Table lfunc_lfunctions
L-functions
{'Lhash': '984553320689906909395558565301', 'a10': [0.0, 0.0], 'a2': [0.5, 0.8660254037844386], 'a3': [0.0, 0.0], 'a4': [-0.5, 0.8660254037844386], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-2.0, 1.7320508075688772], 'a8': [-1.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.0183451964044, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [-0.5, -0.8660254037844386]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [2.0, -1.7320508075688772]]]], 'bad_primes': [2, 3, 7], 'central_character': '378.109', 'coefficient_field': 'CDF', 'conductor': 378, 'conductor_radical': 42, 'conjugate': '2925347943332126061938807023437', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-2.5, 4.330127018922194]], [[1.0, 0], [2.0, -1.7320508075688772]], [[1.0, 0], [3.0, -5.196152422706632], [-5.5, -9.526279441628825]], [[1.0, 0], [-5.0, 0], [13.0, 0]], [[1.0, 0], [3.0, -5.196152422706632], [-8.5, -14.722431864335457]], [[1.0, 0], [-2.0, -3.4641016151377544], [-9.5, 16.454482671904334]], [[1.0, 0], [3.0, 5.196152422706632], [-11.5, 19.91858428704209]], [[1.0, 0], [-6.0, 0], [29.0, 0]], [[1.0, 0], [-0.5, 0.8660254037844386], [-15.5, -26.846787517317598]], [[1.0, 0], [-0.5, -0.8660254037844386], [-18.5, 32.04293994002423]], [[1.0, 0], [6.0, 0], [41.0, 0]], [[1.0, 0], [1.0, 0], [43.0, 0]], [[1.0, 0], [-3.0, -5.196152422706632], [-23.5, 40.703193977868615]], [[1.0, 0], [-3.0, 5.196152422706632], [-26.5, -45.89934640057525]], [[1.0, 0], [-3.0, 5.196152422706632], [-29.5, -51.09549882328188]], [[1.0, 0], [-0.5, -0.8660254037844386], [-30.5, 52.827549630850754]], [[1.0, 0], [-0.5, 0.8660254037844386], [-33.5, -58.023702053557386]], [[1.0, 0], [-12.0, 0], [71.0, 0]], [[1.0, 0], [1.0, -1.7320508075688772], [-36.5, -63.21985447626402]], [[1.0, 0], [-0.5, -0.8660254037844386], [-39.5, 68.41600689897065]], [[1.0, 0], [-6.0, 0], [83.0, 0]], [[1.0, 0], [0, 0], [-44.5, 77.07626093681505]], [[1.0, 0], [-17.0, 0], [97.0, 0]], [[1.0, 0], [6.0, -10.392304845413264], [-50.5, -87.4685657822283]], [[1.0, 0], [-9.5, -16.454482671904334], [-51.5, 89.20061658979718]], [[1.0, 0], [9.0, 15.588457268119896], [-53.5, 92.66471820493493]], [[1.0, 0], [2.5, -4.330127018922194], [-54.5, -94.39676901250381]], [[1.0, 0], [-12.0, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 10110600, 'index': 1, 'label': '2-378-7.4-c1-0-1', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/378/2/g/e/109/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 10}, 'plot_values': [1.274064603674392, 1.093822729787215, 0.9133591219762646, 0.725248584443847, 0.5225656153203952, 0.30008820400375036, 0.055182500813689306, -0.2116418633146037, -0.49646449245483626, -0.7919410847336169, -1.0875385844985073, -1.370033061238173, -1.6242866954655835, -1.8343042795574036, -1.984540321974454, -2.0613906902505135, -2.0547633824624603, -1.9595872368278515, -1.777091022742789, -1.5156740382053226, -1.1911979098671368, -0.8265610476717651, -0.45047309952881726, -0.09542471124936952, 0.2050575927112639, 0.4196795077096477, 0.5228804143608013, 0.49819913011117894, 0.34108786830185184, 0.060756410271066014, -0.31931950557530026, -0.7624826686500304, -1.2216674983227278, -1.6437564642253448, -1.9751945594812372, -2.168324933557748, -2.187736430282531, -2.0158113474419226, -1.6566550040893382, -1.1376937978714776, -0.5084477327779549, 0.1636971900272244, 0.8005029666528396, 1.3220552036650708, 1.6570986561168901, 1.7532482502335964, 1.5856572320595637, 1.1627788521418672, 0.5281180812125693, -0.24267736031210263, -1.0494359386392536, -1.7791633173986605, -2.3205387691606085, -2.5793830230330714, -2.4929544541131623, -2.0409033194364095, -1.251014452790501, -0.19848509549918833, 1.001648131179785, 2.2083128608831615, 3.272816504949358, 4.0594249259713395, 4.465143208280334, 4.435654297188247, 3.974768014866508, 3.145584826061829, 2.062782075232121, 0.8768129007203178, -0.24784805896876397, -1.1572020294436665, -1.7311499837299893, -1.9020257502165567, -1.6650665327977145, -1.0788704746024345, -0.25551074700794035, 0.658267403390977, 1.5057501451153086, 2.1467135134172777, 2.4810523399641227, 2.46536322677693, 2.1194146007051686, 1.5211947087995343, 0.7912966893731675, 0.06940436881605325, -0.5128003168724027, -0.8571964121452668, -0.9183010516318106, -0.7120455769905839, -0.31234933235542267, 