-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '344926543117442127368498630119,389515527802866098274169399042,602098120151503280352741729175,773250875606594180583298654635,799664554552488147117865389566,899462753237871133496572442355,1136545232277488714825747226243,1328960804017545340718695000043,1769180596698369196918601400241', 'a10': 0, 'a2': 5, 'a3': 0, 'a4': 9, 'a5': 0, 'a6': 0, 'a7': -8, 'a8': 5, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.534849286293968e+16, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1]], [37, [1, -9, 36, -84, 126, -126, 84, -36, 9, -1]]], 'bad_primes': [3, 5, 37], 'central_character': '8325.1', 'coefficient_field': '1.1.1.1', 'conductor': 192069399958417858629810333251953125, 'conductor_radical': 555, 'degree': 18, 'euler_factors': [[1, -5, 16, -40, 87, -171, 312, -524, 820, -1196, 1640, -2096, 2496, -2736, 2784, -2560, 2048, -1280, 512], [1], [1], [1, 8, 67, 350, 1751, 6864, 25791, 81794, 251836, 674114, 1762852, 4007906, 8846313, 16480464, 29429057, 41177150, 55177381, 46118408, 40353607], [1, 0, 57, 24, 1603, 1128, 30009, 25256, 420678, 345392, 4627458, 3055976, 39941979, 16515048, 258164753, 42517464, 1110768747, 0, 2357947691], [1, 6, 77, 372, 2876, 11732, 70148, 248108, 1230478, 3777212, 15996214, 41930252, 154115156, 335077652, 1067838668, 1795572948, 4831635809, 4894384326, 10604499373], [1, -18, 251, -2452, 20402, -140812, 862542, -4621668, 22405796, -96841700, 380898532, -1335662052, 4237668846, -11760759052, 28967922514, -59185319188, 102995006923, -125563633938, 118587876497], [1, 4, 89, 290, 4152, 11570, 133580, 329082, 3268744, 7150996, 62106136, 118798602, 916225220, 1507813970, 10280763048, 13643305490, 79554584771, 67934252164, 322687697779], [1, -16, 281, -2900, 29786, -228568, 1710722, -10342828, 60671240, -295554928, 1395438520, -5471356012, 20814354574, -63962697688, 191712912598, -429304078100, 956755950607, -1252975764496, 1801152661463], [1, -2, 151, -192, 11086, -9472, 547218, -367456, 20374196, -11917948, 590851684, -309030496, 13346099802, -6699365632, 227386597814, -114206077632, 2604731322659, -1000492825922, 14507145975869], [1, 6, 117, 652, 7900, 42482, 382924, 1922952, 14422916, 67506176, 447110396, 1847956872, 11407688884, 39233019122, 226170292900, 578652400012, 3218975850987, 5117346224646, 26439622160671], [1, -9, 36, -84, 126, -126, 84, -36, 9, -1], [1, 2, 207, 308, 22135, 23834, 1590167, 1260212, 84684498, 54351400, 3472064418, 2118416372, 109595899807, 67349187674, 2564477009135, 1463032106228, 40314134693367, 15969850458242, 327381934393961], [1, 14, 209, 1776, 13590, 62808, 164694, -1659984, -20033612, -186487436, -861445316, -3069310416, 13094325858, 214728053208, 1997844740370, 11226740775024, 56810089721363, 163634803886414, 502592611936843], [1, -34, 691, -10098, 119667, -1203098, 10717955, -86467054, 648355640, -4565820786, 30472715080, -191005722286, 1112770241965, -5870734451738, 27445028952669, -108848516392242, 350076576239933, -809583746499874, 1119130473102767], [1, 4, 219, 714, 27303, 82394, 2419235, 6546958, 162792322, 393594900, 8627993066, 18390405022, 360168449095, 650128291514, 11417991545379, 15825353846106, 257261739624303, 249038761645444, 3299763591802133], [1, 10, 363, 2748, 56906, 329642, 5349206, 24228380, 368128354, 1449707336, 21719572886, 84338990780, 1098614579074, 3994391114762, 40683482158894, 115912106445468, 903380488989297, 1468304376043210, 8662995818654939], [1, -8, 287, -2428, 46078, -364856, 5023538, -36330404, 402838300, -2591580928, 24573136300, -135185433284, 1140247678778, -5051738163896, 38917308357478, -125091468948508, 901967193938027, -1533658503978248, 11694146092834141], [1, 16, 457, 5334, 91400, 863542, 11351860, 90969834, 1002999192, 6994279188, 67200945864, 408363584826, 3414219469180, 17401339330582, 123401434779800, 482505010489446, 2769745203632611, 6497082840906256, 27206534396294947], [1, 8, 461, 3084, 101579, 577916, 14118333, 68868932, 1373824126, 5759364312, 97541512946, 347168286212, 5053106682363, 14685817036796, 183271813245229, 395061275612364, 4192850393018251, 5166028249966088, 45848500718449031], [1, 8, 463, 3322, 104127, 660254, 14888495, 82668926, 1491866866, 7163969732, 108906281218, 440542706654, 5791877659415, 18750052213214, 215862725764311, 502732299732058, 5114945514341911, 6451680735152648, 58871586708267913], [1, 26, 763, 13592, 240966, 3294462, 43709806, 481618160, 5120271010, 46351492472, 404501409790, 3005778936560, 21550639040434, 128319561751422, 741465972241434, 3304044695441432, 14652582556439317, 39444829057570586, 119851595982618319], [1, -70, 2739, -75488, 1620083, -28461806, 422117107, -5384607998, 59783071428, -581342998750, 4961994928524, -37094564498222, 241361074260209, -1350749525387726, 6381572782033369, -24680074904879072, 74325643660588353, -157660456249732870, 186940255267540403], [1, -8, 241, 444, 10408, 333920, 750216, 23712740, 328869494, 588300176, 29269384966, 187828613540, 528879023304, 20950889114720, 58118890745192, 220659693186684, 10659751709822489, -31492710445616648, 350356403707485209], [1, -2, 435, -2304, 103150, -691808, 17711706, -115122720, 2305098788, -13060706492, 223594582436, -1083189672480, 16164995850138, -61245264830048, 885784147509550, -1919167499356416, 35147253747979155, -15674867188753922, 760231058654565217], [1, -18, 647, -8804, 189791, -2078234, 34417039, -318948144, 4487117854, -36439847388, 453198903254, -3253590016944, 35459909698739, -216261863411834, 1994722484185291, -9345623405891204, 69367157281323547, -194914207013054418, 1093685272684360901], [1, -2, 681, -1504, 221202, -503704, 45141082, -99280256, 6414577064, -12594479052, 660701437592, -1053264235904, 49326879110614, -56692328963224, 2564337437833086, -1795854653979616, 83754410235433647, -25335401627752322, 1304773183829244583], [1, -46, 1453, -33800, 661156, -11066918, 164379928, -2177064712, 26082757228, -282786541240, 2790855023396, -24925213887688, 201372480136904, -1450647195739718, 9273054920626892, -50724685892496200, 233320048532315879, -790365642722683246, 1838459212420154507], [1, -26, 1041, -20396, 461332, -7208416, 117515564, -1500842420, 19185857722, -201379553100, 2091258491698, -17831508792020, 152186063331356, -1017526746282976, 7098164663619268, -34206133860713036, 190298872477017429, -518066286839449946, 2171893279442309389], [1, -20, 585, -9008, 149832, -1779692, 22178040, -217082624, 2405885670, -23146802336, 271865080710, -2771928025856, 32000627381880, -290174083992812, 2760557477848776, -18754221387501872, 137627420606217945, -531688838581286420, 3004041937984268273]], 'euler_factors_factorization': [[[[1, -5, 16, -40, 87, -171, 312, -524, 820, -1196, 1640, -2096, 2496, -2736, 2784, -2560, 2048, -1280, 512], 1]], [1], [1], [[[1, 8, 67, 350, 1751, 6864, 25791, 81794, 251836, 674114, 1762852, 4007906, 8846313, 16480464, 29429057, 41177150, 55177381, 46118408, 40353607], 1]], [[[1, 0, 57, 24, 1603, 1128, 30009, 25256, 420678, 345392, 4627458, 3055976, 39941979, 16515048, 258164753, 42517464, 1110768747, 0, 2357947691], 1]], [[[1, 6, 77, 372, 2876, 11732, 70148, 248108, 1230478, 3777212, 15996214, 41930252, 154115156, 335077652, 1067838668, 1795572948, 4831635809, 4894384326, 10604499373], 1]], [[[1, -18, 251, -2452, 20402, -140812, 862542, -4621668, 22405796, -96841700, 380898532, -1335662052, 4237668846, -11760759052, 28967922514, -59185319188, 102995006923, -125563633938, 118587876497], 1]], [[[1, 4, 89, 290, 4152, 11570, 133580, 329082, 3268744, 7150996, 62106136, 118798602, 916225220, 1507813970, 10280763048, 13643305490, 79554584771, 67934252164, 322687697779], 1]], [[[1, -16, 281, -2900, 29786, -228568, 1710722, -10342828, 60671240, -295554928, 1395438520, -5471356012, 20814354574, -63962697688, 191712912598, -429304078100, 956755950607, -1252975764496, 1801152661463], 1]], [[[1, -2, 151, -192, 11086, -9472, 547218, -367456, 20374196, -11917948, 590851684, -309030496, 13346099802, -6699365632, 227386597814, -114206077632, 2604731322659, -1000492825922, 14507145975869], 1]], [[[1, 6, 117, 652, 7900, 42482, 382924, 1922952, 14422916, 67506176, 447110396, 1847956872, 11407688884, 39233019122, 226170292900, 578652400012, 3218975850987, 5117346224646, 26439622160671], 1]], [[[1, -1], 9]], [[[1, 2, 207, 308, 22135, 23834, 1590167, 1260212, 84684498, 54351400, 3472064418, 2118416372, 109595899807, 67349187674, 2564477009135, 1463032106228, 40314134693367, 15969850458242, 327381934393961], 1]], [[[1, 14, 209, 1776, 13590, 62808, 164694, -1659984, -20033612, -186487436, -861445316, -3069310416, 13094325858, 214728053208, 1997844740370, 11226740775024, 56810089721363, 163634803886414, 502592611936843], 1]], [[[1, -34, 691, -10098, 119667, -1203098, 10717955, -86467054, 648355640, -4565820786, 30472715080, -191005722286, 1112770241965, -5870734451738, 27445028952669, -108848516392242, 350076576239933, -809583746499874, 1119130473102767], 1]], [[[1, 4, 219, 714, 27303, 82394, 2419235, 6546958, 162792322, 393594900, 8627993066, 18390405022, 360168449095, 650128291514, 11417991545379, 15825353846106, 257261739624303, 249038761645444, 3299763591802133], 1]], [[[1, 10, 363, 2748, 56906, 329642, 5349206, 24228380, 368128354, 1449707336, 21719572886, 84338990780, 1098614579074, 3994391114762, 40683482158894, 115912106445468, 903380488989297, 1468304376043210, 8662995818654939], 1]], [[[1, -8, 287, -2428, 46078, -364856, 5023538, -36330404, 402838300, -2591580928, 24573136300, -135185433284, 1140247678778, -5051738163896, 