Basic properties
| Modulus: | \(394\) | |
| Conductor: | \(197\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(98\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{197}(43,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 394.h
\(\chi_{394}(7,\cdot)\) \(\chi_{394}(9,\cdot)\) \(\chi_{394}(15,\cdot)\) \(\chi_{394}(25,\cdot)\) \(\chi_{394}(39,\cdot)\) \(\chi_{394}(41,\cdot)\) \(\chi_{394}(43,\cdot)\) \(\chi_{394}(47,\cdot)\) \(\chi_{394}(55,\cdot)\) \(\chi_{394}(65,\cdot)\) \(\chi_{394}(97,\cdot)\) \(\chi_{394}(107,\cdot)\) \(\chi_{394}(109,\cdot)\) \(\chi_{394}(121,\cdot)\) \(\chi_{394}(127,\cdot)\) \(\chi_{394}(137,\cdot)\) \(\chi_{394}(143,\cdot)\) \(\chi_{394}(155,\cdot)\) \(\chi_{394}(157,\cdot)\) \(\chi_{394}(163,\cdot)\) \(\chi_{394}(169,\cdot)\) \(\chi_{394}(173,\cdot)\) \(\chi_{394}(181,\cdot)\) \(\chi_{394}(201,\cdot)\) \(\chi_{394}(207,\cdot)\) \(\chi_{394}(219,\cdot)\) \(\chi_{394}(223,\cdot)\) \(\chi_{394}(259,\cdot)\) \(\chi_{394}(261,\cdot)\) \(\chi_{394}(289,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{49})$ |
| Fixed field: | Number field defined by a degree 98 polynomial |
Values on generators
\(199\) → \(e\left(\frac{39}{98}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 394 }(43, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{98}\right)\) | \(e\left(\frac{41}{98}\right)\) | \(e\left(\frac{5}{49}\right)\) | \(e\left(\frac{3}{49}\right)\) | \(e\left(\frac{53}{98}\right)\) | \(e\left(\frac{93}{98}\right)\) | \(e\left(\frac{22}{49}\right)\) | \(e\left(\frac{27}{98}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{13}{98}\right)\) |