Basic properties
| Modulus: | \(6028\) | |
| Conductor: | \(1507\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(680\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1507}(29,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6028.cj
\(\chi_{6028}(13,\cdot)\) \(\chi_{6028}(29,\cdot)\) \(\chi_{6028}(57,\cdot)\) \(\chi_{6028}(85,\cdot)\) \(\chi_{6028}(117,\cdot)\) \(\chi_{6028}(149,\cdot)\) \(\chi_{6028}(161,\cdot)\) \(\chi_{6028}(189,\cdot)\) \(\chi_{6028}(217,\cdot)\) \(\chi_{6028}(261,\cdot)\) \(\chi_{6028}(277,\cdot)\) \(\chi_{6028}(305,\cdot)\) \(\chi_{6028}(321,\cdot)\) \(\chi_{6028}(325,\cdot)\) \(\chi_{6028}(349,\cdot)\) \(\chi_{6028}(365,\cdot)\) \(\chi_{6028}(369,\cdot)\) \(\chi_{6028}(437,\cdot)\) \(\chi_{6028}(453,\cdot)\) \(\chi_{6028}(457,\cdot)\) \(\chi_{6028}(469,\cdot)\) \(\chi_{6028}(481,\cdot)\) \(\chi_{6028}(497,\cdot)\) \(\chi_{6028}(501,\cdot)\) \(\chi_{6028}(513,\cdot)\) \(\chi_{6028}(525,\cdot)\) \(\chi_{6028}(545,\cdot)\) \(\chi_{6028}(569,\cdot)\) \(\chi_{6028}(601,\cdot)\) \(\chi_{6028}(633,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{680})$ |
| Fixed field: | Number field defined by a degree 680 polynomial (not computed) |
Values on generators
\((3015,2741,3565)\) → \((1,e\left(\frac{7}{10}\right),e\left(\frac{91}{136}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 6028 }(29, a) \) | \(1\) | \(1\) | \(e\left(\frac{183}{680}\right)\) | \(e\left(\frac{669}{680}\right)\) | \(e\left(\frac{1}{340}\right)\) | \(e\left(\frac{183}{340}\right)\) | \(e\left(\frac{291}{680}\right)\) | \(e\left(\frac{43}{170}\right)\) | \(e\left(\frac{247}{340}\right)\) | \(e\left(\frac{299}{340}\right)\) | \(e\left(\frac{37}{136}\right)\) | \(e\left(\frac{87}{136}\right)\) |