38917308357478, -125091468948508, 901967193938027, -1533658503978248, 11694146092834141], 1]], [[[1, 16, 457, 5334, 91400, 863542, 11351860, 90969834, 1002999192, 6994279188, 67200945864, 408363584826, 3414219469180, 17401339330582, 123401434779800, 482505010489446, 2769745203632611, 6497082840906256, 27206534396294947], 1]], [[[1, 8, 461, 3084, 101579, 577916, 14118333, 68868932, 1373824126, 5759364312, 97541512946, 347168286212, 5053106682363, 14685817036796, 183271813245229, 395061275612364, 4192850393018251, 5166028249966088, 45848500718449031], 1]], [[[1, 8, 463, 3322, 104127, 660254, 14888495, 82668926, 1491866866, 7163969732, 108906281218, 440542706654, 5791877659415, 18750052213214, 215862725764311, 502732299732058, 5114945514341911, 6451680735152648, 58871586708267913], 1]], [[[1, 26, 763, 13592, 240966, 3294462, 43709806, 481618160, 5120271010, 46351492472, 404501409790, 3005778936560, 21550639040434, 128319561751422, 741465972241434, 3304044695441432, 14652582556439317, 39444829057570586, 119851595982618319], 1]], [[[1, -70, 2739, -75488, 1620083, -28461806, 422117107, -5384607998, 59783071428, -581342998750, 4961994928524, -37094564498222, 241361074260209, -1350749525387726, 6381572782033369, -24680074904879072, 74325643660588353, -157660456249732870, 186940255267540403], 1]], [[[1, -8, 241, 444, 10408, 333920, 750216, 23712740, 328869494, 588300176, 29269384966, 187828613540, 528879023304, 20950889114720, 58118890745192, 220659693186684, 10659751709822489, -31492710445616648, 350356403707485209], 1]], [[[1, -2, 435, -2304, 103150, -691808, 17711706, -115122720, 2305098788, -13060706492, 223594582436, -1083189672480, 16164995850138, -61245264830048, 885784147509550, -1919167499356416, 35147253747979155, -15674867188753922, 760231058654565217], 1]], [[[1, -18, 647, -8804, 189791, -2078234, 34417039, -318948144, 4487117854, -36439847388, 453198903254, -3253590016944, 35459909698739, -216261863411834, 1994722484185291, -9345623405891204, 69367157281323547, -194914207013054418, 1093685272684360901], 1]], [[[1, -2, 681, -1504, 221202, -503704, 45141082, -99280256, 6414577064, -12594479052, 660701437592, -1053264235904, 49326879110614, -56692328963224, 2564337437833086, -1795854653979616, 83754410235433647, -25335401627752322, 1304773183829244583], 1]], [[[1, -46, 1453, -33800, 661156, -11066918, 164379928, -2177064712, 26082757228, -282786541240, 2790855023396, -24925213887688, 201372480136904, -1450647195739718, 9273054920626892, -50724685892496200, 233320048532315879, -790365642722683246, 1838459212420154507], 1]], [[[1, -26, 1041, -20396, 461332, -7208416, 117515564, -1500842420, 19185857722, -201379553100, 2091258491698, -17831508792020, 152186063331356, -1017526746282976, 7098164663619268, -34206133860713036, 190298872477017429, -518066286839449946, 2171893279442309389], 1]], [[[1, -20, 585, -9008, 149832, -1779692, 22178040, -217082624, 2405885670, -23146802336, 271865080710, -2771928025856, 32000627381880, -290174083992812, 2760557477848776, -18754221387501872, 137627420606217945, -531688838581286420, 3004041937984268273], 1]]], 'gamma_factors': [[], [0, 0, 0, 0, 0, 0, 0, 0, 0]], 'group': 'GL2', 'index': 0, 'label': '18-8325e9-1.1-c1e9-0-0', 'leading_term': '100.302572100408208357683199816051003177884341920225630234364103577724715507829990845769316', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1, 1, 1, 1, 1, 1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/8325/2/a/cr', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.005208333333333333', 'prec': 67}, 'plot_values': [100.30257210040824, 99.73814232143245, 99.14608671709894, 98.49686735717269, 97.76161850856096, 96.91231500700076, 95.92200548739562, 94.76510663093666, 93.41775326677377, 91.85819756815467, 90.07316791996459, 88.07527186696475, 85.88395649073016, 83.51918935756497, 81.00123761037034, 78.35045838080504, 75.58710232633726, 72.73113177044166, 69.80205460402766, 66.81752817838432, 63.78983468245865, 60.730134987260584, 57.64973763329196, 54.56003487669936, 51.47243671946807, 48.398303347853506, 45.34887643412855, 42.33520978527795, 39.36833647188885, 36.459804735913536, 33.620719107699834, 30.861419038080715, 28.19142717420502, 25.619404602950134, 23.153113299385065, 20.79938595965641, 18.56410333872541, 16.452155112788056, 14.467377262532429, 12.612651734838657, 10.88993709647682, 9.300277457177053, 7.843818084120952, 6.519827546530656, 5.3267261784118825, 4.262120598122293, 3.3228507366751168, 2.505047742966706, 1.8041521983587163, 1.214964576220029, 0.7317086994622815, 0.3480986327855393, 0.057408401927549195, -0.14745608883285108, -0.2738835856106127, -0.32948298403556525, -0.32201017399185616, -0.2592966420970596, -0.1491752747549366, 0.0005926305398627815, 0.18238780875910324, 0.38880030699853396, 0.6126930135608789, 0.8472608871065145, 1.086084070946545, 1.3231731668493316, 1.5530173388791013, 1.7706242185532388, 1.9715519032494573, 2.1519340641534046, 2.308498013752046, 2.438575655092657, 2.54010730808808, 2.611637842866445, 2.652305632696449, 2.6618293780094304, 2.6404855689549955, 2.5890787716092616, 2.508906079863102, 2.401716253959153, 2.269664123781016, 2.115260886100205, 1.941321418389166, 1.7509103001882407, 1.547283194365021, 1.3338266999991726, 1.1139980559187452, 0.8912652448036811, 0.6690483169718537, 0.4506627353126234, 0.23926551568720236, 0.03780554818775437, -0.1510209625257604, -0.3248145963711066, -0.48150962662460156, -0.619404080526008, -0.7371832330311118, -0.8339361878386927, -0.9091652961510297, -0.9627882640393375, -0.9951328738157023, -1.0069249368890059, -0.9992695733298477, -0.973624446446931, -0.9317662017181844, -0.8757508067108838, -0.807868400976574, -0.7305933575838555, -0.6465303422978651, -0.5583575976644383, -0.4687687036093778, -0.3804106110796657, -0.2958219995936266, -0.21737290386166697, -0.1472063586428171, -0.0871831500735918, -0.03883073856354563, -0.0032973790137147568, 0.01868753845250363, 0.02684640245477259, 0.021378999451512674, 0.002978626760029714, -0.027161347543545482, -0.06735078307679382, -0.1154162408721687, -0.1687247931311311, -0.22421816645195053, -0.27845684008516247, -0.32767370607319823, -0.36783875759075296, -0.3947321736744582, -0.40402498142543086, -0.3913664376244864, -0.352476908037479, -0.2832448818944701, -0.1798266341343955, -0.03874737548543613, 0.14299638755200839, 0.36783858387805024, 0.6375500055505987, 0.9531507522650712, 1.3148307436399698, 1.7218800865133117, 2.1726310076242026, 2.6644129556691816, 3.193520917725518, 3.7551961695561746, 4.343632539145545, 4.951999395710464, 5.572482337709291, 6.1963431831203355, 6.813999353329217, 7.415122439134746, 7.988755424669905, 8.52344622865315, 9.007395426699631, 9.428629121695113, 9.775182095673498, 10.035290700574917, 10.197594631372468, 10.251344901853576, 10.18661511526095, 9.994512927966436, 9.66738705337341, 9.199025446311394, 8.584852359141726, 7.822108641656844, 6.9100135951092545, 5.849906499274641, 4.645364592666655, 3.302294485921195, 1.8289942426244947, 0.23617910479608661, -1.463037721556287, -3.253174094045603, -5.116451176981005, -7.032907254793502, -8.980549211663554, -10.935541330893622, -12.872430500071477, -14.764406329105705, -16.58360662356983, -18.301480656396805, -19.889105011069745, -21.317542119056938, -22.558228899954347, -23.58337903920771, -24.366393792856858, -24.88227586318388, -25.1080406085919, -25.023136972498733, -24.60988549982156, -23.853778214625592, -22.743791373940272, -21.272684411085173, -19.4372604001026, -17.23858285571212, -14.682144098653431, -11.77798091674971, -8.540741509362938, -4.989687425810543, -1.1485680532307014, 2.9545249814769194, 7.287353204376759, 11.813788410816528, 16.494130125438847, 21.28548113019126, 26.14217788899218, 31.016300024397722, 35.85831628535365, 40.617626306258366, 45.24313869376707, 49.6838920497728, 53.88969145603012, 57.811752193775945, 61.403342124173285, 64.62041391782358, 67.4222962053241, 69.77254113142057, 71.63927984308845, 72.99563515107043, 73.82014844434845, 74.09714374888107, 73.81702257695163, 72.97648402442026, 71.5786654840598, 69.633312859934, 67.15709062386722, 64.17311759222088, 60.71062668128039, 56.80465105143227, 52.49562865941602, 47.82892945596961, 42.85431063398272, 37.625306448985796, 32.19866837461768, 26.633940607151004, 20.99231522904821, 15.335715801797178, 9.725982050435885, 4.22405193387841, -1.110847290767366, -6.221987389110444, -11.055895388876076, -15.562995674053893, -19.698098711490807, -23.421279978815246, -26.698474440206873, -29.501903750764043, -31.810411433012632, -33.60970089842029, -34.892472600143535, -35.65845808625017, -35.91431784953952, -35.67339650283314, -34.95558104244238, -33.786949328195945, -32.19928812426896, -30.229528271125403, -27.919106135270294, -25.31326164035754, -22.460284188310126, -19.41069965650935, -16.21639290659025, -12.929824550801278, -9.603203826242153, -6.2876587023354515, -3.0324366997477017, 0.11585055357082996, 3.113926770211663, 5.9224831616757205, 8.506759446916769, 10.837097254187485, 12.88924450678096, 14.644599722294258, 16.090374823051597, 17.219650248075492, 18.031322684581433, 18.529947633481317, 18.725480880629146, 18.63295464322097, 18.2721199563994, 17.666821505989216, 16.844367977832547, 15.834878378362605, 14.670586945378686, 13.385120764615847, 12.012764648270231, 10.587728007294276, 9.143446083457711, 7.711932305068919, 6.323057267121432, 5.003944843163449, 3.7784617075883546, 2.666788939097806, 1.6850841045798453, 0.8452403705218409, 