0.16404816464067049, 0.5816805816419136, 0.814682233946486, 0.7736638971663082, 0.425579887822697, -0.19769528446599002, -1.0041526908056202, -1.8591432902248919, -2.612232945400712, -3.127978382006479, -3.314166480470682, -3.141383095902366, -2.649436592107947, -1.938860235295994, -1.1489196427127746, -0.42658093705141975, 0.1069224642574544, 0.3844762442973549, 0.4097884498893464, 0.25811062648373523, 0.060097952765600184, -0.028277932185010318, 0.13648066897201974, 0.6482379307313081, 1.5233369121375013, 2.68898003497933, 3.991541253077166, 5.224118509766845, 6.168194402629462, 6.640757284446404, 6.5365010465952125, 5.855266126588492, 4.707707663801749, 3.2967552378727767, 1.8778046029831927, 0.7055612674766947, -0.021127705679941405, -0.20412963313206517, 0.12996543101600294, 0.8329335570036592, 1.6654437994682476, 2.3491253617882832, 2.629140051850761, 2.333427070678297, 1.415073534721751, -0.03231199065696752, -1.7904661070522538, -3.560772107354517, -5.027585106212543, -5.926570364561795, -6.102594620850815, -5.543840437335974, -4.384113550129717, -2.8726018331420993, -1.3179298181004837, -0.01942650341192526, 0.7984011551731724, 1.0329149413018137, 0.7210350498294212, 0.023752657908717716, -0.8183309526629406, -1.5472089668095625, -1.9519095035290377, -1.919226524566869, -1.4583425515520756, -0.6936148009313498, 0.1720778976371544, 0.9135129756498045, 1.3439412132871817, 1.364538620425817, 0.9895453956881706, 0.3406123222804259, -0.3879183630745279, -0.9832835334658973, -1.2733206812500477, -1.174101487769461, -0.7130602611776871, -0.021124761977054457, 0.7041636641515335, 1.2545078736812438, 1.4702629145763317, 1.286760173625452, 0.7543138649777483, 0.0258358609562443, -0.6850078987933015, -1.163787990514044, -1.256755655666814, -0.9162542241561552, -0.2167560405981273, 0.6637688065721554, 1.492663648764475, 2.0483024389199933, 2.1841872176583976, 1.8727989439567305, 1.2158287506674472, 0.4167071821111212, -0.2778461200013618, -0.6512614114597421, -0.5845511861144033, -0.09761026692669919, 0.6490107873545877, 1.394358144507198, 1.8497559573965088, 1.7844520802467496, 1.1000571894809363, -0.12836834577476502, -1.6582624169875397, -3.133476690164397, -4.173520198761019, -4.474933086685296, -3.8971709072345786, -2.5085835679493007, -0.5782701734417, 1.4858649769131154, 3.237612023773797, 4.305181395293588, 4.485813794544425, 3.7963134688210483, 2.465284118067937, 0.8687883528181656, -0.5731344788517673, -1.510629578195979, -1.7572690101142208, -1.336536088034152, -0.46883254734593, 0.4969046847694272, 1.1871836153848914, 1.313657974698328, 0.7571553285885804, -0.3978339234021323, -1.887657364421034, -3.3453224358009614, -4.405150037839193, -4.805597683113791, -4.460464792743345, -3.478337008732915, -2.1256490042190257, -0.7454926580930901, 0.34275546233388615, 0.9326464636640341, 0.9823353748385522, 0.6142815686711628, 0.06474152962874678, -0.3997114414164872, -0.5714660593303076, -0.36843410623656, 0.14297468580388165, 0.7751228005021636, 1.2870530073720658, 1.470281884267198, 1.2239171372393955, 0.5939672946268353, -0.23666020183019043, -1.0048425669846068, -1.4525264460508647, -1.4128055446637073, -0.8682355352374859, 0.03854538496746148, 1.0464839695307688, 1.8575100627242602, 2.231737943875746, 2.065430258441253, 1.4256959046799431, 0.5296162342812022, -0.32638677427028784, -0.86448448138975, -0.9185993001431093, -0.4914833363071716], 'positive_zeros': ['0.77667562379779309584132223030339', '2.91172864827382921688936916286420', '3.64707567206504421166713519352979', '5.09452636472162406048197616184557', '6.08706715299460033565153939226508', '7.14638130280981763896625698943758', '8.470900719350957092343565843174958', '9.285271695669495452058939774900338', '10.38805947456277925055209132771239', '11.08203437333440760215267638764786'], 'prelabel': '2-378-7.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.737338538225754, 'root_angle': -0.3535062863872795, 'root_number': '-0.6054643436493675 - 0.7958724323465669*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.353506286387', 'prec': 40}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.77667562379779309584132223030', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '2.91172864827382921688936916286', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.64707567206504421166713519353', 'prec': 100}}