Basic properties
Modulus: | \(4410\) | |
Conductor: | \(2205\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{2205}(212,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4410.eg
\(\chi_{4410}(23,\cdot)\) \(\chi_{4410}(137,\cdot)\) \(\chi_{4410}(527,\cdot)\) \(\chi_{4410}(653,\cdot)\) \(\chi_{4410}(767,\cdot)\) \(\chi_{4410}(893,\cdot)\) \(\chi_{4410}(1283,\cdot)\) \(\chi_{4410}(1397,\cdot)\) \(\chi_{4410}(1523,\cdot)\) \(\chi_{4410}(1787,\cdot)\) \(\chi_{4410}(1913,\cdot)\) \(\chi_{4410}(2153,\cdot)\) \(\chi_{4410}(2417,\cdot)\) \(\chi_{4410}(2543,\cdot)\) \(\chi_{4410}(2657,\cdot)\) \(\chi_{4410}(2783,\cdot)\) \(\chi_{4410}(3047,\cdot)\) \(\chi_{4410}(3173,\cdot)\) \(\chi_{4410}(3287,\cdot)\) \(\chi_{4410}(3413,\cdot)\) \(\chi_{4410}(3677,\cdot)\) \(\chi_{4410}(3917,\cdot)\) \(\chi_{4410}(4043,\cdot)\) \(\chi_{4410}(4307,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((3431,2647,1081)\) → \((e\left(\frac{5}{6}\right),i,e\left(\frac{10}{21}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 4410 }(2417, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{11}{84}\right)\) | \(e\left(\frac{55}{84}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{84}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(1\) | \(e\left(\frac{41}{84}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{79}{84}\right)\) |