0.15474720783455093, -0.38334250896250777, -0.770345071366659, -1.011791840506016, -1.1171535046820158, -1.0994665235511634, -0.9748753814171325, -0.7621011435241257, -0.4818484317426101, -0.1561643272394055, 0.1922347091506332, 0.5406529187760166, 0.8671195024403993, 1.1510737285426358, 1.3740153582167214, 1.5201061327920682, 1.5767073152731197, 1.5348394752102534, 1.3895521988040167, 1.140194576274287, 0.7905802757806495, 0.3490269941719699, -0.17172538546652846, -0.7547173712359535, -1.3790924126337378, -2.020535056065472, -2.6518177373408696, -3.2434467424944726, -3.764397335104469, -4.182930794731358, -4.46746214645866, -4.587463297989844, -4.514385290261657, -4.222578778309036, -3.690192103396938, -2.9000262609720084, -1.8403264285759666, -0.5054954280875675, 1.1032876574426846, 2.9776049020989865, 5.101462676691299, 7.451097149060664, 9.994936831105948, 12.693728697458946, 15.500831266510799, 18.36267477030253, 21.21939581648173, 24.005672198600692, 26.65166291637078, 29.084076113645484, 31.22735880108023, 33.00498313881432, 34.340807529192695, 35.160488777370205, 35.39292000416792, 34.97170647862531, 33.83671154553258, 31.93532722483667, 29.223702505807186, 25.66789332238004, 21.24487689043158, 15.943408216932978, 9.76469907290476, 2.7229026157743483, -5.154569976763631, -13.826881084917584, -23.240078895125446, -33.32755096196117, -44.01065951073578, -55.19959304056363, -66.79442335092547, -78.68635322802584, -90.75913636309834, -102.8906569866899, -114.95469005029653, -126.82273151397996, -138.3658589387962, -149.45662486034024, -159.97095047877997, -169.78998730076626, -178.8019146576107, -186.9036418994453, -194.00245947301696, -200.01770374134455, -204.88180111481702, -208.54121657439006, -210.95724993069632, -212.1065980477205, -211.98167330938753, -210.5906728929272, -207.9573978081895, -204.1209163592465, -199.13514128271038, -193.0675983602745, -185.99820149858826, -178.01793992923086, -169.22740396142197, -159.73517570923468, -149.65611344667272, -139.109559947954, -128.21755205431253, -117.1030551558181, -105.88790692780724, -94.69099357752843, -83.62657313130993, -72.80271359555302, -62.31987093247966, -52.26962892349756, -42.733619745756364, -33.782628642909934, -25.475853354840492, -17.86044347414094, -10.971294426931884, -4.83105444021555, 0.5496587613968249, 5.171841486004727, 9.047501289929887, 12.198884530249138, 14.657582648101009, 16.46355746025121, 17.66387215369588, 18.311410889055672, 18.463582575759183, 18.181004964517673, 17.526195196688086, 16.562292056959926, 15.351833808656984, 13.955623414184085, 12.431690834513946, 10.834301228132865, 9.213148507819017, 7.6127073983209845, 6.07173575703207, 4.62293060998485, 3.2927380178504735, 2.10131363358238, 1.0626214584113334, 0.18465246480267067, -0.5301916800095628, -1.084607999550785, -1.4858160182391738, -1.7449093880008415, -1.876154384343087, -1.8962548027498507, -1.823602828064522, -1.6775384530217488, -1.4776325506725425, -1.2429860871162668, -0.9916048793676674, -0.7398520801197517, -0.5019842819024745, -0.28977972782466394, -0.1122645616509449, 0.024459566775497217, 0.11728753320713638, 0.16608612036194936, 0.1735607467908034, 0.14503383096609665, 0.08814586996210683, 0.012489053944106434, -0.07081406724629274, -0.1495732923692847, -0.21102057082872352, -0.24231284910193168, -0.2310359346306819, -0.1656878189389551, -0.03612658910259025, 0.16602627520203195, 0.44703786369099463, 0.8107801103134749, 1.2585175927258674, 1.7887720938109366, 2.39726882063016, 3.0769745502547505, 3.8182144798773865, 4.6088611898461, 5.434593885628797, 6.279220300151518, 7.125052431070683, 7.953326062896857, 8.744653065516049, 9.479508411635756, 10.138763684336439, 10.704140855832971, 11.158658468516679, 11.487059165513797, 11.67619730337047, 11.715377426303814, 11.596635717137875, 11.314958034409138, 10.86844860209711, 10.258461685147106, 9.489538829472323, 8.569309955741165, 7.508344029097528, 6.319934740597457, 5.019827108862676, 3.6258921853743384, 2.157758120546331, 0.636412182315683, -0.9162273830267043, -2.477801226103858, -4.0259682602943085, -5.538846943993041, -6.99543790677686, -8.376018800361056, -9.662503155427444, -10.838756093017807, -11.890874475750675, -12.807452495540506, -13.579714347651626, -14.20159190890771, -14.6697520134214, -14.98356466096843, -15.145014979252814, -15.15856298385927, -15.030956260273536, -14.771020751105242, -14.389454546365988, -13.898475396373138, -13.311485225934804, -12.642743441817293, -11.907038112728328, -11.119362746743715, -10.294605904723538, -9.447260243140146, -8.591168013232675, -7.7393125344079285, -6.903571269029729, -6.094538640284655, -5.321401660121138, -4.591856200143605, -3.9120634751750694, -3.286645312300336, -2.718715868036395, -2.2099494381950677, -1.7606798787918583, -1.3700069503454173, -1.035934976109395, -0.7555305230266955, -0.5250900974979873, -0.3403126762025864, -0.19647209307979507, -0.08858463059722514, -0.011567701540844891, 0.039614264977755984, 0.06982024946111788, 0.08362040628233815, 0.08520374049174634, 0.07830690218044171, 0.0661643931172914, 0.051479819321223176, 0.03641721269284516, 0.022610865663967635, 0.011191689117309552, 0.002828055212892322, -0.002221910841685794, -0.004049435703461093, -0.0030284623406495394, 0.0002538561126578096, 0.005066779782322067, 0.010603168167255945, 0.016041988550146033, 0.020604228736902288, 0.023600178752969932, 0.024467290792287513, 0.02279797663515845, 0.018357029208968822, 0.011088790670355054, 0.0011145654648545768, -0.011278885045188895, -0.02565874532569396, -0.04147236283704006, -0.05807774195823726, -0.07477705436480128, -0.09085167243147414, -0.10559705171540949, -0.11835593298239744, -0.12854847550487478, -0.13569812001562967, -0.13945234990049638, -0.13959747449559162, -0.1360657407735856, -0.1289365044586216, -0.11843127406408051, -0.10490281138770534, -0.08881889684812407, -0.07074156279665679, -0.05130275681104718, -0.03117722301931556, -0.011053154341565381, 0.00839556773141391, 0.026535948552583035, 0.042800478774592324, 0.056708628151111724, 0.06788444277781959, 0.07606962045335063, 0.08113162505549523, 0.08306696013993803, 0.08199963474629675, 0.07817207872121841, 0.07193252031308972, 0.06371885198307652, 0.05403926940067594, 0.04345049039921824, 0.03253443609880419, 0.021874298689563382, 0.012030988559792599, 0.0035209106911651394, -0.0032042342755657293, -0.007774275878726065, -0.009913805491073466, -0.009451485570258109, -0.006325166313980254, -0.000582699872052474, 0.0076214967142584165, 0.018034391961043006, 0.030317673209274452, 0.04406213451847178, 0.05880444778538809, 0.07404587462413294, 0.08927186782729203, 0.10397179892482161, 0.11765806317514613, 0.12988385478622094, 0.14026020610967638, 0.14847335268626333, 0.1542916349447507, 0.15757054600591783, 0.15825534553147577, 0.15638015257430068, 0.15206366802334467, 0.14550180180288452, 0.13695759078376005, 0.1267499774294742, 0.11524255468220908, 0.10282408628413642, 0.08989145651418948, 0.07683422038124188, 0.06402017020675992, 0.05178246797708347, 0.040408810304375875, 0.03013299414415802, 0.021129468772193866, 0.013510822252261693, 0.007325886897074491, 0.0025622134297089007, -0.0008484336819695859, -0.003022395898881683, -0.004114703910267518, -0.004308436328149363, -0.0038034052858662683, -0.00280475051256619, -0.0015120598438726116, -0.00010931195679900897, 0.0012438390395145696, 0.002418866365405135, 0.0033229560089547143, 0.003901195165165096, 0.004136305702247201, 0.004045987882241547, 0.0036780618720843065, 0.003103721865254902, 0.0024092410821142914, 0.0016865808585739383, 0.0010234879906790744, 0.0004936637208357784, 0.00014758739360188478, 4.553148493962421e-06, 4.6426277735349725e-05, 0.00021354706385240806, 0.00040310786525164154, 0.0004702559676989727, 0.0002320107759263057, -0.000526078870115441, -0.0020407428895395565, -0.004559606791330379, -0.008328086356872414, -0.01357513778973241, -0.020498516810237937, -0.029250237127168323, -0.03992306193850627, -0.05253875395109442, -0.06703877473824454, -0.08327806395600472, -0.10102241469711176, -0.11994982258351293, -0.13965602340300626, -0.15966429247664227, -0.179439413337499, -0.19840513389585943, -0.2159648140011365, -0.23152453840655754, -0.2445177850184572, -0.25443064380481334, -0.26082649063681657, -0.26336897064485293, -0.26184216595211024, -0.25616675166877595, -0.246410962338272, -0.2327959897949595, -0.2156949976762514, -0.19562525050767063, -0.1732331609998848, -0.14927233903226364, -0.12457502124497087, -0.10001740556922298, -0.07647978315613845, -0.054804113928784245, -0.03574912203750908, -0.019944614187540375, -0.00784694757269407, 0.0003024900577235414, 0.004513898613903612, 0.0050789333430633484, 0.0025920039760028765, -0.002038790776970881, -0.007591215853466397, -0.012539809646155614, -0.015079071739786275, -0.01315909380427371, -0.0045333877836026895, 0.013181769977284189, 0.04243760127217028, 0.08567535883617204, 0.14524763324037954, 0.22333315283759728, 0.3218492643252428, 0.4423660283670153, 0.5860242257248403, 0.7534600849260145, 0.9447395053817528, 1.159304425680074, 1.3959429858042522, 1.6528051131313242, 1.9273904158016795, 2.2165595142844396, 2.51657092591185, 2.8231365753949023, 3.1314953117666886, 3.436503271927099, 3.7327393997001783, 4.014647675507861, 4.276747453230149, 4.513713101005244, 4.720484799860493, 4.892398261278746, 5.025308963500684, 5.1157074585090685, 5.160822437816147, 5.1587084737859525, 5.108347396398916, 5.0097904502076345, 4.86408023149725, 4.673209487189458, 