# lfunc_search downloaded from the LMFDB on 09 October 2026.
# Search link: https://www.lmfdb.org/L/rational?search_type=Euler&motivic_weight=1&degree=6&n=1-50&euler_constraints=F13%3D2197T^6-507T^5%2B78T^4-16T^3%2B6T^2-3T%2B1
# Query "{'degree': 6, 'rational': True, 'motivic_weight': 1, 'euler13': [1, -3, 6, -16, 78, -507, 2197]}" returned 4 lfunc_searchs, sorted by root analytic conductor.

# Each entry in the following data list has the form:
#    [Label]
# For more details, see the definitions at the bottom of the file.



"6-296e3-1.1-c1e3-0-0"
"6-592e3-1.1-c1e3-0-0"
"6-2664e3-1.1-c1e3-0-2"
"6-5328e3-1.1-c1e3-0-0"


# Label --
#    Each L-function $L$ has a label of the form d-N-q.k-x-y-i, where

#     * $d$ is the degree of $L$.
#     * $N$ is the conductor of $L$.  When $N$ is a perfect power $m^n$ we write $N$ as $m$e$n$, since $N$ can be very large for some imprimitive L-functions.
#     * q.k is the label of the primitive Dirichlet character from which the central character is induced.
#     * x-y is the spectral label encoding the $\mu_j$ and $\nu_j$ in the analytically normalized functional equation.
#     * i is a non-negative integer disambiguating between L-functions that would otherwise have the same label.