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 \(\chi_{2205}(328,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4410.en
\(\chi_{4410}(13,\cdot)\) \(\chi_{4410}(223,\cdot)\) \(\chi_{4410}(517,\cdot)\) \(\chi_{4410}(643,\cdot)\) \(\chi_{4410}(727,\cdot)\) \(\chi_{4410}(853,\cdot)\) \(\chi_{4410}(1147,\cdot)\) \(\chi_{4410}(1357,\cdot)\) \(\chi_{4410}(1483,\cdot)\) \(\chi_{4410}(1777,\cdot)\) \(\chi_{4410}(1903,\cdot)\) \(\chi_{4410}(1987,\cdot)\) \(\chi_{4410}(2113,\cdot)\) \(\chi_{4410}(2407,\cdot)\) \(\chi_{4410}(2533,\cdot)\) \(\chi_{4410}(2617,\cdot)\) \(\chi_{4410}(3163,\cdot)\) \(\chi_{4410}(3247,\cdot)\) \(\chi_{4410}(3373,\cdot)\) \(\chi_{4410}(3667,\cdot)\) \(\chi_{4410}(3793,\cdot)\) \(\chi_{4410}(3877,\cdot)\) \(\chi_{4410}(4003,\cdot)\) \(\chi_{4410}(4297,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((3431,2647,1081)\) → \((e\left(\frac{1}{3}\right),-i,e\left(\frac{3}{14}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 4410 }(2533, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{83}{84}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(1\) | \(e\left(\frac{5}{84}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{73}{84}\right)\) |