Basic properties
Modulus: | \(4410\) | |
Conductor: | \(245\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{245}(87,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4410.ek
\(\chi_{4410}(73,\cdot)\) \(\chi_{4410}(397,\cdot)\) \(\chi_{4410}(523,\cdot)\) \(\chi_{4410}(577,\cdot)\) \(\chi_{4410}(703,\cdot)\) \(\chi_{4410}(1027,\cdot)\) \(\chi_{4410}(1153,\cdot)\) \(\chi_{4410}(1333,\cdot)\) \(\chi_{4410}(1657,\cdot)\) \(\chi_{4410}(1837,\cdot)\) \(\chi_{4410}(1963,\cdot)\) \(\chi_{4410}(2287,\cdot)\) \(\chi_{4410}(2413,\cdot)\) \(\chi_{4410}(2467,\cdot)\) \(\chi_{4410}(2593,\cdot)\) \(\chi_{4410}(2917,\cdot)\) \(\chi_{4410}(3043,\cdot)\) \(\chi_{4410}(3097,\cdot)\) \(\chi_{4410}(3223,\cdot)\) \(\chi_{4410}(3673,\cdot)\) \(\chi_{4410}(3727,\cdot)\) \(\chi_{4410}(4177,\cdot)\) \(\chi_{4410}(4303,\cdot)\) \(\chi_{4410}(4357,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((3431,2647,1081)\) → \((1,i,e\left(\frac{19}{42}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 4410 }(577, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{47}{84}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{79}{84}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{61}{84}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{13}{28}\right)\) |