Basic properties
| Modulus: | \(7350\) | |
| 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 \(\chi_{245}(157,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7350.da
\(\chi_{7350}(157,\cdot)\) \(\chi_{7350}(493,\cdot)\) \(\chi_{7350}(943,\cdot)\) \(\chi_{7350}(1543,\cdot)\) \(\chi_{7350}(1657,\cdot)\) \(\chi_{7350}(1993,\cdot)\) \(\chi_{7350}(2257,\cdot)\) \(\chi_{7350}(2593,\cdot)\) \(\chi_{7350}(2707,\cdot)\) \(\chi_{7350}(3043,\cdot)\) \(\chi_{7350}(3307,\cdot)\) \(\chi_{7350}(3643,\cdot)\) \(\chi_{7350}(3757,\cdot)\) \(\chi_{7350}(4093,\cdot)\) \(\chi_{7350}(4357,\cdot)\) \(\chi_{7350}(4693,\cdot)\) \(\chi_{7350}(4807,\cdot)\) \(\chi_{7350}(5143,\cdot)\) \(\chi_{7350}(5407,\cdot)\) \(\chi_{7350}(5743,\cdot)\) \(\chi_{7350}(5857,\cdot)\) \(\chi_{7350}(6457,\cdot)\) \(\chi_{7350}(6907,\cdot)\) \(\chi_{7350}(7243,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((4901,1177,2551)\) → \((1,i,e\left(\frac{13}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 7350 }(157, a) \) | \(1\) | \(1\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{83}{84}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{43}{84}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{13}{84}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{17}{28}\right)\) |