4.440088031826644, 4.168486699525853, 3.8629594792580657, 3.52874556478297, 3.171653596301263, 2.7979534450079298, 2.4142865410595893, 2.0274193295561465, 1.6440589805695252, 1.2706976769239364, 0.9134635483759017, 0.5779820822533275, 0.2692515506983811, -0.008464386896762984, -0.2517190284098523, -0.4579453283311265, -0.625532217167719, -0.7538422594125463, -0.8431946350811623, -0.894823145443399, -0.9108109196377632, -0.894004106475388, -0.8479073713790054, -0.7765682120341175, -0.6844592747776557, -0.5763287394572628, -0.4570490028277202, -0.33147042240966423, -0.20428145503247536, -0.07987908752930618, 0.03774695825186726, 0.14511326859818313, 0.2393205183558648, 0.3181091313279848, 0.37990783084824753, 0.42385027738541714, 0.4497655566112031, 0.45814655985955155, 0.4500981325042895, 0.4272674382721553, 0.3917594646747363, 0.34604140398776495, 0.29284057354341325, 0.23503486801591547, 0.17554148086267404, 0.11720916289548697, 0.06271742887376713, 0.014485906109218702, -0.025403444847239713, -0.05526904596528812, -0.07387564928144046, -0.080463105314504, -0.07475821886692166, -0.05696739878091549, -0.027751887892383448, 0.011812610093875745, 0.060289854168556166, 0.11594807568364103, 0.176833300125976, 0.240847841156243, 0.30583091014578806, 0.36963983932569894, 0.4302272623970998, 0.485711619355335, 0.5344387741188777, 0.5750327753871367, 0.6064342704058471, 0.6279256009734333, 0.6391423437072803, 0.6400717604094491, 0.6310371117398127, 0.6126700710868546, 0.5858728544246737, 0.5517718260297203, 0.5116647535332145, 0.46696406105231264, 0.41913850625561777, 0.3696557288275953, 0.31992793010882437, 0.27126246180379815, 0.22481962796138474, 0.18157898001298306, 0.14231507236999108, 0.10758327489411035, 0.07771578883066027, 0.052827566733529584, 0.032831350207973946, 0.017460783198232237, 0.0063005913552961765, -0.0011786972026986491, -0.005583117775296266, -0.007556575969055191, -0.007743053896077438, -0.006751594735762336, -0.005125782326314002, -0.003319174075075115, -0.0016778639302339397, -0.00043118041417598493, 0.0003093313471264829, 0.0005426846663668299, 0.0003633734728755427, -6.076215774375994e-05, -0.0005165723443988943, -0.0007780678869922443, -0.0006415975450472438, 3.8246245434291596e-05, 0.001313951119856573, 0.0031134320813637393, 0.005213240420136195, 0.007218312683156415, 0.008549702873483278, 0.008441442211551955, 0.005947314239782708, -4.2209066406437697e-05, -0.010773973433450785, -0.0275972560073168, -0.05192040939904472, -0.08516057957208698, -0.12868811462712468, -0.1837675666012925, -0.2514974079787317, -0.33275073291228485, -0.42812261584766564, -0.5378950811916443, -0.6619955284020763, -0.7999652585556567, -0.9509410978042672, -1.1136490368654324, -1.2864106315394002, -1.4671625005230178, -1.6534888265714898, -1.8426782924171798, -2.0318244735304622, -2.2178697603031643, -2.3976677048018953, -2.5680599000135973, -2.725955232893228, -2.868409172189131, -2.992700722552583, -3.0964047205134686, -3.177476996175701, -3.234372469366361, -3.2660324479308342, -3.2718916581883017, -3.2518907742531145, -3.206475414180878, -3.1365817491091446, -3.043609269199745, -2.929381626716717, -2.7961146946502, -2.646404995933758, -2.4830967505401347, -2.309187292856343, -2.127750187296658, -1.9418591566030687, -1.75451499442421, -1.5685774694039707, -1.3867040068789465, -1.2113054061066815, -1.0445208233953158, -0.8881458953339073, -0.7436024911504603, -0.6119311435879362, -0.49379492110338363, -0.3894939039204205, -0.2989891306878847, -0.221934639716162, -0.15771781071861693, -0.10550489158814871, -0.06427820862602764, -0.032884624562786804, -0.010085979290750348, 0.005392914546209665, 0.014820180761124183, 0.01941789497130769, 0.020329122649869656, 0.018591661773589327, 0.015119065331820137, 0.010688011006769952, 0.005932035874803779, 0.0013418574349782135, -0.002728462875535771, -0.0060504726787886, -0.008506472715737068, -0.010071985679490397, -0.010796680692692906, -0.010784911513712832, -0.010176843466425587, -0.009130805358222095, -0.007807755851331278, -0.006358447921052399, -0.004913636659233992, -0.003577469215921323, -0.0024240001861175657, -0.001496607095466201, -0.0008099168123087717, -0.0003537081928207966, -9.832169703873531e-05, -9.379231577178199e-07, -1.2103357442975455e-05, -8.19356097425135e-05, -0.00016551809021818305, -0.00022709968750058234, -0.00024284071322763044, -0.00020198535186001607, -0.00010647613553726876, 3.084708732979603e-05, 0.00018919457263333493, 0.0003435577867592754, 0.0004687983184509675, 0.0005436400295717347, 0.0005541184543780788, 0.0004960881786562138, 0.0003764694803927331, 0.00021302039666530698, 3.2570742252257455e-05, -0.000132201241655227, -0.0002472108770589764, -0.00028223431191495564, -0.00021646910227150166, -4.3743433833090374e-05, 0.00022334806975571808, 0.0005511370280487984, 0.0008851322024969245, 0.001153492670608186, 0.0012742677409786011, 0.0011667719916936459, 0.0007672411942604089, 4.865216249283685e-05, -0.0009557028039914929, -0.0021256103483998836, -0.003225289888131672, -0.003873852352937043, -0.0035164262698880334, -0.0013976662543102542, 0.003460509609056634, 0.01227503044180643, 0.026509723036393318, 0.047873502050832434, 0.07830781604555538, 0.11996479726667231, 0.17517065087363082, 0.24637565800179906, 0.3360915400456823, 0.44681653538572097, 0.5809494748442205, 0.7406947342902173, 0.9279605207700603, 1.14426067740617, 1.3906408325966158, 1.6675760403366766, 1.9748788224429856, 2.3116235238209724, 2.6760856261098245, 3.0656994909096027, 3.477037667802687, 3.9058144283756744, 4.346941766662435, 4.794684284635414, 5.242699071386826, 5.684125146655199, 6.11171695162393, 6.517997758020095, 6.895429626381, 7.236595817527854, 7.534390924193829, 7.782262473565329, 7.974557803436001, 8.106567618945025, 8.174626625565764, 8.17623704227388, 8.110165003386086, 7.976506120985471, 7.776717277596212, 7.513612634889345, 7.19137381231864, 6.815611037564365, 6.393064082274595, 5.931385899426251, 5.43895395840544, 4.924661008460967, 4.397691189375526, 3.867287920853009, 3.3425203262357313, 2.8320816576481125, 2.344127739799452, 1.8859570931948078, 1.4638112484633585, 1.0827424061798148, 0.746519118432253, 0.45757236847393745, 0.216983125896979, 0.024511125940574266, -0.12133396752252448, -0.22319076068997962, -0.28473005393727546, -0.3104811019041835, -0.3056308229967855, -0.27580984147926846, -0.22687316826100926, -0.16468333877880723, -0.09490357117259192, -0.022810271965533705, 0.04686820152402685, 0.11010071065288822, 0.16366301247542037, 0.20520658708061143, 0.23328780754107054, 0.2473577996014415, 0.24771484914759714, 0.23542262404661476, 0.2121989964531243, 0.18028223862766338, 0.1422774216169546, 0.1009899830437726, 0.05925626063007263, 0.01977880374706075, -0.01502621270888875, -0.04316282503086519, -0.06316465725994262, -0.07417534309951576, -0.0759974451851937, -0.06910702843152243, -0.054632293316588657, -0.03429843422848148, -0.01034172902236282, 0.01460288831049592, 0.03763536051405733, 0.05573881955400889, 0.06593580914039222, 0.06544600616647127, 0.05183737153782611, 0.02316240362969765, -0.021926432669533893, -0.0840875587307017, -0.1632317612262643, -0.25849726473549767, -0.3682598573142287, -0.49017780529703026, -0.6212703274110853, -0.7580279404075313, -0.896547508909271, -1.0326865649091166, -1.162230377469433, -1.2810643941148843, -1.385344389650981, -1.4716567127391862, -1.5371630495303077, -1.5797252883241868, -1.5979912300803756, -1.5914489024659852, -1.5604463006338225, -1.5061740999328967, -1.4306120191588245, -1.33644116821893, -1.226926280785381, -1.1057744081518974, -0.976976445263322, -0.8446292193670893, -0.7127596441061632, -0.5851561082362332, -0.4652133604086053, -0.3557982041921818, -0.2591424138571963, -0.17676806739583342, -0.10944897122867638, -0.05721009715379907, -0.01936602794666409, 0.005403692521010596, 0.01894648910030162, 0.023501159582028135, 0.021541339634868564, 0.0156057737772972, 0.008123970468468158, 0.0012462578153219798, -0.0033123546796319527, -0.004405280264878314, -0.0015577231078341461, 0.0049658934379447055, 0.014135255330626085, 0.024171231742366767, 0.032607704577363054, 0.03639706556875844, 0.03205640695560252, 0.01584771046332358, -0.016019571495729093, -0.0671679227135105, -0.14082326964825154, -0.23958955760050815, -0.36523728714190545, -0.5185167761542124, -0.6990063240287594, -0.9050115506959436, -1.1335428857196381, -1.3803192061271066, -1.6398292704361632, -1.9054555926535632, -2.1696539553944563, -2.424183807724783, -2.6603824841982835, -2.8694740682089597, -3.0429250774271703, -3.1728663089440077, -3.2523721744049245, -3.2757465529968073, -3.238795268367025, -3.1390528686828807, -2.9759531474465395, -2.7509346928686536, -2.467474987888863, -2.131070735272533, -1.7491681902967633, -1.3308685152222268, -0.886625078849955, -0.42790901277977766, 0.03317026492242738, 0.48427618942755835, 0.91327303665621, 1.3086550229255316, 1.6599638645981272, 1.9582039725389788, 2.1962012925601906, 2.368867236512313, 2.4733839789057463, 2.5093060242918472, 2.4785736688922713, 2.3854372878365853, 2.236294746272238, 2.0394626030711738, 1.8049019088116345, 1.5437819550033682, 1.2680244043525553, 0.9898358698833235, 0.7212325347022652, 0.47357543088748577, 0.25713451895085115, 0.08069853594360507, -0.048750962160945044, -0.12629574530004653, -0.1492781894064513, -0.11738100318770983, -0.032604486739871236, 0.10085063698211073, 0.2767889983862722, 0.48730559505202836, 0.7231375288086801, 0.9740659328712111, 