Formats: - HTML - YAML - JSON - 2026-04-28T18:58:39.274320
Query: /api/lfunc_lfunctions/?_offset=0
Show schema

{'Lhash': '3159843578376530115492065733576', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.5, 0.8660254037844386], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-5.0, 0.0], 'a8': [0.0, 0.0], 'a9': [1.5, -2.598076211353316], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.8205891660851936, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.5, -0.8660254037844386]]], [19, [[1.0, 0], [4.0, -1.7320508075688772]]]], 'bad_primes': [2, 3, 19], 'central_character': '228.221', 'coefficient_field': 'CDF', 'conductor': 228, 'conductor_radical': 114, 'conjugate': '3811542430941464889827101196907', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [2.5, -4.330127018922194]], [[1.0, 0], [5.0, 0], [7.0, 0]], [[1.0, 0], [0, 0], [-11.0, 0]], [[1.0, 0], [4.5, 2.598076211353316], [6.5, 11.258330249197702]], [[1.0, 0], [0, 0], [8.5, -14.722431864335457]], [[1.0, 0], [4.0, -1.7320508075688772]], [[1.0, 0], [0, 0], [11.5, 19.91858428704209]], [[1.0, 0], [0, 0], [-14.5, -25.11473670974872]], [[1.0, 0], [0, 8.660254037844387], [-31.0, 0]], [[1.0, 0], [0, -5.196152422706632], [-37.0, 0]], [[1.0, 0], [0, 0], [-20.5, 35.50704155516198]], [[1.0, 0], [-6.5, -11.258330249197702], [-21.5, 37.239092362730865]], [[1.0, 0], [0, 0], [23.5, 40.703193977868615]], [[1.0, 0], [0, 0], [-26.5, -45.89934640057525]], [[1.0, 0], [0, 0], [-29.5, 51.09549882328188]], [[1.0, 0], [0.5, -0.8660254037844386], [-30.5, -52.827549630850754]], [[1.0, 0], [10.5, 6.06217782649107], [33.5, 58.023702053557386]], [[1.0, 0], [0, 0], [-35.5, 61.48780366869514]], [[1.0, 0], [8.5, 14.722431864335457], [-36.5, 63.21985447626402]], [[1.0, 0], [4.5, -2.598076211353316], [39.5, -68.41600689897065]], [[1.0, 0], [0, 0], [-83.0, 0]], [[1.0, 0], [0, 0], [-44.5, -77.07626093681505]], [[1.0, 0], [12.0, -6.928203230275509], [48.5, -84.00446416709055]], [[1.0, 0], [0, 0], [50.5, 87.4685657822283]], [[1.0, 0], [0, 19.05255888325765], [-103.0, 0]], [[1.0, 0], [0, 0], [107.0, 0]], [[1.0, 0], [18.0, -10.392304845413264], [54.5, -94.39676901250381]], [[1.0, 0], [0, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 9702600, 'index': 5, 'label': '2-228-57.50-c1-0-5', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/228/2/p/a/221/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.0876564938040327e-61, -0.1473209172865706, -0.29669194015600453, -0.4523510823747537, -0.6168347852223858, -0.790601496649803, -0.9718661163821157, -1.1565894739261042, -1.3385797178689607, -1.5096924886627627, -1.6601404672525584, -1.7789322017799565, -1.8544564226440758, -1.8752154124865055, -1.830692994099283, -1.7123220230273684, -1.5144951332156649, -1.2355430402879217, -0.8785892475845477, -0.4521809105551964, 0.029404817987854437, 0.5462695207827426, 1.0734860491552631, 1.5822099143319344, 2.041300329215684, 2.4193895471888727, 2.68728334856337, 2.8205216303602354, 2.801882536136267, 2.623583211180154, 2.2889214119724874, 1.8131198126856658, 1.2231816608954107, 0.5566421259828668, -0.14079964424811056, -0.8186647632295981, -1.4258680221278042, -1.9153369513402163, -2.248639529930378, -2.400127903195799, -2.3601001534868398, -2.136535268312178, -1.755069822618439, -1.2570529047426138, -0.6957248877629402, -0.13079482567607903, 0.37808609952967986, 0.7782710975682181, 1.0306786808276382, 1.1151298701149603, 1.03369546675736, 0.8114665612653607, 0.49443720287774284, 0.14453438188132534, -0.1677917271826622, -0.37264305678366655, -0.4103471643073013, -0.24048484396467198, 0.15099562911903613, 0.74769538781227, 1.5025112121776436, 2.3415480651231073, 3.171983720162524, 3.893100815501601, 4.409192732451953, 4.642682344915551, 4.5456339794358955, 4.107931297191207, 3.360745963027646, 2.374504029282086, 1.251301183453612, 0.11252552995017691, -0.9168001330548208, -1.7248650005317048, -2.2287111818402243, -2.386315289046113, -2.203161819169496, -1.7320906352092844, -1.0661663076541172, -0.3253797371746453, 0.3610109189800074, 0.8739271299392297, 1.1227355562991717, 1.059424394606885, 0.6863193126909602, 0.05591975471361066, -0.7373305957903923, -1.5722021241075508, -2.3204344046116216, -2.867900412001026, -3.1336409864665815, -3.0834723470739647, -2.7356935689235042, -2.15771396499154, -1.4539785396921574, -0.7471297543855376, -0.1556263026207713, 