Basic properties
| Modulus: | \(2744\) | |
| Conductor: | \(2744\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(294\) | 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 2744.bu
\(\chi_{2744}(37,\cdot)\) \(\chi_{2744}(53,\cdot)\) \(\chi_{2744}(93,\cdot)\) \(\chi_{2744}(109,\cdot)\) \(\chi_{2744}(149,\cdot)\) \(\chi_{2744}(205,\cdot)\) \(\chi_{2744}(221,\cdot)\) \(\chi_{2744}(261,\cdot)\) \(\chi_{2744}(277,\cdot)\) \(\chi_{2744}(317,\cdot)\) \(\chi_{2744}(333,\cdot)\) \(\chi_{2744}(389,\cdot)\) \(\chi_{2744}(429,\cdot)\) \(\chi_{2744}(445,\cdot)\) \(\chi_{2744}(485,\cdot)\) \(\chi_{2744}(501,\cdot)\) \(\chi_{2744}(541,\cdot)\) \(\chi_{2744}(597,\cdot)\) \(\chi_{2744}(613,\cdot)\) \(\chi_{2744}(653,\cdot)\) \(\chi_{2744}(669,\cdot)\) \(\chi_{2744}(709,\cdot)\) \(\chi_{2744}(725,\cdot)\) \(\chi_{2744}(781,\cdot)\) \(\chi_{2744}(821,\cdot)\) \(\chi_{2744}(837,\cdot)\) \(\chi_{2744}(877,\cdot)\) \(\chi_{2744}(893,\cdot)\) \(\chi_{2744}(933,\cdot)\) \(\chi_{2744}(989,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{147})$ |
| Fixed field: | Number field defined by a degree 294 polynomial (not computed) |
Values on generators
\((687,1373,689)\) → \((1,-1,e\left(\frac{125}{147}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 2744 }(501, a) \) | \(1\) | \(1\) | \(e\left(\frac{103}{294}\right)\) | \(e\left(\frac{47}{294}\right)\) | \(e\left(\frac{103}{147}\right)\) | \(e\left(\frac{109}{294}\right)\) | \(e\left(\frac{83}{98}\right)\) | \(e\left(\frac{25}{49}\right)\) | \(e\left(\frac{38}{147}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{67}{147}\right)\) | \(e\left(\frac{47}{147}\right)\) |