1.2293522263627163, 1.4782040176553402, 1.7102334140506104, 1.9158890379318878, 2.086845275636768, 2.216332692866159, 2.2993962562011467, 2.3330712434208096, 2.3164743219378607, 2.250813316058652, 2.1392824967855053, 1.9868747847450454, 1.8001209904706177, 1.586765790523899, 1.3553960024905292, 1.1150386781064259, 0.874747696715641, 0.6432002118890991, 0.4283207765345598, 0.23693224733577758, 0.07447467689220473, -0.05520125683540001, -0.14996071676195163, -0.20942628358517004, -0.23493389703220846, -0.22940647400816122, -0.1971524550147914, -0.14360047387140215, -0.07498346143197748, 0.0020116621713767483, 0.08061001292156247, 0.154311899061732, 0.2172348241716237, 0.2644171440474993, 0.2920681068388967, 0.29775018132853526, 0.2804791413571428, 0.24074845756812083, 0.18047387439137053, 0.10285964271339933, 0.012194323907390598, -0.08641297475248685, -0.1873419193261965, -0.2847993059101055, -0.37317571465749994, -0.44741012262045105, -0.5032789958249704, -0.5376483173030923, -0.5486712970897138, -0.5359131277391607, -0.5003945194100016, -0.4445498516617638, -0.3721001997348587, -0.28784996303565574, -0.19741039706650015, -0.10683397932650254, -0.022232642425651036, 0.05061425017963337, 0.10664705925484677, 0.1418863289274995, 0.1537452946731047, 0.14127483747599393, 0.1053295602011554, 0.04864918369930501, -0.024204355122002294, -0.10701705547139749, -0.1921940493701982, -0.27112696197815805, -0.3346427066871571, -0.3735140693013758, -0.3790082295675318, -0.34344362383757, -0.2607286515305059, -0.1268678577332491, 0.05962802335324254, 0.2974448395131348, 0.5822990172262131, 0.9069199425044253, 1.2611916460816135, 1.6324576386563214, 2.005988304896205, 2.365608479036136, 2.6944397477182704, 2.9757392388108364, 3.193801245047635, 3.3348801242851893, 3.3880915869624197, 3.346247874468535, 3.206582588771399, 2.971330256150384, 2.6481227982590845, 2.2501071263008643, 1.7958327487426502, 1.3088903094145699, 0.8172923084321878, 0.3526063475372714, -0.05113748237005571, -0.3587325082798777, -0.5352417313311552, -0.5475749627103834, -0.366045156207816, 0.03411812037430368, 0.6713527811312753, 1.5565168432251466, 2.691871004696605, 4.070346310643943, 5.675143252319652, 7.479701883586002, 9.448114023958647, 11.535959691181846, 13.691490238241272, 15.857157964851123, 17.971452245950022, 19.970983764531944, 21.792746121001024, 23.376474036598243, 24.66708454883665, 25.617232793981678, 26.189257226117967, 26.356895656420726, 26.106692693565428, 25.438969163759307, 24.368298824364434, 22.92345468396807, 21.146806221828598, 19.093252799308587, 16.82875706117223, 14.427835543534458, 11.97084180531663, 9.541026006099695, 7.221382630108855, 5.091399926303486, 3.223831771010209, 1.6816155015174097, 0.5150704618182608, -0.2405395849472235, -0.5670417128061379, -0.46468021433922624, 0.047246251290152495, 0.9304529805208348, 2.1284603358116345, 3.5680986224007034, 5.161691167184466, 6.809863316407787, 8.40493446382466, 9.834716096486288, 10.986576268064741, 11.751640844753869, 12.028978549885121, 11.729617482151633, 10.780244325034337, 9.126446438737787, 6.735406556259984, 3.5979576172922907, -0.27040139482126946, -4.829261874384359, -10.01388433771632, -15.73662692125015, -21.889183800907112, -28.34556448369197, -34.96571801686918, -41.599743607300326, -48.09271194343013, -54.289425869684486, -60.03920029660998, -65.20055362322876, -69.64561307978865, -73.2640827894572, -75.96663912154263, -77.68763851742192, -78.38720152687192, -78.05276712709387, -76.69880863307394, -74.36593390662757, -71.11930076189022, -67.04626535388469, -62.25335587869969, -56.86268659294565, -51.007945400049586, -44.8301785329189, -38.473516097751435, -32.08040507693271, -25.787328171502786, -19.720966234072637, -13.994828416510261, -8.706452775503314, -3.9352565405504114, 0.258910744182059, 3.8365041147989936, 6.778343557236702, 9.084847255289477, 10.774617456000945, 11.882488465920575, 12.457123461231495, 12.55827217811463, 12.253810047151088, 11.616682879710375, 10.721885003660393, 9.643563260535645, 8.452330311466763, 7.212991777518018, 5.982706415604708, 4.809612653558225, 3.7319466480032877, 2.777655183801091, 1.9644855817880702, 1.300503909998317, 0.7849874687959418, 0.40971683208389603, 0.16046384089802798, 0.018602358628370817, -0.037232578614513796, -0.029521737922401512, 0.019647184583116872, 0.08990604508816279, 0.1636983155418092, 0.2271040377125552, 0.2703324011234682, 0.2878943105315945, 0.27848000354467356, 0.24456787089984647, 0.1918047818297883, 0.1282085726404971, 0.06325086043665976, 0.006883512841817872, -0.03142882910813854, -0.04360618988797687, -0.023709897132741794, 0.0314773846811956, 0.12207892625306713, 0.2449785632723446, 0.39390933046398247, 0.5597692251622284, 0.7311557896684954, 0.8951186803843529, 1.0379899919331743, 1.1462845522675336, 1.2076236989997418, 1.2116196757721869, 1.1506670128482765, 1.0205922915087493, 0.8211212638545893, 0.5561544975032421, 0.23384412124764156, -0.13372805471458818, -0.5310616897595828, -0.9399344259526992, -1.340272268260392, -1.7111494839203525, -2.0318663100811847, -2.2830480245269054, -2.447709661000914, -2.5122532094012144, -2.4673081593270902, -2.3083349293254316, -2.0359857872916667, -1.656205065626916, -1.1800604722496921, -0.6233111933492183, -0.0057321392323349055, 0.6497681943038465, 1.3182029011789282, 1.9737289473642665, 2.59089499740002, 3.145863912666225, 3.617554576004024, 3.988643822853705, 4.2463765442893555, 4.383142014549373, 4.396800842206583, 4.2907642518429965, 4.073699039696461, 3.7589759934555182, 3.363893374768136, 2.9087075491399124, 2.415525247879512, 1.9071192810979345, 1.4057334986953811, 0.9319466885902856, 0.503647912037539, 0.13515840555056002, -0.16339022263131142, -0.3864104277232385, -0.5329363368116595, -0.606424398883084, -0.6142934782602797, -0.5672364879404053, -0.47835348885500484, -0.36216318902852135, -0.23352485800036318, -0.10658385422479745, 0.006192726564735988, 0.09482958375979154, 0.15245029424865464, 0.17563563303656649, 0.16450730340431485, 0.12253138851442472, 0.056056299676282166, -0.02639591039207126, -0.11502224308063554, -0.19974323234340427, -0.27123809491547285, -0.32192109927128676, -0.3467678971239384, -0.34390495041036373, -0.31488626070411635, -0.26459860460190227, -0.20075608285400792, -0.13297897614894744, -0.07148210810485922, -0.02543004095833255, -0.0010498565988125946, 0.00037628500628405245, -0.015510953429240243, -0.03437144696921985, -0.031775525556729516, 0.027618462711134953, 0.1901426641800492, 0.5122945943554549, 1.0588796949446435, 1.900034262506558, 3.1070933871145288, 4.747329623728139, 6.877697613746002, 9.537906443151892, 12.742778348727064, 16.474295877019777, 20.673735808180624, 25.234283264759842, 29.994578616407214, 34.733672664160075, 39.167869845975645, 42.95025261731655, 45.673930631477376, 46.87658810125813, 46.048477969697466, 42.644028772695094, 36.0968183463946, 25.837789653718723, 11.316440109135897, -7.975433560340885, -32.47759634008877, -62.533758878424734, -98.3670556404861, -140.0551091103276, -187.50629073335125, -240.4386866671832, -298.36278753168665, -360.568894162199, -426.1201677790518, -493.85355479434907, -562.3932435345649, -630.1657007268349, -695.4217846950585, -756.2670881552398, -810.6993846987302, -856.6526300031405, -892.0467251554675, -914.8420136064414, -923.1018056937477, -915.0678225577125, -889.2088675839212, -844.2727248267355, -779.338187013207, -693.8615421729477, -587.715898446498, -461.22184803630034, -315.16814154736704, -150.82534647382715, 30.047483752914673, 225.23746819950117, 432.1141492298213, 647.6730234877052, 868.5902666349875, 1091.2875667531039, 1312.0056714548916, 1526.8849745808604, 1732.0532312819407, 1923.7262404089252, 2098.301365776488, 2252.443435460601, 2383.165892338368, 2487.9044632907885, 2564.581319612368, 2611.6579418201604, 2628.175193769528, 2613.786526585321, 2568.7921920178655, 2494.1147367872027, 2391.2685061317584, 2262.320884778056, 2109.8399738756802, 1936.8302126324136, 1746.657774377169, 1542.9678323535893, 1329.6011238465414, 1110.513725837732, 889.6614074408724, 670.9007485464822, 457.9012413800445, 254.064774452711, 62.454526994853964, -114.26502256280803, -273.8756377519177, -414.63933712211167, -535.3213007812311, -635.2010413367367, -714.0637539168952, -772.1773186436459, -810.2571919771435, -829.4207571738967, -831.1329643130989, -817.145283130174, -789.4316694531361, -750.1253404580972, -701.4453879250575, -645.6277462166166, -584.8617898714616, -521.2328514351034, -456.67212455902995, -392.9150951908425, -331.46929768682736, -273.59240581651096, -220.28072887042427, -172.26351129829922, -130.0084211877883, -93.73603991465114, -63.44150219383752, -38.92196843093484, -19.808483396961932, -5.600707257371269, 4.2969877398349565, 10.539550396235885, 13.806864293287, 14.7719679803936, 14.073024356135788, 12.289878859717744, 9.92577691418585, 7.394562667750008, 5.013433490560087, 3.0010768062189923, 1.4808203802842694, 0.48831128767031107, -0.01716542514183394, -0.13855186593607752, -0.02495465154605712, 0.14541528669583068, 0.1823835667799572, -0.09983071787657594, -0.8678316224420576, -2.2565799297474407, -4.359684015417073, -7.222716429542873, -10.839745209674575, -15.1530891721646, -20.056153144760987, -25.39905781782567, -30.99665592804789, -36.63856884965978, -42.10082480454403, -47.15720485449784, -51.590722479619835, -55.20463603326337, -57.8323340792487, -59.3456287487799, -59.6610809913405, -58.7440847719622, -56.61056661485869, -53.325973614370746, -49.00155643913357, -43.789019692216264, -37.873507728409294, -31.465200398435204, -24.789932079815383, -18.079281242557183, -11.560591388024934, -5.447115890024105, 