Basic properties
| Modulus: | \(1156\) | |
| Conductor: | \(289\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(136\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{289}(25,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1156.q
\(\chi_{1156}(9,\cdot)\) \(\chi_{1156}(25,\cdot)\) \(\chi_{1156}(49,\cdot)\) \(\chi_{1156}(53,\cdot)\) \(\chi_{1156}(77,\cdot)\) \(\chi_{1156}(93,\cdot)\) \(\chi_{1156}(117,\cdot)\) \(\chi_{1156}(121,\cdot)\) \(\chi_{1156}(145,\cdot)\) \(\chi_{1156}(161,\cdot)\) \(\chi_{1156}(185,\cdot)\) \(\chi_{1156}(189,\cdot)\) \(\chi_{1156}(213,\cdot)\) \(\chi_{1156}(229,\cdot)\) \(\chi_{1156}(253,\cdot)\) \(\chi_{1156}(257,\cdot)\) \(\chi_{1156}(281,\cdot)\) \(\chi_{1156}(297,\cdot)\) \(\chi_{1156}(321,\cdot)\) \(\chi_{1156}(325,\cdot)\) \(\chi_{1156}(349,\cdot)\) \(\chi_{1156}(365,\cdot)\) \(\chi_{1156}(389,\cdot)\) \(\chi_{1156}(393,\cdot)\) \(\chi_{1156}(417,\cdot)\) \(\chi_{1156}(433,\cdot)\) \(\chi_{1156}(457,\cdot)\) \(\chi_{1156}(461,\cdot)\) \(\chi_{1156}(485,\cdot)\) \(\chi_{1156}(501,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{136})$ |
| Fixed field: | Number field defined by a degree 136 polynomial (not computed) |
Values on generators
\((579,581)\) → \((1,e\left(\frac{93}{136}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 1156 }(25, a) \) | \(1\) | \(1\) | \(e\left(\frac{93}{136}\right)\) | \(e\left(\frac{81}{136}\right)\) | \(e\left(\frac{135}{136}\right)\) | \(e\left(\frac{25}{68}\right)\) | \(e\left(\frac{99}{136}\right)\) | \(e\left(\frac{1}{34}\right)\) | \(e\left(\frac{19}{68}\right)\) | \(e\left(\frac{39}{68}\right)\) | \(e\left(\frac{23}{34}\right)\) | \(e\left(\frac{67}{136}\right)\) |