Formats: - HTML - YAML - JSON - 2025-12-07T14:49:40.864354
Query: /api/lfunc_lfunctions/?_offset=0
Show schema

{'Lhash': '1429416256969535379745944826125', 'a10': [-1.2143197433775352, 0.0], 'a2': [-1.2143197433775352, 0.0], 'a3': [2.9032119259115534, 0.0], 'a4': [-0.525427560843517, 0.0], 'a5': [1.0, 0.0], 'a6': [-3.525427560843517, 0.0], 'a7': [0.0, 0.0], 'a8': [3.066676547602054, 0.0], 'a9': [5.4286394867550705, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 56.73371063611974, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [-1.0, 0]]], [7, [[1.0, 0], [0, 0]]], [29, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [5, 7, 29], 'central_character': '7105.1', 'coefficient_field': 'CDF', 'conductor': 7105, 'conductor_radical': 1015, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.2143197433775352, 0], [2.0, 0]], [[1.0, 0], [-2.9032119259115534, 0], [3.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-4.903211925911553, 0], [11.0, 0]], [[1.0, 0], [-6.4286394867550705, 0], [13.0, 0]], [[1.0, 0], [2.1476431957754807, 0], [17.0, 0]], [[1.0, 0], [2.2809962909795893, 0], [19.0, 0]], [[1.0, 0], [-6.903211925911553, 0], [23.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [1.7190037090204104, 0], [31.0, 0]], [[1.0, 0], [-7.9540670475985875, 0], [37.0, 0]], [[1.0, 0], [-3.3777843650680364, 0], [41.0, 0]], [[1.0, 0], [1.0967880740884468, 0], [43.0, 0]], [[1.0, 0], [12.70963577773466, 0], [47.0, 0]], [[1.0, 0], [-3.3777843650680364, 0], [53.0, 0]], [[1.0, 0], [-3.1842082168911428, 0], [59.0, 0]], [[1.0, 0], [-2.4286394867550705, 0], [61.0, 0]], [[1.0, 0], [1.0967880740884468, 0], [67.0, 0]], [[1.0, 0], [-3.5713605132449295, 0], [71.0, 0]], [[1.0, 0], [14.189130386176764, 0], [73.0, 0]], [[1.0, 0], [-0.3412193439523743, 0], [79.0, 0]], [[1.0, 0], [-7.331851412666624, 0], [83.0, 0]], [[1.0, 0], [2.949144878312966, 0], [89.0, 0]], [[1.0, 0], [-18.57628268253055, 0], [97.0, 0]], [[1.0, 0], [15.41927155546932, 0], [101.0, 0]], [[1.0, 0], [7.760490899421694, 0], [103.0, 0]], [[1.0, 0], [3.036565021115662, 0], [107.0, 0]], [[1.0, 0], [7.939776947027215, 0], [109.0, 0]], [[1.0, 0], [-7.820713952394478, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 21626397, 'index': 254, 'label': '2-7105-1.1-c1-0-254', 'leading_term': '3.18094725330386823728442860212', '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': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/7105/2/a/p/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [3.1809472533038683, 3.1727248585703967, 3.1480138159554905, 3.1066921373188685, 3.048587703698198, 2.973522474636936, 2.8813695076602, 2.7721185361413485, 2.645945394876108, 2.503280500931886, 2.344871832342084, 2.1718383156341026, 1.9857101500566592, 1.788453290352396, 1.582476030556467, 1.3706163493497157, 1.1561093806374678, 0.9425350596125627, 0.7337466674255234, 0.5337816590951503, 0.3467568080911638, 0.17675033036716012, 0.027674248045085986, -0.09685919917124843, -0.19367281003882517, -0.26015667889791577, -0.29439252590540155, -0.2952650546065506, -0.26255533821960214, -0.19701146502051423, -0.10039209533459156, 0.024520797800254162, 0.17394291879775436, 0.34314428984674417, 0.5265423049180152, 0.7178306745531179, 0.9101423600279851, 1.0962431711205298, 1.2687512841443913, 1.4203765835734938, 1.5441725016609062, 1.6337919865531845, 1.6837384289566937, 1.6896018739722072, 1.648270684164378, 1.5581090378097706, 1.419091265277336, 1.2328850543752106, 1.0028769833444093, 0.7341356413687817, 0.4333097262665312, 0.10846090497033552, -0.23116619448654, -0.5754318139192847, -0.9136390077599891, -1.2349114452013485, -1.5285985187264048, -1.7846932615945261, -1.9942470974110786, -2.1497645275947246, -2.2455605875015543, -2.2780643274017875, -2.246052732472289, -2.1508013888662627, -1.9961408011398767, -1.788410507138739, -1.5363069243866918, -1.2506250706719482, -0.9438987769883703, -0.6299485767958505, -0.3233509190229269, -0.03884651198809553, 0.20929074005690715, 0.4078997893120854, 0.5455669825470315, 0.6132215157191329, 0.6046642991809437, 0.5170039873771234, 0.3509764009024995, 