0.07157676399876303, 4.836245929577333, 8.723358875095286, 11.648983558185883, 13.570848412204827, 14.488537857169634, 14.441873902684483, 13.50761138214986, 11.794694541339636, 9.438008645163066, 6.590618153510874, 3.4161563323627306, 0.08126346792435375, -3.251731929800415, -6.4315809374633774, -9.324059738135093, -11.816868234514965, -13.823592287106996, -15.286988077003294, -16.17910031292759, -16.50027201867696, -16.277157241280666, -15.559659271744644, -14.416995326817293, -12.93311681552735, -11.201731150479548, -9.321357514228653, -7.390644862150814, -5.502779093192904, -3.7411255599956244, -2.175878725479137, -0.8615998871659012, 0.16429785804007124, 0.8821068463236513, 1.289459947253726, 1.400115941501136, 1.2420549620433043, 0.8549884370026549, 0.28729616028620014, -0.407278518730822, -1.1729610350143969, -1.9551287143789466, -2.7031875979338804, -3.3730122389831814, -3.9288587241414836, -4.3447250764931855, -4.605033476845608, -4.704638721399603, -4.648235948959361, -4.449244209246207, -4.12826859073612, -3.711260447655051, -3.2275044743084647, -2.7075779282403247, -2.181408426359702, -1.6764187241793203, -1.2160088224937105, -0.8184288146943507, -0.4960704707031206, -0.2551939641658501, -0.09607807424894395, -0.01355630911643689, 0.0021210055130830964, -0.03582119609564455, -0.11195421000935217, -0.2099896103696366, -0.3140897096695461, -0.4100527370554741, -0.48629481838401595, -0.5345681127428311, -0.5503751776116499, -0.5330629519492024, -0.4856035711854963, -0.4140849663621, -0.32696270496670027, -0.23413933197757172, -0.1459482246765249, -0.07212556314141949, -0.020854342455560865, 0.002041286269158703, -0.0063158544233383, -0.045538122227296036, -0.11195354167292854, -0.19888884000514734, -0.29724105448193605, -0.3962989408669527, -0.4847537868346392, -0.55182124004964, -0.5883824635668348, -0.5880464252013604, -0.5480288995500714, -0.4697466645663512, -0.35906980272588174, -0.22616762864315174, -0.08490991171013722, 0.048184763635167265, 0.15543064979328666, 0.21983144058765705, 0.22722710226712656, 0.16860711088446584, 0.042431084501186205, -0.14315300828697614, -0.36835364929707276, -0.6002046150497586, -0.7916081643781508, -0.8810866106728136, -0.7933513270602502, -0.44075823231492356, 0.2744049643061403, 1.4568472993835528, 3.2143978410861265, 5.653445116768743, 8.873841938307686, 12.96345919246522, 17.992605110803662, 24.008552210692592, 31.030778949837515, 39.04813475370613, 48.01544240391917, 57.85119990375078, 68.43673704555279, 79.61673121774719, 91.2011622098155, 102.96873320491063, 114.67172846693715, 126.04351863805842, 136.81069371749714, 146.69884206519748, 155.44010168615637, 162.78200090575515, 168.49619881343887, 172.38680879660924, 174.29799194132806, 174.1205219588322, 171.79895757036468, 167.34098447552347, 160.81301583531828, 152.33739744933658, 142.0896457291377, 130.29390508957164, 117.21675661081257, 103.15956839969388, 88.44963052003807, 73.43153877927801, 58.45927847365311, 43.880102814312814, 30.022481738885, 17.18621392055195, 5.633614017950297, -4.417936219903066, -12.801835884453373, -19.406333771577405, -24.17665613160774, -27.115722630728364, -28.283386844780285, -27.792436090032332, -25.802660733686658, -22.513498442241236, -18.15556583859578, -12.981420232675708, -7.255910716494966, -1.246678666413612, 4.784778565791657, 10.592839620338873, 15.95604094276344, 20.68382146133716, 24.621748335784478, 27.65509880237537, 29.71074334230881, 30.75734444155645, 30.803982629092577, 29.897511488177887, 28.11846310059357, 25.57567427199701, 22.40010713162454, 18.7381752048545, 14.744881437314683, 10.57706456546062, 6.387028152943268, 2.3168297801521818, -1.5065824581836467, -4.975522447537303, -8.004491798521991, -10.531895697037616, -12.52060060483712, -13.957392270150088, -14.851438334519793, -15.231898073841661, -15.144877592890339, -14.649948546444154, -13.816205827347039, -12.718277546186822, -11.43247022080774, -10.033198958372628, -8.589850533328072, -7.164195172554986, -5.808427126236626, -4.563883099748686, -3.4604376873140517, -2.5165057997454947, -1.739670940981476, -1.1278206227281997, -0.6706706409635705, -0.3515579964174632, -0.14937699224426804, -0.040534868086969274, -0.0008116918407639941, -0.007025763260819704, -0.038420133636577605, -0.07770491728059134, -0.11172744538003856, -0.13176338130036622, -0.13344466443934205, -0.11636152650184368, -0.08339387630059414, -0.03984109356480147, 0.007572269022299004, 0.05172882137252059, 0.0861070542793873, 0.10565743022274404, 0.10750569992467263, 0.09143709560674314, 0.060131462280993635, 0.019137122894810375, -0.023412943586634732, -0.05732103004638404, -0.07101489273253442, -0.05237067285814777, 0.010387484483030328, 0.12777496884126044, 0.30818376375428513, 0.5571278033189965, 0.8766483213175923, 1.2649398944575174, 1.7162876158092435, 2.221175465731378, 2.766615373591862, 3.3366970953633386, 3.9133173384218867, 4.477046236210559, 5.008081474080362, 5.4872355006236555, 5.896972795893795, 6.222540568878115, 6.452523520690997, 6.579303623425726, 6.5993789506126594, 6.513463740341815, 6.326368868394915, 6.046674306480396, 5.686216625739187, 5.259491511084137, 4.783036723621426, 4.27430608718555, 3.750723805738155, 3.2288665718422767, 2.7237412930671856, 2.248194472579098, 1.8124798893414313, 1.4240005641314843, 1.0872467517386029, 0.8039104019713731, 0.5730451849628129, 0.39145123537336984, 0.25417926701092397, 0.15508648172877135, 0.08740190511860546, 0.04426080709775917, 0.019172599490230532, 0.006393976655745561, 0.0011864347685107235, -5.0606000746701755e-05, 0.0002336599262465322, 0.0006409268222379275, 0.0006310921039336642, 0.0002678493553602262, -6.212543375458137e-05, 8.069901011744237e-05, 0.0009648556370869961, 0.0025411694677804487, 0.004396588059662673, 0.0058210276681421565, 0.005986685858768464, 0.004225346072934918, 0.0003753087138171986, -0.004843193786713003, -0.00947586637313804, -0.010064833380648461, -0.0015259886431663024, 0.022763845043753197, 0.07061681433978031, 0.15037803802730068, 0.2699376755321337, 0.4354061740573865, 0.6494721311847871, 0.90948860717526, 1.2053596864090852, 1.5173277898073025, 1.8137986004627433, 2.0493339970638598, 2.162966850639975, 2.0769972205060765, 1.6964246420499771, 0.9091585528287899, -0.41287292735772135, -2.4116329984402416, -5.239892688112453, -9.05712637062734, -14.024436462963171, -20.29861895247419, -28.025524482817634, -37.33292178402448, -48.32311523917427, -61.06560568404385, -75.59034288093572, -91.8824720753902, -109.87707530478787, -129.45532004671406, -150.4423634638252, -172.60707566827193, -195.66374695957154, -219.27587446745935, -243.06204529159564, -266.6047980401255, -289.4638103898372, -311.18534509012136, -331.3138976797582, -349.4054335952633, -365.0409669870302, -377.8400024385702, -387.4733425646383, -393.67476553468316, -396.25259311805075, -395.1021127789919, -390.2062250857341, -381.63619207880146, -369.5510313922549, -354.19402288473, -335.88638739184296, -315.0183064468557, -292.0375575301178, -267.4371095512881, -241.74232264768546, -215.490685171619, -189.21431916877157, -163.4239937731624, -138.59406959780807, -115.14892545091628, -93.45136409314193, -73.79341868483648, -56.390015436229305, -41.37547391499845, -28.802276290263585, -18.643931062662638, -10.800906861283968, -5.109085771492025, -1.3503334596956003, 0.7352985351216869, 1.4362847997172832, 1.0558381540101136, -0.10189661646082845, -1.745048961479037, -3.6057432018038833, -5.449960588765331, -7.085196085228285, -8.365643898656128, -9.1947628103243, -9.525194983284981, -9.356209385283075, -8.72889069132468, -7.718756966751416, -6.427009915936567, -4.9708553462179985, -3.4733599025980473, -2.0534058780087134, -0.8162930937771714, 0.15450156193498826, 0.8039857210400188, 1.1104190151587718, 1.0876181923608303, 0.784814359708025, 0.28414817171530804, -0.3040747891377367, -0.8481168230343534, -1.2031727312208134, -1.2209217328823, -0.7597825859925859, 0.3046049748014414, 2.0695550955940596, 4.596671300823013, 7.904776521952409, 11.964877007773774, 16.697494742758018, 21.972591483381322, 27.612184138857383, 33.39569630834242, 39.0681795051856, 44.350495983899926, 48.951105398001395, 52.57905803876101, 54.957580480141445, 55.837627790648696, 55.01076578159448, 52.320764834687445, 47.673578815518844, 41.04537906542021, 32.48609271116299, 22.120270030178407, 10.14501156161435, -3.175255186748252, -17.516975206018497, -32.508333849364476, -47.74236459580205, -62.79193110760131, -77.22658735931073, -90.62917235660339, -102.61166811652362, -112.83000794680251, -120.99715078952536, -126.89386785037149, -130.37678794407287, -131.38336761980653, -129.9341055211267, -126.1324092492431, -120.15784427557264, -112.25727788509901, -102.73395398373671, -91.93449812507264, -80.23444372092075, -68.02292666977998, -55.68722262103202, -43.59798759433187, -32.095687484072855, -21.47742368142043, -11.986995269838284, -3.807928785402039, 2.9405761343431136, 8.204697137242334, 11.99408735226559, 14.37720812426663, 15.474269832465856, 15.448262010937627, 14.49398842022243, 12.826203824512687, 10.667512751809923, 8.236587452074723, 5.737280642080504, 3.3491489174689866, 1.2198192159427703, -0.540479325450415, -1.8620518821615826, -2.716349777637599, -3.114066337437946, -3.1009809055737105, -2.751859085127433, -2.162806450727106, -1.4425479107601666, -0.7031552152593772, -0.050768600318910416, 