.1626030292847473, 0.0011091952477472141, -0.6624549396394686, -0.7236489722496844, -0.2516760293528536, 0.5330512091315548, 1.3231301846191823, 1.812336639175827, 1.783151943646919, 1.1691746335502322, 0.07494448375294163], 'positive_zeros': ['2.01294238944729982403051570765037', '3.05980952932106609294136929095113', '5.18088861471269145153166646196853', '5.84012799422825265211009764262721', '7.11357940921124990242723898275975', '8.016594154601279002216180292584852', '9.048411507020811325532386508582418', '10.24284093269802154477966409202129', '11.28883901914629846712481762417914', '11.99958183134376279732849961531164'], 'prelabel': '2-15e2-5.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6435463152389933, 'root_angle': 0.6475836176504333, 'root_number': '-0.4472135954999579 + 0.8944271909999159*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.323791808825', 'prec': 47}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.01294238944729982403051570765', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.05980952932106609294136929095', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.18088861471269145153166646197', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 13.275429751291645, 'bad_primes': [3, 5], 'central_character': '5.4', 'conductor': 225, 'conductor_radical': 15, 'degree': 2, 'index': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/225/4/b/e/199/1'], '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': '2-15e2-5.4-c3-0-18', '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': '2-15e2-5.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6435463152389933, 'root_angle': 0.32379180882521663, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '2.01294238944729982403051570765', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2551707628207715927103078552094', 'Lhash_array': ['2551707628207715927103078552094'], 'label': '2-15e2-5.4-c3-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/225/4/b/e/199/1'}