Basic properties
| Modulus: | \(6815\) | |
| Conductor: | \(6815\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(92\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6815.bx
\(\chi_{6815}(17,\cdot)\) \(\chi_{6815}(128,\cdot)\) \(\chi_{6815}(162,\cdot)\) \(\chi_{6815}(307,\cdot)\) \(\chi_{6815}(418,\cdot)\) \(\chi_{6815}(708,\cdot)\) \(\chi_{6815}(742,\cdot)\) \(\chi_{6815}(853,\cdot)\) \(\chi_{6815}(1177,\cdot)\) \(\chi_{6815}(1322,\cdot)\) \(\chi_{6815}(1578,\cdot)\) \(\chi_{6815}(1612,\cdot)\) \(\chi_{6815}(1757,\cdot)\) \(\chi_{6815}(2337,\cdot)\) \(\chi_{6815}(2448,\cdot)\) \(\chi_{6815}(2593,\cdot)\) \(\chi_{6815}(2627,\cdot)\) \(\chi_{6815}(2738,\cdot)\) \(\chi_{6815}(2883,\cdot)\) \(\chi_{6815}(2917,\cdot)\) \(\chi_{6815}(3062,\cdot)\) \(\chi_{6815}(3173,\cdot)\) \(\chi_{6815}(3318,\cdot)\) \(\chi_{6815}(3463,\cdot)\) \(\chi_{6815}(3608,\cdot)\) \(\chi_{6815}(3787,\cdot)\) \(\chi_{6815}(4333,\cdot)\) \(\chi_{6815}(4623,\cdot)\) \(\chi_{6815}(4657,\cdot)\) \(\chi_{6815}(4768,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{92})$ |
| Fixed field: | Number field defined by a degree 92 polynomial |
Values on generators
\((2727,2351,146)\) → \((i,-i,e\left(\frac{8}{23}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 6815 }(17, a) \) | \(1\) | \(1\) | \(e\left(\frac{6}{23}\right)\) | \(e\left(\frac{21}{46}\right)\) | \(e\left(\frac{12}{23}\right)\) | \(e\left(\frac{33}{46}\right)\) | \(e\left(\frac{35}{92}\right)\) | \(e\left(\frac{18}{23}\right)\) | \(e\left(\frac{21}{23}\right)\) | \(e\left(\frac{17}{92}\right)\) | \(e\left(\frac{45}{46}\right)\) | \(e\left(\frac{7}{92}\right)\) |