Basic properties
| Modulus: | \(8788\) | |
| Conductor: | \(2197\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(338\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2197}(1169,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8788.ba
\(\chi_{8788}(25,\cdot)\) \(\chi_{8788}(77,\cdot)\) \(\chi_{8788}(129,\cdot)\) \(\chi_{8788}(181,\cdot)\) \(\chi_{8788}(233,\cdot)\) \(\chi_{8788}(285,\cdot)\) \(\chi_{8788}(389,\cdot)\) \(\chi_{8788}(441,\cdot)\) \(\chi_{8788}(493,\cdot)\) \(\chi_{8788}(545,\cdot)\) \(\chi_{8788}(597,\cdot)\) \(\chi_{8788}(649,\cdot)\) \(\chi_{8788}(701,\cdot)\) \(\chi_{8788}(753,\cdot)\) \(\chi_{8788}(805,\cdot)\) \(\chi_{8788}(857,\cdot)\) \(\chi_{8788}(909,\cdot)\) \(\chi_{8788}(961,\cdot)\) \(\chi_{8788}(1065,\cdot)\) \(\chi_{8788}(1117,\cdot)\) \(\chi_{8788}(1169,\cdot)\) \(\chi_{8788}(1221,\cdot)\) \(\chi_{8788}(1273,\cdot)\) \(\chi_{8788}(1325,\cdot)\) \(\chi_{8788}(1377,\cdot)\) \(\chi_{8788}(1429,\cdot)\) \(\chi_{8788}(1481,\cdot)\) \(\chi_{8788}(1533,\cdot)\) \(\chi_{8788}(1585,\cdot)\) \(\chi_{8788}(1637,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{169})$ |
| Fixed field: | Number field defined by a degree 338 polynomial (not computed) |
Values on generators
\((4395,6593)\) → \((1,e\left(\frac{161}{338}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 8788 }(1169, a) \) | \(1\) | \(1\) | \(e\left(\frac{128}{169}\right)\) | \(e\left(\frac{279}{338}\right)\) | \(e\left(\frac{15}{338}\right)\) | \(e\left(\frac{87}{169}\right)\) | \(e\left(\frac{229}{338}\right)\) | \(e\left(\frac{197}{338}\right)\) | \(e\left(\frac{79}{169}\right)\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{271}{338}\right)\) | \(e\left(\frac{7}{13}\right)\) |