0.11112722109003623, -0.1941574232263877, -0.5527821762775399, -0.9492387577238658, -1.36506369477952, -1.7794466838634084, -2.169971717887027, -2.51346645618974, -2.7869293793975376, -2.968499365816484, -3.0384287239208922, -2.98001864691547, -2.78047569215698, -2.4316493331305247, -1.9306139096043153, -1.280063354286372, -0.4884937586886784, 0.42984306865307537, 1.455222703705151, 2.5629655887149423, 3.724176365357073, 4.9066824164055785, 6.07613946210198, 7.19726360955151, 8.235142299306798, 9.15657151164738, 9.931363692622664, 10.533570353265839, 10.942565296600668, 11.143938933897182, 11.130161042807282, 10.900978356232228, 10.463524201633223, 9.832129587198315, 9.027838124804695, 8.077640403748878, 7.013456266872081, 5.870905273860311, 4.687915876327058, 3.503231946509968, 2.354880854649717, 1.2786699508303758, 0.3067778796473461, -0.5334964081098846, -1.2207706782301904, -1.7403555704076654, -2.0847347287365734, -2.25372732113037, -2.2543261433584783, -2.1002197755119787, -1.811022272232652, -1.4112478698187718, -0.9290804668588971, -0.39499753872569426, 0.15968485130535287, 0.7042755710673039, 1.2101099031154166, 1.6518217995295512, 2.0084265108628205, 2.264163089964956, 2.4090587786448956, 2.4391917640235636, 2.356644490022745, 2.1691558004595586, 1.8894958149135426, 1.53460175330013, 1.1245251483095602, 0.681250341365095, 0.22745031818384895, -0.21475154703128635, -0.624946555113219, -0.9854702917197501, -1.2822430073569728, -1.5053784667932906, -1.6495327829118862, -1.7139801167478055, -1.702418155990793, -1.6225220448822786, -1.4852800028140936, -1.3041563727814247, -1.0941375342095567, -0.8707224084115757, -0.6489217884902946, -0.4423292735751198, -0.2623212534578318, -0.11743448582888938, -0.012957869484395782, 0.04923922772857945, 0.0706353961212659, 0.055751786848704216, 0.011637839049464284, -0.05281297424647757, -0.12766704132741993, -0.20281563313373543, -0.268838206484319, -0.31780099870431183, -0.34393203310228543, -0.34412181931907854, -0.31821078195029934, -0.2690390707368666, -0.20225097733414063, -0.1258636383970657, -0.04962688895635795, 0.01578312161658577, 0.059680728051514184, 0.07233243013079672, 0.04589247676705251, -0.024759313172495596, -0.14134488833683706, -0.3017387518718052, -0.49978700444519236, -0.725422342706188, -0.9650830084332548, -1.2024226166466272, -1.4192767299594444, -1.5968324095733553, -1.7169301365889766, -1.7634147026003633, -1.7234439372671377, -1.5886621985158291, -1.356149769986182, -1.0290696706091107, -0.616949458365081, -0.1355565878650284, 0.3936494104010507, 0.944477682571184, 1.487341905895388, 1.9909069990464465, 2.423958957898781, 2.7573911789012167, 2.966187713966911, 3.0312780525895846, 2.9411399153334647, 2.6930363624455493, 2.2937909648495616, 1.7600290450109437, 1.1178427992041011, 0.4018717874336141, -0.3461741571365918, -1.0794872608706496, -1.7485342661461698, -2.3037057643018617, -2.698097600945183, -2.8902661333465063, -2.8467949481329926, -2.5445162755833466, -1.972245718279532, -1.1319133843773028, -0.0390068252443344, 1.2777204590047082, 2.777278976810104, 4.408172160943093, 6.110742534534398, 7.820015189264985, 9.468886837640387, 10.991485438931981, 12.326512290542524, 13.420376534659544, 14.229941581990401, 14.72472360884821, 14.888412940589117, 14.719628040472056, 14.231856672856923, 13.4525868830667, 12.42167876616259, 11.189073556633444, 9.811976468947188, 8.35168138793577, 6.870226877106572, 5.427082609395071, 4.076062536458497, 2.86264600322071, 1.8218614875134183, 0.976851354200657, 0.33819226358543086, -0.09600252433259211, -0.33922261891965644, -0.41501357662083915], 'positive_zeros': ['1.12761060241061810473361705458000', '1.56503817374943733498433387672782', '2.60623157879286125064908707259688', '3.61288715485897760290241410415294', '4.03139828592322363796410529060850', '4.85203624926965596232531902646725', '6.16209761953115404062443472328622', '6.73931351724103514585702257618675', '7.49064375217977951495362617948326', '8.387140486793883124101093356104633'], 'prelabel': '2-7105-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.5321783460111815, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.12761060241061810473361705458', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.56503817374943733498433387673', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.60623157879286125064908707260', 'prec': 103}}