Basic properties
| Modulus: | \(4334\) | |
| Conductor: | \(2167\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(980\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2167}(149,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4334.bj
\(\chi_{4334}(13,\cdot)\) \(\chi_{4334}(17,\cdot)\) \(\chi_{4334}(35,\cdot)\) \(\chi_{4334}(57,\cdot)\) \(\chi_{4334}(73,\cdot)\) \(\chi_{4334}(79,\cdot)\) \(\chi_{4334}(95,\cdot)\) \(\chi_{4334}(117,\cdot)\) \(\chi_{4334}(123,\cdot)\) \(\chi_{4334}(139,\cdot)\) \(\chi_{4334}(145,\cdot)\) \(\chi_{4334}(149,\cdot)\) \(\chi_{4334}(151,\cdot)\) \(\chi_{4334}(167,\cdot)\) \(\chi_{4334}(189,\cdot)\) \(\chi_{4334}(195,\cdot)\) \(\chi_{4334}(205,\cdot)\) \(\chi_{4334}(215,\cdot)\) \(\chi_{4334}(227,\cdot)\) \(\chi_{4334}(249,\cdot)\) \(\chi_{4334}(255,\cdot)\) \(\chi_{4334}(271,\cdot)\) \(\chi_{4334}(277,\cdot)\) \(\chi_{4334}(283,\cdot)\) \(\chi_{4334}(299,\cdot)\) \(\chi_{4334}(303,\cdot)\) \(\chi_{4334}(305,\cdot)\) \(\chi_{4334}(315,\cdot)\) \(\chi_{4334}(321,\cdot)\) \(\chi_{4334}(327,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{980})$ |
| Fixed field: | Number field defined by a degree 980 polynomial (not computed) |
Values on generators
\((1971,199)\) → \((e\left(\frac{9}{10}\right),e\left(\frac{87}{196}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 4334 }(149, a) \) | \(1\) | \(1\) | \(e\left(\frac{531}{980}\right)\) | \(e\left(\frac{103}{980}\right)\) | \(e\left(\frac{26}{245}\right)\) | \(e\left(\frac{41}{490}\right)\) | \(e\left(\frac{977}{980}\right)\) | \(e\left(\frac{317}{490}\right)\) | \(e\left(\frac{663}{980}\right)\) | \(e\left(\frac{2}{35}\right)\) | \(e\left(\frac{127}{196}\right)\) | \(e\left(\frac{13}{49}\right)\) |