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 \(\chi_{2205}(1858,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4410.ea
\(\chi_{4410}(157,\cdot)\) \(\chi_{4410}(187,\cdot)\) \(\chi_{4410}(283,\cdot)\) \(\chi_{4410}(787,\cdot)\) \(\chi_{4410}(817,\cdot)\) \(\chi_{4410}(943,\cdot)\) \(\chi_{4410}(1417,\cdot)\) \(\chi_{4410}(1447,\cdot)\) \(\chi_{4410}(1543,\cdot)\) \(\chi_{4410}(1573,\cdot)\) \(\chi_{4410}(2047,\cdot)\) \(\chi_{4410}(2173,\cdot)\) \(\chi_{4410}(2203,\cdot)\) \(\chi_{4410}(2707,\cdot)\) \(\chi_{4410}(2803,\cdot)\) \(\chi_{4410}(2833,\cdot)\) \(\chi_{4410}(3307,\cdot)\) \(\chi_{4410}(3337,\cdot)\) \(\chi_{4410}(3433,\cdot)\) \(\chi_{4410}(3463,\cdot)\) \(\chi_{4410}(3937,\cdot)\) \(\chi_{4410}(3967,\cdot)\) \(\chi_{4410}(4063,\cdot)\) \(\chi_{4410}(4093,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((3431,2647,1081)\) → \((e\left(\frac{1}{3}\right),-i,e\left(\frac{31}{42}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 4410 }(4063, a) \) | \(1\) | \(1\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{23}{84}\right)\) | \(e\left(\frac{17}{84}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{31}{84}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{1}{84}\right)\) |