0.42316156197273386, 0.6495812300573482, 0.5879945821262992, 0.23075755587552593, -0.3947429942865989, -1.226161742250313, -2.168535047571318, -3.098782892986427, -3.8721592470193618, -4.330316904716283, -4.310430217303377, -3.6549612398810534, -2.2215573113497853, 0.10746240342835506, 3.4165511831981226, 7.749789147919635, 13.105562574404953, 19.433548379686094, 26.634671690479067, 34.562915997159955, 43.029479489255486, 51.80924656295041, 60.64921937522158, 69.27854280102567, 77.41967401681303, 84.80018612644979, 91.16517431594608, 96.29036165908838, 99.99099536778517, 102.12980522280273, 102.62343380301205, 101.44656112370075, 98.63351379304561, 94.27726267841304, 88.52583213109409, 81.57667834449101, 73.66938673109401, 65.07375531648825, 56.07783161048713, 46.975710658542866, 38.055156771109246, 29.58560448795456, 21.80707711093802, 14.920520130126148, 9.080050224394508, 4.3874259886184435, 0.8886365365433013, -1.4264674895771619, -2.621869067455152, -2.810650447751603, -2.148069866492193, -0.8227856829836504, 0.9533549745618782, 2.956583091279593, 4.963200215834449, 6.760871448146946, 8.159215086315085, 8.999242252458615, 9.161156376277791, 8.570173470136814, 7.200115868896418, 5.074633423024874, 2.26606952809575, -1.108105317160011, -4.891587447730559, -8.897029908349133, -12.9151613134477, -16.724899021433274, -20.103988163375462, -22.83968215883914, -24.738985377465795, -25.63815152537615, -25.411202804844564, -23.97576617421063, -21.297037816983607, -17.38975459376981, -12.317997273237511, -6.192869379551279, 0.8318139447448335, 8.565610109404641, 16.78910913022457, 25.263251881345415, 33.739123827360025, 41.96771772863064, 49.70950515635965, 56.743405408547645, 62.87479193376381, 67.94222897845798, 71.82269510501068, 74.43551746937622, 75.74537855664398, 75.76105712271742, 74.53297624183871, 72.14953902202966, 68.732110633667, 64.4289179156494, 59.40817245005139, 53.85074278007633, 47.942937409335734, 41.86974366742271, 35.8070142749417, 29.915212124729457, 24.334469214503127, 19.180830857115353, 14.543774832421606, 10.48503297838158, 7.038682539125724, 4.212429226182935, 1.9898933844606719, 0.3337035709880063, -0.8105911811274183, -1.5101606979276683, -1.840352165888019, -1.8801969870234079, -1.7081776113352198, -1.3984393176970484, -1.0176031893631547, -0.622286618786352, -0.2573642716807798, 0.04493580376381647, 0.2651406012906632, 0.3959137162350806, 0.44080388468041104, 0.412480909225296, 0.3305982551707733, 0.21943169389347403, 0.10544321611662985, 0.014931123030291298, -0.02809745887648064, -0.0037330964546031195, 0.10243257292808164, 0.2983623638770457, 0.5851149350755426, 0.9568703148737625, 1.4014122949840129, 1.9010205197446772, 2.4336846589843035, 2.974552916101253, 3.4975182104764473, 3.9768390717490756, 4.3886954079496325, 4.712587239709234, 4.932497287389745, 5.037794830998633, 5.023801187496267, 4.891669372654673, 4.64809483260815, 4.304797662761476, 3.877764428831145, 3.386301518932878, 2.8519583200240786, 2.2973816803234786, 1.7452718793877873, 1.2176690955712532, 0.7346102632396659, 0.31291662395175196, -0.03473117298442058, -0.300443720716231, -0.4814501324057288, -0.5800751500224121, -0.6033646979845869, -0.5625294542730798, -0.4717008501887943, -0.3452014016599868, -0.1963742162444317, -0.03703876389027544, 0.12278123367956204, 0.2749082604747052, 0.4128934180480052], 'positive_zeros': ['0.27209906503837975590985142012538', '0.30727357186020914191399400022210', '0.47497166809458440741922416833188', '0.60998738569395788131668772795102', '0.63082410437743297666258354527023', '0.70955100173181058963718795376163', '0.896576100759044872422466053790663', '1.04836522286052447997522316072968', '1.25410797349971780675882248606634', '1.39563740701092533448103691750053', '1.54823061841367043817677571334654', '1.59610614603109010110900058469178', '1.65981694307123596143991567705646', '1.74131751438987520965523153831806', '1.87686254345079078516334174830722', '2.14005692804397796711108720603097', '2.26165419488015092312702968037334', '2.34268436215160821641546194057565', '2.37579386693807429951329819300034', '2.41255066414760367903019367965623', '2.58547665957490445473834213478631', '2.81869847189867481422999757075175', '2.87748820499453005226978796780324', '2.89551315231614828929880403789606', '2.94842751386816726814229854727317', '3.06021745932115770831450582389140', '3.15357675980321499142051530085527', '3.18271824959387129517755257455845', '3.35267059430444272107380662923414', '3.39103236554175777842184530050105', '3.46432971975595020400596646306701', '3.46526790592799558682330347670775', '3.49169711971668579052444022874045', '3.69245622322086862439860021947092', '3.71145735381319461107159329323661', '3.74123982528989120469861008307781', '3.98420644522934291399063417804495', '4.07120260291662482526892678452197', '4.16321611186104038428954041964986', '4.20169581626729240114209884326690', '4.37920753356183536616345529731774', '4.42444416145452993608890468612902', '4.44204185471466239743207909746323', '4.46333502676627517976148921354124', '4.50518109022471362874648656433381', '4.81041870204827440762959512516622', '4.85579646585013298319325010841572', '4.94806447016670639833521950082790', '4.95149392344258258994081471525124', '4.98850798836195132663921394663704', '5.03741839091751550445875763485887', '5.06347938521660418167902030785054', '5.10445415148215811800975826785735', '5.13731755206451746593784146183194', '5.43827204220655642389256862959842', '5.49125349513362546660628206338093', '5.56535276200486265217604638471642', '5.61152603034531108224992821288536', '5.64874976391269848881359210748065', '5.83194884460882889736243075173428', '5.86572401518160359595563354247370', '5.88172864208998093030214428074171', '5.91961006339255585396623229342623', '6.07774913997143546080558106262573', '6.19050138724154898441574804987919', '6.21499684715695860001480771636461', '6.35177937564336824171874049221992', '6.39570053003730489097201731274815', '6.45378420060517604957858522603275', '6.53794496416733056135247621845068', '6.57649777040774506494456111121499', '6.62869365149884668534210920000867', '6.74406804179566840793508370644450', '6.77048515360021923419364758968714', '6.94591289576082436191131734595548', '6.96318665123783022222127260395927', '7.04653990293108210747914158888929', '7.21840522777640307536760914613528', '7.33966534625328628411026342273324', '7.35243452431666261146473803859759', '7.41221358504784497579563779059270', '7.42974330195337793343109679019463', '7.51379254827318083485513964119036', '7.59379659363756853399081327376148', '7.70532630584835389400688466788001', '7.76010364340234992841959273594986', '7.79527913713107333935450530465050', '7.86505730808031806054090994167465', '7.87000450986959475432101413456261', '7.888970686226809574156289358374529'], 'prelabel': '18-8325e9-1.1-c1e9-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.153248412915918, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e9-0', 'trace_hash': 544295857199861890, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.27209906503837975590985142013', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.30727357186020914191399400022', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '0.47497166809458440741922416833', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 2.534849286293968e+16, 'bad_primes': [3, 5, 37], 'central_character': '1.1', 'conductor': 192069399958417858629810333251953125, 'conductor_radical': 555, 'degree': 18, 'dirichlet_coefficients': [1, 5, 0, 9, 0, 0, -8, 5, 0, 0, 0, 0, -6, -40, 0, -6, 18, 0, -4, 0, 0, 0, 16, 0, 0, -30, 0, -72, 2, 0, -6, -14, 0, 90, 0, 0, 9, -20, 0, 0, -2, 0, -14, 0, 0, 80, 34, 0, -3, 0, 0, -54, -4, 0, 0, -40, 0, 10, -10, 0, 8, -30, 0, -14, 0, 0, -16, 162, 0, 0, -8, 0, -8, 45, 0, -36, 0, 0, -26, 0, 0, -10, 70, 0, 0, -70, 0, 0, 8, 0, 48, 144, 0, 170, 0, 0, 2, -15, 0, 0], 'euler11': [1, 0, 57, 24, 1603, 1128, 30009, 25256, 420678, 345392, 4627458, 3055976, 39941979, 16515048, 258164753, 42517464, 1110768747, 0, 2357947691], 'euler13': [1, 6, 77, 372, 2876, 11732, 70148, 248108, 1230478, 3777212, 15996214, 41930252, 154115156, 335077652, 1067838668, 1795572948, 4831635809, 4894384326, 10604499373], 'euler17': [1, -18, 251, -2452, 20402, -140812, 862542, -4621668, 22405796, -96841700, 380898532, -1335662052, 4237668846, -11760759052, 28967922514, -59185319188, 102995006923, -125563633938, 118587876497], 'euler19': [1, 4, 89, 290, 4152, 11570, 133580, 329082, 3268744, 7150996, 62106136, 118798602, 916225220, 1507813970, 10280763048, 13643305490, 79554584771, 67934252164, 322687697779], 'euler2': [1, -5, 16, -40, 87, -171, 312, -524, 820, -1196, 1640, -2096, 2496, -2736, 2784, -2560, 2048, -1280, 512], 'euler23': [1, -16, 281, -2900, 29786, -228568, 1710722, -10342828, 60671240, -295554928, 1395438520, -5471356012, 20814354574, -63962697688, 191712912598, -429304078100, 956755950607, -1252975764496, 1801152661463], 'euler29': [1, -2, 151, -192, 11086, -9472, 547218, -367456, 20374196, -11917948, 590851684, -309030496, 13346099802, -6699365632, 227386597814, -114206077632, 2604731322659, -1000492825922, 14507145975869], 'euler3': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler31': [1, 6, 117, 652, 7900, 42482, 382924, 1922952, 14422916, 67506176, 447110396, 1847956872, 11407688884, 39233019122, 226170292900, 578652400012, 3218975850987, 5117346224646, 26439622160671], 'euler37': [1, -9, 