0.22820147699965193, 0.35560978452128145, 0.2310310426453365, -0.08826536446799502, -0.5027358076720999, -0.889737438976511, -1.1280074634430344, -1.1229800049400633, -0.8281009334195988, -0.2578265512232491, 0.5106352451838653, 1.347778653182851, 2.0930994257013893, 2.583745255624106, 2.6854366800498783, 2.319887393263084, 1.4833365197536155, 0.2522438340568495, -1.2255341137880356, -2.753073504423551, -4.116585370604174, -5.121828522534248, -5.628056907705522, -5.573067726255403, -4.984421279878309, -3.9744236736265, -2.719538722414423, -1.4279342072122947, -0.3012611788517172, 0.5019895022600487, 0.894400960267767, 0.8732976997128868, 0.5174400970626305, -0.032573853736451795, -0.6061813489624424, -1.0404092605673994, -1.215264787025609, -1.0794853669082232, -0.6611267496738753, -0.06063800642800512, 0.5721890953623614, 1.0724906537829098, 1.2983852052518448, 1.164412734568238, 0.662817225736798, -0.13232273162535804, -1.079390821712378, -1.9991285681165036, -2.713715465910184, -3.0863729659086876, -3.052472949298068, -2.6348052519213034, -1.9390565159183848, -1.1299635327047102, -0.3930606480398239, 0.10957240182361533, 0.2794718322256862, 0.10834209891777477, -0.31573647981988284, -0.8247420571845003, -1.206947782533993, -1.25544003934008, -0.818268175757428, 0.16122449105801204, 1.6235386704743506, 3.3971972680000464, 5.228036520188321, 6.827984384666882, 7.933109462097483, 8.358334244748285, 8.036635755574574, 7.033784280868682, 5.53502272249814, 3.8063749184059366, 2.1390497893598828, 0.7893203940378802, -0.07264891807147177, -0.3935848778872577, -0.24078164833164073, 0.22170258200826992, 0.7782354615923144, 1.2170500022097372, 1.382410740819189, 1.2108652301942942, 0.7429128774582023, 0.1075495304204679, -0.5160614456281878, -0.9497626862255328, -1.0670877634430638, -0.8301633239764851, -0.3029627216692781, 0.3629455135807328, 0.9669032583556588, 1.3122613644163406, 1.2603606504629334, 0.7710964354892156, -0.08111821370597905, -1.1210640883530036, -2.1135656827409854, -2.8217629427301065, -3.0682151215360998, -2.783015461259474, -2.025938844685234, -0.9759522901173462, 0.11033872362135282, 0.9616360336863643, 1.360766508676062, 1.2018417433910455, 0.5206964624133923, -0.5100210461330811, -1.620880898955334, -2.5115603812658103, -2.926435663436597, -2.720829370762259, -1.900819417490413, -0.6259215193770316, 0.8267441279794066, 2.1283573811296477, 2.9781061053260083, 3.176690786927184, 2.675006381327615, 1.5856093809040404, 0.1540794741463012, -1.3022947510756175, -2.4726457340331787, -3.12731322340428, -3.1701303221879105, -2.6551224392245225, -1.764071564504807, -0.7518578473544257, 0.12495310351280359, 0.6764880776680412, 0.8262321052763022, 0.6235657590788055, 0.2194582340874868, -0.18694036493826022, -0.41477221551035176, -0.3612074788857871, -0.03651471704007385, 0.43640069648811947, 0.858544416502508, 1.017353404884346, 0.7571088433097299, 0.03625298778955014, -1.0462646976459706, -2.26508296294451, -3.321009829467775, -3.918878268404655, -3.8496177074165225, -3.0533962394069976, -1.6451395307686363, 0.10634664602742835, 1.8416905289370942, 3.200734493188166, 3.914947045537792, 3.877254069231982, 3.1697382838159918, 2.040926804120704, 0.8382100797832445, -0.08653792282437257], 'positive_zeros': ['2.49267706559491071174247924841301', '4.22478096844127391068925617324298', '5.65532936585661186980171838388091', '6.67930668148245683984310915948258', '7.20942662953002707868174072265341', '8.887804814931416945255008589054049', '9.931643418350333875369967605453931', '10.63449001845275867671211080364643', '12.04201154941349638477142678929545'], 'prelabel': '2-228-57.50-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3492920981333856, 'root_angle': 0.45054331069780507, 'root_number': '-0.9521058707330924 + 0.30576855776155254*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.450543310698', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.49267706559491071174247924841', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.22478096844127391068925617324', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.65532936585661186980171838388', 'prec': 103}}