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 \(\chi_{2205}(1073,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4410.ep
\(\chi_{4410}(317,\cdot)\) \(\chi_{4410}(347,\cdot)\) \(\chi_{4410}(443,\cdot)\) \(\chi_{4410}(473,\cdot)\) \(\chi_{4410}(947,\cdot)\) \(\chi_{4410}(977,\cdot)\) \(\chi_{4410}(1073,\cdot)\) \(\chi_{4410}(1103,\cdot)\) \(\chi_{4410}(1577,\cdot)\) \(\chi_{4410}(1607,\cdot)\) \(\chi_{4410}(1703,\cdot)\) \(\chi_{4410}(2207,\cdot)\) \(\chi_{4410}(2237,\cdot)\) \(\chi_{4410}(2363,\cdot)\) \(\chi_{4410}(2837,\cdot)\) \(\chi_{4410}(2867,\cdot)\) \(\chi_{4410}(2963,\cdot)\) \(\chi_{4410}(2993,\cdot)\) \(\chi_{4410}(3467,\cdot)\) \(\chi_{4410}(3593,\cdot)\) \(\chi_{4410}(3623,\cdot)\) \(\chi_{4410}(4127,\cdot)\) \(\chi_{4410}(4223,\cdot)\) \(\chi_{4410}(4253,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((3431,2647,1081)\) → \((e\left(\frac{1}{6}\right),-i,e\left(\frac{4}{21}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 4410 }(1073, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{73}{84}\right)\) | \(e\left(\frac{1}{84}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{71}{84}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{5}{84}\right)\) |