36, -84, 126, -126, 84, -36, 9, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler41': [1, 2, 207, 308, 22135, 23834, 1590167, 1260212, 84684498, 54351400, 3472064418, 2118416372, 109595899807, 67349187674, 2564477009135, 1463032106228, 40314134693367, 15969850458242, 327381934393961], 'euler43': [1, 14, 209, 1776, 13590, 62808, 164694, -1659984, -20033612, -186487436, -861445316, -3069310416, 13094325858, 214728053208, 1997844740370, 11226740775024, 56810089721363, 163634803886414, 502592611936843], 'euler47': [1, -34, 691, -10098, 119667, -1203098, 10717955, -86467054, 648355640, -4565820786, 30472715080, -191005722286, 1112770241965, -5870734451738, 27445028952669, -108848516392242, 350076576239933, -809583746499874, 1119130473102767], 'euler5': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler53': [1, 4, 219, 714, 27303, 82394, 2419235, 6546958, 162792322, 393594900, 8627993066, 18390405022, 360168449095, 650128291514, 11417991545379, 15825353846106, 257261739624303, 249038761645444, 3299763591802133], 'euler59': [1, 10, 363, 2748, 56906, 329642, 5349206, 24228380, 368128354, 1449707336, 21719572886, 84338990780, 1098614579074, 3994391114762, 40683482158894, 115912106445468, 903380488989297, 1468304376043210, 8662995818654939], 'euler61': [1, -8, 287, -2428, 46078, -364856, 5023538, -36330404, 402838300, -2591580928, 24573136300, -135185433284, 1140247678778, -5051738163896, 38917308357478, -125091468948508, 901967193938027, -1533658503978248, 11694146092834141], 'euler67': [1, 16, 457, 5334, 91400, 863542, 11351860, 90969834, 1002999192, 6994279188, 67200945864, 408363584826, 3414219469180, 17401339330582, 123401434779800, 482505010489446, 2769745203632611, 6497082840906256, 27206534396294947], 'euler7': [1, 8, 67, 350, 1751, 6864, 25791, 81794, 251836, 674114, 1762852, 4007906, 8846313, 16480464, 29429057, 41177150, 55177381, 46118408, 40353607], 'euler71': [1, 8, 461, 3084, 101579, 577916, 14118333, 68868932, 1373824126, 5759364312, 97541512946, 347168286212, 5053106682363, 14685817036796, 183271813245229, 395061275612364, 4192850393018251, 5166028249966088, 45848500718449031], 'euler73': [1, 8, 463, 3322, 104127, 660254, 14888495, 82668926, 1491866866, 7163969732, 108906281218, 440542706654, 5791877659415, 18750052213214, 215862725764311, 502732299732058, 5114945514341911, 6451680735152648, 58871586708267913], 'euler79': [1, 26, 763, 13592, 240966, 3294462, 43709806, 481618160, 5120271010, 46351492472, 404501409790, 3005778936560, 21550639040434, 128319561751422, 741465972241434, 3304044695441432, 14652582556439317, 39444829057570586, 119851595982618319], 'euler83': [1, -70, 2739, -75488, 1620083, -28461806, 422117107, -5384607998, 59783071428, -581342998750, 4961994928524, -37094564498222, 241361074260209, -1350749525387726, 6381572782033369, -24680074904879072, 74325643660588353, -157660456249732870, 186940255267540403], 'euler89': [1, -8, 241, 444, 10408, 333920, 750216, 23712740, 328869494, 588300176, 29269384966, 187828613540, 528879023304, 20950889114720, 58118890745192, 220659693186684, 10659751709822489, -31492710445616648, 350356403707485209], 'euler97': [1, -2, 435, -2304, 103150, -691808, 17711706, -115122720, 2305098788, -13060706492, 223594582436, -1083189672480, 16164995850138, -61245264830048, 885784147509550, -1919167499356416, 35147253747979155, -15674867188753922, 760231058654565217], 'euler_factors': [[1, -5, 16, -40, 87, -171, 312, -524, 820, -1196, 1640, -2096, 2496, -2736, 2784, -2560, 2048, -1280, 512], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 8, 67, 350, 1751, 6864, 25791, 81794, 251836, 674114, 1762852, 4007906, 8846313, 16480464, 29429057, 41177150, 55177381, 46118408, 40353607], [1, 0, 57, 24, 1603, 1128, 30009, 25256, 420678, 345392, 4627458, 3055976, 39941979, 16515048, 258164753, 42517464, 1110768747, 0, 2357947691], [1, 6, 77, 372, 2876, 11732, 70148, 248108, 1230478, 3777212, 15996214, 41930252, 154115156, 335077652, 1067838668, 1795572948, 4831635809, 4894384326, 10604499373], [1, -18, 251, -2452, 20402, -140812, 862542, -4621668, 22405796, -96841700, 380898532, -1335662052, 4237668846, -11760759052, 28967922514, -59185319188, 102995006923, -125563633938, 118587876497], [1, 4, 89, 290, 4152, 11570, 133580, 329082, 3268744, 7150996, 62106136, 118798602, 916225220, 1507813970, 10280763048, 13643305490, 79554584771, 67934252164, 322687697779], [1, -16, 281, -2900, 29786, -228568, 1710722, -10342828, 60671240, -295554928, 1395438520, -5471356012, 20814354574, -63962697688, 191712912598, -429304078100, 956755950607, -1252975764496, 1801152661463], [1, -2, 151, -192, 11086, -9472, 547218, -367456, 20374196, -11917948, 590851684, -309030496, 13346099802, -6699365632, 227386597814, -114206077632, 2604731322659, -1000492825922, 14507145975869], [1, 6, 117, 652, 7900, 42482, 382924, 1922952, 14422916, 67506176, 447110396, 1847956872, 11407688884, 39233019122, 226170292900, 578652400012, 3218975850987, 5117346224646, 26439622160671], [1, -9, 36, -84, 126, -126, 84, -36, 9, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 2, 207, 308, 22135, 23834, 1590167, 1260212, 84684498, 54351400, 3472064418, 2118416372, 109595899807, 67349187674, 2564477009135, 1463032106228, 40314134693367, 15969850458242, 327381934393961], [1, 14, 209, 1776, 13590, 62808, 164694, -1659984, -20033612, -186487436, -861445316, -3069310416, 13094325858, 214728053208, 1997844740370, 11226740775024, 56810089721363, 163634803886414, 502592611936843], [1, -34, 691, -10098, 119667, -1203098, 10717955, -86467054, 648355640, -4565820786, 30472715080, -191005722286, 1112770241965, -5870734451738, 27445028952669, -108848516392242, 350076576239933, -809583746499874, 1119130473102767], [1, 4, 219, 714, 27303, 82394, 2419235, 6546958, 162792322, 393594900, 8627993066, 18390405022, 360168449095, 650128291514, 11417991545379, 15825353846106, 257261739624303, 249038761645444, 3299763591802133], [1, 10, 363, 2748, 56906, 329642, 5349206, 24228380, 368128354, 1449707336, 21719572886, 84338990780, 1098614579074, 3994391114762, 40683482158894, 115912106445468, 903380488989297, 1468304376043210, 8662995818654939], [1, -8, 287, -2428, 46078, -364856, 5023538, -36330404, 402838300, -2591580928, 24573136300, -135185433284, 1140247678778, -5051738163896, 38917308357478, -125091468948508, 901967193938027, -1533658503978248, 11694146092834141], [1, 16, 457, 5334, 91400, 863542, 11351860, 90969834, 1002999192, 6994279188, 67200945864, 408363584826, 3414219469180, 17401339330582, 123401434779800, 482505010489446, 2769745203632611, 6497082840906256, 27206534396294947], [1, 8, 461, 3084, 101579, 577916, 14118333, 68868932, 1373824126, 5759364312, 97541512946, 347168286212, 5053106682363, 14685817036796, 183271813245229, 395061275612364, 4192850393018251, 5166028249966088, 45848500718449031], [1, 8, 463, 3322, 104127, 660254, 14888495, 82668926, 1491866866, 7163969732, 108906281218, 440542706654, 5791877659415, 18750052213214, 215862725764311, 502732299732058, 5114945514341911, 6451680735152648, 58871586708267913], [1, 26, 763, 13592, 240966, 3294462, 43709806, 481618160, 5120271010, 46351492472, 404501409790, 3005778936560, 21550639040434, 128319561751422, 741465972241434, 3304044695441432, 14652582556439317, 39444829057570586, 119851595982618319], [1, -70, 2739, -75488, 1620083, -28461806, 422117107, -5384607998, 59783071428, -581342998750, 4961994928524, -37094564498222, 241361074260209, -1350749525387726, 6381572782033369, -24680074904879072, 74325643660588353, -157660456249732870, 186940255267540403], [1, -8, 241, 444, 10408, 333920, 750216, 23712740, 328869494, 588300176, 29269384966, 187828613540, 528879023304, 20950889114720, 58118890745192, 220659693186684, 10659751709822489, -31492710445616648, 350356403707485209], [1, -2, 435, -2304, 103150, -691808, 17711706, -115122720, 2305098788, -13060706492, 223594582436, -1083189672480, 16164995850138, -61245264830048, 885784147509550, -1919167499356416, 35147253747979155, -15674867188753922, 760231058654565217]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8325/2/a/cr'], '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': '18-8325e9-1.1-c1e9-0-0', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1, 1, 1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '18-8325e9-1.1-c1e9-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.153248412915918, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e9-0', 'trace_hash': 544295857199861890, 'z1': {'__RealLiteral__': 0, 'data': '0.27209906503837975590985142013', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '344926543117442127368498630119,389515527802866098274169399042,602098120151503280352741729175,773250875606594180583298654635,799664554552488147117865389566,899462753237871133496572442355,1136545232277488714825747226243,1328960804017545340718695000043,1769180596698369196918601400241', 'Lhash_array': ['344926543117442127368498630119', '389515527802866098274169399042', '602098120151503280352741729175', '773250875606594180583298654635', '799664554552488147117865389566', '899462753237871133496572442355', '1136545232277488714825747226243', '1328960804017545340718695000043', '1769180596698369196918601400241'], 'factors': ['2-8325-1.1-c1-0-5', '2-8325-1.1-c1-0-8', '2-8325-1.1-c1-0-28', '2-8325-1.1-c1-0-55', '2-8325-1.1-c1-0-61', '2-8325-1.1-c1-0-75', '2-8325-1.1-c1-0-119', '2-8325-1.1-c1-0-161', '2-8325-1.1-c1-0-243'], 'label': '18-8325e9-1.1-c1e9-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8325/2/a/cr'}