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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_79.54', 'a10': [0.8854560256532099, -0.46472317204376856], 'a2': [-0.6324453755953773, 0.7746049618276546], 'a3': [0.8451900855437947, 0.5344658261278011], 'a4': [-0.20002569377604443, -0.9797906520422677], 'a5': [-0.9199794436588242, -0.3919666098600751], 'a6': [-0.9485364419471455, 0.3166679938014725], 'a7': [0.040265940109415144, -0.9991889981715696], 'a8': [0.8854560256532099, 0.46472317204376856], 'a9': [0.4286925614030542, 0.9034504346103823], 'algebraic': True, 'analytic_conductor': 8.489729058775376, 'analytic_normalization': 0, 'bad_lfactors': [[79, [1]]], 'bad_primes': [79], 'central_character': '79.54', 'coeff_info': ['x^78 - 1', '0.996757308134210 + 0.0804665687167259*I', '\\\\zeta_{78}'], 'conductor': 79, 'conductor_radical': 79, 'conjugate': 'dirichlet_L_79.60', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^28', 'a^7', 'a^56', 'a^44', 'a^35', 'a^59', 'a^6', 'a^14', 'a^72', 'a^8', 'a^63', 'a^4', 'a^9', 'a^51', 'a^34', 'a^69', 'a^42', 'a^68', 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[]], 'index': 0, 'label': '1-79-79.54-r1-0-0', 'leading_term': '1.36687150282502864704991359585+0.582902585891731898340061903991*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/79/54', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.485972116116053, 1.4378934962501801, 1.1390497088686762, 0.5426676095763929, -0.35448850935367526, -1.4663861661963742, -2.603499504069474, -3.5034470205381156, -3.903544151202805, -3.635862572399653, -2.7114229514741304, -1.3555509508078798, 0.032832964716365334, 0.9989704510268518, 1.1941739127098363, 0.5217765146049321, -0.7984828903958244, -2.28892962369558, -3.3875161116822814, -3.673957609539785, -3.0517994741542696, -1.7975997022774672, -0.44182844443888913, 0.474736300800312, 0.6577560697703737, 0.19965346575425993, -0.4776296690269898, 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'184.02838561596503620833800705619', '184.946166028063890690424588036734', '185.617609875749341366556876547093', '186.78214477018213713035337949087', '187.36191267867940804833980977255', '187.88822680441515359606263315830', '188.44100489041286246653677176870', '189.76029367587972944789272340398', '190.61224329981912298877015567561', '191.15023016587780561127865285611', '191.944072805137454464553496744240', '192.34443415452145675522405994464', '193.501559516831279371747041553445', '194.91237381833938931152896973689', '195.24705441027827741135440699862', '196.31120349614766392933108339820', '197.03891735930283433918144652203', '197.805215653229425653411770975041', '198.46547165025475489161342112924', '198.90672294211822747382252725603'], 'prelabel': '1-79-79.54-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.489729058775376, 'root_angle': 0.1283101783526076, 'root_number': '0.692248173300258766481274278166+0.721659522602213644386300970973*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.128310178353', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(78)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.979422711611870306202651409469+0.341426083976522561776389837920*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.1374927087', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '3.74182724694', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.8242583868', 'prec': 40}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 8.489729058775376, 'bad_primes': [79], 'central_character': '79.54', 'conductor': 79, 'conductor_radical': 79, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/79/54'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, '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': '1-79-79.54-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-79-79.54-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.489729058775376, 'root_angle': 0.1283101783526076, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.1374927087', 'prec': 40}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_79.54', 'Lhash_array': ['dirichlet_L_79.54'], 'factors': ['1-79-79.54-r1-0-0'], 'label': '1-79-79.54-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/79/54'}
Lfunction data - 1-79-79.54-r1-0-0