Basic properties
| Modulus: | \(7581\) | |
| Conductor: | \(7581\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(342\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7581.er
\(\chi_{7581}(41,\cdot)\) \(\chi_{7581}(146,\cdot)\) \(\chi_{7581}(167,\cdot)\) \(\chi_{7581}(230,\cdot)\) \(\chi_{7581}(314,\cdot)\) \(\chi_{7581}(356,\cdot)\) \(\chi_{7581}(440,\cdot)\) \(\chi_{7581}(545,\cdot)\) \(\chi_{7581}(566,\cdot)\) \(\chi_{7581}(629,\cdot)\) \(\chi_{7581}(713,\cdot)\) \(\chi_{7581}(755,\cdot)\) \(\chi_{7581}(839,\cdot)\) \(\chi_{7581}(944,\cdot)\) \(\chi_{7581}(965,\cdot)\) \(\chi_{7581}(1028,\cdot)\) \(\chi_{7581}(1112,\cdot)\) \(\chi_{7581}(1154,\cdot)\) \(\chi_{7581}(1238,\cdot)\) \(\chi_{7581}(1343,\cdot)\) \(\chi_{7581}(1364,\cdot)\) \(\chi_{7581}(1427,\cdot)\) \(\chi_{7581}(1511,\cdot)\) \(\chi_{7581}(1553,\cdot)\) \(\chi_{7581}(1637,\cdot)\) \(\chi_{7581}(1742,\cdot)\) \(\chi_{7581}(1763,\cdot)\) \(\chi_{7581}(1826,\cdot)\) \(\chi_{7581}(1910,\cdot)\) \(\chi_{7581}(1952,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{171})$ |
| Fixed field: | Number field defined by a degree 342 polynomial (not computed) |
Values on generators
\((2528,6499,1807)\) → \((-1,-1,e\left(\frac{67}{342}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(20\) |
| \( \chi_{ 7581 }(41, a) \) | \(-1\) | \(1\) | \(e\left(\frac{119}{171}\right)\) | \(e\left(\frac{67}{171}\right)\) | \(e\left(\frac{77}{171}\right)\) | \(e\left(\frac{5}{57}\right)\) | \(e\left(\frac{25}{171}\right)\) | \(e\left(\frac{55}{114}\right)\) | \(e\left(\frac{163}{171}\right)\) | \(e\left(\frac{134}{171}\right)\) | \(e\left(\frac{47}{171}\right)\) | \(e\left(\frac{16}{19}\right)\) |